%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : NUM467+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n016.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Mon Jul 18 08:44:47 EDT 2022

% Result   : Theorem 8.43s 2.69s
% Output   : Proof 15.29s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : NUM467+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n016.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 : Thu Jul  7 09:29:21 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.57/0.60          ____       _                          
% 0.57/0.60    ___  / __ \_____(_)___  ________  __________
% 0.57/0.60   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.60  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.57/0.60  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.57/0.60  
% 0.57/0.60  A Theorem Prover for First-Order Logic
% 0.57/0.60  (ePrincess v.1.0)
% 0.57/0.60  
% 0.57/0.60  (c) Philipp Rümmer, 2009-2015
% 0.57/0.60  (c) Peter Backeman, 2014-2015
% 0.57/0.60  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.60  Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.60  Bug reports to peter@backeman.se
% 0.57/0.60  
% 0.57/0.60  For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.60  
% 0.57/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.66  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.86/1.01  Prover 0: Preprocessing ...
% 3.36/1.47  Prover 0: Constructing countermodel ...
% 8.43/2.69  Prover 0: proved (2031ms)
% 8.43/2.69  
% 8.43/2.69  No countermodel exists, formula is valid
% 8.43/2.69  % SZS status Theorem for theBenchmark
% 8.43/2.69  
% 8.43/2.69  Generating proof ... found it (size 135)
% 14.30/4.07  
% 14.30/4.07  % SZS output start Proof for theBenchmark
% 14.30/4.07  Assumed formulas after preprocessing and simplification: 
% 14.30/4.07  | (0)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (sz10 = sz00) & sdtasdt0(xl, v2) = xm & sdtasdt0(xl, v1) = xn & sdtpldt0(xm, xn) = v0 & doDivides0(xl, xn) & doDivides0(xl, xm) & aNaturalNumber0(v2) & aNaturalNumber0(v1) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & aNaturalNumber0(xl) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) &  ~ doDivides0(xl, v0) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (sdtasdt0(v5, v3) = v7) |  ~ (sdtasdt0(v4, v3) = v6) |  ~ (sdtpldt0(v6, v7) = v8) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] : (sdtasdt0(v9, v3) = v8 & sdtasdt0(v3, v9) = v10 & sdtasdt0(v3, v5) = v12 & sdtasdt0(v3, v4) = v11 & sdtpldt0(v11, v12) = v10 & sdtpldt0(v4, v5) = v9)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (sdtasdt0(v3, v5) = v7) |  ~ (sdtasdt0(v3, v4) = v6) |  ~ (sdtpldt0(v6, v7) = v8) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] : (sdtasdt0(v9, v3) = v10 & sdtasdt0(v5, v3) = v12 & sdtasdt0(v4, v3) = v11 & sdtasdt0(v3, v9) = v8 & sdtpldt0(v11, v12) = v10 & sdtpldt0(v4, v5) = v9)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 | v3 = sz00 |  ~ (sdtasdt0(v5, v3) = v7) |  ~ (sdtasdt0(v4, v3) = v6) |  ~ sdtlseqdt0(v4, v5) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | sdtlseqdt0(v6, v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 | v3 = sz00 |  ~ (sdtasdt0(v5, v3) = v7) |  ~ (sdtasdt0(v4, v3) = v6) |  ~ sdtlseqdt0(v4, v5) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v8] :  ? [v9] : ( ~ (v9 = v8) & sdtasdt0(v3, v5) = v9 & sdtasdt0(v3, v4) = v8 & sdtlseqdt0(v8, v9))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 | v3 = sz00 |  ~ (sdtasdt0(v5, v3) = v7) |  ~ (sdtasdt0(v4, v3) = v6) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v8] :  ? [v9] : ( ~ (v9 = v8) & sdtasdt0(v3, v5) = v9 & sdtasdt0(v3, v4) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 | v3 = sz00 |  ~ (sdtasdt0(v5, v3) = v7) |  ~ (sdtasdt0(v3, v4) = v6) |  ~ sdtlseqdt0(v4, v5) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v8] :  ? [v9] : ( ~ (v9 = v7) &  ~ (v8 = v6) & sdtasdt0(v4, v3) = v9 & sdtasdt0(v3, v5) = v8 & sdtlseqdt0(v9, v7) & sdtlseqdt0(v6, v8))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 | v3 = sz00 |  ~ (sdtasdt0(v5, v3) = v7) |  ~ (sdtasdt0(v3, v4) = v6) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v8] :  ? [v9] : ( ~ (v9 = v7) &  ~ (v8 = v6) & sdtasdt0(v4, v3) = v9 & sdtasdt0(v3, v5) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 | v3 = sz00 |  ~ (sdtasdt0(v4, v3) = v7) |  ~ (sdtasdt0(v3, v5) = v6) |  ~ sdtlseqdt0(v4, v5) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v8] :  ? [v9] : ( ~ (v9 = v7) &  ~ (v8 = v6) & sdtasdt0(v5, v3) = v9 & sdtasdt0(v3, v4) = v8 & sdtlseqdt0(v8, v6) & sdtlseqdt0(v7, v9))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 | v3 = sz00 |  ~ (sdtasdt0(v4, v3) = v7) |  ~ (sdtasdt0(v3, v5) = v6) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v8] :  ? [v9] : ( ~ (v9 = v7) &  ~ (v8 = v6) & sdtasdt0(v5, v3) = v9 & sdtasdt0(v3, v4) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 | v3 = sz00 |  ~ (sdtasdt0(v3, v5) = v7) |  ~ (sdtasdt0(v3, v4) = v6) |  ~ sdtlseqdt0(v4, v5) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | sdtlseqdt0(v6, v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 | v3 = sz00 |  ~ (sdtasdt0(v3, v5) = v7) |  ~ (sdtasdt0(v3, v4) = v6) |  ~ sdtlseqdt0(v4, v5) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v8] :  ? [v9] : ( ~ (v9 = v8) & sdtasdt0(v5, v3) = v9 & sdtasdt0(v4, v3) = v8 & sdtlseqdt0(v8, v9))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 | v3 = sz00 |  ~ (sdtasdt0(v3, v5) = v7) |  ~ (sdtasdt0(v3, v4) = v6) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v8] :  ? [v9] : ( ~ (v9 = v8) & sdtasdt0(v5, v3) = v9 & sdtasdt0(v4, v3) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (sdtpldt0(v5, v3) = v7) |  ~ (sdtpldt0(v4, v3) = v6) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v8] :  ? [v9] : ( ~ (v9 = v8) & sdtpldt0(v3, v5) = v9 & sdtpldt0(v3, v4) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (sdtpldt0(v5, v3) = v7) |  ~ (sdtpldt0(v3, v4) = v6) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v8] :  ? [v9] : ( ~ (v9 = v7) &  ~ (v8 = v6) & sdtpldt0(v4, v3) = v9 & sdtpldt0(v3, v5) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (sdtpldt0(v4, v3) = v7) |  ~ (sdtpldt0(v3, v5) = v6) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v8] :  ? [v9] : ( ~ (v9 = v7) &  ~ (v8 = v6) & sdtpldt0(v5, v3) = v9 & sdtpldt0(v3, v4) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (sdtpldt0(v3, v5) = v7) |  ~ (sdtpldt0(v3, v4) = v6) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v8] :  ? [v9] : ( ~ (v9 = v8) & sdtpldt0(v5, v3) = v9 & sdtpldt0(v4, v3) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (sdtasdt0(v6, v5) = v7) |  ~ (sdtasdt0(v3, v4) = v6) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v8] : (sdtasdt0(v4, v5) = v8 & sdtasdt0(v3, v8) = v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (sdtasdt0(v6, v3) = v7) |  ~ (sdtpldt0(v4, v5) = v6) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] : (sdtasdt0(v5, v3) = v12 & sdtasdt0(v4, v3) = v11 & sdtasdt0(v3, v6) = v8 & sdtasdt0(v3, v5) = v10 & sdtasdt0(v3, v4) = v9 & sdtpldt0(v11, v12) = v7 & sdtpldt0(v9, v10) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (sdtasdt0(v4, v5) = v6) |  ~ (sdtasdt0(v3, v6) = v7) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v8] : (sdtasdt0(v8, v5) = v7 & sdtasdt0(v3, v4) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (sdtasdt0(v3, v6) = v7) |  ~ (sdtpldt0(v4, v5) = v6) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] : (sdtasdt0(v6, v3) = v10 & sdtasdt0(v5, v3) = v12 & sdtasdt0(v4, v3) = v11 & sdtasdt0(v3, v5) = v9 & sdtasdt0(v3, v4) = v8 & sdtpldt0(v11, v12) = v10 & sdtpldt0(v8, v9) = v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (sdtpldt0(v6, v5) = v7) |  ~ (sdtpldt0(v3, v4) = v6) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v8] : (sdtpldt0(v4, v5) = v8 & sdtpldt0(v3, v8) = v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (sdtpldt0(v4, v5) = v6) |  ~ (sdtpldt0(v3, v6) = v7) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v8] : (sdtpldt0(v8, v5) = v7 & sdtpldt0(v3, v4) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = v5 | v3 = sz00 |  ~ (sdtsldt0(v4, v3) = v5) |  ~ (sdtasdt0(v3, v6) = v4) |  ~ doDivides0(v3, v4) |  ~ aNaturalNumber0(v6) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = v5 |  ~ (sdtmndt0(v4, v3) = v5) |  ~ (sdtpldt0(v3, v6) = v4) |  ~ sdtlseqdt0(v3, v4) |  ~ aNaturalNumber0(v6) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = v4 | v3 = sz00 |  ~ (sdtsldt0(v4, v3) = v5) |  ~ (sdtasdt0(v3, v5) = v6) |  ~ doDivides0(v3, v4) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = v4 |  ~ (sdtmndt0(v4, v3) = v5) |  ~ (sdtpldt0(v3, v5) = v6) |  ~ sdtlseqdt0(v3, v4) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 | v3 = sz00 |  ~ (sdtasdt0(v5, v3) = v6) |  ~ (sdtasdt0(v4, v3) = v6) |  ~ sdtlseqdt0(v4, v5) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 | v3 = sz00 |  ~ (sdtasdt0(v5, v3) = v6) |  ~ (sdtasdt0(v4, v3) = v6) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 | v3 = sz00 |  ~ (sdtasdt0(v3, v5) = v6) |  ~ (sdtasdt0(v3, v4) = v6) |  ~ sdtlseqdt0(v4, v5) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 | v3 = sz00 |  ~ (sdtasdt0(v3, v5) = v6) |  ~ (sdtasdt0(v3, v4) = v6) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (sdtpldt0(v5, v3) = v6) |  ~ (sdtpldt0(v4, v3) = v6) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (sdtpldt0(v3, v5) = v6) |  ~ (sdtpldt0(v3, v4) = v6) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (sdtsldt0(v6, v5) = v4) |  ~ (sdtsldt0(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (sdtmndt0(v6, v5) = v4) |  ~ (sdtmndt0(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (sdtasdt0(v6, v5) = v4) |  ~ (sdtasdt0(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (sdtpldt0(v6, v5) = v4) |  ~ (sdtpldt0(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (sdtpldt0(v5, v4) = v6) |  ~ sdtlseqdt0(v3, v4) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v7] :  ? [v8] :  ? [v9] : ( ~ (v9 = v8) &  ~ (v7 = v6) & sdtpldt0(v5, v3) = v7 & sdtpldt0(v4, v5) = v9 & sdtpldt0(v3, v5) = v8 & sdtlseqdt0(v8, v9) & sdtlseqdt0(v7, v6))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (sdtpldt0(v5, v3) = v6) |  ~ sdtlseqdt0(v3, v4) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v7] :  ? [v8] :  ? [v9] : ( ~ (v9 = v8) &  ~ (v7 = v6) & sdtpldt0(v5, v4) = v7 & sdtpldt0(v4, v5) = v9 & sdtpldt0(v3, v5) = v8 & sdtlseqdt0(v8, v9) & sdtlseqdt0(v6, v7))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (sdtpldt0(v4, v5) = v6) |  ~ sdtlseqdt0(v3, v4) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v7] :  ? [v8] :  ? [v9] : ( ~ (v9 = v6) &  ~ (v8 = v7) & sdtpldt0(v5, v4) = v8 & sdtpldt0(v5, v3) = v7 & sdtpldt0(v3, v5) = v9 & sdtlseqdt0(v9, v6) & sdtlseqdt0(v7, v8))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (sdtpldt0(v3, v5) = v6) |  ~ sdtlseqdt0(v3, v4) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v7] :  ? [v8] :  ? [v9] : ( ~ (v9 = v6) &  ~ (v8 = v7) & sdtpldt0(v5, v4) = v8 & sdtpldt0(v5, v3) = v7 & sdtpldt0(v4, v5) = v9 & sdtlseqdt0(v7, v8) & sdtlseqdt0(v6, v9))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v3 = sz00 |  ~ (sdtsldt0(v4, v3) = v5) |  ~ (sdtasdt0(v3, v5) = v6) |  ~ doDivides0(v3, v4) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | aNaturalNumber0(v5)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (sdtmndt0(v4, v3) = v5) |  ~ (sdtpldt0(v3, v5) = v6) |  ~ sdtlseqdt0(v3, v4) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | aNaturalNumber0(v5)) &  ! [v3] :  ! [v4] :  ! [v5] : (v3 = sz00 |  ~ (sdtasdt0(v4, v3) = v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | sdtlseqdt0(v4, v5)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (sdtasdt0(v4, v3) = v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | sdtasdt0(v3, v4) = v5) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (sdtasdt0(v3, v5) = v4) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | doDivides0(v3, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (sdtasdt0(v3, v4) = v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | sdtasdt0(v4, v3) = v5) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (sdtasdt0(v3, v4) = v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | aNaturalNumber0(v5)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (sdtpldt0(v4, v3) = v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | sdtpldt0(v3, v4) = v5) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (sdtpldt0(v3, v5) = v4) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | sdtlseqdt0(v3, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (sdtpldt0(v3, v4) = v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | sdtpldt0(v4, v3) = v5) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (sdtpldt0(v3, v4) = v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | aNaturalNumber0(v5)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ doDivides0(v4, v5) |  ~ doDivides0(v3, v4) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | doDivides0(v3, v5)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ sdtlseqdt0(v4, v5) |  ~ sdtlseqdt0(v3, v4) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | sdtlseqdt0(v3, v5)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (sdtasdt0(v3, sz10) = v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (sdtasdt0(sz10, v3) = v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (sdtpldt0(v3, sz00) = v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (sdtpldt0(sz00, v3) = v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ sdtlseqdt0(v4, v3) |  ~ sdtlseqdt0(v3, v4) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ sdtlseqdt0(v3, v4) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | iLess0(v3, v4)) &  ! [v3] :  ! [v4] : (v4 = sz00 | v3 = sz00 |  ~ (sdtasdt0(v3, v4) = sz00) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] : (v4 = sz00 |  ~ (sdtasdt0(v3, sz00) = v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] : (v4 = sz00 |  ~ (sdtasdt0(sz00, v3) = v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] : (v4 = sz00 |  ~ (sdtpldt0(v3, v4) = sz00) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] : (v3 = sz00 |  ~ (sdtpldt0(v3, v4) = sz00) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] : ( ~ (sdtasdt0(v3, sz10) = v4) |  ~ aNaturalNumber0(v3) | sdtasdt0(sz10, v3) = v3) &  ! [v3] :  ! [v4] : ( ~ (sdtasdt0(v3, sz00) = v4) |  ~ aNaturalNumber0(v3) | sdtasdt0(sz00, v3) = sz00) &  ! [v3] :  ! [v4] : ( ~ (sdtasdt0(sz10, v3) = v4) |  ~ aNaturalNumber0(v3) | sdtasdt0(v3, sz10) = v3) &  ! [v3] :  ! [v4] : ( ~ (sdtasdt0(sz00, v3) = v4) |  ~ aNaturalNumber0(v3) | sdtasdt0(v3, sz00) = sz00) &  ! [v3] :  ! [v4] : ( ~ (sdtpldt0(v3, sz00) = v4) |  ~ aNaturalNumber0(v3) | sdtpldt0(sz00, v3) = v3) &  ! [v3] :  ! [v4] : ( ~ (sdtpldt0(sz00, v3) = v4) |  ~ aNaturalNumber0(v3) | sdtpldt0(v3, sz00) = v3) &  ! [v3] :  ! [v4] : ( ~ doDivides0(v3, v4) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v5] : (sdtasdt0(v3, v5) = v4 & aNaturalNumber0(v5))) &  ! [v3] :  ! [v4] : ( ~ sdtlseqdt0(v3, v4) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) |  ? [v5] : (sdtpldt0(v3, v5) = v4 & aNaturalNumber0(v5))) &  ! [v3] :  ! [v4] : ( ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | sdtlseqdt0(v4, v3) | sdtlseqdt0(v3, v4)) &  ! [v3] : (v3 = sz10 | v3 = sz00 |  ~ aNaturalNumber0(v3) | sdtlseqdt0(sz10, v3)) &  ! [v3] : ( ~ aNaturalNumber0(v3) | sdtlseqdt0(v3, v3)) &  ! [v3] : ( ~ aNaturalNumber0(v3) |  ? [v4] : ( ~ (v4 = v0) & sdtasdt0(xl, v3) = v4)))
% 14.95/4.14  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 14.95/4.14  | (1)  ~ (sz10 = sz00) & sdtasdt0(xl, all_0_0_0) = xm & sdtasdt0(xl, all_0_1_1) = xn & sdtpldt0(xm, xn) = all_0_2_2 & 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_2_2) &  ! [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_2_2) & sdtasdt0(xl, v0) = v1))
% 14.95/4.16  |
% 14.95/4.16  | Applying alpha-rule on (1) yields:
% 14.95/4.16  | (2)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 14.95/4.16  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtpldt0(v3, v2) = v1) |  ~ (sdtpldt0(v3, v2) = v0))
% 14.95/4.16  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v3) = v1) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v3) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 14.95/4.16  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 14.95/4.16  | (6)  ! [v0] :  ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0)
% 14.95/4.16  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 | v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v0, v2) = v3) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 14.95/4.16  | (8)  ! [v0] :  ! [v1] :  ! [v2] : (v0 = sz00 |  ~ (sdtasdt0(v1, v0) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 14.95/4.16  | (9)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtasdt0(v0, sz10) = v1) |  ~ aNaturalNumber0(v0))
% 14.95/4.16  | (10)  ! [v0] :  ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 14.95/4.16  | (11)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ sdtlseqdt0(v1, v0) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 14.95/4.16  | (12)  ! [v0] :  ! [v1] : ( ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 14.95/4.16  | (13)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtasdt0(sz10, v0) = v1) |  ~ aNaturalNumber0(v0))
% 14.95/4.16  | (14)  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ (sdtasdt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0))
% 14.95/4.16  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v2, v0) = v3) |  ~ (sdtasdt0(v1, v0) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 14.95/4.16  | (16) aNaturalNumber0(xn)
% 14.95/4.16  | (17)  ! [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))
% 14.95/4.16  | (18)  ! [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))
% 14.95/4.16  | (19)  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0)
% 14.95/4.16  | (20)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2)
% 14.95/4.16  | (21)  ! [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))
% 14.95/4.17  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v2) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 14.95/4.17  | (23) aNaturalNumber0(all_0_0_0)
% 14.95/4.17  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v0, v2) = v3) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 14.95/4.17  | (25) aNaturalNumber0(xl)
% 14.95/4.17  | (26)  ! [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))
% 14.95/4.17  | (27)  ! [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)))
% 14.95/4.17  | (28)  ! [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)))
% 14.95/4.17  | (29)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 14.95/4.17  | (30)  ! [v0] :  ! [v1] : (v0 = sz00 |  ~ (sdtpldt0(v0, v1) = sz00) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 14.95/4.17  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 |  ~ (sdtpldt0(v0, v2) = v3) |  ~ (sdtpldt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 14.95/4.17  | (32)  ! [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)))
% 14.95/4.17  | (33)  ! [v0] :  ! [v1] : ( ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 14.95/4.17  | (34) doDivides0(xl, xn)
% 14.95/4.17  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v2) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 14.95/4.17  | (36)  ! [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))
% 14.95/4.17  | (37)  ! [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))
% 14.95/4.17  | (38)  ! [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))
% 14.95/4.17  | (39)  ! [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))
% 14.95/4.17  | (40) sdtasdt0(xl, all_0_0_0) = xm
% 14.95/4.17  | (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)))
% 14.95/4.17  | (42)  ! [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))
% 14.95/4.17  | (43)  ! [v0] : (v0 = sz10 | v0 = sz00 |  ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 14.95/4.17  | (44) aNaturalNumber0(sz10)
% 14.95/4.17  | (45)  ! [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)))
% 14.95/4.17  | (46) aNaturalNumber0(sz00)
% 14.95/4.17  | (47)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtasdt0(v3, v2) = v1) |  ~ (sdtasdt0(v3, v2) = v0))
% 14.95/4.17  | (48)  ! [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))
% 14.95/4.17  | (49)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2)
% 14.95/4.17  | (50)  ! [v0] :  ! [v1] : ( ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 14.95/4.17  | (51)  ! [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))
