TSTP Solution File: NUM482+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM482+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 08:44:58 EDT 2022
% Result : Theorem 22.24s 6.79s
% Output : Proof 35.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM482+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jul 7 05:45:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.50/0.60 ____ _
% 0.50/0.60 ___ / __ \_____(_)___ ________ __________
% 0.50/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.60
% 0.50/0.60 A Theorem Prover for First-Order Logic
% 0.50/0.60 (ePrincess v.1.0)
% 0.50/0.60
% 0.50/0.60 (c) Philipp Rümmer, 2009-2015
% 0.50/0.60 (c) Peter Backeman, 2014-2015
% 0.50/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.60 Bug reports to peter@backeman.se
% 0.50/0.60
% 0.50/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.60
% 0.50/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.84/1.01 Prover 0: Preprocessing ...
% 3.48/1.45 Prover 0: Constructing countermodel ...
% 18.50/5.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 18.84/6.02 Prover 1: Preprocessing ...
% 19.58/6.18 Prover 1: Constructing countermodel ...
% 19.82/6.22 Prover 1: gave up
% 19.82/6.22 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 20.02/6.26 Prover 2: Preprocessing ...
% 20.92/6.47 Prover 2: Warning: ignoring some quantifiers
% 20.92/6.48 Prover 2: Constructing countermodel ...
% 22.24/6.79 Prover 2: proved (567ms)
% 22.24/6.79 Prover 0: stopped
% 22.24/6.79
% 22.24/6.79 No countermodel exists, formula is valid
% 22.24/6.79 % SZS status Theorem for theBenchmark
% 22.24/6.79
% 22.24/6.79 Generating proof ... Warning: ignoring some quantifiers
% 34.31/10.25 found it (size 311)
% 34.31/10.25
% 34.31/10.25 % SZS output start Proof for theBenchmark
% 34.31/10.25 Assumed formulas after preprocessing and simplification:
% 34.31/10.25 | (0) ~ (xk = sz10) & ~ (xk = sz00) & ~ (sz10 = sz00) & isPrime0(xk) = 0 & aNaturalNumber0(xk) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 & ~ (isPrime0(sz10) = 0) & ~ (isPrime0(sz00) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | v0 = sz00 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v5 = 0 & ~ (v7 = v6) & ~ (v4 = v3) & sdtlseqdt0(v6, v7) = 0 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6) | ( ~ (v6 = 0) & sdtlseqdt0(v1, v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | v0 = sz00 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v5 = 0 & ~ (v7 = v6) & ~ (v4 = v3) & sdtlseqdt0(v6, v7) = 0 & sdtasdt0(v2, v0) = v7 & sdtasdt0(v1, v0) = v6) | ( ~ (v6 = 0) & sdtlseqdt0(v1, v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = v5 & v10 = v7 & sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & v7 = v5 & sdtasdt0(v6, v0) = v8 & sdtasdt0(v2, v0) = v10 & sdtasdt0(v1, v0) = v9 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v9, v10) = v8 & sdtpldt0(v1, v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (doDivides0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ? [v5] : (( ~ (v5 = 0) & doDivides0(v0, v2) = v5) | ( ~ (v5 = 0) & doDivides0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v0, v2) = v6 & sdtpldt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : (( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ? [v5] : ? [v6] : (( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v2) = v4) | ? [v5] : ? [v6] : ((v6 = v4 & sdtsldt0(v5, v0) = v4 & sdtasdt0(v3, v1) = v5) | ( ~ (v5 = 0) & doDivides0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v3) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ? [v5] : ? [v6] : ((v6 = v5 & sdtsldt0(v4, v0) = v5 & sdtasdt0(v3, v2) = v5) | ( ~ (v5 = 0) & doDivides0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v3) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v5] : ? [v6] : ((v6 = v4 & sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = v4 & v8 = v5 & sdtasdt0(v2, v0) = v10 & sdtasdt0(v1, v0) = v9 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v9, v10) = v4 & sdtpldt0(v6, v7) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ? [v5] : ? [v6] : ((v6 = v4 & sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & v7 = v4 & sdtasdt0(v3, v0) = v8 & sdtasdt0(v2, v0) = v10 & sdtasdt0(v1, v0) = v9 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v9, v10) = v8 & sdtpldt0(v5, v6) = v4) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ((v6 = v4 & sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ? [v5] : ? [v6] : ((v6 = v4 & sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : (( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : (( ~ (v4 = v1) & sdtasdt0(v0, v3) = v4) | ( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : (( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : (( ~ (v4 = v1) & sdtpldt0(v0, v3) = v4) | ( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (aNaturalNumber0(v2) = v3) | ? [v4] : (( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (doDivides0(v1, v2) = 0) | ~ (doDivides0(v0, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (doDivides0(v0, v2) = v3) | ~ (doDivides0(v0, v1) = 0) | ? [v4] : (( ~ (v4 = 0) & doDivides0(v1, v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (doDivides0(v0, v2) = v3) | ~ (aNaturalNumber0(v1) = 0) | ? [v4] : (( ~ (v4 = 0) & doDivides0(v1, v2) = v4) | ( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (sdtmndt0(v1, v0) = v2) | ~ (aNaturalNumber0(v2) = v3) | ? [v4] : (( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (sdtlseqdt0(v1, v2) = 0) | ~ (sdtlseqdt0(v0, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (sdtlseqdt0(v0, v2) = v3) | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v4] : (( ~ (v4 = 0) & sdtlseqdt0(v1, v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (sdtlseqdt0(v0, v2) = v3) | ~ (aNaturalNumber0(v1) = 0) | ? [v4] : (( ~ (v4 = 0) & sdtlseqdt0(v1, v2) = v4) | ( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v3) & ~ (v5 = v4) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtasdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v3) | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v3) & ~ (v5 = v4) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtasdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtasdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtasdt0(v0, v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (aNaturalNumber0(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5 & sdtpldt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v3) | ~ (aNaturalNumber0(v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v2) = v5 & sdtpldt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (aNaturalNumber0(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 & sdtpldt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v1) = v3) | ~ (aNaturalNumber0(v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 & sdtpldt0(v0, v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (doDivides0(v0, v1) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (doDivides0(v0, v1) = v2) | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : (( ~ (v4 = v1) & sdtasdt0(v0, v3) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : (( ~ (v4 = v1) & sdtpldt0(v0, v3) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ~ (sdtpldt0(v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v5 = 0 & ~ (v7 = v6) & ~ (v4 = v3) & sdtlseqdt0(v6, v7) = 0 & sdtlseqdt0(v4, v3) = 0 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v7 & sdtpldt0(v0, v2) = v6) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ~ (sdtpldt0(v2, v0) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v5 = 0 & ~ (v7 = v6) & ~ (v4 = v3) & sdtlseqdt0(v6, v7) = 0 & sdtlseqdt0(v3, v4) = 0 & sdtpldt0(v2, v1) = v4 & sdtpldt0(v1, v2) = v7 & sdtpldt0(v0, v2) = v6) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ~ (sdtpldt0(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v6 = 0 & ~ (v7 = v3) & ~ (v5 = v4) & sdtlseqdt0(v7, v3) = 0 & sdtlseqdt0(v4, v5) = 0 & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v0, v2) = v7) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v6 = 0 & ~ (v7 = v3) & ~ (v5 = v4) & sdtlseqdt0(v4, v5) = 0 & sdtlseqdt0(v3, v7) = 0 & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v7) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = v4 & sdtsldt0(v5, v0) = v4 & sdtasdt0(v3, v2) = v4 & sdtasdt0(v3, v1) = v5) | ( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (aNaturalNumber0(v2) = v3) | ? [v4] : ((v4 = v1 & sdtasdt0(v0, v2) = v1) | ( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (doDivides0(v0, v3) = 0) | ~ (sdtpldt0(v1, v2) = v3) | ? [v4] : ((v4 = 0 & doDivides0(v0, v2) = 0) | ( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (aNaturalNumber0(v2) = v3) | ? [v4] : ((v4 = v1 & sdtpldt0(v0, v2) = v1) | ( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | v0 = sz00 | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtasdt0(v0, v2) = v4 & sdtasdt0(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 & sdtpldt0(v0, v2) = v4 & sdtpldt0(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (iLess0(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & sdtlseqdt0(v0, v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = sz00 | ~ (sdtlseqdt0(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & doDivides0(v0, v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (sdtlseqdt0(v1, v0) = v2) | ? [v3] : ((v3 = 0 & sdtlseqdt0(v0, v1) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ? [v3] : ((v3 = 0 & ~ (v1 = v0) & sdtlseqdt0(v1, v0) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ~ (aNaturalNumber0(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v5 = 0 & ~ (v7 = v6) & ~ (v4 = v3) & sdtlseqdt0(v6, v7) = 0 & sdtlseqdt0(v3, v4) = 0 & sdtpldt0(v2, v1) = v4 & sdtpldt0(v2, v0) = v3 & sdtpldt0(v1, v2) = v7 & sdtpldt0(v0, v2) = v6) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ? [v3] : ((v3 = 0 & sdtlseqdt0(v1, v2) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (doDivides0(v1, v2) = 0) | ~ (doDivides0(v0, v1) = 0) | ? [v3] : ((v3 = 0 & doDivides0(v0, v2) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (doDivides0(v1, v2) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v3] : ((v3 = 0 & doDivides0(v0, v2) = 0) | ( ~ (v3 = 0) & doDivides0(v0, v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (doDivides0(v0, v1) = 0) | ~ (aNaturalNumber0(v2) = 0) | ? [v3] : ((v3 = 0 & doDivides0(v0, v2) = 0) | ( ~ (v3 = 0) & doDivides0(v1, v2) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtlseqdt0(v1, v2) = 0) | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v3] : ((v3 = 0 & sdtlseqdt0(v0, v2) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtlseqdt0(v1, v2) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v3] : ((v3 = 0 & sdtlseqdt0(v0, v2) = 0) | ( ~ (v3 = 0) & sdtlseqdt0(v0, v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtlseqdt0(v0, v1) = 0) | ~ (aNaturalNumber0(v2) = 0) | ? [v3] : ((v3 = 0 & sdtlseqdt0(v0, v2) = 0) | ( ~ (v3 = 0) & sdtlseqdt0(v1, v2) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ? [v3] : ((v3 = v2 & sdtasdt0(v0, v1) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ((v3 = v2 & sdtasdt0(v1, v0) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ((v3 = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ? [v3] : ((v3 = v2 & sdtpldt0(v0, v1) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ((v3 = v2 & sdtpldt0(v1, v0) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ((v3 = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v3] : ((v3 = 0 & doDivides0(v0, v2) = 0) | ( ~ (v3 = 0) & doDivides0(v1, v2) = v3) | ( ~ (v3 = 0) & doDivides0(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v3] : ((v3 = 0 & sdtlseqdt0(v0, v2) = 0) | ( ~ (v3 = 0) & sdtlseqdt0(v1, v2) = v3) | ( ~ (v3 = 0) & sdtlseqdt0(v0, v1) = v3))) & ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ (isPrime0(v0) = 0) | ~ (doDivides0(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ (isPrime0(v0) = 0) | ~ (aNaturalNumber0(v1) = 0) | ? [v2] : (( ~ (v2 = 0) & doDivides0(v1, v0) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtlseqdt0(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & sdtlseqdt0(v0, v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ((v2 = 0 & iLess0(v0, v1) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : (( ~ (v2 = 0) & sdtlseqdt0(v1, v0) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (doDivides0(v0, v1) = 0) | ? [v2] : ((v2 = 0 & sdtlseqdt0(v0, v1) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (isPrime0(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & ~ (v2 = v0) & ~ (v2 = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)) & ! [v0] : ! [v1] : (v0 = sz00 | ~ (doDivides0(v0, v1) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (sdtsldt0(v1, v0) = v2 & ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ? [v5] : ? [v6] : ((v6 = v4 & sdtsldt0(v5, v0) = v4 & sdtasdt0(v3, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v3) = v5))) & ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v1) = v4) | ? [v5] : ? [v6] : ((v6 = v5 & sdtsldt0(v4, v0) = v5 & sdtasdt0(v3, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v3) = v5))) & ! [v3] : ( ~ (aNaturalNumber0(v3) = 0) | ? [v4] : ? [v5] : (sdtsldt0(v5, v0) = v4 & sdtasdt0(v3, v2) = v4 & sdtasdt0(v3, v1) = v5))))) & ! [v0] : ! [v1] : (v0 = sz00 | ~ (doDivides0(v0, v1) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (sdtsldt0(v1, v0) = v2 & ! [v3] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)) & ! [v3] : (v3 = v2 | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : ( ~ (v4 = v1) & sdtasdt0(v0, v3) = v4)) & ! [v3] : (v3 = v1 | ~ (sdtasdt0(v0, v2) = v3)) & ! [v3] : (v3 = 0 | ~ (aNaturalNumber0(v2) = v3)) & ! [v3] : ( ~ (sdtasdt0(v0, v2) = v3) | aNaturalNumber0(v2) = 0) & ! [v3] : ( ~ (aNaturalNumber0(v2) = v3) | sdtasdt0(v0, v2) = v1)))) & ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (doDivides0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (sdtmndt0(v1, v0) = v2 & ! [v3] : (v3 = v2 | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)) & ! [v3] : (v3 = v2 | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : ( ~ (v4 = v1) & sdtpldt0(v0, v3) = v4)) & ! [v3] : (v3 = v1 | ~ (sdtpldt0(v0, v2) = v3)) & ! [v3] : (v3 = 0 | ~ (aNaturalNumber0(v2) = v3)) & ! [v3] : ( ~ (sdtpldt0(v0, v2) = v3) | aNaturalNumber0(v2) = 0) & ! [v3] : ( ~ (aNaturalNumber0(v2) = v3) | sdtpldt0(v0, v2) = v1)))) & ! [v0] : ! [v1] : ( ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtasdt0(sz10, v0) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ? [v2] : ((v2 = sz00 & v1 = sz00 & sdtasdt0(sz00, v0) = sz00) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtasdt0(v0, sz10) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ((v2 = sz00 & v1 = sz00 & sdtasdt0(v0, sz00) = sz00) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtpldt0(sz00, v0) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtpldt0(v0, sz00) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (iLess0(v0, xk) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0) | ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1))) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | sdtlseqdt0(sz10, v0) = 0) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0) | ( ~ (v1 = 0) & iLess0(v0, xk) = v1))) & ! [v0] : ( ~ (isPrime0(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & doDivides0(v0, xk) = v1) | ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1))) & ! [v0] : ( ~ (doDivides0(v0, xk) = 0) | ? [v1] : (( ~ (v1 = 0) & isPrime0(v0) = v1) | ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1))) & ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | sdtlseqdt0(v0, v0) = 0) & ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v0 = sz10 | v0 = sz00 | (v4 = 0 & v3 = 0 & ~ (v2 = v0) & ~ (v2 = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0) | (v1 = 0 & isPrime0(v0) = 0)) & (( ~ (v1 = 0) & isPrime0(v0) = v1) | ( ~ (v0 = sz10) & ~ (v0 = sz00) & ! [v5] : (v5 = v0 | v5 = sz10 | ~ (doDivides0(v5, v0) = 0) | ? [v6] : ( ~ (v6 = 0) & aNaturalNumber0(v5) = v6)) & ! [v5] : (v5 = v0 | v5 = sz10 | ~ (aNaturalNumber0(v5) = 0) | ? [v6] : ( ~ (v6 = 0) & doDivides0(v5, v0) = v6)))))) & ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & isPrime0(v0) = v1) | ( ~ (v1 = 0) & doDivides0(v0, xk) = v1))) & ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | (sdtasdt0(v0, sz10) = v0 & sdtasdt0(sz10, v0) = v0)) & ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | (sdtasdt0(v0, sz00) = sz00 & sdtasdt0(sz00, v0) = sz00)) & ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | (sdtpldt0(v0, sz00) = v0 & sdtpldt0(sz00, v0) = v0)) & ? [v0] : ? [v1] : ? [v2] : sdtsldt0(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : doDivides0(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : iLess0(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : sdtmndt0(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : sdtlseqdt0(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : sdtasdt0(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : sdtpldt0(v1, v0) = v2 & ? [v0] : ? [v1] : isPrime0(v0) = v1 & ? [v0] : ? [v1] : aNaturalNumber0(v0) = v1
% 34.61/10.36 | Applying alpha-rule on (0) yields:
% 34.61/10.36 | (1) ? [v0] : ? [v1] : isPrime0(v0) = v1
% 34.82/10.37 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | v0 = sz00 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v5 = 0 & ~ (v7 = v6) & ~ (v4 = v3) & sdtlseqdt0(v6, v7) = 0 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6) | ( ~ (v6 = 0) & sdtlseqdt0(v1, v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v0) = v6)))
% 34.82/10.37 | (3) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0) | ( ~ (v1 = 0) & iLess0(v0, xk) = v1)))
% 34.82/10.37 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ((v3 = v2 & sdtpldt0(v1, v0) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 34.82/10.37 | (5) ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | sdtlseqdt0(v0, v0) = 0)
% 34.82/10.37 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : (( ~ (v4 = v1) & sdtpldt0(v0, v3) = v4) | ( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.37 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ? [v5] : ? [v6] : ((v6 = v5 & sdtsldt0(v4, v0) = v5 & sdtasdt0(v3, v2) = v5) | ( ~ (v5 = 0) & doDivides0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v3) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 34.82/10.37 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5)))
% 34.82/10.37 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v5] : ? [v6] : ((v6 = v4 & sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 34.82/10.37 | (10) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtpldt0(v0, sz00) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 34.82/10.37 | (11) isPrime0(xk) = 0
% 34.82/10.37 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : (( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.37 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & v7 = v4 & sdtasdt0(v3, v0) = v8 & sdtasdt0(v2, v0) = v10 & sdtasdt0(v1, v0) = v9 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v9, v10) = v8 & sdtpldt0(v5, v6) = v4) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 34.82/10.37 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtlseqdt0(v1, v2) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v3] : ((v3 = 0 & sdtlseqdt0(v0, v2) = 0) | ( ~ (v3 = 0) & sdtlseqdt0(v0, v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3)))
% 34.82/10.37 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtasdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4)))
% 34.82/10.37 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtlseqdt0(v1, v2) = 0) | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v3] : ((v3 = 0 & sdtlseqdt0(v0, v2) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 34.82/10.37 | (17) ! [v0] : ! [v1] : ( ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 34.82/10.37 | (18) ~ (isPrime0(sz10) = 0)
% 34.82/10.38 | (19) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtasdt0(v0, sz10) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 34.82/10.38 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (doDivides0(v0, v1) = 0) | ~ (aNaturalNumber0(v2) = 0) | ? [v3] : ((v3 = 0 & doDivides0(v0, v2) = 0) | ( ~ (v3 = 0) & doDivides0(v1, v2) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 34.82/10.38 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ? [v3] : ((v3 = 0 & ~ (v1 = v0) & sdtlseqdt0(v1, v0) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 34.82/10.38 | (22) ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (isPrime0(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & ~ (v2 = v0) & ~ (v2 = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 34.82/10.38 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (doDivides0(v0, v2) = v3) | ~ (aNaturalNumber0(v1) = 0) | ? [v4] : (( ~ (v4 = 0) & doDivides0(v1, v2) = v4) | ( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.38 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ((v6 = v4 & sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 34.82/10.38 | (25) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ((v2 = 0 & iLess0(v0, v1) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 34.82/10.38 | (26) ! [v0] : ! [v1] : ( ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 34.82/10.38 | (27) ? [v0] : ? [v1] : ? [v2] : sdtasdt0(v1, v0) = v2
% 34.82/10.38 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.38 | (29) ! [v0] : ( ~ (doDivides0(v0, xk) = 0) | ? [v1] : (( ~ (v1 = 0) & isPrime0(v0) = v1) | ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)))
% 34.82/10.38 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5)))
% 34.82/10.38 | (31) ? [v0] : ? [v1] : ? [v2] : doDivides0(v1, v0) = v2
% 34.82/10.38 | (32) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtlseqdt0(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & sdtlseqdt0(v0, v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 34.82/10.38 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : (( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 34.82/10.38 | (34) ? [v0] : ? [v1] : ? [v2] : sdtmndt0(v1, v0) = v2
% 34.82/10.38 | (35) ! [v0] : ! [v1] : ( ~ (doDivides0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 34.82/10.38 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (aNaturalNumber0(v2) = v3) | ? [v4] : ((v4 = v1 & sdtasdt0(v0, v2) = v1) | ( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.38 | (37) ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v0 = sz10 | v0 = sz00 | (v4 = 0 & v3 = 0 & ~ (v2 = v0) & ~ (v2 = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0) | (v1 = 0 & isPrime0(v0) = 0)) & (( ~ (v1 = 0) & isPrime0(v0) = v1) | ( ~ (v0 = sz10) & ~ (v0 = sz00) & ! [v5] : (v5 = v0 | v5 = sz10 | ~ (doDivides0(v5, v0) = 0) | ? [v6] : ( ~ (v6 = 0) & aNaturalNumber0(v5) = v6)) & ! [v5] : (v5 = v0 | v5 = sz10 | ~ (aNaturalNumber0(v5) = 0) | ? [v6] : ( ~ (v6 = 0) & doDivides0(v5, v0) = v6))))))
% 34.82/10.38 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : (( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.39 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ((v3 = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 34.82/10.39 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.39 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ~ (sdtpldt0(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v6 = 0 & ~ (v7 = v3) & ~ (v5 = v4) & sdtlseqdt0(v7, v3) = 0 & sdtlseqdt0(v4, v5) = 0 & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v0, v2) = v7) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.39 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (doDivides0(v1, v2) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v3] : ((v3 = 0 & doDivides0(v0, v2) = 0) | ( ~ (v3 = 0) & doDivides0(v0, v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3)))
% 34.82/10.39 | (43) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 34.82/10.39 | (44) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : (( ~ (v2 = 0) & sdtlseqdt0(v1, v0) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 34.82/10.39 | (45) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | v0 = sz00 | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtasdt0(v0, v2) = v4 & sdtasdt0(v0, v1) = v3))
% 34.82/10.39 | (46) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 34.82/10.39 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v3) & ~ (v5 = v4) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtasdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4)))
% 34.82/10.39 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (doDivides0(v0, v1) = v2) | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : (( ~ (v4 = v1) & sdtasdt0(v0, v3) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.39 | (49) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (sdtlseqdt0(v1, v0) = v2) | ? [v3] : ((v3 = 0 & sdtlseqdt0(v0, v1) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 34.82/10.39 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ? [v5] : ? [v6] : (( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 34.82/10.39 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (sdtlseqdt0(v0, v2) = v3) | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v4] : (( ~ (v4 = 0) & sdtlseqdt0(v1, v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.39 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v3] : ((v3 = 0 & doDivides0(v0, v2) = 0) | ( ~ (v3 = 0) & doDivides0(v1, v2) = v3) | ( ~ (v3 = 0) & doDivides0(v0, v1) = v3)))
% 34.82/10.39 | (53) ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | (sdtpldt0(v0, sz00) = v0 & sdtpldt0(sz00, v0) = v0))
% 34.82/10.39 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0))
