ePrincess---1.0.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : NUM487+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Mon Jul 18 08:45:01 EDT 2022

% Result   : Theorem 43.42s 16.61s
% Output   : Proof 82.81s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUM487+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.33  % Computer : n003.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Wed Jul  6 13:31:41 EDT 2022
% 0.13/0.33  % 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
% 0.19/0.58  (ePrincess v.1.0)
% 0.19/0.58  
% 0.19/0.58  (c) Philipp Rümmer, 2009-2015
% 0.19/0.58  (c) Peter Backeman, 2014-2015
% 0.19/0.58  (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/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
% 1.89/1.03  Prover 0: Preprocessing ...
% 3.87/1.53  Prover 0: Constructing countermodel ...
% 19.64/5.95  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 20.12/6.04  Prover 1: Preprocessing ...
% 20.52/6.20  Prover 1: Constructing countermodel ...
% 29.98/8.55  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 30.31/8.61  Prover 2: Preprocessing ...
% 30.67/8.78  Prover 2: Warning: ignoring some quantifiers
% 30.67/8.79  Prover 2: Constructing countermodel ...
% 36.68/11.56  Prover 0: stopped
% 36.99/11.76  Prover 3: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 36.99/11.79  Prover 3: Preprocessing ...
% 37.29/11.84  Prover 3: Constructing countermodel ...
% 43.33/16.61  Prover 3: proved (4845ms)
% 43.42/16.61  Prover 1: stopped
% 43.42/16.61  Prover 2: stopped
% 43.42/16.61  
% 43.42/16.61  No countermodel exists, formula is valid
% 43.42/16.61  % SZS status Theorem for theBenchmark
% 43.42/16.61  
% 43.42/16.61  Generating proof ... found it (size 804)
% 81.88/42.90  
% 81.88/42.90  % SZS output start Proof for theBenchmark
% 81.88/42.90  Assumed formulas after preprocessing and simplification: 
% 81.88/42.90  | (0)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (sz10 = sz00) & sdtmndt0(xn, xp) = xr & sdtasdt0(xn, xm) = v2 & sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) = v0 & isPrime0(xp) & doDivides0(xp, v2) & sdtlseqdt0(xp, xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) &  ~ isPrime0(sz10) &  ~ isPrime0(sz00) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v3 = sz00 |  ~ (sdtsldt0(v7, v3) = v8) |  ~ (sdtsldt0(v4, v3) = v5) |  ~ (sdtasdt0(v6, v4) = v7) |  ~ doDivides0(v3, v4) |  ~ aNaturalNumber0(v6) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | sdtasdt0(v6, v5) = v8) &  ! [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(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(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] : ( ~ (sdtpldt0(v6, v5) = v7) |  ~ (sdtpldt0(v3, v4) = v6) |  ~ isPrime0(v5) |  ~ iLess0(v7, v1) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | doDivides0(v5, v4) | doDivides0(v5, v3) |  ? [v8] : (sdtasdt0(v3, v4) = v8 &  ~ doDivides0(v5, v8))) &  ! [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] : (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(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(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(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] :  ! [v6] : ( ~ (sdtpldt0(v4, v5) = v6) |  ~ doDivides0(v3, v6) |  ~ doDivides0(v3, v4) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | doDivides0(v3, v5)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (sdtpldt0(v4, v5) = v6) |  ~ doDivides0(v3, v5) |  ~ doDivides0(v3, v4) |  ~ aNaturalNumber0(v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | doDivides0(v3, v6)) &  ! [v3] :  ! [v4] :  ! [v5] : (v3 = sz00 |  ~ (sdtasdt0(v4, v3) = v5) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | sdtlseqdt0(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(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 | v4 = sz10 |  ~ isPrime0(v3) |  ~ doDivides0(v4, v3) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (sdtasdt0(sz10, v3) = 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(sz00, v3) = v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] : (v4 = sz00 |  ~ (sdtpldt0(v3, v4) = sz00) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3)) &  ! [v3] :  ! [v4] : (v4 = sz00 |  ~ doDivides0(v3, v4) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3) | sdtlseqdt0(v3, v4)) &  ! [v3] :  ! [v4] : (v3 = sz00 |  ~ (sdtpldt0(v3, v4) = sz00) |  ~ aNaturalNumber0(v4) |  ~ aNaturalNumber0(v3)) &  ! [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(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) | isPrime0(v3) |  ? [v4] : ( ~ (v4 = v3) &  ~ (v4 = sz10) & doDivides0(v4, v3) & aNaturalNumber0(v4))) &  ! [v3] : (v3 = sz10 | v3 = sz00 |  ~ aNaturalNumber0(v3) | sdtlseqdt0(sz10, v3)) &  ! [v3] : (v3 = sz10 | v3 = sz00 |  ~ aNaturalNumber0(v3) |  ? [v4] : (isPrime0(v4) & doDivides0(v4, v3) & aNaturalNumber0(v4))) &  ! [v3] : ( ~ aNaturalNumber0(v3) | sdtlseqdt0(v3, v3)) & (xr = xn |  ~ sdtlseqdt0(xr, xn)))
% 81.88/42.96  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 81.88/42.96  | (1)  ~ (sz10 = sz00) & sdtmndt0(xn, xp) = xr & sdtasdt0(xn, xm) = all_0_0_0 & sdtpldt0(all_0_2_2, xp) = all_0_1_1 & sdtpldt0(xn, xm) = all_0_2_2 & isPrime0(xp) & doDivides0(xp, all_0_0_0) & sdtlseqdt0(xp, xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) &  ~ isPrime0(sz10) &  ~ isPrime0(sz00) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v0 = sz00 |  ~ (sdtsldt0(v4, v0) = v5) |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v3, v1) = v4) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v3) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v3, v2) = v5) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (sdtasdt0(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(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(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] : ( ~ (sdtpldt0(v3, v2) = v4) |  ~ (sdtpldt0(v0, v1) = v3) |  ~ isPrime0(v2) |  ~ iLess0(v4, all_0_1_1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) |  ? [v5] : (sdtasdt0(v0, v1) = v5 &  ~ doDivides0(v2, v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) |  ~ (sdtpldt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (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(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(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(v0, v2) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v6 = v3) &  ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v0, v2) = v3) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v2) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) |  ~ doDivides0(v0, v3) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) |  ~ doDivides0(v0, v2) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v0, v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v0 = sz00 |  ~ (sdtasdt0(v1, v0) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(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(v0, v2) = v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ doDivides0(v1, v2) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ sdtlseqdt0(v1, v2) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2)) &  ! [v0] :  ! [v1] : (v1 = v0 | v1 = sz10 |  ~ isPrime0(v0) |  ~ doDivides0(v1, v0) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtasdt0(sz10, v0) = 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(sz00, v0) = v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ (sdtpldt0(v0, v1) = sz00) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) &  ! [v0] :  ! [v1] : (v0 = sz00 |  ~ (sdtpldt0(v0, v1) = sz00) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0)) &  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0) &  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00) &  ! [v0] :  ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0) &  ! [v0] :  ! [v1] : ( ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2))) &  ! [v0] :  ! [v1] : ( ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2))) &  ! [v0] :  ! [v1] : ( ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) &  ! [v0] : (v0 = sz10 | v0 = sz00 |  ~ aNaturalNumber0(v0) | isPrime0(v0) |  ? [v1] : ( ~ (v1 = v0) &  ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1))) &  ! [v0] : (v0 = sz10 | v0 = sz00 |  ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) &  ! [v0] : (v0 = sz10 | v0 = sz00 |  ~ aNaturalNumber0(v0) |  ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1))) &  ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) & (xr = xn |  ~ sdtlseqdt0(xr, xn))
% 81.88/42.97  |
% 81.88/42.97  | Applying alpha-rule on (1) yields:
% 81.88/42.97  | (2)  ! [v0] :  ! [v1] : ( ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 81.88/42.97  | (3)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtpldt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0))
% 81.88/42.98  | (4) sdtpldt0(all_0_2_2, xp) = all_0_1_1
% 81.88/42.98  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) |  ~ doDivides0(v0, v2) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v0, v3))
% 81.88/42.98  | (6)  ! [v0] :  ! [v1] : (v1 = v0 | v1 = sz10 |  ~ isPrime0(v0) |  ~ doDivides0(v1, v0) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 81.88/42.98  | (7)  ! [v0] :  ! [v1] : (v0 = sz00 |  ~ (sdtpldt0(v0, v1) = sz00) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 81.88/42.98  | (8)  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 81.88/42.98  | (9) doDivides0(xp, all_0_0_0)
% 81.88/42.98  | (10) aNaturalNumber0(sz10)
% 81.88/42.98  | (11)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ sdtlseqdt0(v1, v0) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 81.88/42.98  | (12)  ~ isPrime0(sz00)
% 81.88/42.98  | (13)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 81.88/42.98  | (14)  ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 81.88/42.98  | (15)  ! [v0] :  ! [v1] : (v1 = sz00 | v0 = sz00 |  ~ (sdtasdt0(v0, v1) = sz00) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 81.88/42.98  | (16) aNaturalNumber0(xm)
% 81.88/42.98  | (17) aNaturalNumber0(xp)
% 81.88/42.98  | (18)  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 81.88/42.98  | (19) aNaturalNumber0(sz00)
% 81.88/42.98  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtsldt0(v3, v2) = v1) |  ~ (sdtsldt0(v3, v2) = v0))
% 81.88/42.98  | (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) |  ? [v5] :  ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtlseqdt0(v5, v6)))
% 81.88/42.98  | (22)  ! [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))
% 81.88/42.98  | (23)  ! [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))
% 81.88/42.98  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtpldt0(v3, v2) = v1) |  ~ (sdtpldt0(v3, v2) = v0))
% 81.88/42.98  | (25)  ~ (sz10 = sz00)
% 81.88/42.98  | (26)  ! [v0] :  ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 81.88/42.98  | (27)  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ (sdtasdt0(sz00, v0) = v1) |  ~ aNaturalNumber0(v0))
% 81.88/42.98  | (28) sdtpldt0(xn, xm) = all_0_2_2
% 81.88/42.98  | (29)  ! [v0] : (v0 = sz10 | v0 = sz00 |  ~ aNaturalNumber0(v0) |  ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 81.88/42.98  | (30) xr = xn |  ~ sdtlseqdt0(xr, xn)
% 81.88/42.98  | (31)  ! [v0] :  ! [v1] : (v1 = sz00 |  ~ (sdtpldt0(v0, v1) = sz00) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 81.88/42.98  | (32)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 81.88/42.98  | (33)  ! [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))
% 81.88/42.98  | (34)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ doDivides0(v1, v2) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 81.88/42.98  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v2) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 81.88/42.98  | (36)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 81.88/42.98  | (37)  ~ isPrime0(sz10)
% 81.88/42.98  | (38) aNaturalNumber0(xn)
% 81.88/42.98  | (39)  ! [v0] :  ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 81.88/42.98  | (40)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 81.88/42.98  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 |  ~ (sdtpldt0(v0, v2) = v3) |  ~ (sdtpldt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 81.88/42.98  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 | v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v0, v2) = v3) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 81.88/42.99  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v0, v2) = v4) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v5] :  ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5))
% 81.88/42.99  | (44)  ! [v0] : (v0 = sz10 | v0 = sz00 |  ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 81.88/42.99  | (45)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 81.88/42.99  | (46)  ! [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))
% 81.88/42.99  | (47)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (sdtasdt0(sz10, v0) = v1) |  ~ aNaturalNumber0(v0))
% 81.88/42.99  | (48)  ! [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))
% 81.88/42.99  | (49)  ! [v0] : (v0 = sz10 | v0 = sz00 |  ~ aNaturalNumber0(v0) | isPrime0(v0) |  ? [v1] : ( ~ (v1 = v0) &  ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 82.26/42.99  | (50)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v0 = sz00 |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v0, v2) = v3) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 82.26/42.99  | (51) sdtlseqdt0(xp, xn)
% 82.26/42.99  | (52)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v3) = v1) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v3) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 82.26/42.99  | (53)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) |  ~ (sdtpldt0(v0, v1) = v3) |  ~ isPrime0(v2) |  ~ iLess0(v4, all_0_1_1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) |  ? [v5] : (sdtasdt0(v0, v1) = v5 &  ~ doDivides0(v2, v5)))
% 82.26/42.99  | (54)  ! [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))
% 82.26/42.99  | (55)  ! [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)))
% 82.26/42.99  | (56) sdtmndt0(xn, xp) = xr
% 82.26/42.99  | (57)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) |  ~ doDivides0(v0, v3) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 82.26/42.99  | (58)  ! [v0] :  ! [v1] : ( ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) |  ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 82.26/42.99  | (59)  ! [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))
% 82.26/42.99  | (60)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtasdt0(v3, v2) = v1) |  ~ (sdtasdt0(v3, v2) = v0))
% 82.26/42.99  | (61)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 | v0 = sz00 |  ~ (sdtasdt0(v0, v2) = v3) |  ~ (sdtasdt0(v0, v1) = v3) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 82.26/42.99  | (62)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v0 = sz00 |  ~ (sdtsldt0(v4, v0) = v5) |  ~ (sdtsldt0(v1, v0) = v2) |  ~ (sdtasdt0(v3, v1) = v4) |  ~ doDivides0(v0, v1) |  ~ aNaturalNumber0(v3) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v3, v2) = v5)
% 82.26/42.99  | (63)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sdtmndt0(v3, v2) = v1) |  ~ (sdtmndt0(v3, v2) = v0))
% 82.26/42.99  | (64)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ sdtlseqdt0(v1, v2) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 82.26/42.99  | (65)  ! [v0] :  ! [v1] : ( ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 82.26/42.99  | (66)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (sdtmndt0(v1, v0) = v2) |  ~ (sdtpldt0(v0, v2) = v3) |  ~ sdtlseqdt0(v0, v1) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0))
% 82.26/42.99  | (67)  ! [v0] :  ! [v1] :  ! [v2] : (v0 = sz00 |  ~ (sdtasdt0(v1, v0) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 82.26/42.99  | (68) isPrime0(xp)
% 82.26/42.99  | (69)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 82.26/43.00  | (70)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) |  ~ aNaturalNumber0(v1) |  ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 82.26/43.00  | (71) sdtasdt0(xn, xm) = all_0_0_0
% 82.26/43.00  |
% 82.26/43.00  | Using (68) and (37) yields:
% 82.26/43.00  | (72)  ~ (xp = sz10)
% 82.26/43.00  |
% 82.26/43.00  | Using (68) and (12) yields:
% 82.26/43.00  | (73)  ~ (xp = sz00)
% 82.26/43.00  |
% 82.26/43.00  | Instantiating formula (58) with xp, xp and discharging atoms aNaturalNumber0(xp), yields:
% 82.26/43.00  | (74)  ~ doDivides0(xp, xp) |  ? [v0] : (sdtasdt0(xp, v0) = xp & aNaturalNumber0(v0))
% 82.26/43.00  |
% 82.26/43.00  | Instantiating formula (2) with xn, xn and discharging atoms aNaturalNumber0(xn), yields:
% 82.26/43.00  | (75)  ~ sdtlseqdt0(xn, xn) |  ? [v0] : (sdtpldt0(xn, v0) = xn & aNaturalNumber0(v0))
% 82.26/43.00  |
% 82.26/43.00  | Instantiating formula (65) with xp, xp and discharging atoms aNaturalNumber0(xp), yields:
% 82.26/43.00  | (76) sdtlseqdt0(xp, xp)
% 82.26/43.00  |
% 82.26/43.00  | Instantiating formula (44) with xp and discharging atoms aNaturalNumber0(xp), yields:
% 82.26/43.00  | (77) xp = sz10 | xp = sz00 | sdtlseqdt0(sz10, xp)
% 82.26/43.00  |
% 82.26/43.00  | Instantiating formula (29) with xp and discharging atoms aNaturalNumber0(xp), yields:
% 82.26/43.00  | (78) xp = sz10 | xp = sz00 |  ? [v0] : (isPrime0(v0) & doDivides0(v0, xp) & aNaturalNumber0(v0))
% 82.26/43.00  |
% 82.26/43.00  | Instantiating formula (70) with all_0_0_0, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_0_0, aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 82.26/43.00  | (79) sdtasdt0(xm, xn) = all_0_0_0
% 82.26/43.00  |
% 82.26/43.00  | Instantiating formula (45) with all_0_0_0, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_0_0, aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 82.26/43.00  | (80) aNaturalNumber0(all_0_0_0)
% 82.26/43.00  |
% 82.26/43.00  | Instantiating formula (69) with all_0_2_2, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_2_2, aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 82.26/43.00  | (81) sdtpldt0(xm, xn) = all_0_2_2
% 82.26/43.00  |
% 82.26/43.00  | Instantiating formula (36) with all_0_2_2, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_2_2, aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 82.26/43.00  | (82) aNaturalNumber0(all_0_2_2)
% 82.26/43.00  |
% 82.26/43.00  | Instantiating formula (2) with xn, xp and discharging atoms sdtlseqdt0(xp, xn), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 82.26/43.00  | (83)  ? [v0] : (sdtpldt0(xp, v0) = xn & aNaturalNumber0(v0))
% 82.26/43.00  |
% 82.26/43.00  | Instantiating formula (65) with xm, xm and discharging atoms aNaturalNumber0(xm), yields:
% 82.26/43.00  | (84) sdtlseqdt0(xm, xm)
% 82.26/43.00  |
% 82.26/43.00  | Instantiating formula (54) with all_0_1_1, all_0_2_2, xp, xm, xn and discharging atoms sdtpldt0(all_0_2_2, xp) = all_0_1_1, sdtpldt0(xn, xm) = all_0_2_2, aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 82.26/43.00  | (85)  ? [v0] : (sdtpldt0(xm, xp) = v0 & sdtpldt0(xn, v0) = all_0_1_1)
% 82.26/43.00  |
% 82.26/43.00  | Instantiating formula (65) with xn, xn and discharging atoms aNaturalNumber0(xn), yields:
% 82.26/43.00  | (86) sdtlseqdt0(xn, xn)
% 82.26/43.00  |
% 82.26/43.00  | Instantiating formula (65) with sz00, xm and discharging atoms aNaturalNumber0(xm), aNaturalNumber0(sz00), yields:
% 82.26/43.00  | (87) sdtlseqdt0(xm, sz00) | sdtlseqdt0(sz00, xm)
% 82.26/43.00  |
% 82.26/43.00  | Instantiating formula (65) with sz00, sz00 and discharging atoms aNaturalNumber0(sz00), yields:
% 82.26/43.00  | (88) sdtlseqdt0(sz00, sz00)
% 82.26/43.00  |
% 82.26/43.00  | Instantiating (83) with all_13_0_3 yields:
% 82.26/43.00  | (89) sdtpldt0(xp, all_13_0_3) = xn & aNaturalNumber0(all_13_0_3)
% 82.26/43.00  |
% 82.26/43.00  | Applying alpha-rule on (89) yields:
% 82.26/43.00  | (90) sdtpldt0(xp, all_13_0_3) = xn
% 82.26/43.00  | (91) aNaturalNumber0(all_13_0_3)
% 82.26/43.00  |
% 82.26/43.00  | Instantiating (85) with all_15_0_4 yields:
% 82.26/43.00  | (92) sdtpldt0(xm, xp) = all_15_0_4 & sdtpldt0(xn, all_15_0_4) = all_0_1_1
% 82.26/43.00  |
% 82.26/43.00  | Applying alpha-rule on (92) yields:
% 82.26/43.00  | (93) sdtpldt0(xm, xp) = all_15_0_4
% 82.26/43.00  | (94) sdtpldt0(xn, all_15_0_4) = all_0_1_1
% 82.26/43.00  |
% 82.26/43.00  +-Applying beta-rule and splitting (77), into two cases.
% 82.26/43.00  |-Branch one:
% 82.26/43.00  | (95) sdtlseqdt0(sz10, xp)
% 82.26/43.00  |
% 82.26/43.00  	+-Applying beta-rule and splitting (75), into two cases.
% 82.26/43.00  	|-Branch one:
% 82.26/43.00  	| (96)  ~ sdtlseqdt0(xn, xn)
% 82.26/43.00  	|
% 82.26/43.00  		| Using (86) and (96) yields:
% 82.26/43.00  		| (97) $false
% 82.26/43.00  		|
% 82.26/43.00  		|-The branch is then unsatisfiable
% 82.26/43.00  	|-Branch two:
% 82.26/43.00  	| (86) sdtlseqdt0(xn, xn)
% 82.26/43.00  	| (99)  ? [v0] : (sdtpldt0(xn, v0) = xn & aNaturalNumber0(v0))
% 82.26/43.00  	|
% 82.26/43.00  		| Instantiating (99) with all_25_0_5 yields:
% 82.26/43.00  		| (100) sdtpldt0(xn, all_25_0_5) = xn & aNaturalNumber0(all_25_0_5)
% 82.26/43.00  		|
% 82.26/43.00  		| Applying alpha-rule on (100) yields:
% 82.26/43.00  		| (101) sdtpldt0(xn, all_25_0_5) = xn
% 82.26/43.00  		| (102) aNaturalNumber0(all_25_0_5)
% 82.26/43.00  		|
% 82.26/43.00  		+-Applying beta-rule and splitting (78), into two cases.
% 82.26/43.00  		|-Branch one:
% 82.26/43.00  		| (103) xp = sz00
% 82.26/43.00  		|
% 82.26/43.00  			| Equations (103) can reduce 73 to:
% 82.26/43.00  			| (104) $false
% 82.26/43.00  			|
% 82.26/43.00  			|-The branch is then unsatisfiable
% 82.26/43.00  		|-Branch two:
% 82.26/43.00  		| (73)  ~ (xp = sz00)
% 82.26/43.00  		| (106) xp = sz10 |  ? [v0] : (isPrime0(v0) & doDivides0(v0, xp) & aNaturalNumber0(v0))
% 82.26/43.00  		|
% 82.26/43.00  			+-Applying beta-rule and splitting (106), into two cases.
% 82.26/43.00  			|-Branch one:
% 82.26/43.00  			| (107) xp = sz10
% 82.26/43.00  			|
% 82.26/43.00  				| Equations (107) can reduce 72 to:
% 82.26/43.00  				| (104) $false
% 82.26/43.00  				|
% 82.26/43.00  				|-The branch is then unsatisfiable
% 82.26/43.00  			|-Branch two:
% 82.26/43.00  			| (72)  ~ (xp = sz10)
% 82.26/43.00  			| (110)  ? [v0] : (isPrime0(v0) & doDivides0(v0, xp) & aNaturalNumber0(v0))
% 82.26/43.00  			|
% 82.26/43.00  				| Instantiating (110) with all_34_0_6 yields:
% 82.26/43.00  				| (111) isPrime0(all_34_0_6) & doDivides0(all_34_0_6, xp) & aNaturalNumber0(all_34_0_6)
% 82.26/43.00  				|
% 82.26/43.00  				| Applying alpha-rule on (111) yields:
% 82.26/43.00  				| (112) isPrime0(all_34_0_6)
% 82.26/43.00  				| (113) doDivides0(all_34_0_6, xp)
% 82.26/43.00  				| (114) aNaturalNumber0(all_34_0_6)
% 82.26/43.00  				|
% 82.26/43.00  				| Instantiating formula (31) with xp, xm and discharging atoms aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 82.26/43.00  				| (115) xp = sz00 |  ~ (sdtpldt0(xm, xp) = sz00)
% 82.26/43.01  				|
% 82.26/43.01  				| Using (112) and (37) yields:
% 82.26/43.01  				| (116)  ~ (all_34_0_6 = sz10)
% 82.26/43.01  				|
% 82.26/43.01  				| Using (112) and (12) yields:
% 82.26/43.01  				| (117)  ~ (all_34_0_6 = sz00)
% 82.26/43.01  				|
% 82.26/43.01  				| Instantiating formula (52) with all_13_0_3, xr, xn, xp and discharging atoms sdtmndt0(xn, xp) = xr, sdtpldt0(xp, all_13_0_3) = xn, sdtlseqdt0(xp, xn), aNaturalNumber0(all_13_0_3), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 82.26/43.01  				| (118) all_13_0_3 = xr
% 82.26/43.01  				|
% 82.26/43.01  				| Instantiating formula (6) with all_34_0_6, xp and discharging atoms isPrime0(xp), doDivides0(all_34_0_6, xp), aNaturalNumber0(all_34_0_6), aNaturalNumber0(xp), yields:
% 82.26/43.01  				| (119) all_34_0_6 = xp | all_34_0_6 = sz10
% 82.26/43.01  				|
% 82.26/43.01  				| Instantiating formula (7) with all_13_0_3, xp and discharging atoms aNaturalNumber0(all_13_0_3), aNaturalNumber0(xp), yields:
% 82.26/43.01  				| (120) xp = sz00 |  ~ (sdtpldt0(xp, all_13_0_3) = sz00)
% 82.26/43.01  				|
% 82.26/43.01  				| From (118) and (90) follows:
% 82.26/43.01  				| (121) sdtpldt0(xp, xr) = xn
% 82.26/43.01  				|
% 82.26/43.01  				| From (118) and (91) follows:
% 82.26/43.01  				| (122) aNaturalNumber0(xr)
% 82.26/43.01  				|
% 82.26/43.01  				+-Applying beta-rule and splitting (120), into two cases.
% 82.26/43.01  				|-Branch one:
% 82.26/43.01  				| (123)  ~ (sdtpldt0(xp, all_13_0_3) = sz00)
% 82.26/43.01  				|
% 82.26/43.01  					| From (118) and (123) follows:
% 82.26/43.01  					| (124)  ~ (sdtpldt0(xp, xr) = sz00)
% 82.26/43.01  					|
% 82.26/43.01  					+-Applying beta-rule and splitting (119), into two cases.
% 82.26/43.01  					|-Branch one:
% 82.26/43.01  					| (125) all_34_0_6 = xp
% 82.26/43.01  					|
% 82.26/43.01  						| Equations (125) can reduce 117 to:
% 82.26/43.01  						| (73)  ~ (xp = sz00)
% 82.26/43.01  						|
% 82.26/43.01  						| From (125) and (113) follows:
% 82.26/43.01  						| (127) doDivides0(xp, xp)
% 82.26/43.01  						|
% 82.26/43.01  						| From (125) and (114) follows:
% 82.26/43.01  						| (17) aNaturalNumber0(xp)
% 82.26/43.01  						|
% 82.26/43.01  						+-Applying beta-rule and splitting (74), into two cases.
% 82.26/43.01  						|-Branch one:
% 82.26/43.01  						| (129)  ~ doDivides0(xp, xp)
% 82.26/43.01  						|
% 82.26/43.01  							| Using (127) and (129) yields:
% 82.26/43.01  							| (97) $false
% 82.26/43.01  							|
% 82.26/43.01  							|-The branch is then unsatisfiable
% 82.26/43.01  						|-Branch two:
% 82.26/43.01  						| (127) doDivides0(xp, xp)
% 82.26/43.01  						| (132)  ? [v0] : (sdtasdt0(xp, v0) = xp & aNaturalNumber0(v0))
% 82.26/43.01  						|
% 82.26/43.01  							| Instantiating (132) with all_59_0_7 yields:
% 82.26/43.01  							| (133) sdtasdt0(xp, all_59_0_7) = xp & aNaturalNumber0(all_59_0_7)
% 82.26/43.01  							|
% 82.26/43.01  							| Applying alpha-rule on (133) yields:
% 82.26/43.01  							| (134) sdtasdt0(xp, all_59_0_7) = xp
% 82.26/43.01  							| (135) aNaturalNumber0(all_59_0_7)
% 82.26/43.01  							|
% 82.26/43.01  							+-Applying beta-rule and splitting (115), into two cases.
