%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : NUM494+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n014.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 08:45:06 EDT 2022

% Result   : Theorem 6.57s 2.24s
% Output   : Proof 15.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : NUM494+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.11/0.31  % Computer : n014.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 600
% 0.11/0.31  % DateTime : Wed Jul  6 10:04:22 EDT 2022
% 0.11/0.31  % CPUTime  : 
% 0.53/0.58          ____       _                          
% 0.53/0.58    ___  / __ \_____(_)___  ________  __________
% 0.53/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.53/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.53/0.58  
% 0.53/0.58  A Theorem Prover for First-Order Logic
% 0.53/0.58  (ePrincess v.1.0)
% 0.53/0.58  
% 0.53/0.58  (c) Philipp Rümmer, 2009-2015
% 0.53/0.58  (c) Peter Backeman, 2014-2015
% 0.53/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.58  Bug reports to peter@backeman.se
% 0.53/0.58  
% 0.53/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.58  
% 0.53/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.66  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.81/1.03  Prover 0: Preprocessing ...
% 3.61/1.51  Prover 0: Constructing countermodel ...
% 6.57/2.24  Prover 0: proved (1584ms)
% 6.57/2.24  
% 6.57/2.24  No countermodel exists, formula is valid
% 6.57/2.24  % SZS status Theorem for theBenchmark
% 6.57/2.24  
% 6.57/2.24  Generating proof ... found it (size 141)
% 14.46/4.05  
% 14.46/4.05  % SZS output start Proof for theBenchmark
% 14.46/4.05  Assumed formulas after preprocessing and simplification: 
% 14.46/4.05  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (xr = xn) &  ~ (sz10 = sz00) & sdtmndt0(xn, xp) = xr & sdtasdt0(xr, xm) = v3 & sdtasdt0(xn, xm) = v2 & sdtpldt0(v4, xp) = v5 & sdtpldt0(v0, xp) = v1 & sdtpldt0(xr, xm) = v4 & sdtpldt0(xn, xm) = v0 & isPrime0(xp) & doDivides0(xp, v3) & doDivides0(xp, v2) & sdtlseqdt0(xr, xn) & sdtlseqdt0(xp, xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) &  ~ isPrime0(sz10) &  ~ isPrime0(sz00) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v6 = sz00 |  ~ (sdtsldt0(v10, v6) = v11) |  ~ (sdtsldt0(v7, v6) = v8) |  ~ (sdtasdt0(v9, v7) = v10) |  ~ doDivides0(v6, v7) |  ~ aNaturalNumber0(v9) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | sdtasdt0(v9, v8) = v11) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (sdtasdt0(v8, v6) = v10) |  ~ (sdtasdt0(v7, v6) = v9) |  ~ (sdtpldt0(v9, v10) = v11) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] : (sdtasdt0(v12, v6) = v11 & sdtasdt0(v6, v12) = v13 & sdtasdt0(v6, v8) = v15 & sdtasdt0(v6, v7) = v14 & sdtpldt0(v14, v15) = v13 & sdtpldt0(v7, v8) = v12)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (sdtasdt0(v6, v8) = v10) |  ~ (sdtasdt0(v6, v7) = v9) |  ~ (sdtpldt0(v9, v10) = v11) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] : (sdtasdt0(v12, v6) = v13 & sdtasdt0(v8, v6) = v15 & sdtasdt0(v7, v6) = v14 & sdtasdt0(v6, v12) = v11 & sdtpldt0(v14, v15) = v13 & sdtpldt0(v7, v8) = v12)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 | v6 = sz00 |  ~ (sdtasdt0(v8, v6) = v10) |  ~ (sdtasdt0(v7, v6) = v9) |  ~ sdtlseqdt0(v7, v8) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | sdtlseqdt0(v9, v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 | v6 = sz00 |  ~ (sdtasdt0(v8, v6) = v10) |  ~ (sdtasdt0(v7, v6) = v9) |  ~ sdtlseqdt0(v7, v8) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v11] :  ? [v12] : ( ~ (v12 = v11) & sdtasdt0(v6, v8) = v12 & sdtasdt0(v6, v7) = v11 & sdtlseqdt0(v11, v12))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 | v6 = sz00 |  ~ (sdtasdt0(v8, v6) = v10) |  ~ (sdtasdt0(v7, v6) = v9) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v11] :  ? [v12] : ( ~ (v12 = v11) & sdtasdt0(v6, v8) = v12 & sdtasdt0(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 | v6 = sz00 |  ~ (sdtasdt0(v8, v6) = v10) |  ~ (sdtasdt0(v6, v7) = v9) |  ~ sdtlseqdt0(v7, v8) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v11] :  ? [v12] : ( ~ (v12 = v10) &  ~ (v11 = v9) & sdtasdt0(v7, v6) = v12 & sdtasdt0(v6, v8) = v11 & sdtlseqdt0(v12, v10) & sdtlseqdt0(v9, v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 | v6 = sz00 |  ~ (sdtasdt0(v8, v6) = v10) |  ~ (sdtasdt0(v6, v7) = v9) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v11] :  ? [v12] : ( ~ (v12 = v10) &  ~ (v11 = v9) & sdtasdt0(v7, v6) = v12 & sdtasdt0(v6, v8) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 | v6 = sz00 |  ~ (sdtasdt0(v7, v6) = v10) |  ~ (sdtasdt0(v6, v8) = v9) |  ~ sdtlseqdt0(v7, v8) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v11] :  ? [v12] : ( ~ (v12 = v10) &  ~ (v11 = v9) & sdtasdt0(v8, v6) = v12 & sdtasdt0(v6, v7) = v11 & sdtlseqdt0(v11, v9) & sdtlseqdt0(v10, v12))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 | v6 = sz00 |  ~ (sdtasdt0(v7, v6) = v10) |  ~ (sdtasdt0(v6, v8) = v9) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v11] :  ? [v12] : ( ~ (v12 = v10) &  ~ (v11 = v9) & sdtasdt0(v8, v6) = v12 & sdtasdt0(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 | v6 = sz00 |  ~ (sdtasdt0(v6, v8) = v10) |  ~ (sdtasdt0(v6, v7) = v9) |  ~ sdtlseqdt0(v7, v8) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | sdtlseqdt0(v9, v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 | v6 = sz00 |  ~ (sdtasdt0(v6, v8) = v10) |  ~ (sdtasdt0(v6, v7) = v9) |  ~ sdtlseqdt0(v7, v8) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v11] :  ? [v12] : ( ~ (v12 = v11) & sdtasdt0(v8, v6) = v12 & sdtasdt0(v7, v6) = v11 & sdtlseqdt0(v11, v12))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 | v6 = sz00 |  ~ (sdtasdt0(v6, v8) = v10) |  ~ (sdtasdt0(v6, v7) = v9) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v11] :  ? [v12] : ( ~ (v12 = v11) & sdtasdt0(v8, v6) = v12 & sdtasdt0(v7, v6) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (sdtpldt0(v8, v6) = v10) |  ~ (sdtpldt0(v7, v6) = v9) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v11] :  ? [v12] : ( ~ (v12 = v11) & sdtpldt0(v6, v8) = v12 & sdtpldt0(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (sdtpldt0(v8, v6) = v10) |  ~ (sdtpldt0(v6, v7) = v9) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v11] :  ? [v12] : ( ~ (v12 = v10) &  ~ (v11 = v9) & sdtpldt0(v7, v6) = v12 & sdtpldt0(v6, v8) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (sdtpldt0(v7, v6) = v10) |  ~ (sdtpldt0(v6, v8) = v9) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v11] :  ? [v12] : ( ~ (v12 = v10) &  ~ (v11 = v9) & sdtpldt0(v8, v6) = v12 & sdtpldt0(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (sdtpldt0(v6, v8) = v10) |  ~ (sdtpldt0(v6, v7) = v9) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v11] :  ? [v12] : ( ~ (v12 = v11) & sdtpldt0(v8, v6) = v12 & sdtpldt0(v7, v6) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v6 = sz00 |  ~ (sdtsldt0(v7, v6) = v8) |  ~ (sdtasdt0(v9, v8) = v10) |  ~ doDivides0(v6, v7) |  ~ aNaturalNumber0(v9) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v11] : (sdtsldt0(v11, v6) = v10 & sdtasdt0(v9, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (sdtasdt0(v9, v8) = v10) |  ~ (sdtasdt0(v6, v7) = v9) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v11] : (sdtasdt0(v7, v8) = v11 & sdtasdt0(v6, v11) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (sdtasdt0(v9, v6) = v10) |  ~ (sdtpldt0(v7, v8) = v9) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] : (sdtasdt0(v8, v6) = v15 & sdtasdt0(v7, v6) = v14 & sdtasdt0(v6, v9) = v11 & sdtasdt0(v6, v8) = v13 & sdtasdt0(v6, v7) = v12 & sdtpldt0(v14, v15) = v10 & sdtpldt0(v12, v13) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (sdtasdt0(v7, v8) = v9) |  ~ (sdtasdt0(v6, v9) = v10) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v11] : (sdtasdt0(v11, v8) = v10 & sdtasdt0(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (sdtasdt0(v6, v9) = v10) |  ~ (sdtpldt0(v7, v8) = v9) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] : (sdtasdt0(v9, v6) = v13 & sdtasdt0(v8, v6) = v15 & sdtasdt0(v7, v6) = v14 & sdtasdt0(v6, v8) = v12 & sdtasdt0(v6, v7) = v11 & sdtpldt0(v14, v15) = v13 & sdtpldt0(v11, v12) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (sdtpldt0(v9, v8) = v10) |  ~ (sdtpldt0(v6, v7) = v9) |  ~ isPrime0(v8) |  ~ iLess0(v10, v1) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | doDivides0(v8, v7) | doDivides0(v8, v6) |  ? [v11] : (sdtasdt0(v6, v7) = v11 &  ~ doDivides0(v8, v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (sdtpldt0(v9, v8) = v10) |  ~ (sdtpldt0(v6, v7) = v9) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v11] : (sdtpldt0(v7, v8) = v11 & sdtpldt0(v6, v11) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (sdtpldt0(v7, v8) = v9) |  ~ (sdtpldt0(v6, v9) = v10) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v11] : (sdtpldt0(v11, v8) = v10 & sdtpldt0(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v8 | v6 = sz00 |  ~ (sdtsldt0(v7, v6) = v8) |  ~ (sdtasdt0(v6, v9) = v7) |  ~ doDivides0(v6, v7) |  ~ aNaturalNumber0(v9) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (sdtmndt0(v7, v6) = v8) |  ~ (sdtpldt0(v6, v9) = v7) |  ~ sdtlseqdt0(v6, v7) |  ~ aNaturalNumber0(v9) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v7 | v6 = sz00 |  ~ (sdtsldt0(v7, v6) = v8) |  ~ (sdtasdt0(v6, v8) = v9) |  ~ doDivides0(v6, v7) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v7 |  ~ (sdtmndt0(v7, v6) = v8) |  ~ (sdtpldt0(v6, v8) = v9) |  ~ sdtlseqdt0(v6, v7) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 | v6 = sz00 |  ~ (sdtasdt0(v8, v6) = v9) |  ~ (sdtasdt0(v7, v6) = v9) |  ~ sdtlseqdt0(v7, v8) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 | v6 = sz00 |  ~ (sdtasdt0(v8, v6) = v9) |  ~ (sdtasdt0(v7, v6) = v9) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 | v6 = sz00 |  ~ (sdtasdt0(v6, v8) = v9) |  ~ (sdtasdt0(v6, v7) = v9) |  ~ sdtlseqdt0(v7, v8) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 | v6 = sz00 |  ~ (sdtasdt0(v6, v8) = v9) |  ~ (sdtasdt0(v6, v7) = v9) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (sdtpldt0(v8, v6) = v9) |  ~ (sdtpldt0(v7, v6) = v9) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (sdtpldt0(v6, v8) = v9) |  ~ (sdtpldt0(v6, v7) = v9) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (sdtsldt0(v9, v8) = v7) |  ~ (sdtsldt0(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (sdtmndt0(v9, v8) = v7) |  ~ (sdtmndt0(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (sdtasdt0(v9, v8) = v7) |  ~ (sdtasdt0(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (sdtpldt0(v9, v8) = v7) |  ~ (sdtpldt0(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (sdtpldt0(v8, v7) = v9) |  ~ sdtlseqdt0(v6, v7) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v10] :  ? [v11] :  ? [v12] : ( ~ (v12 = v11) &  ~ (v10 = v9) & sdtpldt0(v8, v6) = v10 & sdtpldt0(v7, v8) = v12 & sdtpldt0(v6, v8) = v11 & sdtlseqdt0(v11, v12) & sdtlseqdt0(v10, v9))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (sdtpldt0(v8, v6) = v9) |  ~ sdtlseqdt0(v6, v7) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v10] :  ? [v11] :  ? [v12] : ( ~ (v12 = v11) &  ~ (v10 = v9) & sdtpldt0(v8, v7) = v10 & sdtpldt0(v7, v8) = v12 & sdtpldt0(v6, v8) = v11 & sdtlseqdt0(v11, v12) & sdtlseqdt0(v9, v10))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (sdtpldt0(v7, v8) = v9) |  ~ sdtlseqdt0(v6, v7) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v10] :  ? [v11] :  ? [v12] : ( ~ (v12 = v9) &  ~ (v11 = v10) & sdtpldt0(v8, v7) = v11 & sdtpldt0(v8, v6) = v10 & sdtpldt0(v6, v8) = v12 & sdtlseqdt0(v12, v9) & sdtlseqdt0(v10, v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (sdtpldt0(v6, v8) = v9) |  ~ sdtlseqdt0(v6, v7) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v10] :  ? [v11] :  ? [v12] : ( ~ (v12 = v9) &  ~ (v11 = v10) & sdtpldt0(v8, v7) = v11 & sdtpldt0(v8, v6) = v10 & sdtpldt0(v7, v8) = v12 & sdtlseqdt0(v10, v11) & sdtlseqdt0(v9, v12))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v6 = sz00 |  ~ (sdtsldt0(v7, v6) = v8) |  ~ (sdtasdt0(v6, v8) = v9) |  ~ doDivides0(v6, v7) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | aNaturalNumber0(v8)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (sdtmndt0(v7, v6) = v8) |  ~ (sdtpldt0(v6, v8) = v9) |  ~ sdtlseqdt0(v6, v7) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | aNaturalNumber0(v8)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (sdtpldt0(v7, v8) = v9) |  ~ doDivides0(v6, v9) |  ~ doDivides0(v6, v7) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | doDivides0(v6, v8)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (sdtpldt0(v7, v8) = v9) |  ~ doDivides0(v6, v8) |  ~ doDivides0(v6, v7) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | doDivides0(v6, v9)) &  ! [v6] :  ! [v7] :  ! [v8] : (v6 = sz00 |  ~ (sdtasdt0(v7, v6) = v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | sdtlseqdt0(v7, v8)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (sdtasdt0(v7, v6) = v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | sdtasdt0(v6, v7) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (sdtasdt0(v6, v8) = v7) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | doDivides0(v6, v7)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (sdtasdt0(v6, v7) = v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | sdtasdt0(v7, v6) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (sdtasdt0(v6, v7) = v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | aNaturalNumber0(v8)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (sdtpldt0(v7, v6) = v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | sdtpldt0(v6, v7) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (sdtpldt0(v6, v8) = v7) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | sdtlseqdt0(v6, v7)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (sdtpldt0(v6, v7) = v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | sdtpldt0(v7, v6) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (sdtpldt0(v6, v7) = v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | aNaturalNumber0(v8)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ doDivides0(v7, v8) |  ~ doDivides0(v6, v7) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | doDivides0(v6, v8)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ sdtlseqdt0(v7, v8) |  ~ sdtlseqdt0(v6, v7) |  ~ aNaturalNumber0(v8) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | sdtlseqdt0(v6, v8)) &  ! [v6] :  ! [v7] : (v7 = v6 | v7 = sz10 |  ~ isPrime0(v6) |  ~ doDivides0(v7, v6) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (sdtasdt0(v6, sz10) = v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (sdtasdt0(sz10, v6) = v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (sdtpldt0(v6, sz00) = v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (sdtpldt0(sz00, v6) = v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ sdtlseqdt0(v7, v6) |  ~ sdtlseqdt0(v6, v7) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ sdtlseqdt0(v6, v7) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | iLess0(v6, v7)) &  ! [v6] :  ! [v7] : (v7 = sz00 | v6 = sz00 |  ~ (sdtasdt0(v6, v7) = sz00) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] : (v7 = sz00 |  ~ (sdtasdt0(v6, sz00) = v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] : (v7 = sz00 |  ~ (sdtasdt0(sz00, v6) = v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] : (v7 = sz00 |  ~ (sdtpldt0(v6, v7) = sz00) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] : (v7 = sz00 |  ~ doDivides0(v6, v7) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | sdtlseqdt0(v6, v7)) &  ! [v6] :  ! [v7] : (v6 = sz00 |  ~ (sdtpldt0(v6, v7) = sz00) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6)) &  ! [v6] :  ! [v7] : ( ~ (sdtasdt0(v6, sz10) = v7) |  ~ aNaturalNumber0(v6) | sdtasdt0(sz10, v6) = v6) &  ! [v6] :  ! [v7] : ( ~ (sdtasdt0(v6, sz00) = v7) |  ~ aNaturalNumber0(v6) | sdtasdt0(sz00, v6) = sz00) &  ! [v6] :  ! [v7] : ( ~ (sdtasdt0(sz10, v6) = v7) |  ~ aNaturalNumber0(v6) | sdtasdt0(v6, sz10) = v6) &  ! [v6] :  ! [v7] : ( ~ (sdtasdt0(sz00, v6) = v7) |  ~ aNaturalNumber0(v6) | sdtasdt0(v6, sz00) = sz00) &  ! [v6] :  ! [v7] : ( ~ (sdtpldt0(v6, sz00) = v7) |  ~ aNaturalNumber0(v6) | sdtpldt0(sz00, v6) = v6) &  ! [v6] :  ! [v7] : ( ~ (sdtpldt0(sz00, v6) = v7) |  ~ aNaturalNumber0(v6) | sdtpldt0(v6, sz00) = v6) &  ! [v6] :  ! [v7] : ( ~ doDivides0(v6, v7) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v8] : (sdtasdt0(v6, v8) = v7 & aNaturalNumber0(v8))) &  ! [v6] :  ! [v7] : ( ~ sdtlseqdt0(v6, v7) |  ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) |  ? [v8] : (sdtpldt0(v6, v8) = v7 & aNaturalNumber0(v8))) &  ! [v6] :  ! [v7] : ( ~ aNaturalNumber0(v7) |  ~ aNaturalNumber0(v6) | sdtlseqdt0(v7, v6) | sdtlseqdt0(v6, v7)) &  ! [v6] : (v6 = sz10 | v6 = sz00 |  ~ aNaturalNumber0(v6) | isPrime0(v6) |  ? [v7] : ( ~ (v7 = v6) &  ~ (v7 = sz10) & doDivides0(v7, v6) & aNaturalNumber0(v7))) &  ! [v6] : (v6 = sz10 | v6 = sz00 |  ~ aNaturalNumber0(v6) | sdtlseqdt0(sz10, v6)) &  ! [v6] : (v6 = sz10 | v6 = sz00 |  ~ aNaturalNumber0(v6) |  ? [v7] : (isPrime0(v7) & doDivides0(v7, v6) & aNaturalNumber0(v7))) &  ! [v6] : ( ~ aNaturalNumber0(v6) | sdtlseqdt0(v6, v6)) & (v5 = v1 |  ~ sdtlseqdt0(v5, v1)))
% 14.68/4.13  | 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 yields:
% 14.68/4.13  | (1)  ~ (xr = xn) &  ~ (sz10 = sz00) & sdtmndt0(xn, xp) = xr & sdtasdt0(xr, xm) = all_0_2_2 & sdtasdt0(xn, xm) = all_0_3_3 & sdtpldt0(all_0_1_1, xp) = all_0_0_0 & sdtpldt0(all_0_5_5, xp) = all_0_4_4 & sdtpldt0(xr, xm) = all_0_1_1 & sdtpldt0(xn, xm) = all_0_5_5 & isPrime0(xp) & doDivides0(xp, all_0_2_2) & doDivides0(xp, all_0_3_3) & sdtlseqdt0(xr, xn) & sdtlseqdt0(xp, xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) &  ~ isPrime0(sz10) &  ~ isPrime0(sz00) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v0 = sz00 |  ~ (sdtsldt0(v4, v0) = v5) |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v3, v1) = v4) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v3) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v3, v2) = v5) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) |  ~ (sdtasdt0(v1, v0) = v3) |  ~ (sdtpldt0(v3, v4) = v5) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ (sdtpldt0(v3, v4) = v5) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v2, v0) = v4) |  ~ (sdtasdt0(v1, v0) = v3) |  ~ sdtlseqdt0(v1, v2) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v2, v0) = v4) |  ~ (sdtasdt0(v1, v0) = v3) |  ~ sdtlseqdt0(v1, v2) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v2, v0) = v4) |  ~ (sdtasdt0(v1, v0) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v2, v0) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ sdtlseqdt0(v1, v2) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v4) &  ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtlseqdt0(v6, v4) & sdtlseqdt0(v3, v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v2, v0) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v4) &  ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v1, v0) = v4) |  ~ (sdtasdt0(v0, v2) = v3) |  ~ sdtlseqdt0(v1, v2) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v4) &  ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v3) & sdtlseqdt0(v4, v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v1, v0) = v4) |  ~ (sdtasdt0(v0, v2) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v4) &  ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v0, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ sdtlseqdt0(v1, v2) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v0, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ sdtlseqdt0(v1, v2) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtlseqdt0(v5, v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v0, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (sdtpldt0(v2, v0) = v4) |  ~ (sdtpldt0(v1, v0) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v0, v2) = v6 & sdtpldt0(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (sdtpldt0(v2, v0) = v4) |  ~ (sdtpldt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v4) &  ~ (v5 = v3) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (sdtpldt0(v1, v0) = v4) |  ~ (sdtpldt0(v0, v2) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v4) &  ~ (v5 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (sdtpldt0(v0, v2) = v4) |  ~ (sdtpldt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v3, v2) = v4) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v3) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] : (sdtsldt0(v5, v0) = v4 & sdtasdt0(v3, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) |  ~ (sdtpldt0(v1, v2) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v6, v7) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) |  ~ (sdtasdt0(v0, v3) = v4) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) |  ~ (sdtpldt0(v1, v2) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) |  ~ (sdtpldt0(v0, v1) = v3) |  ~ isPrime0(v2) |  ~ iLess0(v4, all_0_4_4) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) |  ? [v5] : (sdtasdt0(v0, v1) = v5 &  ~ doDivides0(v2, v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) |  ~ (sdtpldt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) |  ~ (sdtpldt0(v0, v3) = v4) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 | v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v0, v3) = v1) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v3) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v3) = v1) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v3) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 | v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v0, v2) = v3) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v2) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v2, v0) = v3) |  ~ (sdtasdt0(v1, v0) = v3) |  ~ sdtlseqdt0(v1, v2) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v2, v0) = v3) |  ~ (sdtasdt0(v1, v0) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v0, v2) = v3) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ sdtlseqdt0(v1, v2) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v0, v2) = v3) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 |  ~ (sdtpldt0(v2, v0) = v3) |  ~ (sdtpldt0(v1, v0) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 |  ~ (sdtpldt0(v0, v2) = v3) |  ~ (sdtpldt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtsldt0(v3, v2) = v1) |  ~ (sdtsldt0(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtmndt0(v3, v2) = v1) |  ~ (sdtmndt0(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] : (v1 = v0 |  ~ (sdtpldt0(v2, v1) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v6 = v5) &  ~ (v4 = v3) & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v4, v3))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtpldt0(v2, v0) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v6 = v5) &  ~ (v4 = v3) & sdtpldt0(v2, v1) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v3, v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtpldt0(v1, v2) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v6 = v3) &  ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v0, v2) = v6 & sdtlseqdt0(v6, v3) & sdtlseqdt0(v4, v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtpldt0(v0, v2) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v6 = v3) &  ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v0, v2) = v3) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v2) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) |  ~ doDivides0(v0, v3) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) |  ~ doDivides0(v0, v2) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v0, v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v0 = sz00 |  ~ (sdtasdt0(v1, v0) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ doDivides0(v1, v2) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ sdtlseqdt0(v1, v2) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2)) &  ! [v0] :  ! [v1] : (v1 = v0 | v1 = sz10 |  ~ isPrime0(v0) |  ~ doDivides0(v1, v0) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtasdt0(v0, sz10) = v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtasdt0(sz10, v0) = v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtpldt0(v0, sz00) = v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtpldt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ sdtlseqdt0(v1, v0) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | iLess0(v0, v1)) &  ! [v0] :  ! [v1] : (v1 = sz00 | v0 = sz00 |  ~ (sdtasdt0(v0, v1) = sz00) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ (sdtasdt0(v0, sz00) = v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ (sdtasdt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ (sdtpldt0(v0, v1) = sz00) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) &  ! [v0] :  ! [v1] : (v0 = sz00 |  ~ (sdtpldt0(v0, v1) = sz00) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0) &  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00) &  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0) &  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00) &  ! [v0] :  ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0) &  ! [v0] :  ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0) &  ! [v0] :  ! [v1] : ( ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2))) &  ! [v0] :  ! [v1] : ( ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2))) &  ! [v0] :  ! [v1] : ( ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) &  ! [v0] : (v0 = sz10 | v0 = sz00 |  ~ aNaturalNumber0(v0) | isPrime0(v0) |  ? [v1] : ( ~ (v1 = v0) &  ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1))) &  ! [v0] : (v0 = sz10 | v0 = sz00 |  ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) &  ! [v0] : (v0 = sz10 | v0 = sz00 |  ~ aNaturalNumber0(v0) |  ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1))) &  ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) & (all_0_0_0 = all_0_4_4 |  ~ sdtlseqdt0(all_0_0_0, all_0_4_4))
% 15.06/4.15  |
% 15.06/4.15  | Applying alpha-rule on (1) yields:
% 15.06/4.15  | (2)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ sdtlseqdt0(v1, v0) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.06/4.15  | (3)  ! [v0] :  ! [v1] : ( ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 15.06/4.15  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 | v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v0, v2) = v3) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.06/4.15  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v2, v0) = v3) |  ~ (sdtasdt0(v1, v0) = v3) |  ~ sdtlseqdt0(v1, v2) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.06/4.15  | (6)  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ (sdtasdt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0))
% 15.06/4.15  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) |  ~ (sdtasdt0(v1, v0) = v3) |  ~ (sdtpldt0(v3, v4) = v5) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6))
% 15.06/4.15  | (8)  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 15.06/4.15  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2)
% 15.06/4.15  | (10)  ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 15.06/4.15  | (11) all_0_0_0 = all_0_4_4 |  ~ sdtlseqdt0(all_0_0_0, all_0_4_4)
% 15.06/4.15  | (12)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2)
% 15.06/4.15  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v2, v0) = v4) |  ~ (sdtasdt0(v1, v0) = v3) |  ~ sdtlseqdt0(v1, v2) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4))
% 15.06/4.16  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (sdtpldt0(v2, v0) = v4) |  ~ (sdtpldt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v4) &  ~ (v5 = v3) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5))
% 15.06/4.16  | (15)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 15.06/4.16  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) |  ~ (sdtpldt0(v0, v1) = v3) |  ~ isPrime0(v2) |  ~ iLess0(v4, all_0_4_4) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) |  ? [v5] : (sdtasdt0(v0, v1) = v5 &  ~ doDivides0(v2, v5)))
% 15.06/4.16  | (17) sdtlseqdt0(xp, xn)
% 15.06/4.16  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v0, v2) = v3) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ sdtlseqdt0(v1, v2) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.06/4.16  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 |  ~ (sdtpldt0(v0, v2) = v3) |  ~ (sdtpldt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.06/4.16  | (20) sdtpldt0(xr, xm) = all_0_1_1
% 15.06/4.16  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v2) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.06/4.16  | (22) doDivides0(xp, all_0_3_3)
% 15.06/4.16  | (23) sdtlseqdt0(xr, xn)
% 15.06/4.16  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) |  ~ (sdtpldt0(v1, v2) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4))
% 15.06/4.16  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) |  ~ (sdtpldt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4))
% 15.06/4.16  | (26)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 15.06/4.16  | (27)  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 15.06/4.16  | (28) aNaturalNumber0(xp)
% 15.06/4.16  | (29) isPrime0(xp)
% 15.06/4.16  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ (sdtpldt0(v3, v4) = v5) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6))
% 15.06/4.16  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtpldt0(v0, v2) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v6 = v3) &  ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6)))
% 15.06/4.16  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v2, v0) = v4) |  ~ (sdtasdt0(v1, v0) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5))
% 15.06/4.16  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v0 = sz00 |  ~ (sdtsldt0(v4, v0) = v5) |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v3, v1) = v4) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v3) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v3, v2) = v5)