% 34.82/10.39 | (55) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtpldt0(sz00, v0) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 34.82/10.39 | (56) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtasdt0(sz10, v0) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 34.82/10.39 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (doDivides0(v0, v2) = v3) | ~ (doDivides0(v0, v1) = 0) | ? [v4] : (( ~ (v4 = 0) & doDivides0(v1, v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.40 | (58) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ? [v2] : ((v2 = sz00 & v1 = sz00 & sdtasdt0(sz00, v0) = sz00) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 34.82/10.40 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v0, v2) = v6 & sdtpldt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 34.82/10.40 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5)))
% 34.82/10.40 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (doDivides0(v1, v2) = 0) | ~ (doDivides0(v0, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.40 | (62) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 34.82/10.40 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v3) | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v3) & ~ (v5 = v4) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtasdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4)))
% 34.82/10.40 | (64) aNaturalNumber0(sz10) = 0
% 34.82/10.40 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 34.82/10.40 | (66) ! [v0] : ! [v1] : ( ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (sdtmndt0(v1, v0) = v2 & ! [v3] : (v3 = v2 | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)) & ! [v3] : (v3 = v2 | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : ( ~ (v4 = v1) & sdtpldt0(v0, v3) = v4)) & ! [v3] : (v3 = v1 | ~ (sdtpldt0(v0, v2) = v3)) & ! [v3] : (v3 = 0 | ~ (aNaturalNumber0(v2) = v3)) & ! [v3] : ( ~ (sdtpldt0(v0, v2) = v3) | aNaturalNumber0(v2) = 0) & ! [v3] : ( ~ (aNaturalNumber0(v2) = v3) | sdtpldt0(v0, v2) = v1))))
% 34.82/10.40 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v1) = v3) | ~ (aNaturalNumber0(v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 & sdtpldt0(v0, v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.40 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtasdt0(v0, v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4)))
% 34.82/10.40 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.40 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = v4 & sdtsldt0(v5, v0) = v4 & sdtasdt0(v3, v2) = v4 & sdtasdt0(v3, v1) = v5) | ( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.40 | (71) ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & isPrime0(v0) = v1) | ( ~ (v1 = 0) & doDivides0(v0, xk) = v1)))
% 34.82/10.40 | (72) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (iLess0(v0, xk) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0) | ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)))
% 34.82/10.40 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.40 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : (( ~ (v4 = v1) & sdtasdt0(v0, v3) = v4) | ( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.40 | (75) aNaturalNumber0(sz00) = 0
% 34.82/10.40 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.40 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v3) | ~ (aNaturalNumber0(v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v2) = v5 & sdtpldt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.41 | (78) ~ (sz10 = sz00)
% 34.82/10.41 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : (( ~ (v4 = v1) & sdtpldt0(v0, v3) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.41 | (80) ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 34.82/10.41 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 34.82/10.41 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = v5 & v10 = v7 & sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v0) = v6)))
% 34.82/10.41 | (83) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ (isPrime0(v0) = 0) | ~ (doDivides0(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 34.82/10.41 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 34.82/10.41 | (85) ? [v0] : ? [v1] : ? [v2] : sdtpldt0(v1, v0) = v2
% 34.82/10.41 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (doDivides0(v0, v1) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.41 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v2) = v4) | ? [v5] : ? [v6] : ((v6 = v4 & sdtsldt0(v5, v0) = v4 & sdtasdt0(v3, v1) = v5) | ( ~ (v5 = 0) & doDivides0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v3) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 34.82/10.41 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (aNaturalNumber0(v2) = v3) | ? [v4] : (( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.41 | (89) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 & sdtpldt0(v0, v2) = v4 & sdtpldt0(v0, v1) = v3))
% 34.82/10.41 | (90) ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ? [v3] : ((v3 = 0 & sdtlseqdt0(v1, v2) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 34.82/10.41 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (sdtmndt0(v1, v0) = v2) | ~ (aNaturalNumber0(v2) = v3) | ? [v4] : (( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.41 | (92) ~ (isPrime0(sz00) = 0)
% 34.82/10.41 | (93) ? [v0] : ? [v1] : aNaturalNumber0(v0) = v1
% 34.82/10.41 | (94) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ~ (aNaturalNumber0(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v5 = 0 & ~ (v7 = v6) & ~ (v4 = v3) & sdtlseqdt0(v6, v7) = 0 & sdtlseqdt0(v3, v4) = 0 & sdtpldt0(v2, v1) = v4 & sdtpldt0(v2, v0) = v3 & sdtpldt0(v1, v2) = v7 & sdtpldt0(v0, v2) = v6) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 34.82/10.41 | (95) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = sz00 | ~ (sdtlseqdt0(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & doDivides0(v0, v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 34.82/10.41 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | v0 = sz00 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v5 = 0 & ~ (v7 = v6) & ~ (v4 = v3) & sdtlseqdt0(v6, v7) = 0 & sdtasdt0(v2, v0) = v7 & sdtasdt0(v1, v0) = v6) | ( ~ (v6 = 0) & sdtlseqdt0(v1, v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v0) = v6)))
% 34.82/10.41 | (97) ! [v0] : ! [v1] : (v0 = sz00 | ~ (doDivides0(v0, v1) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (sdtsldt0(v1, v0) = v2 & ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ? [v5] : ? [v6] : ((v6 = v4 & sdtsldt0(v5, v0) = v4 & sdtasdt0(v3, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v3) = v5))) & ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v1) = v4) | ? [v5] : ? [v6] : ((v6 = v5 & sdtsldt0(v4, v0) = v5 & sdtasdt0(v3, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v3) = v5))) & ! [v3] : ( ~ (aNaturalNumber0(v3) = 0) | ? [v4] : ? [v5] : (sdtsldt0(v5, v0) = v4 & sdtasdt0(v3, v2) = v4 & sdtasdt0(v3, v1) = v5)))))
% 34.82/10.41 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ? [v5] : ? [v6] : ((v6 = v4 & sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 34.82/10.41 | (99) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ? [v3] : ((v3 = v2 & sdtasdt0(v0, v1) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 34.82/10.41 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0))
% 34.82/10.41 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (aNaturalNumber0(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 & sdtpldt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.41 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 34.82/10.42 | (103) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ((v2 = sz00 & v1 = sz00 & sdtasdt0(v0, sz00) = sz00) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 34.82/10.42 | (104) ~ (xk = sz00)
% 34.82/10.42 | (105) ! [v0] : ! [v1] : ! [v2] : ( ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v3] : ((v3 = 0 & sdtlseqdt0(v0, v2) = 0) | ( ~ (v3 = 0) & sdtlseqdt0(v1, v2) = v3) | ( ~ (v3 = 0) & sdtlseqdt0(v0, v1) = v3)))
% 34.82/10.42 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0))
% 34.82/10.42 | (107) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ (isPrime0(v0) = 0) | ~ (aNaturalNumber0(v1) = 0) | ? [v2] : (( ~ (v2 = 0) & doDivides0(v1, v0) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 34.82/10.42 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ? [v5] : ? [v6] : ((v6 = v4 & sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 34.82/10.42 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ~ (sdtpldt0(v2, v0) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v5 = 0 & ~ (v7 = v6) & ~ (v4 = v3) & sdtlseqdt0(v6, v7) = 0 & sdtlseqdt0(v3, v4) = 0 & sdtpldt0(v2, v1) = v4 & sdtpldt0(v1, v2) = v7 & sdtpldt0(v0, v2) = v6) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.42 | (110) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (iLess0(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & sdtlseqdt0(v0, v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 34.82/10.42 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (aNaturalNumber0(v2) = v3) | ? [v4] : ((v4 = v1 & sdtpldt0(v0, v2) = v1) | ( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.42 | (112) ! [v0] : ! [v1] : (v1 = sz00 | ~ (doDivides0(v0, v1) = 0) | ? [v2] : ((v2 = 0 & sdtlseqdt0(v0, v1) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 34.82/10.42 | (113) ~ (xk = sz10)
% 34.82/10.42 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (doDivides0(v0, v3) = 0) | ~ (sdtpldt0(v1, v2) = v3) | ? [v4] : ((v4 = 0 & doDivides0(v0, v2) = 0) | ( ~ (v4 = 0) & doDivides0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.42 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ~ (sdtpldt0(v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v5 = 0 & ~ (v7 = v6) & ~ (v4 = v3) & sdtlseqdt0(v6, v7) = 0 & sdtlseqdt0(v4, v3) = 0 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v7 & sdtpldt0(v0, v2) = v6) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.42 | (116) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtlseqdt0(v0, v1) = 0) | ~ (aNaturalNumber0(v2) = 0) | ? [v3] : ((v3 = 0 & sdtlseqdt0(v0, v2) = 0) | ( ~ (v3 = 0) & sdtlseqdt0(v1, v2) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 34.82/10.42 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & v7 = v5 & sdtasdt0(v6, v0) = v8 & sdtasdt0(v2, v0) = v10 & sdtasdt0(v1, v0) = v9 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v9, v10) = v8 & sdtpldt0(v1, v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v0) = v6)))
% 34.82/10.42 | (118) aNaturalNumber0(xk) = 0
% 34.82/10.42 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 34.82/10.42 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (sdtlseqdt0(v0, v2) = v3) | ~ (aNaturalNumber0(v1) = 0) | ? [v4] : (( ~ (v4 = 0) & sdtlseqdt0(v1, v2) = v4) | ( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.42 | (121) ! [v0] : ! [v1] : ! [v2] : ( ~ (doDivides0(v1, v2) = 0) | ~ (doDivides0(v0, v1) = 0) | ? [v3] : ((v3 = 0 & doDivides0(v0, v2) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 34.82/10.42 | (122) ? [v0] : ? [v1] : ? [v2] : sdtsldt0(v1, v0) = v2
% 34.82/10.42 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (sdtlseqdt0(v1, v2) = 0) | ~ (sdtlseqdt0(v0, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.42 | (124) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0))
% 34.82/10.42 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = v4 & v8 = v5 & sdtasdt0(v2, v0) = v10 & sdtasdt0(v1, v0) = v9 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v9, v10) = v4 & sdtpldt0(v6, v7) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 34.82/10.42 | (126) ? [v0] : ? [v1] : ? [v2] : iLess0(v1, v0) = v2
% 34.82/10.42 | (127) ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | (sdtasdt0(v0, sz10) = v0 & sdtasdt0(sz10, v0) = v0))
% 34.82/10.42 | (128) ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 34.82/10.42 | (129) ! [v0] : ! [v1] : (v0 = sz00 | ~ (doDivides0(v0, v1) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (sdtsldt0(v1, v0) = v2 & ! [v3] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)) & ! [v3] : (v3 = v2 | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : ( ~ (v4 = v1) & sdtasdt0(v0, v3) = v4)) & ! [v3] : (v3 = v1 | ~ (sdtasdt0(v0, v2) = v3)) & ! [v3] : (v3 = 0 | ~ (aNaturalNumber0(v2) = v3)) & ! [v3] : ( ~ (sdtasdt0(v0, v2) = v3) | aNaturalNumber0(v2) = 0) & ! [v3] : ( ~ (aNaturalNumber0(v2) = v3) | sdtasdt0(v0, v2) = v1))))
% 34.82/10.42 | (130) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5)))
% 34.82/10.42 | (131) ? [v0] : ? [v1] : ? [v2] : sdtlseqdt0(v1, v0) = v2
% 34.82/10.42 | (132) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (aNaturalNumber0(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5 & sdtpldt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.43 | (133) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ((v3 = v2 & sdtasdt0(v1, v0) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 34.82/10.43 | (134) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v6 = 0 & ~ (v7 = v3) & ~ (v5 = v4) & sdtlseqdt0(v4, v5) = 0 & sdtlseqdt0(v3, v7) = 0 & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v7) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 34.82/10.43 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (doDivides0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ? [v5] : (( ~ (v5 = 0) & doDivides0(v0, v2) = v5) | ( ~ (v5 = 0) & doDivides0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 34.82/10.43 | (136) ! [v0] : ( ~ (isPrime0(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & doDivides0(v0, xk) = v1) | ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)))
