TSTP Solution File: NUM469+2 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : NUM469+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n013.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 08:44:49 EDT 2022

% Result   : Theorem 8.99s 2.77s
% Output   : Proof 15.63s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM469+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n013.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Tue Jul  5 04:17:14 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.58          ____       _                          
% 0.19/0.58    ___  / __ \_____(_)___  ________  __________
% 0.19/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.58  
% 0.19/0.58  A Theorem Prover for First-Order Logic
% 0.19/0.59  (ePrincess v.1.0)
% 0.19/0.59  
% 0.19/0.59  (c) Philipp Rümmer, 2009-2015
% 0.19/0.59  (c) Peter Backeman, 2014-2015
% 0.19/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.59  Bug reports to peter@backeman.se
% 0.19/0.59  
% 0.19/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.59  
% 0.19/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.67  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.83/1.02  Prover 0: Preprocessing ...
% 3.62/1.51  Prover 0: Constructing countermodel ...
% 8.99/2.76  Prover 0: proved (2095ms)
% 8.99/2.77  
% 8.99/2.77  No countermodel exists, formula is valid
% 8.99/2.77  % SZS status Theorem for theBenchmark
% 8.99/2.77  
% 8.99/2.77  Generating proof ... found it (size 138)
% 14.94/4.18  
% 14.94/4.18  % SZS output start Proof for theBenchmark
% 14.94/4.18  Assumed formulas after preprocessing and simplification: 
% 14.94/4.18  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : ( ~ (sz10 = sz00) & sdtsldt0(xn, xl) = v2 & sdtsldt0(xm, xl) = v0 & sdtasdt0(xl, v8) = xm & sdtasdt0(xl, v7) = xn & sdtasdt0(xl, v5) = v6 & sdtasdt0(xl, v2) = v3 & sdtasdt0(xl, v0) = v1 & sdtpldt0(v0, v2) = v5 & sdtpldt0(xm, xn) = v4 & doDivides0(xl, xn) & doDivides0(xl, xm) & aNaturalNumber0(v8) & aNaturalNumber0(v7) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & aNaturalNumber0(xl) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) &  ~ doDivides0(xl, v4) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (sdtasdt0(v11, v9) = v13) |  ~ (sdtasdt0(v10, v9) = v12) |  ~ (sdtpldt0(v12, v13) = v14) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] : (sdtasdt0(v15, v9) = v14 & sdtasdt0(v9, v15) = v16 & sdtasdt0(v9, v11) = v18 & sdtasdt0(v9, v10) = v17 & sdtpldt0(v17, v18) = v16 & sdtpldt0(v10, v11) = v15)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (sdtasdt0(v9, v11) = v13) |  ~ (sdtasdt0(v9, v10) = v12) |  ~ (sdtpldt0(v12, v13) = v14) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] : (sdtasdt0(v15, v9) = v16 & sdtasdt0(v11, v9) = v18 & sdtasdt0(v10, v9) = v17 & sdtasdt0(v9, v15) = v14 & sdtpldt0(v17, v18) = v16 & sdtpldt0(v10, v11) = v15)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 | v9 = sz00 |  ~ (sdtasdt0(v11, v9) = v13) |  ~ (sdtasdt0(v10, v9) = v12) |  ~ sdtlseqdt0(v10, v11) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) | sdtlseqdt0(v12, v13)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 | v9 = sz00 |  ~ (sdtasdt0(v11, v9) = v13) |  ~ (sdtasdt0(v10, v9) = v12) |  ~ sdtlseqdt0(v10, v11) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v14] :  ? [v15] : ( ~ (v15 = v14) & sdtasdt0(v9, v11) = v15 & sdtasdt0(v9, v10) = v14 & sdtlseqdt0(v14, v15))) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 | v9 = sz00 |  ~ (sdtasdt0(v11, v9) = v13) |  ~ (sdtasdt0(v10, v9) = v12) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v14] :  ? [v15] : ( ~ (v15 = v14) & sdtasdt0(v9, v11) = v15 & sdtasdt0(v9, v10) = v14)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 | v9 = sz00 |  ~ (sdtasdt0(v11, v9) = v13) |  ~ (sdtasdt0(v9, v10) = v12) |  ~ sdtlseqdt0(v10, v11) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v14] :  ? [v15] : ( ~ (v15 = v13) &  ~ (v14 = v12) & sdtasdt0(v10, v9) = v15 & sdtasdt0(v9, v11) = v14 & sdtlseqdt0(v15, v13) & sdtlseqdt0(v12, v14))) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 | v9 = sz00 |  ~ (sdtasdt0(v11, v9) = v13) |  ~ (sdtasdt0(v9, v10) = v12) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v14] :  ? [v15] : ( ~ (v15 = v13) &  ~ (v14 = v12) & sdtasdt0(v10, v9) = v15 & sdtasdt0(v9, v11) = v14)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 | v9 = sz00 |  ~ (sdtasdt0(v10, v9) = v13) |  ~ (sdtasdt0(v9, v11) = v12) |  ~ sdtlseqdt0(v10, v11) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v14] :  ? [v15] : ( ~ (v15 = v13) &  ~ (v14 = v12) & sdtasdt0(v11, v9) = v15 & sdtasdt0(v9, v10) = v14 & sdtlseqdt0(v14, v12) & sdtlseqdt0(v13, v15))) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 | v9 = sz00 |  ~ (sdtasdt0(v10, v9) = v13) |  ~ (sdtasdt0(v9, v11) = v12) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v14] :  ? [v15] : ( ~ (v15 = v13) &  ~ (v14 = v12) & sdtasdt0(v11, v9) = v15 & sdtasdt0(v9, v10) = v14)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 | v9 = sz00 |  ~ (sdtasdt0(v9, v11) = v13) |  ~ (sdtasdt0(v9, v10) = v12) |  ~ sdtlseqdt0(v10, v11) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) | sdtlseqdt0(v12, v13)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 | v9 = sz00 |  ~ (sdtasdt0(v9, v11) = v13) |  ~ (sdtasdt0(v9, v10) = v12) |  ~ sdtlseqdt0(v10, v11) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v14] :  ? [v15] : ( ~ (v15 = v14) & sdtasdt0(v11, v9) = v15 & sdtasdt0(v10, v9) = v14 & sdtlseqdt0(v14, v15))) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 | v9 = sz00 |  ~ (sdtasdt0(v9, v11) = v13) |  ~ (sdtasdt0(v9, v10) = v12) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v14] :  ? [v15] : ( ~ (v15 = v14) & sdtasdt0(v11, v9) = v15 & sdtasdt0(v10, v9) = v14)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 |  ~ (sdtpldt0(v11, v9) = v13) |  ~ (sdtpldt0(v10, v9) = v12) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v14] :  ? [v15] : ( ~ (v15 = v14) & sdtpldt0(v9, v11) = v15 & sdtpldt0(v9, v10) = v14)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 |  ~ (sdtpldt0(v11, v9) = v13) |  ~ (sdtpldt0(v9, v10) = v12) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v14] :  ? [v15] : ( ~ (v15 = v13) &  ~ (v14 = v12) & sdtpldt0(v10, v9) = v15 & sdtpldt0(v9, v11) = v14)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 |  ~ (sdtpldt0(v10, v9) = v13) |  ~ (sdtpldt0(v9, v11) = v12) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v14] :  ? [v15] : ( ~ (v15 = v13) &  ~ (v14 = v12) & sdtpldt0(v11, v9) = v15 & sdtpldt0(v9, v10) = v14)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 |  ~ (sdtpldt0(v9, v11) = v13) |  ~ (sdtpldt0(v9, v10) = v12) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v14] :  ? [v15] : ( ~ (v15 = v14) & sdtpldt0(v11, v9) = v15 & sdtpldt0(v10, v9) = v14)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (sdtasdt0(v12, v11) = v13) |  ~ (sdtasdt0(v9, v10) = v12) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v14] : (sdtasdt0(v10, v11) = v14 & sdtasdt0(v9, v14) = v13)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (sdtasdt0(v12, v9) = v13) |  ~ (sdtpldt0(v10, v11) = v12) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] : (sdtasdt0(v11, v9) = v18 & sdtasdt0(v10, v9) = v17 & sdtasdt0(v9, v12) = v14 & sdtasdt0(v9, v11) = v16 & sdtasdt0(v9, v10) = v15 & sdtpldt0(v17, v18) = v13 & sdtpldt0(v15, v16) = v14)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (sdtasdt0(v10, v11) = v12) |  ~ (sdtasdt0(v9, v12) = v13) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v14] : (sdtasdt0(v14, v11) = v13 & sdtasdt0(v9, v10) = v14)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (sdtasdt0(v9, v12) = v13) |  ~ (sdtpldt0(v10, v11) = v12) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] : (sdtasdt0(v12, v9) = v16 & sdtasdt0(v11, v9) = v18 & sdtasdt0(v10, v9) = v17 & sdtasdt0(v9, v11) = v15 & sdtasdt0(v9, v10) = v14 & sdtpldt0(v17, v18) = v16 & sdtpldt0(v14, v15) = v13)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (sdtpldt0(v12, v11) = v13) |  ~ (sdtpldt0(v9, v10) = v12) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v14] : (sdtpldt0(v10, v11) = v14 & sdtpldt0(v9, v14) = v13)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (sdtpldt0(v10, v11) = v12) |  ~ (sdtpldt0(v9, v12) = v13) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v14] : (sdtpldt0(v14, v11) = v13 & sdtpldt0(v9, v10) = v14)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = v11 | v9 = sz00 |  ~ (sdtsldt0(v10, v9) = v11) |  ~ (sdtasdt0(v9, v12) = v10) |  ~ doDivides0(v9, v10) |  ~ aNaturalNumber0(v12) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = v11 |  ~ (sdtmndt0(v10, v9) = v11) |  ~ (sdtpldt0(v9, v12) = v10) |  ~ sdtlseqdt0(v9, v10) |  ~ aNaturalNumber0(v12) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = v10 | v9 = sz00 |  ~ (sdtsldt0(v10, v9) = v11) |  ~ (sdtasdt0(v9, v11) = v12) |  ~ doDivides0(v9, v10) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = v10 |  ~ (sdtmndt0(v10, v9) = v11) |  ~ (sdtpldt0(v9, v11) = v12) |  ~ sdtlseqdt0(v9, v10) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v11 = v10 | v9 = sz00 |  ~ (sdtasdt0(v11, v9) = v12) |  ~ (sdtasdt0(v10, v9) = v12) |  ~ sdtlseqdt0(v10, v11) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v11 = v10 | v9 = sz00 |  ~ (sdtasdt0(v11, v9) = v12) |  ~ (sdtasdt0(v10, v9) = v12) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v11 = v10 | v9 = sz00 |  ~ (sdtasdt0(v9, v11) = v12) |  ~ (sdtasdt0(v9, v10) = v12) |  ~ sdtlseqdt0(v10, v11) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v11 = v10 | v9 = sz00 |  ~ (sdtasdt0(v9, v11) = v12) |  ~ (sdtasdt0(v9, v10) = v12) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v11 = v10 |  ~ (sdtpldt0(v11, v9) = v12) |  ~ (sdtpldt0(v10, v9) = v12) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v11 = v10 |  ~ (sdtpldt0(v9, v11) = v12) |  ~ (sdtpldt0(v9, v10) = v12) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v10 = v9 |  ~ (sdtsldt0(v12, v11) = v10) |  ~ (sdtsldt0(v12, v11) = v9)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v10 = v9 |  ~ (sdtmndt0(v12, v11) = v10) |  ~ (sdtmndt0(v12, v11) = v9)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v10 = v9 |  ~ (sdtasdt0(v12, v11) = v10) |  ~ (sdtasdt0(v12, v11) = v9)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v10 = v9 |  ~ (sdtpldt0(v12, v11) = v10) |  ~ (sdtpldt0(v12, v11) = v9)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v10 = v9 |  ~ (sdtpldt0(v11, v10) = v12) |  ~ sdtlseqdt0(v9, v10) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v13] :  ? [v14] :  ? [v15] : ( ~ (v15 = v14) &  ~ (v13 = v12) & sdtpldt0(v11, v9) = v13 & sdtpldt0(v10, v11) = v15 & sdtpldt0(v9, v11) = v14 & sdtlseqdt0(v14, v15) & sdtlseqdt0(v13, v12))) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v10 = v9 |  ~ (sdtpldt0(v11, v9) = v12) |  ~ sdtlseqdt0(v9, v10) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v13] :  ? [v14] :  ? [v15] : ( ~ (v15 = v14) &  ~ (v13 = v12) & sdtpldt0(v11, v10) = v13 & sdtpldt0(v10, v11) = v15 & sdtpldt0(v9, v11) = v14 & sdtlseqdt0(v14, v15) & sdtlseqdt0(v12, v13))) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v10 = v9 |  ~ (sdtpldt0(v10, v11) = v12) |  ~ sdtlseqdt0(v9, v10) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v13] :  ? [v14] :  ? [v15] : ( ~ (v15 = v12) &  ~ (v14 = v13) & sdtpldt0(v11, v10) = v14 & sdtpldt0(v11, v9) = v13 & sdtpldt0(v9, v11) = v15 & sdtlseqdt0(v15, v12) & sdtlseqdt0(v13, v14))) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v10 = v9 |  ~ (sdtpldt0(v9, v11) = v12) |  ~ sdtlseqdt0(v9, v10) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v13] :  ? [v14] :  ? [v15] : ( ~ (v15 = v12) &  ~ (v14 = v13) & sdtpldt0(v11, v10) = v14 & sdtpldt0(v11, v9) = v13 & sdtpldt0(v10, v11) = v15 & sdtlseqdt0(v13, v14) & sdtlseqdt0(v12, v15))) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v9 = sz00 |  ~ (sdtsldt0(v10, v9) = v11) |  ~ (sdtasdt0(v9, v11) = v12) |  ~ doDivides0(v9, v10) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) | aNaturalNumber0(v11)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (sdtmndt0(v10, v9) = v11) |  ~ (sdtpldt0(v9, v11) = v12) |  ~ sdtlseqdt0(v9, v10) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) | aNaturalNumber0(v11)) &  ! [v9] :  ! [v10] :  ! [v11] : (v9 = sz00 |  ~ (sdtasdt0(v10, v9) = v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) | sdtlseqdt0(v10, v11)) &  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (sdtasdt0(v10, v9) = v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) | sdtasdt0(v9, v10) = v11) &  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (sdtasdt0(v9, v11) = v10) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) | doDivides0(v9, v10)) &  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (sdtasdt0(v9, v10) = v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) | sdtasdt0(v10, v9) = v11) &  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (sdtasdt0(v9, v10) = v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) | aNaturalNumber0(v11)) &  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (sdtpldt0(v10, v9) = v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) | sdtpldt0(v9, v10) = v11) &  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (sdtpldt0(v9, v11) = v10) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) | sdtlseqdt0(v9, v10)) &  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (sdtpldt0(v9, v10) = v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) | sdtpldt0(v10, v9) = v11) &  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (sdtpldt0(v9, v10) = v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) | aNaturalNumber0(v11)) &  ! [v9] :  ! [v10] :  ! [v11] : ( ~ doDivides0(v10, v11) |  ~ doDivides0(v9, v10) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) | doDivides0(v9, v11)) &  ! [v9] :  ! [v10] :  ! [v11] : ( ~ sdtlseqdt0(v10, v11) |  ~ sdtlseqdt0(v9, v10) |  ~ aNaturalNumber0(v11) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) | sdtlseqdt0(v9, v11)) &  ! [v9] :  ! [v10] : (v10 = v9 |  ~ (sdtasdt0(v9, sz10) = v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] : (v10 = v9 |  ~ (sdtasdt0(sz10, v9) = v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] : (v10 = v9 |  ~ (sdtpldt0(v9, sz00) = v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] : (v10 = v9 |  ~ (sdtpldt0(sz00, v9) = v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] : (v10 = v9 |  ~ sdtlseqdt0(v10, v9) |  ~ sdtlseqdt0(v9, v10) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] : (v10 = v9 |  ~ sdtlseqdt0(v9, v10) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) | iLess0(v9, v10)) &  ! [v9] :  ! [v10] : (v10 = sz00 | v9 = sz00 |  ~ (sdtasdt0(v9, v10) = sz00) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] : (v10 = sz00 |  ~ (sdtasdt0(v9, sz00) = v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] : (v10 = sz00 |  ~ (sdtasdt0(sz00, v9) = v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] : (v10 = sz00 |  ~ (sdtpldt0(v9, v10) = sz00) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] : (v9 = sz00 |  ~ (sdtpldt0(v9, v10) = sz00) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9)) &  ! [v9] :  ! [v10] : ( ~ (sdtasdt0(v9, sz10) = v10) |  ~ aNaturalNumber0(v9) | sdtasdt0(sz10, v9) = v9) &  ! [v9] :  ! [v10] : ( ~ (sdtasdt0(v9, sz00) = v10) |  ~ aNaturalNumber0(v9) | sdtasdt0(sz00, v9) = sz00) &  ! [v9] :  ! [v10] : ( ~ (sdtasdt0(sz10, v9) = v10) |  ~ aNaturalNumber0(v9) | sdtasdt0(v9, sz10) = v9) &  ! [v9] :  ! [v10] : ( ~ (sdtasdt0(sz00, v9) = v10) |  ~ aNaturalNumber0(v9) | sdtasdt0(v9, sz00) = sz00) &  ! [v9] :  ! [v10] : ( ~ (sdtpldt0(v9, sz00) = v10) |  ~ aNaturalNumber0(v9) | sdtpldt0(sz00, v9) = v9) &  ! [v9] :  ! [v10] : ( ~ (sdtpldt0(sz00, v9) = v10) |  ~ aNaturalNumber0(v9) | sdtpldt0(v9, sz00) = v9) &  ! [v9] :  ! [v10] : ( ~ doDivides0(v9, v10) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v11] : (sdtasdt0(v9, v11) = v10 & aNaturalNumber0(v11))) &  ! [v9] :  ! [v10] : ( ~ sdtlseqdt0(v9, v10) |  ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) |  ? [v11] : (sdtpldt0(v9, v11) = v10 & aNaturalNumber0(v11))) &  ! [v9] :  ! [v10] : ( ~ aNaturalNumber0(v10) |  ~ aNaturalNumber0(v9) | sdtlseqdt0(v10, v9) | sdtlseqdt0(v9, v10)) &  ! [v9] : (v9 = sz10 | v9 = sz00 |  ~ aNaturalNumber0(v9) | sdtlseqdt0(sz10, v9)) &  ! [v9] : ( ~ aNaturalNumber0(v9) | sdtlseqdt0(v9, v9)) &  ! [v9] : ( ~ aNaturalNumber0(v9) |  ? [v10] : ( ~ (v10 = v4) & sdtasdt0(xl, v9) = v10)) & (xl = sz00 | (v6 = v4 & v3 = xn & v1 = xm & aNaturalNumber0(v2) & aNaturalNumber0(v0))))
% 15.28/4.26  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 yields:
% 15.28/4.26  | (1)  ~ (sz10 = sz00) & sdtsldt0(xn, xl) = all_0_6_6 & sdtsldt0(xm, xl) = all_0_8_8 & sdtasdt0(xl, all_0_0_0) = xm & sdtasdt0(xl, all_0_1_1) = xn & sdtasdt0(xl, all_0_3_3) = all_0_2_2 & sdtasdt0(xl, all_0_6_6) = all_0_5_5 & sdtasdt0(xl, all_0_8_8) = all_0_7_7 & sdtpldt0(all_0_8_8, all_0_6_6) = all_0_3_3 & sdtpldt0(xm, xn) = all_0_4_4 & doDivides0(xl, xn) & doDivides0(xl, xm) & aNaturalNumber0(all_0_0_0) & aNaturalNumber0(all_0_1_1) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & aNaturalNumber0(xl) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) &  ~ doDivides0(xl, all_0_4_4) &  ! [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] : ( ~ (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) |  ~ 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] : (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 |  ~ (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] : (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) | sdtlseqdt0(sz10, v0)) &  ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) &  ! [v0] : ( ~ aNaturalNumber0(v0) |  ? [v1] : ( ~ (v1 = all_0_4_4) & sdtasdt0(xl, v0) = v1)) & (xl = sz00 | (all_0_2_2 = all_0_4_4 & all_0_5_5 = xn & all_0_7_7 = xm & aNaturalNumber0(all_0_6_6) & aNaturalNumber0(all_0_8_8)))
% 15.63/4.28  |
% 15.63/4.28  | Applying alpha-rule on (1) yields:
% 15.63/4.28  | (2)  ! [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))
% 15.63/4.28  | (3)  ! [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))
% 15.63/4.28  | (4)  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ (sdtasdt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0))
% 15.63/4.29  | (5)  ! [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))
% 15.63/4.29  | (6)  ! [v0] :  ! [v1] : (v1 = sz00 | v0 = sz00 |  ~ (sdtasdt0(v0, v1) = sz00) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.63/4.29  | (7)  ! [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))
% 15.63/4.29  | (8) sdtsldt0(xm, xl) = all_0_8_8
% 15.63/4.29  | (9)  ! [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)))
% 15.63/4.29  | (10)  ! [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)))
% 15.63/4.29  | (11)  ! [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))
% 15.63/4.29  | (12)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 15.63/4.29  | (13)  ! [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))
% 15.63/4.29  | (14) xl = sz00 | (all_0_2_2 = all_0_4_4 & all_0_5_5 = xn & all_0_7_7 = xm & aNaturalNumber0(all_0_6_6) & aNaturalNumber0(all_0_8_8))
% 15.63/4.29  | (15)  ! [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))
% 15.63/4.29  | (16)  ! [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))
% 15.63/4.29  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v3) = v1) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v3) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.63/4.29  | (18)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2)
% 15.63/4.29  | (19)  ! [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))
% 15.63/4.29  | (20) sdtasdt0(xl, all_0_0_0) = xm
% 15.63/4.29  | (21)  ! [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))
% 15.63/4.29  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtsldt0(v3, v2) = v1) |  ~ (sdtsldt0(v3, v2) = v0))
% 15.63/4.29  | (23)  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ (sdtpldt0(v0, v1) = sz00) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.63/4.29  | (24) aNaturalNumber0(xn)
% 15.63/4.29  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v2) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.63/4.29  | (26)  ~ (sz10 = sz00)
% 15.63/4.29  | (27)  ! [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))
% 15.63/4.30  | (28) doDivides0(xl, xm)
% 15.63/4.30  | (29) aNaturalNumber0(all_0_1_1)
% 15.63/4.30  | (30)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtasdt0(sz10, v0) = v1) |  ~ aNaturalNumber0(v0))
% 15.63/4.30  | (31)  ! [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))
% 15.63/4.30  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v2, v0) = v3) |  ~ (sdtasdt0(v1, v0) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.63/4.30  | (33)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 15.63/4.30  | (34) sdtasdt0(xl, all_0_8_8) = all_0_7_7
% 15.63/4.30  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v0, v2) = v3) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.63/4.30  | (36)  ! [v0] :  ! [v1] : (v0 = sz00 |  ~ (sdtpldt0(v0, v1) = sz00) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.63/4.30  | (37) aNaturalNumber0(sz10)
% 15.63/4.30  | (38) doDivides0(xl, xn)
% 15.63/4.30  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v0, v2) = v3) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 15.63/4.30  | (40)  ! [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)))
% 15.63/4.30  | (41)  ! [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)))
% 15.63/4.30  | (42)  ! [v0] : ( ~ aNaturalNumber0(v0) |  ? [v1] : ( ~ (v1 = all_0_4_4) & sdtasdt0(xl, v0) = v1))
% 15.63/4.30  | (43)  ! [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)))
% 15.63/4.30  | (44)  ! [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))
% 15.63/4.30  | (45)  ! [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))
% 15.63/4.30  | (46) aNaturalNumber0(sz00)
% 15.63/4.30  | (47)  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ (sdtasdt0(v0, sz00) = v1) |  ~ aNaturalNumber0(v0))
% 15.63/4.30  | (48) aNaturalNumber0(all_0_0_0)