% 14.95/4.17  | (52)  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 14.95/4.18  | (53)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 14.95/4.18  | (54)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 14.95/4.18  | (55)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 14.95/4.18  | (56)  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 14.95/4.18  | (57)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 |  ~ (sdtpldt0(v2, v0) = v3) |  ~ (sdtpldt0(v1, v0) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 14.95/4.18  | (58)  ~ (sz10 = sz00)
% 14.95/4.18  | (59)  ! [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))
% 14.95/4.18  | (60)  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ (sdtasdt0(v0, sz00) = v1) |  ~ aNaturalNumber0(v0))
% 14.95/4.18  | (61)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v0, v2) = v3) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 14.95/4.18  | (62) doDivides0(xl, xm)
% 14.95/4.18  | (63)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtmndt0(v3, v2) = v1) |  ~ (sdtmndt0(v3, v2) = v0))
% 14.95/4.18  | (64)  ! [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))
% 14.95/4.18  | (65)  ~ doDivides0(xl, all_0_2_2)
% 14.95/4.18  | (66) sdtasdt0(xl, all_0_1_1) = xn
% 14.95/4.18  | (67) aNaturalNumber0(xm)
% 14.95/4.18  | (68)  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ (sdtpldt0(v0, v1) = sz00) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 14.95/4.18  | (69)  ! [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)))
% 14.95/4.18  | (70)  ! [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))
% 14.95/4.18  | (71) aNaturalNumber0(all_0_1_1)
% 14.95/4.18  | (72)  ! [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))
% 14.95/4.18  | (73)  ! [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)))
% 14.95/4.18  | (74)  ! [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))
% 14.95/4.18  | (75)  ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 14.95/4.18  | (76)  ! [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)))
% 14.95/4.18  | (77)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ doDivides0(v1, v2) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 14.95/4.18  | (78)  ! [v0] :  ! [v1] : (v1 = sz00 | v0 = sz00 |  ~ (sdtasdt0(v0, v1) = sz00) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 14.95/4.18  | (79)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtsldt0(v3, v2) = v1) |  ~ (sdtsldt0(v3, v2) = v0))
% 14.95/4.18  | (80)  ! [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))
% 14.95/4.18  | (81)  ! [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))
% 14.95/4.18  | (82)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtpldt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0))
% 14.95/4.18  | (83)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 14.95/4.19  | (84)  ! [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))
% 14.95/4.19  | (85) sdtpldt0(xm, xn) = all_0_2_2
% 14.95/4.19  | (86)  ! [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))
% 14.95/4.19  | (87)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ sdtlseqdt0(v1, v2) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 14.95/4.19  | (88)  ! [v0] : ( ~ aNaturalNumber0(v0) |  ? [v1] : ( ~ (v1 = all_0_2_2) & sdtasdt0(xl, v0) = v1))
% 14.95/4.19  | (89)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtpldt0(v0, sz00) = v1) |  ~ aNaturalNumber0(v0))
% 14.95/4.19  | (90)  ! [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))
% 14.95/4.19  | (91)  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00)
% 14.95/4.19  |
% 14.95/4.19  | Instantiating formula (88) with all_0_0_0 and discharging atoms aNaturalNumber0(all_0_0_0), yields:
% 14.95/4.19  | (92)  ? [v0] : ( ~ (v0 = all_0_2_2) & sdtasdt0(xl, all_0_0_0) = v0)
% 14.95/4.19  |
% 14.95/4.19  | Instantiating formula (88) with all_0_1_1 and discharging atoms aNaturalNumber0(all_0_1_1), yields:
% 14.95/4.19  | (93)  ? [v0] : ( ~ (v0 = all_0_2_2) & sdtasdt0(xl, all_0_1_1) = v0)
% 14.95/4.19  |
% 14.95/4.19  | Instantiating formula (20) with all_0_2_2, xm, xn and discharging atoms sdtpldt0(xm, xn) = all_0_2_2, aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 14.95/4.19  | (94) sdtpldt0(xn, xm) = all_0_2_2
% 14.95/4.19  |
% 14.95/4.19  | Instantiating formula (5) with all_0_2_2, xn, xm and discharging atoms sdtpldt0(xm, xn) = all_0_2_2, aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 14.95/4.19  | (95) aNaturalNumber0(all_0_2_2)
% 14.95/4.19  |
% 14.95/4.19  | Instantiating formula (49) 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:
% 14.95/4.19  | (96) sdtasdt0(all_0_0_0, xl) = xm
% 14.95/4.19  |
% 14.95/4.19  | Instantiating formula (17) with all_0_2_2, 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_2_2, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 14.95/4.19  | (97)  ? [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_2_2 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_0_0_0, all_0_1_1) = v0)
% 14.95/4.19  |
% 14.95/4.19  | Instantiating formula (49) 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:
% 14.95/4.19  | (98) sdtasdt0(all_0_1_1, xl) = xn
% 14.95/4.19  |
% 14.95/4.19  | Instantiating formula (12) with xn, xl and discharging atoms doDivides0(xl, xn), aNaturalNumber0(xn), aNaturalNumber0(xl), yields:
% 14.95/4.19  | (99)  ? [v0] : (sdtasdt0(xl, v0) = xn & aNaturalNumber0(v0))
% 14.95/4.19  |
% 14.95/4.19  | Instantiating formula (12) with xm, xl and discharging atoms doDivides0(xl, xm), aNaturalNumber0(xm), aNaturalNumber0(xl), yields:
% 14.95/4.19  | (100)  ? [v0] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0))
% 14.95/4.19  |
% 14.95/4.19  | Instantiating formula (88) with sz10 and discharging atoms aNaturalNumber0(sz10), yields:
% 14.95/4.19  | (101)  ? [v0] : ( ~ (v0 = all_0_2_2) & sdtasdt0(xl, sz10) = v0)
% 14.95/4.19  |
% 14.95/4.19  | Instantiating (92) with all_9_0_3 yields:
% 14.95/4.19  | (102)  ~ (all_9_0_3 = all_0_2_2) & sdtasdt0(xl, all_0_0_0) = all_9_0_3
% 14.95/4.19  |
% 14.95/4.19  | Applying alpha-rule on (102) yields:
% 14.95/4.19  | (103)  ~ (all_9_0_3 = all_0_2_2)
% 14.95/4.19  | (104) sdtasdt0(xl, all_0_0_0) = all_9_0_3
% 14.95/4.19  |
% 14.95/4.19  | Instantiating (100) with all_11_0_4 yields:
% 14.95/4.19  | (105) sdtasdt0(xl, all_11_0_4) = xm & aNaturalNumber0(all_11_0_4)
% 14.95/4.19  |
% 14.95/4.19  | Applying alpha-rule on (105) yields:
% 14.95/4.19  | (106) sdtasdt0(xl, all_11_0_4) = xm
% 14.95/4.19  | (107) aNaturalNumber0(all_11_0_4)
% 14.95/4.19  |
% 14.95/4.19  | Instantiating (93) with all_13_0_5 yields:
% 14.95/4.19  | (108)  ~ (all_13_0_5 = all_0_2_2) & sdtasdt0(xl, all_0_1_1) = all_13_0_5
% 14.95/4.19  |
% 14.95/4.19  | Applying alpha-rule on (108) yields:
% 14.95/4.19  | (109)  ~ (all_13_0_5 = all_0_2_2)
% 14.95/4.19  | (110) sdtasdt0(xl, all_0_1_1) = all_13_0_5
% 14.95/4.19  |
% 14.95/4.19  | Instantiating (99) with all_15_0_6 yields:
% 14.95/4.19  | (111) sdtasdt0(xl, all_15_0_6) = xn & aNaturalNumber0(all_15_0_6)
% 14.95/4.19  |
% 14.95/4.19  | Applying alpha-rule on (111) yields:
% 14.95/4.19  | (112) sdtasdt0(xl, all_15_0_6) = xn
% 14.95/4.19  | (113) aNaturalNumber0(all_15_0_6)
% 14.95/4.19  |
% 14.95/4.19  | Instantiating (97) with all_19_0_8, all_19_1_9, all_19_2_10, all_19_3_11 yields:
% 14.95/4.19  | (114) sdtasdt0(all_19_3_11, xl) = all_19_2_10 & sdtasdt0(all_0_0_0, xl) = all_19_1_9 & sdtasdt0(all_0_1_1, xl) = all_19_0_8 & sdtasdt0(xl, all_19_3_11) = all_0_2_2 & sdtpldt0(all_19_1_9, all_19_0_8) = all_19_2_10 & sdtpldt0(all_0_0_0, all_0_1_1) = all_19_3_11
% 14.95/4.19  |
% 14.95/4.19  | Applying alpha-rule on (114) yields:
% 14.95/4.19  | (115) sdtasdt0(xl, all_19_3_11) = all_0_2_2
% 14.95/4.19  | (116) sdtasdt0(all_0_0_0, xl) = all_19_1_9
% 14.95/4.19  | (117) sdtasdt0(all_19_3_11, xl) = all_19_2_10
% 14.95/4.19  | (118) sdtasdt0(all_0_1_1, xl) = all_19_0_8
% 14.95/4.19  | (119) sdtpldt0(all_0_0_0, all_0_1_1) = all_19_3_11
% 14.95/4.19  | (120) sdtpldt0(all_19_1_9, all_19_0_8) = all_19_2_10
% 14.95/4.19  |
% 14.95/4.19  | Instantiating (101) with all_23_0_13 yields:
% 14.95/4.19  | (121)  ~ (all_23_0_13 = all_0_2_2) & sdtasdt0(xl, sz10) = all_23_0_13
% 14.95/4.19  |
% 14.95/4.19  | Applying alpha-rule on (121) yields:
% 14.95/4.19  | (122)  ~ (all_23_0_13 = all_0_2_2)
% 14.95/4.19  | (123) sdtasdt0(xl, sz10) = all_23_0_13
% 14.95/4.19  |
% 14.95/4.19  | Instantiating formula (47) with all_0_0_0, xl, xm, all_19_1_9 and discharging atoms sdtasdt0(all_0_0_0, xl) = all_19_1_9, sdtasdt0(all_0_0_0, xl) = xm, yields:
% 14.95/4.19  | (124) all_19_1_9 = xm
% 14.95/4.19  |
% 14.95/4.19  | Instantiating formula (47) with all_0_1_1, xl, xn, all_19_0_8 and discharging atoms sdtasdt0(all_0_1_1, xl) = all_19_0_8, sdtasdt0(all_0_1_1, xl) = xn, yields:
% 14.95/4.19  | (125) all_19_0_8 = xn
% 14.95/4.19  |
% 14.95/4.19  | Instantiating formula (47) with xl, all_0_0_0, all_9_0_3, xm and discharging atoms sdtasdt0(xl, all_0_0_0) = all_9_0_3, sdtasdt0(xl, all_0_0_0) = xm, yields:
% 14.95/4.19  | (126) all_9_0_3 = xm
% 14.95/4.20  |
% 14.95/4.20  | Instantiating formula (47) with xl, all_0_1_1, all_13_0_5, xn and discharging atoms sdtasdt0(xl, all_0_1_1) = all_13_0_5, sdtasdt0(xl, all_0_1_1) = xn, yields:
% 14.95/4.20  | (127) all_13_0_5 = xn
% 14.95/4.20  |
% 14.95/4.20  | Instantiating formula (9) with all_23_0_13, xl and discharging atoms sdtasdt0(xl, sz10) = all_23_0_13, aNaturalNumber0(xl), yields:
% 14.95/4.20  | (128) all_23_0_13 = xl
% 14.95/4.20  |
% 14.95/4.20  | From (124) and (116) follows:
% 14.95/4.20  | (96) sdtasdt0(all_0_0_0, xl) = xm
% 14.95/4.20  |
% 14.95/4.20  | From (125) and (118) follows:
% 14.95/4.20  | (98) sdtasdt0(all_0_1_1, xl) = xn
% 14.95/4.20  |
% 14.95/4.20  | From (126) and (104) follows:
% 14.95/4.20  | (40) sdtasdt0(xl, all_0_0_0) = xm
% 14.95/4.20  |
% 14.95/4.20  | From (127) and (110) follows:
% 14.95/4.20  | (66) sdtasdt0(xl, all_0_1_1) = xn
% 14.95/4.20  |
% 14.95/4.20  | From (128) and (123) follows:
% 14.95/4.20  | (133) sdtasdt0(xl, sz10) = xl
% 14.95/4.20  |
% 14.95/4.20  | From (124)(125) and (120) follows:
% 14.95/4.20  | (134) sdtpldt0(xm, xn) = all_19_2_10
% 14.95/4.20  |
% 14.95/4.20  | Instantiating formula (3) with xm, xn, all_19_2_10, all_0_2_2 and discharging atoms sdtpldt0(xm, xn) = all_19_2_10, sdtpldt0(xm, xn) = all_0_2_2, yields:
% 14.95/4.20  | (135) all_19_2_10 = all_0_2_2
% 14.95/4.20  |
% 14.95/4.20  | From (135) and (134) follows:
% 14.95/4.20  | (85) sdtpldt0(xm, xn) = all_0_2_2
% 14.95/4.20  |
% 14.95/4.20  | Instantiating formula (72) 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:
% 14.95/4.20  | (137)  ? [v0] : (sdtasdt0(v0, sz10) = xn & sdtasdt0(all_0_1_1, xl) = v0)
% 14.95/4.20  |
% 14.95/4.20  | Instantiating formula (20) with all_19_3_11, all_0_0_0, all_0_1_1 and discharging atoms sdtpldt0(all_0_0_0, all_0_1_1) = all_19_3_11, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_1_1), yields:
% 14.95/4.20  | (138) sdtpldt0(all_0_1_1, all_0_0_0) = all_19_3_11
% 14.95/4.20  |
% 14.95/4.20  | Instantiating formula (5) with all_19_3_11, all_0_1_1, all_0_0_0 and discharging atoms sdtpldt0(all_0_0_0, all_0_1_1) = all_19_3_11, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_1_1), yields:
% 14.95/4.20  | (139) aNaturalNumber0(all_19_3_11)
% 14.95/4.20  |
% 14.95/4.20  | Instantiating formula (17) with all_0_2_2, 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_2_2, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 14.95/4.20  | (140)  ? [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_2_2 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_0_1_1, all_0_0_0) = v0)
% 14.95/4.20  |
% 14.95/4.20  | Instantiating formula (86) with all_0_2_2, 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_2_2, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 14.95/4.20  | (141)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, xl) = all_0_2_2 & 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)
% 14.95/4.20  |
% 14.95/4.20  | Instantiating formula (17) with all_0_2_2, xm, xn, all_0_0_0, all_15_0_6, xl and discharging atoms sdtasdt0(xl, all_15_0_6) = xn, sdtasdt0(xl, all_0_0_0) = xm, sdtpldt0(xn, xm) = all_0_2_2, aNaturalNumber0(all_15_0_6), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), yields:
% 14.95/4.20  | (142)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_15_0_6, xl) = v2 & sdtasdt0(all_0_0_0, xl) = v3 & sdtasdt0(xl, v0) = all_0_2_2 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_15_0_6, all_0_0_0) = v0)
% 14.95/4.20  |
% 14.95/4.20  | Instantiating formula (17) with all_0_2_2, xn, xm, all_15_0_6, all_0_0_0, xl and discharging atoms sdtasdt0(xl, all_15_0_6) = xn, sdtasdt0(xl, all_0_0_0) = xm, sdtpldt0(xm, xn) = all_0_2_2, aNaturalNumber0(all_15_0_6), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), yields:
% 14.95/4.20  | (143)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_15_0_6, xl) = v3 & sdtasdt0(all_0_0_0, xl) = v2 & sdtasdt0(xl, v0) = all_0_2_2 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_0_0_0, all_15_0_6) = v0)
% 14.95/4.20  |
% 14.95/4.20  | Instantiating formula (49) with xn, xl, all_15_0_6 and discharging atoms sdtasdt0(xl, all_15_0_6) = xn, aNaturalNumber0(all_15_0_6), aNaturalNumber0(xl), yields:
% 14.95/4.20  | (144) sdtasdt0(all_15_0_6, xl) = xn
% 14.95/4.20  |
% 14.95/4.20  | Instantiating formula (17) with all_0_2_2, xn, xm, all_0_1_1, all_11_0_4, xl and discharging atoms sdtasdt0(xl, all_11_0_4) = xm, sdtasdt0(xl, all_0_1_1) = xn, sdtpldt0(xm, xn) = all_0_2_2, aNaturalNumber0(all_11_0_4), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 14.95/4.20  | (145)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_11_0_4, xl) = v2 & sdtasdt0(all_0_1_1, xl) = v3 & sdtasdt0(xl, v0) = all_0_2_2 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_11_0_4, all_0_1_1) = v0)