% 82.26/43.01  							|-Branch one:
% 82.26/43.01  							| (136)  ~ (sdtpldt0(xm, xp) = sz00)
% 82.26/43.01  							|
% 82.26/43.01  								| Using (121) and (124) yields:
% 82.26/43.01  								| (137)  ~ (xn = sz00)
% 82.26/43.01  								|
% 82.26/43.01  								| Using (93) and (136) yields:
% 82.26/43.01  								| (138)  ~ (all_15_0_4 = sz00)
% 82.26/43.01  								|
% 82.26/43.01  								| Instantiating formula (54) with xm, xm, xp, xp, xm and discharging atoms aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 82.26/43.01  								| (139)  ~ (sdtpldt0(xm, xp) = xm) |  ? [v0] : (sdtpldt0(xp, xp) = v0 & sdtpldt0(xm, v0) = xm)
% 82.26/43.01  								|
% 82.26/43.01  								| Instantiating formula (69) with all_15_0_4, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_15_0_4, aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 82.26/43.01  								| (140) sdtpldt0(xp, xm) = all_15_0_4
% 82.26/43.01  								|
% 82.26/43.01  								| Instantiating formula (36) with all_15_0_4, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_15_0_4, aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 82.26/43.01  								| (141) aNaturalNumber0(all_15_0_4)
% 82.26/43.01  								|
% 82.26/43.01  								| Instantiating formula (54) with all_0_1_1, all_0_2_2, xp, xn, xm and discharging atoms sdtpldt0(all_0_2_2, xp) = all_0_1_1, sdtpldt0(xm, xn) = all_0_2_2, aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 82.26/43.01  								| (142)  ? [v0] : (sdtpldt0(xm, v0) = all_0_1_1 & sdtpldt0(xn, xp) = v0)
% 82.26/43.01  								|
% 82.26/43.01  								| Instantiating formula (54) with all_0_2_2, xn, xm, xp, xn and discharging atoms sdtpldt0(xn, xm) = all_0_2_2, aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 82.26/43.01  								| (143)  ~ (sdtpldt0(xn, xp) = xn) |  ? [v0] : (sdtpldt0(xp, xm) = v0 & sdtpldt0(xn, v0) = all_0_2_2)
% 82.26/43.01  								|
% 82.26/43.01  								| Instantiating formula (2) with xp, xp and discharging atoms sdtlseqdt0(xp, xp), aNaturalNumber0(xp), yields:
% 82.26/43.01  								| (144)  ? [v0] : (sdtpldt0(xp, v0) = xp & aNaturalNumber0(v0))
% 82.26/43.01  								|
% 82.26/43.01  								| Instantiating formula (2) with xm, xm and discharging atoms sdtlseqdt0(xm, xm), aNaturalNumber0(xm), yields:
% 82.26/43.01  								| (145)  ? [v0] : (sdtpldt0(xm, v0) = xm & aNaturalNumber0(v0))
% 82.26/43.01  								|
% 82.26/43.01  								| Instantiating formula (2) with sz00, sz00 and discharging atoms sdtlseqdt0(sz00, sz00), aNaturalNumber0(sz00), yields:
% 82.26/43.01  								| (146)  ? [v0] : (sdtpldt0(sz00, v0) = sz00 & aNaturalNumber0(v0))
% 82.26/43.01  								|
% 82.26/43.01  								| Instantiating formula (64) with xn, xp, sz10 and discharging atoms sdtlseqdt0(xp, xn), sdtlseqdt0(sz10, xp), aNaturalNumber0(xp), aNaturalNumber0(xn), aNaturalNumber0(sz10), yields:
% 82.26/43.01  								| (147) sdtlseqdt0(sz10, xn)
% 82.26/43.01  								|
% 82.26/43.01  								| Instantiating formula (2) with xp, sz10 and discharging atoms sdtlseqdt0(sz10, xp), aNaturalNumber0(xp), aNaturalNumber0(sz10), yields:
% 82.26/43.01  								| (148)  ? [v0] : (sdtpldt0(sz10, v0) = xp & aNaturalNumber0(v0))
% 82.26/43.01  								|
% 82.26/43.01  								| Instantiating formula (2) with xn, sz10 and discharging atoms aNaturalNumber0(xn), aNaturalNumber0(sz10), yields:
% 82.26/43.01  								| (149)  ~ sdtlseqdt0(sz10, xn) |  ? [v0] : (sdtpldt0(sz10, v0) = xn & aNaturalNumber0(v0))
% 82.26/43.01  								|
% 82.26/43.01  								| Instantiating formula (13) with xm, all_0_0_0, xn and discharging atoms sdtasdt0(xn, xm) = all_0_0_0, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 82.26/43.01  								| (150) doDivides0(xn, all_0_0_0)
% 82.26/43.01  								|
% 82.26/43.01  								| Instantiating formula (70) with xp, all_59_0_7, xp and discharging atoms sdtasdt0(xp, all_59_0_7) = xp, aNaturalNumber0(all_59_0_7), aNaturalNumber0(xp), yields:
% 82.26/43.01  								| (151) sdtasdt0(all_59_0_7, xp) = xp
% 82.26/43.01  								|
% 82.26/43.01  								| Instantiating formula (13) with xn, all_0_0_0, xm and discharging atoms sdtasdt0(xm, xn) = all_0_0_0, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 82.26/43.01  								| (152) doDivides0(xm, all_0_0_0)
% 82.26/43.01  								|
% 82.26/43.01  								| Instantiating formula (36) with all_0_1_1, xp, all_0_2_2 and discharging atoms sdtpldt0(all_0_2_2, xp) = all_0_1_1, aNaturalNumber0(all_0_2_2), aNaturalNumber0(xp), yields:
% 82.26/43.01  								| (153) aNaturalNumber0(all_0_1_1)
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating formula (54) with all_0_2_2, xn, xm, xr, xp and discharging atoms sdtpldt0(xp, xr) = xn, sdtpldt0(xn, xm) = all_0_2_2, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 82.26/43.02  								| (154)  ? [v0] : (sdtpldt0(xr, xm) = v0 & sdtpldt0(xp, v0) = all_0_2_2)
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating formula (54) with all_0_2_2, xn, xm, all_25_0_5, xn and discharging atoms sdtpldt0(xn, all_25_0_5) = xn, sdtpldt0(xn, xm) = all_0_2_2, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 82.26/43.02  								| (155)  ? [v0] : (sdtpldt0(all_25_0_5, xm) = v0 & sdtpldt0(xn, v0) = all_0_2_2)
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating formula (32) with xm, all_0_2_2, xn and discharging atoms sdtpldt0(xn, xm) = all_0_2_2, aNaturalNumber0(all_0_2_2), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 82.26/43.02  								| (156) sdtlseqdt0(xn, all_0_2_2)
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating formula (69) with xn, xr, xp and discharging atoms sdtpldt0(xp, xr) = xn, aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 82.26/43.02  								| (157) sdtpldt0(xr, xp) = xn
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating formula (32) with xp, all_15_0_4, xm and discharging atoms sdtpldt0(xm, xp) = all_15_0_4, aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 82.26/43.02  								| (158)  ~ aNaturalNumber0(all_15_0_4) | sdtlseqdt0(xm, all_15_0_4)
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating formula (69) with xn, all_25_0_5, xn and discharging atoms sdtpldt0(xn, all_25_0_5) = xn, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xn), yields:
% 82.26/43.02  								| (159) sdtpldt0(all_25_0_5, xn) = xn
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating formula (69) with all_0_1_1, all_15_0_4, xn and discharging atoms sdtpldt0(xn, all_15_0_4) = all_0_1_1, aNaturalNumber0(xn), yields:
% 82.26/43.02  								| (160)  ~ aNaturalNumber0(all_15_0_4) | sdtpldt0(all_15_0_4, xn) = all_0_1_1
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating formula (54) with xn, xn, xp, xp, xn and discharging atoms aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 82.26/43.02  								| (161)  ~ (sdtpldt0(xn, xp) = xn) |  ? [v0] : (sdtpldt0(xp, xp) = v0 & sdtpldt0(xn, v0) = xn)
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating formula (54) with xn, xn, all_25_0_5, all_25_0_5, xn and discharging atoms sdtpldt0(xn, all_25_0_5) = xn, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xn), yields:
% 82.26/43.02  								| (162)  ? [v0] : (sdtpldt0(all_25_0_5, all_25_0_5) = v0 & sdtpldt0(xn, v0) = xn)
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating formula (54) with xn, xn, all_25_0_5, xr, xp and discharging atoms sdtpldt0(xp, xr) = xn, sdtpldt0(xn, all_25_0_5) = xn, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 82.26/43.02  								| (163)  ? [v0] : (sdtpldt0(xr, all_25_0_5) = v0 & sdtpldt0(xp, v0) = xn)
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating formula (54) with all_0_1_1, xn, all_15_0_4, all_25_0_5, xn and discharging atoms sdtpldt0(xn, all_25_0_5) = xn, sdtpldt0(xn, all_15_0_4) = all_0_1_1, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xn), yields:
% 82.26/43.02  								| (164)  ~ aNaturalNumber0(all_15_0_4) |  ? [v0] : (sdtpldt0(all_25_0_5, all_15_0_4) = v0 & sdtpldt0(xn, v0) = all_0_1_1)
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating formula (65) with all_25_0_5, all_25_0_5 and discharging atoms aNaturalNumber0(all_25_0_5), yields:
% 82.26/43.02  								| (165) sdtlseqdt0(all_25_0_5, all_25_0_5)
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating formula (58) with all_0_0_0, xm and discharging atoms aNaturalNumber0(all_0_0_0), aNaturalNumber0(xm), yields:
% 82.26/43.02  								| (166)  ~ doDivides0(xm, all_0_0_0) |  ? [v0] : (sdtasdt0(xm, v0) = all_0_0_0 & aNaturalNumber0(v0))
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating formula (58) with all_0_0_0, xn and discharging atoms aNaturalNumber0(all_0_0_0), aNaturalNumber0(xn), yields:
% 82.26/43.02  								| (167)  ~ doDivides0(xn, all_0_0_0) |  ? [v0] : (sdtasdt0(xn, v0) = all_0_0_0 & aNaturalNumber0(v0))
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating formula (54) with all_0_2_2, all_0_2_2, xp, xp, all_0_2_2 and discharging atoms aNaturalNumber0(all_0_2_2), aNaturalNumber0(xp), yields:
% 82.26/43.02  								| (168)  ~ (sdtpldt0(all_0_2_2, xp) = all_0_2_2) |  ? [v0] : (sdtpldt0(all_0_2_2, v0) = all_0_2_2 & sdtpldt0(xp, xp) = v0)
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating formula (32) with xp, all_0_1_1, all_0_2_2 and discharging atoms sdtpldt0(all_0_2_2, xp) = all_0_1_1, aNaturalNumber0(all_0_2_2), aNaturalNumber0(xp), yields:
% 82.26/43.02  								| (169)  ~ aNaturalNumber0(all_0_1_1) | sdtlseqdt0(all_0_2_2, all_0_1_1)
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating formula (54) with all_0_1_1, xn, all_15_0_4, xr, xp and discharging atoms sdtpldt0(xp, xr) = xn, sdtpldt0(xn, all_15_0_4) = all_0_1_1, aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 82.26/43.02  								| (170)  ~ aNaturalNumber0(all_15_0_4) |  ? [v0] : (sdtpldt0(xr, all_15_0_4) = v0 & sdtpldt0(xp, v0) = all_0_1_1)
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating (163) with all_89_0_9 yields:
% 82.26/43.02  								| (171) sdtpldt0(xr, all_25_0_5) = all_89_0_9 & sdtpldt0(xp, all_89_0_9) = xn
% 82.26/43.02  								|
% 82.26/43.02  								| Applying alpha-rule on (171) yields:
% 82.26/43.02  								| (172) sdtpldt0(xr, all_25_0_5) = all_89_0_9
% 82.26/43.02  								| (173) sdtpldt0(xp, all_89_0_9) = xn
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating (162) with all_91_0_10 yields:
% 82.26/43.02  								| (174) sdtpldt0(all_25_0_5, all_25_0_5) = all_91_0_10 & sdtpldt0(xn, all_91_0_10) = xn
% 82.26/43.02  								|
% 82.26/43.02  								| Applying alpha-rule on (174) yields:
% 82.26/43.02  								| (175) sdtpldt0(all_25_0_5, all_25_0_5) = all_91_0_10
% 82.26/43.02  								| (176) sdtpldt0(xn, all_91_0_10) = xn
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating (146) with all_93_0_11 yields:
% 82.26/43.02  								| (177) sdtpldt0(sz00, all_93_0_11) = sz00 & aNaturalNumber0(all_93_0_11)
% 82.26/43.02  								|
% 82.26/43.02  								| Applying alpha-rule on (177) yields:
% 82.26/43.02  								| (178) sdtpldt0(sz00, all_93_0_11) = sz00
% 82.26/43.02  								| (179) aNaturalNumber0(all_93_0_11)
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating (142) with all_97_0_13 yields:
% 82.26/43.02  								| (180) sdtpldt0(xm, all_97_0_13) = all_0_1_1 & sdtpldt0(xn, xp) = all_97_0_13
% 82.26/43.02  								|
% 82.26/43.02  								| Applying alpha-rule on (180) yields:
% 82.26/43.02  								| (181) sdtpldt0(xm, all_97_0_13) = all_0_1_1
% 82.26/43.02  								| (182) sdtpldt0(xn, xp) = all_97_0_13
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating (154) with all_101_0_15 yields:
% 82.26/43.02  								| (183) sdtpldt0(xr, xm) = all_101_0_15 & sdtpldt0(xp, all_101_0_15) = all_0_2_2
% 82.26/43.02  								|
% 82.26/43.02  								| Applying alpha-rule on (183) yields:
% 82.26/43.02  								| (184) sdtpldt0(xr, xm) = all_101_0_15
% 82.26/43.02  								| (185) sdtpldt0(xp, all_101_0_15) = all_0_2_2
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating (155) with all_103_0_16 yields:
% 82.26/43.02  								| (186) sdtpldt0(all_25_0_5, xm) = all_103_0_16 & sdtpldt0(xn, all_103_0_16) = all_0_2_2
% 82.26/43.02  								|
% 82.26/43.02  								| Applying alpha-rule on (186) yields:
% 82.26/43.02  								| (187) sdtpldt0(all_25_0_5, xm) = all_103_0_16
% 82.26/43.02  								| (188) sdtpldt0(xn, all_103_0_16) = all_0_2_2
% 82.26/43.02  								|
% 82.26/43.02  								| Instantiating (148) with all_105_0_17 yields:
% 82.26/43.02  								| (189) sdtpldt0(sz10, all_105_0_17) = xp & aNaturalNumber0(all_105_0_17)
% 82.26/43.03  								|
% 82.26/43.03  								| Applying alpha-rule on (189) yields:
% 82.26/43.03  								| (190) sdtpldt0(sz10, all_105_0_17) = xp
% 82.26/43.03  								| (191) aNaturalNumber0(all_105_0_17)
% 82.26/43.03  								|
% 82.26/43.03  								| Instantiating (145) with all_107_0_18 yields:
% 82.26/43.03  								| (192) sdtpldt0(xm, all_107_0_18) = xm & aNaturalNumber0(all_107_0_18)
% 82.26/43.03  								|
% 82.26/43.03  								| Applying alpha-rule on (192) yields:
% 82.26/43.03  								| (193) sdtpldt0(xm, all_107_0_18) = xm
% 82.26/43.03  								| (194) aNaturalNumber0(all_107_0_18)
% 82.26/43.03  								|
% 82.26/43.03  								| Instantiating (144) with all_109_0_19 yields:
% 82.26/43.03  								| (195) sdtpldt0(xp, all_109_0_19) = xp & aNaturalNumber0(all_109_0_19)
% 82.26/43.03  								|
% 82.26/43.03  								| Applying alpha-rule on (195) yields:
% 82.26/43.03  								| (196) sdtpldt0(xp, all_109_0_19) = xp
% 82.26/43.03  								| (197) aNaturalNumber0(all_109_0_19)
% 82.26/43.03  								|
% 82.26/43.03  								+-Applying beta-rule and splitting (158), into two cases.
% 82.26/43.03  								|-Branch one:
% 82.26/43.03  								| (198)  ~ aNaturalNumber0(all_15_0_4)
% 82.26/43.03  								|
% 82.26/43.03  									| Using (141) and (198) yields:
% 82.26/43.03  									| (97) $false
% 82.26/43.03  									|
% 82.26/43.03  									|-The branch is then unsatisfiable
% 82.26/43.03  								|-Branch two:
% 82.26/43.03  								| (141) aNaturalNumber0(all_15_0_4)
% 82.26/43.03  								| (201) sdtlseqdt0(xm, all_15_0_4)
% 82.26/43.03  								|
% 82.26/43.03  									+-Applying beta-rule and splitting (164), into two cases.
% 82.26/43.03  									|-Branch one:
% 82.26/43.03  									| (198)  ~ aNaturalNumber0(all_15_0_4)
% 82.26/43.03  									|
% 82.26/43.03  										| Using (141) and (198) yields:
% 82.26/43.03  										| (97) $false
% 82.26/43.03  										|
% 82.26/43.03  										|-The branch is then unsatisfiable
% 82.26/43.03  									|-Branch two:
% 82.26/43.03  									| (141) aNaturalNumber0(all_15_0_4)
% 82.26/43.03  									| (205)  ? [v0] : (sdtpldt0(all_25_0_5, all_15_0_4) = v0 & sdtpldt0(xn, v0) = all_0_1_1)
% 82.26/43.03  									|
% 82.26/43.03  										| Instantiating (205) with all_122_0_20 yields:
% 82.26/43.03  										| (206) sdtpldt0(all_25_0_5, all_15_0_4) = all_122_0_20 & sdtpldt0(xn, all_122_0_20) = all_0_1_1
% 82.26/43.03  										|
% 82.26/43.03  										| Applying alpha-rule on (206) yields:
% 82.26/43.03  										| (207) sdtpldt0(all_25_0_5, all_15_0_4) = all_122_0_20
% 82.26/43.03  										| (208) sdtpldt0(xn, all_122_0_20) = all_0_1_1
% 82.26/43.03  										|
% 82.26/43.03  										+-Applying beta-rule and splitting (149), into two cases.
% 82.26/43.03  										|-Branch one:
% 82.26/43.03  										| (209)  ~ sdtlseqdt0(sz10, xn)
% 82.26/43.03  										|
% 82.26/43.03  											| Using (147) and (209) yields:
% 82.26/43.03  											| (97) $false
% 82.26/43.03  											|
% 82.26/43.03  											|-The branch is then unsatisfiable
% 82.26/43.03  										|-Branch two:
% 82.26/43.03  										| (147) sdtlseqdt0(sz10, xn)
% 82.26/43.03  										| (212)  ? [v0] : (sdtpldt0(sz10, v0) = xn & aNaturalNumber0(v0))
% 82.26/43.03  										|
% 82.26/43.03  											| Instantiating (212) with all_127_0_21 yields:
% 82.26/43.03  											| (213) sdtpldt0(sz10, all_127_0_21) = xn & aNaturalNumber0(all_127_0_21)
% 82.26/43.03  											|
% 82.26/43.03  											| Applying alpha-rule on (213) yields:
% 82.26/43.03  											| (214) sdtpldt0(sz10, all_127_0_21) = xn
% 82.26/43.03  											| (215) aNaturalNumber0(all_127_0_21)
% 82.26/43.03  											|
% 82.26/43.03  											+-Applying beta-rule and splitting (167), into two cases.
% 82.26/43.03  											|-Branch one:
% 82.26/43.03  											| (216)  ~ doDivides0(xn, all_0_0_0)
% 82.26/43.03  											|
% 82.26/43.03  												| Using (150) and (216) yields:
% 82.26/43.03  												| (97) $false
% 82.26/43.03  												|
% 82.26/43.03  												|-The branch is then unsatisfiable
% 82.26/43.03  											|-Branch two:
% 82.26/43.03  											| (150) doDivides0(xn, all_0_0_0)
% 82.26/43.03  											| (219)  ? [v0] : (sdtasdt0(xn, v0) = all_0_0_0 & aNaturalNumber0(v0))
% 82.26/43.03  											|
% 82.26/43.03  												| Instantiating (219) with all_132_0_22 yields:
% 82.26/43.03  												| (220) sdtasdt0(xn, all_132_0_22) = all_0_0_0 & aNaturalNumber0(all_132_0_22)
% 82.26/43.03  												|
% 82.26/43.03  												| Applying alpha-rule on (220) yields:
% 82.26/43.03  												| (221) sdtasdt0(xn, all_132_0_22) = all_0_0_0
% 82.26/43.03  												| (222) aNaturalNumber0(all_132_0_22)
% 82.26/43.03  												|
% 82.26/43.03  												+-Applying beta-rule and splitting (166), into two cases.
% 82.26/43.03  												|-Branch one:
% 82.26/43.03  												| (223)  ~ doDivides0(xm, all_0_0_0)
% 82.26/43.03  												|
% 82.26/43.03  													| Using (152) and (223) yields:
% 82.26/43.03  													| (97) $false
% 82.26/43.03  													|
% 82.26/43.03  													|-The branch is then unsatisfiable
% 82.26/43.03  												|-Branch two:
% 82.26/43.03  												| (152) doDivides0(xm, all_0_0_0)
% 82.26/43.03  												| (226)  ? [v0] : (sdtasdt0(xm, v0) = all_0_0_0 & aNaturalNumber0(v0))
% 82.26/43.03  												|
% 82.26/43.03  													| Instantiating (226) with all_137_0_23 yields:
% 82.26/43.03  													| (227) sdtasdt0(xm, all_137_0_23) = all_0_0_0 & aNaturalNumber0(all_137_0_23)
% 82.26/43.03  													|
% 82.26/43.03  													| Applying alpha-rule on (227) yields:
% 82.26/43.03  													| (228) sdtasdt0(xm, all_137_0_23) = all_0_0_0
% 82.26/43.03  													| (229) aNaturalNumber0(all_137_0_23)
% 82.26/43.03  													|
% 82.26/43.03  													+-Applying beta-rule and splitting (170), into two cases.
% 82.26/43.03  													|-Branch one:
% 82.26/43.03  													| (198)  ~ aNaturalNumber0(all_15_0_4)
% 82.26/43.03  													|
% 82.26/43.03  														| Using (141) and (198) yields:
% 82.26/43.03  														| (97) $false
% 82.26/43.03  														|
% 82.26/43.03  														|-The branch is then unsatisfiable
% 82.26/43.03  													|-Branch two:
% 82.26/43.03  													| (141) aNaturalNumber0(all_15_0_4)
% 82.26/43.03  													| (233)  ? [v0] : (sdtpldt0(xr, all_15_0_4) = v0 & sdtpldt0(xp, v0) = all_0_1_1)
% 82.26/43.03  													|
% 82.26/43.03  														+-Applying beta-rule and splitting (169), into two cases.
% 82.26/43.03  														|-Branch one:
% 82.26/43.03  														| (234)  ~ aNaturalNumber0(all_0_1_1)
% 82.26/43.03  														|
% 82.26/43.03  															| Using (153) and (234) yields:
% 82.26/43.03  															| (97) $false
% 82.26/43.03  															|
% 82.26/43.03  															|-The branch is then unsatisfiable
% 82.26/43.03  														|-Branch two:
% 82.26/43.03  														| (153) aNaturalNumber0(all_0_1_1)
% 82.26/43.03  														| (237) sdtlseqdt0(all_0_2_2, all_0_1_1)
% 82.26/43.03  														|
% 82.26/43.03  															+-Applying beta-rule and splitting (160), into two cases.
% 82.26/43.03  															|-Branch one:
% 82.26/43.03  															| (198)  ~ aNaturalNumber0(all_15_0_4)
% 82.26/43.03  															|
% 82.26/43.03  																| Using (141) and (198) yields:
% 82.26/43.03  																| (97) $false
% 82.26/43.03  																|
% 82.26/43.03  																|-The branch is then unsatisfiable
% 82.26/43.03  															|-Branch two:
% 82.26/43.03  															| (141) aNaturalNumber0(all_15_0_4)
% 82.26/43.03  															| (241) sdtpldt0(all_15_0_4, xn) = all_0_1_1
% 82.26/43.03  															|
% 82.26/43.03  																| Instantiating formula (24) with xm, xn, all_0_1_1, all_0_2_2 and discharging atoms sdtpldt0(xm, xn) = all_0_2_2, yields:
% 82.26/43.03  																| (242) all_0_1_1 = all_0_2_2 |  ~ (sdtpldt0(xm, xn) = all_0_1_1)
% 82.26/43.03  																|
% 82.26/43.03  																| Instantiating formula (41) with xn, all_25_0_5, xp, xr and discharging atoms sdtpldt0(xr, xp) = xn, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 82.26/43.03  																| (243) all_25_0_5 = xp |  ~ (sdtpldt0(xr, all_25_0_5) = xn)
% 82.26/43.03  																|
% 82.26/43.03  																| Instantiating formula (24) with xr, xp, xn, all_89_0_9 and discharging atoms sdtpldt0(xr, xp) = xn, yields:
% 82.26/43.03  																| (244) all_89_0_9 = xn |  ~ (sdtpldt0(xr, xp) = all_89_0_9)
% 82.26/43.03  																|
% 82.26/43.03  																| Instantiating formula (24) with xm, xp, xm, all_15_0_4 and discharging atoms sdtpldt0(xm, xp) = all_15_0_4, yields:
% 82.26/43.03  																| (245) all_15_0_4 = xm |  ~ (sdtpldt0(xm, xp) = xm)
% 82.26/43.03  																|
% 82.26/43.03  																| Instantiating formula (41) with xn, all_25_0_5, sz00, xn and discharging atoms sdtpldt0(xn, all_25_0_5) = xn, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xn), aNaturalNumber0(sz00), yields:
% 82.26/43.03  																| (246) all_25_0_5 = sz00 |  ~ (sdtpldt0(xn, sz00) = xn)
% 82.26/43.04  																|
% 82.26/43.04  																| Instantiating formula (24) with xn, xp, all_97_0_13, xn and discharging atoms sdtpldt0(xn, xp) = all_97_0_13, yields:
% 82.26/43.04  																| (247) all_97_0_13 = xn |  ~ (sdtpldt0(xn, xp) = xn)
% 82.26/43.04  																|
% 82.26/43.04  																| Instantiating formula (61) with all_0_0_0, xn, all_137_0_23, xm and discharging atoms sdtasdt0(xm, all_137_0_23) = all_0_0_0, sdtasdt0(xm, xn) = all_0_0_0, aNaturalNumber0(all_137_0_23), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 82.26/43.04  																| (248) all_137_0_23 = xn | xm = sz00
% 82.26/43.04  																|
% 82.26/43.04  																| Instantiating formula (61) with all_0_0_0, xm, all_132_0_22, xn and discharging atoms sdtasdt0(xn, all_132_0_22) = all_0_0_0, sdtasdt0(xn, xm) = all_0_0_0, aNaturalNumber0(all_132_0_22), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 82.26/43.04  																| (249) all_132_0_22 = xm | xn = sz00
% 82.26/43.04  																|
% 82.26/43.04  																| Instantiating formula (41) with xn, all_25_0_5, all_91_0_10, xn and discharging atoms sdtpldt0(xn, all_91_0_10) = xn, sdtpldt0(xn, all_25_0_5) = xn, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xn), yields:
% 82.26/43.04  																| (250) all_91_0_10 = all_25_0_5 |  ~ aNaturalNumber0(all_91_0_10)
% 82.26/43.04  																|
% 82.26/43.04  																| Instantiating formula (41) with all_0_2_2, xm, all_103_0_16, xn and discharging atoms sdtpldt0(xn, all_103_0_16) = all_0_2_2, sdtpldt0(xn, xm) = all_0_2_2, aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 82.26/43.04  																| (251) all_103_0_16 = xm |  ~ aNaturalNumber0(all_103_0_16)
% 82.26/43.04  																|
% 82.26/43.04  																| Instantiating formula (3) with sz00, all_93_0_11 and discharging atoms sdtpldt0(sz00, all_93_0_11) = sz00, aNaturalNumber0(all_93_0_11), yields:
% 82.26/43.04  																| (252) all_93_0_11 = sz00
% 82.26/43.04  																|
% 82.26/43.04  																| Instantiating formula (41) with xm, xp, all_107_0_18, xm and discharging atoms sdtpldt0(xm, all_107_0_18) = xm, aNaturalNumber0(all_107_0_18), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 82.26/43.04  																| (253) all_107_0_18 = xp |  ~ (sdtpldt0(xm, xp) = xm)
% 82.26/43.04  																|
% 82.26/43.04  																| Instantiating formula (41) with all_0_1_1, all_15_0_4, all_122_0_20, xn and discharging atoms sdtpldt0(xn, all_122_0_20) = all_0_1_1, sdtpldt0(xn, all_15_0_4) = all_0_1_1, aNaturalNumber0(all_15_0_4), aNaturalNumber0(xn), yields:
% 82.26/43.04  																| (254) all_122_0_20 = all_15_0_4 |  ~ aNaturalNumber0(all_122_0_20)
% 82.26/43.04  																|
% 82.26/43.04  																| Instantiating formula (31) with all_15_0_4, all_25_0_5 and discharging atoms aNaturalNumber0(all_25_0_5), aNaturalNumber0(all_15_0_4), yields:
% 82.26/43.04  																| (255) all_15_0_4 = sz00 |  ~ (sdtpldt0(all_25_0_5, all_15_0_4) = sz00)
% 82.26/43.04  																|
% 82.26/43.04  																| From (252) and (179) follows:
% 82.26/43.04  																| (19) aNaturalNumber0(sz00)
% 82.26/43.04  																|
% 82.26/43.04  																+-Applying beta-rule and splitting (249), into two cases.