% 15.63/4.30  | (49)  ! [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))
% 15.63/4.30  | (50)  ! [v0] :  ! [v1] : ( ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 15.63/4.30  | (51)  ! [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)))
% 15.63/4.30  | (52)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 |  ~ (sdtpldt0(v2, v0) = v3) |  ~ (sdtpldt0(v1, v0) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.63/4.30  | (53)  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 15.63/4.30  | (54)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtasdt0(v3, v2) = v1) |  ~ (sdtasdt0(v3, v2) = v0))
% 15.63/4.30  | (55) sdtsldt0(xn, xl) = all_0_6_6
% 15.63/4.30  | (56)  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00)
% 15.63/4.31  | (57)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ sdtlseqdt0(v1, v2) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 15.63/4.31  | (58) aNaturalNumber0(xm)
% 15.63/4.31  | (59)  ! [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)))
% 15.63/4.31  | (60)  ! [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))
% 15.63/4.31  | (61)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 15.63/4.31  | (62)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtpldt0(v0, sz00) = v1) |  ~ aNaturalNumber0(v0))
% 15.63/4.31  | (63)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 | v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v0, v2) = v3) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.63/4.31  | (64)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ sdtlseqdt0(v1, v0) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.63/4.31  | (65)  ! [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)))
% 15.63/4.31  | (66) sdtpldt0(xm, xn) = all_0_4_4
% 15.63/4.31  | (67)  ! [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))
% 15.63/4.31  | (68)  ! [v0] : (v0 = sz10 | v0 = sz00 |  ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 15.63/4.31  | (69)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtasdt0(v0, sz10) = v1) |  ~ aNaturalNumber0(v0))
% 15.63/4.31  | (70)  ! [v0] :  ! [v1] : ( ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 15.63/4.31  | (71) aNaturalNumber0(xl)
% 15.63/4.31  | (72)  ! [v0] :  ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 15.63/4.31  | (73)  ! [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))
% 15.63/4.31  | (74)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtpldt0(v3, v2) = v1) |  ~ (sdtpldt0(v3, v2) = v0))
% 15.63/4.31  | (75) sdtasdt0(xl, all_0_6_6) = all_0_5_5
% 15.63/4.31  | (76)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ doDivides0(v1, v2) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 15.63/4.31  | (77)  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 15.63/4.31  | (78)  ! [v0] :  ! [v1] : ( ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 15.63/4.31  | (79)  ! [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))
% 15.63/4.31  | (80)  ! [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))
% 15.63/4.31  | (81)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 |  ~ (sdtpldt0(v0, v2) = v3) |  ~ (sdtpldt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 15.63/4.31  | (82)  ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 15.63/4.31  | (83)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 15.63/4.31  | (84)  ~ doDivides0(xl, all_0_4_4)
% 15.63/4.31  | (85)  ! [v0] :  ! [v1] :  ! [v2] : (v0 = sz00 |  ~ (sdtasdt0(v1, v0) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 15.63/4.32  | (86)  ! [v0] :  ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0)
% 15.63/4.32  | (87) sdtasdt0(xl, all_0_3_3) = all_0_2_2
% 15.63/4.32  | (88)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 15.63/4.32  | (89)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2)
% 15.63/4.32  | (90)  ! [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))
% 15.63/4.32  | (91) sdtasdt0(xl, all_0_1_1) = xn
% 15.63/4.32  | (92)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtmndt0(v3, v2) = v1) |  ~ (sdtmndt0(v3, v2) = v0))
% 15.63/4.32  | (93)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtpldt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0))
% 15.63/4.32  | (94)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 15.63/4.32  | (95)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v2) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 15.63/4.32  | (96)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 15.63/4.32  | (97) sdtpldt0(all_0_8_8, all_0_6_6) = all_0_3_3
% 15.63/4.32  | (98)  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0)
% 15.63/4.32  |
% 15.63/4.32  | Instantiating formula (42) with all_0_0_0 and discharging atoms aNaturalNumber0(all_0_0_0), yields:
% 15.63/4.32  | (99)  ? [v0] : ( ~ (v0 = all_0_4_4) & sdtasdt0(xl, all_0_0_0) = v0)
% 15.63/4.32  |
% 15.63/4.32  | Instantiating formula (42) with all_0_1_1 and discharging atoms aNaturalNumber0(all_0_1_1), yields:
% 15.63/4.32  | (100)  ? [v0] : ( ~ (v0 = all_0_4_4) & sdtasdt0(xl, all_0_1_1) = v0)
% 15.63/4.32  |
% 15.63/4.32  | Instantiating formula (42) with xn and discharging atoms aNaturalNumber0(xn), yields:
% 15.63/4.32  | (101)  ? [v0] : ( ~ (v0 = all_0_4_4) & sdtasdt0(xl, xn) = v0)
% 15.63/4.32  |
% 15.63/4.32  | Instantiating formula (18) with all_0_4_4, xm, xn and discharging atoms sdtpldt0(xm, xn) = all_0_4_4, aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 15.63/4.32  | (102) sdtpldt0(xn, xm) = all_0_4_4
% 15.63/4.32  |
% 15.63/4.32  | Instantiating formula (61) with all_0_4_4, xn, xm and discharging atoms sdtpldt0(xm, xn) = all_0_4_4, aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 15.63/4.32  | (103) aNaturalNumber0(all_0_4_4)
% 15.63/4.32  |
% 15.63/4.32  | Instantiating formula (89) with xm, xl, all_0_0_0 and discharging atoms sdtasdt0(xl, all_0_0_0) = xm, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), yields:
% 15.63/4.32  | (104) sdtasdt0(all_0_0_0, xl) = xm
% 15.63/4.32  |
% 15.63/4.32  | Instantiating formula (3) with all_0_4_4, xn, xm, all_0_1_1, all_0_0_0, xl and discharging atoms sdtasdt0(xl, all_0_0_0) = xm, sdtasdt0(xl, all_0_1_1) = xn, sdtpldt0(xm, xn) = all_0_4_4, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 15.63/4.32  | (105)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_0_0_0, xl) = v2 & sdtasdt0(all_0_1_1, xl) = v3 & sdtasdt0(xl, v0) = all_0_4_4 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_0_0_0, all_0_1_1) = v0)
% 15.63/4.32  |
% 15.63/4.32  | Instantiating formula (89) with xn, xl, all_0_1_1 and discharging atoms sdtasdt0(xl, all_0_1_1) = xn, aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 15.63/4.32  | (106) sdtasdt0(all_0_1_1, xl) = xn
% 15.63/4.32  |
% 15.63/4.33  | Instantiating formula (70) with xn, xl and discharging atoms doDivides0(xl, xn), aNaturalNumber0(xn), aNaturalNumber0(xl), yields:
% 15.63/4.33  | (107)  ? [v0] : (sdtasdt0(xl, v0) = xn & aNaturalNumber0(v0))
% 15.63/4.33  |
% 15.63/4.33  | Instantiating formula (70) with xm, xl and discharging atoms doDivides0(xl, xm), aNaturalNumber0(xm), aNaturalNumber0(xl), yields:
% 15.63/4.33  | (108)  ? [v0] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0))
% 15.63/4.33  |
% 15.63/4.33  | Instantiating formula (42) with sz10 and discharging atoms aNaturalNumber0(sz10), yields:
% 15.63/4.33  | (109)  ? [v0] : ( ~ (v0 = all_0_4_4) & sdtasdt0(xl, sz10) = v0)