% 34.82/10.43 | (137) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ? [v3] : ((v3 = v2 & sdtpldt0(v0, v1) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 34.82/10.43 | (138) ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | (sdtasdt0(v0, sz00) = sz00 & sdtasdt0(sz00, v0) = sz00))
% 34.82/10.43 | (139) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | sdtlseqdt0(sz10, v0) = 0)
% 34.82/10.43 | (140) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0))
% 34.82/10.43 | (141) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ((v3 = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 34.82/10.43 |
% 34.82/10.43 | Instantiating formula (136) with xk and discharging atoms isPrime0(xk) = 0, yields:
% 34.82/10.43 | (142) ? [v0] : (( ~ (v0 = 0) & doDivides0(xk, xk) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xk) = v0))
% 34.82/10.43 |
% 34.82/10.43 | Instantiating formula (52) with xk, xk, xk and discharging atoms aNaturalNumber0(xk) = 0, yields:
% 34.82/10.43 | (143) ? [v0] : ((v0 = 0 & doDivides0(xk, xk) = 0) | ( ~ (v0 = 0) & doDivides0(xk, xk) = v0))
% 34.82/10.43 |
% 34.82/10.43 | Instantiating formula (3) with xk and discharging atoms aNaturalNumber0(xk) = 0, yields:
% 34.82/10.43 | (144) xk = sz10 | xk = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & isPrime0(v0) = 0 & doDivides0(v0, xk) = 0 & aNaturalNumber0(v0) = 0) | ( ~ (v0 = 0) & iLess0(xk, xk) = v0))
% 34.82/10.43 |
% 34.82/10.43 | Instantiating formula (37) with xk and discharging atoms aNaturalNumber0(xk) = 0, yields:
% 34.82/10.43 | (145) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((xk = sz10 | xk = sz00 | (v3 = 0 & v2 = 0 & ~ (v1 = xk) & ~ (v1 = sz10) & doDivides0(v1, xk) = 0 & aNaturalNumber0(v1) = 0) | (v0 = 0 & isPrime0(xk) = 0)) & (( ~ (v0 = 0) & isPrime0(xk) = v0) | ( ~ (xk = sz10) & ~ (xk = sz00) & ! [v4] : (v4 = xk | v4 = sz10 | ~ (doDivides0(v4, xk) = 0) | ? [v5] : ( ~ (v5 = 0) & aNaturalNumber0(v4) = v5)) & ! [v4] : (v4 = xk | v4 = sz10 | ~ (aNaturalNumber0(v4) = 0) | ? [v5] : ( ~ (v5 = 0) & doDivides0(v4, xk) = v5)))))
% 34.82/10.43 |
% 34.82/10.43 | Instantiating formula (71) with xk and discharging atoms aNaturalNumber0(xk) = 0, yields:
% 34.82/10.43 | (146) ? [v0] : (( ~ (v0 = 0) & isPrime0(xk) = v0) | ( ~ (v0 = 0) & doDivides0(xk, xk) = v0))
% 34.82/10.43 |
% 34.82/10.43 | Instantiating formula (127) with xk and discharging atoms aNaturalNumber0(xk) = 0, yields:
% 34.82/10.43 | (147) sdtasdt0(xk, sz10) = xk & sdtasdt0(sz10, xk) = xk
% 34.82/10.43 |
% 34.82/10.43 | Applying alpha-rule on (147) yields:
% 34.82/10.43 | (148) sdtasdt0(xk, sz10) = xk
% 34.82/10.43 | (149) sdtasdt0(sz10, xk) = xk
% 34.82/10.43 |
% 34.82/10.43 | Instantiating formula (45) with sz10, xk, xk and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz10) = 0, yields:
% 34.82/10.43 | (150) xk = sz10 | xk = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, xk) = v2 & sdtasdt0(xk, xk) = v0 & sdtasdt0(xk, sz10) = v1 & sdtasdt0(sz10, xk) = v3)
% 34.82/10.43 |
% 34.82/10.43 | Instantiating formula (45) with xk, sz10, xk and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz10) = 0, yields:
% 34.82/10.43 | (151) xk = sz10 | xk = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, xk) = v3 & sdtasdt0(xk, xk) = v1 & sdtasdt0(xk, sz10) = v0 & sdtasdt0(sz10, xk) = v2)
% 34.82/10.43 |
% 34.82/10.43 | Instantiating formula (89) with sz10, xk, xk and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz10) = 0, yields:
% 34.82/10.43 | (152) xk = sz10 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, xk) = v2 & sdtpldt0(xk, xk) = v0 & sdtpldt0(xk, sz10) = v1 & sdtpldt0(sz10, xk) = v3)
% 34.82/10.43 |
% 34.82/10.43 | Instantiating formula (89) with xk, sz10, xk and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz10) = 0, yields:
% 34.82/10.43 | (153) xk = sz10 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, xk) = v3 & sdtpldt0(xk, xk) = v1 & sdtpldt0(xk, sz10) = v0 & sdtpldt0(sz10, xk) = v2)
% 34.82/10.43 |
% 34.82/10.43 | Instantiating formula (89) with sz10, xk, sz10 and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz10) = 0, yields:
% 34.82/10.43 | (154) xk = sz10 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz10) = v2 & sdtpldt0(sz10, xk) = v0 & sdtpldt0(sz10, sz10) = v3 & sdtpldt0(sz10, sz10) = v1)
% 34.82/10.43 |
% 34.82/10.43 | Instantiating formula (89) with xk, sz10, sz10 and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz10) = 0, yields:
% 34.82/10.43 | (155) xk = sz10 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz10) = v3 & sdtpldt0(sz10, xk) = v1 & sdtpldt0(sz10, sz10) = v2 & sdtpldt0(sz10, sz10) = v0)
% 34.82/10.43 |
% 34.82/10.43 | Instantiating formula (127) with sz10 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 34.82/10.43 | (156) sdtasdt0(sz10, sz10) = sz10
% 34.82/10.43 |
% 34.82/10.43 | Instantiating formula (45) with sz00, xk, xk and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz00) = 0, yields:
% 34.82/10.43 | (157) xk = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, xk) = v2 & sdtasdt0(xk, xk) = v0 & sdtasdt0(xk, sz00) = v1 & sdtasdt0(sz00, xk) = v3)
% 34.82/10.43 |
% 34.82/10.43 | Instantiating formula (45) with xk, sz00, xk and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz00) = 0, yields:
% 34.82/10.43 | (158) xk = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, xk) = v3 & sdtasdt0(xk, xk) = v1 & sdtasdt0(xk, sz00) = v0 & sdtasdt0(sz00, xk) = v2)
% 34.82/10.43 |
% 34.82/10.43 | Instantiating formula (89) with sz00, xk, xk and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz00) = 0, yields:
% 34.82/10.43 | (159) xk = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, xk) = v2 & sdtpldt0(xk, xk) = v0 & sdtpldt0(xk, sz00) = v1 & sdtpldt0(sz00, xk) = v3)
% 34.82/10.43 |
% 34.82/10.43 | Instantiating formula (89) with xk, sz00, xk and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz00) = 0, yields:
% 34.82/10.43 | (160) xk = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, xk) = v3 & sdtpldt0(xk, xk) = v1 & sdtpldt0(xk, sz00) = v0 & sdtpldt0(sz00, xk) = v2)
% 34.82/10.43 |
% 34.82/10.43 | Instantiating formula (45) with sz00, xk, sz10 and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 34.82/10.43 | (161) xk = sz00 | sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, sz10) = v2 & sdtasdt0(sz10, xk) = v0 & sdtasdt0(sz10, sz00) = v1 & sdtasdt0(sz00, sz10) = v3)
% 34.82/10.43 |
% 34.82/10.43 | Instantiating formula (45) with xk, sz00, sz10 and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 34.82/10.44 | (162) xk = sz00 | sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, sz10) = v3 & sdtasdt0(sz10, xk) = v1 & sdtasdt0(sz10, sz00) = v0 & sdtasdt0(sz00, sz10) = v2)
% 34.82/10.44 |
% 34.82/10.44 | Instantiating formula (89) with sz00, xk, sz10 and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 34.82/10.44 | (163) xk = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz10) = v2 & sdtpldt0(sz10, xk) = v0 & sdtpldt0(sz10, sz00) = v1 & sdtpldt0(sz00, sz10) = v3)
% 34.82/10.44 |
% 34.82/10.44 | Instantiating formula (89) with xk, sz00, sz10 and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 34.82/10.44 | (164) xk = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz10) = v3 & sdtpldt0(sz10, xk) = v1 & sdtpldt0(sz10, sz00) = v0 & sdtpldt0(sz00, sz10) = v2)
% 34.82/10.44 |
% 34.82/10.44 | Instantiating formula (89) with xk, sz10, sz00 and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 34.82/10.44 | (165) xk = sz10 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz00) = v3 & sdtpldt0(sz10, sz00) = v2 & sdtpldt0(sz00, xk) = v1 & sdtpldt0(sz00, sz10) = v0)
% 34.82/10.44 |
% 34.82/10.44 | Instantiating formula (89) with sz00, xk, sz00 and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz00) = 0, yields:
% 34.82/10.44 | (166) xk = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz00) = v2 & sdtpldt0(sz00, xk) = v0 & sdtpldt0(sz00, sz00) = v3 & sdtpldt0(sz00, sz00) = v1)
% 34.82/10.44 |
% 34.82/10.44 | Instantiating formula (89) with xk, sz00, sz00 and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz00) = 0, yields:
% 34.82/10.44 | (167) xk = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz00) = v3 & sdtpldt0(sz00, xk) = v1 & sdtpldt0(sz00, sz00) = v2 & sdtpldt0(sz00, sz00) = v0)
% 34.82/10.44 |
% 34.82/10.44 | Instantiating formula (45) with sz00, sz10, xk and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 34.82/10.44 | (168) xk = sz00 | sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, sz10) = v0 & sdtasdt0(xk, sz00) = v1 & sdtasdt0(sz10, xk) = v2 & sdtasdt0(sz00, xk) = v3)
% 34.82/10.44 |
% 34.82/10.44 | Instantiating formula (45) with sz10, sz00, xk and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 34.82/10.44 | (169) xk = sz00 | sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, sz10) = v1 & sdtasdt0(xk, sz00) = v0 & sdtasdt0(sz10, xk) = v3 & sdtasdt0(sz00, xk) = v2)
% 34.82/10.44 |
% 34.82/10.44 | Instantiating formula (89) with sz10, sz00, xk and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 34.82/10.44 | (170) sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz10) = v1 & sdtpldt0(xk, sz00) = v0 & sdtpldt0(sz10, xk) = v3 & sdtpldt0(sz00, xk) = v2)
% 34.82/10.44 |
% 34.82/10.44 | Instantiating formula (89) with sz10, xk, sz00 and discharging atoms aNaturalNumber0(xk) = 0, aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 34.82/10.44 | (171) xk = sz10 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz00) = v2 & sdtpldt0(sz10, sz00) = v3 & sdtpldt0(sz00, xk) = v0 & sdtpldt0(sz00, sz10) = v1)
% 34.82/10.44 |
% 34.82/10.44 | Instantiating formula (89) with sz00, sz10, sz10 and discharging atoms aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 34.82/10.44 | (172) sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz10) = v2 & sdtpldt0(sz10, sz10) = v0 & sdtpldt0(sz10, sz00) = v1 & sdtpldt0(sz00, sz10) = v3)
% 34.82/10.44 |
% 34.82/10.44 | Instantiating formula (89) with sz10, sz00, sz10 and discharging atoms aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 34.82/10.44 | (173) sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz10) = v3 & sdtpldt0(sz10, sz10) = v1 & sdtpldt0(sz10, sz00) = v0 & sdtpldt0(sz00, sz10) = v2)
% 34.82/10.44 |
% 34.82/10.44 | Instantiating formula (89) with sz00, sz10, sz00 and discharging atoms aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 34.82/10.44 | (174) sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz00) = v2 & sdtpldt0(sz00, sz10) = v0 & sdtpldt0(sz00, sz00) = v3 & sdtpldt0(sz00, sz00) = v1)
% 34.82/10.44 |
% 34.82/10.44 | Instantiating (146) with all_30_0_29 yields:
% 34.82/10.44 | (175) ( ~ (all_30_0_29 = 0) & isPrime0(xk) = all_30_0_29) | ( ~ (all_30_0_29 = 0) & doDivides0(xk, xk) = all_30_0_29)
% 34.82/10.44 |
% 34.82/10.44 | Instantiating (145) with all_44_0_43, all_44_1_44, all_44_2_45, all_44_3_46 yields:
% 34.82/10.44 | (176) (xk = sz10 | xk = sz00 | (all_44_0_43 = 0 & all_44_1_44 = 0 & ~ (all_44_2_45 = xk) & ~ (all_44_2_45 = sz10) & doDivides0(all_44_2_45, xk) = 0 & aNaturalNumber0(all_44_2_45) = 0) | (all_44_3_46 = 0 & isPrime0(xk) = 0)) & (( ~ (all_44_3_46 = 0) & isPrime0(xk) = all_44_3_46) | ( ~ (xk = sz10) & ~ (xk = sz00) & ! [v0] : (v0 = xk | v0 = sz10 | ~ (doDivides0(v0, xk) = 0) | ? [v1] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) & ! [v0] : (v0 = xk | v0 = sz10 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & doDivides0(v0, xk) = v1))))
% 34.82/10.44 |
% 34.82/10.44 | Applying alpha-rule on (176) yields:
% 34.82/10.44 | (177) xk = sz10 | xk = sz00 | (all_44_0_43 = 0 & all_44_1_44 = 0 & ~ (all_44_2_45 = xk) & ~ (all_44_2_45 = sz10) & doDivides0(all_44_2_45, xk) = 0 & aNaturalNumber0(all_44_2_45) = 0) | (all_44_3_46 = 0 & isPrime0(xk) = 0)
% 34.82/10.44 | (178) ( ~ (all_44_3_46 = 0) & isPrime0(xk) = all_44_3_46) | ( ~ (xk = sz10) & ~ (xk = sz00) & ! [v0] : (v0 = xk | v0 = sz10 | ~ (doDivides0(v0, xk) = 0) | ? [v1] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) & ! [v0] : (v0 = xk | v0 = sz10 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & doDivides0(v0, xk) = v1)))
% 34.82/10.44 |
% 34.82/10.44 | Instantiating (143) with all_75_0_76 yields:
% 34.82/10.44 | (179) (all_75_0_76 = 0 & doDivides0(xk, xk) = 0) | ( ~ (all_75_0_76 = 0) & doDivides0(xk, xk) = all_75_0_76)
% 34.82/10.44 |
% 34.82/10.44 | Instantiating (142) with all_80_0_80 yields:
% 34.82/10.44 | (180) ( ~ (all_80_0_80 = 0) & doDivides0(xk, xk) = all_80_0_80) | ( ~ (all_80_0_80 = 0) & aNaturalNumber0(xk) = all_80_0_80)
% 34.82/10.44 |
% 34.82/10.44 +-Applying beta-rule and splitting (175), into two cases.