% 82.26/43.04  																|-Branch one:
% 82.26/43.04  																| (257) xn = sz00
% 82.26/43.04  																|
% 82.26/43.04  																	| Equations (257) can reduce 137 to:
% 82.26/43.04  																	| (104) $false
% 82.26/43.04  																	|
% 82.26/43.04  																	|-The branch is then unsatisfiable
% 82.26/43.04  																|-Branch two:
% 82.26/43.04  																| (137)  ~ (xn = sz00)
% 82.26/43.04  																| (260) all_132_0_22 = xm
% 82.26/43.04  																|
% 82.26/43.04  																	| From (260) and (222) follows:
% 82.26/43.04  																	| (16) aNaturalNumber0(xm)
% 82.26/43.04  																	|
% 82.26/43.04  																	+-Applying beta-rule and splitting (255), into two cases.
% 82.26/43.04  																	|-Branch one:
% 82.26/43.04  																	| (262)  ~ (sdtpldt0(all_25_0_5, all_15_0_4) = sz00)
% 82.26/43.04  																	|
% 82.26/43.04  																		| Instantiating formula (54) with xn, xp, xr, all_25_0_5, all_25_0_5 and discharging atoms sdtpldt0(xp, xr) = xn, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xr), yields:
% 82.26/43.04  																		| (263)  ~ (sdtpldt0(all_25_0_5, all_25_0_5) = xp) |  ? [v0] : (sdtpldt0(all_25_0_5, v0) = xn & sdtpldt0(all_25_0_5, xr) = v0)
% 82.26/43.04  																		|
% 82.26/43.04  																		| Instantiating formula (36) with all_91_0_10, all_25_0_5, all_25_0_5 and discharging atoms sdtpldt0(all_25_0_5, all_25_0_5) = all_91_0_10, aNaturalNumber0(all_25_0_5), yields:
% 82.26/43.04  																		| (264) aNaturalNumber0(all_91_0_10)
% 82.26/43.04  																		|
% 82.26/43.04  																		| Instantiating formula (69) with all_122_0_20, all_15_0_4, all_25_0_5 and discharging atoms sdtpldt0(all_25_0_5, all_15_0_4) = all_122_0_20, aNaturalNumber0(all_25_0_5), aNaturalNumber0(all_15_0_4), yields:
% 82.26/43.04  																		| (265) sdtpldt0(all_15_0_4, all_25_0_5) = all_122_0_20
% 82.26/43.04  																		|
% 82.26/43.04  																		| Instantiating formula (36) with all_122_0_20, all_15_0_4, all_25_0_5 and discharging atoms sdtpldt0(all_25_0_5, all_15_0_4) = all_122_0_20, aNaturalNumber0(all_25_0_5), aNaturalNumber0(all_15_0_4), yields:
% 82.26/43.04  																		| (266) aNaturalNumber0(all_122_0_20)
% 82.26/43.04  																		|
% 82.26/43.04  																		| Instantiating formula (54) with all_103_0_16, all_25_0_5, xm, all_25_0_5, all_25_0_5 and discharging atoms sdtpldt0(all_25_0_5, xm) = all_103_0_16, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xm), yields:
% 82.26/43.04  																		| (267)  ~ (sdtpldt0(all_25_0_5, all_25_0_5) = all_25_0_5) |  ? [v0] : (sdtpldt0(all_25_0_5, v0) = all_103_0_16 & sdtpldt0(all_25_0_5, xm) = v0)
% 82.26/43.04  																		|
% 82.26/43.04  																		| Instantiating formula (69) with all_103_0_16, xm, all_25_0_5 and discharging atoms sdtpldt0(all_25_0_5, xm) = all_103_0_16, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xm), yields:
% 82.26/43.04  																		| (268) sdtpldt0(xm, all_25_0_5) = all_103_0_16
% 82.26/43.04  																		|
% 82.26/43.04  																		| Instantiating formula (36) with all_103_0_16, xm, all_25_0_5 and discharging atoms sdtpldt0(all_25_0_5, xm) = all_103_0_16, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xm), yields:
% 82.26/43.04  																		| (269) aNaturalNumber0(all_103_0_16)
% 82.26/43.04  																		|
% 82.26/43.04  																		| Instantiating formula (54) with xn, xn, xp, xn, xp and discharging atoms aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 82.26/43.04  																		| (270)  ~ (sdtpldt0(xp, xn) = xn) |  ~ (sdtpldt0(xn, xp) = xn) |  ? [v0] : (sdtpldt0(xp, v0) = xn & sdtpldt0(xn, xp) = v0)
% 82.26/43.04  																		|
% 82.26/43.04  																		| Instantiating formula (36) with all_89_0_9, all_25_0_5, xr and discharging atoms sdtpldt0(xr, all_25_0_5) = all_89_0_9, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xr), yields:
% 82.26/43.04  																		| (271) aNaturalNumber0(all_89_0_9)
% 82.26/43.04  																		|
% 82.26/43.04  																		| Instantiating formula (54) with xn, xn, all_25_0_5, xp, xr and discharging atoms sdtpldt0(xr, xp) = xn, sdtpldt0(xn, all_25_0_5) = xn, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 82.26/43.05  																		| (272)  ? [v0] : (sdtpldt0(xr, v0) = xn & sdtpldt0(xp, all_25_0_5) = v0)
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (54) with all_0_1_1, xn, all_15_0_4, xp, xr and discharging atoms sdtpldt0(xr, xp) = xn, sdtpldt0(xn, all_15_0_4) = all_0_1_1, aNaturalNumber0(all_15_0_4), aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 82.26/43.05  																		| (273)  ? [v0] : (sdtpldt0(xr, v0) = all_0_1_1 & sdtpldt0(xp, all_15_0_4) = v0)
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (32) with xp, xn, xr and discharging atoms sdtpldt0(xr, xp) = xn, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 82.26/43.05  																		| (274) sdtlseqdt0(xr, xn)
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (23) with xp, xp, xp, all_59_0_7, all_59_0_7, xp and discharging atoms sdtasdt0(xp, all_59_0_7) = xp, aNaturalNumber0(all_59_0_7), aNaturalNumber0(xp), yields:
% 82.26/43.05  																		| (275)  ~ (sdtpldt0(xp, xp) = xp) |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, xp) = v1 & sdtasdt0(all_59_0_7, xp) = v3 & sdtasdt0(all_59_0_7, xp) = v2 & sdtasdt0(xp, v0) = xp & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_59_0_7, all_59_0_7) = v0)
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (23) with xp, xp, xp, xp, xp, all_59_0_7 and discharging atoms sdtasdt0(all_59_0_7, xp) = xp, aNaturalNumber0(all_59_0_7), aNaturalNumber0(xp), yields:
% 82.26/43.05  																		| (276)  ~ (sdtpldt0(xp, xp) = xp) |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, all_59_0_7) = v1 & sdtasdt0(all_59_0_7, v0) = xp & sdtasdt0(xp, all_59_0_7) = v3 & sdtasdt0(xp, all_59_0_7) = v2 & sdtpldt0(v2, v3) = v1 & sdtpldt0(xp, xp) = v0)
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (54) with xn, xp, xr, all_25_0_5, xp and discharging atoms sdtpldt0(xp, xr) = xn, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 82.26/43.05  																		| (277)  ~ (sdtpldt0(xp, all_25_0_5) = xp) |  ? [v0] : (sdtpldt0(all_25_0_5, xr) = v0 & sdtpldt0(xp, v0) = xn)
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (54) with all_15_0_4, xp, xm, all_25_0_5, all_25_0_5 and discharging atoms sdtpldt0(xp, xm) = all_15_0_4, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xm), yields:
% 82.26/43.05  																		| (278)  ~ (sdtpldt0(all_25_0_5, all_25_0_5) = xp) |  ? [v0] : (sdtpldt0(all_25_0_5, v0) = all_15_0_4 & sdtpldt0(all_25_0_5, xm) = v0)
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (54) with all_15_0_4, xp, xm, all_25_0_5, xp and discharging atoms sdtpldt0(xp, xm) = all_15_0_4, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 82.26/43.05  																		| (279)  ~ (sdtpldt0(xp, all_25_0_5) = xp) |  ? [v0] : (sdtpldt0(all_25_0_5, xm) = v0 & sdtpldt0(xp, v0) = all_15_0_4)
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (54) with all_15_0_4, xp, xm, xp, xp and discharging atoms sdtpldt0(xp, xm) = all_15_0_4, aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 82.26/43.05  																		| (280)  ~ (sdtpldt0(xp, xp) = xp) |  ? [v0] : (sdtpldt0(xp, v0) = all_15_0_4 & sdtpldt0(xp, xm) = v0)
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (54) with all_15_0_4, xm, xp, all_25_0_5, xm and discharging atoms sdtpldt0(xm, xp) = all_15_0_4, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 82.26/43.05  																		| (281)  ~ (sdtpldt0(xm, all_25_0_5) = xm) |  ? [v0] : (sdtpldt0(all_25_0_5, xp) = v0 & sdtpldt0(xm, v0) = all_15_0_4)
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (54) with all_15_0_4, xm, xp, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_15_0_4, aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 82.26/43.05  																		| (282)  ~ (sdtpldt0(xm, xp) = xm) |  ? [v0] : (sdtpldt0(xp, xp) = v0 & sdtpldt0(xm, v0) = all_15_0_4)
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (54) with all_97_0_13, xn, xp, xr, xp and discharging atoms sdtpldt0(xp, xr) = xn, sdtpldt0(xn, xp) = all_97_0_13, aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 82.26/43.05  																		| (283)  ? [v0] : (sdtpldt0(xr, xp) = v0 & sdtpldt0(xp, v0) = all_97_0_13)
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (54) with all_97_0_13, xn, xp, all_25_0_5, xn and discharging atoms sdtpldt0(xn, all_25_0_5) = xn, sdtpldt0(xn, xp) = all_97_0_13, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 82.26/43.05  																		| (284)  ? [v0] : (sdtpldt0(all_25_0_5, xp) = v0 & sdtpldt0(xn, v0) = all_97_0_13)
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (54) with all_97_0_13, xn, xp, xn, all_25_0_5 and discharging atoms sdtpldt0(all_25_0_5, xn) = xn, sdtpldt0(xn, xp) = all_97_0_13, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 82.26/43.05  																		| (285)  ? [v0] : (sdtpldt0(all_25_0_5, v0) = all_97_0_13 & sdtpldt0(xn, xp) = v0)
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (54) with all_97_0_13, xn, xp, all_25_0_5, xr and discharging atoms sdtpldt0(xn, xp) = all_97_0_13, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 82.26/43.05  																		| (286)  ~ (sdtpldt0(xr, all_25_0_5) = xn) |  ? [v0] : (sdtpldt0(all_25_0_5, xp) = v0 & sdtpldt0(xr, v0) = all_97_0_13)
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (54) with all_97_0_13, xn, xp, xp, xr and discharging atoms sdtpldt0(xr, xp) = xn, sdtpldt0(xn, xp) = all_97_0_13, aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 82.26/43.05  																		| (287)  ? [v0] : (sdtpldt0(xr, v0) = all_97_0_13 & sdtpldt0(xp, xp) = v0)
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (54) with xn, xr, xp, xp, xn and discharging atoms sdtpldt0(xr, xp) = xn, aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 82.26/43.05  																		| (288)  ~ (sdtpldt0(xn, xp) = xr) |  ? [v0] : (sdtpldt0(xp, xp) = v0 & sdtpldt0(xn, v0) = xn)
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (54) with all_101_0_15, xr, xm, xp, xn and discharging atoms sdtpldt0(xr, xm) = all_101_0_15, aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 82.26/43.05  																		| (289)  ~ (sdtpldt0(xn, xp) = xr) |  ? [v0] : (sdtpldt0(xp, xm) = v0 & sdtpldt0(xn, v0) = all_101_0_15)
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (2) with all_25_0_5, all_25_0_5 and discharging atoms sdtlseqdt0(all_25_0_5, all_25_0_5), aNaturalNumber0(all_25_0_5), yields:
% 82.26/43.05  																		| (290)  ? [v0] : (sdtpldt0(all_25_0_5, v0) = all_25_0_5 & aNaturalNumber0(v0))
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (55) with all_15_0_4, xp, sz00, xm and discharging atoms sdtpldt0(xm, xp) = all_15_0_4, aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(sz00), yields:
% 82.26/43.05  																		| (291) xm = sz00 |  ~ sdtlseqdt0(xm, sz00) |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = all_15_0_4) &  ~ (v1 = v0) & sdtpldt0(xp, xm) = v0 & sdtpldt0(xp, sz00) = v1 & sdtpldt0(sz00, xp) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_15_0_4, v2))
% 82.26/43.05  																		|
% 82.26/43.05  																		| Instantiating formula (55) with all_0_2_2, xn, sz00, xm and discharging atoms sdtpldt0(xm, xn) = all_0_2_2, aNaturalNumber0(xm), aNaturalNumber0(xn), aNaturalNumber0(sz00), yields:
% 82.26/43.06  																		| (292) xm = sz00 |  ~ sdtlseqdt0(xm, sz00) |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = all_0_2_2) &  ~ (v1 = v0) & sdtpldt0(xn, xm) = v0 & sdtpldt0(xn, sz00) = v1 & sdtpldt0(sz00, xn) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_2_2, v2))
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (40) with sz00, xm and discharging atoms aNaturalNumber0(xm), aNaturalNumber0(sz00), yields:
% 82.26/43.06  																		| (293) xm = sz00 |  ~ sdtlseqdt0(xm, sz00) | iLess0(xm, sz00)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (2) with sz00, xm and discharging atoms aNaturalNumber0(xm), aNaturalNumber0(sz00), yields:
% 82.26/43.06  																		| (294)  ~ sdtlseqdt0(xm, sz00) |  ? [v0] : (sdtpldt0(xm, v0) = sz00 & aNaturalNumber0(v0))
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (2) with all_0_2_2, xn and discharging atoms sdtlseqdt0(xn, all_0_2_2), aNaturalNumber0(all_0_2_2), aNaturalNumber0(xn), yields:
% 82.26/43.06  																		| (295)  ? [v0] : (sdtpldt0(xn, v0) = all_0_2_2 & aNaturalNumber0(v0))
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with all_0_1_1, all_0_2_2, xp, all_103_0_16, xn and discharging atoms sdtpldt0(all_0_2_2, xp) = all_0_1_1, sdtpldt0(xn, all_103_0_16) = all_0_2_2, aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 82.26/43.06  																		| (296)  ~ aNaturalNumber0(all_103_0_16) |  ? [v0] : (sdtpldt0(all_103_0_16, xp) = v0 & sdtpldt0(xn, v0) = all_0_1_1)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with all_15_0_4, xm, xp, all_107_0_18, xm and discharging atoms sdtpldt0(xm, all_107_0_18) = xm, sdtpldt0(xm, xp) = all_15_0_4, aNaturalNumber0(all_107_0_18), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 82.26/43.06  																		| (297)  ? [v0] : (sdtpldt0(all_107_0_18, xp) = v0 & sdtpldt0(xm, v0) = all_15_0_4)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with all_0_2_2, xn, xm, all_91_0_10, xn and discharging atoms sdtpldt0(xn, all_91_0_10) = xn, sdtpldt0(xn, xm) = all_0_2_2, aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 82.26/43.06  																		| (298)  ~ aNaturalNumber0(all_91_0_10) |  ? [v0] : (sdtpldt0(all_91_0_10, xm) = v0 & sdtpldt0(xn, v0) = all_0_2_2)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with all_15_0_4, xp, xm, all_109_0_19, xp and discharging atoms sdtpldt0(xp, all_109_0_19) = xp, sdtpldt0(xp, xm) = all_15_0_4, aNaturalNumber0(all_109_0_19), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 82.26/43.06  																		| (299)  ? [v0] : (sdtpldt0(all_109_0_19, xm) = v0 & sdtpldt0(xp, v0) = all_15_0_4)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (69) with xm, all_107_0_18, xm and discharging atoms sdtpldt0(xm, all_107_0_18) = xm, aNaturalNumber0(all_107_0_18), aNaturalNumber0(xm), yields:
% 82.26/43.06  																		| (300) sdtpldt0(all_107_0_18, xm) = xm
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with all_0_1_1, xn, all_122_0_20, all_25_0_5, xn and discharging atoms sdtpldt0(xn, all_122_0_20) = all_0_1_1, sdtpldt0(xn, all_25_0_5) = xn, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xn), yields:
% 82.26/43.06  																		| (301)  ~ aNaturalNumber0(all_122_0_20) |  ? [v0] : (sdtpldt0(all_25_0_5, all_122_0_20) = v0 & sdtpldt0(xn, v0) = all_0_1_1)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (69) with all_0_1_1, all_122_0_20, xn and discharging atoms sdtpldt0(xn, all_122_0_20) = all_0_1_1, aNaturalNumber0(xn), yields:
% 82.26/43.06  																		| (302)  ~ aNaturalNumber0(all_122_0_20) | sdtpldt0(all_122_0_20, xn) = all_0_1_1
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (69) with all_0_2_2, all_103_0_16, xn and discharging atoms sdtpldt0(xn, all_103_0_16) = all_0_2_2, aNaturalNumber0(xn), yields:
% 82.26/43.06  																		| (303)  ~ aNaturalNumber0(all_103_0_16) | sdtpldt0(all_103_0_16, xn) = all_0_2_2
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with xn, xn, all_91_0_10, all_25_0_5, xn and discharging atoms sdtpldt0(xn, all_91_0_10) = xn, sdtpldt0(xn, all_25_0_5) = xn, aNaturalNumber0(all_25_0_5), aNaturalNumber0(xn), yields:
% 82.26/43.06  																		| (304)  ~ aNaturalNumber0(all_91_0_10) |  ? [v0] : (sdtpldt0(all_25_0_5, all_91_0_10) = v0 & sdtpldt0(xn, v0) = xn)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with xn, xn, all_91_0_10, xp, xr and discharging atoms sdtpldt0(xr, xp) = xn, sdtpldt0(xn, all_91_0_10) = xn, aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 82.26/43.06  																		| (305)  ~ aNaturalNumber0(all_91_0_10) |  ? [v0] : (sdtpldt0(xr, v0) = xn & sdtpldt0(xp, all_91_0_10) = v0)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (69) with xn, all_91_0_10, xn and discharging atoms sdtpldt0(xn, all_91_0_10) = xn, aNaturalNumber0(xn), yields:
% 82.26/43.06  																		| (306)  ~ aNaturalNumber0(all_91_0_10) | sdtpldt0(all_91_0_10, xn) = xn
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with all_97_0_13, xn, xp, all_89_0_9, xp and discharging atoms sdtpldt0(xp, all_89_0_9) = xn, sdtpldt0(xn, xp) = all_97_0_13, aNaturalNumber0(xp), yields:
% 82.26/43.06  																		| (307)  ~ aNaturalNumber0(all_89_0_9) |  ? [v0] : (sdtpldt0(all_89_0_9, xp) = v0 & sdtpldt0(xp, v0) = all_97_0_13)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with all_97_0_13, xn, xp, all_91_0_10, xn and discharging atoms sdtpldt0(xn, all_91_0_10) = xn, sdtpldt0(xn, xp) = all_97_0_13, aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 82.26/43.06  																		| (308)  ~ aNaturalNumber0(all_91_0_10) |  ? [v0] : (sdtpldt0(all_91_0_10, xp) = v0 & sdtpldt0(xn, v0) = all_97_0_13)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with xn, xn, xp, all_127_0_21, sz10 and discharging atoms sdtpldt0(sz10, all_127_0_21) = xn, aNaturalNumber0(all_127_0_21), aNaturalNumber0(xp), aNaturalNumber0(sz10), yields:
% 82.26/43.06  																		| (309)  ~ (sdtpldt0(xn, xp) = xn) |  ? [v0] : (sdtpldt0(all_127_0_21, xp) = v0 & sdtpldt0(sz10, v0) = xn)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with all_0_2_2, xn, xm, all_109_0_19, xn and discharging atoms sdtpldt0(xn, xm) = all_0_2_2, aNaturalNumber0(all_109_0_19), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 82.26/43.06  																		| (310)  ~ (sdtpldt0(xn, all_109_0_19) = xn) |  ? [v0] : (sdtpldt0(all_109_0_19, xm) = v0 & sdtpldt0(xn, v0) = all_0_2_2)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (29) with all_109_0_19 and discharging atoms aNaturalNumber0(all_109_0_19), yields:
% 82.26/43.06  																		| (311) all_109_0_19 = sz10 | all_109_0_19 = sz00 |  ? [v0] : (isPrime0(v0) & doDivides0(v0, all_109_0_19) & aNaturalNumber0(v0))
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with xp, xp, all_107_0_18, all_107_0_18, xp and discharging atoms aNaturalNumber0(all_107_0_18), aNaturalNumber0(xp), yields:
% 82.26/43.06  																		| (312)  ~ (sdtpldt0(xp, all_107_0_18) = xp) |  ? [v0] : (sdtpldt0(all_107_0_18, all_107_0_18) = v0 & sdtpldt0(xp, v0) = xp)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with all_15_0_4, xp, xm, all_107_0_18, xp and discharging atoms sdtpldt0(xp, xm) = all_15_0_4, aNaturalNumber0(all_107_0_18), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 82.26/43.06  																		| (313)  ~ (sdtpldt0(xp, all_107_0_18) = xp) |  ? [v0] : (sdtpldt0(all_107_0_18, xm) = v0 & sdtpldt0(xp, v0) = all_15_0_4)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with xm, xm, all_25_0_5, all_25_0_5, xm and discharging atoms aNaturalNumber0(all_25_0_5), aNaturalNumber0(xm), yields:
% 82.26/43.06  																		| (314)  ~ (sdtpldt0(xm, all_25_0_5) = xm) |  ? [v0] : (sdtpldt0(all_25_0_5, all_25_0_5) = v0 & sdtpldt0(xm, v0) = xm)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with xm, xm, all_107_0_18, xp, xm and discharging atoms sdtpldt0(xm, all_107_0_18) = xm, aNaturalNumber0(all_107_0_18), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 82.26/43.06  																		| (315)  ~ (sdtpldt0(xm, xp) = xm) |  ? [v0] : (sdtpldt0(xp, all_107_0_18) = v0 & sdtpldt0(xm, v0) = xm)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with xn, xn, all_107_0_18, all_25_0_5, xn and discharging atoms sdtpldt0(xn, all_25_0_5) = xn, aNaturalNumber0(all_107_0_18), aNaturalNumber0(all_25_0_5), aNaturalNumber0(xn), yields:
% 82.26/43.06  																		| (316)  ~ (sdtpldt0(xn, all_107_0_18) = xn) |  ? [v0] : (sdtpldt0(all_25_0_5, all_107_0_18) = v0 & sdtpldt0(xn, v0) = xn)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (55) with xm, all_107_0_18, sz00, xm and discharging atoms sdtpldt0(xm, all_107_0_18) = xm, aNaturalNumber0(all_107_0_18), aNaturalNumber0(xm), aNaturalNumber0(sz00), yields:
% 82.26/43.06  																		| (317) xm = sz00 |  ~ sdtlseqdt0(xm, sz00) |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = xm) &  ~ (v1 = v0) & sdtpldt0(all_107_0_18, xm) = v0 & sdtpldt0(all_107_0_18, sz00) = v1 & sdtpldt0(sz00, all_107_0_18) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xm, v2))
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with all_0_1_1, xm, all_97_0_13, all_107_0_18, xm and discharging atoms sdtpldt0(xm, all_107_0_18) = xm, sdtpldt0(xm, all_97_0_13) = all_0_1_1, aNaturalNumber0(all_107_0_18), aNaturalNumber0(xm), yields:
% 82.26/43.06  																		| (318)  ~ aNaturalNumber0(all_97_0_13) |  ? [v0] : (sdtpldt0(all_107_0_18, all_97_0_13) = v0 & sdtpldt0(xm, v0) = all_0_1_1)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with xp, xp, all_107_0_18, all_105_0_17, sz10 and discharging atoms sdtpldt0(sz10, all_105_0_17) = xp, aNaturalNumber0(all_107_0_18), aNaturalNumber0(all_105_0_17), aNaturalNumber0(sz10), yields:
% 82.26/43.06  																		| (319)  ~ (sdtpldt0(xp, all_107_0_18) = xp) |  ? [v0] : (sdtpldt0(all_105_0_17, all_107_0_18) = v0 & sdtpldt0(sz10, v0) = xp)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with all_0_2_2, all_0_2_2, xp, xn, all_15_0_4 and discharging atoms aNaturalNumber0(all_15_0_4), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 82.26/43.06  																		| (320)  ~ (sdtpldt0(all_15_0_4, xn) = all_0_2_2) |  ~ (sdtpldt0(all_0_2_2, xp) = all_0_2_2) |  ? [v0] : (sdtpldt0(all_15_0_4, v0) = all_0_2_2 & sdtpldt0(xn, xp) = v0)
% 82.26/43.06  																		|
% 82.26/43.06  																		| Instantiating formula (54) with all_0_1_1, all_0_2_2, xp, all_15_0_4, xr and discharging atoms sdtpldt0(all_0_2_2, xp) = all_0_1_1, aNaturalNumber0(all_15_0_4), aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 82.26/43.06  																		| (321)  ~ (sdtpldt0(xr, all_15_0_4) = all_0_2_2) |  ? [v0] : (sdtpldt0(all_15_0_4, xp) = v0 & sdtpldt0(xr, v0) = all_0_1_1)
% 82.26/43.06  																		|
% 82.26/43.07  																		| Instantiating formula (54) with all_0_1_1, xn, all_15_0_4, all_91_0_10, xn and discharging atoms sdtpldt0(xn, all_91_0_10) = xn, sdtpldt0(xn, all_15_0_4) = all_0_1_1, aNaturalNumber0(all_15_0_4), aNaturalNumber0(xn), yields:
% 82.26/43.07  																		| (322)  ~ aNaturalNumber0(all_91_0_10) |  ? [v0] : (sdtpldt0(all_91_0_10, all_15_0_4) = v0 & sdtpldt0(xn, v0) = all_0_1_1)
% 82.26/43.07  																		|
% 82.26/43.07  																		| Instantiating formula (32) with all_15_0_4, all_0_1_1, xn and discharging atoms sdtpldt0(xn, all_15_0_4) = all_0_1_1, aNaturalNumber0(all_15_0_4), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xn), yields:
% 82.26/43.07  																		| (323) sdtlseqdt0(xn, all_0_1_1)
% 82.26/43.07  																		|
% 82.26/43.07  																		| Instantiating formula (54) with all_122_0_20, all_25_0_5, all_15_0_4, all_25_0_5, all_25_0_5 and discharging atoms sdtpldt0(all_25_0_5, all_15_0_4) = all_122_0_20, aNaturalNumber0(all_25_0_5), aNaturalNumber0(all_15_0_4), yields:
% 82.26/43.07  																		| (324)  ~ (sdtpldt0(all_25_0_5, all_25_0_5) = all_25_0_5) |  ? [v0] : (sdtpldt0(all_25_0_5, v0) = all_122_0_20 & sdtpldt0(all_25_0_5, all_15_0_4) = v0)
% 82.26/43.07  																		|
% 82.26/43.07  																		| Instantiating formula (26) with all_122_0_20, all_15_0_4 and discharging atoms aNaturalNumber0(all_15_0_4), yields:
% 82.26/43.07  																		| (325)  ~ (sdtpldt0(sz00, all_15_0_4) = all_122_0_20) | sdtpldt0(all_15_0_4, sz00) = all_15_0_4
% 82.26/43.07  																		|
% 82.26/43.07  																		| Instantiating formula (54) with all_0_1_1, xm, xn, xp, xm and discharging atoms aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 82.26/43.07  																		| (326)  ~ (sdtpldt0(xm, xp) = xm) |  ~ (sdtpldt0(xm, xn) = all_0_1_1) |  ? [v0] : (sdtpldt0(xp, xn) = v0 & sdtpldt0(xm, v0) = all_0_1_1)
% 82.26/43.07  																		|
% 82.26/43.07  																		| Instantiating formula (54) with xm, xm, all_107_0_18, all_15_0_4, all_25_0_5 and discharging atoms sdtpldt0(xm, all_107_0_18) = xm, aNaturalNumber0(all_107_0_18), aNaturalNumber0(all_25_0_5), aNaturalNumber0(all_15_0_4), yields:
% 82.26/43.07  																		| (327)  ~ (sdtpldt0(all_25_0_5, all_15_0_4) = xm) |  ? [v0] : (sdtpldt0(all_25_0_5, v0) = xm & sdtpldt0(all_15_0_4, all_107_0_18) = v0)
% 82.26/43.07  																		|
% 82.26/43.07  																		| Instantiating formula (40) with all_15_0_4, sz00 and discharging atoms aNaturalNumber0(all_15_0_4), aNaturalNumber0(sz00), yields:
% 82.26/43.07  																		| (328) all_15_0_4 = sz00 |  ~ sdtlseqdt0(sz00, all_15_0_4) | iLess0(sz00, all_15_0_4)
% 82.26/43.07  																		|
% 82.26/43.07  																		| Instantiating formula (2) with all_15_0_4, sz00 and discharging atoms aNaturalNumber0(all_15_0_4), aNaturalNumber0(sz00), yields:
% 82.26/43.07  																		| (329)  ~ sdtlseqdt0(sz00, all_15_0_4) |  ? [v0] : (sdtpldt0(sz00, v0) = all_15_0_4 & aNaturalNumber0(v0))
% 82.26/43.07  																		|
% 82.26/43.07  																		| Instantiating formula (2) with all_0_1_1, xr and discharging atoms aNaturalNumber0(all_0_1_1), aNaturalNumber0(xr), yields:
% 82.26/43.07  																		| (330)  ~ sdtlseqdt0(xr, all_0_1_1) |  ? [v0] : (sdtpldt0(xr, v0) = all_0_1_1 & aNaturalNumber0(v0))
% 82.26/43.07  																		|
% 82.26/43.07  																		| Instantiating formula (2) with all_0_1_1, xn and discharging atoms aNaturalNumber0(all_0_1_1), aNaturalNumber0(xn), yields:
% 82.26/43.07  																		| (331)  ~ sdtlseqdt0(xn, all_0_1_1) |  ? [v0] : (sdtpldt0(xn, v0) = all_0_1_1 & aNaturalNumber0(v0))
% 82.26/43.07  																		|
% 82.26/43.07  																		| Instantiating (299) with all_238_0_25 yields:
% 82.26/43.07  																		| (332) sdtpldt0(all_109_0_19, xm) = all_238_0_25 & sdtpldt0(xp, all_238_0_25) = all_15_0_4
% 82.26/43.07  																		|
% 82.26/43.07  																		| Applying alpha-rule on (332) yields:
% 82.26/43.07  																		| (333) sdtpldt0(all_109_0_19, xm) = all_238_0_25
% 82.26/43.07  																		| (334) sdtpldt0(xp, all_238_0_25) = all_15_0_4
% 82.26/43.07  																		|
% 82.26/43.07  																		| Instantiating (284) with all_250_0_31 yields:
% 82.26/43.07  																		| (335) sdtpldt0(all_25_0_5, xp) = all_250_0_31 & sdtpldt0(xn, all_250_0_31) = all_97_0_13
% 82.26/43.07  																		|
% 82.26/43.07  																		| Applying alpha-rule on (335) yields:
% 82.26/43.07  																		| (336) sdtpldt0(all_25_0_5, xp) = all_250_0_31
% 82.26/43.07  																		| (337) sdtpldt0(xn, all_250_0_31) = all_97_0_13
% 82.26/43.07  																		|
% 82.26/43.07  																		| Instantiating (297) with all_262_0_37 yields:
% 82.26/43.07  																		| (338) sdtpldt0(all_107_0_18, xp) = all_262_0_37 & sdtpldt0(xm, all_262_0_37) = all_15_0_4
% 82.26/43.07  																		|
% 82.26/43.07  																		| Applying alpha-rule on (338) yields:
% 82.26/43.07  																		| (339) sdtpldt0(all_107_0_18, xp) = all_262_0_37
% 82.26/43.07  																		| (340) sdtpldt0(xm, all_262_0_37) = all_15_0_4
% 82.26/43.07  																		|
% 82.26/43.07  																		| Instantiating (287) with all_268_0_40 yields:
% 82.26/43.07  																		| (341) sdtpldt0(xr, all_268_0_40) = all_97_0_13 & sdtpldt0(xp, xp) = all_268_0_40
% 82.26/43.07  																		|
% 82.26/43.07  																		| Applying alpha-rule on (341) yields:
% 82.26/43.07  																		| (342) sdtpldt0(xr, all_268_0_40) = all_97_0_13
% 82.26/43.07  																		| (343) sdtpldt0(xp, xp) = all_268_0_40
% 82.26/43.07  																		|
% 82.26/43.07  																		| Instantiating (295) with all_270_0_41 yields:
% 82.26/43.07  																		| (344) sdtpldt0(xn, all_270_0_41) = all_0_2_2 & aNaturalNumber0(all_270_0_41)
% 82.26/43.07  																		|
% 82.26/43.07  																		| Applying alpha-rule on (344) yields:
% 82.26/43.07  																		| (345) sdtpldt0(xn, all_270_0_41) = all_0_2_2
% 82.26/43.07  																		| (346) aNaturalNumber0(all_270_0_41)
% 82.26/43.07  																		|
% 82.26/43.07  																		| Instantiating (290) with all_284_0_48 yields:
% 82.26/43.07  																		| (347) sdtpldt0(all_25_0_5, all_284_0_48) = all_25_0_5 & aNaturalNumber0(all_284_0_48)
% 82.26/43.07  																		|
% 82.26/43.07  																		| Applying alpha-rule on (347) yields:
% 82.26/43.07  																		| (348) sdtpldt0(all_25_0_5, all_284_0_48) = all_25_0_5
% 82.26/43.07  																		| (349) aNaturalNumber0(all_284_0_48)
% 82.26/43.07  																		|
% 82.26/43.07  																		| Instantiating (285) with all_294_0_53 yields:
% 82.26/43.07  																		| (350) sdtpldt0(all_25_0_5, all_294_0_53) = all_97_0_13 & sdtpldt0(xn, xp) = all_294_0_53
% 82.26/43.07  																		|
% 82.26/43.07  																		| Applying alpha-rule on (350) yields:
% 82.26/43.07  																		| (351) sdtpldt0(all_25_0_5, all_294_0_53) = all_97_0_13
% 82.26/43.07  																		| (352) sdtpldt0(xn, xp) = all_294_0_53
% 82.26/43.07  																		|
% 82.26/43.07  																		| Instantiating (283) with all_296_0_54 yields:
% 82.26/43.07  																		| (353) sdtpldt0(xr, xp) = all_296_0_54 & sdtpldt0(xp, all_296_0_54) = all_97_0_13
% 82.26/43.07  																		|
% 82.26/43.07  																		| Applying alpha-rule on (353) yields:
% 82.26/43.07  																		| (354) sdtpldt0(xr, xp) = all_296_0_54
% 82.26/43.07  																		| (355) sdtpldt0(xp, all_296_0_54) = all_97_0_13
% 82.26/43.07  																		|
% 82.26/43.07  																		| Instantiating (272) with all_306_0_59 yields:
% 82.26/43.07  																		| (356) sdtpldt0(xr, all_306_0_59) = xn & sdtpldt0(xp, all_25_0_5) = all_306_0_59
% 82.26/43.07  																		|
% 82.26/43.07  																		| Applying alpha-rule on (356) yields:
% 82.26/43.07  																		| (357) sdtpldt0(xr, all_306_0_59) = xn
% 82.26/43.07  																		| (358) sdtpldt0(xp, all_25_0_5) = all_306_0_59
% 82.26/43.07  																		|
% 82.26/43.07  																		| Instantiating (273) with all_310_0_61 yields:
% 82.26/43.07  																		| (359) sdtpldt0(xr, all_310_0_61) = all_0_1_1 & sdtpldt0(xp, all_15_0_4) = all_310_0_61
% 82.26/43.07  																		|
% 82.26/43.07  																		| Applying alpha-rule on (359) yields:
% 82.26/43.07  																		| (360) sdtpldt0(xr, all_310_0_61) = all_0_1_1
% 82.26/43.07  																		| (361) sdtpldt0(xp, all_15_0_4) = all_310_0_61
% 82.26/43.07  																		|
% 82.26/43.07  																		+-Applying beta-rule and splitting (303), into two cases.