% 15.06/4.16  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) |  ~ (sdtpldt0(v0, v3) = v4) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5))
% 15.06/4.16  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v2, v0) = v4) |  ~ (sdtasdt0(v1, v0) = v3) |  ~ sdtlseqdt0(v1, v2) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v6)))
% 15.06/4.16  | (36)  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ (sdtpldt0(v0, v1) = sz00) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.06/4.16  | (37)  ! [v0] : (v0 = sz10 | v0 = sz00 |  ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 15.06/4.16  | (38)  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ (sdtasdt0(v0, sz00) = v1) |  ~ aNaturalNumber0(v0))
% 15.06/4.16  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v3, v2) = v4) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v3) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] : (sdtsldt0(v5, v0) = v4 & sdtasdt0(v3, v1) = v5))
% 15.06/4.16  | (40)  ! [v0] :  ! [v1] : (v1 = v0 | v1 = sz10 |  ~ isPrime0(v0) |  ~ doDivides0(v1, v0) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.06/4.16  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtpldt0(v2, v1) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v6 = v5) &  ~ (v4 = v3) & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v4, v3)))
% 15.06/4.16  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v0, v2) = v3) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.06/4.16  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v0, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5))
% 15.06/4.17  | (44)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) |  ~ (sdtasdt0(v0, v3) = v4) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5))
% 15.06/4.17  | (45)  ~ (xr = xn)
% 15.06/4.17  | (46)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 15.06/4.17  | (47)  ! [v0] :  ! [v1] : ( ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 15.06/4.17  | (48)  ~ isPrime0(sz00)
% 15.06/4.17  | (49)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 | v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v0, v3) = v1) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v3) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.06/4.17  | (50) aNaturalNumber0(sz10)
% 15.06/4.17  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v0, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ sdtlseqdt0(v1, v2) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtlseqdt0(v5, v6)))
% 15.06/4.17  | (52)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (sdtpldt0(v0, v2) = v4) |  ~ (sdtpldt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5))
% 15.06/4.17  | (53)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtmndt0(v3, v2) = v1) |  ~ (sdtmndt0(v3, v2) = v0))
% 15.06/4.17  | (54)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v2, v0) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ sdtlseqdt0(v1, v2) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v4) &  ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtlseqdt0(v6, v4) & sdtlseqdt0(v3, v5)))
% 15.06/4.17  | (55)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtsldt0(v3, v2) = v1) |  ~ (sdtsldt0(v3, v2) = v0))
% 15.06/4.17  | (56)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v0, v2) = v3) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 15.06/4.17  | (57) sdtasdt0(xr, xm) = all_0_2_2
% 15.06/4.17  | (58)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 15.06/4.17  | (59)  ~ isPrime0(sz10)
% 15.06/4.17  | (60)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) |  ~ (sdtpldt0(v1, v2) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v6, v7) = v5))
% 15.06/4.17  | (61)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ sdtlseqdt0(v1, v2) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 15.06/4.17  | (62)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (sdtpldt0(v2, v0) = v4) |  ~ (sdtpldt0(v1, v0) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v0, v2) = v6 & sdtpldt0(v0, v1) = v5))
% 15.06/4.17  | (63) doDivides0(xp, all_0_2_2)
% 15.06/4.17  | (64)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtasdt0(v0, sz10) = v1) |  ~ aNaturalNumber0(v0))
% 15.06/4.17  | (65)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtpldt0(v1, v2) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v6 = v3) &  ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v0, v2) = v6 & sdtlseqdt0(v6, v3) & sdtlseqdt0(v4, v5)))
% 15.19/4.17  | (66)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) |  ~ doDivides0(v0, v2) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v0, v3))
% 15.19/4.17  | (67)  ! [v0] : (v0 = sz10 | v0 = sz00 |  ~ aNaturalNumber0(v0) | isPrime0(v0) |  ? [v1] : ( ~ (v1 = v0) &  ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 15.19/4.17  | (68)  ! [v0] :  ! [v1] :  ! [v2] : (v0 = sz00 |  ~ (sdtasdt0(v1, v0) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 15.19/4.17  | (69)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 15.19/4.17  | (70)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 15.19/4.17  | (71) sdtpldt0(xn, xm) = all_0_5_5
% 15.19/4.17  | (72)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ doDivides0(v1, v2) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 15.19/4.17  | (73)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtpldt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0))
% 15.19/4.17  | (74)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) |  ~ doDivides0(v0, v3) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 15.19/4.17  | (75)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (sdtpldt0(v1, v0) = v4) |  ~ (sdtpldt0(v0, v2) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v4) &  ~ (v5 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v1) = v5))
% 15.19/4.18  | (76)  ~ (sz10 = sz00)
% 15.19/4.18  | (77)  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 15.19/4.18  | (78)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtasdt0(v3, v2) = v1) |  ~ (sdtasdt0(v3, v2) = v0))
% 15.19/4.18  | (79) sdtasdt0(xn, xm) = all_0_3_3
% 15.19/4.18  | (80) sdtmndt0(xn, xp) = xr
% 15.19/4.18  | (81)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v2, v0) = v3) |  ~ (sdtasdt0(v1, v0) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.19/4.18  | (82)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v2, v0) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v4) &  ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5))
% 15.19/4.18  | (83)  ! [v0] :  ! [v1] : ( ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 15.19/4.18  | (84)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 15.19/4.18  | (85)  ! [v0] :  ! [v1] : (v0 = sz00 |  ~ (sdtpldt0(v0, v1) = sz00) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.19/4.18  | (86)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v1, v0) = v4) |  ~ (sdtasdt0(v0, v2) = v3) |  ~ sdtlseqdt0(v1, v2) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v4) &  ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v3) & sdtlseqdt0(v4, v6)))
% 15.19/4.18  | (87) aNaturalNumber0(xm)
% 15.19/4.18  | (88) aNaturalNumber0(sz00)
% 15.19/4.18  | (89)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtpldt0(v0, sz00) = v1) |  ~ aNaturalNumber0(v0))
% 15.19/4.18  | (90)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtpldt0(v2, v0) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v6 = v5) &  ~ (v4 = v3) & sdtpldt0(v2, v1) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v3, v4)))
% 15.19/4.18  | (91)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 |  ~ (sdtpldt0(v2, v0) = v3) |  ~ (sdtpldt0(v1, v0) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.19/4.18  | (92)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtpldt0(v3, v2) = v1) |  ~ (sdtpldt0(v3, v2) = v0))
% 15.19/4.18  | (93)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4))
% 15.19/4.18  | (94)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v2) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 15.19/4.18  | (95)  ! [v0] :  ! [v1] : (v1 = sz00 | v0 = sz00 |  ~ (sdtasdt0(v0, v1) = sz00) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.19/4.18  | (96) aNaturalNumber0(xn)
% 15.19/4.18  | (97)  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0)
% 15.19/4.18  | (98)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtasdt0(sz10, v0) = v1) |  ~ aNaturalNumber0(v0))
% 15.19/4.18  | (99)  ! [v0] : (v0 = sz10 | v0 = sz00 |  ~ aNaturalNumber0(v0) |  ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 15.19/4.18  | (100)  ! [v0] :  ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0)
% 15.19/4.18  | (101)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v1, v0) = v4) |  ~ (sdtasdt0(v0, v2) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v4) &  ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5))
% 15.19/4.18  | (102)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v3) = v1) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v3) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.19/4.18  | (103) sdtpldt0(all_0_5_5, xp) = all_0_4_4
% 15.19/4.18  | (104) sdtpldt0(all_0_1_1, xp) = all_0_0_0
% 15.19/4.18  | (105)  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00)
% 15.19/4.18  | (106)  ! [v0] :  ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 15.19/4.18  | (107)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v0, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ sdtlseqdt0(v1, v2) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4))
% 15.19/4.18  |
% 15.19/4.18  | Instantiating formula (25) with all_0_4_4, all_0_5_5, xp, xm, xn and discharging atoms sdtpldt0(all_0_5_5, xp) = all_0_4_4, sdtpldt0(xn, xm) = all_0_5_5, aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 15.19/4.18  | (108)  ? [v0] : (sdtpldt0(xm, xp) = v0 & sdtpldt0(xn, v0) = all_0_4_4)
% 15.19/4.18  |
% 15.19/4.18  | Instantiating formula (12) with all_0_5_5, xn, xm and discharging atoms sdtpldt0(xn, xm) = all_0_5_5, aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 15.19/4.18  | (109) sdtpldt0(xm, xn) = all_0_5_5
% 15.19/4.18  |