% 14.95/4.20  |
% 14.95/4.20  | Instantiating formula (17) with all_0_2_2, xn, xm, all_15_0_6, all_11_0_4, xl and discharging atoms sdtasdt0(xl, all_15_0_6) = xn, sdtasdt0(xl, all_11_0_4) = xm, sdtpldt0(xm, xn) = all_0_2_2, aNaturalNumber0(all_15_0_6), aNaturalNumber0(all_11_0_4), aNaturalNumber0(xl), yields:
% 14.95/4.20  | (146)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_15_0_6, xl) = v3 & sdtasdt0(all_11_0_4, xl) = v2 & sdtasdt0(xl, v0) = all_0_2_2 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_11_0_4, all_15_0_6) = v0)
% 14.95/4.20  |
% 14.95/4.20  | Instantiating formula (17) with all_0_2_2, xm, xn, all_11_0_4, all_0_1_1, xl and discharging atoms sdtasdt0(xl, all_11_0_4) = xm, sdtasdt0(xl, all_0_1_1) = xn, sdtpldt0(xn, xm) = all_0_2_2, aNaturalNumber0(all_11_0_4), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 14.95/4.20  | (147)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_11_0_4, xl) = v3 & sdtasdt0(all_0_1_1, xl) = v2 & sdtasdt0(xl, v0) = all_0_2_2 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_0_1_1, all_11_0_4) = v0)
% 14.95/4.20  |
% 14.95/4.20  | Instantiating formula (17) with all_0_2_2, xm, xn, all_11_0_4, all_15_0_6, xl and discharging atoms sdtasdt0(xl, all_15_0_6) = xn, sdtasdt0(xl, all_11_0_4) = xm, sdtpldt0(xn, xm) = all_0_2_2, aNaturalNumber0(all_15_0_6), aNaturalNumber0(all_11_0_4), aNaturalNumber0(xl), yields:
% 14.95/4.20  | (148)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_15_0_6, xl) = v2 & sdtasdt0(all_11_0_4, xl) = v3 & sdtasdt0(xl, v0) = all_0_2_2 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_15_0_6, all_11_0_4) = v0)
% 14.95/4.20  |
% 14.95/4.20  | Instantiating formula (49) with xm, xl, all_11_0_4 and discharging atoms sdtasdt0(xl, all_11_0_4) = xm, aNaturalNumber0(all_11_0_4), aNaturalNumber0(xl), yields:
% 14.95/4.20  | (149) sdtasdt0(all_11_0_4, xl) = xm
% 14.95/4.20  |
% 14.95/4.20  | Instantiating (137) with all_45_0_17 yields:
% 14.95/4.20  | (150) sdtasdt0(all_45_0_17, sz10) = xn & sdtasdt0(all_0_1_1, xl) = all_45_0_17
% 14.95/4.20  |
% 14.95/4.20  | Applying alpha-rule on (150) yields:
% 14.95/4.20  | (151) sdtasdt0(all_45_0_17, sz10) = xn
% 14.95/4.21  | (152) sdtasdt0(all_0_1_1, xl) = all_45_0_17
% 14.95/4.21  |
% 14.95/4.21  | Instantiating (148) with all_57_0_23, all_57_1_24, all_57_2_25, all_57_3_26 yields:
% 14.95/4.21  | (153) sdtasdt0(all_57_3_26, xl) = all_57_2_25 & sdtasdt0(all_15_0_6, xl) = all_57_1_24 & sdtasdt0(all_11_0_4, xl) = all_57_0_23 & sdtasdt0(xl, all_57_3_26) = all_0_2_2 & sdtpldt0(all_57_1_24, all_57_0_23) = all_57_2_25 & sdtpldt0(all_15_0_6, all_11_0_4) = all_57_3_26
% 14.95/4.21  |
% 14.95/4.21  | Applying alpha-rule on (153) yields:
% 14.95/4.21  | (154) sdtpldt0(all_57_1_24, all_57_0_23) = all_57_2_25
% 14.95/4.21  | (155) sdtasdt0(all_11_0_4, xl) = all_57_0_23
% 14.95/4.21  | (156) sdtasdt0(all_57_3_26, xl) = all_57_2_25
% 14.95/4.21  | (157) sdtpldt0(all_15_0_6, all_11_0_4) = all_57_3_26
% 14.95/4.21  | (158) sdtasdt0(all_15_0_6, xl) = all_57_1_24
% 14.95/4.21  | (159) sdtasdt0(xl, all_57_3_26) = all_0_2_2
% 14.95/4.21  |
% 14.95/4.21  | Instantiating (145) with all_59_0_27, all_59_1_28, all_59_2_29, all_59_3_30 yields:
% 14.95/4.21  | (160) sdtasdt0(all_59_3_30, xl) = all_59_2_29 & sdtasdt0(all_11_0_4, xl) = all_59_1_28 & sdtasdt0(all_0_1_1, xl) = all_59_0_27 & sdtasdt0(xl, all_59_3_30) = all_0_2_2 & sdtpldt0(all_59_1_28, all_59_0_27) = all_59_2_29 & sdtpldt0(all_11_0_4, all_0_1_1) = all_59_3_30
% 14.95/4.21  |
% 14.95/4.21  | Applying alpha-rule on (160) yields:
% 14.95/4.21  | (161) sdtpldt0(all_11_0_4, all_0_1_1) = all_59_3_30
% 14.95/4.21  | (162) sdtasdt0(all_0_1_1, xl) = all_59_0_27
% 14.95/4.21  | (163) sdtasdt0(all_59_3_30, xl) = all_59_2_29
% 14.95/4.21  | (164) sdtasdt0(xl, all_59_3_30) = all_0_2_2
% 14.95/4.21  | (165) sdtasdt0(all_11_0_4, xl) = all_59_1_28
% 14.95/4.21  | (166) sdtpldt0(all_59_1_28, all_59_0_27) = all_59_2_29
% 14.95/4.21  |
% 14.95/4.21  | Instantiating (146) with all_65_0_33, all_65_1_34, all_65_2_35, all_65_3_36 yields:
% 14.95/4.21  | (167) sdtasdt0(all_65_3_36, xl) = all_65_2_35 & sdtasdt0(all_15_0_6, xl) = all_65_0_33 & sdtasdt0(all_11_0_4, xl) = all_65_1_34 & sdtasdt0(xl, all_65_3_36) = all_0_2_2 & sdtpldt0(all_65_1_34, all_65_0_33) = all_65_2_35 & sdtpldt0(all_11_0_4, all_15_0_6) = all_65_3_36
% 14.95/4.21  |
% 14.95/4.21  | Applying alpha-rule on (167) yields:
% 14.95/4.21  | (168) sdtasdt0(xl, all_65_3_36) = all_0_2_2
% 14.95/4.21  | (169) sdtasdt0(all_65_3_36, xl) = all_65_2_35
% 14.95/4.21  | (170) sdtpldt0(all_11_0_4, all_15_0_6) = all_65_3_36
% 14.95/4.21  | (171) sdtasdt0(all_15_0_6, xl) = all_65_0_33
% 14.95/4.21  | (172) sdtpldt0(all_65_1_34, all_65_0_33) = all_65_2_35
% 14.95/4.21  | (173) sdtasdt0(all_11_0_4, xl) = all_65_1_34
% 14.95/4.21  |
% 14.95/4.21  | Instantiating (140) with all_85_0_46, all_85_1_47, all_85_2_48, all_85_3_49 yields:
% 14.95/4.21  | (174) sdtasdt0(all_85_3_49, xl) = all_85_2_48 & sdtasdt0(all_0_0_0, xl) = all_85_0_46 & sdtasdt0(all_0_1_1, xl) = all_85_1_47 & sdtasdt0(xl, all_85_3_49) = all_0_2_2 & sdtpldt0(all_85_1_47, all_85_0_46) = all_85_2_48 & sdtpldt0(all_0_1_1, all_0_0_0) = all_85_3_49
% 14.95/4.21  |
% 14.95/4.21  | Applying alpha-rule on (174) yields:
% 14.95/4.21  | (175) sdtasdt0(all_0_0_0, xl) = all_85_0_46
% 14.95/4.21  | (176) sdtasdt0(xl, all_85_3_49) = all_0_2_2
% 14.95/4.21  | (177) sdtpldt0(all_85_1_47, all_85_0_46) = all_85_2_48
% 15.29/4.21  | (178) sdtasdt0(all_85_3_49, xl) = all_85_2_48
% 15.29/4.21  | (179) sdtpldt0(all_0_1_1, all_0_0_0) = all_85_3_49
% 15.29/4.21  | (180) sdtasdt0(all_0_1_1, xl) = all_85_1_47
% 15.29/4.21  |
% 15.29/4.21  | Instantiating (143) with all_93_0_53, all_93_1_54, all_93_2_55, all_93_3_56 yields:
% 15.29/4.21  | (181) sdtasdt0(all_93_3_56, xl) = all_93_2_55 & sdtasdt0(all_15_0_6, xl) = all_93_0_53 & sdtasdt0(all_0_0_0, xl) = all_93_1_54 & sdtasdt0(xl, all_93_3_56) = all_0_2_2 & sdtpldt0(all_93_1_54, all_93_0_53) = all_93_2_55 & sdtpldt0(all_0_0_0, all_15_0_6) = all_93_3_56
% 15.29/4.21  |
% 15.29/4.21  | Applying alpha-rule on (181) yields:
% 15.29/4.21  | (182) sdtpldt0(all_0_0_0, all_15_0_6) = all_93_3_56
% 15.29/4.21  | (183) sdtasdt0(all_93_3_56, xl) = all_93_2_55
% 15.29/4.21  | (184) sdtasdt0(all_0_0_0, xl) = all_93_1_54
% 15.29/4.21  | (185) sdtasdt0(xl, all_93_3_56) = all_0_2_2
% 15.29/4.21  | (186) sdtasdt0(all_15_0_6, xl) = all_93_0_53
% 15.29/4.21  | (187) sdtpldt0(all_93_1_54, all_93_0_53) = all_93_2_55
% 15.29/4.21  |
% 15.29/4.21  | Instantiating (142) with all_95_0_57, all_95_1_58, all_95_2_59, all_95_3_60 yields:
% 15.29/4.21  | (188) sdtasdt0(all_95_3_60, xl) = all_95_2_59 & sdtasdt0(all_15_0_6, xl) = all_95_1_58 & sdtasdt0(all_0_0_0, xl) = all_95_0_57 & sdtasdt0(xl, all_95_3_60) = all_0_2_2 & sdtpldt0(all_95_1_58, all_95_0_57) = all_95_2_59 & sdtpldt0(all_15_0_6, all_0_0_0) = all_95_3_60
% 15.29/4.21  |
% 15.29/4.21  | Applying alpha-rule on (188) yields:
% 15.29/4.21  | (189) sdtasdt0(all_0_0_0, xl) = all_95_0_57
% 15.29/4.21  | (190) sdtasdt0(all_15_0_6, xl) = all_95_1_58
% 15.29/4.21  | (191) sdtpldt0(all_15_0_6, all_0_0_0) = all_95_3_60
% 15.29/4.21  | (192) sdtasdt0(xl, all_95_3_60) = all_0_2_2
% 15.29/4.21  | (193) sdtpldt0(all_95_1_58, all_95_0_57) = all_95_2_59
% 15.29/4.21  | (194) sdtasdt0(all_95_3_60, xl) = all_95_2_59
% 15.29/4.21  |
% 15.29/4.21  | Instantiating (141) with all_103_0_64, all_103_1_65, all_103_2_66, all_103_3_67 yields:
% 15.29/4.21  | (195) sdtasdt0(all_103_3_67, xl) = all_0_2_2 & sdtasdt0(xl, all_103_3_67) = all_103_2_66 & sdtasdt0(xl, all_0_0_0) = all_103_0_64 & sdtasdt0(xl, all_0_1_1) = all_103_1_65 & sdtpldt0(all_103_1_65, all_103_0_64) = all_103_2_66 & sdtpldt0(all_0_1_1, all_0_0_0) = all_103_3_67
% 15.29/4.21  |
% 15.29/4.21  | Applying alpha-rule on (195) yields:
% 15.29/4.21  | (196) sdtasdt0(xl, all_0_1_1) = all_103_1_65
% 15.29/4.21  | (197) sdtasdt0(all_103_3_67, xl) = all_0_2_2
% 15.29/4.21  | (198) sdtasdt0(xl, all_103_3_67) = all_103_2_66
% 15.29/4.21  | (199) sdtpldt0(all_103_1_65, all_103_0_64) = all_103_2_66
% 15.29/4.21  | (200) sdtpldt0(all_0_1_1, all_0_0_0) = all_103_3_67
% 15.29/4.21  | (201) sdtasdt0(xl, all_0_0_0) = all_103_0_64
% 15.29/4.21  |
% 15.29/4.21  | Instantiating (147) with all_105_0_68, all_105_1_69, all_105_2_70, all_105_3_71 yields:
% 15.29/4.21  | (202) sdtasdt0(all_105_3_71, xl) = all_105_2_70 & sdtasdt0(all_11_0_4, xl) = all_105_0_68 & sdtasdt0(all_0_1_1, xl) = all_105_1_69 & sdtasdt0(xl, all_105_3_71) = all_0_2_2 & sdtpldt0(all_105_1_69, all_105_0_68) = all_105_2_70 & sdtpldt0(all_0_1_1, all_11_0_4) = all_105_3_71
% 15.29/4.21  |
% 15.29/4.21  | Applying alpha-rule on (202) yields:
% 15.29/4.21  | (203) sdtasdt0(all_0_1_1, xl) = all_105_1_69
% 15.29/4.21  | (204) sdtasdt0(all_105_3_71, xl) = all_105_2_70
% 15.29/4.21  | (205) sdtasdt0(xl, all_105_3_71) = all_0_2_2
% 15.29/4.21  | (206) sdtasdt0(all_11_0_4, xl) = all_105_0_68
% 15.29/4.21  | (207) sdtpldt0(all_0_1_1, all_11_0_4) = all_105_3_71
% 15.29/4.21  | (208) sdtpldt0(all_105_1_69, all_105_0_68) = all_105_2_70
% 15.29/4.22  |
% 15.29/4.22  | Instantiating formula (47) with all_15_0_6, xl, all_93_0_53, all_95_1_58 and discharging atoms sdtasdt0(all_15_0_6, xl) = all_95_1_58, sdtasdt0(all_15_0_6, xl) = all_93_0_53, yields:
% 15.29/4.22  | (209) all_95_1_58 = all_93_0_53
% 15.29/4.22  |
% 15.29/4.22  | Instantiating formula (47) with all_15_0_6, xl, all_65_0_33, all_95_1_58 and discharging atoms sdtasdt0(all_15_0_6, xl) = all_95_1_58, sdtasdt0(all_15_0_6, xl) = all_65_0_33, yields:
% 15.29/4.22  | (210) all_95_1_58 = all_65_0_33
% 15.29/4.22  |
% 15.29/4.22  | Instantiating formula (47) with all_15_0_6, xl, all_57_1_24, all_65_0_33 and discharging atoms sdtasdt0(all_15_0_6, xl) = all_65_0_33, sdtasdt0(all_15_0_6, xl) = all_57_1_24, yields:
% 15.29/4.22  | (211) all_65_0_33 = all_57_1_24
% 15.29/4.22  |
% 15.29/4.22  | Instantiating formula (47) with all_15_0_6, xl, xn, all_95_1_58 and discharging atoms sdtasdt0(all_15_0_6, xl) = all_95_1_58, sdtasdt0(all_15_0_6, xl) = xn, yields:
% 15.29/4.22  | (212) all_95_1_58 = xn
% 15.29/4.22  |
% 15.29/4.22  | Instantiating formula (47) with all_11_0_4, xl, all_65_1_34, all_105_0_68 and discharging atoms sdtasdt0(all_11_0_4, xl) = all_105_0_68, sdtasdt0(all_11_0_4, xl) = all_65_1_34, yields:
% 15.29/4.22  | (213) all_105_0_68 = all_65_1_34
% 15.29/4.22  |
% 15.29/4.22  | Instantiating formula (47) with all_11_0_4, xl, all_59_1_28, all_105_0_68 and discharging atoms sdtasdt0(all_11_0_4, xl) = all_105_0_68, sdtasdt0(all_11_0_4, xl) = all_59_1_28, yields:
% 15.29/4.22  | (214) all_105_0_68 = all_59_1_28
% 15.29/4.22  |
% 15.29/4.22  | Instantiating formula (47) with all_11_0_4, xl, all_57_0_23, all_105_0_68 and discharging atoms sdtasdt0(all_11_0_4, xl) = all_105_0_68, sdtasdt0(all_11_0_4, xl) = all_57_0_23, yields:
% 15.29/4.22  | (215) all_105_0_68 = all_57_0_23
% 15.29/4.22  |
% 15.29/4.22  | Instantiating formula (47) with all_11_0_4, xl, xm, all_59_1_28 and discharging atoms sdtasdt0(all_11_0_4, xl) = all_59_1_28, sdtasdt0(all_11_0_4, xl) = xm, yields:
% 15.29/4.22  | (216) all_59_1_28 = xm
% 15.29/4.22  |
% 15.29/4.22  | Instantiating formula (47) with all_0_0_0, xl, all_95_0_57, xm and discharging atoms sdtasdt0(all_0_0_0, xl) = all_95_0_57, sdtasdt0(all_0_0_0, xl) = xm, yields:
% 15.29/4.22  | (217) all_95_0_57 = xm
% 15.29/4.22  |
% 15.29/4.22  | Instantiating formula (47) with all_0_0_0, xl, all_93_1_54, all_95_0_57 and discharging atoms sdtasdt0(all_0_0_0, xl) = all_95_0_57, sdtasdt0(all_0_0_0, xl) = all_93_1_54, yields:
% 15.29/4.22  | (218) all_95_0_57 = all_93_1_54
% 15.29/4.22  |
% 15.29/4.22  | Instantiating formula (47) with all_0_0_0, xl, all_85_0_46, all_93_1_54 and discharging atoms sdtasdt0(all_0_0_0, xl) = all_93_1_54, sdtasdt0(all_0_0_0, xl) = all_85_0_46, yields:
% 15.29/4.22  | (219) all_93_1_54 = all_85_0_46
% 15.29/4.22  |
% 15.29/4.22  | Instantiating formula (47) with all_0_1_1, xl, all_85_1_47, all_105_1_69 and discharging atoms sdtasdt0(all_0_1_1, xl) = all_105_1_69, sdtasdt0(all_0_1_1, xl) = all_85_1_47, yields:
% 15.29/4.22  | (220) all_105_1_69 = all_85_1_47
% 15.29/4.22  |
% 15.29/4.22  | Instantiating formula (47) with all_0_1_1, xl, all_59_0_27, xn and discharging atoms sdtasdt0(all_0_1_1, xl) = all_59_0_27, sdtasdt0(all_0_1_1, xl) = xn, yields:
% 15.29/4.22  | (221) all_59_0_27 = xn
% 15.29/4.22  |
% 15.29/4.22  | Instantiating formula (47) with all_0_1_1, xl, all_59_0_27, all_85_1_47 and discharging atoms sdtasdt0(all_0_1_1, xl) = all_85_1_47, sdtasdt0(all_0_1_1, xl) = all_59_0_27, yields:
% 15.29/4.22  | (222) all_85_1_47 = all_59_0_27
% 15.29/4.22  |
% 15.29/4.22  | Instantiating formula (47) with all_0_1_1, xl, all_45_0_17, all_105_1_69 and discharging atoms sdtasdt0(all_0_1_1, xl) = all_105_1_69, sdtasdt0(all_0_1_1, xl) = all_45_0_17, yields:
% 15.29/4.22  | (223) all_105_1_69 = all_45_0_17
% 15.29/4.22  |
% 15.29/4.22  | Instantiating formula (47) with xl, all_0_0_0, all_103_0_64, xm and discharging atoms sdtasdt0(xl, all_0_0_0) = all_103_0_64, sdtasdt0(xl, all_0_0_0) = xm, yields:
% 15.29/4.22  | (224) all_103_0_64 = xm
% 15.29/4.22  |
% 15.29/4.22  | Instantiating formula (47) with xl, all_0_1_1, all_103_1_65, xn and discharging atoms sdtasdt0(xl, all_0_1_1) = all_103_1_65, sdtasdt0(xl, all_0_1_1) = xn, yields:
% 15.29/4.22  | (225) all_103_1_65 = xn
% 15.29/4.22  |
% 15.29/4.22  | Instantiating formula (3) with all_0_1_1, all_0_0_0, all_19_3_11, all_103_3_67 and discharging atoms sdtpldt0(all_0_1_1, all_0_0_0) = all_103_3_67, sdtpldt0(all_0_1_1, all_0_0_0) = all_19_3_11, yields:
% 15.29/4.22  | (226) all_103_3_67 = all_19_3_11
% 15.29/4.22  |
% 15.29/4.22  | Combining equations (214,213) yields a new equation:
% 15.29/4.22  | (227) all_65_1_34 = all_59_1_28
% 15.29/4.22  |
% 15.29/4.22  | Combining equations (215,213) yields a new equation:
% 15.29/4.22  | (228) all_65_1_34 = all_57_0_23
% 15.29/4.22  |
% 15.29/4.22  | Combining equations (220,223) yields a new equation:
% 15.29/4.22  | (229) all_85_1_47 = all_45_0_17
% 15.29/4.22  |
% 15.29/4.22  | Simplifying 229 yields:
% 15.29/4.22  | (230) all_85_1_47 = all_45_0_17
% 15.29/4.22  |
% 15.29/4.22  | Combining equations (218,217) yields a new equation:
% 15.29/4.22  | (231) all_93_1_54 = xm
% 15.29/4.22  |
% 15.29/4.22  | Simplifying 231 yields:
% 15.29/4.22  | (232) all_93_1_54 = xm
% 15.29/4.22  |
% 15.29/4.22  | Combining equations (212,209) yields a new equation:
% 15.29/4.22  | (233) all_93_0_53 = xn
% 15.29/4.22  |
% 15.29/4.22  | Combining equations (210,209) yields a new equation:
% 15.29/4.22  | (234) all_93_0_53 = all_65_0_33
% 15.29/4.22  |
% 15.29/4.22  | Combining equations (234,233) yields a new equation:
% 15.29/4.22  | (235) all_65_0_33 = xn
% 15.29/4.22  |
% 15.29/4.22  | Simplifying 235 yields:
% 15.29/4.22  | (236) all_65_0_33 = xn
% 15.29/4.22  |
% 15.29/4.22  | Combining equations (219,232) yields a new equation:
% 15.29/4.22  | (237) all_85_0_46 = xm
% 15.29/4.22  |
% 15.29/4.22  | Simplifying 237 yields:
% 15.29/4.22  | (238) all_85_0_46 = xm
% 15.29/4.22  |
% 15.29/4.22  | Combining equations (222,230) yields a new equation:
% 15.29/4.22  | (239) all_59_0_27 = all_45_0_17
% 15.29/4.22  |
% 15.29/4.22  | Simplifying 239 yields:
% 15.29/4.22  | (240) all_59_0_27 = all_45_0_17
% 15.29/4.22  |
% 15.29/4.22  | Combining equations (211,236) yields a new equation:
% 15.29/4.22  | (241) all_57_1_24 = xn
% 15.29/4.22  |
% 15.29/4.22  | Simplifying 241 yields:
% 15.29/4.22  | (242) all_57_1_24 = xn
% 15.29/4.22  |
% 15.29/4.22  | Combining equations (227,228) yields a new equation:
% 15.29/4.22  | (243) all_59_1_28 = all_57_0_23
% 15.29/4.22  |
% 15.29/4.22  | Simplifying 243 yields:
% 15.29/4.22  | (244) all_59_1_28 = all_57_0_23
% 15.29/4.22  |
% 15.29/4.22  | Combining equations (240,221) yields a new equation:
% 15.29/4.22  | (245) all_45_0_17 = xn
% 15.29/4.22  |
% 15.29/4.22  | Simplifying 245 yields:
% 15.29/4.22  | (246) all_45_0_17 = xn
% 15.29/4.22  |
% 15.29/4.22  | Combining equations (216,244) yields a new equation:
% 15.29/4.22  | (247) all_57_0_23 = xm
% 15.29/4.22  |
% 15.29/4.22  | Combining equations (247,228) yields a new equation:
% 15.29/4.22  | (248) all_65_1_34 = xm
% 15.29/4.22  |
% 15.29/4.22  | Combining equations (246,230) yields a new equation:
% 15.29/4.22  | (249) all_85_1_47 = xn
% 15.29/4.22  |
% 15.29/4.22  | Combining equations (233,209) yields a new equation:
% 15.29/4.22  | (212) all_95_1_58 = xn
% 15.29/4.22  |
% 15.29/4.22  | Combining equations (246,223) yields a new equation:
% 15.29/4.22  | (251) all_105_1_69 = xn
% 15.29/4.22  |
% 15.29/4.22  | Combining equations (248,213) yields a new equation:
% 15.29/4.22  | (252) all_105_0_68 = xm
% 15.29/4.22  |
% 15.29/4.22  | From (226) and (198) follows:
% 15.29/4.23  | (253) sdtasdt0(xl, all_19_3_11) = all_103_2_66
% 15.29/4.23  |
% 15.29/4.23  | From (251)(252) and (208) follows:
% 15.29/4.23  | (254) sdtpldt0(xn, xm) = all_105_2_70
% 15.29/4.23  |
% 15.29/4.23  | From (225)(224) and (199) follows:
% 15.29/4.23  | (255) sdtpldt0(xn, xm) = all_103_2_66
% 15.29/4.23  |
% 15.29/4.23  | From (212)(217) and (193) follows:
% 15.29/4.23  | (256) sdtpldt0(xn, xm) = all_95_2_59
% 15.29/4.23  |
% 15.29/4.23  | From (249)(238) and (177) follows:
% 15.29/4.23  | (257) sdtpldt0(xn, xm) = all_85_2_48
% 15.29/4.23  |
% 15.29/4.23  | From (242)(247) and (154) follows:
% 15.29/4.23  | (258) sdtpldt0(xn, xm) = all_57_2_25
% 15.29/4.23  |
% 15.29/4.23  | Instantiating formula (3) with xn, xm, all_103_2_66, all_105_2_70 and discharging atoms sdtpldt0(xn, xm) = all_105_2_70, sdtpldt0(xn, xm) = all_103_2_66, yields:
% 15.29/4.23  | (259) all_105_2_70 = all_103_2_66
% 15.29/4.23  |
% 15.29/4.23  | Instantiating formula (3) with xn, xm, all_95_2_59, all_103_2_66 and discharging atoms sdtpldt0(xn, xm) = all_103_2_66, sdtpldt0(xn, xm) = all_95_2_59, yields:
% 15.29/4.23  | (260) all_103_2_66 = all_95_2_59
% 15.29/4.23  |
% 15.29/4.23  | Instantiating formula (3) with xn, xm, all_85_2_48, all_0_2_2 and discharging atoms sdtpldt0(xn, xm) = all_85_2_48, sdtpldt0(xn, xm) = all_0_2_2, yields:
% 15.29/4.23  | (261) all_85_2_48 = all_0_2_2
% 15.29/4.23  |
% 15.29/4.23  | Instantiating formula (3) with xn, xm, all_85_2_48, all_95_2_59 and discharging atoms sdtpldt0(xn, xm) = all_95_2_59, sdtpldt0(xn, xm) = all_85_2_48, yields:
% 15.29/4.23  | (262) all_95_2_59 = all_85_2_48
% 15.29/4.23  |
% 15.29/4.23  | Instantiating formula (3) with xn, xm, all_57_2_25, all_105_2_70 and discharging atoms sdtpldt0(xn, xm) = all_105_2_70, sdtpldt0(xn, xm) = all_57_2_25, yields:
% 15.29/4.23  | (263) all_105_2_70 = all_57_2_25
% 15.29/4.23  |
% 15.29/4.23  | Combining equations (259,263) yields a new equation:
% 15.29/4.23  | (264) all_103_2_66 = all_57_2_25
% 15.29/4.23  |
% 15.29/4.23  | Simplifying 264 yields:
% 15.29/4.23  | (265) all_103_2_66 = all_57_2_25
% 15.29/4.23  |
% 15.29/4.23  | Combining equations (260,265) yields a new equation:
% 15.29/4.23  | (266) all_95_2_59 = all_57_2_25
% 15.29/4.23  |
% 15.29/4.23  | Simplifying 266 yields:
% 15.29/4.23  | (267) all_95_2_59 = all_57_2_25
% 15.29/4.23  |
% 15.29/4.23  | Combining equations (262,267) yields a new equation:
% 15.29/4.23  | (268) all_85_2_48 = all_57_2_25
% 15.29/4.23  |
% 15.29/4.23  | Simplifying 268 yields:
% 15.29/4.23  | (269) all_85_2_48 = all_57_2_25
% 15.29/4.23  |
% 15.29/4.23  | Combining equations (269,261) yields a new equation:
% 15.29/4.23  | (270) all_57_2_25 = all_0_2_2
% 15.29/4.23  |
% 15.29/4.23  | Simplifying 270 yields:
% 15.29/4.23  | (271) all_57_2_25 = all_0_2_2
% 15.29/4.23  |
% 15.29/4.23  | Combining equations (271,265) yields a new equation:
% 15.29/4.23  | (272) all_103_2_66 = all_0_2_2
% 15.29/4.23  |
% 15.29/4.23  | From (272) and (253) follows:
% 15.29/4.23  | (115) sdtasdt0(xl, all_19_3_11) = all_0_2_2
% 15.29/4.23  |
% 15.29/4.23  | Instantiating formula (2) with all_19_3_11, all_0_2_2, xl and discharging atoms sdtasdt0(xl, all_19_3_11) = all_0_2_2, aNaturalNumber0(all_19_3_11), aNaturalNumber0(all_0_2_2), aNaturalNumber0(xl),  ~ doDivides0(xl, all_0_2_2), yields:
% 15.29/4.23  | (274) $false
% 15.29/4.23  |
% 15.29/4.23  |-The branch is then unsatisfiable
% 15.29/4.23  % SZS output end Proof for theBenchmark
% 15.29/4.23  
% 15.29/4.23  3613ms
%------------------------------------------------------------------------------