% 82.26/43.07  																		|-Branch one:
% 82.26/43.07  																		| (362)  ~ aNaturalNumber0(all_103_0_16)
% 82.26/43.07  																		|
% 82.26/43.07  																			| Using (269) and (362) yields:
% 82.26/43.07  																			| (97) $false
% 82.26/43.07  																			|
% 82.26/43.07  																			|-The branch is then unsatisfiable
% 82.26/43.07  																		|-Branch two:
% 82.26/43.07  																		| (269) aNaturalNumber0(all_103_0_16)
% 82.26/43.07  																		| (365) sdtpldt0(all_103_0_16, xn) = all_0_2_2
% 82.26/43.07  																		|
% 82.26/43.07  																			+-Applying beta-rule and splitting (306), into two cases.
% 82.26/43.07  																			|-Branch one:
% 82.26/43.07  																			| (366)  ~ aNaturalNumber0(all_91_0_10)
% 82.26/43.07  																			|
% 82.26/43.07  																				| Using (264) and (366) yields:
% 82.26/43.07  																				| (97) $false
% 82.26/43.07  																				|
% 82.26/43.07  																				|-The branch is then unsatisfiable
% 82.26/43.07  																			|-Branch two:
% 82.26/43.07  																			| (264) aNaturalNumber0(all_91_0_10)
% 82.26/43.07  																			| (369) sdtpldt0(all_91_0_10, xn) = xn
% 82.26/43.07  																			|
% 82.26/43.07  																				+-Applying beta-rule and splitting (30), into two cases.
% 82.26/43.07  																				|-Branch one:
% 82.26/43.07  																				| (370)  ~ sdtlseqdt0(xr, xn)
% 82.26/43.07  																				|
% 82.26/43.07  																					| Using (274) and (370) yields:
% 82.26/43.07  																					| (97) $false
% 82.26/43.07  																					|
% 82.26/43.07  																					|-The branch is then unsatisfiable
% 82.26/43.07  																				|-Branch two:
% 82.26/43.07  																				| (274) sdtlseqdt0(xr, xn)
% 82.26/43.07  																				| (373) xr = xn
% 82.26/43.07  																				|
% 82.26/43.07  																					| From (373) and (172) follows:
% 82.26/43.07  																					| (374) sdtpldt0(xn, all_25_0_5) = all_89_0_9
% 82.26/43.07  																					|
% 82.26/43.07  																					| From (373) and (354) follows:
% 82.26/43.07  																					| (375) sdtpldt0(xn, xp) = all_296_0_54
% 82.26/43.07  																					|
% 82.26/43.07  																					+-Applying beta-rule and splitting (251), into two cases.
% 82.26/43.07  																					|-Branch one:
% 82.26/43.07  																					| (362)  ~ aNaturalNumber0(all_103_0_16)
% 82.26/43.07  																					|
% 82.26/43.07  																						| Using (269) and (362) yields:
% 82.26/43.07  																						| (97) $false
% 82.26/43.07  																						|
% 82.26/43.07  																						|-The branch is then unsatisfiable
% 82.26/43.07  																					|-Branch two:
% 82.26/43.07  																					| (269) aNaturalNumber0(all_103_0_16)
% 82.26/43.07  																					| (379) all_103_0_16 = xm
% 82.26/43.07  																					|
% 82.26/43.07  																						| From (379) and (268) follows:
% 82.26/43.07  																						| (380) sdtpldt0(xm, all_25_0_5) = xm
% 82.26/43.07  																						|
% 82.26/43.07  																						+-Applying beta-rule and splitting (243), into two cases.
% 82.26/43.07  																						|-Branch one:
% 82.26/43.07  																						| (381)  ~ (sdtpldt0(xr, all_25_0_5) = xn)
% 82.26/43.07  																						|
% 82.26/43.07  																							| From (373) and (381) follows:
% 82.26/43.07  																							| (382)  ~ (sdtpldt0(xn, all_25_0_5) = xn)
% 82.26/43.07  																							|
% 82.26/43.07  																							| Using (101) and (382) yields:
% 82.26/43.07  																							| (97) $false
% 82.26/43.07  																							|
% 82.26/43.07  																							|-The branch is then unsatisfiable
% 82.26/43.07  																						|-Branch two:
% 82.26/43.07  																						| (384) sdtpldt0(xr, all_25_0_5) = xn
% 82.26/43.07  																						| (385) all_25_0_5 = xp
% 82.26/43.07  																						|
% 82.26/43.07  																							| From (385)(385) and (348) follows:
% 82.26/43.07  																							| (386) sdtpldt0(xp, all_284_0_48) = xp
% 82.26/43.07  																							|
% 82.26/43.07  																							| From (385)(385) and (175) follows:
% 82.26/43.07  																							| (387) sdtpldt0(xp, xp) = all_91_0_10
% 82.26/43.07  																							|
% 82.26/43.07  																							| From (385) and (336) follows:
% 82.26/43.07  																							| (388) sdtpldt0(xp, xp) = all_250_0_31
% 82.26/43.07  																							|
% 82.26/43.07  																							| From (385) and (265) follows:
% 82.26/43.07  																							| (389) sdtpldt0(all_15_0_4, xp) = all_122_0_20
% 82.26/43.07  																							|
% 82.26/43.07  																							| From (385) and (358) follows:
% 82.26/43.07  																							| (390) sdtpldt0(xp, xp) = all_306_0_59
% 82.26/43.07  																							|
% 82.26/43.07  																							| From (385) and (380) follows:
% 82.26/43.07  																							| (391) sdtpldt0(xm, xp) = xm
% 82.26/43.07  																							|
% 82.26/43.07  																							| From (385) and (374) follows:
% 82.26/43.07  																							| (392) sdtpldt0(xn, xp) = all_89_0_9
% 82.26/43.07  																							|
% 82.26/43.07  																							| From (385) and (101) follows:
% 82.26/43.07  																							| (393) sdtpldt0(xn, xp) = xn
% 82.26/43.07  																							|
% 82.26/43.07  																							| From (385) and (262) follows:
% 82.26/43.07  																							| (394)  ~ (sdtpldt0(xp, all_15_0_4) = sz00)
% 82.26/43.07  																							|
% 82.26/43.07  																							+-Applying beta-rule and splitting (247), into two cases.
% 82.26/43.07  																							|-Branch one:
% 82.26/43.07  																							| (395)  ~ (sdtpldt0(xn, xp) = xn)
% 82.26/43.07  																							|
% 82.26/43.07  																								| Using (393) and (395) yields:
% 82.26/43.07  																								| (97) $false
% 82.26/43.07  																								|
% 82.26/43.07  																								|-The branch is then unsatisfiable
% 82.26/43.07  																							|-Branch two:
% 82.26/43.07  																							| (393) sdtpldt0(xn, xp) = xn
% 82.26/43.07  																							| (398) all_97_0_13 = xn
% 82.26/43.07  																							|
% 82.26/43.07  																								| From (398) and (181) follows:
% 82.26/43.07  																								| (399) sdtpldt0(xm, xn) = all_0_1_1
% 82.26/43.07  																								|
% 82.26/43.07  																								| From (398) and (337) follows:
% 82.26/43.07  																								| (400) sdtpldt0(xn, all_250_0_31) = xn
% 82.26/43.07  																								|
% 82.26/43.07  																								+-Applying beta-rule and splitting (304), into two cases.
% 82.26/43.07  																								|-Branch one:
% 82.26/43.07  																								| (366)  ~ aNaturalNumber0(all_91_0_10)
% 82.26/43.07  																								|
% 82.26/43.07  																									| Using (264) and (366) yields:
% 82.26/43.07  																									| (97) $false
% 82.26/43.07  																									|
% 82.26/43.07  																									|-The branch is then unsatisfiable
% 82.26/43.07  																								|-Branch two:
% 82.26/43.07  																								| (264) aNaturalNumber0(all_91_0_10)
% 82.26/43.08  																								| (404)  ? [v0] : (sdtpldt0(all_25_0_5, all_91_0_10) = v0 & sdtpldt0(xn, v0) = xn)
% 82.26/43.08  																								|
% 82.26/43.08  																									| Instantiating (404) with all_347_0_66 yields:
% 82.26/43.08  																									| (405) sdtpldt0(all_25_0_5, all_91_0_10) = all_347_0_66 & sdtpldt0(xn, all_347_0_66) = xn
% 82.26/43.08  																									|
% 82.26/43.08  																									| Applying alpha-rule on (405) yields:
% 82.26/43.08  																									| (406) sdtpldt0(all_25_0_5, all_91_0_10) = all_347_0_66
% 82.26/43.08  																									| (407) sdtpldt0(xn, all_347_0_66) = xn
% 82.26/43.08  																									|
% 82.26/43.08  																									| From (385) and (406) follows:
% 82.26/43.08  																									| (408) sdtpldt0(xp, all_91_0_10) = all_347_0_66
% 82.26/43.08  																									|
% 82.26/43.08  																									+-Applying beta-rule and splitting (305), into two cases.
% 82.26/43.08  																									|-Branch one:
% 82.26/43.08  																									| (366)  ~ aNaturalNumber0(all_91_0_10)
% 82.26/43.08  																									|
% 82.26/43.08  																										| Using (264) and (366) yields:
% 82.26/43.08  																										| (97) $false
% 82.26/43.08  																										|
% 82.26/43.08  																										|-The branch is then unsatisfiable
% 82.26/43.08  																									|-Branch two:
% 82.26/43.08  																									| (264) aNaturalNumber0(all_91_0_10)
% 82.26/43.08  																									| (412)  ? [v0] : (sdtpldt0(xr, v0) = xn & sdtpldt0(xp, all_91_0_10) = v0)
% 82.26/43.08  																									|
% 82.26/43.08  																										| Instantiating (412) with all_352_0_67 yields:
% 82.26/43.08  																										| (413) sdtpldt0(xr, all_352_0_67) = xn & sdtpldt0(xp, all_91_0_10) = all_352_0_67
% 82.26/43.08  																										|
% 82.26/43.08  																										| Applying alpha-rule on (413) yields:
% 82.26/43.08  																										| (414) sdtpldt0(xr, all_352_0_67) = xn
% 82.26/43.08  																										| (415) sdtpldt0(xp, all_91_0_10) = all_352_0_67
% 82.26/43.08  																										|
% 82.26/43.08  																										+-Applying beta-rule and splitting (307), into two cases.
% 82.26/43.08  																										|-Branch one:
% 82.26/43.08  																										| (416)  ~ aNaturalNumber0(all_89_0_9)
% 82.26/43.08  																										|
% 82.26/43.08  																											| Using (271) and (416) yields:
% 82.26/43.08  																											| (97) $false
% 82.26/43.08  																											|
% 82.26/43.08  																											|-The branch is then unsatisfiable
% 82.26/43.08  																										|-Branch two:
% 82.26/43.08  																										| (271) aNaturalNumber0(all_89_0_9)
% 82.26/43.08  																										| (419)  ? [v0] : (sdtpldt0(all_89_0_9, xp) = v0 & sdtpldt0(xp, v0) = all_97_0_13)
% 82.26/43.08  																										|
% 82.26/43.08  																											| Instantiating (419) with all_357_0_68 yields:
% 82.26/43.08  																											| (420) sdtpldt0(all_89_0_9, xp) = all_357_0_68 & sdtpldt0(xp, all_357_0_68) = all_97_0_13
% 82.26/43.08  																											|
% 82.26/43.08  																											| Applying alpha-rule on (420) yields:
% 82.26/43.08  																											| (421) sdtpldt0(all_89_0_9, xp) = all_357_0_68
% 82.26/43.08  																											| (422) sdtpldt0(xp, all_357_0_68) = all_97_0_13
% 82.26/43.08  																											|
% 82.26/43.08  																											+-Applying beta-rule and splitting (242), into two cases.
% 82.26/43.08  																											|-Branch one:
% 82.26/43.08  																											| (423)  ~ (sdtpldt0(xm, xn) = all_0_1_1)
% 82.26/43.08  																											|
% 82.26/43.08  																												| Using (399) and (423) yields:
% 82.26/43.08  																												| (97) $false
% 82.26/43.08  																												|
% 82.26/43.08  																												|-The branch is then unsatisfiable
% 82.26/43.08  																											|-Branch two:
% 82.26/43.08  																											| (399) sdtpldt0(xm, xn) = all_0_1_1
% 82.26/43.08  																											| (426) all_0_1_1 = all_0_2_2
% 82.26/43.08  																											|
% 82.26/43.08  																												| From (426) and (4) follows:
% 82.26/43.08  																												| (427) sdtpldt0(all_0_2_2, xp) = all_0_2_2
% 82.26/43.08  																												|
% 82.26/43.08  																												| From (426) and (208) follows:
% 82.26/43.08  																												| (428) sdtpldt0(xn, all_122_0_20) = all_0_2_2
% 82.26/43.08  																												|
% 82.26/43.08  																												| From (426) and (323) follows:
% 82.26/43.08  																												| (156) sdtlseqdt0(xn, all_0_2_2)
% 82.26/43.08  																												|
% 82.26/43.08  																												+-Applying beta-rule and splitting (244), into two cases.
% 82.26/43.08  																												|-Branch one:
% 82.26/43.08  																												| (430)  ~ (sdtpldt0(xr, xp) = all_89_0_9)
% 82.26/43.08  																												|
% 82.26/43.08  																													| From (373) and (430) follows:
% 82.26/43.08  																													| (431)  ~ (sdtpldt0(xn, xp) = all_89_0_9)
% 82.26/43.08  																													|
% 82.26/43.08  																													| Using (392) and (431) yields:
% 82.26/43.08  																													| (97) $false
% 82.26/43.08  																													|
% 82.26/43.08  																													|-The branch is then unsatisfiable
% 82.26/43.08  																												|-Branch two:
% 82.26/43.08  																												| (433) sdtpldt0(xr, xp) = all_89_0_9
% 82.26/43.08  																												| (434) all_89_0_9 = xn
% 82.26/43.08  																												|
% 82.26/43.08  																													| From (434) and (421) follows:
% 82.26/43.08  																													| (435) sdtpldt0(xn, xp) = all_357_0_68
% 82.26/43.08  																													|
% 82.26/43.08  																													+-Applying beta-rule and splitting (246), into two cases.
% 82.26/43.08  																													|-Branch one:
% 82.26/43.08  																													| (436)  ~ (sdtpldt0(xn, sz00) = xn)
% 82.26/43.08  																													|
% 82.26/43.08  																														+-Applying beta-rule and splitting (245), into two cases.
% 82.26/43.08  																														|-Branch one:
% 82.26/43.08  																														| (437)  ~ (sdtpldt0(xm, xp) = xm)
% 82.26/43.08  																														|
% 82.26/43.08  																															| Using (391) and (437) yields:
% 82.26/43.08  																															| (97) $false
% 82.26/43.08  																															|
% 82.26/43.08  																															|-The branch is then unsatisfiable
% 82.26/43.08  																														|-Branch two:
% 82.26/43.08  																														| (391) sdtpldt0(xm, xp) = xm
% 82.26/43.08  																														| (440) all_15_0_4 = xm
% 82.26/43.08  																														|
% 82.26/43.08  																															| Equations (440) can reduce 138 to:
% 82.26/43.08  																															| (441)  ~ (xm = sz00)
% 82.26/43.08  																															|
% 82.26/43.08  																															| From (440) and (389) follows:
% 82.26/43.08  																															| (442) sdtpldt0(xm, xp) = all_122_0_20
% 82.26/43.08  																															|
% 82.26/43.08  																															| From (440) and (361) follows:
% 82.26/43.08  																															| (443) sdtpldt0(xp, xm) = all_310_0_61
% 82.26/43.08  																															|
% 82.26/43.08  																															| From (440) and (93) follows:
% 82.26/43.08  																															| (391) sdtpldt0(xm, xp) = xm
% 82.26/43.08  																															|
% 82.26/43.08  																															| From (440) and (394) follows:
% 82.26/43.08  																															| (445)  ~ (sdtpldt0(xp, xm) = sz00)
% 82.26/43.08  																															|
% 82.26/43.08  																															+-Applying beta-rule and splitting (248), into two cases.
% 82.26/43.08  																															|-Branch one:
% 82.26/43.08  																															| (446) xm = sz00
% 82.26/43.08  																															|
% 82.26/43.08  																																| Equations (446) can reduce 441 to:
% 82.26/43.08  																																| (104) $false
% 82.26/43.08  																																|
% 82.26/43.08  																																|-The branch is then unsatisfiable
% 82.26/43.08  																															|-Branch two:
% 82.26/43.08  																															| (441)  ~ (xm = sz00)
% 82.26/43.08  																															| (449) all_137_0_23 = xn
% 82.26/43.08  																															|
% 82.26/43.08  																																| From (449) and (229) follows:
% 82.26/43.08  																																| (38) aNaturalNumber0(xn)
% 82.26/43.08  																																|
% 82.26/43.08  																																+-Applying beta-rule and splitting (139), into two cases.
% 82.26/43.08  																																|-Branch one:
% 82.26/43.08  																																| (437)  ~ (sdtpldt0(xm, xp) = xm)
% 82.26/43.08  																																|
% 82.26/43.08  																																	| Using (391) and (437) yields:
% 82.26/43.08  																																	| (97) $false
% 82.26/43.08  																																	|
% 82.26/43.08  																																	|-The branch is then unsatisfiable
% 82.26/43.08  																																|-Branch two:
% 82.26/43.08  																																| (391) sdtpldt0(xm, xp) = xm
% 82.26/43.08  																																| (454)  ? [v0] : (sdtpldt0(xp, xp) = v0 & sdtpldt0(xm, v0) = xm)
% 82.26/43.08  																																|
% 82.26/43.08  																																	| Instantiating (454) with all_426_0_73 yields:
% 82.26/43.08  																																	| (455) sdtpldt0(xp, xp) = all_426_0_73 & sdtpldt0(xm, all_426_0_73) = xm
% 82.26/43.08  																																	|
% 82.26/43.08  																																	| Applying alpha-rule on (455) yields:
% 82.26/43.08  																																	| (456) sdtpldt0(xp, xp) = all_426_0_73
% 82.26/43.08  																																	| (457) sdtpldt0(xm, all_426_0_73) = xm
% 82.26/43.08  																																	|
% 82.26/43.08  																																	+-Applying beta-rule and splitting (302), into two cases.
% 82.26/43.08  																																	|-Branch one:
% 82.26/43.08  																																	| (458)  ~ aNaturalNumber0(all_122_0_20)
% 82.26/43.08  																																	|
% 82.26/43.08  																																		| Using (266) and (458) yields:
% 82.26/43.08  																																		| (97) $false
% 82.26/43.08  																																		|
% 82.26/43.08  																																		|-The branch is then unsatisfiable
% 82.26/43.08  																																	|-Branch two:
% 82.26/43.08  																																	| (266) aNaturalNumber0(all_122_0_20)
% 82.26/43.08  																																	| (461) sdtpldt0(all_122_0_20, xn) = all_0_1_1
% 82.26/43.08  																																	|
% 82.26/43.08  																																		| From (426) and (461) follows:
% 82.26/43.08  																																		| (462) sdtpldt0(all_122_0_20, xn) = all_0_2_2
% 82.26/43.08  																																		|
% 82.26/43.08  																																		+-Applying beta-rule and splitting (254), into two cases.
% 82.26/43.08  																																		|-Branch one:
% 82.26/43.08  																																		| (458)  ~ aNaturalNumber0(all_122_0_20)
% 82.26/43.08  																																		|
% 82.26/43.08  																																			| Using (266) and (458) yields:
% 82.26/43.08  																																			| (97) $false
% 82.26/43.08  																																			|
% 82.26/43.08  																																			|-The branch is then unsatisfiable
% 82.26/43.08  																																		|-Branch two:
% 82.26/43.08  																																		| (266) aNaturalNumber0(all_122_0_20)
% 82.26/43.08  																																		| (466) all_122_0_20 = all_15_0_4
% 82.26/43.08  																																		|
% 82.26/43.08  																																			| Combining equations (440,466) yields a new equation:
% 82.26/43.08  																																			| (467) all_122_0_20 = xm
% 82.26/43.08  																																			|
% 82.26/43.08  																																			| From (467) and (462) follows:
% 82.26/43.08  																																			| (81) sdtpldt0(xm, xn) = all_0_2_2
% 82.26/43.08  																																			|
% 82.26/43.08  																																			| From (467) and (442) follows:
% 82.26/43.08  																																			| (391) sdtpldt0(xm, xp) = xm
% 82.26/43.08  																																			|
% 82.26/43.08  																																			| From (467) and (428) follows:
% 82.26/43.08  																																			| (28) sdtpldt0(xn, xm) = all_0_2_2
% 82.26/43.08  																																			|
% 82.26/43.08  																																			| From (467) and (266) follows:
% 82.26/43.08  																																			| (16) aNaturalNumber0(xm)
% 82.26/43.08  																																			|
% 82.26/43.08  																																			+-Applying beta-rule and splitting (250), into two cases.