% 15.19/4.18  | Instantiating formula (3) with xn, xp and discharging atoms sdtlseqdt0(xp, xn), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 15.19/4.18  | (110)  ? [v0] : (sdtpldt0(xp, v0) = xn & aNaturalNumber0(v0))
% 15.19/4.18  |
% 15.19/4.18  | Instantiating formula (83) with xn, xn and discharging atoms aNaturalNumber0(xn), yields:
% 15.19/4.18  | (111) sdtlseqdt0(xn, xn)
% 15.19/4.18  |
% 15.19/4.18  | Instantiating (110) with all_9_0_6 yields:
% 15.19/4.18  | (112) sdtpldt0(xp, all_9_0_6) = xn & aNaturalNumber0(all_9_0_6)
% 15.19/4.18  |
% 15.19/4.18  | Applying alpha-rule on (112) yields:
% 15.19/4.18  | (113) sdtpldt0(xp, all_9_0_6) = xn
% 15.19/4.18  | (114) aNaturalNumber0(all_9_0_6)
% 15.19/4.18  |
% 15.19/4.18  | Instantiating (108) with all_11_0_7 yields:
% 15.19/4.18  | (115) sdtpldt0(xm, xp) = all_11_0_7 & sdtpldt0(xn, all_11_0_7) = all_0_4_4
% 15.19/4.18  |
% 15.19/4.18  | Applying alpha-rule on (115) yields:
% 15.19/4.18  | (116) sdtpldt0(xm, xp) = all_11_0_7
% 15.19/4.18  | (117) sdtpldt0(xn, all_11_0_7) = all_0_4_4
% 15.19/4.18  |
% 15.19/4.18  | Instantiating formula (102) with all_9_0_6, xr, xn, xp and discharging atoms sdtmndt0(xn, xp) = xr, sdtpldt0(xp, all_9_0_6) = xn, sdtlseqdt0(xp, xn), aNaturalNumber0(all_9_0_6), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 15.19/4.18  | (118) all_9_0_6 = xr
% 15.19/4.18  |
% 15.19/4.18  | From (118) and (113) follows:
% 15.19/4.19  | (119) sdtpldt0(xp, xr) = xn
% 15.19/4.19  |
% 15.19/4.19  | From (118) and (114) follows:
% 15.19/4.19  | (120) aNaturalNumber0(xr)
% 15.19/4.19  |
% 15.19/4.19  | Instantiating formula (58) with all_11_0_7, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_11_0_7, aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 15.19/4.19  | (121) aNaturalNumber0(all_11_0_7)
% 15.19/4.19  |
% 15.19/4.19  | Instantiating formula (3) with xn, xn and discharging atoms sdtlseqdt0(xn, xn), aNaturalNumber0(xn), yields:
% 15.19/4.19  | (122)  ? [v0] : (sdtpldt0(xn, v0) = xn & aNaturalNumber0(v0))
% 15.19/4.19  |
% 15.19/4.19  | Instantiating formula (25) with all_0_0_0, all_0_1_1, xp, xm, xr and discharging atoms sdtpldt0(all_0_1_1, xp) = all_0_0_0, sdtpldt0(xr, xm) = all_0_1_1, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 15.19/4.19  | (123)  ? [v0] : (sdtpldt0(xr, v0) = all_0_0_0 & sdtpldt0(xm, xp) = v0)
% 15.19/4.19  |
% 15.19/4.19  | Instantiating formula (62) with all_0_1_1, all_0_5_5, xr, xn, xm and discharging atoms sdtpldt0(xr, xm) = all_0_1_1, sdtpldt0(xn, xm) = all_0_5_5, aNaturalNumber0(xr), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 15.19/4.19  | (124) xr = xn |  ? [v0] :  ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xm, xr) = v1 & sdtpldt0(xm, xn) = v0)
% 15.19/4.19  |
% 15.19/4.19  | Instantiating formula (14) with all_0_1_1, all_0_5_5, xr, xn, xm and discharging atoms sdtpldt0(xr, xm) = all_0_1_1, sdtpldt0(xm, xn) = all_0_5_5, aNaturalNumber0(xr), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 15.19/4.19  | (125) xr = xn |  ? [v0] :  ? [v1] : ( ~ (v1 = all_0_1_1) &  ~ (v0 = all_0_5_5) & sdtpldt0(xm, xr) = v0 & sdtpldt0(xn, xm) = v1)
% 15.19/4.19  |
% 15.19/4.19  | Instantiating formula (31) with all_0_1_1, xm, xn, xr and discharging atoms sdtpldt0(xr, xm) = all_0_1_1, sdtlseqdt0(xr, xn), aNaturalNumber0(xr), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 15.19/4.19  | (126) xr = xn |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = all_0_1_1) &  ~ (v1 = v0) & sdtpldt0(xm, xr) = v0 & sdtpldt0(xm, xn) = v1 & sdtpldt0(xn, xm) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_1_1, v2))
% 15.19/4.19  |
% 15.19/4.19  | Instantiating formula (65) with all_0_5_5, xm, xn, xr and discharging atoms sdtpldt0(xn, xm) = all_0_5_5, sdtlseqdt0(xr, xn), aNaturalNumber0(xr), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 15.19/4.19  | (127) xr = xn |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = all_0_5_5) &  ~ (v1 = v0) & sdtpldt0(xr, xm) = v2 & sdtpldt0(xm, xr) = v0 & sdtpldt0(xm, xn) = v1 & sdtlseqdt0(v2, all_0_5_5) & sdtlseqdt0(v0, v1))
% 15.19/4.19  |
% 15.19/4.19  | Instantiating formula (34) with all_0_5_5, xn, xr, xp, xm and discharging atoms sdtpldt0(xp, xr) = xn, sdtpldt0(xm, xn) = all_0_5_5, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 15.19/4.19  | (128)  ? [v0] : (sdtpldt0(v0, xr) = all_0_5_5 & sdtpldt0(xm, xp) = v0)
% 15.19/4.19  |
% 15.19/4.19  | Instantiating formula (90) with xn, xp, xn, xr and discharging atoms sdtpldt0(xp, xr) = xn, sdtlseqdt0(xr, xn), aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 15.19/4.19  | (129) xr = xn |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = v1) &  ~ (v0 = xn) & sdtpldt0(xr, xp) = v1 & sdtpldt0(xp, xn) = v0 & sdtpldt0(xn, xp) = v2 & sdtlseqdt0(v1, v2) & sdtlseqdt0(xn, v0))
% 15.19/4.19  |
% 15.19/4.19  | Instantiating formula (12) with xn, xp, xr and discharging atoms sdtpldt0(xp, xr) = xn, aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 15.19/4.19  | (130) sdtpldt0(xr, xp) = xn
% 15.19/4.19  |
% 15.19/4.19  | Instantiating formula (41) with all_0_5_5, xm, xn, xr and discharging atoms sdtpldt0(xm, xn) = all_0_5_5, sdtlseqdt0(xr, xn), aNaturalNumber0(xr), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 15.19/4.19  | (131) xr = xn |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = v1) &  ~ (v0 = all_0_5_5) & sdtpldt0(xr, xm) = v1 & sdtpldt0(xm, xr) = v0 & sdtpldt0(xn, xm) = v2 & sdtlseqdt0(v1, v2) & sdtlseqdt0(v0, all_0_5_5))
% 15.19/4.19  |
% 15.19/4.19  | Instantiating formula (3) with xn, xr and discharging atoms sdtlseqdt0(xr, xn), aNaturalNumber0(xr), aNaturalNumber0(xn), yields:
% 15.19/4.19  | (132)  ? [v0] : (sdtpldt0(xr, v0) = xn & aNaturalNumber0(v0))
% 15.19/4.19  |
% 15.19/4.19  | Instantiating (122) with all_27_0_10 yields:
% 15.19/4.19  | (133) sdtpldt0(xn, all_27_0_10) = xn & aNaturalNumber0(all_27_0_10)
% 15.19/4.19  |
% 15.19/4.19  | Applying alpha-rule on (133) yields:
% 15.19/4.19  | (134) sdtpldt0(xn, all_27_0_10) = xn
% 15.19/4.19  | (135) aNaturalNumber0(all_27_0_10)
% 15.19/4.19  |
% 15.19/4.19  | Instantiating (132) with all_31_0_12 yields:
% 15.19/4.19  | (136) sdtpldt0(xr, all_31_0_12) = xn & aNaturalNumber0(all_31_0_12)
% 15.19/4.19  |
% 15.19/4.19  | Applying alpha-rule on (136) yields:
% 15.19/4.19  | (137) sdtpldt0(xr, all_31_0_12) = xn
% 15.19/4.19  | (138) aNaturalNumber0(all_31_0_12)
% 15.19/4.19  |
% 15.19/4.19  | Instantiating (128) with all_37_0_15 yields:
% 15.19/4.19  | (139) sdtpldt0(all_37_0_15, xr) = all_0_5_5 & sdtpldt0(xm, xp) = all_37_0_15
% 15.19/4.19  |
% 15.19/4.19  | Applying alpha-rule on (139) yields:
% 15.19/4.19  | (140) sdtpldt0(all_37_0_15, xr) = all_0_5_5
% 15.19/4.19  | (141) sdtpldt0(xm, xp) = all_37_0_15
% 15.19/4.19  |
% 15.19/4.19  | Instantiating (123) with all_43_0_18 yields:
% 15.19/4.19  | (142) sdtpldt0(xr, all_43_0_18) = all_0_0_0 & sdtpldt0(xm, xp) = all_43_0_18
% 15.19/4.19  |
% 15.19/4.19  | Applying alpha-rule on (142) yields:
% 15.19/4.19  | (143) sdtpldt0(xr, all_43_0_18) = all_0_0_0
% 15.19/4.19  | (144) sdtpldt0(xm, xp) = all_43_0_18
% 15.19/4.19  |
% 15.19/4.19  +-Applying beta-rule and splitting (131), into two cases.
% 15.19/4.19  |-Branch one:
% 15.19/4.19  | (145) xr = xn
% 15.19/4.19  |
% 15.19/4.19  	| Equations (145) can reduce 45 to:
% 15.19/4.19  	| (146) $false
% 15.19/4.19  	|
% 15.19/4.19  	|-The branch is then unsatisfiable
% 15.19/4.19  |-Branch two:
% 15.19/4.19  | (45)  ~ (xr = xn)
% 15.19/4.19  | (148)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = v1) &  ~ (v0 = all_0_5_5) & sdtpldt0(xr, xm) = v1 & sdtpldt0(xm, xr) = v0 & sdtpldt0(xn, xm) = v2 & sdtlseqdt0(v1, v2) & sdtlseqdt0(v0, all_0_5_5))
% 15.19/4.19  |
% 15.19/4.19  	+-Applying beta-rule and splitting (126), into two cases.
% 15.19/4.19  	|-Branch one:
% 15.19/4.19  	| (145) xr = xn
% 15.19/4.19  	|
% 15.19/4.19  		| Equations (145) can reduce 45 to:
% 15.19/4.19  		| (146) $false
% 15.19/4.19  		|
% 15.19/4.19  		|-The branch is then unsatisfiable
% 15.19/4.19  	|-Branch two:
% 15.19/4.19  	| (45)  ~ (xr = xn)
% 15.19/4.19  	| (152)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = all_0_1_1) &  ~ (v1 = v0) & sdtpldt0(xm, xr) = v0 & sdtpldt0(xm, xn) = v1 & sdtpldt0(xn, xm) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_1_1, v2))
% 15.19/4.19  	|
% 15.19/4.19  		+-Applying beta-rule and splitting (127), into two cases.
% 15.19/4.19  		|-Branch one:
% 15.19/4.19  		| (145) xr = xn
% 15.19/4.19  		|
% 15.19/4.19  			| Equations (145) can reduce 45 to:
% 15.19/4.19  			| (146) $false
% 15.19/4.19  			|
% 15.19/4.19  			|-The branch is then unsatisfiable
% 15.19/4.19  		|-Branch two:
% 15.19/4.19  		| (45)  ~ (xr = xn)
% 15.19/4.19  		| (156)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = all_0_5_5) &  ~ (v1 = v0) & sdtpldt0(xr, xm) = v2 & sdtpldt0(xm, xr) = v0 & sdtpldt0(xm, xn) = v1 & sdtlseqdt0(v2, all_0_5_5) & sdtlseqdt0(v0, v1))
% 15.19/4.19  		|
% 15.19/4.19  			+-Applying beta-rule and splitting (125), into two cases.
% 15.19/4.19  			|-Branch one:
% 15.19/4.19  			| (145) xr = xn
% 15.19/4.19  			|
% 15.19/4.19  				| Equations (145) can reduce 45 to:
% 15.19/4.19  				| (146) $false
% 15.19/4.19  				|
% 15.19/4.19  				|-The branch is then unsatisfiable
% 15.19/4.19  			|-Branch two:
% 15.19/4.19  			| (45)  ~ (xr = xn)
% 15.19/4.19  			| (160)  ? [v0] :  ? [v1] : ( ~ (v1 = all_0_1_1) &  ~ (v0 = all_0_5_5) & sdtpldt0(xm, xr) = v0 & sdtpldt0(xn, xm) = v1)
% 15.19/4.19  			|
% 15.19/4.19  				+-Applying beta-rule and splitting (124), into two cases.
% 15.19/4.19  				|-Branch one:
% 15.19/4.19  				| (145) xr = xn
% 15.19/4.19  				|
% 15.19/4.19  					| Equations (145) can reduce 45 to:
% 15.19/4.19  					| (146) $false
% 15.19/4.19  					|
% 15.19/4.19  					|-The branch is then unsatisfiable
% 15.19/4.19  				|-Branch two:
% 15.19/4.19  				| (45)  ~ (xr = xn)
% 15.19/4.19  				| (164)  ? [v0] :  ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xm, xr) = v1 & sdtpldt0(xm, xn) = v0)
% 15.19/4.19  				|
% 15.19/4.19  					+-Applying beta-rule and splitting (129), into two cases.