% 34.82/10.44 |-Branch one:
% 34.82/10.44 | (181) ~ (all_30_0_29 = 0) & isPrime0(xk) = all_30_0_29
% 34.82/10.44 |
% 34.82/10.44 | Applying alpha-rule on (181) yields:
% 34.82/10.44 | (182) ~ (all_30_0_29 = 0)
% 34.82/10.44 | (183) isPrime0(xk) = all_30_0_29
% 34.82/10.44 |
% 34.82/10.44 | Instantiating formula (124) with xk, all_30_0_29, 0 and discharging atoms isPrime0(xk) = all_30_0_29, isPrime0(xk) = 0, yields:
% 34.82/10.44 | (184) all_30_0_29 = 0
% 34.82/10.44 |
% 34.82/10.44 | Equations (184) can reduce 182 to:
% 34.82/10.44 | (185) $false
% 34.82/10.44 |
% 34.82/10.44 |-The branch is then unsatisfiable
% 34.82/10.44 |-Branch two:
% 34.82/10.44 | (186) ~ (all_30_0_29 = 0) & doDivides0(xk, xk) = all_30_0_29
% 34.82/10.44 |
% 34.82/10.44 | Applying alpha-rule on (186) yields:
% 34.82/10.44 | (182) ~ (all_30_0_29 = 0)
% 34.82/10.44 | (188) doDivides0(xk, xk) = all_30_0_29
% 34.82/10.44 |
% 34.82/10.44 +-Applying beta-rule and splitting (157), into two cases.
% 34.82/10.44 |-Branch one:
% 34.82/10.44 | (189) xk = sz00
% 34.82/10.44 |
% 34.82/10.44 | Equations (189) can reduce 104 to:
% 34.82/10.44 | (185) $false
% 34.82/10.44 |
% 34.82/10.44 |-The branch is then unsatisfiable
% 34.82/10.44 |-Branch two:
% 34.82/10.44 | (104) ~ (xk = sz00)
% 34.82/10.44 | (192) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, xk) = v2 & sdtasdt0(xk, xk) = v0 & sdtasdt0(xk, sz00) = v1 & sdtasdt0(sz00, xk) = v3)
% 34.82/10.44 |
% 34.82/10.44 +-Applying beta-rule and splitting (151), into two cases.
% 34.82/10.44 |-Branch one:
% 34.82/10.44 | (189) xk = sz00
% 34.82/10.44 |
% 34.82/10.44 | Equations (189) can reduce 104 to:
% 34.82/10.44 | (185) $false
% 34.82/10.44 |
% 34.82/10.44 |-The branch is then unsatisfiable
% 34.82/10.44 |-Branch two:
% 34.82/10.44 | (104) ~ (xk = sz00)
% 34.82/10.44 | (196) xk = sz10 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, xk) = v3 & sdtasdt0(xk, xk) = v1 & sdtasdt0(xk, sz10) = v0 & sdtasdt0(sz10, xk) = v2)
% 34.82/10.44 |
% 34.82/10.44 +-Applying beta-rule and splitting (150), into two cases.
% 34.82/10.44 |-Branch one:
% 34.82/10.44 | (189) xk = sz00
% 34.82/10.44 |
% 34.82/10.44 | Equations (189) can reduce 104 to:
% 34.82/10.44 | (185) $false
% 34.82/10.44 |
% 34.82/10.44 |-The branch is then unsatisfiable
% 34.82/10.44 |-Branch two:
% 34.82/10.44 | (104) ~ (xk = sz00)
% 34.82/10.45 | (200) xk = sz10 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, xk) = v2 & sdtasdt0(xk, xk) = v0 & sdtasdt0(xk, sz10) = v1 & sdtasdt0(sz10, xk) = v3)
% 34.82/10.45 |
% 34.82/10.45 +-Applying beta-rule and splitting (154), into two cases.
% 34.82/10.45 |-Branch one:
% 34.82/10.45 | (201) xk = sz10
% 34.82/10.45 |
% 34.82/10.45 | Equations (201) can reduce 113 to:
% 34.82/10.45 | (185) $false
% 34.82/10.45 |
% 34.82/10.45 |-The branch is then unsatisfiable
% 34.82/10.45 |-Branch two:
% 34.82/10.45 | (113) ~ (xk = sz10)
% 34.82/10.45 | (204) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz10) = v2 & sdtpldt0(sz10, xk) = v0 & sdtpldt0(sz10, sz10) = v3 & sdtpldt0(sz10, sz10) = v1)
% 34.82/10.45 |
% 34.82/10.45 | Instantiating (204) with all_107_0_186, all_107_1_187, all_107_2_188, all_107_3_189 yields:
% 34.82/10.45 | (205) ~ (all_107_0_186 = all_107_1_187) & ~ (all_107_2_188 = all_107_3_189) & sdtpldt0(xk, sz10) = all_107_1_187 & sdtpldt0(sz10, xk) = all_107_3_189 & sdtpldt0(sz10, sz10) = all_107_0_186 & sdtpldt0(sz10, sz10) = all_107_2_188
% 34.82/10.45 |
% 34.82/10.45 | Applying alpha-rule on (205) yields:
% 34.82/10.45 | (206) ~ (all_107_0_186 = all_107_1_187)
% 34.82/10.45 | (207) sdtpldt0(xk, sz10) = all_107_1_187
% 34.82/10.45 | (208) sdtpldt0(sz10, sz10) = all_107_0_186
% 34.82/10.45 | (209) ~ (all_107_2_188 = all_107_3_189)
% 34.82/10.45 | (210) sdtpldt0(sz10, xk) = all_107_3_189
% 34.82/10.45 | (211) sdtpldt0(sz10, sz10) = all_107_2_188
% 34.82/10.45 |
% 34.82/10.45 +-Applying beta-rule and splitting (155), into two cases.
% 34.82/10.45 |-Branch one:
% 34.82/10.45 | (201) xk = sz10
% 34.82/10.45 |
% 34.82/10.45 | Equations (201) can reduce 113 to:
% 34.82/10.45 | (185) $false
% 34.82/10.45 |
% 34.82/10.45 |-The branch is then unsatisfiable
% 34.82/10.45 |-Branch two:
% 34.82/10.45 | (113) ~ (xk = sz10)
% 34.82/10.45 | (215) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz10) = v3 & sdtpldt0(sz10, xk) = v1 & sdtpldt0(sz10, sz10) = v2 & sdtpldt0(sz10, sz10) = v0)
% 34.82/10.45 |
% 34.82/10.45 | Instantiating (215) with all_112_0_190, all_112_1_191, all_112_2_192, all_112_3_193 yields:
% 34.82/10.45 | (216) ~ (all_112_0_190 = all_112_1_191) & ~ (all_112_2_192 = all_112_3_193) & sdtpldt0(xk, sz10) = all_112_0_190 & sdtpldt0(sz10, xk) = all_112_2_192 & sdtpldt0(sz10, sz10) = all_112_1_191 & sdtpldt0(sz10, sz10) = all_112_3_193
% 34.82/10.45 |
% 34.82/10.45 | Applying alpha-rule on (216) yields:
% 34.82/10.45 | (217) ~ (all_112_0_190 = all_112_1_191)
% 34.82/10.45 | (218) sdtpldt0(sz10, sz10) = all_112_3_193
% 34.82/10.45 | (219) sdtpldt0(sz10, sz10) = all_112_1_191
% 34.82/10.45 | (220) sdtpldt0(xk, sz10) = all_112_0_190
% 34.82/10.45 | (221) sdtpldt0(sz10, xk) = all_112_2_192
% 34.82/10.45 | (222) ~ (all_112_2_192 = all_112_3_193)
% 34.82/10.45 |
% 34.82/10.45 +-Applying beta-rule and splitting (153), into two cases.
% 34.82/10.45 |-Branch one:
% 34.82/10.45 | (201) xk = sz10
% 34.82/10.45 |
% 34.82/10.45 | Equations (201) can reduce 113 to:
% 34.82/10.45 | (185) $false
% 34.82/10.45 |
% 34.82/10.45 |-The branch is then unsatisfiable
% 34.82/10.45 |-Branch two:
% 34.82/10.45 | (113) ~ (xk = sz10)
% 34.82/10.45 | (226) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, xk) = v3 & sdtpldt0(xk, xk) = v1 & sdtpldt0(xk, sz10) = v0 & sdtpldt0(sz10, xk) = v2)
% 34.82/10.45 |
% 34.82/10.45 | Instantiating (226) with all_117_0_194, all_117_1_195, all_117_2_196, all_117_3_197 yields:
% 34.82/10.45 | (227) ~ (all_117_0_194 = all_117_1_195) & ~ (all_117_2_196 = all_117_3_197) & sdtpldt0(xk, xk) = all_117_0_194 & sdtpldt0(xk, xk) = all_117_2_196 & sdtpldt0(xk, sz10) = all_117_3_197 & sdtpldt0(sz10, xk) = all_117_1_195
% 34.82/10.45 |
% 34.82/10.45 | Applying alpha-rule on (227) yields:
% 34.82/10.45 | (228) ~ (all_117_0_194 = all_117_1_195)
% 34.82/10.45 | (229) ~ (all_117_2_196 = all_117_3_197)
% 34.82/10.45 | (230) sdtpldt0(xk, sz10) = all_117_3_197
% 34.82/10.45 | (231) sdtpldt0(sz10, xk) = all_117_1_195
% 34.82/10.45 | (232) sdtpldt0(xk, xk) = all_117_0_194
% 34.82/10.45 | (233) sdtpldt0(xk, xk) = all_117_2_196
% 34.82/10.45 |
% 34.82/10.45 +-Applying beta-rule and splitting (160), into two cases.
% 34.82/10.45 |-Branch one:
% 34.82/10.45 | (189) xk = sz00
% 34.82/10.45 |
% 34.82/10.45 | Equations (189) can reduce 104 to:
% 34.82/10.45 | (185) $false
% 34.82/10.45 |
% 34.82/10.45 |-The branch is then unsatisfiable
% 34.82/10.45 |-Branch two:
% 34.82/10.45 | (104) ~ (xk = sz00)
% 34.82/10.45 | (237) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, xk) = v3 & sdtpldt0(xk, xk) = v1 & sdtpldt0(xk, sz00) = v0 & sdtpldt0(sz00, xk) = v2)
% 34.82/10.45 |
% 34.82/10.45 +-Applying beta-rule and splitting (167), into two cases.
% 34.82/10.45 |-Branch one:
% 34.82/10.45 | (189) xk = sz00
% 34.82/10.45 |
% 34.82/10.45 | Equations (189) can reduce 104 to:
% 34.82/10.45 | (185) $false
% 34.82/10.45 |
% 34.82/10.45 |-The branch is then unsatisfiable
% 34.82/10.45 |-Branch two:
% 34.82/10.45 | (104) ~ (xk = sz00)
% 34.82/10.45 | (241) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz00) = v3 & sdtpldt0(sz00, xk) = v1 & sdtpldt0(sz00, sz00) = v2 & sdtpldt0(sz00, sz00) = v0)
% 34.82/10.45 |
% 34.82/10.45 +-Applying beta-rule and splitting (166), into two cases.