% 82.26/43.08  																																			|-Branch one:
% 82.26/43.08  																																			| (366)  ~ aNaturalNumber0(all_91_0_10)
% 82.26/43.08  																																			|
% 82.26/43.08  																																				| Using (264) and (366) yields:
% 82.26/43.08  																																				| (97) $false
% 82.26/43.08  																																				|
% 82.26/43.08  																																				|-The branch is then unsatisfiable
% 82.26/43.08  																																			|-Branch two:
% 82.26/43.08  																																			| (264) aNaturalNumber0(all_91_0_10)
% 82.26/43.08  																																			| (475) all_91_0_10 = all_25_0_5
% 82.26/43.08  																																			|
% 82.26/43.08  																																				| Combining equations (385,475) yields a new equation:
% 82.26/43.08  																																				| (476) all_91_0_10 = xp
% 82.26/43.08  																																				|
% 82.26/43.08  																																				| From (476) and (369) follows:
% 82.26/43.08  																																				| (477) sdtpldt0(xp, xn) = xn
% 82.26/43.08  																																				|
% 82.26/43.08  																																				| From (476) and (415) follows:
% 82.26/43.08  																																				| (478) sdtpldt0(xp, xp) = all_352_0_67
% 82.26/43.08  																																				|
% 82.26/43.08  																																				| From (476) and (408) follows:
% 82.26/43.08  																																				| (479) sdtpldt0(xp, xp) = all_347_0_66
% 82.26/43.08  																																				|
% 82.26/43.08  																																				| From (476) and (387) follows:
% 82.26/43.08  																																				| (480) sdtpldt0(xp, xp) = xp
% 82.26/43.08  																																				|
% 82.26/43.08  																																				| From (476) and (176) follows:
% 82.26/43.08  																																				| (393) sdtpldt0(xn, xp) = xn
% 82.26/43.08  																																				|
% 82.26/43.08  																																				| From (476) and (264) follows:
% 82.26/43.08  																																				| (17) aNaturalNumber0(xp)
% 82.26/43.08  																																				|
% 82.26/43.08  																																				+-Applying beta-rule and splitting (168), into two cases.
% 82.26/43.08  																																				|-Branch one:
% 82.26/43.08  																																				| (483)  ~ (sdtpldt0(all_0_2_2, xp) = all_0_2_2)
% 82.26/43.08  																																				|
% 82.26/43.08  																																					| Using (427) and (483) yields:
% 82.26/43.08  																																					| (97) $false
% 82.26/43.08  																																					|
% 82.26/43.08  																																					|-The branch is then unsatisfiable
% 82.26/43.08  																																				|-Branch two:
% 82.26/43.08  																																				| (427) sdtpldt0(all_0_2_2, xp) = all_0_2_2
% 82.26/43.08  																																				| (486)  ? [v0] : (sdtpldt0(all_0_2_2, v0) = all_0_2_2 & sdtpldt0(xp, xp) = v0)
% 82.26/43.08  																																				|
% 82.26/43.08  																																					| Instantiating (486) with all_460_0_77 yields:
% 82.26/43.08  																																					| (487) sdtpldt0(all_0_2_2, all_460_0_77) = all_0_2_2 & sdtpldt0(xp, xp) = all_460_0_77
% 82.26/43.08  																																					|
% 82.26/43.08  																																					| Applying alpha-rule on (487) yields:
% 82.26/43.08  																																					| (488) sdtpldt0(all_0_2_2, all_460_0_77) = all_0_2_2
% 82.26/43.08  																																					| (489) sdtpldt0(xp, xp) = all_460_0_77
% 82.26/43.08  																																					|
% 82.26/43.08  																																					+-Applying beta-rule and splitting (277), into two cases.
% 82.26/43.08  																																					|-Branch one:
% 82.26/43.08  																																					| (490)  ~ (sdtpldt0(xp, all_25_0_5) = xp)
% 82.26/43.08  																																					|
% 82.26/43.08  																																						| From (385) and (490) follows:
% 82.26/43.08  																																						| (491)  ~ (sdtpldt0(xp, xp) = xp)
% 82.26/43.08  																																						|
% 82.26/43.08  																																						| Using (480) and (491) yields:
% 82.26/43.08  																																						| (97) $false
% 82.26/43.08  																																						|
% 82.26/43.08  																																						|-The branch is then unsatisfiable
% 82.26/43.08  																																					|-Branch two:
% 82.26/43.08  																																					| (493) sdtpldt0(xp, all_25_0_5) = xp
% 82.26/43.08  																																					| (494)  ? [v0] : (sdtpldt0(all_25_0_5, xr) = v0 & sdtpldt0(xp, v0) = xn)
% 82.26/43.08  																																					|
% 82.26/43.08  																																						| From (385) and (493) follows:
% 82.26/43.08  																																						| (480) sdtpldt0(xp, xp) = xp
% 82.26/43.08  																																						|
% 82.26/43.08  																																						+-Applying beta-rule and splitting (280), into two cases.
% 82.26/43.08  																																						|-Branch one:
% 82.26/43.08  																																						| (491)  ~ (sdtpldt0(xp, xp) = xp)
% 82.26/43.08  																																						|
% 82.26/43.08  																																							| Using (480) and (491) yields:
% 82.26/43.08  																																							| (97) $false
% 82.26/43.08  																																							|
% 82.26/43.08  																																							|-The branch is then unsatisfiable
% 82.26/43.08  																																						|-Branch two:
% 82.26/43.08  																																						| (480) sdtpldt0(xp, xp) = xp
% 82.26/43.08  																																						| (499)  ? [v0] : (sdtpldt0(xp, v0) = all_15_0_4 & sdtpldt0(xp, xm) = v0)
% 82.26/43.08  																																						|
% 82.26/43.08  																																							+-Applying beta-rule and splitting (309), into two cases.
% 82.26/43.08  																																							|-Branch one:
% 82.26/43.08  																																							| (395)  ~ (sdtpldt0(xn, xp) = xn)
% 82.26/43.08  																																							|
% 82.26/43.08  																																								| Using (393) and (395) yields:
% 82.26/43.08  																																								| (97) $false
% 82.26/43.08  																																								|
% 82.26/43.08  																																								|-The branch is then unsatisfiable
% 82.26/43.08  																																							|-Branch two:
% 82.26/43.08  																																							| (393) sdtpldt0(xn, xp) = xn
% 82.26/43.08  																																							| (503)  ? [v0] : (sdtpldt0(all_127_0_21, xp) = v0 & sdtpldt0(sz10, v0) = xn)
% 82.26/43.08  																																							|
% 82.26/43.08  																																								+-Applying beta-rule and splitting (288), into two cases.
% 82.26/43.08  																																								|-Branch one:
% 82.26/43.08  																																								| (504)  ~ (sdtpldt0(xn, xp) = xr)
% 82.26/43.08  																																								|
% 82.26/43.08  																																									| From (373) and (504) follows:
% 82.26/43.08  																																									| (395)  ~ (sdtpldt0(xn, xp) = xn)
% 82.26/43.08  																																									|
% 82.26/43.08  																																									| Using (393) and (395) yields:
% 82.26/43.08  																																									| (97) $false
% 82.26/43.08  																																									|
% 82.26/43.08  																																									|-The branch is then unsatisfiable
% 82.26/43.08  																																								|-Branch two:
% 82.26/43.08  																																								| (507) sdtpldt0(xn, xp) = xr
% 82.26/43.08  																																								| (508)  ? [v0] : (sdtpldt0(xp, xp) = v0 & sdtpldt0(xn, v0) = xn)
% 82.26/43.08  																																								|
% 82.26/43.09  																																									| Instantiating (508) with all_520_0_82 yields:
% 82.26/43.09  																																									| (509) sdtpldt0(xp, xp) = all_520_0_82 & sdtpldt0(xn, all_520_0_82) = xn
% 82.26/43.09  																																									|
% 82.26/43.09  																																									| Applying alpha-rule on (509) yields:
% 82.26/43.09  																																									| (510) sdtpldt0(xp, xp) = all_520_0_82
% 82.26/43.09  																																									| (511) sdtpldt0(xn, all_520_0_82) = xn
% 82.26/43.09  																																									|
% 82.26/43.09  																																									| From (373) and (507) follows:
% 82.26/43.09  																																									| (393) sdtpldt0(xn, xp) = xn
% 82.26/43.09  																																									|
% 82.26/43.09  																																									+-Applying beta-rule and splitting (282), into two cases.
% 82.26/43.09  																																									|-Branch one:
% 82.26/43.09  																																									| (437)  ~ (sdtpldt0(xm, xp) = xm)
% 82.26/43.09  																																									|
% 82.26/43.09  																																										| Using (391) and (437) yields:
% 82.26/43.09  																																										| (97) $false
% 82.26/43.09  																																										|
% 82.26/43.09  																																										|-The branch is then unsatisfiable
% 82.26/43.09  																																									|-Branch two:
% 82.26/43.09  																																									| (391) sdtpldt0(xm, xp) = xm
% 82.26/43.09  																																									| (516)  ? [v0] : (sdtpldt0(xp, xp) = v0 & sdtpldt0(xm, v0) = all_15_0_4)
% 82.26/43.09  																																									|
% 82.26/43.09  																																										| Instantiating (516) with all_531_0_84 yields:
% 82.26/43.09  																																										| (517) sdtpldt0(xp, xp) = all_531_0_84 & sdtpldt0(xm, all_531_0_84) = all_15_0_4
% 82.26/43.09  																																										|
% 82.26/43.09  																																										| Applying alpha-rule on (517) yields:
% 82.26/43.09  																																										| (518) sdtpldt0(xp, xp) = all_531_0_84
% 82.26/43.09  																																										| (519) sdtpldt0(xm, all_531_0_84) = all_15_0_4
% 82.26/43.09  																																										|
% 82.26/43.09  																																										+-Applying beta-rule and splitting (143), into two cases.
% 82.26/43.09  																																										|-Branch one:
% 82.26/43.09  																																										| (395)  ~ (sdtpldt0(xn, xp) = xn)
% 82.26/43.09  																																										|
% 82.26/43.09  																																											| Using (393) and (395) yields:
% 82.26/43.09  																																											| (97) $false
% 82.26/43.09  																																											|
% 82.26/43.09  																																											|-The branch is then unsatisfiable
% 82.26/43.09  																																										|-Branch two:
% 82.26/43.09  																																										| (393) sdtpldt0(xn, xp) = xn
% 82.26/43.09  																																										| (523)  ? [v0] : (sdtpldt0(xp, xm) = v0 & sdtpldt0(xn, v0) = all_0_2_2)
% 82.26/43.09  																																										|
% 82.26/43.09  																																											| Instantiating (523) with all_537_0_85 yields:
% 82.26/43.09  																																											| (524) sdtpldt0(xp, xm) = all_537_0_85 & sdtpldt0(xn, all_537_0_85) = all_0_2_2
% 82.26/43.09  																																											|
% 82.73/43.09  																																											| Applying alpha-rule on (524) yields:
% 82.73/43.09  																																											| (525) sdtpldt0(xp, xm) = all_537_0_85
% 82.73/43.09  																																											| (526) sdtpldt0(xn, all_537_0_85) = all_0_2_2
% 82.73/43.09  																																											|
% 82.73/43.09  																																											+-Applying beta-rule and splitting (267), into two cases.
% 82.73/43.09  																																											|-Branch one:
% 82.73/43.09  																																											| (527)  ~ (sdtpldt0(all_25_0_5, all_25_0_5) = all_25_0_5)
% 82.73/43.09  																																											|
% 82.73/43.09  																																												| From (385)(385)(385) and (527) follows:
% 82.73/43.09  																																												| (491)  ~ (sdtpldt0(xp, xp) = xp)
% 82.73/43.09  																																												|
% 82.73/43.09  																																												| Using (480) and (491) yields:
% 82.73/43.09  																																												| (97) $false
% 82.73/43.09  																																												|
% 82.73/43.09  																																												|-The branch is then unsatisfiable
% 82.73/43.09  																																											|-Branch two:
% 82.73/43.09  																																											| (530) sdtpldt0(all_25_0_5, all_25_0_5) = all_25_0_5
% 82.73/43.09  																																											| (531)  ? [v0] : (sdtpldt0(all_25_0_5, v0) = all_103_0_16 & sdtpldt0(all_25_0_5, xm) = v0)
% 82.73/43.09  																																											|
% 82.73/43.09  																																												| Instantiating (531) with all_543_0_86 yields:
% 82.73/43.09  																																												| (532) sdtpldt0(all_25_0_5, all_543_0_86) = all_103_0_16 & sdtpldt0(all_25_0_5, xm) = all_543_0_86
% 82.73/43.09  																																												|
% 82.73/43.09  																																												| Applying alpha-rule on (532) yields:
% 82.73/43.09  																																												| (533) sdtpldt0(all_25_0_5, all_543_0_86) = all_103_0_16
% 82.73/43.09  																																												| (534) sdtpldt0(all_25_0_5, xm) = all_543_0_86
% 82.73/43.09  																																												|
% 82.73/43.09  																																												| From (385)(385)(385) and (530) follows:
% 82.73/43.09  																																												| (480) sdtpldt0(xp, xp) = xp
% 82.73/43.09  																																												|
% 82.73/43.09  																																												| From (385) and (534) follows:
% 82.73/43.09  																																												| (536) sdtpldt0(xp, xm) = all_543_0_86
% 82.73/43.09  																																												|
% 82.73/43.09  																																												+-Applying beta-rule and splitting (322), into two cases.
% 82.73/43.09  																																												|-Branch one:
% 82.73/43.09  																																												| (366)  ~ aNaturalNumber0(all_91_0_10)
% 82.73/43.09  																																												|
% 82.73/43.09  																																													| From (476) and (366) follows:
% 82.73/43.09  																																													| (538)  ~ aNaturalNumber0(xp)
% 82.73/43.09  																																													|
% 82.73/43.09  																																													| Using (17) and (538) yields:
% 82.73/43.09  																																													| (97) $false
% 82.73/43.09  																																													|
% 82.73/43.09  																																													|-The branch is then unsatisfiable
% 82.73/43.09  																																												|-Branch two:
% 82.73/43.09  																																												| (264) aNaturalNumber0(all_91_0_10)
% 82.73/43.09  																																												| (541)  ? [v0] : (sdtpldt0(all_91_0_10, all_15_0_4) = v0 & sdtpldt0(xn, v0) = all_0_1_1)
% 82.73/43.09  																																												|
% 82.73/43.09  																																													| Instantiating (541) with all_557_0_87 yields:
% 82.73/43.09  																																													| (542) sdtpldt0(all_91_0_10, all_15_0_4) = all_557_0_87 & sdtpldt0(xn, all_557_0_87) = all_0_1_1
% 82.73/43.09  																																													|
% 82.73/43.09  																																													| Applying alpha-rule on (542) yields:
% 82.73/43.09  																																													| (543) sdtpldt0(all_91_0_10, all_15_0_4) = all_557_0_87
% 82.73/43.09  																																													| (544) sdtpldt0(xn, all_557_0_87) = all_0_1_1
% 82.73/43.09  																																													|
% 82.73/43.09  																																													| From (476)(440) and (543) follows:
% 82.73/43.09  																																													| (545) sdtpldt0(xp, xm) = all_557_0_87
% 82.73/43.09  																																													|
% 82.73/43.09  																																													+-Applying beta-rule and splitting (326), into two cases.
% 82.73/43.09  																																													|-Branch one:
% 82.73/43.09  																																													| (423)  ~ (sdtpldt0(xm, xn) = all_0_1_1)
% 82.73/43.09  																																													|
% 82.73/43.09  																																														| From (426) and (423) follows:
% 82.73/43.09  																																														| (547)  ~ (sdtpldt0(xm, xn) = all_0_2_2)
% 82.73/43.09  																																														|
% 82.73/43.09  																																														| Using (81) and (547) yields:
% 82.73/43.09  																																														| (97) $false
% 82.73/43.09  																																														|
% 82.73/43.09  																																														|-The branch is then unsatisfiable
% 82.73/43.09  																																													|-Branch two:
% 82.73/43.09  																																													| (399) sdtpldt0(xm, xn) = all_0_1_1
% 82.73/43.09  																																													| (550)  ~ (sdtpldt0(xm, xp) = xm) |  ? [v0] : (sdtpldt0(xp, xn) = v0 & sdtpldt0(xm, v0) = all_0_1_1)
% 82.73/43.09  																																													|
% 82.73/43.09  																																														| From (426) and (399) follows:
% 82.73/43.09  																																														| (81) sdtpldt0(xm, xn) = all_0_2_2
% 82.73/43.09  																																														|
% 82.73/43.09  																																														+-Applying beta-rule and splitting (550), into two cases.
% 82.73/43.09  																																														|-Branch one:
% 82.73/43.09  																																														| (437)  ~ (sdtpldt0(xm, xp) = xm)
% 82.73/43.09  																																														|
% 82.73/43.09  																																															| Using (391) and (437) yields:
% 82.73/43.09  																																															| (97) $false
% 82.73/43.09  																																															|
% 82.73/43.09  																																															|-The branch is then unsatisfiable
% 82.73/43.09  																																														|-Branch two:
% 82.73/43.09  																																														| (391) sdtpldt0(xm, xp) = xm
% 82.73/43.09  																																														| (555)  ? [v0] : (sdtpldt0(xp, xn) = v0 & sdtpldt0(xm, v0) = all_0_1_1)
% 82.73/43.09  																																														|
% 82.73/43.09  																																															+-Applying beta-rule and splitting (324), into two cases.
% 82.73/43.09  																																															|-Branch one:
% 82.73/43.09  																																															| (527)  ~ (sdtpldt0(all_25_0_5, all_25_0_5) = all_25_0_5)
% 82.73/43.09  																																															|
% 82.73/43.09  																																																| From (385)(385)(385) and (527) follows:
% 82.73/43.09  																																																| (491)  ~ (sdtpldt0(xp, xp) = xp)
% 82.73/43.09  																																																|
% 82.73/43.09  																																																| Using (480) and (491) yields:
% 82.73/43.09  																																																| (97) $false
% 82.73/43.09  																																																|
% 82.73/43.09  																																																|-The branch is then unsatisfiable
% 82.73/43.09  																																															|-Branch two:
% 82.73/43.09  																																															| (530) sdtpldt0(all_25_0_5, all_25_0_5) = all_25_0_5
% 82.73/43.09  																																															| (560)  ? [v0] : (sdtpldt0(all_25_0_5, v0) = all_122_0_20 & sdtpldt0(all_25_0_5, all_15_0_4) = v0)
% 82.73/43.09  																																															|
% 82.73/43.09  																																																| Instantiating (560) with all_584_0_93 yields:
% 82.73/43.09  																																																| (561) sdtpldt0(all_25_0_5, all_584_0_93) = all_122_0_20 & sdtpldt0(all_25_0_5, all_15_0_4) = all_584_0_93
% 82.73/43.09  																																																|
% 82.73/43.09  																																																| Applying alpha-rule on (561) yields:
% 82.73/43.09  																																																| (562) sdtpldt0(all_25_0_5, all_584_0_93) = all_122_0_20
% 82.73/43.09  																																																| (563) sdtpldt0(all_25_0_5, all_15_0_4) = all_584_0_93
% 82.73/43.09  																																																|
% 82.73/43.09  																																																| From (385)(385)(385) and (530) follows:
% 82.73/43.09  																																																| (480) sdtpldt0(xp, xp) = xp
% 82.73/43.09  																																																|
% 82.73/43.09  																																																| From (385)(440) and (563) follows:
% 82.73/43.09  																																																| (565) sdtpldt0(xp, xm) = all_584_0_93
% 82.73/43.09  																																																|
% 82.73/43.09  																																																+-Applying beta-rule and splitting (321), into two cases.
% 82.73/43.09  																																																|-Branch one:
% 82.73/43.09  																																																| (566)  ~ (sdtpldt0(xr, all_15_0_4) = all_0_2_2)
% 82.73/43.09  																																																|
% 82.73/43.09  																																																	| From (373)(440) and (566) follows:
% 82.73/43.09  																																																	| (567)  ~ (sdtpldt0(xn, xm) = all_0_2_2)
% 82.73/43.09  																																																	|
% 82.73/43.09  																																																	| Using (28) and (567) yields:
% 82.73/43.09  																																																	| (97) $false
% 82.73/43.09  																																																	|
% 82.73/43.09  																																																	|-The branch is then unsatisfiable
% 82.73/43.09  																																																|-Branch two:
% 82.73/43.09  																																																| (569) sdtpldt0(xr, all_15_0_4) = all_0_2_2
% 82.73/43.09  																																																| (570)  ? [v0] : (sdtpldt0(all_15_0_4, xp) = v0 & sdtpldt0(xr, v0) = all_0_1_1)
% 82.73/43.09  																																																|
% 82.73/43.09  																																																	| From (373)(440) and (569) follows:
% 82.73/43.09  																																																	| (28) sdtpldt0(xn, xm) = all_0_2_2
% 82.73/43.09  																																																	|
% 82.73/43.09  																																																	+-Applying beta-rule and splitting (301), into two cases.
% 82.73/43.09  																																																	|-Branch one:
% 82.73/43.09  																																																	| (458)  ~ aNaturalNumber0(all_122_0_20)
% 82.73/43.09  																																																	|
% 82.73/43.09  																																																		| From (467) and (458) follows:
% 82.73/43.09  																																																		| (573)  ~ aNaturalNumber0(xm)
% 82.73/43.09  																																																		|
% 82.73/43.09  																																																		| Using (16) and (573) yields:
% 82.73/43.09  																																																		| (97) $false
% 82.73/43.09  																																																		|
% 82.73/43.09  																																																		|-The branch is then unsatisfiable
% 82.73/43.09  																																																	|-Branch two:
% 82.73/43.09  																																																	| (266) aNaturalNumber0(all_122_0_20)
% 82.73/43.09  																																																	| (576)  ? [v0] : (sdtpldt0(all_25_0_5, all_122_0_20) = v0 & sdtpldt0(xn, v0) = all_0_1_1)
% 82.73/43.09  																																																	|
% 82.73/43.09  																																																		| Instantiating (576) with all_596_0_95 yields:
% 82.73/43.09  																																																		| (577) sdtpldt0(all_25_0_5, all_122_0_20) = all_596_0_95 & sdtpldt0(xn, all_596_0_95) = all_0_1_1
% 82.73/43.09  																																																		|
% 82.73/43.09  																																																		| Applying alpha-rule on (577) yields:
% 82.73/43.09  																																																		| (578) sdtpldt0(all_25_0_5, all_122_0_20) = all_596_0_95
% 82.73/43.09  																																																		| (579) sdtpldt0(xn, all_596_0_95) = all_0_1_1
% 82.73/43.09  																																																		|
% 82.73/43.09  																																																		| From (385)(467) and (578) follows:
% 82.73/43.09  																																																		| (580) sdtpldt0(xp, xm) = all_596_0_95
% 82.73/43.09  																																																		|
% 82.73/43.09  																																																		| From (467) and (266) follows:
% 82.73/43.09  																																																		| (16) aNaturalNumber0(xm)
% 82.73/43.09  																																																		|
% 82.73/43.09  																																																		+-Applying beta-rule and splitting (320), into two cases.
% 82.73/43.09  																																																		|-Branch one:
% 82.73/43.09  																																																		| (582)  ~ (sdtpldt0(all_15_0_4, xn) = all_0_2_2)
% 82.73/43.09  																																																		|
% 82.73/43.09  																																																			| From (440) and (582) follows:
% 82.73/43.09  																																																			| (547)  ~ (sdtpldt0(xm, xn) = all_0_2_2)
% 82.73/43.09  																																																			|
% 82.73/43.09  																																																			| Using (81) and (547) yields:
% 82.73/43.09  																																																			| (97) $false
% 82.73/43.09  																																																			|
% 82.73/43.09  																																																			|-The branch is then unsatisfiable
% 82.73/43.09  																																																		|-Branch two:
% 82.73/43.09  																																																		| (585) sdtpldt0(all_15_0_4, xn) = all_0_2_2
% 82.73/43.09  																																																		| (586)  ~ (sdtpldt0(all_0_2_2, xp) = all_0_2_2) |  ? [v0] : (sdtpldt0(all_15_0_4, v0) = all_0_2_2 & sdtpldt0(xn, xp) = v0)
% 82.73/43.09  																																																		|
% 82.73/43.09  																																																			+-Applying beta-rule and splitting (586), into two cases.
% 82.73/43.09  																																																			|-Branch one:
% 82.73/43.09  																																																			| (483)  ~ (sdtpldt0(all_0_2_2, xp) = all_0_2_2)
% 82.73/43.09  																																																			|
% 82.73/43.09  																																																				| Using (427) and (483) yields:
% 82.73/43.09  																																																				| (97) $false
% 82.73/43.09  																																																				|
% 82.73/43.09  																																																				|-The branch is then unsatisfiable
% 82.73/43.09  																																																			|-Branch two:
% 82.73/43.09  																																																			| (427) sdtpldt0(all_0_2_2, xp) = all_0_2_2
% 82.73/43.09  																																																			| (590)  ? [v0] : (sdtpldt0(all_15_0_4, v0) = all_0_2_2 & sdtpldt0(xn, xp) = v0)
% 82.73/43.09  																																																			|
% 82.73/43.09  																																																				| Instantiating (590) with all_606_0_96 yields:
% 82.73/43.09  																																																				| (591) sdtpldt0(all_15_0_4, all_606_0_96) = all_0_2_2 & sdtpldt0(xn, xp) = all_606_0_96
% 82.73/43.09  																																																				|
% 82.73/43.09  																																																				| Applying alpha-rule on (591) yields:
% 82.73/43.09  																																																				| (592) sdtpldt0(all_15_0_4, all_606_0_96) = all_0_2_2
% 82.73/43.09  																																																				| (593) sdtpldt0(xn, xp) = all_606_0_96
% 82.73/43.09  																																																				|
% 82.73/43.09  																																																				+-Applying beta-rule and splitting (253), into two cases.
% 82.73/43.09  																																																				|-Branch one:
% 82.73/43.09  																																																				| (437)  ~ (sdtpldt0(xm, xp) = xm)
% 82.73/43.09  																																																				|
% 82.73/43.09  																																																					| Using (391) and (437) yields:
% 82.73/43.09  																																																					| (97) $false
% 82.73/43.09  																																																					|
% 82.73/43.09  																																																					|-The branch is then unsatisfiable
% 82.73/43.09  																																																				|-Branch two:
% 82.73/43.09  																																																				| (391) sdtpldt0(xm, xp) = xm
% 82.73/43.09  																																																				| (597) all_107_0_18 = xp
% 82.73/43.09  																																																				|
% 82.73/43.09  																																																					| From (597) and (339) follows:
% 82.73/43.09  																																																					| (598) sdtpldt0(xp, xp) = all_262_0_37
% 82.73/43.09  																																																					|
% 82.73/43.09  																																																					| From (597) and (300) follows:
% 82.73/43.09  																																																					| (599) sdtpldt0(xp, xm) = xm
% 82.73/43.09  																																																					|
% 82.73/43.09  																																																					| From (597) and (193) follows:
% 82.73/43.09  																																																					| (391) sdtpldt0(xm, xp) = xm
% 82.73/43.09  																																																					|
% 82.73/43.09  																																																					| From (597) and (194) follows:
% 82.73/43.09  																																																					| (17) aNaturalNumber0(xp)
% 82.73/43.09  																																																					|
% 82.73/43.09  																																																					+-Applying beta-rule and splitting (161), into two cases.
% 82.73/43.09  																																																					|-Branch one:
% 82.73/43.09  																																																					| (395)  ~ (sdtpldt0(xn, xp) = xn)
% 82.73/43.09  																																																					|
% 82.73/43.09  																																																						| Using (393) and (395) yields:
% 82.73/43.09  																																																						| (97) $false
% 82.73/43.09  																																																						|
% 82.73/43.10  																																																						|-The branch is then unsatisfiable
% 82.73/43.10  																																																					|-Branch two:
% 82.73/43.10  																																																					| (393) sdtpldt0(xn, xp) = xn
% 82.73/43.10  																																																					| (508)  ? [v0] : (sdtpldt0(xp, xp) = v0 & sdtpldt0(xn, v0) = xn)
% 82.73/43.10  																																																					|
% 82.73/43.10  																																																						| Instantiating (508) with all_616_0_97 yields:
% 82.73/43.10  																																																						| (606) sdtpldt0(xp, xp) = all_616_0_97 & sdtpldt0(xn, all_616_0_97) = xn
% 82.73/43.10  																																																						|
% 82.73/43.10  																																																						| Applying alpha-rule on (606) yields:
% 82.73/43.10  																																																						| (607) sdtpldt0(xp, xp) = all_616_0_97
% 82.73/43.10  																																																						| (608) sdtpldt0(xn, all_616_0_97) = xn
% 82.73/43.10  																																																						|
% 82.73/43.10  																																																						+-Applying beta-rule and splitting (279), into two cases.