% 15.19/4.19  					|-Branch one:
% 15.19/4.19  					| (145) xr = xn
% 15.19/4.19  					|
% 15.19/4.19  						| Equations (145) can reduce 45 to:
% 15.19/4.19  						| (146) $false
% 15.19/4.19  						|
% 15.19/4.19  						|-The branch is then unsatisfiable
% 15.19/4.19  					|-Branch two:
% 15.19/4.19  					| (45)  ~ (xr = xn)
% 15.19/4.19  					| (168)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = v1) &  ~ (v0 = xn) & sdtpldt0(xr, xp) = v1 & sdtpldt0(xp, xn) = v0 & sdtpldt0(xn, xp) = v2 & sdtlseqdt0(v1, v2) & sdtlseqdt0(xn, v0))
% 15.19/4.19  					|
% 15.19/4.19  						| Instantiating formula (92) with xm, xp, all_43_0_18, all_11_0_7 and discharging atoms sdtpldt0(xm, xp) = all_43_0_18, sdtpldt0(xm, xp) = all_11_0_7, yields:
% 15.19/4.19  						| (169) all_43_0_18 = all_11_0_7
% 15.19/4.19  						|
% 15.19/4.19  						| Instantiating formula (92) with xm, xp, all_37_0_15, all_43_0_18 and discharging atoms sdtpldt0(xm, xp) = all_43_0_18, sdtpldt0(xm, xp) = all_37_0_15, yields:
% 15.19/4.19  						| (170) all_43_0_18 = all_37_0_15
% 15.19/4.19  						|
% 15.19/4.19  						| Instantiating formula (19) with xn, all_31_0_12, xp, xr and discharging atoms sdtpldt0(xr, all_31_0_12) = xn, sdtpldt0(xr, xp) = xn, aNaturalNumber0(all_31_0_12), aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 15.19/4.19  						| (171) all_31_0_12 = xp
% 15.19/4.19  						|
% 15.19/4.19  						| Combining equations (170,169) yields a new equation:
% 15.19/4.19  						| (172) all_37_0_15 = all_11_0_7
% 15.19/4.19  						|
% 15.19/4.19  						| Simplifying 172 yields:
% 15.19/4.19  						| (173) all_37_0_15 = all_11_0_7
% 15.19/4.19  						|
% 15.19/4.19  						| From (173) and (140) follows:
% 15.19/4.19  						| (174) sdtpldt0(all_11_0_7, xr) = all_0_5_5
% 15.19/4.20  						|
% 15.19/4.20  						| From (169) and (143) follows:
% 15.19/4.20  						| (175) sdtpldt0(xr, all_11_0_7) = all_0_0_0
% 15.19/4.20  						|
% 15.19/4.20  						| From (171) and (138) follows:
% 15.19/4.20  						| (28) aNaturalNumber0(xp)
% 15.19/4.20  						|
% 15.19/4.20  						| Instantiating formula (65) with xn, all_27_0_10, xn, xr and discharging atoms sdtpldt0(xn, all_27_0_10) = xn, sdtlseqdt0(xr, xn), aNaturalNumber0(all_27_0_10), aNaturalNumber0(xr), aNaturalNumber0(xn), yields:
% 15.19/4.20  						| (177) xr = xn |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = xn) &  ~ (v1 = v0) & sdtpldt0(all_27_0_10, xr) = v0 & sdtpldt0(all_27_0_10, xn) = v1 & sdtpldt0(xr, all_27_0_10) = v2 & sdtlseqdt0(v2, xn) & sdtlseqdt0(v0, v1))
% 15.19/4.20  						|
% 15.19/4.20  						| Instantiating formula (25) with all_0_4_4, xn, all_11_0_7, xr, xp and discharging atoms sdtpldt0(xp, xr) = xn, sdtpldt0(xn, all_11_0_7) = all_0_4_4, aNaturalNumber0(all_11_0_7), aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 15.19/4.20  						| (178)  ? [v0] : (sdtpldt0(xr, all_11_0_7) = v0 & sdtpldt0(xp, v0) = all_0_4_4)
% 15.19/4.20  						|
% 15.19/4.20  						| Instantiating formula (75) with all_0_4_4, all_0_5_5, xr, xn, all_11_0_7 and discharging atoms sdtpldt0(all_11_0_7, xr) = all_0_5_5, sdtpldt0(xn, all_11_0_7) = all_0_4_4, aNaturalNumber0(all_11_0_7), aNaturalNumber0(xr), aNaturalNumber0(xn), yields:
% 15.19/4.20  						| (179) xr = xn |  ? [v0] :  ? [v1] : ( ~ (v1 = all_0_4_4) &  ~ (v0 = all_0_5_5) & sdtpldt0(all_11_0_7, xn) = v0 & sdtpldt0(xr, all_11_0_7) = v1)
% 15.19/4.20  						|
% 15.19/4.20  						| Instantiating formula (65) with all_0_4_4, all_11_0_7, xn, xr and discharging atoms sdtpldt0(xn, all_11_0_7) = all_0_4_4, sdtlseqdt0(xr, xn), aNaturalNumber0(all_11_0_7), aNaturalNumber0(xr), aNaturalNumber0(xn), yields:
% 15.19/4.20  						| (180) xr = xn |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = all_0_4_4) &  ~ (v1 = v0) & sdtpldt0(all_11_0_7, xr) = v0 & sdtpldt0(all_11_0_7, xn) = v1 & sdtpldt0(xr, all_11_0_7) = v2 & sdtlseqdt0(v2, all_0_4_4) & sdtlseqdt0(v0, v1))
% 15.19/4.20  						|
% 15.19/4.20  						| Instantiating formula (12) with all_0_4_4, xn, all_11_0_7 and discharging atoms sdtpldt0(xn, all_11_0_7) = all_0_4_4, aNaturalNumber0(all_11_0_7), aNaturalNumber0(xn), yields:
% 15.19/4.20  						| (181) sdtpldt0(all_11_0_7, xn) = all_0_4_4
% 15.19/4.20  						|
% 15.19/4.20  						| Instantiating formula (90) with all_0_5_5, all_11_0_7, xn, xr and discharging atoms sdtpldt0(all_11_0_7, xr) = all_0_5_5, sdtlseqdt0(xr, xn), aNaturalNumber0(all_11_0_7), aNaturalNumber0(xr), aNaturalNumber0(xn), yields:
% 15.19/4.20  						| (182) xr = xn |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = v1) &  ~ (v0 = all_0_5_5) & sdtpldt0(all_11_0_7, xn) = v0 & sdtpldt0(xr, all_11_0_7) = v1 & sdtpldt0(xn, all_11_0_7) = v2 & sdtlseqdt0(v1, v2) & sdtlseqdt0(all_0_5_5, v0))
% 15.19/4.20  						|
% 15.19/4.20  						| Instantiating formula (12) with all_0_5_5, all_11_0_7, xr and discharging atoms sdtpldt0(all_11_0_7, xr) = all_0_5_5, aNaturalNumber0(all_11_0_7), aNaturalNumber0(xr), yields:
% 15.19/4.20  						| (183) sdtpldt0(xr, all_11_0_7) = all_0_5_5
% 15.19/4.20  						|
% 15.19/4.20  						| Instantiating formula (62) with all_0_0_0, all_0_4_4, xr, xn, all_11_0_7 and discharging atoms sdtpldt0(xr, all_11_0_7) = all_0_0_0, sdtpldt0(xn, all_11_0_7) = all_0_4_4, aNaturalNumber0(all_11_0_7), aNaturalNumber0(xr), aNaturalNumber0(xn), yields:
% 15.19/4.20  						| (184) xr = xn |  ? [v0] :  ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_11_0_7, xr) = v1 & sdtpldt0(all_11_0_7, xn) = v0)
% 15.19/4.20  						|
% 15.19/4.20  						| Instantiating formula (31) with all_0_0_0, all_11_0_7, xn, xr and discharging atoms sdtpldt0(xr, all_11_0_7) = all_0_0_0, sdtlseqdt0(xr, xn), aNaturalNumber0(all_11_0_7), aNaturalNumber0(xr), aNaturalNumber0(xn), yields:
% 15.19/4.20  						| (185) xr = xn |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = all_0_0_0) &  ~ (v1 = v0) & sdtpldt0(all_11_0_7, xr) = v0 & sdtpldt0(all_11_0_7, xn) = v1 & sdtpldt0(xn, all_11_0_7) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_0_0, v2))
% 15.19/4.20  						|
% 15.19/4.20  						| Instantiating (178) with all_181_0_122 yields:
% 15.19/4.20  						| (186) sdtpldt0(xr, all_11_0_7) = all_181_0_122 & sdtpldt0(xp, all_181_0_122) = all_0_4_4
% 15.19/4.20  						|
% 15.19/4.20  						| Applying alpha-rule on (186) yields:
% 15.19/4.20  						| (187) sdtpldt0(xr, all_11_0_7) = all_181_0_122
% 15.19/4.20  						| (188) sdtpldt0(xp, all_181_0_122) = all_0_4_4
% 15.19/4.20  						|
% 15.19/4.20  						+-Applying beta-rule and splitting (185), into two cases.
% 15.19/4.20  						|-Branch one:
% 15.19/4.20  						| (145) xr = xn
% 15.19/4.20  						|
% 15.19/4.20  							| Equations (145) can reduce 45 to:
% 15.19/4.20  							| (146) $false
% 15.19/4.20  							|
% 15.19/4.20  							|-The branch is then unsatisfiable
% 15.19/4.20  						|-Branch two:
% 15.19/4.20  						| (45)  ~ (xr = xn)
% 15.19/4.20  						| (192)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = all_0_0_0) &  ~ (v1 = v0) & sdtpldt0(all_11_0_7, xr) = v0 & sdtpldt0(all_11_0_7, xn) = v1 & sdtpldt0(xn, all_11_0_7) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_0_0, v2))
% 15.19/4.20  						|
% 15.19/4.20  							| Instantiating (192) with all_235_0_163, all_235_1_164, all_235_2_165 yields:
% 15.19/4.20  							| (193)  ~ (all_235_0_163 = all_0_0_0) &  ~ (all_235_1_164 = all_235_2_165) & sdtpldt0(all_11_0_7, xr) = all_235_2_165 & sdtpldt0(all_11_0_7, xn) = all_235_1_164 & sdtpldt0(xn, all_11_0_7) = all_235_0_163 & sdtlseqdt0(all_235_2_165, all_235_1_164) & sdtlseqdt0(all_0_0_0, all_235_0_163)
% 15.19/4.20  							|
% 15.19/4.20  							| Applying alpha-rule on (193) yields:
% 15.19/4.20  							| (194)  ~ (all_235_1_164 = all_235_2_165)
% 15.19/4.20  							| (195)  ~ (all_235_0_163 = all_0_0_0)
% 15.19/4.20  							| (196) sdtpldt0(xn, all_11_0_7) = all_235_0_163
% 15.19/4.20  							| (197) sdtpldt0(all_11_0_7, xn) = all_235_1_164
% 15.19/4.20  							| (198) sdtpldt0(all_11_0_7, xr) = all_235_2_165
% 15.19/4.20  							| (199) sdtlseqdt0(all_0_0_0, all_235_0_163)
% 15.19/4.20  							| (200) sdtlseqdt0(all_235_2_165, all_235_1_164)
% 15.19/4.20  							|
% 15.19/4.20  							+-Applying beta-rule and splitting (182), into two cases.