% 15.63/4.33  |
% 15.63/4.33  | Instantiating (108) with all_9_0_9 yields:
% 15.63/4.33  | (110) sdtasdt0(xl, all_9_0_9) = xm & aNaturalNumber0(all_9_0_9)
% 15.63/4.33  |
% 15.63/4.33  | Applying alpha-rule on (110) yields:
% 15.63/4.33  | (111) sdtasdt0(xl, all_9_0_9) = xm
% 15.63/4.33  | (112) aNaturalNumber0(all_9_0_9)
% 15.63/4.33  |
% 15.63/4.33  | Instantiating (99) with all_13_0_11 yields:
% 15.63/4.33  | (113)  ~ (all_13_0_11 = all_0_4_4) & sdtasdt0(xl, all_0_0_0) = all_13_0_11
% 15.63/4.33  |
% 15.63/4.33  | Applying alpha-rule on (113) yields:
% 15.63/4.33  | (114)  ~ (all_13_0_11 = all_0_4_4)
% 15.63/4.33  | (115) sdtasdt0(xl, all_0_0_0) = all_13_0_11
% 15.63/4.33  |
% 15.63/4.33  | Instantiating (100) with all_15_0_12 yields:
% 15.63/4.33  | (116)  ~ (all_15_0_12 = all_0_4_4) & sdtasdt0(xl, all_0_1_1) = all_15_0_12
% 15.63/4.33  |
% 15.63/4.33  | Applying alpha-rule on (116) yields:
% 15.63/4.33  | (117)  ~ (all_15_0_12 = all_0_4_4)
% 15.63/4.33  | (118) sdtasdt0(xl, all_0_1_1) = all_15_0_12
% 15.63/4.33  |
% 15.63/4.33  | Instantiating (109) with all_17_0_13 yields:
% 15.63/4.33  | (119)  ~ (all_17_0_13 = all_0_4_4) & sdtasdt0(xl, sz10) = all_17_0_13
% 15.63/4.33  |
% 15.63/4.33  | Applying alpha-rule on (119) yields:
% 15.63/4.33  | (120)  ~ (all_17_0_13 = all_0_4_4)
% 15.63/4.33  | (121) sdtasdt0(xl, sz10) = all_17_0_13
% 15.63/4.33  |
% 15.63/4.33  | Instantiating (101) with all_19_0_14 yields:
% 15.63/4.33  | (122)  ~ (all_19_0_14 = all_0_4_4) & sdtasdt0(xl, xn) = all_19_0_14
% 15.63/4.33  |
% 15.63/4.33  | Applying alpha-rule on (122) yields:
% 15.63/4.33  | (123)  ~ (all_19_0_14 = all_0_4_4)
% 15.63/4.33  | (124) sdtasdt0(xl, xn) = all_19_0_14
% 15.63/4.33  |
% 15.63/4.33  | Instantiating (107) with all_21_0_15 yields:
% 15.63/4.33  | (125) sdtasdt0(xl, all_21_0_15) = xn & aNaturalNumber0(all_21_0_15)
% 15.63/4.33  |
% 15.63/4.33  | Applying alpha-rule on (125) yields:
% 15.63/4.33  | (126) sdtasdt0(xl, all_21_0_15) = xn
% 15.63/4.33  | (127) aNaturalNumber0(all_21_0_15)
% 15.63/4.33  |
% 15.63/4.33  | Instantiating (105) with all_27_0_18, all_27_1_19, all_27_2_20, all_27_3_21 yields:
% 15.63/4.33  | (128) sdtasdt0(all_27_3_21, xl) = all_27_2_20 & sdtasdt0(all_0_0_0, xl) = all_27_1_19 & sdtasdt0(all_0_1_1, xl) = all_27_0_18 & sdtasdt0(xl, all_27_3_21) = all_0_4_4 & sdtpldt0(all_27_1_19, all_27_0_18) = all_27_2_20 & sdtpldt0(all_0_0_0, all_0_1_1) = all_27_3_21
% 15.63/4.33  |
% 15.63/4.33  | Applying alpha-rule on (128) yields:
% 15.63/4.33  | (129) sdtasdt0(all_0_0_0, xl) = all_27_1_19
% 15.63/4.33  | (130) sdtpldt0(all_0_0_0, all_0_1_1) = all_27_3_21
% 15.63/4.33  | (131) sdtasdt0(all_0_1_1, xl) = all_27_0_18
% 15.63/4.33  | (132) sdtpldt0(all_27_1_19, all_27_0_18) = all_27_2_20
% 15.63/4.33  | (133) sdtasdt0(all_27_3_21, xl) = all_27_2_20
% 15.63/4.33  | (134) sdtasdt0(xl, all_27_3_21) = all_0_4_4
% 15.63/4.33  |
% 15.63/4.33  | Instantiating formula (54) with all_0_0_0, xl, xm, all_27_1_19 and discharging atoms sdtasdt0(all_0_0_0, xl) = all_27_1_19, sdtasdt0(all_0_0_0, xl) = xm, yields:
% 15.63/4.33  | (135) all_27_1_19 = xm
% 15.63/4.33  |
% 15.63/4.33  | Instantiating formula (54) with all_0_1_1, xl, xn, all_27_0_18 and discharging atoms sdtasdt0(all_0_1_1, xl) = all_27_0_18, sdtasdt0(all_0_1_1, xl) = xn, yields:
% 15.63/4.33  | (136) all_27_0_18 = xn
% 15.63/4.33  |
% 15.63/4.33  | Instantiating formula (54) with xl, all_0_0_0, all_13_0_11, xm and discharging atoms sdtasdt0(xl, all_0_0_0) = all_13_0_11, sdtasdt0(xl, all_0_0_0) = xm, yields:
% 15.63/4.33  | (137) all_13_0_11 = xm
% 15.63/4.33  |
% 15.63/4.33  | Instantiating formula (54) with xl, all_0_1_1, all_15_0_12, xn and discharging atoms sdtasdt0(xl, all_0_1_1) = all_15_0_12, sdtasdt0(xl, all_0_1_1) = xn, yields:
% 15.63/4.33  | (138) all_15_0_12 = xn
% 15.63/4.33  |
% 15.63/4.33  | Instantiating formula (69) with all_17_0_13, xl and discharging atoms sdtasdt0(xl, sz10) = all_17_0_13, aNaturalNumber0(xl), yields:
% 15.63/4.33  | (139) all_17_0_13 = xl
% 15.63/4.33  |
% 15.63/4.33  | From (135) and (129) follows:
% 15.63/4.33  | (104) sdtasdt0(all_0_0_0, xl) = xm
% 15.63/4.33  |
% 15.63/4.33  | From (136) and (131) follows:
% 15.63/4.33  | (106) sdtasdt0(all_0_1_1, xl) = xn
% 15.63/4.33  |
% 15.63/4.33  | From (137) and (115) follows:
% 15.63/4.33  | (20) sdtasdt0(xl, all_0_0_0) = xm
% 15.63/4.33  |
% 15.63/4.33  | From (138) and (118) follows:
% 15.63/4.33  | (91) sdtasdt0(xl, all_0_1_1) = xn
% 15.63/4.33  |
% 15.63/4.33  | From (139) and (121) follows:
% 15.63/4.33  | (144) sdtasdt0(xl, sz10) = xl
% 15.63/4.33  |
% 15.63/4.33  | From (135)(136) and (132) follows:
% 15.63/4.33  | (145) sdtpldt0(xm, xn) = all_27_2_20
% 15.63/4.33  |
% 15.63/4.33  | Instantiating formula (74) with xm, xn, all_27_2_20, all_0_4_4 and discharging atoms sdtpldt0(xm, xn) = all_27_2_20, sdtpldt0(xm, xn) = all_0_4_4, yields:
% 15.63/4.33  | (146) all_27_2_20 = all_0_4_4
% 15.63/4.33  |
% 15.63/4.33  | From (146) and (145) follows:
% 15.63/4.33  | (66) sdtpldt0(xm, xn) = all_0_4_4
% 15.63/4.33  |
% 15.63/4.33  | Instantiating formula (11) with all_19_0_14, xn, xl, all_0_1_1, xl and discharging atoms sdtasdt0(all_0_1_1, xl) = xn, sdtasdt0(xl, xn) = all_19_0_14, aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 15.63/4.33  | (148)  ? [v0] : (sdtasdt0(v0, xl) = all_19_0_14 & sdtasdt0(xl, all_0_1_1) = v0)
% 15.63/4.33  |
% 15.63/4.33  | Instantiating formula (11) with xn, xl, sz10, xl, all_0_1_1 and discharging atoms sdtasdt0(all_0_1_1, xl) = xn, sdtasdt0(xl, sz10) = xl, aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), aNaturalNumber0(sz10), yields:
% 15.63/4.34  | (149)  ? [v0] : (sdtasdt0(v0, sz10) = xn & sdtasdt0(all_0_1_1, xl) = v0)
% 15.63/4.34  |
% 15.63/4.34  | Instantiating formula (18) with all_27_3_21, all_0_0_0, all_0_1_1 and discharging atoms sdtpldt0(all_0_0_0, all_0_1_1) = all_27_3_21, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_1_1), yields:
% 15.63/4.34  | (150) sdtpldt0(all_0_1_1, all_0_0_0) = all_27_3_21
% 15.63/4.34  |
% 15.63/4.34  | Instantiating formula (61) with all_27_3_21, all_0_1_1, all_0_0_0 and discharging atoms sdtpldt0(all_0_0_0, all_0_1_1) = all_27_3_21, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_1_1), yields:
% 15.63/4.34  | (151) aNaturalNumber0(all_27_3_21)
% 15.63/4.34  |
% 15.63/4.34  | Instantiating formula (3) with all_0_4_4, xm, xn, all_0_0_0, all_0_1_1, xl and discharging atoms sdtasdt0(xl, all_0_0_0) = xm, sdtasdt0(xl, all_0_1_1) = xn, sdtpldt0(xn, xm) = all_0_4_4, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 15.63/4.34  | (152)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_0_0_0, xl) = v3 & sdtasdt0(all_0_1_1, xl) = v2 & sdtasdt0(xl, v0) = all_0_4_4 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_0_1_1, all_0_0_0) = v0)
% 15.63/4.34  |
% 15.63/4.34  | Instantiating formula (79) with all_0_4_4, xm, xn, all_0_0_0, all_0_1_1, xl and discharging atoms sdtasdt0(all_0_0_0, xl) = xm, sdtasdt0(all_0_1_1, xl) = xn, sdtpldt0(xn, xm) = all_0_4_4, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 15.63/4.34  | (153)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, xl) = all_0_4_4 & sdtasdt0(xl, v0) = v1 & sdtasdt0(xl, all_0_0_0) = v3 & sdtasdt0(xl, all_0_1_1) = v2 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_0_1_1, all_0_0_0) = v0)
% 15.63/4.34  |