% 34.82/10.45 |-Branch one:
% 34.82/10.45 | (189) xk = sz00
% 34.82/10.45 |
% 34.82/10.45 | Equations (189) can reduce 104 to:
% 34.82/10.45 | (185) $false
% 34.82/10.45 |
% 34.82/10.45 |-The branch is then unsatisfiable
% 34.82/10.45 |-Branch two:
% 34.82/10.45 | (104) ~ (xk = sz00)
% 34.82/10.45 | (245) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz00) = v2 & sdtpldt0(sz00, xk) = v0 & sdtpldt0(sz00, sz00) = v3 & sdtpldt0(sz00, sz00) = v1)
% 34.82/10.45 |
% 34.82/10.45 +-Applying beta-rule and splitting (159), into two cases.
% 34.82/10.45 |-Branch one:
% 34.82/10.45 | (189) xk = sz00
% 34.82/10.45 |
% 34.82/10.45 | Equations (189) can reduce 104 to:
% 34.82/10.45 | (185) $false
% 34.82/10.45 |
% 34.82/10.45 |-The branch is then unsatisfiable
% 34.82/10.45 |-Branch two:
% 34.82/10.45 | (104) ~ (xk = sz00)
% 34.82/10.45 | (249) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, xk) = v2 & sdtpldt0(xk, xk) = v0 & sdtpldt0(xk, sz00) = v1 & sdtpldt0(sz00, xk) = v3)
% 34.82/10.45 |
% 34.82/10.45 +-Applying beta-rule and splitting (171), into two cases.
% 34.82/10.45 |-Branch one:
% 34.82/10.45 | (201) xk = sz10
% 34.82/10.45 |
% 34.82/10.45 | Equations (201) can reduce 113 to:
% 34.82/10.45 | (185) $false
% 34.82/10.45 |
% 34.82/10.45 |-The branch is then unsatisfiable
% 34.82/10.45 |-Branch two:
% 34.82/10.45 | (113) ~ (xk = sz10)
% 34.82/10.45 | (253) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz00) = v2 & sdtpldt0(sz10, sz00) = v3 & sdtpldt0(sz00, xk) = v0 & sdtpldt0(sz00, sz10) = v1)
% 34.82/10.45 |
% 34.82/10.45 +-Applying beta-rule and splitting (172), into two cases.
% 34.82/10.45 |-Branch one:
% 34.82/10.45 | (254) sz10 = sz00
% 34.82/10.45 |
% 34.82/10.45 | Equations (254) can reduce 78 to:
% 34.82/10.45 | (185) $false
% 34.82/10.45 |
% 34.82/10.45 |-The branch is then unsatisfiable
% 34.82/10.45 |-Branch two:
% 34.82/10.45 | (78) ~ (sz10 = sz00)
% 34.82/10.45 | (257) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz10) = v2 & sdtpldt0(sz10, sz10) = v0 & sdtpldt0(sz10, sz00) = v1 & sdtpldt0(sz00, sz10) = v3)
% 34.82/10.45 |
% 34.82/10.45 +-Applying beta-rule and splitting (165), into two cases.
% 34.82/10.45 |-Branch one:
% 34.82/10.45 | (201) xk = sz10
% 34.82/10.45 |
% 34.82/10.45 | Equations (201) can reduce 113 to:
% 34.82/10.45 | (185) $false
% 34.82/10.45 |
% 34.82/10.45 |-The branch is then unsatisfiable
% 34.82/10.45 |-Branch two:
% 34.82/10.45 | (113) ~ (xk = sz10)
% 34.82/10.45 | (261) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz00) = v3 & sdtpldt0(sz10, sz00) = v2 & sdtpldt0(sz00, xk) = v1 & sdtpldt0(sz00, sz10) = v0)
% 34.82/10.45 |
% 34.82/10.45 +-Applying beta-rule and splitting (164), into two cases.
% 34.82/10.45 |-Branch one:
% 34.82/10.45 | (189) xk = sz00
% 34.82/10.45 |
% 34.82/10.45 | Equations (189) can reduce 104 to:
% 34.82/10.45 | (185) $false
% 34.82/10.45 |
% 34.82/10.45 |-The branch is then unsatisfiable
% 34.82/10.45 |-Branch two:
% 34.82/10.45 | (104) ~ (xk = sz00)
% 34.82/10.45 | (265) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz10) = v3 & sdtpldt0(sz10, xk) = v1 & sdtpldt0(sz10, sz00) = v0 & sdtpldt0(sz00, sz10) = v2)
% 34.82/10.45 |
% 34.82/10.45 | Instantiating (265) with all_165_0_226, all_165_1_227, all_165_2_228, all_165_3_229 yields:
% 34.82/10.45 | (266) ~ (all_165_0_226 = all_165_1_227) & ~ (all_165_2_228 = all_165_3_229) & sdtpldt0(xk, sz10) = all_165_0_226 & sdtpldt0(sz10, xk) = all_165_2_228 & sdtpldt0(sz10, sz00) = all_165_3_229 & sdtpldt0(sz00, sz10) = all_165_1_227
% 34.82/10.45 |
% 34.82/10.45 | Applying alpha-rule on (266) yields:
% 34.82/10.45 | (267) sdtpldt0(sz10, xk) = all_165_2_228
% 34.82/10.45 | (268) sdtpldt0(xk, sz10) = all_165_0_226
% 34.82/10.45 | (269) sdtpldt0(sz10, sz00) = all_165_3_229
% 34.82/10.45 | (270) ~ (all_165_2_228 = all_165_3_229)
% 34.82/10.45 | (271) ~ (all_165_0_226 = all_165_1_227)
% 34.82/10.45 | (272) sdtpldt0(sz00, sz10) = all_165_1_227
% 34.82/10.45 |
% 34.82/10.45 +-Applying beta-rule and splitting (170), into two cases.
% 34.82/10.45 |-Branch one:
% 34.82/10.45 | (254) sz10 = sz00
% 34.82/10.45 |
% 34.82/10.45 | Equations (254) can reduce 78 to:
% 34.82/10.45 | (185) $false
% 34.82/10.45 |
% 34.82/10.45 |-The branch is then unsatisfiable
% 34.82/10.45 |-Branch two:
% 34.82/10.45 | (78) ~ (sz10 = sz00)
% 34.82/10.45 | (276) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz10) = v1 & sdtpldt0(xk, sz00) = v0 & sdtpldt0(sz10, xk) = v3 & sdtpldt0(sz00, xk) = v2)
% 34.82/10.45 |
% 34.82/10.45 | Instantiating (276) with all_171_0_230, all_171_1_231, all_171_2_232, all_171_3_233 yields:
% 34.82/10.45 | (277) ~ (all_171_0_230 = all_171_1_231) & ~ (all_171_2_232 = all_171_3_233) & sdtpldt0(xk, sz10) = all_171_2_232 & sdtpldt0(xk, sz00) = all_171_3_233 & sdtpldt0(sz10, xk) = all_171_0_230 & sdtpldt0(sz00, xk) = all_171_1_231
% 34.82/10.45 |
% 34.82/10.45 | Applying alpha-rule on (277) yields:
% 34.82/10.45 | (278) sdtpldt0(xk, sz10) = all_171_2_232
% 34.82/10.45 | (279) sdtpldt0(xk, sz00) = all_171_3_233
% 34.82/10.45 | (280) ~ (all_171_2_232 = all_171_3_233)
% 34.82/10.45 | (281) ~ (all_171_0_230 = all_171_1_231)
% 34.82/10.45 | (282) sdtpldt0(sz00, xk) = all_171_1_231
% 34.82/10.45 | (283) sdtpldt0(sz10, xk) = all_171_0_230
% 34.82/10.45 |
% 34.82/10.45 +-Applying beta-rule and splitting (179), into two cases.
% 34.82/10.45 |-Branch one:
% 34.82/10.45 | (284) all_75_0_76 = 0 & doDivides0(xk, xk) = 0
% 34.82/10.45 |
% 34.82/10.45 | Applying alpha-rule on (284) yields:
% 34.82/10.46 | (285) all_75_0_76 = 0
% 34.82/10.46 | (286) doDivides0(xk, xk) = 0
% 34.82/10.46 |
% 34.82/10.46 | Instantiating formula (100) with xk, xk, 0, all_30_0_29 and discharging atoms doDivides0(xk, xk) = all_30_0_29, doDivides0(xk, xk) = 0, yields:
% 34.82/10.46 | (184) all_30_0_29 = 0
% 34.82/10.46 |
% 34.82/10.46 | Equations (184) can reduce 182 to:
% 34.82/10.46 | (185) $false
% 34.82/10.46 |
% 34.82/10.46 |-The branch is then unsatisfiable
% 34.82/10.46 |-Branch two:
% 34.82/10.46 | (289) ~ (all_75_0_76 = 0) & doDivides0(xk, xk) = all_75_0_76
% 34.82/10.46 |
% 34.82/10.46 | Applying alpha-rule on (289) yields:
% 34.82/10.46 | (290) ~ (all_75_0_76 = 0)
% 34.82/10.46 | (291) doDivides0(xk, xk) = all_75_0_76
% 34.82/10.46 |
% 34.82/10.46 +-Applying beta-rule and splitting (200), into two cases.
% 34.82/10.46 |-Branch one:
% 34.82/10.46 | (201) xk = sz10
% 34.82/10.46 |
% 34.82/10.46 | Equations (201) can reduce 113 to:
% 34.82/10.46 | (185) $false
% 34.82/10.46 |
% 34.82/10.46 |-The branch is then unsatisfiable
% 34.82/10.46 |-Branch two:
% 34.82/10.46 | (113) ~ (xk = sz10)
% 34.82/10.46 | (295) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, xk) = v2 & sdtasdt0(xk, xk) = v0 & sdtasdt0(xk, sz10) = v1 & sdtasdt0(sz10, xk) = v3)
% 34.82/10.46 |
% 34.82/10.46 | Instantiating (295) with all_181_0_316, all_181_1_317, all_181_2_318, all_181_3_319 yields:
% 34.82/10.46 | (296) ~ (all_181_0_316 = all_181_1_317) & ~ (all_181_2_318 = all_181_3_319) & sdtasdt0(xk, xk) = all_181_1_317 & sdtasdt0(xk, xk) = all_181_3_319 & sdtasdt0(xk, sz10) = all_181_2_318 & sdtasdt0(sz10, xk) = all_181_0_316
% 34.82/10.46 |
% 34.82/10.46 | Applying alpha-rule on (296) yields:
% 34.82/10.46 | (297) sdtasdt0(xk, xk) = all_181_3_319
% 34.82/10.46 | (298) ~ (all_181_0_316 = all_181_1_317)
% 34.82/10.46 | (299) ~ (all_181_2_318 = all_181_3_319)
% 34.82/10.46 | (300) sdtasdt0(xk, xk) = all_181_1_317
% 34.82/10.46 | (301) sdtasdt0(sz10, xk) = all_181_0_316
% 34.82/10.46 | (302) sdtasdt0(xk, sz10) = all_181_2_318
% 34.82/10.46 |
% 34.82/10.46 +-Applying beta-rule and splitting (163), into two cases.
% 34.82/10.46 |-Branch one:
% 34.82/10.46 | (189) xk = sz00
% 34.82/10.46 |
% 34.82/10.46 | Equations (189) can reduce 104 to:
% 34.82/10.46 | (185) $false
% 34.82/10.46 |
% 34.82/10.46 |-The branch is then unsatisfiable
% 34.82/10.46 |-Branch two:
% 34.82/10.46 | (104) ~ (xk = sz00)
% 34.82/10.46 | (306) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz10) = v2 & sdtpldt0(sz10, xk) = v0 & sdtpldt0(sz10, sz00) = v1 & sdtpldt0(sz00, sz10) = v3)
% 34.82/10.46 |
% 34.82/10.46 | Instantiating (306) with all_191_0_320, all_191_1_321, all_191_2_322, all_191_3_323 yields:
% 34.82/10.46 | (307) ~ (all_191_0_320 = all_191_1_321) & ~ (all_191_2_322 = all_191_3_323) & sdtpldt0(xk, sz10) = all_191_1_321 & sdtpldt0(sz10, xk) = all_191_3_323 & sdtpldt0(sz10, sz00) = all_191_2_322 & sdtpldt0(sz00, sz10) = all_191_0_320
% 34.82/10.46 |
% 34.82/10.46 | Applying alpha-rule on (307) yields:
% 34.82/10.46 | (308) ~ (all_191_2_322 = all_191_3_323)
% 34.82/10.46 | (309) sdtpldt0(sz00, sz10) = all_191_0_320
% 34.82/10.46 | (310) sdtpldt0(sz10, sz00) = all_191_2_322
% 34.82/10.46 | (311) ~ (all_191_0_320 = all_191_1_321)
% 34.82/10.46 | (312) sdtpldt0(sz10, xk) = all_191_3_323
% 34.82/10.46 | (313) sdtpldt0(xk, sz10) = all_191_1_321
% 34.82/10.46 |
% 34.82/10.46 +-Applying beta-rule and splitting (144), into two cases.