% 15.19/4.20  							|-Branch one:
% 15.19/4.20  							| (145) xr = xn
% 15.19/4.20  							|
% 15.19/4.20  								| Equations (145) can reduce 45 to:
% 15.19/4.20  								| (146) $false
% 15.19/4.20  								|
% 15.19/4.20  								|-The branch is then unsatisfiable
% 15.19/4.20  							|-Branch two:
% 15.19/4.20  							| (45)  ~ (xr = xn)
% 15.19/4.20  							| (204)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = v1) &  ~ (v0 = all_0_5_5) & sdtpldt0(all_11_0_7, xn) = v0 & sdtpldt0(xr, all_11_0_7) = v1 & sdtpldt0(xn, all_11_0_7) = v2 & sdtlseqdt0(v1, v2) & sdtlseqdt0(all_0_5_5, v0))
% 15.19/4.20  							|
% 15.19/4.20  								| Instantiating (204) with all_245_0_166, all_245_1_167, all_245_2_168 yields:
% 15.19/4.20  								| (205)  ~ (all_245_0_166 = all_245_1_167) &  ~ (all_245_2_168 = all_0_5_5) & sdtpldt0(all_11_0_7, xn) = all_245_2_168 & sdtpldt0(xr, all_11_0_7) = all_245_1_167 & sdtpldt0(xn, all_11_0_7) = all_245_0_166 & sdtlseqdt0(all_245_1_167, all_245_0_166) & sdtlseqdt0(all_0_5_5, all_245_2_168)
% 15.19/4.20  								|
% 15.19/4.20  								| Applying alpha-rule on (205) yields:
% 15.19/4.20  								| (206) sdtlseqdt0(all_245_1_167, all_245_0_166)
% 15.19/4.20  								| (207)  ~ (all_245_2_168 = all_0_5_5)
% 15.19/4.20  								| (208) sdtlseqdt0(all_0_5_5, all_245_2_168)
% 15.19/4.20  								| (209) sdtpldt0(xn, all_11_0_7) = all_245_0_166
% 15.19/4.20  								| (210) sdtpldt0(all_11_0_7, xn) = all_245_2_168
% 15.19/4.20  								| (211) sdtpldt0(xr, all_11_0_7) = all_245_1_167
% 15.19/4.20  								| (212)  ~ (all_245_0_166 = all_245_1_167)
% 15.19/4.20  								|
% 15.19/4.20  								+-Applying beta-rule and splitting (180), into two cases.
% 15.19/4.20  								|-Branch one:
% 15.19/4.20  								| (145) xr = xn
% 15.19/4.20  								|
% 15.19/4.20  									| Equations (145) can reduce 45 to:
% 15.19/4.20  									| (146) $false
% 15.19/4.20  									|
% 15.19/4.20  									|-The branch is then unsatisfiable
% 15.19/4.20  								|-Branch two:
% 15.19/4.20  								| (45)  ~ (xr = xn)
% 15.19/4.20  								| (216)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = all_0_4_4) &  ~ (v1 = v0) & sdtpldt0(all_11_0_7, xr) = v0 & sdtpldt0(all_11_0_7, xn) = v1 & sdtpldt0(xr, all_11_0_7) = v2 & sdtlseqdt0(v2, all_0_4_4) & sdtlseqdt0(v0, v1))
% 15.19/4.20  								|
% 15.19/4.20  									| Instantiating (216) with all_257_0_172, all_257_1_173, all_257_2_174 yields:
% 15.19/4.20  									| (217)  ~ (all_257_0_172 = all_0_4_4) &  ~ (all_257_1_173 = all_257_2_174) & sdtpldt0(all_11_0_7, xr) = all_257_2_174 & sdtpldt0(all_11_0_7, xn) = all_257_1_173 & sdtpldt0(xr, all_11_0_7) = all_257_0_172 & sdtlseqdt0(all_257_0_172, all_0_4_4) & sdtlseqdt0(all_257_2_174, all_257_1_173)
% 15.19/4.20  									|
% 15.19/4.20  									| Applying alpha-rule on (217) yields:
% 15.19/4.20  									| (218) sdtpldt0(all_11_0_7, xr) = all_257_2_174
% 15.19/4.20  									| (219)  ~ (all_257_1_173 = all_257_2_174)
% 15.19/4.20  									| (220)  ~ (all_257_0_172 = all_0_4_4)
% 15.19/4.20  									| (221) sdtpldt0(all_11_0_7, xn) = all_257_1_173
% 15.19/4.20  									| (222) sdtpldt0(xr, all_11_0_7) = all_257_0_172
% 15.19/4.20  									| (223) sdtlseqdt0(all_257_0_172, all_0_4_4)
% 15.19/4.20  									| (224) sdtlseqdt0(all_257_2_174, all_257_1_173)
% 15.19/4.20  									|
% 15.19/4.20  									+-Applying beta-rule and splitting (177), into two cases.
% 15.19/4.20  									|-Branch one:
% 15.19/4.20  									| (145) xr = xn
% 15.19/4.20  									|
% 15.19/4.20  										| Equations (145) can reduce 45 to:
% 15.19/4.20  										| (146) $false
% 15.19/4.20  										|
% 15.19/4.20  										|-The branch is then unsatisfiable
% 15.19/4.20  									|-Branch two:
% 15.19/4.20  									| (45)  ~ (xr = xn)
% 15.19/4.20  									| (228)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = xn) &  ~ (v1 = v0) & sdtpldt0(all_27_0_10, xr) = v0 & sdtpldt0(all_27_0_10, xn) = v1 & sdtpldt0(xr, all_27_0_10) = v2 & sdtlseqdt0(v2, xn) & sdtlseqdt0(v0, v1))
% 15.19/4.20  									|
% 15.19/4.20  										+-Applying beta-rule and splitting (179), into two cases.
% 15.19/4.20  										|-Branch one:
% 15.19/4.20  										| (145) xr = xn
% 15.19/4.20  										|
% 15.19/4.20  											| Equations (145) can reduce 45 to:
% 15.19/4.20  											| (146) $false
% 15.19/4.20  											|
% 15.19/4.20  											|-The branch is then unsatisfiable
% 15.19/4.20  										|-Branch two:
% 15.19/4.20  										| (45)  ~ (xr = xn)
% 15.19/4.20  										| (232)  ? [v0] :  ? [v1] : ( ~ (v1 = all_0_4_4) &  ~ (v0 = all_0_5_5) & sdtpldt0(all_11_0_7, xn) = v0 & sdtpldt0(xr, all_11_0_7) = v1)
% 15.19/4.20  										|
% 15.19/4.20  											| Instantiating (232) with all_274_0_181, all_274_1_182 yields:
% 15.19/4.20  											| (233)  ~ (all_274_0_181 = all_0_4_4) &  ~ (all_274_1_182 = all_0_5_5) & sdtpldt0(all_11_0_7, xn) = all_274_1_182 & sdtpldt0(xr, all_11_0_7) = all_274_0_181
% 15.19/4.20  											|
% 15.19/4.20  											| Applying alpha-rule on (233) yields:
% 15.19/4.20  											| (234)  ~ (all_274_0_181 = all_0_4_4)
% 15.19/4.20  											| (235)  ~ (all_274_1_182 = all_0_5_5)
% 15.19/4.20  											| (236) sdtpldt0(all_11_0_7, xn) = all_274_1_182
% 15.19/4.20  											| (237) sdtpldt0(xr, all_11_0_7) = all_274_0_181
% 15.19/4.20  											|
% 15.19/4.20  											+-Applying beta-rule and splitting (184), into two cases.