% 82.73/43.10  																																																						|-Branch one:
% 82.73/43.10  																																																						| (490)  ~ (sdtpldt0(xp, all_25_0_5) = xp)
% 82.73/43.10  																																																						|
% 82.73/43.10  																																																							| From (385) and (490) follows:
% 82.73/43.10  																																																							| (491)  ~ (sdtpldt0(xp, xp) = xp)
% 82.73/43.10  																																																							|
% 82.73/43.10  																																																							| Using (480) and (491) yields:
% 82.73/43.10  																																																							| (97) $false
% 82.73/43.10  																																																							|
% 82.73/43.10  																																																							|-The branch is then unsatisfiable
% 82.73/43.10  																																																						|-Branch two:
% 82.73/43.10  																																																						| (493) sdtpldt0(xp, all_25_0_5) = xp
% 82.73/43.10  																																																						| (613)  ? [v0] : (sdtpldt0(all_25_0_5, xm) = v0 & sdtpldt0(xp, v0) = all_15_0_4)
% 82.73/43.10  																																																						|
% 82.73/43.10  																																																							| From (385) and (493) follows:
% 82.73/43.10  																																																							| (480) sdtpldt0(xp, xp) = xp
% 82.77/43.10  																																																							|
% 82.77/43.10  																																																							+-Applying beta-rule and splitting (289), into two cases.
% 82.77/43.10  																																																							|-Branch one:
% 82.77/43.10  																																																							| (504)  ~ (sdtpldt0(xn, xp) = xr)
% 82.77/43.10  																																																							|
% 82.77/43.10  																																																								| From (373) and (504) follows:
% 82.77/43.10  																																																								| (395)  ~ (sdtpldt0(xn, xp) = xn)
% 82.77/43.10  																																																								|
% 82.77/43.10  																																																								| Using (393) and (395) yields:
% 82.77/43.10  																																																								| (97) $false
% 82.77/43.10  																																																								|
% 82.77/43.10  																																																								|-The branch is then unsatisfiable
% 82.77/43.10  																																																							|-Branch two:
% 82.77/43.10  																																																							| (507) sdtpldt0(xn, xp) = xr
% 82.77/43.10  																																																							| (619)  ? [v0] : (sdtpldt0(xp, xm) = v0 & sdtpldt0(xn, v0) = all_101_0_15)
% 82.77/43.10  																																																							|
% 82.77/43.10  																																																								| Instantiating (619) with all_636_0_100 yields:
% 82.77/43.10  																																																								| (620) sdtpldt0(xp, xm) = all_636_0_100 & sdtpldt0(xn, all_636_0_100) = all_101_0_15
% 82.77/43.10  																																																								|
% 82.77/43.10  																																																								| Applying alpha-rule on (620) yields:
% 82.77/43.10  																																																								| (621) sdtpldt0(xp, xm) = all_636_0_100
% 82.77/43.10  																																																								| (622) sdtpldt0(xn, all_636_0_100) = all_101_0_15
% 82.77/43.10  																																																								|
% 82.77/43.10  																																																								| From (373) and (507) follows:
% 82.77/43.10  																																																								| (393) sdtpldt0(xn, xp) = xn
% 82.77/43.10  																																																								|
% 82.77/43.10  																																																								+-Applying beta-rule and splitting (263), into two cases.
% 82.77/43.10  																																																								|-Branch one:
% 82.77/43.10  																																																								| (624)  ~ (sdtpldt0(all_25_0_5, all_25_0_5) = xp)
% 82.77/43.10  																																																								|
% 82.77/43.10  																																																									| From (385)(385) and (624) follows:
% 82.77/43.10  																																																									| (491)  ~ (sdtpldt0(xp, xp) = xp)
% 82.77/43.10  																																																									|
% 82.77/43.10  																																																									| Using (480) and (491) yields:
% 82.77/43.10  																																																									| (97) $false
% 82.77/43.10  																																																									|
% 82.77/43.10  																																																									|-The branch is then unsatisfiable
% 82.77/43.10  																																																								|-Branch two:
% 82.77/43.10  																																																								| (627) sdtpldt0(all_25_0_5, all_25_0_5) = xp
% 82.77/43.10  																																																								| (628)  ? [v0] : (sdtpldt0(all_25_0_5, v0) = xn & sdtpldt0(all_25_0_5, xr) = v0)
% 82.77/43.10  																																																								|
% 82.77/43.10  																																																									| From (385)(385) and (627) follows:
% 82.77/43.10  																																																									| (480) sdtpldt0(xp, xp) = xp
% 82.77/43.10  																																																									|
% 82.77/43.10  																																																									+-Applying beta-rule and splitting (276), into two cases.
% 82.77/43.10  																																																									|-Branch one:
% 82.77/43.10  																																																									| (491)  ~ (sdtpldt0(xp, xp) = xp)
% 82.77/43.10  																																																									|
% 82.77/43.10  																																																										| Using (480) and (491) yields:
% 82.77/43.10  																																																										| (97) $false
% 82.77/43.10  																																																										|
% 82.77/43.10  																																																										|-The branch is then unsatisfiable
% 82.77/43.10  																																																									|-Branch two:
% 82.77/43.10  																																																									| (480) sdtpldt0(xp, xp) = xp
% 82.77/43.10  																																																									| (633)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, all_59_0_7) = v1 & sdtasdt0(all_59_0_7, v0) = xp & sdtasdt0(xp, all_59_0_7) = v3 & sdtasdt0(xp, all_59_0_7) = v2 & sdtpldt0(v2, v3) = v1 & sdtpldt0(xp, xp) = v0)
% 82.77/43.10  																																																									|
% 82.77/43.10  																																																										| Instantiating (633) with all_665_0_103, all_665_1_104, all_665_2_105, all_665_3_106 yields:
% 82.77/43.10  																																																										| (634) sdtasdt0(all_665_3_106, all_59_0_7) = all_665_2_105 & sdtasdt0(all_59_0_7, all_665_3_106) = xp & sdtasdt0(xp, all_59_0_7) = all_665_0_103 & sdtasdt0(xp, all_59_0_7) = all_665_1_104 & sdtpldt0(all_665_1_104, all_665_0_103) = all_665_2_105 & sdtpldt0(xp, xp) = all_665_3_106
% 82.77/43.10  																																																										|
% 82.77/43.10  																																																										| Applying alpha-rule on (634) yields:
% 82.77/43.10  																																																										| (635) sdtasdt0(xp, all_59_0_7) = all_665_1_104
% 82.77/43.10  																																																										| (636) sdtasdt0(xp, all_59_0_7) = all_665_0_103
% 82.77/43.10  																																																										| (637) sdtasdt0(all_665_3_106, all_59_0_7) = all_665_2_105
% 82.77/43.10  																																																										| (638) sdtpldt0(all_665_1_104, all_665_0_103) = all_665_2_105
% 82.77/43.10  																																																										| (639) sdtasdt0(all_59_0_7, all_665_3_106) = xp
% 82.77/43.10  																																																										| (640) sdtpldt0(xp, xp) = all_665_3_106
% 82.77/43.10  																																																										|
% 82.77/43.10  																																																										+-Applying beta-rule and splitting (275), into two cases.
% 82.77/43.10  																																																										|-Branch one:
% 82.77/43.10  																																																										| (491)  ~ (sdtpldt0(xp, xp) = xp)
% 82.77/43.10  																																																										|
% 82.77/43.10  																																																											| Using (480) and (491) yields:
% 82.77/43.10  																																																											| (97) $false
% 82.77/43.10  																																																											|
% 82.77/43.10  																																																											|-The branch is then unsatisfiable
% 82.77/43.10  																																																										|-Branch two:
% 82.77/43.10  																																																										| (480) sdtpldt0(xp, xp) = xp
% 82.77/43.10  																																																										| (644)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (sdtasdt0(v0, xp) = v1 & sdtasdt0(all_59_0_7, xp) = v3 & sdtasdt0(all_59_0_7, xp) = v2 & sdtasdt0(xp, v0) = xp & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_59_0_7, all_59_0_7) = v0)
% 82.77/43.10  																																																										|
% 82.77/43.10  																																																											+-Applying beta-rule and splitting (286), into two cases.
% 82.77/43.10  																																																											|-Branch one:
% 82.77/43.10  																																																											| (381)  ~ (sdtpldt0(xr, all_25_0_5) = xn)
% 82.77/43.10  																																																											|
% 82.77/43.10  																																																												| From (373)(385) and (381) follows:
% 82.77/43.10  																																																												| (395)  ~ (sdtpldt0(xn, xp) = xn)
% 82.77/43.10  																																																												|
% 82.77/43.10  																																																												| Using (393) and (395) yields:
% 82.77/43.10  																																																												| (97) $false
% 82.77/43.10  																																																												|
% 82.77/43.10  																																																												|-The branch is then unsatisfiable
% 82.77/43.10  																																																											|-Branch two:
% 82.77/43.10  																																																											| (384) sdtpldt0(xr, all_25_0_5) = xn
% 82.77/43.10  																																																											| (649)  ? [v0] : (sdtpldt0(all_25_0_5, xp) = v0 & sdtpldt0(xr, v0) = all_97_0_13)
% 82.77/43.10  																																																											|
% 82.77/43.10  																																																												| Instantiating (649) with all_676_0_111 yields:
% 82.77/43.10  																																																												| (650) sdtpldt0(all_25_0_5, xp) = all_676_0_111 & sdtpldt0(xr, all_676_0_111) = all_97_0_13
% 82.77/43.10  																																																												|
% 82.77/43.10  																																																												| Applying alpha-rule on (650) yields:
% 82.77/43.10  																																																												| (651) sdtpldt0(all_25_0_5, xp) = all_676_0_111
% 82.77/43.10  																																																												| (652) sdtpldt0(xr, all_676_0_111) = all_97_0_13
% 82.77/43.10  																																																												|
% 82.77/43.10  																																																												| From (385) and (651) follows:
% 82.77/43.10  																																																												| (653) sdtpldt0(xp, xp) = all_676_0_111
% 82.77/43.10  																																																												|
% 82.77/43.10  																																																												| From (373)(385) and (384) follows:
% 82.77/43.10  																																																												| (393) sdtpldt0(xn, xp) = xn
% 82.77/43.10  																																																												|
% 82.77/43.10  																																																												+-Applying beta-rule and splitting (281), into two cases.
% 82.77/43.10  																																																												|-Branch one:
% 82.77/43.10  																																																												| (655)  ~ (sdtpldt0(xm, all_25_0_5) = xm)
% 82.77/43.10  																																																												|
% 82.77/43.10  																																																													| From (385) and (655) follows:
% 82.77/43.10  																																																													| (437)  ~ (sdtpldt0(xm, xp) = xm)
% 82.77/43.10  																																																													|
% 82.77/43.10  																																																													| Using (391) and (437) yields:
% 82.77/43.10  																																																													| (97) $false
% 82.77/43.10  																																																													|
% 82.77/43.10  																																																													|-The branch is then unsatisfiable
% 82.77/43.10  																																																												|-Branch two:
% 82.77/43.10  																																																												| (380) sdtpldt0(xm, all_25_0_5) = xm
% 82.77/43.10  																																																												| (659)  ? [v0] : (sdtpldt0(all_25_0_5, xp) = v0 & sdtpldt0(xm, v0) = all_15_0_4)
% 82.77/43.10  																																																												|
% 82.77/43.10  																																																													| Instantiating (659) with all_682_0_112 yields:
% 82.77/43.10  																																																													| (660) sdtpldt0(all_25_0_5, xp) = all_682_0_112 & sdtpldt0(xm, all_682_0_112) = all_15_0_4
% 82.77/43.10  																																																													|
% 82.77/43.10  																																																													| Applying alpha-rule on (660) yields:
% 82.77/43.10  																																																													| (661) sdtpldt0(all_25_0_5, xp) = all_682_0_112
% 82.77/43.10  																																																													| (662) sdtpldt0(xm, all_682_0_112) = all_15_0_4
% 82.77/43.10  																																																													|
% 82.77/43.10  																																																													| From (385) and (661) follows:
% 82.77/43.10  																																																													| (663) sdtpldt0(xp, xp) = all_682_0_112
% 82.77/43.10  																																																													|
% 82.77/43.10  																																																													| From (385) and (380) follows:
% 82.77/43.10  																																																													| (391) sdtpldt0(xm, xp) = xm
% 82.77/43.10  																																																													|
% 82.77/43.10  																																																													+-Applying beta-rule and splitting (319), into two cases.
% 82.77/43.10  																																																													|-Branch one:
% 82.77/43.10  																																																													| (665)  ~ (sdtpldt0(xp, all_107_0_18) = xp)
% 82.77/43.10  																																																													|
% 82.77/43.10  																																																														| From (597) and (665) follows:
% 82.77/43.10  																																																														| (491)  ~ (sdtpldt0(xp, xp) = xp)
% 82.77/43.10  																																																														|
% 82.77/43.10  																																																														| Using (480) and (491) yields:
% 82.77/43.10  																																																														| (97) $false
% 82.77/43.10  																																																														|
% 82.77/43.10  																																																														|-The branch is then unsatisfiable
% 82.77/43.10  																																																													|-Branch two:
% 82.77/43.10  																																																													| (668) sdtpldt0(xp, all_107_0_18) = xp
% 82.77/43.10  																																																													| (669)  ? [v0] : (sdtpldt0(all_105_0_17, all_107_0_18) = v0 & sdtpldt0(sz10, v0) = xp)
% 82.77/43.10  																																																													|
% 82.77/43.10  																																																														| From (597) and (668) follows:
% 82.77/43.10  																																																														| (480) sdtpldt0(xp, xp) = xp
% 82.77/43.10  																																																														|
% 82.77/43.10  																																																														+-Applying beta-rule and splitting (270), into two cases.
% 82.77/43.10  																																																														|-Branch one:
% 82.77/43.10  																																																														| (671)  ~ (sdtpldt0(xp, xn) = xn)
% 82.77/43.10  																																																														|
% 82.77/43.10  																																																															| Using (477) and (671) yields:
% 82.77/43.10  																																																															| (97) $false
% 82.77/43.10  																																																															|
% 82.77/43.10  																																																															|-The branch is then unsatisfiable
% 82.77/43.10  																																																														|-Branch two:
% 82.77/43.10  																																																														| (477) sdtpldt0(xp, xn) = xn
% 82.77/43.10  																																																														| (674)  ~ (sdtpldt0(xn, xp) = xn) |  ? [v0] : (sdtpldt0(xp, v0) = xn & sdtpldt0(xn, xp) = v0)
% 82.77/43.10  																																																														|
% 82.77/43.10  																																																															+-Applying beta-rule and splitting (674), into two cases.
% 82.77/43.10  																																																															|-Branch one:
% 82.77/43.10  																																																															| (395)  ~ (sdtpldt0(xn, xp) = xn)
% 82.77/43.10  																																																															|
% 82.77/43.10  																																																																| Using (393) and (395) yields:
% 82.77/43.10  																																																																| (97) $false
% 82.77/43.10  																																																																|
% 82.77/43.10  																																																																|-The branch is then unsatisfiable
% 82.77/43.10  																																																															|-Branch two:
% 82.77/43.10  																																																															| (393) sdtpldt0(xn, xp) = xn
% 82.77/43.10  																																																															| (678)  ? [v0] : (sdtpldt0(xp, v0) = xn & sdtpldt0(xn, xp) = v0)
% 82.77/43.10  																																																															|
% 82.77/43.10  																																																																| Instantiating (678) with all_697_0_114 yields:
% 82.77/43.10  																																																																| (679) sdtpldt0(xp, all_697_0_114) = xn & sdtpldt0(xn, xp) = all_697_0_114
% 82.77/43.10  																																																																|
% 82.77/43.10  																																																																| Applying alpha-rule on (679) yields:
% 82.77/43.10  																																																																| (680) sdtpldt0(xp, all_697_0_114) = xn
% 82.77/43.10  																																																																| (681) sdtpldt0(xn, xp) = all_697_0_114
% 82.77/43.10  																																																																|
% 82.77/43.10  																																																																+-Applying beta-rule and splitting (316), into two cases.
% 82.77/43.10  																																																																|-Branch one:
% 82.77/43.10  																																																																| (682)  ~ (sdtpldt0(xn, all_107_0_18) = xn)
% 82.77/43.10  																																																																|
% 82.77/43.10  																																																																	| From (597) and (682) follows:
% 82.77/43.10  																																																																	| (395)  ~ (sdtpldt0(xn, xp) = xn)
% 82.77/43.10  																																																																	|
% 82.77/43.10  																																																																	| Using (393) and (395) yields:
% 82.77/43.10  																																																																	| (97) $false
% 82.77/43.10  																																																																	|
% 82.77/43.10  																																																																	|-The branch is then unsatisfiable
% 82.77/43.10  																																																																|-Branch two:
% 82.77/43.10  																																																																| (685) sdtpldt0(xn, all_107_0_18) = xn
% 82.77/43.10  																																																																| (686)  ? [v0] : (sdtpldt0(all_25_0_5, all_107_0_18) = v0 & sdtpldt0(xn, v0) = xn)
% 82.77/43.10  																																																																|
% 82.77/43.10  																																																																	| Instantiating (686) with all_703_0_115 yields:
% 82.77/43.10  																																																																	| (687) sdtpldt0(all_25_0_5, all_107_0_18) = all_703_0_115 & sdtpldt0(xn, all_703_0_115) = xn
% 82.77/43.10  																																																																	|
% 82.77/43.10  																																																																	| Applying alpha-rule on (687) yields:
% 82.77/43.10  																																																																	| (688) sdtpldt0(all_25_0_5, all_107_0_18) = all_703_0_115
% 82.77/43.10  																																																																	| (689) sdtpldt0(xn, all_703_0_115) = xn
% 82.77/43.11  																																																																	|
% 82.77/43.11  																																																																	| From (385)(597) and (688) follows:
% 82.77/43.11  																																																																	| (690) sdtpldt0(xp, xp) = all_703_0_115
% 82.77/43.11  																																																																	|
% 82.77/43.11  																																																																	| From (597) and (685) follows:
% 82.77/43.11  																																																																	| (393) sdtpldt0(xn, xp) = xn
% 82.77/43.11  																																																																	|
% 82.77/43.11  																																																																	+-Applying beta-rule and splitting (327), into two cases.
% 82.77/43.11  																																																																	|-Branch one:
% 82.77/43.11  																																																																	| (692)  ~ (sdtpldt0(all_25_0_5, all_15_0_4) = xm)
% 82.77/43.11  																																																																	|
% 82.77/43.11  																																																																		| From (385)(440) and (692) follows:
% 82.77/43.11  																																																																		| (693)  ~ (sdtpldt0(xp, xm) = xm)
% 82.77/43.11  																																																																		|
% 82.77/43.11  																																																																		| Using (599) and (693) yields:
% 82.77/43.11  																																																																		| (97) $false
% 82.77/43.11  																																																																		|
% 82.77/43.11  																																																																		|-The branch is then unsatisfiable
% 82.77/43.11  																																																																	|-Branch two:
% 82.77/43.11  																																																																	| (695) sdtpldt0(all_25_0_5, all_15_0_4) = xm
% 82.77/43.11  																																																																	| (696)  ? [v0] : (sdtpldt0(all_25_0_5, v0) = xm & sdtpldt0(all_15_0_4, all_107_0_18) = v0)
% 82.77/43.11  																																																																	|
% 82.77/43.11  																																																																		| From (385)(440) and (695) follows:
% 82.77/43.11  																																																																		| (599) sdtpldt0(xp, xm) = xm
% 82.77/43.11  																																																																		|
% 82.77/43.11  																																																																		+-Applying beta-rule and splitting (318), into two cases.
% 82.77/43.11  																																																																		|-Branch one:
% 82.77/43.11  																																																																		| (698)  ~ aNaturalNumber0(all_97_0_13)
% 82.77/43.11  																																																																		|
% 82.77/43.11  																																																																			| From (398) and (698) follows:
% 82.77/43.11  																																																																			| (699)  ~ aNaturalNumber0(xn)
% 82.81/43.11  																																																																			|
% 82.81/43.11  																																																																			| Using (38) and (699) yields:
% 82.81/43.11  																																																																			| (97) $false
% 82.81/43.11  																																																																			|
% 82.81/43.11  																																																																			|-The branch is then unsatisfiable
% 82.81/43.11  																																																																		|-Branch two:
% 82.81/43.11  																																																																		| (701) aNaturalNumber0(all_97_0_13)
% 82.81/43.11  																																																																		| (702)  ? [v0] : (sdtpldt0(all_107_0_18, all_97_0_13) = v0 & sdtpldt0(xm, v0) = all_0_1_1)
% 82.81/43.11  																																																																		|
% 82.81/43.11  																																																																			| From (398) and (701) follows:
% 82.81/43.11  																																																																			| (38) aNaturalNumber0(xn)
% 82.81/43.11  																																																																			|
% 82.81/43.11  																																																																			+-Applying beta-rule and splitting (314), into two cases.
% 82.81/43.11  																																																																			|-Branch one:
% 82.81/43.11  																																																																			| (655)  ~ (sdtpldt0(xm, all_25_0_5) = xm)
% 82.81/43.11  																																																																			|
% 82.81/43.11  																																																																				| From (385) and (655) follows:
% 82.81/43.11  																																																																				| (437)  ~ (sdtpldt0(xm, xp) = xm)
% 82.81/43.11  																																																																				|
% 82.81/43.11  																																																																				| Using (391) and (437) yields:
% 82.81/43.11  																																																																				| (97) $false
% 82.81/43.11  																																																																				|
% 82.81/43.11  																																																																				|-The branch is then unsatisfiable
% 82.81/43.11  																																																																			|-Branch two:
% 82.81/43.11  																																																																			| (380) sdtpldt0(xm, all_25_0_5) = xm
% 82.81/43.11  																																																																			| (708)  ? [v0] : (sdtpldt0(all_25_0_5, all_25_0_5) = v0 & sdtpldt0(xm, v0) = xm)
% 82.81/43.11  																																																																			|
% 82.81/43.11  																																																																				| Instantiating (708) with all_721_0_118 yields:
% 82.81/43.11  																																																																				| (709) sdtpldt0(all_25_0_5, all_25_0_5) = all_721_0_118 & sdtpldt0(xm, all_721_0_118) = xm
% 82.81/43.11  																																																																				|
% 82.81/43.11  																																																																				| Applying alpha-rule on (709) yields:
% 82.81/43.11  																																																																				| (710) sdtpldt0(all_25_0_5, all_25_0_5) = all_721_0_118
% 82.81/43.11  																																																																				| (711) sdtpldt0(xm, all_721_0_118) = xm
% 82.81/43.11  																																																																				|
% 82.81/43.11  																																																																				| From (385)(385) and (710) follows:
% 82.81/43.11  																																																																				| (712) sdtpldt0(xp, xp) = all_721_0_118
% 82.81/43.11  																																																																				|
% 82.81/43.11  																																																																				| From (385) and (380) follows:
% 82.81/43.11  																																																																				| (391) sdtpldt0(xm, xp) = xm
% 82.81/43.11  																																																																				|
% 82.81/43.11  																																																																				+-Applying beta-rule and splitting (278), into two cases.
% 82.81/43.11  																																																																				|-Branch one:
% 82.81/43.11  																																																																				| (624)  ~ (sdtpldt0(all_25_0_5, all_25_0_5) = xp)
% 82.81/43.11  																																																																				|
% 82.81/43.11  																																																																					| From (385)(385) and (624) follows:
% 82.81/43.11  																																																																					| (491)  ~ (sdtpldt0(xp, xp) = xp)
% 82.81/43.11  																																																																					|
% 82.81/43.11  																																																																					| Using (480) and (491) yields:
% 82.81/43.11  																																																																					| (97) $false
% 82.81/43.11  																																																																					|
% 82.81/43.11  																																																																					|-The branch is then unsatisfiable
% 82.81/43.11  																																																																				|-Branch two:
% 82.81/43.11  																																																																				| (627) sdtpldt0(all_25_0_5, all_25_0_5) = xp
% 82.81/43.11  																																																																				| (718)  ? [v0] : (sdtpldt0(all_25_0_5, v0) = all_15_0_4 & sdtpldt0(all_25_0_5, xm) = v0)
% 82.81/43.11  																																																																				|
% 82.81/43.11  																																																																					| Instantiating (718) with all_727_0_119 yields:
% 82.81/43.11  																																																																					| (719) sdtpldt0(all_25_0_5, all_727_0_119) = all_15_0_4 & sdtpldt0(all_25_0_5, xm) = all_727_0_119
% 82.81/43.11  																																																																					|
% 82.81/43.11  																																																																					| Applying alpha-rule on (719) yields:
% 82.81/43.11  																																																																					| (720) sdtpldt0(all_25_0_5, all_727_0_119) = all_15_0_4
% 82.81/43.11  																																																																					| (721) sdtpldt0(all_25_0_5, xm) = all_727_0_119
% 82.81/43.11  																																																																					|
% 82.81/43.11  																																																																					| From (385)(385) and (627) follows:
% 82.81/43.11  																																																																					| (480) sdtpldt0(xp, xp) = xp
% 82.81/43.11  																																																																					|
% 82.81/43.11  																																																																					| From (385) and (721) follows:
% 82.81/43.11  																																																																					| (723) sdtpldt0(xp, xm) = all_727_0_119
% 82.81/43.11  																																																																					|
% 82.81/43.11  																																																																					+-Applying beta-rule and splitting (330), into two cases.
% 82.81/43.11  																																																																					|-Branch one:
% 82.81/43.11  																																																																					| (724)  ~ sdtlseqdt0(xr, all_0_1_1)
% 82.81/43.11  																																																																					|
% 82.81/43.11  																																																																						| From (373)(426) and (724) follows:
% 82.81/43.11  																																																																						| (725)  ~ sdtlseqdt0(xn, all_0_2_2)
% 82.81/43.11  																																																																						|
% 82.81/43.11  																																																																						| Using (156) and (725) yields:
% 82.81/43.11  																																																																						| (97) $false
% 82.81/43.11  																																																																						|
% 82.81/43.11  																																																																						|-The branch is then unsatisfiable
% 82.81/43.11  																																																																					|-Branch two:
% 82.81/43.11  																																																																					| (727) sdtlseqdt0(xr, all_0_1_1)
% 82.81/43.11  																																																																					| (728)  ? [v0] : (sdtpldt0(xr, v0) = all_0_1_1 & aNaturalNumber0(v0))
% 82.81/43.11  																																																																					|
% 82.81/43.11  																																																																						| Instantiating (728) with all_747_0_123 yields:
% 82.81/43.11  																																																																						| (729) sdtpldt0(xr, all_747_0_123) = all_0_1_1 & aNaturalNumber0(all_747_0_123)
% 82.81/43.11  																																																																						|
% 82.81/43.11  																																																																						| Applying alpha-rule on (729) yields:
% 82.81/43.11  																																																																						| (730) sdtpldt0(xr, all_747_0_123) = all_0_1_1
% 82.81/43.11  																																																																						| (731) aNaturalNumber0(all_747_0_123)
% 82.81/43.11  																																																																						|
% 82.81/43.11  																																																																						| From (373)(426) and (730) follows:
% 82.81/43.11  																																																																						| (732) sdtpldt0(xn, all_747_0_123) = all_0_2_2
% 82.81/43.11  																																																																						|
% 82.81/43.11  																																																																						| From (373)(426) and (727) follows:
% 82.81/43.11  																																																																						| (156) sdtlseqdt0(xn, all_0_2_2)
% 82.81/43.11  																																																																						|
% 82.81/43.11  																																																																						+-Applying beta-rule and splitting (331), into two cases.
% 82.81/43.11  																																																																						|-Branch one:
% 82.81/43.11  																																																																						| (734)  ~ sdtlseqdt0(xn, all_0_1_1)
% 82.81/43.11  																																																																						|
% 82.81/43.11  																																																																							| From (426) and (734) follows:
% 82.81/43.11  																																																																							| (725)  ~ sdtlseqdt0(xn, all_0_2_2)
% 82.81/43.11  																																																																							|
% 82.81/43.11  																																																																							| Using (156) and (725) yields:
% 82.81/43.11  																																																																							| (97) $false
% 82.81/43.11  																																																																							|
% 82.81/43.11  																																																																							|-The branch is then unsatisfiable
% 82.81/43.11  																																																																						|-Branch two:
% 82.81/43.11  																																																																						| (323) sdtlseqdt0(xn, all_0_1_1)
% 82.81/43.11  																																																																						| (738)  ? [v0] : (sdtpldt0(xn, v0) = all_0_1_1 & aNaturalNumber0(v0))
% 82.81/43.11  																																																																						|
% 82.81/43.11  																																																																							| Instantiating (738) with all_752_0_124 yields:
% 82.81/43.11  																																																																							| (739) sdtpldt0(xn, all_752_0_124) = all_0_1_1 & aNaturalNumber0(all_752_0_124)
% 82.81/43.11  																																																																							|
% 82.81/43.11  																																																																							| Applying alpha-rule on (739) yields:
% 82.81/43.11  																																																																							| (740) sdtpldt0(xn, all_752_0_124) = all_0_1_1
% 82.81/43.11  																																																																							| (741) aNaturalNumber0(all_752_0_124)
% 82.81/43.11  																																																																							|
% 82.81/43.11  																																																																							| From (426) and (740) follows:
% 82.81/43.11  																																																																							| (742) sdtpldt0(xn, all_752_0_124) = all_0_2_2
% 82.81/43.11  																																																																							|
% 82.81/43.11  																																																																							+-Applying beta-rule and splitting (308), into two cases.