% 15.63/4.34  | Instantiating formula (3) with all_0_4_4, xm, xn, all_0_0_0, all_21_0_15, xl and discharging atoms sdtasdt0(xl, all_21_0_15) = xn, sdtasdt0(xl, all_0_0_0) = xm, sdtpldt0(xn, xm) = all_0_4_4, aNaturalNumber0(all_21_0_15), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), yields:
% 15.63/4.34  | (154)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_21_0_15, xl) = v2 & sdtasdt0(all_0_0_0, xl) = v3 & sdtasdt0(xl, v0) = all_0_4_4 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_21_0_15, all_0_0_0) = v0)
% 15.63/4.34  |
% 15.63/4.34  | Instantiating formula (3) with all_0_4_4, xn, xm, all_21_0_15, all_0_0_0, xl and discharging atoms sdtasdt0(xl, all_21_0_15) = xn, sdtasdt0(xl, all_0_0_0) = xm, sdtpldt0(xm, xn) = all_0_4_4, aNaturalNumber0(all_21_0_15), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), yields:
% 15.63/4.34  | (155)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_21_0_15, xl) = v3 & sdtasdt0(all_0_0_0, xl) = v2 & sdtasdt0(xl, v0) = all_0_4_4 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_0_0_0, all_21_0_15) = v0)
% 15.63/4.34  |
% 15.63/4.34  | Instantiating formula (89) with xn, xl, all_21_0_15 and discharging atoms sdtasdt0(xl, all_21_0_15) = xn, aNaturalNumber0(all_21_0_15), aNaturalNumber0(xl), yields:
% 15.63/4.34  | (156) sdtasdt0(all_21_0_15, xl) = xn
% 15.63/4.34  |
% 15.63/4.34  | Instantiating formula (3) with all_0_4_4, xn, xm, all_0_1_1, all_9_0_9, xl and discharging atoms sdtasdt0(xl, all_9_0_9) = xm, sdtasdt0(xl, all_0_1_1) = xn, sdtpldt0(xm, xn) = all_0_4_4, aNaturalNumber0(all_9_0_9), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 15.63/4.34  | (157)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_9_0_9, xl) = v2 & sdtasdt0(all_0_1_1, xl) = v3 & sdtasdt0(xl, v0) = all_0_4_4 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_9_0_9, all_0_1_1) = v0)
% 15.63/4.34  |
% 15.63/4.34  | Instantiating formula (3) with all_0_4_4, xn, xm, all_21_0_15, all_9_0_9, xl and discharging atoms sdtasdt0(xl, all_21_0_15) = xn, sdtasdt0(xl, all_9_0_9) = xm, sdtpldt0(xm, xn) = all_0_4_4, aNaturalNumber0(all_21_0_15), aNaturalNumber0(all_9_0_9), aNaturalNumber0(xl), yields:
% 15.63/4.34  | (158)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_21_0_15, xl) = v3 & sdtasdt0(all_9_0_9, xl) = v2 & sdtasdt0(xl, v0) = all_0_4_4 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_9_0_9, all_21_0_15) = v0)
% 15.63/4.34  |
% 15.63/4.34  | Instantiating formula (3) with all_0_4_4, xm, xn, all_9_0_9, all_0_1_1, xl and discharging atoms sdtasdt0(xl, all_9_0_9) = xm, sdtasdt0(xl, all_0_1_1) = xn, sdtpldt0(xn, xm) = all_0_4_4, aNaturalNumber0(all_9_0_9), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 15.63/4.34  | (159)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_9_0_9, xl) = v3 & sdtasdt0(all_0_1_1, xl) = v2 & sdtasdt0(xl, v0) = all_0_4_4 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_0_1_1, all_9_0_9) = v0)
% 15.63/4.34  |
% 15.63/4.34  | Instantiating formula (3) with all_0_4_4, xm, xn, all_9_0_9, all_21_0_15, xl and discharging atoms sdtasdt0(xl, all_21_0_15) = xn, sdtasdt0(xl, all_9_0_9) = xm, sdtpldt0(xn, xm) = all_0_4_4, aNaturalNumber0(all_21_0_15), aNaturalNumber0(all_9_0_9), aNaturalNumber0(xl), yields:
% 15.63/4.34  | (160)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_21_0_15, xl) = v2 & sdtasdt0(all_9_0_9, xl) = v3 & sdtasdt0(xl, v0) = all_0_4_4 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_21_0_15, all_9_0_9) = v0)
% 15.63/4.34  |
% 15.63/4.34  | Instantiating formula (89) with xm, xl, all_9_0_9 and discharging atoms sdtasdt0(xl, all_9_0_9) = xm, aNaturalNumber0(all_9_0_9), aNaturalNumber0(xl), yields:
% 15.63/4.34  | (161) sdtasdt0(all_9_0_9, xl) = xm
% 15.63/4.34  |
% 15.63/4.34  | Instantiating (157) with all_49_0_25, all_49_1_26, all_49_2_27, all_49_3_28 yields:
% 15.63/4.34  | (162) sdtasdt0(all_49_3_28, xl) = all_49_2_27 & sdtasdt0(all_9_0_9, xl) = all_49_1_26 & sdtasdt0(all_0_1_1, xl) = all_49_0_25 & sdtasdt0(xl, all_49_3_28) = all_0_4_4 & sdtpldt0(all_49_1_26, all_49_0_25) = all_49_2_27 & sdtpldt0(all_9_0_9, all_0_1_1) = all_49_3_28
% 15.63/4.34  |
% 15.63/4.34  | Applying alpha-rule on (162) yields:
% 15.63/4.34  | (163) sdtpldt0(all_49_1_26, all_49_0_25) = all_49_2_27
% 15.63/4.34  | (164) sdtasdt0(all_49_3_28, xl) = all_49_2_27
% 15.63/4.34  | (165) sdtasdt0(xl, all_49_3_28) = all_0_4_4
% 15.63/4.34  | (166) sdtasdt0(all_0_1_1, xl) = all_49_0_25
% 15.63/4.34  | (167) sdtasdt0(all_9_0_9, xl) = all_49_1_26
% 15.63/4.34  | (168) sdtpldt0(all_9_0_9, all_0_1_1) = all_49_3_28
% 15.63/4.34  |
% 15.63/4.34  | Instantiating (160) with all_51_0_29, all_51_1_30, all_51_2_31, all_51_3_32 yields:
% 15.63/4.34  | (169) sdtasdt0(all_51_3_32, xl) = all_51_2_31 & sdtasdt0(all_21_0_15, xl) = all_51_1_30 & sdtasdt0(all_9_0_9, xl) = all_51_0_29 & sdtasdt0(xl, all_51_3_32) = all_0_4_4 & sdtpldt0(all_51_1_30, all_51_0_29) = all_51_2_31 & sdtpldt0(all_21_0_15, all_9_0_9) = all_51_3_32
% 15.63/4.34  |
% 15.63/4.34  | Applying alpha-rule on (169) yields:
% 15.63/4.34  | (170) sdtasdt0(all_21_0_15, xl) = all_51_1_30
% 15.63/4.34  | (171) sdtpldt0(all_51_1_30, all_51_0_29) = all_51_2_31
% 15.63/4.34  | (172) sdtpldt0(all_21_0_15, all_9_0_9) = all_51_3_32
% 15.63/4.34  | (173) sdtasdt0(xl, all_51_3_32) = all_0_4_4
% 15.63/4.34  | (174) sdtasdt0(all_9_0_9, xl) = all_51_0_29
% 15.63/4.34  | (175) sdtasdt0(all_51_3_32, xl) = all_51_2_31
% 15.63/4.34  |
% 15.63/4.34  | Instantiating (159) with all_53_0_33, all_53_1_34, all_53_2_35, all_53_3_36 yields:
% 15.63/4.34  | (176) sdtasdt0(all_53_3_36, xl) = all_53_2_35 & sdtasdt0(all_9_0_9, xl) = all_53_0_33 & sdtasdt0(all_0_1_1, xl) = all_53_1_34 & sdtasdt0(xl, all_53_3_36) = all_0_4_4 & sdtpldt0(all_53_1_34, all_53_0_33) = all_53_2_35 & sdtpldt0(all_0_1_1, all_9_0_9) = all_53_3_36
% 15.63/4.34  |
% 15.63/4.34  | Applying alpha-rule on (176) yields:
% 15.63/4.34  | (177) sdtasdt0(xl, all_53_3_36) = all_0_4_4
% 15.63/4.34  | (178) sdtasdt0(all_0_1_1, xl) = all_53_1_34
% 15.63/4.34  | (179) sdtasdt0(all_9_0_9, xl) = all_53_0_33
% 15.63/4.34  | (180) sdtpldt0(all_53_1_34, all_53_0_33) = all_53_2_35
% 15.63/4.34  | (181) sdtasdt0(all_53_3_36, xl) = all_53_2_35
% 15.63/4.34  | (182) sdtpldt0(all_0_1_1, all_9_0_9) = all_53_3_36
% 15.63/4.34  |
% 15.63/4.34  | Instantiating (158) with all_71_0_45, all_71_1_46, all_71_2_47, all_71_3_48 yields:
% 15.63/4.35  | (183) sdtasdt0(all_71_3_48, xl) = all_71_2_47 & sdtasdt0(all_21_0_15, xl) = all_71_0_45 & sdtasdt0(all_9_0_9, xl) = all_71_1_46 & sdtasdt0(xl, all_71_3_48) = all_0_4_4 & sdtpldt0(all_71_1_46, all_71_0_45) = all_71_2_47 & sdtpldt0(all_9_0_9, all_21_0_15) = all_71_3_48
% 15.63/4.35  |
% 15.63/4.35  | Applying alpha-rule on (183) yields:
% 15.63/4.35  | (184) sdtasdt0(xl, all_71_3_48) = all_0_4_4
% 15.63/4.35  | (185) sdtasdt0(all_9_0_9, xl) = all_71_1_46
% 15.63/4.35  | (186) sdtpldt0(all_9_0_9, all_21_0_15) = all_71_3_48
% 15.63/4.35  | (187) sdtasdt0(all_21_0_15, xl) = all_71_0_45
% 15.63/4.35  | (188) sdtasdt0(all_71_3_48, xl) = all_71_2_47
% 15.63/4.35  | (189) sdtpldt0(all_71_1_46, all_71_0_45) = all_71_2_47
% 15.63/4.35  |
% 15.63/4.35  | Instantiating (149) with all_73_0_49 yields:
% 15.63/4.35  | (190) sdtasdt0(all_73_0_49, sz10) = xn & sdtasdt0(all_0_1_1, xl) = all_73_0_49
% 15.63/4.35  |
% 15.63/4.35  | Applying alpha-rule on (190) yields:
% 15.63/4.35  | (191) sdtasdt0(all_73_0_49, sz10) = xn
% 15.63/4.35  | (192) sdtasdt0(all_0_1_1, xl) = all_73_0_49