% 34.82/10.46 |-Branch one:
% 34.82/10.46 | (189) xk = sz00
% 34.82/10.46 |
% 34.82/10.46 | Equations (189) can reduce 104 to:
% 34.82/10.46 | (185) $false
% 34.82/10.46 |
% 34.82/10.46 |-The branch is then unsatisfiable
% 34.82/10.46 |-Branch two:
% 34.82/10.46 | (104) ~ (xk = sz00)
% 34.82/10.46 | (317) xk = sz10 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & isPrime0(v0) = 0 & doDivides0(v0, xk) = 0 & aNaturalNumber0(v0) = 0) | ( ~ (v0 = 0) & iLess0(xk, xk) = v0))
% 34.82/10.46 |
% 34.82/10.46 +-Applying beta-rule and splitting (169), into two cases.
% 34.82/10.46 |-Branch one:
% 34.82/10.46 | (189) xk = sz00
% 34.82/10.46 |
% 34.82/10.46 | Equations (189) can reduce 104 to:
% 34.82/10.46 | (185) $false
% 34.82/10.46 |
% 34.82/10.46 |-The branch is then unsatisfiable
% 34.82/10.46 |-Branch two:
% 34.82/10.46 | (104) ~ (xk = sz00)
% 34.82/10.46 | (321) sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, sz10) = v1 & sdtasdt0(xk, sz00) = v0 & sdtasdt0(sz10, xk) = v3 & sdtasdt0(sz00, xk) = v2)
% 34.82/10.46 |
% 34.82/10.46 +-Applying beta-rule and splitting (168), into two cases.
% 34.82/10.46 |-Branch one:
% 34.82/10.46 | (189) xk = sz00
% 34.82/10.46 |
% 34.82/10.46 | Equations (189) can reduce 104 to:
% 34.82/10.46 | (185) $false
% 34.82/10.46 |
% 34.82/10.46 |-The branch is then unsatisfiable
% 34.82/10.46 |-Branch two:
% 34.82/10.46 | (104) ~ (xk = sz00)
% 34.82/10.46 | (325) sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, sz10) = v0 & sdtasdt0(xk, sz00) = v1 & sdtasdt0(sz10, xk) = v2 & sdtasdt0(sz00, xk) = v3)
% 34.82/10.46 |
% 34.82/10.46 +-Applying beta-rule and splitting (180), into two cases.
% 34.82/10.46 |-Branch one:
% 34.82/10.46 | (326) ~ (all_80_0_80 = 0) & doDivides0(xk, xk) = all_80_0_80
% 34.82/10.46 |
% 34.82/10.46 | Applying alpha-rule on (326) yields:
% 34.82/10.46 | (327) ~ (all_80_0_80 = 0)
% 34.82/10.46 | (328) doDivides0(xk, xk) = all_80_0_80
% 34.82/10.46 |
% 34.82/10.46 +-Applying beta-rule and splitting (178), into two cases.
% 34.82/10.46 |-Branch one:
% 34.82/10.46 | (329) ~ (all_44_3_46 = 0) & isPrime0(xk) = all_44_3_46
% 34.82/10.46 |
% 34.82/10.46 | Applying alpha-rule on (329) yields:
% 34.82/10.46 | (330) ~ (all_44_3_46 = 0)
% 34.82/10.46 | (331) isPrime0(xk) = all_44_3_46
% 34.82/10.46 |
% 34.82/10.46 | Instantiating formula (124) with xk, all_44_3_46, 0 and discharging atoms isPrime0(xk) = all_44_3_46, isPrime0(xk) = 0, yields:
% 34.82/10.46 | (332) all_44_3_46 = 0
% 34.82/10.46 |
% 34.82/10.46 | Equations (332) can reduce 330 to:
% 34.82/10.46 | (185) $false
% 34.82/10.46 |
% 34.82/10.46 |-The branch is then unsatisfiable
% 34.82/10.46 |-Branch two:
% 34.82/10.46 | (334) ~ (xk = sz10) & ~ (xk = sz00) & ! [v0] : (v0 = xk | v0 = sz10 | ~ (doDivides0(v0, xk) = 0) | ? [v1] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) & ! [v0] : (v0 = xk | v0 = sz10 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & doDivides0(v0, xk) = v1))
% 34.82/10.46 |
% 34.82/10.46 | Applying alpha-rule on (334) yields:
% 34.82/10.46 | (113) ~ (xk = sz10)
% 34.82/10.46 | (104) ~ (xk = sz00)
% 34.82/10.46 | (337) ! [v0] : (v0 = xk | v0 = sz10 | ~ (doDivides0(v0, xk) = 0) | ? [v1] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1))
% 34.82/10.46 | (338) ! [v0] : (v0 = xk | v0 = sz10 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & doDivides0(v0, xk) = v1))
% 34.82/10.46 |
% 34.82/10.46 | Instantiating formula (338) with sz00 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 34.82/10.46 | (339) xk = sz00 | sz10 = sz00 | ? [v0] : ( ~ (v0 = 0) & doDivides0(sz00, xk) = v0)
% 34.82/10.46 |
% 34.82/10.46 +-Applying beta-rule and splitting (317), into two cases.
% 34.82/10.46 |-Branch one:
% 34.82/10.46 | (201) xk = sz10
% 34.82/10.46 |
% 34.82/10.46 | Equations (201) can reduce 113 to:
% 34.82/10.46 | (185) $false
% 34.82/10.46 |
% 34.82/10.46 |-The branch is then unsatisfiable
% 34.82/10.46 |-Branch two:
% 34.82/10.46 | (113) ~ (xk = sz10)
% 34.82/10.46 | (343) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & isPrime0(v0) = 0 & doDivides0(v0, xk) = 0 & aNaturalNumber0(v0) = 0) | ( ~ (v0 = 0) & iLess0(xk, xk) = v0))
% 34.82/10.46 |
% 34.82/10.46 +-Applying beta-rule and splitting (325), into two cases.
% 34.82/10.46 |-Branch one:
% 34.82/10.46 | (254) sz10 = sz00
% 34.82/10.46 |
% 34.82/10.46 | Equations (254) can reduce 78 to:
% 34.82/10.46 | (185) $false
% 34.82/10.46 |
% 34.82/10.46 |-The branch is then unsatisfiable
% 34.82/10.46 |-Branch two:
% 34.82/10.46 | (78) ~ (sz10 = sz00)
% 34.82/10.46 | (347) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, sz10) = v0 & sdtasdt0(xk, sz00) = v1 & sdtasdt0(sz10, xk) = v2 & sdtasdt0(sz00, xk) = v3)
% 34.82/10.46 |
% 34.82/10.46 | Instantiating (347) with all_220_0_365, all_220_1_366, all_220_2_367, all_220_3_368 yields:
% 34.82/10.46 | (348) ~ (all_220_0_365 = all_220_1_366) & ~ (all_220_2_367 = all_220_3_368) & sdtasdt0(xk, sz10) = all_220_3_368 & sdtasdt0(xk, sz00) = all_220_2_367 & sdtasdt0(sz10, xk) = all_220_1_366 & sdtasdt0(sz00, xk) = all_220_0_365
% 34.82/10.46 |
% 34.82/10.46 | Applying alpha-rule on (348) yields:
% 34.82/10.46 | (349) sdtasdt0(xk, sz10) = all_220_3_368
% 34.82/10.46 | (350) sdtasdt0(sz00, xk) = all_220_0_365
% 34.82/10.46 | (351) sdtasdt0(sz10, xk) = all_220_1_366
% 34.82/10.46 | (352) sdtasdt0(xk, sz00) = all_220_2_367
% 34.82/10.46 | (353) ~ (all_220_0_365 = all_220_1_366)
% 34.82/10.46 | (354) ~ (all_220_2_367 = all_220_3_368)
% 34.82/10.46 |
% 34.82/10.46 +-Applying beta-rule and splitting (339), into two cases.
% 34.82/10.46 |-Branch one:
% 34.82/10.46 | (189) xk = sz00
% 34.82/10.46 |
% 34.82/10.46 | Equations (189) can reduce 104 to:
% 34.82/10.46 | (185) $false
% 34.82/10.46 |
% 34.82/10.46 |-The branch is then unsatisfiable
% 34.82/10.46 |-Branch two:
% 34.82/10.46 | (104) ~ (xk = sz00)
% 34.82/10.46 | (358) sz10 = sz00 | ? [v0] : ( ~ (v0 = 0) & doDivides0(sz00, xk) = v0)
% 34.82/10.46 |
% 34.82/10.46 +-Applying beta-rule and splitting (158), into two cases.
% 34.82/10.46 |-Branch one:
% 34.82/10.46 | (189) xk = sz00
% 34.82/10.46 |
% 34.82/10.46 | Equations (189) can reduce 104 to:
% 34.82/10.46 | (185) $false
% 34.82/10.46 |
% 34.82/10.46 |-The branch is then unsatisfiable
% 34.82/10.46 |-Branch two:
% 34.82/10.46 | (104) ~ (xk = sz00)
% 34.82/10.46 | (362) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, xk) = v3 & sdtasdt0(xk, xk) = v1 & sdtasdt0(xk, sz00) = v0 & sdtasdt0(sz00, xk) = v2)
% 34.82/10.46 |
% 34.82/10.46 +-Applying beta-rule and splitting (358), into two cases.
% 34.82/10.46 |-Branch one:
% 34.82/10.46 | (254) sz10 = sz00
% 34.82/10.46 |
% 34.82/10.46 | Equations (254) can reduce 78 to:
% 34.82/10.46 | (185) $false
% 34.82/10.46 |
% 34.82/10.46 |-The branch is then unsatisfiable
% 34.82/10.46 |-Branch two:
% 34.82/10.46 | (78) ~ (sz10 = sz00)
% 34.82/10.46 | (366) ? [v0] : ( ~ (v0 = 0) & doDivides0(sz00, xk) = v0)
% 34.82/10.46 |
% 34.82/10.46 +-Applying beta-rule and splitting (174), into two cases.
% 34.82/10.46 |-Branch one:
% 34.82/10.46 | (254) sz10 = sz00
% 34.82/10.46 |
% 34.82/10.47 | Equations (254) can reduce 78 to:
% 34.82/10.47 | (185) $false
% 34.82/10.47 |
% 34.82/10.47 |-The branch is then unsatisfiable
% 34.82/10.47 |-Branch two:
% 34.82/10.47 | (78) ~ (sz10 = sz00)
% 35.30/10.47 | (370) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz00) = v2 & sdtpldt0(sz00, sz10) = v0 & sdtpldt0(sz00, sz00) = v3 & sdtpldt0(sz00, sz00) = v1)
% 35.30/10.47 |
% 35.30/10.47 +-Applying beta-rule and splitting (161), into two cases.
% 35.30/10.47 |-Branch one:
% 35.30/10.47 | (189) xk = sz00
% 35.30/10.47 |
% 35.30/10.47 | Equations (189) can reduce 104 to:
% 35.30/10.47 | (185) $false
% 35.30/10.47 |
% 35.30/10.47 |-The branch is then unsatisfiable
% 35.30/10.47 |-Branch two:
% 35.30/10.47 | (104) ~ (xk = sz00)
% 35.30/10.47 | (374) sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, sz10) = v2 & sdtasdt0(sz10, xk) = v0 & sdtasdt0(sz10, sz00) = v1 & sdtasdt0(sz00, sz10) = v3)
% 35.30/10.47 |
% 35.30/10.47 +-Applying beta-rule and splitting (162), into two cases.
% 35.30/10.47 |-Branch one:
% 35.30/10.47 | (189) xk = sz00
% 35.30/10.47 |
% 35.30/10.47 | Equations (189) can reduce 104 to:
% 35.30/10.47 | (185) $false
% 35.30/10.47 |
% 35.30/10.47 |-The branch is then unsatisfiable
% 35.30/10.47 |-Branch two:
% 35.30/10.47 | (104) ~ (xk = sz00)
% 35.30/10.47 | (378) sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, sz10) = v3 & sdtasdt0(sz10, xk) = v1 & sdtasdt0(sz10, sz00) = v0 & sdtasdt0(sz00, sz10) = v2)
% 35.30/10.47 |
% 35.30/10.47 +-Applying beta-rule and splitting (152), into two cases.