% 82.81/43.11  																																																																							|-Branch one:
% 82.81/43.11  																																																																							| (366)  ~ aNaturalNumber0(all_91_0_10)
% 82.81/43.11  																																																																							|
% 82.81/43.11  																																																																								| From (476) and (366) follows:
% 82.81/43.11  																																																																								| (538)  ~ aNaturalNumber0(xp)
% 82.81/43.11  																																																																								|
% 82.81/43.11  																																																																								| Using (17) and (538) yields:
% 82.81/43.11  																																																																								| (97) $false
% 82.81/43.11  																																																																								|
% 82.81/43.11  																																																																								|-The branch is then unsatisfiable
% 82.81/43.11  																																																																							|-Branch two:
% 82.81/43.11  																																																																							| (264) aNaturalNumber0(all_91_0_10)
% 82.81/43.11  																																																																							| (747)  ? [v0] : (sdtpldt0(all_91_0_10, xp) = v0 & sdtpldt0(xn, v0) = all_97_0_13)
% 82.81/43.11  																																																																							|
% 82.81/43.11  																																																																								| Instantiating (747) with all_768_0_129 yields:
% 82.81/43.11  																																																																								| (748) sdtpldt0(all_91_0_10, xp) = all_768_0_129 & sdtpldt0(xn, all_768_0_129) = all_97_0_13
% 82.81/43.11  																																																																								|
% 82.81/43.11  																																																																								| Applying alpha-rule on (748) yields:
% 82.81/43.11  																																																																								| (749) sdtpldt0(all_91_0_10, xp) = all_768_0_129
% 82.81/43.11  																																																																								| (750) sdtpldt0(xn, all_768_0_129) = all_97_0_13
% 82.81/43.11  																																																																								|
% 82.81/43.11  																																																																								| From (476) and (749) follows:
% 82.81/43.11  																																																																								| (751) sdtpldt0(xp, xp) = all_768_0_129
% 82.81/43.11  																																																																								|
% 82.81/43.11  																																																																								| From (476) and (264) follows:
% 82.81/43.11  																																																																								| (17) aNaturalNumber0(xp)
% 82.81/43.11  																																																																								|
% 82.81/43.11  																																																																								+-Applying beta-rule and splitting (315), into two cases.
% 82.81/43.11  																																																																								|-Branch one:
% 82.81/43.11  																																																																								| (437)  ~ (sdtpldt0(xm, xp) = xm)
% 82.81/43.11  																																																																								|
% 82.81/43.11  																																																																									| Using (391) and (437) yields:
% 82.81/43.11  																																																																									| (97) $false
% 82.81/43.11  																																																																									|
% 82.81/43.11  																																																																									|-The branch is then unsatisfiable
% 82.81/43.11  																																																																								|-Branch two:
% 82.81/43.11  																																																																								| (391) sdtpldt0(xm, xp) = xm
% 82.81/43.11  																																																																								| (756)  ? [v0] : (sdtpldt0(xp, all_107_0_18) = v0 & sdtpldt0(xm, v0) = xm)
% 82.81/43.11  																																																																								|
% 82.81/43.11  																																																																									| Instantiating (756) with all_774_0_130 yields:
% 82.81/43.11  																																																																									| (757) sdtpldt0(xp, all_107_0_18) = all_774_0_130 & sdtpldt0(xm, all_774_0_130) = xm
% 82.81/43.11  																																																																									|
% 82.81/43.11  																																																																									| Applying alpha-rule on (757) yields:
% 82.81/43.11  																																																																									| (758) sdtpldt0(xp, all_107_0_18) = all_774_0_130
% 82.81/43.11  																																																																									| (759) sdtpldt0(xm, all_774_0_130) = xm
% 82.81/43.11  																																																																									|
% 82.81/43.11  																																																																									| From (597) and (758) follows:
% 82.81/43.11  																																																																									| (760) sdtpldt0(xp, xp) = all_774_0_130
% 82.81/43.11  																																																																									|
% 82.81/43.11  																																																																									+-Applying beta-rule and splitting (296), into two cases.
% 82.81/43.11  																																																																									|-Branch one:
% 82.81/43.11  																																																																									| (362)  ~ aNaturalNumber0(all_103_0_16)
% 82.81/43.11  																																																																									|
% 82.81/43.11  																																																																										| From (379) and (362) follows:
% 82.81/43.11  																																																																										| (573)  ~ aNaturalNumber0(xm)
% 82.81/43.11  																																																																										|
% 82.81/43.11  																																																																										| Using (16) and (573) yields:
% 82.81/43.11  																																																																										| (97) $false
% 82.81/43.11  																																																																										|
% 82.81/43.11  																																																																										|-The branch is then unsatisfiable
% 82.81/43.11  																																																																									|-Branch two:
% 82.81/43.11  																																																																									| (269) aNaturalNumber0(all_103_0_16)
% 82.81/43.11  																																																																									| (765)  ? [v0] : (sdtpldt0(all_103_0_16, xp) = v0 & sdtpldt0(xn, v0) = all_0_1_1)
% 82.81/43.11  																																																																									|
% 82.81/43.11  																																																																										| From (379) and (269) follows:
% 82.81/43.11  																																																																										| (16) aNaturalNumber0(xm)
% 82.81/43.11  																																																																										|
% 82.81/43.11  																																																																										+-Applying beta-rule and splitting (298), into two cases.
% 82.81/43.11  																																																																										|-Branch one:
% 82.81/43.11  																																																																										| (366)  ~ aNaturalNumber0(all_91_0_10)
% 82.81/43.11  																																																																										|
% 82.81/43.11  																																																																											| From (476) and (366) follows:
% 82.81/43.11  																																																																											| (538)  ~ aNaturalNumber0(xp)
% 82.81/43.11  																																																																											|
% 82.81/43.11  																																																																											| Using (17) and (538) yields:
% 82.81/43.11  																																																																											| (97) $false
% 82.81/43.11  																																																																											|
% 82.81/43.11  																																																																											|-The branch is then unsatisfiable
% 82.81/43.11  																																																																										|-Branch two:
% 82.81/43.11  																																																																										| (264) aNaturalNumber0(all_91_0_10)
% 82.81/43.11  																																																																										| (771)  ? [v0] : (sdtpldt0(all_91_0_10, xm) = v0 & sdtpldt0(xn, v0) = all_0_2_2)
% 82.81/43.11  																																																																										|
% 82.81/43.11  																																																																											| Instantiating (771) with all_786_0_132 yields:
% 82.81/43.11  																																																																											| (772) sdtpldt0(all_91_0_10, xm) = all_786_0_132 & sdtpldt0(xn, all_786_0_132) = all_0_2_2
% 82.81/43.11  																																																																											|
% 82.81/43.11  																																																																											| Applying alpha-rule on (772) yields:
% 82.81/43.11  																																																																											| (773) sdtpldt0(all_91_0_10, xm) = all_786_0_132
% 82.81/43.11  																																																																											| (774) sdtpldt0(xn, all_786_0_132) = all_0_2_2
% 82.81/43.11  																																																																											|
% 82.81/43.11  																																																																											| From (476) and (773) follows:
% 82.81/43.11  																																																																											| (775) sdtpldt0(xp, xm) = all_786_0_132
% 82.81/43.11  																																																																											|
% 82.81/43.11  																																																																											| From (476) and (264) follows:
% 82.81/43.11  																																																																											| (17) aNaturalNumber0(xp)
% 82.81/43.11  																																																																											|
% 82.81/43.11  																																																																											+-Applying beta-rule and splitting (312), into two cases.
% 82.81/43.11  																																																																											|-Branch one:
% 82.81/43.11  																																																																											| (665)  ~ (sdtpldt0(xp, all_107_0_18) = xp)
% 82.81/43.11  																																																																											|
% 82.81/43.11  																																																																												| From (597) and (665) follows:
% 82.81/43.11  																																																																												| (491)  ~ (sdtpldt0(xp, xp) = xp)
% 82.81/43.12  																																																																												|
% 82.81/43.12  																																																																												| Using (480) and (491) yields:
% 82.81/43.12  																																																																												| (97) $false
% 82.81/43.12  																																																																												|
% 82.81/43.12  																																																																												|-The branch is then unsatisfiable
% 82.81/43.12  																																																																											|-Branch two:
% 82.81/43.12  																																																																											| (668) sdtpldt0(xp, all_107_0_18) = xp
% 82.81/43.12  																																																																											| (781)  ? [v0] : (sdtpldt0(all_107_0_18, all_107_0_18) = v0 & sdtpldt0(xp, v0) = xp)
% 82.81/43.12  																																																																											|
% 82.81/43.12  																																																																												| Instantiating (781) with all_792_0_133 yields:
% 82.81/43.12  																																																																												| (782) sdtpldt0(all_107_0_18, all_107_0_18) = all_792_0_133 & sdtpldt0(xp, all_792_0_133) = xp
% 82.81/43.12  																																																																												|
% 82.81/43.12  																																																																												| Applying alpha-rule on (782) yields:
% 82.81/43.12  																																																																												| (783) sdtpldt0(all_107_0_18, all_107_0_18) = all_792_0_133
% 82.81/43.12  																																																																												| (784) sdtpldt0(xp, all_792_0_133) = xp
% 82.81/43.12  																																																																												|
% 82.81/43.12  																																																																												| From (597)(597) and (783) follows:
% 82.81/43.12  																																																																												| (785) sdtpldt0(xp, xp) = all_792_0_133
% 82.81/43.12  																																																																												|
% 82.81/43.12  																																																																												| From (597) and (668) follows:
% 82.81/43.12  																																																																												| (480) sdtpldt0(xp, xp) = xp
% 82.81/43.12  																																																																												|
% 82.81/43.12  																																																																												+-Applying beta-rule and splitting (313), into two cases.
% 82.81/43.12  																																																																												|-Branch one:
% 82.81/43.12  																																																																												| (665)  ~ (sdtpldt0(xp, all_107_0_18) = xp)
% 82.81/43.12  																																																																												|
% 82.81/43.12  																																																																													| From (597) and (665) follows:
% 82.81/43.12  																																																																													| (491)  ~ (sdtpldt0(xp, xp) = xp)
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Using (480) and (491) yields:
% 82.81/43.12  																																																																													| (97) $false
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													|-The branch is then unsatisfiable
% 82.81/43.12  																																																																												|-Branch two:
% 82.81/43.12  																																																																												| (668) sdtpldt0(xp, all_107_0_18) = xp
% 82.81/43.12  																																																																												| (791)  ? [v0] : (sdtpldt0(all_107_0_18, xm) = v0 & sdtpldt0(xp, v0) = all_15_0_4)
% 82.81/43.12  																																																																												|
% 82.81/43.12  																																																																													| Instantiating (791) with all_798_0_134 yields:
% 82.81/43.12  																																																																													| (792) sdtpldt0(all_107_0_18, xm) = all_798_0_134 & sdtpldt0(xp, all_798_0_134) = all_15_0_4
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Applying alpha-rule on (792) yields:
% 82.81/43.12  																																																																													| (793) sdtpldt0(all_107_0_18, xm) = all_798_0_134
% 82.81/43.12  																																																																													| (794) sdtpldt0(xp, all_798_0_134) = all_15_0_4
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| From (597) and (793) follows:
% 82.81/43.12  																																																																													| (795) sdtpldt0(xp, xm) = all_798_0_134
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| From (597) and (668) follows:
% 82.81/43.12  																																																																													| (480) sdtpldt0(xp, xp) = xp
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xp, all_768_0_129, all_774_0_130 and discharging atoms sdtpldt0(xp, xp) = all_774_0_130, sdtpldt0(xp, xp) = all_768_0_129, yields:
% 82.81/43.12  																																																																													| (797) all_774_0_130 = all_768_0_129
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xp, all_721_0_118, all_774_0_130 and discharging atoms sdtpldt0(xp, xp) = all_774_0_130, sdtpldt0(xp, xp) = all_721_0_118, yields:
% 82.81/43.12  																																																																													| (798) all_774_0_130 = all_721_0_118
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xp, all_703_0_115, xp and discharging atoms sdtpldt0(xp, xp) = all_703_0_115, sdtpldt0(xp, xp) = xp, yields:
% 82.81/43.12  																																																																													| (799) all_703_0_115 = xp
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xp, all_682_0_112, all_792_0_133 and discharging atoms sdtpldt0(xp, xp) = all_792_0_133, sdtpldt0(xp, xp) = all_682_0_112, yields:
% 82.81/43.12  																																																																													| (800) all_792_0_133 = all_682_0_112
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xp, all_676_0_111, all_682_0_112 and discharging atoms sdtpldt0(xp, xp) = all_682_0_112, sdtpldt0(xp, xp) = all_676_0_111, yields:
% 82.81/43.12  																																																																													| (801) all_682_0_112 = all_676_0_111
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xp, all_665_3_106, all_676_0_111 and discharging atoms sdtpldt0(xp, xp) = all_676_0_111, sdtpldt0(xp, xp) = all_665_3_106, yields:
% 82.81/43.12  																																																																													| (802) all_676_0_111 = all_665_3_106
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xp, all_616_0_97, all_768_0_129 and discharging atoms sdtpldt0(xp, xp) = all_768_0_129, sdtpldt0(xp, xp) = all_616_0_97, yields:
% 82.81/43.12  																																																																													| (803) all_768_0_129 = all_616_0_97
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xp, all_616_0_97, all_665_3_106 and discharging atoms sdtpldt0(xp, xp) = all_665_3_106, sdtpldt0(xp, xp) = all_616_0_97, yields:
% 82.81/43.12  																																																																													| (804) all_665_3_106 = all_616_0_97
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xp, all_531_0_84, all_792_0_133 and discharging atoms sdtpldt0(xp, xp) = all_792_0_133, sdtpldt0(xp, xp) = all_531_0_84, yields:
% 82.81/43.12  																																																																													| (805) all_792_0_133 = all_531_0_84
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xp, all_520_0_82, all_616_0_97 and discharging atoms sdtpldt0(xp, xp) = all_616_0_97, sdtpldt0(xp, xp) = all_520_0_82, yields:
% 82.81/43.12  																																																																													| (806) all_616_0_97 = all_520_0_82
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xp, all_460_0_77, all_520_0_82 and discharging atoms sdtpldt0(xp, xp) = all_520_0_82, sdtpldt0(xp, xp) = all_460_0_77, yields:
% 82.81/43.12  																																																																													| (807) all_520_0_82 = all_460_0_77
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xp, all_426_0_73, all_460_0_77 and discharging atoms sdtpldt0(xp, xp) = all_460_0_77, sdtpldt0(xp, xp) = all_426_0_73, yields:
% 82.81/43.12  																																																																													| (808) all_460_0_77 = all_426_0_73
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xp, all_352_0_67, all_703_0_115 and discharging atoms sdtpldt0(xp, xp) = all_703_0_115, sdtpldt0(xp, xp) = all_352_0_67, yields:
% 82.81/43.12  																																																																													| (809) all_703_0_115 = all_352_0_67
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xp, all_352_0_67, all_426_0_73 and discharging atoms sdtpldt0(xp, xp) = all_426_0_73, sdtpldt0(xp, xp) = all_352_0_67, yields:
% 82.81/43.12  																																																																													| (810) all_426_0_73 = all_352_0_67
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xp, all_347_0_66, all_768_0_129 and discharging atoms sdtpldt0(xp, xp) = all_768_0_129, sdtpldt0(xp, xp) = all_347_0_66, yields:
% 82.81/43.12  																																																																													| (811) all_768_0_129 = all_347_0_66
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xp, all_306_0_59, all_352_0_67 and discharging atoms sdtpldt0(xp, xp) = all_352_0_67, sdtpldt0(xp, xp) = all_306_0_59, yields:
% 82.81/43.12  																																																																													| (812) all_352_0_67 = all_306_0_59
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xp, all_268_0_40, all_306_0_59 and discharging atoms sdtpldt0(xp, xp) = all_306_0_59, sdtpldt0(xp, xp) = all_268_0_40, yields:
% 82.81/43.12  																																																																													| (813) all_306_0_59 = all_268_0_40
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xp, all_262_0_37, all_268_0_40 and discharging atoms sdtpldt0(xp, xp) = all_268_0_40, sdtpldt0(xp, xp) = all_262_0_37, yields:
% 82.81/43.12  																																																																													| (814) all_268_0_40 = all_262_0_37
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xp, all_250_0_31, all_262_0_37 and discharging atoms sdtpldt0(xp, xp) = all_262_0_37, sdtpldt0(xp, xp) = all_250_0_31, yields:
% 82.81/43.12  																																																																													| (815) all_262_0_37 = all_250_0_31
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xm, all_727_0_119, xm and discharging atoms sdtpldt0(xp, xm) = all_727_0_119, sdtpldt0(xp, xm) = xm, yields:
% 82.81/43.12  																																																																													| (816) all_727_0_119 = xm
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xm, all_727_0_119, all_786_0_132 and discharging atoms sdtpldt0(xp, xm) = all_786_0_132, sdtpldt0(xp, xm) = all_727_0_119, yields:
% 82.81/43.12  																																																																													| (817) all_786_0_132 = all_727_0_119
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xm, all_636_0_100, all_786_0_132 and discharging atoms sdtpldt0(xp, xm) = all_786_0_132, sdtpldt0(xp, xm) = all_636_0_100, yields:
% 82.81/43.12  																																																																													| (818) all_786_0_132 = all_636_0_100
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xm, all_596_0_95, all_786_0_132 and discharging atoms sdtpldt0(xp, xm) = all_786_0_132, sdtpldt0(xp, xm) = all_596_0_95, yields:
% 82.81/43.12  																																																																													| (819) all_786_0_132 = all_596_0_95
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xm, all_584_0_93, all_596_0_95 and discharging atoms sdtpldt0(xp, xm) = all_596_0_95, sdtpldt0(xp, xm) = all_584_0_93, yields:
% 82.81/43.12  																																																																													| (820) all_596_0_95 = all_584_0_93
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xm, all_557_0_87, all_238_0_25 and discharging atoms sdtpldt0(xp, xm) = all_557_0_87, yields:
% 82.81/43.12  																																																																													| (821) all_557_0_87 = all_238_0_25 |  ~ (sdtpldt0(xp, xm) = all_238_0_25)
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xm, all_557_0_87, all_798_0_134 and discharging atoms sdtpldt0(xp, xm) = all_798_0_134, sdtpldt0(xp, xm) = all_557_0_87, yields:
% 82.81/43.12  																																																																													| (822) all_798_0_134 = all_557_0_87
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xm, all_543_0_86, all_584_0_93 and discharging atoms sdtpldt0(xp, xm) = all_584_0_93, sdtpldt0(xp, xm) = all_543_0_86, yields:
% 82.81/43.12  																																																																													| (823) all_584_0_93 = all_543_0_86
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xm, all_543_0_86, all_557_0_87 and discharging atoms sdtpldt0(xp, xm) = all_557_0_87, sdtpldt0(xp, xm) = all_543_0_86, yields:
% 82.81/43.12  																																																																													| (824) all_557_0_87 = all_543_0_86
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xm, all_537_0_85, all_557_0_87 and discharging atoms sdtpldt0(xp, xm) = all_557_0_87, sdtpldt0(xp, xm) = all_537_0_85, yields:
% 82.81/43.12  																																																																													| (825) all_557_0_87 = all_537_0_85
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xp, xm, all_310_0_61, all_798_0_134 and discharging atoms sdtpldt0(xp, xm) = all_798_0_134, sdtpldt0(xp, xm) = all_310_0_61, yields:
% 82.81/43.12  																																																																													| (826) all_798_0_134 = all_310_0_61
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (41) with xm, xp, sz00, xm and discharging atoms sdtpldt0(xm, xp) = xm, aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(sz00), yields:
% 82.81/43.12  																																																																													| (827) xp = sz00 |  ~ (sdtpldt0(xm, sz00) = xm)
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xn, xp, all_697_0_114, xn and discharging atoms sdtpldt0(xn, xp) = all_697_0_114, sdtpldt0(xn, xp) = xn, yields:
% 82.81/43.12  																																																																													| (828) all_697_0_114 = xn
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xn, xp, all_357_0_68, all_697_0_114 and discharging atoms sdtpldt0(xn, xp) = all_697_0_114, sdtpldt0(xn, xp) = all_357_0_68, yields:
% 82.81/43.12  																																																																													| (829) all_697_0_114 = all_357_0_68
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xn, xp, all_357_0_68, all_606_0_96 and discharging atoms sdtpldt0(xn, xp) = all_606_0_96, sdtpldt0(xn, xp) = all_357_0_68, yields:
% 82.81/43.12  																																																																													| (830) all_606_0_96 = all_357_0_68
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xn, xp, all_296_0_54, all_606_0_96 and discharging atoms sdtpldt0(xn, xp) = all_606_0_96, sdtpldt0(xn, xp) = all_296_0_54, yields:
% 82.81/43.12  																																																																													| (831) all_606_0_96 = all_296_0_54
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (24) with xn, xp, all_294_0_53, all_606_0_96 and discharging atoms sdtpldt0(xn, xp) = all_606_0_96, sdtpldt0(xn, xp) = all_294_0_53, yields:
% 82.81/43.12  																																																																													| (832) all_606_0_96 = all_294_0_53
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (41) with xp, all_109_0_19, all_284_0_48, xp and discharging atoms sdtpldt0(xp, all_284_0_48) = xp, sdtpldt0(xp, all_109_0_19) = xp, aNaturalNumber0(all_284_0_48), aNaturalNumber0(all_109_0_19), aNaturalNumber0(xp), yields:
% 82.81/43.12  																																																																													| (833) all_284_0_48 = all_109_0_19
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (41) with all_0_2_2, xm, all_747_0_123, xn and discharging atoms sdtpldt0(xn, all_747_0_123) = all_0_2_2, sdtpldt0(xn, xm) = all_0_2_2, aNaturalNumber0(all_747_0_123), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 82.81/43.12  																																																																													| (834) all_747_0_123 = xm
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (41) with xp, all_284_0_48, xp, xp and discharging atoms sdtpldt0(xp, all_284_0_48) = xp, sdtpldt0(xp, xp) = xp, aNaturalNumber0(all_284_0_48), aNaturalNumber0(xp), yields:
% 82.81/43.12  																																																																													| (835) all_284_0_48 = xp
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (41) with all_0_2_2, all_752_0_124, all_747_0_123, xn and discharging atoms sdtpldt0(xn, all_752_0_124) = all_0_2_2, sdtpldt0(xn, all_747_0_123) = all_0_2_2, aNaturalNumber0(all_752_0_124), aNaturalNumber0(all_747_0_123), aNaturalNumber0(xn), yields:
% 82.81/43.12  																																																																													| (836) all_752_0_124 = all_747_0_123
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Instantiating formula (41) with all_0_2_2, all_752_0_124, all_270_0_41, xn and discharging atoms sdtpldt0(xn, all_752_0_124) = all_0_2_2, sdtpldt0(xn, all_270_0_41) = all_0_2_2, aNaturalNumber0(all_752_0_124), aNaturalNumber0(all_270_0_41), aNaturalNumber0(xn), yields:
% 82.81/43.12  																																																																													| (837) all_752_0_124 = all_270_0_41
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Using (400) and (436) yields:
% 82.81/43.12  																																																																													| (838)  ~ (all_250_0_31 = sz00)
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Combining equations (822,826) yields a new equation:
% 82.81/43.12  																																																																													| (839) all_557_0_87 = all_310_0_61
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Simplifying 839 yields:
% 82.81/43.12  																																																																													| (840) all_557_0_87 = all_310_0_61
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Combining equations (800,805) yields a new equation:
% 82.81/43.12  																																																																													| (841) all_682_0_112 = all_531_0_84
% 82.81/43.12  																																																																													|
% 82.81/43.12  																																																																													| Simplifying 841 yields:
% 82.81/43.12  																																																																													| (842) all_682_0_112 = all_531_0_84
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (817,818) yields a new equation:
% 82.81/43.13  																																																																													| (843) all_727_0_119 = all_636_0_100
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 843 yields:
% 82.81/43.13  																																																																													| (844) all_727_0_119 = all_636_0_100
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (819,818) yields a new equation:
% 82.81/43.13  																																																																													| (845) all_636_0_100 = all_596_0_95
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (797,798) yields a new equation:
% 82.81/43.13  																																																																													| (846) all_768_0_129 = all_721_0_118
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 846 yields:
% 82.81/43.13  																																																																													| (847) all_768_0_129 = all_721_0_118
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (803,847) yields a new equation:
% 82.81/43.13  																																																																													| (848) all_721_0_118 = all_616_0_97
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (811,847) yields a new equation:
% 82.81/43.13  																																																																													| (849) all_721_0_118 = all_347_0_66
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (836,837) yields a new equation:
% 82.81/43.13  																																																																													| (850) all_747_0_123 = all_270_0_41
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 850 yields:
% 82.81/43.13  																																																																													| (851) all_747_0_123 = all_270_0_41
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (851,834) yields a new equation:
% 82.81/43.13  																																																																													| (852) all_270_0_41 = xm
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 852 yields:
% 82.81/43.13  																																																																													| (853) all_270_0_41 = xm
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (844,816) yields a new equation:
% 82.81/43.13  																																																																													| (854) all_636_0_100 = xm
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 854 yields:
% 82.81/43.13  																																																																													| (855) all_636_0_100 = xm
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (848,849) yields a new equation:
% 82.81/43.13  																																																																													| (856) all_616_0_97 = all_347_0_66
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 856 yields:
% 82.81/43.13  																																																																													| (857) all_616_0_97 = all_347_0_66
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (809,799) yields a new equation:
% 82.81/43.13  																																																																													| (858) all_352_0_67 = xp
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 858 yields:
% 82.81/43.13  																																																																													| (859) all_352_0_67 = xp
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (829,828) yields a new equation:
% 82.81/43.13  																																																																													| (860) all_357_0_68 = xn
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 860 yields:
% 82.81/43.13  																																																																													| (861) all_357_0_68 = xn
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (801,842) yields a new equation:
% 82.81/43.13  																																																																													| (862) all_676_0_111 = all_531_0_84
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 862 yields:
% 82.81/43.13  																																																																													| (863) all_676_0_111 = all_531_0_84
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (802,863) yields a new equation:
% 82.81/43.13  																																																																													| (864) all_665_3_106 = all_531_0_84
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 864 yields:
% 82.81/43.13  																																																																													| (865) all_665_3_106 = all_531_0_84
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (804,865) yields a new equation:
% 82.81/43.13  																																																																													| (866) all_616_0_97 = all_531_0_84
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 866 yields:
% 82.81/43.13  																																																																													| (867) all_616_0_97 = all_531_0_84
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (845,855) yields a new equation:
% 82.81/43.13  																																																																													| (868) all_596_0_95 = xm
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 868 yields:
% 82.81/43.13  																																																																													| (869) all_596_0_95 = xm
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (806,867) yields a new equation:
% 82.81/43.13  																																																																													| (870) all_531_0_84 = all_520_0_82
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (857,867) yields a new equation:
% 82.81/43.13  																																																																													| (871) all_531_0_84 = all_347_0_66
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (832,831) yields a new equation:
% 82.81/43.13  																																																																													| (872) all_296_0_54 = all_294_0_53
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (830,831) yields a new equation:
% 82.81/43.13  																																																																													| (873) all_357_0_68 = all_296_0_54
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 873 yields:
% 82.81/43.13  																																																																													| (874) all_357_0_68 = all_296_0_54
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (820,869) yields a new equation:
% 82.81/43.13  																																																																													| (875) all_584_0_93 = xm
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 875 yields:
% 82.81/43.13  																																																																													| (876) all_584_0_93 = xm
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (823,876) yields a new equation:
% 82.81/43.13  																																																																													| (877) all_543_0_86 = xm
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 877 yields:
% 82.81/43.13  																																																																													| (878) all_543_0_86 = xm
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (824,825) yields a new equation:
% 82.81/43.13  																																																																													| (879) all_543_0_86 = all_537_0_85
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 879 yields:
% 82.81/43.13  																																																																													| (880) all_543_0_86 = all_537_0_85
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (840,825) yields a new equation:
% 82.81/43.13  																																																																													| (881) all_537_0_85 = all_310_0_61
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (880,878) yields a new equation:
% 82.81/43.13  																																																																													| (882) all_537_0_85 = xm
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 882 yields:
% 82.81/43.13  																																																																													| (883) all_537_0_85 = xm
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (883,881) yields a new equation:
% 82.81/43.13  																																																																													| (884) all_310_0_61 = xm
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (870,871) yields a new equation:
% 82.81/43.13  																																																																													| (885) all_520_0_82 = all_347_0_66
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 885 yields:
% 82.81/43.13  																																																																													| (886) all_520_0_82 = all_347_0_66
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (807,886) yields a new equation:
% 82.81/43.13  																																																																													| (887) all_460_0_77 = all_347_0_66
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 887 yields:
% 82.81/43.13  																																																																													| (888) all_460_0_77 = all_347_0_66
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (808,888) yields a new equation:
% 82.81/43.13  																																																																													| (889) all_426_0_73 = all_347_0_66
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 889 yields:
% 82.81/43.13  																																																																													| (890) all_426_0_73 = all_347_0_66
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (810,890) yields a new equation:
% 82.81/43.13  																																																																													| (891) all_352_0_67 = all_347_0_66
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 891 yields:
% 82.81/43.13  																																																																													| (892) all_352_0_67 = all_347_0_66
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (874,861) yields a new equation:
% 82.81/43.13  																																																																													| (893) all_296_0_54 = xn
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 893 yields:
% 82.81/43.13  																																																																													| (894) all_296_0_54 = xn
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (859,892) yields a new equation:
% 82.81/43.13  																																																																													| (895) all_347_0_66 = xp
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (812,892) yields a new equation:
% 82.81/43.13  																																																																													| (896) all_347_0_66 = all_306_0_59
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (896,895) yields a new equation:
% 82.81/43.13  																																																																													| (897) all_306_0_59 = xp
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 897 yields:
% 82.81/43.13  																																																																													| (898) all_306_0_59 = xp
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (813,898) yields a new equation:
% 82.81/43.13  																																																																													| (899) all_268_0_40 = xp
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 899 yields:
% 82.81/43.13  																																																																													| (900) all_268_0_40 = xp
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (872,894) yields a new equation:
% 82.81/43.13  																																																																													| (901) all_294_0_53 = xn
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 901 yields:
% 82.81/43.13  																																																																													| (902) all_294_0_53 = xn
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (835,833) yields a new equation:
% 82.81/43.13  																																																																													| (903) all_109_0_19 = xp
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (814,900) yields a new equation:
% 82.81/43.13  																																																																													| (904) all_262_0_37 = xp
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 904 yields:
% 82.81/43.13  																																																																													| (905) all_262_0_37 = xp
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (815,905) yields a new equation:
% 82.81/43.13  																																																																													| (906) all_250_0_31 = xp
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Simplifying 906 yields:
% 82.81/43.13  																																																																													| (907) all_250_0_31 = xp
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (884,881) yields a new equation:
% 82.81/43.13  																																																																													| (883) all_537_0_85 = xm
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Combining equations (883,825) yields a new equation:
% 82.81/43.13  																																																																													| (909) all_557_0_87 = xm
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| Equations (907) can reduce 838 to:
% 82.81/43.13  																																																																													| (73)  ~ (xp = sz00)
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| From (903) and (333) follows:
% 82.81/43.13  																																																																													| (911) sdtpldt0(xp, xm) = all_238_0_25
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| From (902) and (352) follows:
% 82.81/43.13  																																																																													| (393) sdtpldt0(xn, xp) = xn
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													| From (853) and (346) follows:
% 82.81/43.13  																																																																													| (16) aNaturalNumber0(xm)
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																													+-Applying beta-rule and splitting (311), into two cases.