% 15.63/4.35  |
% 15.63/4.35  | Instantiating (152) with all_85_0_55, all_85_1_56, all_85_2_57, all_85_3_58 yields:
% 15.63/4.35  | (193) sdtasdt0(all_85_3_58, xl) = all_85_2_57 & sdtasdt0(all_0_0_0, xl) = all_85_0_55 & sdtasdt0(all_0_1_1, xl) = all_85_1_56 & sdtasdt0(xl, all_85_3_58) = all_0_4_4 & sdtpldt0(all_85_1_56, all_85_0_55) = all_85_2_57 & sdtpldt0(all_0_1_1, all_0_0_0) = all_85_3_58
% 15.63/4.35  |
% 15.63/4.35  | Applying alpha-rule on (193) yields:
% 15.63/4.35  | (194) sdtasdt0(all_85_3_58, xl) = all_85_2_57
% 15.63/4.35  | (195) sdtpldt0(all_0_1_1, all_0_0_0) = all_85_3_58
% 15.63/4.35  | (196) sdtasdt0(all_0_0_0, xl) = all_85_0_55
% 15.63/4.35  | (197) sdtasdt0(xl, all_85_3_58) = all_0_4_4
% 15.63/4.35  | (198) sdtpldt0(all_85_1_56, all_85_0_55) = all_85_2_57
% 15.63/4.35  | (199) sdtasdt0(all_0_1_1, xl) = all_85_1_56
% 15.63/4.35  |
% 15.63/4.35  | Instantiating (148) with all_97_0_64 yields:
% 15.63/4.35  | (200) sdtasdt0(all_97_0_64, xl) = all_19_0_14 & sdtasdt0(xl, all_0_1_1) = all_97_0_64
% 15.63/4.35  |
% 15.63/4.35  | Applying alpha-rule on (200) yields:
% 15.63/4.35  | (201) sdtasdt0(all_97_0_64, xl) = all_19_0_14
% 15.63/4.35  | (202) sdtasdt0(xl, all_0_1_1) = all_97_0_64
% 15.63/4.35  |
% 15.63/4.35  | Instantiating (155) with all_101_0_66, all_101_1_67, all_101_2_68, all_101_3_69 yields:
% 15.63/4.35  | (203) sdtasdt0(all_101_3_69, xl) = all_101_2_68 & sdtasdt0(all_21_0_15, xl) = all_101_0_66 & sdtasdt0(all_0_0_0, xl) = all_101_1_67 & sdtasdt0(xl, all_101_3_69) = all_0_4_4 & sdtpldt0(all_101_1_67, all_101_0_66) = all_101_2_68 & sdtpldt0(all_0_0_0, all_21_0_15) = all_101_3_69
% 15.63/4.35  |
% 15.63/4.35  | Applying alpha-rule on (203) yields:
% 15.63/4.35  | (204) sdtpldt0(all_0_0_0, all_21_0_15) = all_101_3_69
% 15.63/4.35  | (205) sdtasdt0(xl, all_101_3_69) = all_0_4_4
% 15.63/4.35  | (206) sdtpldt0(all_101_1_67, all_101_0_66) = all_101_2_68
% 15.63/4.35  | (207) sdtasdt0(all_21_0_15, xl) = all_101_0_66
% 15.63/4.35  | (208) sdtasdt0(all_101_3_69, xl) = all_101_2_68
% 15.63/4.35  | (209) sdtasdt0(all_0_0_0, xl) = all_101_1_67
% 15.63/4.35  |
% 15.63/4.35  | Instantiating (154) with all_103_0_70, all_103_1_71, all_103_2_72, all_103_3_73 yields:
% 15.63/4.35  | (210) sdtasdt0(all_103_3_73, xl) = all_103_2_72 & sdtasdt0(all_21_0_15, xl) = all_103_1_71 & sdtasdt0(all_0_0_0, xl) = all_103_0_70 & sdtasdt0(xl, all_103_3_73) = all_0_4_4 & sdtpldt0(all_103_1_71, all_103_0_70) = all_103_2_72 & sdtpldt0(all_21_0_15, all_0_0_0) = all_103_3_73
% 15.63/4.35  |
% 15.63/4.35  | Applying alpha-rule on (210) yields:
% 15.63/4.35  | (211) sdtasdt0(all_0_0_0, xl) = all_103_0_70
% 15.63/4.35  | (212) sdtasdt0(all_103_3_73, xl) = all_103_2_72
% 15.63/4.35  | (213) sdtpldt0(all_103_1_71, all_103_0_70) = all_103_2_72
% 15.63/4.35  | (214) sdtasdt0(xl, all_103_3_73) = all_0_4_4
% 15.63/4.35  | (215) sdtasdt0(all_21_0_15, xl) = all_103_1_71
% 15.63/4.35  | (216) sdtpldt0(all_21_0_15, all_0_0_0) = all_103_3_73
% 15.63/4.35  |
% 15.63/4.35  | Instantiating (153) with all_111_0_77, all_111_1_78, all_111_2_79, all_111_3_80 yields:
% 15.63/4.35  | (217) sdtasdt0(all_111_3_80, xl) = all_0_4_4 & sdtasdt0(xl, all_111_3_80) = all_111_2_79 & sdtasdt0(xl, all_0_0_0) = all_111_0_77 & sdtasdt0(xl, all_0_1_1) = all_111_1_78 & sdtpldt0(all_111_1_78, all_111_0_77) = all_111_2_79 & sdtpldt0(all_0_1_1, all_0_0_0) = all_111_3_80
% 15.63/4.35  |
% 15.63/4.35  | Applying alpha-rule on (217) yields:
% 15.63/4.35  | (218) sdtasdt0(xl, all_0_0_0) = all_111_0_77
% 15.63/4.35  | (219) sdtpldt0(all_111_1_78, all_111_0_77) = all_111_2_79
% 15.63/4.35  | (220) sdtasdt0(xl, all_0_1_1) = all_111_1_78
% 15.63/4.35  | (221) sdtasdt0(all_111_3_80, xl) = all_0_4_4
% 15.63/4.35  | (222) sdtasdt0(xl, all_111_3_80) = all_111_2_79
% 15.63/4.35  | (223) sdtpldt0(all_0_1_1, all_0_0_0) = all_111_3_80
% 15.63/4.35  |
% 15.63/4.35  | Instantiating formula (54) with all_21_0_15, xl, all_101_0_66, all_103_1_71 and discharging atoms sdtasdt0(all_21_0_15, xl) = all_103_1_71, sdtasdt0(all_21_0_15, xl) = all_101_0_66, yields:
% 15.63/4.35  | (224) all_103_1_71 = all_101_0_66
% 15.63/4.35  |
% 15.63/4.35  | Instantiating formula (54) with all_21_0_15, xl, all_71_0_45, all_101_0_66 and discharging atoms sdtasdt0(all_21_0_15, xl) = all_101_0_66, sdtasdt0(all_21_0_15, xl) = all_71_0_45, yields:
% 15.63/4.35  | (225) all_101_0_66 = all_71_0_45
% 15.63/4.35  |
% 15.63/4.35  | Instantiating formula (54) with all_21_0_15, xl, all_51_1_30, all_71_0_45 and discharging atoms sdtasdt0(all_21_0_15, xl) = all_71_0_45, sdtasdt0(all_21_0_15, xl) = all_51_1_30, yields:
% 15.63/4.35  | (226) all_71_0_45 = all_51_1_30
% 15.63/4.35  |
% 15.63/4.35  | Instantiating formula (54) with all_21_0_15, xl, xn, all_103_1_71 and discharging atoms sdtasdt0(all_21_0_15, xl) = all_103_1_71, sdtasdt0(all_21_0_15, xl) = xn, yields:
% 15.63/4.35  | (227) all_103_1_71 = xn
% 15.63/4.35  |
% 15.63/4.35  | Instantiating formula (54) with all_9_0_9, xl, all_53_0_33, all_71_1_46 and discharging atoms sdtasdt0(all_9_0_9, xl) = all_71_1_46, sdtasdt0(all_9_0_9, xl) = all_53_0_33, yields:
% 15.63/4.35  | (228) all_71_1_46 = all_53_0_33
% 15.63/4.35  |
% 15.63/4.35  | Instantiating formula (54) with all_9_0_9, xl, all_51_0_29, all_53_0_33 and discharging atoms sdtasdt0(all_9_0_9, xl) = all_53_0_33, sdtasdt0(all_9_0_9, xl) = all_51_0_29, yields:
% 15.63/4.35  | (229) all_53_0_33 = all_51_0_29
% 15.63/4.35  |
% 15.63/4.35  | Instantiating formula (54) with all_9_0_9, xl, all_49_1_26, all_71_1_46 and discharging atoms sdtasdt0(all_9_0_9, xl) = all_71_1_46, sdtasdt0(all_9_0_9, xl) = all_49_1_26, yields:
% 15.63/4.35  | (230) all_71_1_46 = all_49_1_26
% 15.63/4.35  |
% 15.63/4.35  | Instantiating formula (54) with all_9_0_9, xl, xm, all_51_0_29 and discharging atoms sdtasdt0(all_9_0_9, xl) = all_51_0_29, sdtasdt0(all_9_0_9, xl) = xm, yields:
% 15.63/4.35  | (231) all_51_0_29 = xm
% 15.63/4.35  |
% 15.63/4.35  | Instantiating formula (54) with all_0_0_0, xl, all_103_0_70, xm and discharging atoms sdtasdt0(all_0_0_0, xl) = all_103_0_70, sdtasdt0(all_0_0_0, xl) = xm, yields:
% 15.63/4.35  | (232) all_103_0_70 = xm
% 15.63/4.35  |
% 15.63/4.35  | Instantiating formula (54) with all_0_0_0, xl, all_101_1_67, all_103_0_70 and discharging atoms sdtasdt0(all_0_0_0, xl) = all_103_0_70, sdtasdt0(all_0_0_0, xl) = all_101_1_67, yields:
% 15.63/4.35  | (233) all_103_0_70 = all_101_1_67
% 15.63/4.35  |
% 15.63/4.35  | Instantiating formula (54) with all_0_0_0, xl, all_85_0_55, all_101_1_67 and discharging atoms sdtasdt0(all_0_0_0, xl) = all_101_1_67, sdtasdt0(all_0_0_0, xl) = all_85_0_55, yields:
% 15.63/4.35  | (234) all_101_1_67 = all_85_0_55
% 15.63/4.35  |
% 15.63/4.35  | Instantiating formula (54) with all_0_1_1, xl, all_85_1_56, xn and discharging atoms sdtasdt0(all_0_1_1, xl) = all_85_1_56, sdtasdt0(all_0_1_1, xl) = xn, yields:
% 15.63/4.35  | (235) all_85_1_56 = xn
% 15.63/4.35  |
% 15.63/4.35  | Instantiating formula (54) with all_0_1_1, xl, all_73_0_49, all_85_1_56 and discharging atoms sdtasdt0(all_0_1_1, xl) = all_85_1_56, sdtasdt0(all_0_1_1, xl) = all_73_0_49, yields:
% 15.63/4.35  | (236) all_85_1_56 = all_73_0_49
% 15.63/4.35  |
% 15.63/4.35  | Instantiating formula (54) with all_0_1_1, xl, all_53_1_34, all_85_1_56 and discharging atoms sdtasdt0(all_0_1_1, xl) = all_85_1_56, sdtasdt0(all_0_1_1, xl) = all_53_1_34, yields:
% 15.63/4.35  | (237) all_85_1_56 = all_53_1_34
% 15.63/4.35  |
% 15.63/4.35  | Instantiating formula (54) with xl, all_0_0_0, all_111_0_77, xm and discharging atoms sdtasdt0(xl, all_0_0_0) = all_111_0_77, sdtasdt0(xl, all_0_0_0) = xm, yields:
% 15.63/4.35  | (238) all_111_0_77 = xm
% 15.63/4.35  |
% 15.63/4.35  | Instantiating formula (54) with xl, all_0_1_1, all_111_1_78, xn and discharging atoms sdtasdt0(xl, all_0_1_1) = all_111_1_78, sdtasdt0(xl, all_0_1_1) = xn, yields:
% 15.63/4.35  | (239) all_111_1_78 = xn
% 15.63/4.35  |
% 15.63/4.35  | Instantiating formula (54) with xl, all_0_1_1, all_97_0_64, all_111_1_78 and discharging atoms sdtasdt0(xl, all_0_1_1) = all_111_1_78, sdtasdt0(xl, all_0_1_1) = all_97_0_64, yields:
% 15.63/4.35  | (240) all_111_1_78 = all_97_0_64
% 15.63/4.35  |
% 15.63/4.35  | Instantiating formula (74) with all_0_1_1, all_0_0_0, all_27_3_21, all_111_3_80 and discharging atoms sdtpldt0(all_0_1_1, all_0_0_0) = all_111_3_80, sdtpldt0(all_0_1_1, all_0_0_0) = all_27_3_21, yields:
% 15.63/4.35  | (241) all_111_3_80 = all_27_3_21
% 15.63/4.35  |
% 15.63/4.35  | Combining equations (239,240) yields a new equation:
% 15.63/4.35  | (242) all_97_0_64 = xn
% 15.63/4.35  |
% 15.63/4.35  | Combining equations (233,232) yields a new equation:
% 15.63/4.35  | (243) all_101_1_67 = xm
% 15.63/4.35  |
% 15.63/4.35  | Simplifying 243 yields:
% 15.63/4.35  | (244) all_101_1_67 = xm
% 15.63/4.35  |
% 15.63/4.35  | Combining equations (224,227) yields a new equation:
% 15.63/4.35  | (245) all_101_0_66 = xn
% 15.63/4.36  |
% 15.63/4.36  | Simplifying 245 yields:
% 15.63/4.36  | (246) all_101_0_66 = xn
% 15.63/4.36  |
% 15.63/4.36  | Combining equations (225,246) yields a new equation:
% 15.63/4.36  | (247) all_71_0_45 = xn
% 15.63/4.36  |
% 15.63/4.36  | Simplifying 247 yields:
% 15.63/4.36  | (248) all_71_0_45 = xn
% 15.63/4.36  |
% 15.63/4.36  | Combining equations (234,244) yields a new equation:
% 15.63/4.36  | (249) all_85_0_55 = xm
% 15.63/4.36  |
% 15.63/4.36  | Simplifying 249 yields:
% 15.63/4.36  | (250) all_85_0_55 = xm
% 15.63/4.36  |
% 15.63/4.36  | Combining equations (237,236) yields a new equation:
% 15.63/4.36  | (251) all_73_0_49 = all_53_1_34
% 15.63/4.36  |
% 15.63/4.36  | Combining equations (235,236) yields a new equation:
% 15.63/4.36  | (252) all_73_0_49 = xn
% 15.63/4.36  |
% 15.63/4.36  | Combining equations (251,252) yields a new equation:
% 15.63/4.36  | (253) all_53_1_34 = xn
% 15.63/4.36  |
% 15.63/4.36  | Simplifying 253 yields:
% 15.63/4.36  | (254) all_53_1_34 = xn
% 15.63/4.36  |
% 15.63/4.36  | Combining equations (226,248) yields a new equation:
% 15.63/4.36  | (255) all_51_1_30 = xn
% 15.63/4.36  |
% 15.63/4.36  | Simplifying 255 yields:
% 15.63/4.36  | (256) all_51_1_30 = xn
% 15.63/4.36  |
% 15.63/4.36  | Combining equations (228,230) yields a new equation:
% 15.63/4.36  | (257) all_53_0_33 = all_49_1_26
% 15.63/4.36  |
% 15.63/4.36  | Simplifying 257 yields:
% 15.63/4.36  | (258) all_53_0_33 = all_49_1_26
% 15.63/4.36  |
% 15.63/4.36  | Combining equations (229,258) yields a new equation:
% 15.63/4.36  | (259) all_51_0_29 = all_49_1_26
% 15.63/4.36  |
% 15.63/4.36  | Simplifying 259 yields:
% 15.63/4.36  | (260) all_51_0_29 = all_49_1_26
% 15.63/4.36  |
% 15.63/4.36  | Combining equations (231,260) yields a new equation:
% 15.63/4.36  | (261) all_49_1_26 = xm
% 15.63/4.36  |
% 15.63/4.36  | Combining equations (261,260) yields a new equation:
% 15.63/4.36  | (231) all_51_0_29 = xm
% 15.63/4.36  |
% 15.63/4.36  | Combining equations (261,258) yields a new equation:
% 15.63/4.36  | (263) all_53_0_33 = xm
% 15.63/4.36  |
% 15.63/4.36  | Combining equations (252,236) yields a new equation:
% 15.63/4.36  | (235) all_85_1_56 = xn
% 15.63/4.36  |
% 15.63/4.36  | Combining equations (242,240) yields a new equation:
% 15.63/4.36  | (239) all_111_1_78 = xn
% 15.63/4.36  |
% 15.63/4.36  | From (241) and (222) follows:
% 15.63/4.36  | (266) sdtasdt0(xl, all_27_3_21) = all_111_2_79
% 15.63/4.36  |
% 15.63/4.36  | From (239)(238) and (219) follows:
% 15.63/4.36  | (267) sdtpldt0(xn, xm) = all_111_2_79
% 15.63/4.36  |
% 15.63/4.36  | From (227)(232) and (213) follows:
% 15.63/4.36  | (268) sdtpldt0(xn, xm) = all_103_2_72
% 15.63/4.36  |
% 15.63/4.36  | From (235)(250) and (198) follows:
% 15.63/4.36  | (269) sdtpldt0(xn, xm) = all_85_2_57
% 15.63/4.36  |
% 15.63/4.36  | From (254)(263) and (180) follows:
% 15.63/4.36  | (270) sdtpldt0(xn, xm) = all_53_2_35
% 15.63/4.36  |
% 15.63/4.36  | From (256)(231) and (171) follows:
% 15.63/4.36  | (271) sdtpldt0(xn, xm) = all_51_2_31
% 15.63/4.36  |
% 15.63/4.36  | Instantiating formula (74) with xn, xm, all_103_2_72, all_111_2_79 and discharging atoms sdtpldt0(xn, xm) = all_111_2_79, sdtpldt0(xn, xm) = all_103_2_72, yields:
% 15.63/4.36  | (272) all_111_2_79 = all_103_2_72
% 15.63/4.36  |
% 15.63/4.36  | Instantiating formula (74) with xn, xm, all_85_2_57, all_0_4_4 and discharging atoms sdtpldt0(xn, xm) = all_85_2_57, sdtpldt0(xn, xm) = all_0_4_4, yields:
% 15.63/4.36  | (273) all_85_2_57 = all_0_4_4
% 15.63/4.36  |
% 15.63/4.36  | Instantiating formula (74) with xn, xm, all_53_2_35, all_103_2_72 and discharging atoms sdtpldt0(xn, xm) = all_103_2_72, sdtpldt0(xn, xm) = all_53_2_35, yields:
% 15.63/4.36  | (274) all_103_2_72 = all_53_2_35
% 15.63/4.36  |
% 15.63/4.36  | Instantiating formula (74) with xn, xm, all_53_2_35, all_85_2_57 and discharging atoms sdtpldt0(xn, xm) = all_85_2_57, sdtpldt0(xn, xm) = all_53_2_35, yields:
% 15.63/4.36  | (275) all_85_2_57 = all_53_2_35
% 15.63/4.36  |
% 15.63/4.36  | Instantiating formula (74) with xn, xm, all_51_2_31, all_111_2_79 and discharging atoms sdtpldt0(xn, xm) = all_111_2_79, sdtpldt0(xn, xm) = all_51_2_31, yields:
% 15.63/4.36  | (276) all_111_2_79 = all_51_2_31
% 15.63/4.36  |
% 15.63/4.36  | Combining equations (272,276) yields a new equation:
% 15.63/4.36  | (277) all_103_2_72 = all_51_2_31
% 15.63/4.36  |
% 15.63/4.36  | Simplifying 277 yields:
% 15.63/4.36  | (278) all_103_2_72 = all_51_2_31
% 15.63/4.36  |
% 15.63/4.36  | Combining equations (274,278) yields a new equation:
% 15.63/4.36  | (279) all_53_2_35 = all_51_2_31
% 15.63/4.36  |
% 15.63/4.36  | Simplifying 279 yields:
% 15.63/4.36  | (280) all_53_2_35 = all_51_2_31
% 15.63/4.36  |
% 15.63/4.36  | Combining equations (275,273) yields a new equation:
% 15.63/4.36  | (281) all_53_2_35 = all_0_4_4
% 15.63/4.36  |
% 15.63/4.36  | Simplifying 281 yields:
% 15.63/4.36  | (282) all_53_2_35 = all_0_4_4
% 15.63/4.36  |
% 15.63/4.36  | Combining equations (282,280) yields a new equation:
% 15.63/4.36  | (283) all_51_2_31 = all_0_4_4
% 15.63/4.36  |
% 15.63/4.36  | Combining equations (283,276) yields a new equation:
% 15.63/4.36  | (284) all_111_2_79 = all_0_4_4
% 15.63/4.36  |
% 15.63/4.36  | From (284) and (266) follows:
% 15.63/4.36  | (134) sdtasdt0(xl, all_27_3_21) = all_0_4_4
% 15.63/4.36  |
% 15.63/4.36  | Instantiating formula (94) with all_27_3_21, all_0_4_4, xl and discharging atoms sdtasdt0(xl, all_27_3_21) = all_0_4_4, aNaturalNumber0(all_27_3_21), aNaturalNumber0(all_0_4_4), aNaturalNumber0(xl),  ~ doDivides0(xl, all_0_4_4), yields:
% 15.63/4.36  | (286) $false
% 15.63/4.36  |
% 15.63/4.36  |-The branch is then unsatisfiable
% 15.63/4.36  % SZS output end Proof for theBenchmark
% 15.63/4.36  
% 15.63/4.36  3751ms
%------------------------------------------------------------------------------