% 15.19/4.20  											|-Branch one:
% 15.19/4.20  											| (145) xr = xn
% 15.19/4.20  											|
% 15.19/4.20  												| Equations (145) can reduce 45 to:
% 15.19/4.20  												| (146) $false
% 15.19/4.20  												|
% 15.19/4.20  												|-The branch is then unsatisfiable
% 15.19/4.20  											|-Branch two:
% 15.19/4.20  											| (45)  ~ (xr = xn)
% 15.19/4.20  											| (241)  ? [v0] :  ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_11_0_7, xr) = v1 & sdtpldt0(all_11_0_7, xn) = v0)
% 15.19/4.20  											|
% 15.19/4.20  												| Instantiating (241) with all_316_0_197, all_316_1_198 yields:
% 15.19/4.20  												| (242)  ~ (all_316_0_197 = all_316_1_198) & sdtpldt0(all_11_0_7, xr) = all_316_0_197 & sdtpldt0(all_11_0_7, xn) = all_316_1_198
% 15.19/4.20  												|
% 15.19/4.20  												| Applying alpha-rule on (242) yields:
% 15.19/4.20  												| (243)  ~ (all_316_0_197 = all_316_1_198)
% 15.19/4.20  												| (244) sdtpldt0(all_11_0_7, xr) = all_316_0_197
% 15.19/4.20  												| (245) sdtpldt0(all_11_0_7, xn) = all_316_1_198
% 15.19/4.20  												|
% 15.19/4.20  												| Instantiating formula (92) with all_11_0_7, xr, all_316_0_197, all_0_5_5 and discharging atoms sdtpldt0(all_11_0_7, xr) = all_316_0_197, sdtpldt0(all_11_0_7, xr) = all_0_5_5, yields:
% 15.19/4.20  												| (246) all_316_0_197 = all_0_5_5
% 15.19/4.20  												|
% 15.19/4.20  												| Instantiating formula (92) with all_11_0_7, xr, all_257_2_174, all_316_0_197 and discharging atoms sdtpldt0(all_11_0_7, xr) = all_316_0_197, sdtpldt0(all_11_0_7, xr) = all_257_2_174, yields:
% 15.19/4.20  												| (247) all_316_0_197 = all_257_2_174
% 15.19/4.20  												|
% 15.19/4.20  												| Instantiating formula (92) with all_11_0_7, xr, all_235_2_165, all_257_2_174 and discharging atoms sdtpldt0(all_11_0_7, xr) = all_257_2_174, sdtpldt0(all_11_0_7, xr) = all_235_2_165, yields:
% 15.19/4.20  												| (248) all_257_2_174 = all_235_2_165
% 15.19/4.20  												|
% 15.19/4.20  												| Instantiating formula (92) with all_11_0_7, xn, all_274_1_182, all_316_1_198 and discharging atoms sdtpldt0(all_11_0_7, xn) = all_316_1_198, sdtpldt0(all_11_0_7, xn) = all_274_1_182, yields:
% 15.19/4.20  												| (249) all_316_1_198 = all_274_1_182
% 15.19/4.20  												|
% 15.19/4.20  												| Instantiating formula (92) with all_11_0_7, xn, all_257_1_173, all_316_1_198 and discharging atoms sdtpldt0(all_11_0_7, xn) = all_316_1_198, sdtpldt0(all_11_0_7, xn) = all_257_1_173, yields:
% 15.19/4.20  												| (250) all_316_1_198 = all_257_1_173
% 15.19/4.20  												|
% 15.19/4.20  												| Instantiating formula (92) with all_11_0_7, xn, all_245_2_168, all_316_1_198 and discharging atoms sdtpldt0(all_11_0_7, xn) = all_316_1_198, sdtpldt0(all_11_0_7, xn) = all_245_2_168, yields:
% 15.19/4.21  												| (251) all_316_1_198 = all_245_2_168
% 15.19/4.21  												|
% 15.19/4.21  												| Instantiating formula (92) with all_11_0_7, xn, all_235_1_164, all_316_1_198 and discharging atoms sdtpldt0(all_11_0_7, xn) = all_316_1_198, sdtpldt0(all_11_0_7, xn) = all_235_1_164, yields:
% 15.19/4.21  												| (252) all_316_1_198 = all_235_1_164
% 15.19/4.21  												|
% 15.19/4.21  												| Instantiating formula (92) with all_11_0_7, xn, all_0_4_4, all_274_1_182 and discharging atoms sdtpldt0(all_11_0_7, xn) = all_274_1_182, sdtpldt0(all_11_0_7, xn) = all_0_4_4, yields:
% 15.19/4.21  												| (253) all_274_1_182 = all_0_4_4
% 15.19/4.21  												|
% 15.19/4.21  												| Instantiating formula (92) with xr, all_11_0_7, all_257_0_172, all_274_0_181 and discharging atoms sdtpldt0(xr, all_11_0_7) = all_274_0_181, sdtpldt0(xr, all_11_0_7) = all_257_0_172, yields:
% 15.19/4.21  												| (254) all_274_0_181 = all_257_0_172
% 15.19/4.21  												|
% 15.19/4.21  												| Instantiating formula (92) with xr, all_11_0_7, all_245_1_167, all_0_0_0 and discharging atoms sdtpldt0(xr, all_11_0_7) = all_245_1_167, sdtpldt0(xr, all_11_0_7) = all_0_0_0, yields:
% 15.19/4.21  												| (255) all_245_1_167 = all_0_0_0
% 15.19/4.21  												|
% 15.19/4.21  												| Instantiating formula (92) with xr, all_11_0_7, all_245_1_167, all_257_0_172 and discharging atoms sdtpldt0(xr, all_11_0_7) = all_257_0_172, sdtpldt0(xr, all_11_0_7) = all_245_1_167, yields:
% 15.19/4.21  												| (256) all_257_0_172 = all_245_1_167
% 15.19/4.21  												|
% 15.19/4.21  												| Instantiating formula (92) with xr, all_11_0_7, all_181_0_122, all_245_1_167 and discharging atoms sdtpldt0(xr, all_11_0_7) = all_245_1_167, sdtpldt0(xr, all_11_0_7) = all_181_0_122, yields:
% 15.19/4.21  												| (257) all_245_1_167 = all_181_0_122
% 15.19/4.21  												|
% 15.19/4.21  												| Instantiating formula (92) with xr, all_11_0_7, all_0_5_5, all_274_0_181 and discharging atoms sdtpldt0(xr, all_11_0_7) = all_274_0_181, sdtpldt0(xr, all_11_0_7) = all_0_5_5, yields:
% 15.19/4.21  												| (258) all_274_0_181 = all_0_5_5
% 15.19/4.21  												|
% 15.19/4.21  												| Combining equations (247,246) yields a new equation:
% 15.19/4.21  												| (259) all_257_2_174 = all_0_5_5
% 15.19/4.21  												|
% 15.19/4.21  												| Simplifying 259 yields:
% 15.19/4.21  												| (260) all_257_2_174 = all_0_5_5
% 15.19/4.21  												|
% 15.19/4.21  												| Combining equations (249,250) yields a new equation:
% 15.19/4.21  												| (261) all_274_1_182 = all_257_1_173
% 15.19/4.21  												|
% 15.19/4.21  												| Simplifying 261 yields:
% 15.19/4.21  												| (262) all_274_1_182 = all_257_1_173
% 15.19/4.21  												|
% 15.19/4.21  												| Combining equations (252,250) yields a new equation:
% 15.19/4.21  												| (263) all_257_1_173 = all_235_1_164
% 15.19/4.21  												|
% 15.19/4.21  												| Combining equations (251,250) yields a new equation:
% 15.19/4.21  												| (264) all_257_1_173 = all_245_2_168
% 15.19/4.21  												|
% 15.19/4.21  												| Combining equations (254,258) yields a new equation:
% 15.19/4.21  												| (265) all_257_0_172 = all_0_5_5
% 15.19/4.21  												|
% 15.19/4.21  												| Simplifying 265 yields:
% 15.19/4.21  												| (266) all_257_0_172 = all_0_5_5
% 15.19/4.21  												|
% 15.19/4.21  												| Combining equations (262,253) yields a new equation:
% 15.19/4.21  												| (267) all_257_1_173 = all_0_4_4
% 15.19/4.21  												|
% 15.19/4.21  												| Simplifying 267 yields:
% 15.19/4.21  												| (268) all_257_1_173 = all_0_4_4
% 15.19/4.21  												|
% 15.19/4.21  												| Combining equations (256,266) yields a new equation:
% 15.19/4.21  												| (269) all_245_1_167 = all_0_5_5
% 15.19/4.21  												|
% 15.19/4.21  												| Simplifying 269 yields:
% 15.19/4.21  												| (270) all_245_1_167 = all_0_5_5
% 15.19/4.21  												|
% 15.19/4.21  												| Combining equations (263,264) yields a new equation:
% 15.19/4.21  												| (271) all_245_2_168 = all_235_1_164
% 15.19/4.21  												|
% 15.19/4.21  												| Combining equations (268,264) yields a new equation:
% 15.19/4.21  												| (272) all_245_2_168 = all_0_4_4
% 15.19/4.21  												|
% 15.19/4.21  												| Combining equations (260,248) yields a new equation:
% 15.19/4.21  												| (273) all_235_2_165 = all_0_5_5
% 15.19/4.21  												|
% 15.19/4.21  												| Combining equations (255,257) yields a new equation:
% 15.19/4.21  												| (274) all_181_0_122 = all_0_0_0
% 15.19/4.21  												|
% 15.19/4.21  												| Combining equations (270,257) yields a new equation:
% 15.19/4.21  												| (275) all_181_0_122 = all_0_5_5
% 15.19/4.21  												|
% 15.19/4.21  												| Combining equations (271,272) yields a new equation:
% 15.19/4.21  												| (276) all_235_1_164 = all_0_4_4
% 15.19/4.21  												|
% 15.19/4.21  												| Simplifying 276 yields:
% 15.19/4.21  												| (277) all_235_1_164 = all_0_4_4
% 15.19/4.21  												|
% 15.19/4.21  												| Combining equations (274,275) yields a new equation:
% 15.19/4.21  												| (278) all_0_0_0 = all_0_5_5
% 15.19/4.21  												|
% 15.19/4.21  												| Simplifying 278 yields:
% 15.19/4.21  												| (279) all_0_0_0 = all_0_5_5
% 15.19/4.21  												|
% 15.19/4.21  												| Equations (277,273) can reduce 194 to:
% 15.19/4.21  												| (280)  ~ (all_0_4_4 = all_0_5_5)
% 15.19/4.21  												|
% 15.19/4.21  												| From (272) and (208) follows:
% 15.19/4.21  												| (281) sdtlseqdt0(all_0_5_5, all_0_4_4)
% 15.19/4.21  												|
% 15.19/4.21  												+-Applying beta-rule and splitting (11), into two cases.
% 15.19/4.21  												|-Branch one:
% 15.19/4.21  												| (282)  ~ sdtlseqdt0(all_0_0_0, all_0_4_4)
% 15.19/4.21  												|
% 15.19/4.21  													| From (279) and (282) follows:
% 15.19/4.21  													| (283)  ~ sdtlseqdt0(all_0_5_5, all_0_4_4)
% 15.19/4.21  													|
% 15.19/4.21  													| Using (281) and (283) yields:
% 15.19/4.21  													| (284) $false
% 15.19/4.21  													|
% 15.19/4.21  													|-The branch is then unsatisfiable
% 15.19/4.21  												|-Branch two:
% 15.19/4.21  												| (285) sdtlseqdt0(all_0_0_0, all_0_4_4)
% 15.19/4.21  												| (286) all_0_0_0 = all_0_4_4
% 15.19/4.21  												|
% 15.19/4.21  													| Combining equations (279,286) yields a new equation:
% 15.19/4.21  													| (287) all_0_4_4 = all_0_5_5
% 15.19/4.21  													|
% 15.19/4.21  													| Equations (287) can reduce 280 to:
% 15.19/4.21  													| (146) $false
% 15.19/4.21  													|
% 15.19/4.21  													|-The branch is then unsatisfiable
% 15.19/4.21  % SZS output end Proof for theBenchmark
% 15.19/4.21  
% 15.19/4.21  3614ms
%------------------------------------------------------------------------------