% 82.81/43.13  																																																																													|-Branch one:
% 82.81/43.13  																																																																													| (914) all_109_0_19 = sz00
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																														| Combining equations (903,914) yields a new equation:
% 82.81/43.13  																																																																														| (915) xp = sz00
% 82.81/43.13  																																																																														|
% 82.81/43.13  																																																																														| Simplifying 915 yields:
% 82.81/43.13  																																																																														| (103) xp = sz00
% 82.81/43.13  																																																																														|
% 82.81/43.13  																																																																														| Equations (103) can reduce 73 to:
% 82.81/43.13  																																																																														| (104) $false
% 82.81/43.13  																																																																														|
% 82.81/43.13  																																																																														|-The branch is then unsatisfiable
% 82.81/43.13  																																																																													|-Branch two:
% 82.81/43.13  																																																																													| (918)  ~ (all_109_0_19 = sz00)
% 82.81/43.13  																																																																													| (919) all_109_0_19 = sz10 |  ? [v0] : (isPrime0(v0) & doDivides0(v0, all_109_0_19) & aNaturalNumber0(v0))
% 82.81/43.13  																																																																													|
% 82.81/43.13  																																																																														| Equations (903) can reduce 918 to:
% 82.81/43.13  																																																																														| (73)  ~ (xp = sz00)
% 82.81/43.13  																																																																														|
% 82.81/43.13  																																																																														+-Applying beta-rule and splitting (310), into two cases.
% 82.81/43.13  																																																																														|-Branch one:
% 82.81/43.13  																																																																														| (921)  ~ (sdtpldt0(xn, all_109_0_19) = xn)
% 82.81/43.13  																																																																														|
% 82.81/43.13  																																																																															| From (903) and (921) follows:
% 82.81/43.13  																																																																															| (395)  ~ (sdtpldt0(xn, xp) = xn)
% 82.81/43.13  																																																																															|
% 82.81/43.13  																																																																															| Using (393) and (395) yields:
% 82.81/43.13  																																																																															| (97) $false
% 82.81/43.13  																																																																															|
% 82.81/43.13  																																																																															|-The branch is then unsatisfiable
% 82.81/43.13  																																																																														|-Branch two:
% 82.81/43.13  																																																																														| (924) sdtpldt0(xn, all_109_0_19) = xn
% 82.81/43.13  																																																																														| (925)  ? [v0] : (sdtpldt0(all_109_0_19, xm) = v0 & sdtpldt0(xn, v0) = all_0_2_2)
% 82.81/43.13  																																																																														|
% 82.81/43.13  																																																																															| Instantiating (925) with all_840_0_138 yields:
% 82.81/43.13  																																																																															| (926) sdtpldt0(all_109_0_19, xm) = all_840_0_138 & sdtpldt0(xn, all_840_0_138) = all_0_2_2
% 82.81/43.13  																																																																															|
% 82.81/43.13  																																																																															| Applying alpha-rule on (926) yields:
% 82.81/43.13  																																																																															| (927) sdtpldt0(all_109_0_19, xm) = all_840_0_138
% 82.81/43.13  																																																																															| (928) sdtpldt0(xn, all_840_0_138) = all_0_2_2
% 82.81/43.13  																																																																															|
% 82.81/43.13  																																																																															| From (903) and (927) follows:
% 82.81/43.13  																																																																															| (929) sdtpldt0(xp, xm) = all_840_0_138
% 82.81/43.13  																																																																															|
% 82.81/43.13  																																																																															+-Applying beta-rule and splitting (821), into two cases.
% 82.81/43.13  																																																																															|-Branch one:
% 82.81/43.13  																																																																															| (930)  ~ (sdtpldt0(xp, xm) = all_238_0_25)
% 82.81/43.13  																																																																															|
% 82.81/43.13  																																																																																| Using (911) and (930) yields:
% 82.81/43.13  																																																																																| (97) $false
% 82.81/43.13  																																																																																|
% 82.81/43.13  																																																																																|-The branch is then unsatisfiable
% 82.81/43.13  																																																																															|-Branch two:
% 82.81/43.13  																																																																															| (911) sdtpldt0(xp, xm) = all_238_0_25
% 82.81/43.13  																																																																															| (933) all_557_0_87 = all_238_0_25
% 82.81/43.13  																																																																															|
% 82.81/43.13  																																																																																| Combining equations (933,909) yields a new equation:
% 82.81/43.13  																																																																																| (934) all_238_0_25 = xm
% 82.81/43.13  																																																																																|
% 82.81/43.13  																																																																																| Simplifying 934 yields:
% 82.81/43.13  																																																																																| (935) all_238_0_25 = xm
% 82.81/43.13  																																																																																|
% 82.81/43.13  																																																																																| From (935) and (911) follows:
% 82.81/43.13  																																																																																| (599) sdtpldt0(xp, xm) = xm
% 82.81/43.13  																																																																																|
% 82.81/43.13  																																																																																+-Applying beta-rule and splitting (827), into two cases.
% 82.81/43.13  																																																																																|-Branch one:
% 82.81/43.13  																																																																																| (937)  ~ (sdtpldt0(xm, sz00) = xm)
% 82.81/43.13  																																																																																|
% 82.81/43.13  																																																																																	+-Applying beta-rule and splitting (325), into two cases.
% 82.81/43.13  																																																																																	|-Branch one:
% 82.81/43.13  																																																																																	| (938)  ~ (sdtpldt0(sz00, all_15_0_4) = all_122_0_20)
% 82.81/43.13  																																																																																	|
% 82.81/43.13  																																																																																		| From (440)(467) and (938) follows:
% 82.81/43.13  																																																																																		| (939)  ~ (sdtpldt0(sz00, xm) = xm)
% 82.81/43.13  																																																																																		|
% 82.81/43.13  																																																																																		| Instantiating formula (24) with xp, xm, all_840_0_138, xm and discharging atoms sdtpldt0(xp, xm) = all_840_0_138, sdtpldt0(xp, xm) = xm, yields:
% 82.81/43.13  																																																																																		| (940) all_840_0_138 = xm
% 82.81/43.13  																																																																																		|
% 82.81/43.13  																																																																																		| Using (929) and (445) yields:
% 82.81/43.13  																																																																																		| (941)  ~ (all_840_0_138 = sz00)
% 82.81/43.13  																																																																																		|
% 82.81/43.13  																																																																																		| Equations (940) can reduce 941 to:
% 82.81/43.13  																																																																																		| (441)  ~ (xm = sz00)
% 82.81/43.13  																																																																																		|
% 82.81/43.13  																																																																																		+-Applying beta-rule and splitting (87), into two cases.
% 82.81/43.13  																																																																																		|-Branch one:
% 82.81/43.13  																																																																																		| (943) sdtlseqdt0(xm, sz00)
% 82.81/43.13  																																																																																		|
% 82.81/43.13  																																																																																			+-Applying beta-rule and splitting (293), into two cases.
% 82.81/43.13  																																																																																			|-Branch one:
% 82.81/43.13  																																																																																			| (944)  ~ sdtlseqdt0(xm, sz00)
% 82.81/43.13  																																																																																			|
% 82.81/43.13  																																																																																				| Using (943) and (944) yields:
% 82.81/43.13  																																																																																				| (97) $false
% 82.81/43.13  																																																																																				|
% 82.81/43.13  																																																																																				|-The branch is then unsatisfiable
% 82.81/43.13  																																																																																			|-Branch two:
% 82.81/43.13  																																																																																			| (943) sdtlseqdt0(xm, sz00)
% 82.81/43.13  																																																																																			| (947) xm = sz00 | iLess0(xm, sz00)
% 82.81/43.14  																																																																																			|
% 82.81/43.14  																																																																																				+-Applying beta-rule and splitting (292), into two cases.
% 82.81/43.14  																																																																																				|-Branch one:
% 82.81/43.14  																																																																																				| (944)  ~ sdtlseqdt0(xm, sz00)
% 82.81/43.14  																																																																																				|
% 82.81/43.14  																																																																																					| Using (943) and (944) yields:
% 82.81/43.14  																																																																																					| (97) $false
% 82.81/43.14  																																																																																					|
% 82.81/43.14  																																																																																					|-The branch is then unsatisfiable
% 82.81/43.14  																																																																																				|-Branch two:
% 82.81/43.14  																																																																																				| (943) sdtlseqdt0(xm, sz00)
% 82.81/43.14  																																																																																				| (951) xm = sz00 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = all_0_2_2) &  ~ (v1 = v0) & sdtpldt0(xn, xm) = v0 & sdtpldt0(xn, sz00) = v1 & sdtpldt0(sz00, xn) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_2_2, v2))
% 82.81/43.14  																																																																																				|
% 82.81/43.14  																																																																																					+-Applying beta-rule and splitting (291), into two cases.
% 82.81/43.14  																																																																																					|-Branch one:
% 82.81/43.14  																																																																																					| (944)  ~ sdtlseqdt0(xm, sz00)
% 82.81/43.14  																																																																																					|
% 82.81/43.14  																																																																																						| Using (943) and (944) yields:
% 82.81/43.14  																																																																																						| (97) $false
% 82.81/43.14  																																																																																						|
% 82.81/43.14  																																																																																						|-The branch is then unsatisfiable
% 82.81/43.14  																																																																																					|-Branch two:
% 82.81/43.14  																																																																																					| (943) sdtlseqdt0(xm, sz00)
% 82.81/43.14  																																																																																					| (955) xm = sz00 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = all_15_0_4) &  ~ (v1 = v0) & sdtpldt0(xp, xm) = v0 & sdtpldt0(xp, sz00) = v1 & sdtpldt0(sz00, xp) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_15_0_4, v2))
% 82.81/43.14  																																																																																					|
% 82.81/43.14  																																																																																						+-Applying beta-rule and splitting (317), into two cases.
% 82.81/43.14  																																																																																						|-Branch one:
% 82.81/43.14  																																																																																						| (944)  ~ sdtlseqdt0(xm, sz00)
% 82.81/43.14  																																																																																						|
% 82.81/43.14  																																																																																							| Using (943) and (944) yields:
% 82.81/43.14  																																																																																							| (97) $false
% 82.81/43.14  																																																																																							|
% 82.81/43.14  																																																																																							|-The branch is then unsatisfiable
% 82.81/43.14  																																																																																						|-Branch two:
% 82.81/43.14  																																																																																						| (943) sdtlseqdt0(xm, sz00)
% 82.81/43.14  																																																																																						| (959) xm = sz00 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = xm) &  ~ (v1 = v0) & sdtpldt0(all_107_0_18, xm) = v0 & sdtpldt0(all_107_0_18, sz00) = v1 & sdtpldt0(sz00, all_107_0_18) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xm, v2))
% 82.81/43.14  																																																																																						|
% 82.81/43.14  																																																																																							+-Applying beta-rule and splitting (294), into two cases.
% 82.81/43.14  																																																																																							|-Branch one:
% 82.81/43.14  																																																																																							| (944)  ~ sdtlseqdt0(xm, sz00)
% 82.81/43.14  																																																																																							|
% 82.81/43.14  																																																																																								| Using (943) and (944) yields:
% 82.81/43.14  																																																																																								| (97) $false
% 82.81/43.14  																																																																																								|
% 82.81/43.14  																																																																																								|-The branch is then unsatisfiable
% 82.81/43.14  																																																																																							|-Branch two:
% 82.81/43.14  																																																																																							| (943) sdtlseqdt0(xm, sz00)
% 82.81/43.14  																																																																																							| (963)  ? [v0] : (sdtpldt0(xm, v0) = sz00 & aNaturalNumber0(v0))
% 82.81/43.14  																																																																																							|
% 82.81/43.14  																																																																																								| Instantiating (963) with all_1130_0_141 yields:
% 82.81/43.14  																																																																																								| (964) sdtpldt0(xm, all_1130_0_141) = sz00 & aNaturalNumber0(all_1130_0_141)
% 82.81/43.14  																																																																																								|
% 82.81/43.14  																																																																																								| Applying alpha-rule on (964) yields:
% 82.81/43.14  																																																																																								| (965) sdtpldt0(xm, all_1130_0_141) = sz00
% 82.81/43.14  																																																																																								| (966) aNaturalNumber0(all_1130_0_141)
% 82.81/43.14  																																																																																								|
% 82.81/43.14  																																																																																								+-Applying beta-rule and splitting (951), into two cases.
% 82.81/43.14  																																																																																								|-Branch one:
% 82.81/43.14  																																																																																								| (446) xm = sz00
% 82.81/43.14  																																																																																								|
% 82.81/43.14  																																																																																									| Equations (446) can reduce 441 to:
% 82.81/43.14  																																																																																									| (104) $false
% 82.81/43.14  																																																																																									|
% 82.81/43.14  																																																																																									|-The branch is then unsatisfiable
% 82.81/43.14  																																																																																								|-Branch two:
% 82.81/43.14  																																																																																								| (441)  ~ (xm = sz00)
% 82.81/43.14  																																																																																								| (970)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = all_0_2_2) &  ~ (v1 = v0) & sdtpldt0(xn, xm) = v0 & sdtpldt0(xn, sz00) = v1 & sdtpldt0(sz00, xn) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_2_2, v2))
% 82.81/43.14  																																																																																								|
% 82.81/43.14  																																																																																									+-Applying beta-rule and splitting (955), into two cases.
% 82.81/43.14  																																																																																									|-Branch one:
% 82.81/43.14  																																																																																									| (446) xm = sz00
% 82.81/43.14  																																																																																									|
% 82.81/43.14  																																																																																										| Equations (446) can reduce 441 to:
% 82.81/43.14  																																																																																										| (104) $false
% 82.81/43.14  																																																																																										|
% 82.81/43.14  																																																																																										|-The branch is then unsatisfiable
% 82.81/43.14  																																																																																									|-Branch two:
% 82.81/43.14  																																																																																									| (441)  ~ (xm = sz00)
% 82.81/43.14  																																																																																									| (974)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = all_15_0_4) &  ~ (v1 = v0) & sdtpldt0(xp, xm) = v0 & sdtpldt0(xp, sz00) = v1 & sdtpldt0(sz00, xp) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_15_0_4, v2))
% 82.81/43.14  																																																																																									|
% 82.81/43.14  																																																																																										+-Applying beta-rule and splitting (959), into two cases.
% 82.81/43.14  																																																																																										|-Branch one:
% 82.81/43.14  																																																																																										| (446) xm = sz00
% 82.81/43.14  																																																																																										|
% 82.81/43.14  																																																																																											| Equations (446) can reduce 441 to:
% 82.81/43.14  																																																																																											| (104) $false
% 82.81/43.14  																																																																																											|
% 82.81/43.14  																																																																																											|-The branch is then unsatisfiable
% 82.81/43.14  																																																																																										|-Branch two:
% 82.81/43.14  																																																																																										| (441)  ~ (xm = sz00)
% 82.81/43.14  																																																																																										| (978)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = xm) &  ~ (v1 = v0) & sdtpldt0(all_107_0_18, xm) = v0 & sdtpldt0(all_107_0_18, sz00) = v1 & sdtpldt0(sz00, all_107_0_18) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xm, v2))
% 82.81/43.14  																																																																																										|
% 82.81/43.14  																																																																																											| Instantiating formula (7) with all_1130_0_141, xm and discharging atoms sdtpldt0(xm, all_1130_0_141) = sz00, aNaturalNumber0(all_1130_0_141), aNaturalNumber0(xm), yields:
% 82.81/43.14  																																																																																											| (446) xm = sz00
% 82.81/43.14  																																																																																											|
% 82.81/43.14  																																																																																											| Equations (446) can reduce 441 to:
% 82.81/43.14  																																																																																											| (104) $false
% 82.81/43.14  																																																																																											|
% 82.81/43.14  																																																																																											|-The branch is then unsatisfiable
% 82.81/43.14  																																																																																		|-Branch two:
% 82.81/43.14  																																																																																		| (944)  ~ sdtlseqdt0(xm, sz00)
% 82.81/43.14  																																																																																		| (982) sdtlseqdt0(sz00, xm)
% 82.81/43.14  																																																																																		|
% 82.81/43.14  																																																																																			+-Applying beta-rule and splitting (328), into two cases.
% 82.81/43.14  																																																																																			|-Branch one:
% 82.81/43.14  																																																																																			| (983)  ~ sdtlseqdt0(sz00, all_15_0_4)
% 82.81/43.14  																																																																																			|
% 82.81/43.14  																																																																																				| From (440) and (983) follows:
% 82.81/43.14  																																																																																				| (984)  ~ sdtlseqdt0(sz00, xm)
% 82.81/43.14  																																																																																				|
% 82.81/43.14  																																																																																				| Using (982) and (984) yields:
% 82.81/43.14  																																																																																				| (97) $false
% 82.81/43.14  																																																																																				|
% 82.81/43.14  																																																																																				|-The branch is then unsatisfiable
% 82.81/43.14  																																																																																			|-Branch two:
% 82.81/43.14  																																																																																			| (986) sdtlseqdt0(sz00, all_15_0_4)
% 82.81/43.14  																																																																																			| (987) all_15_0_4 = sz00 | iLess0(sz00, all_15_0_4)
% 82.81/43.14  																																																																																			|
% 82.81/43.14  																																																																																				| From (440) and (986) follows:
% 82.81/43.14  																																																																																				| (982) sdtlseqdt0(sz00, xm)
% 82.81/43.14  																																																																																				|
% 82.81/43.14  																																																																																				+-Applying beta-rule and splitting (329), into two cases.
% 82.81/43.14  																																																																																				|-Branch one:
% 82.81/43.14  																																																																																				| (983)  ~ sdtlseqdt0(sz00, all_15_0_4)
% 82.81/43.14  																																																																																				|
% 82.81/43.14  																																																																																					| From (440) and (983) follows:
% 82.81/43.14  																																																																																					| (984)  ~ sdtlseqdt0(sz00, xm)
% 82.81/43.14  																																																																																					|
% 82.81/43.14  																																																																																					| Using (982) and (984) yields:
% 82.81/43.14  																																																																																					| (97) $false
% 82.81/43.14  																																																																																					|
% 82.81/43.14  																																																																																					|-The branch is then unsatisfiable
% 82.81/43.14  																																																																																				|-Branch two:
% 82.81/43.14  																																																																																				| (986) sdtlseqdt0(sz00, all_15_0_4)
% 82.81/43.14  																																																																																				| (993)  ? [v0] : (sdtpldt0(sz00, v0) = all_15_0_4 & aNaturalNumber0(v0))
% 82.81/43.14  																																																																																				|
% 82.81/43.14  																																																																																					| Instantiating (993) with all_1121_0_151 yields:
% 82.81/43.14  																																																																																					| (994) sdtpldt0(sz00, all_1121_0_151) = all_15_0_4 & aNaturalNumber0(all_1121_0_151)
% 82.81/43.14  																																																																																					|
% 82.81/43.14  																																																																																					| Applying alpha-rule on (994) yields:
% 82.81/43.14  																																																																																					| (995) sdtpldt0(sz00, all_1121_0_151) = all_15_0_4
% 82.81/43.14  																																																																																					| (996) aNaturalNumber0(all_1121_0_151)
% 82.81/43.14  																																																																																					|
% 82.81/43.14  																																																																																					| From (440) and (995) follows:
% 82.81/43.14  																																																																																					| (997) sdtpldt0(sz00, all_1121_0_151) = xm
% 82.81/43.14  																																																																																					|
% 82.81/43.14  																																																																																					| Using (997) and (939) yields:
% 82.81/43.14  																																																																																					| (998)  ~ (all_1121_0_151 = xm)
% 82.81/43.14  																																																																																					|
% 82.81/43.14  																																																																																					| Instantiating formula (3) with xm, all_1121_0_151 and discharging atoms sdtpldt0(sz00, all_1121_0_151) = xm, aNaturalNumber0(all_1121_0_151), yields:
% 82.81/43.14  																																																																																					| (999) all_1121_0_151 = xm
% 82.81/43.14  																																																																																					|
% 82.81/43.14  																																																																																					| Equations (999) can reduce 998 to:
% 82.81/43.14  																																																																																					| (104) $false
% 82.81/43.14  																																																																																					|
% 82.81/43.14  																																																																																					|-The branch is then unsatisfiable
% 82.81/43.14  																																																																																	|-Branch two:
% 82.81/43.14  																																																																																	| (1001) sdtpldt0(sz00, all_15_0_4) = all_122_0_20
% 82.81/43.14  																																																																																	| (1002) sdtpldt0(all_15_0_4, sz00) = all_15_0_4
% 82.81/43.14  																																																																																	|
% 82.81/43.14  																																																																																		| From (440)(440) and (1002) follows:
% 82.81/43.14  																																																																																		| (1003) sdtpldt0(xm, sz00) = xm
% 82.81/43.14  																																																																																		|
% 82.81/43.14  																																																																																		| Using (1003) and (937) yields:
% 82.81/43.14  																																																																																		| (97) $false
% 82.81/43.14  																																																																																		|
% 82.81/43.14  																																																																																		|-The branch is then unsatisfiable
% 82.81/43.14  																																																																																|-Branch two:
% 82.81/43.14  																																																																																| (1003) sdtpldt0(xm, sz00) = xm
% 82.81/43.14  																																																																																| (103) xp = sz00
% 82.81/43.14  																																																																																|
% 82.81/43.14  																																																																																	| Equations (103) can reduce 73 to:
% 82.81/43.14  																																																																																	| (104) $false
% 82.81/43.14  																																																																																	|
% 82.81/43.14  																																																																																	|-The branch is then unsatisfiable
% 82.81/43.14  																													|-Branch two:
% 82.81/43.14  																													| (1008) sdtpldt0(xn, sz00) = xn
% 82.81/43.14  																													| (1009) all_25_0_5 = sz00
% 82.81/43.14  																													|
% 82.81/43.14  																														| Combining equations (385,1009) yields a new equation:
% 82.81/43.14  																														| (915) xp = sz00
% 82.81/43.14  																														|
% 82.81/43.14  																														| Simplifying 915 yields:
% 82.81/43.14  																														| (103) xp = sz00
% 82.81/43.14  																														|
% 82.81/43.14  																														| Equations (103) can reduce 73 to:
% 82.81/43.14  																														| (104) $false
% 82.81/43.14  																														|
% 82.81/43.14  																														|-The branch is then unsatisfiable
% 82.81/43.14  																	|-Branch two:
% 82.81/43.14  																	| (1013) sdtpldt0(all_25_0_5, all_15_0_4) = sz00
% 82.81/43.14  																	| (1014) all_15_0_4 = sz00
% 82.81/43.14  																	|
% 82.81/43.14  																		| Equations (1014) can reduce 138 to:
% 82.81/43.14  																		| (104) $false
% 82.81/43.14  																		|
% 82.81/43.14  																		|-The branch is then unsatisfiable
% 82.81/43.14  							|-Branch two:
% 82.81/43.14  							| (1016) sdtpldt0(xm, xp) = sz00
% 82.81/43.14  							| (103) xp = sz00
% 82.81/43.14  							|
% 82.81/43.14  								| Equations (103) can reduce 73 to:
% 82.81/43.14  								| (104) $false
% 82.81/43.14  								|
% 82.81/43.14  								|-The branch is then unsatisfiable
% 82.81/43.14  					|-Branch two:
% 82.81/43.14  					| (1019)  ~ (all_34_0_6 = xp)
% 82.81/43.14  					| (1020) all_34_0_6 = sz10
% 82.81/43.14  					|
% 82.81/43.14  						| Equations (1020) can reduce 116 to:
% 82.81/43.14  						| (104) $false
% 82.81/43.14  						|
% 82.81/43.14  						|-The branch is then unsatisfiable
% 82.81/43.14  				|-Branch two:
% 82.81/43.14  				| (1022) sdtpldt0(xp, all_13_0_3) = sz00
% 82.81/43.14  				| (103) xp = sz00
% 82.81/43.14  				|
% 82.81/43.14  					| Equations (103) can reduce 73 to:
% 82.81/43.14  					| (104) $false
% 82.81/43.14  					|
% 82.81/43.14  					|-The branch is then unsatisfiable
% 82.81/43.14  |-Branch two:
% 82.81/43.14  | (1025)  ~ sdtlseqdt0(sz10, xp)
% 82.81/43.14  | (1026) xp = sz10 | xp = sz00
% 82.81/43.14  |
% 82.81/43.14  	+-Applying beta-rule and splitting (1026), into two cases.
% 82.81/43.14  	|-Branch one:
% 82.81/43.14  	| (103) xp = sz00
% 82.81/43.15  	|
% 82.81/43.15  		| Equations (103) can reduce 73 to:
% 82.81/43.15  		| (104) $false
% 82.81/43.15  		|
% 82.81/43.15  		|-The branch is then unsatisfiable
% 82.81/43.15  	|-Branch two:
% 82.81/43.15  	| (73)  ~ (xp = sz00)
% 82.81/43.15  	| (107) xp = sz10
% 82.81/43.15  	|
% 82.81/43.15  		| Equations (107) can reduce 72 to:
% 82.81/43.15  		| (104) $false
% 82.81/43.15  		|
% 82.81/43.15  		|-The branch is then unsatisfiable
% 82.81/43.15  % SZS output end Proof for theBenchmark
% 82.81/43.15  
% 82.81/43.15  42544ms
%------------------------------------------------------------------------------