% 35.30/10.47 |-Branch one:
% 35.30/10.47 | (201) xk = sz10
% 35.30/10.47 |
% 35.30/10.47 | Equations (201) can reduce 113 to:
% 35.30/10.47 | (185) $false
% 35.30/10.47 |
% 35.30/10.47 |-The branch is then unsatisfiable
% 35.30/10.47 |-Branch two:
% 35.30/10.47 | (113) ~ (xk = sz10)
% 35.30/10.47 | (382) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, xk) = v2 & sdtpldt0(xk, xk) = v0 & sdtpldt0(xk, sz10) = v1 & sdtpldt0(sz10, xk) = v3)
% 35.30/10.47 |
% 35.30/10.47 | Instantiating (382) with all_254_0_378, all_254_1_379, all_254_2_380, all_254_3_381 yields:
% 35.30/10.47 | (383) ~ (all_254_0_378 = all_254_1_379) & ~ (all_254_2_380 = all_254_3_381) & sdtpldt0(xk, xk) = all_254_1_379 & sdtpldt0(xk, xk) = all_254_3_381 & sdtpldt0(xk, sz10) = all_254_2_380 & sdtpldt0(sz10, xk) = all_254_0_378
% 35.30/10.47 |
% 35.30/10.47 | Applying alpha-rule on (383) yields:
% 35.30/10.47 | (384) ~ (all_254_2_380 = all_254_3_381)
% 35.30/10.47 | (385) sdtpldt0(sz10, xk) = all_254_0_378
% 35.30/10.47 | (386) sdtpldt0(xk, xk) = all_254_1_379
% 35.30/10.47 | (387) sdtpldt0(xk, sz10) = all_254_2_380
% 35.30/10.47 | (388) ~ (all_254_0_378 = all_254_1_379)
% 35.30/10.47 | (389) sdtpldt0(xk, xk) = all_254_3_381
% 35.30/10.47 |
% 35.30/10.47 +-Applying beta-rule and splitting (196), into two cases.
% 35.30/10.47 |-Branch one:
% 35.30/10.47 | (201) xk = sz10
% 35.30/10.47 |
% 35.30/10.47 | Equations (201) can reduce 113 to:
% 35.30/10.47 | (185) $false
% 35.30/10.47 |
% 35.30/10.47 |-The branch is then unsatisfiable
% 35.30/10.47 |-Branch two:
% 35.30/10.47 | (113) ~ (xk = sz10)
% 35.30/10.47 | (393) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, xk) = v3 & sdtasdt0(xk, xk) = v1 & sdtasdt0(xk, sz10) = v0 & sdtasdt0(sz10, xk) = v2)
% 35.30/10.47 |
% 35.30/10.47 | Instantiating (393) with all_260_0_382, all_260_1_383, all_260_2_384, all_260_3_385 yields:
% 35.30/10.47 | (394) ~ (all_260_0_382 = all_260_1_383) & ~ (all_260_2_384 = all_260_3_385) & sdtasdt0(xk, xk) = all_260_0_382 & sdtasdt0(xk, xk) = all_260_2_384 & sdtasdt0(xk, sz10) = all_260_3_385 & sdtasdt0(sz10, xk) = all_260_1_383
% 35.30/10.47 |
% 35.30/10.47 | Applying alpha-rule on (394) yields:
% 35.30/10.47 | (395) sdtasdt0(xk, xk) = all_260_0_382
% 35.30/10.47 | (396) ~ (all_260_2_384 = all_260_3_385)
% 35.30/10.47 | (397) ~ (all_260_0_382 = all_260_1_383)
% 35.30/10.47 | (398) sdtasdt0(xk, xk) = all_260_2_384
% 35.30/10.47 | (399) sdtasdt0(xk, sz10) = all_260_3_385
% 35.30/10.47 | (400) sdtasdt0(sz10, xk) = all_260_1_383
% 35.30/10.47 |
% 35.30/10.47 +-Applying beta-rule and splitting (378), into two cases.
% 35.30/10.47 |-Branch one:
% 35.30/10.47 | (254) sz10 = sz00
% 35.30/10.47 |
% 35.30/10.47 | Equations (254) can reduce 78 to:
% 35.30/10.47 | (185) $false
% 35.30/10.47 |
% 35.30/10.47 |-The branch is then unsatisfiable
% 35.30/10.47 |-Branch two:
% 35.30/10.47 | (78) ~ (sz10 = sz00)
% 35.30/10.47 | (404) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, sz10) = v3 & sdtasdt0(sz10, xk) = v1 & sdtasdt0(sz10, sz00) = v0 & sdtasdt0(sz00, sz10) = v2)
% 35.30/10.47 |
% 35.30/10.47 | Instantiating (404) with all_266_0_386, all_266_1_387, all_266_2_388, all_266_3_389 yields:
% 35.30/10.47 | (405) ~ (all_266_0_386 = all_266_1_387) & ~ (all_266_2_388 = all_266_3_389) & sdtasdt0(xk, sz10) = all_266_0_386 & sdtasdt0(sz10, xk) = all_266_2_388 & sdtasdt0(sz10, sz00) = all_266_3_389 & sdtasdt0(sz00, sz10) = all_266_1_387
% 35.30/10.47 |
% 35.30/10.47 | Applying alpha-rule on (405) yields:
% 35.30/10.47 | (406) sdtasdt0(sz10, xk) = all_266_2_388
% 35.30/10.47 | (407) sdtasdt0(sz00, sz10) = all_266_1_387
% 35.30/10.47 | (408) sdtasdt0(sz10, sz00) = all_266_3_389
% 35.30/10.47 | (409) ~ (all_266_2_388 = all_266_3_389)
% 35.30/10.47 | (410) ~ (all_266_0_386 = all_266_1_387)
% 35.30/10.47 | (411) sdtasdt0(xk, sz10) = all_266_0_386
% 35.30/10.47 |
% 35.30/10.47 +-Applying beta-rule and splitting (173), into two cases.
% 35.30/10.47 |-Branch one:
% 35.30/10.47 | (254) sz10 = sz00
% 35.30/10.47 |
% 35.30/10.47 | Equations (254) can reduce 78 to:
% 35.30/10.47 | (185) $false
% 35.30/10.47 |
% 35.30/10.47 |-The branch is then unsatisfiable
% 35.30/10.47 |-Branch two:
% 35.30/10.47 | (78) ~ (sz10 = sz00)
% 35.30/10.47 | (415) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz10) = v3 & sdtpldt0(sz10, sz10) = v1 & sdtpldt0(sz10, sz00) = v0 & sdtpldt0(sz00, sz10) = v2)
% 35.30/10.47 |
% 35.30/10.47 +-Applying beta-rule and splitting (321), into two cases.
% 35.30/10.47 |-Branch one:
% 35.30/10.47 | (254) sz10 = sz00
% 35.30/10.47 |
% 35.30/10.47 | Equations (254) can reduce 78 to:
% 35.30/10.47 | (185) $false
% 35.30/10.47 |
% 35.30/10.47 |-The branch is then unsatisfiable
% 35.30/10.47 |-Branch two:
% 35.30/10.47 | (78) ~ (sz10 = sz00)
% 35.30/10.47 | (419) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, sz10) = v1 & sdtasdt0(xk, sz00) = v0 & sdtasdt0(sz10, xk) = v3 & sdtasdt0(sz00, xk) = v2)
% 35.30/10.47 |
% 35.30/10.47 | Instantiating (419) with all_282_0_394, all_282_1_395, all_282_2_396, all_282_3_397 yields:
% 35.30/10.47 | (420) ~ (all_282_0_394 = all_282_1_395) & ~ (all_282_2_396 = all_282_3_397) & sdtasdt0(xk, sz10) = all_282_2_396 & sdtasdt0(xk, sz00) = all_282_3_397 & sdtasdt0(sz10, xk) = all_282_0_394 & sdtasdt0(sz00, xk) = all_282_1_395
% 35.30/10.47 |
% 35.30/10.47 | Applying alpha-rule on (420) yields:
% 35.30/10.47 | (421) sdtasdt0(xk, sz10) = all_282_2_396
% 35.30/10.47 | (422) ~ (all_282_0_394 = all_282_1_395)
% 35.30/10.47 | (423) ~ (all_282_2_396 = all_282_3_397)
% 35.30/10.47 | (424) sdtasdt0(xk, sz00) = all_282_3_397
% 35.30/10.47 | (425) sdtasdt0(sz10, xk) = all_282_0_394
% 35.30/10.47 | (426) sdtasdt0(sz00, xk) = all_282_1_395
% 35.30/10.47 |
% 35.30/10.47 +-Applying beta-rule and splitting (374), into two cases.
% 35.30/10.47 |-Branch one:
% 35.30/10.47 | (254) sz10 = sz00
% 35.30/10.47 |
% 35.30/10.47 | Equations (254) can reduce 78 to:
% 35.30/10.47 | (185) $false
% 35.30/10.47 |
% 35.30/10.47 |-The branch is then unsatisfiable
% 35.30/10.47 |-Branch two:
% 35.30/10.47 | (78) ~ (sz10 = sz00)
% 35.30/10.47 | (430) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, sz10) = v2 & sdtasdt0(sz10, xk) = v0 & sdtasdt0(sz10, sz00) = v1 & sdtasdt0(sz00, sz10) = v3)
% 35.30/10.47 |
% 35.30/10.47 | Instantiating (430) with all_296_0_398, all_296_1_399, all_296_2_400, all_296_3_401 yields:
% 35.30/10.47 | (431) ~ (all_296_0_398 = all_296_1_399) & ~ (all_296_2_400 = all_296_3_401) & sdtasdt0(xk, sz10) = all_296_1_399 & sdtasdt0(sz10, xk) = all_296_3_401 & sdtasdt0(sz10, sz00) = all_296_2_400 & sdtasdt0(sz00, sz10) = all_296_0_398
% 35.30/10.47 |
% 35.30/10.47 | Applying alpha-rule on (431) yields:
% 35.30/10.47 | (432) ~ (all_296_0_398 = all_296_1_399)
% 35.30/10.47 | (433) sdtasdt0(sz10, xk) = all_296_3_401
% 35.30/10.47 | (434) sdtasdt0(sz00, sz10) = all_296_0_398
% 35.30/10.47 | (435) ~ (all_296_2_400 = all_296_3_401)
% 35.30/10.47 | (436) sdtasdt0(sz10, sz00) = all_296_2_400
% 35.30/10.47 | (437) sdtasdt0(xk, sz10) = all_296_1_399
% 35.30/10.47 |
% 35.30/10.47 | Instantiating formula (100) with xk, xk, all_75_0_76, all_80_0_80 and discharging atoms doDivides0(xk, xk) = all_80_0_80, doDivides0(xk, xk) = all_75_0_76, yields:
% 35.30/10.47 | (438) all_80_0_80 = all_75_0_76
% 35.30/10.47 |
% 35.30/10.47 | Instantiating formula (100) with xk, xk, all_30_0_29, all_80_0_80 and discharging atoms doDivides0(xk, xk) = all_80_0_80, doDivides0(xk, xk) = all_30_0_29, yields:
% 35.30/10.48 | (439) all_80_0_80 = all_30_0_29
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (65) with xk, sz10, all_266_0_386, all_282_2_396 and discharging atoms sdtasdt0(xk, sz10) = all_282_2_396, sdtasdt0(xk, sz10) = all_266_0_386, yields:
% 35.30/10.48 | (440) all_282_2_396 = all_266_0_386
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (65) with xk, sz10, all_260_3_385, all_296_1_399 and discharging atoms sdtasdt0(xk, sz10) = all_296_1_399, sdtasdt0(xk, sz10) = all_260_3_385, yields:
% 35.30/10.48 | (441) all_296_1_399 = all_260_3_385
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (65) with xk, sz10, all_260_3_385, all_266_0_386 and discharging atoms sdtasdt0(xk, sz10) = all_266_0_386, sdtasdt0(xk, sz10) = all_260_3_385, yields:
% 35.30/10.48 | (442) all_266_0_386 = all_260_3_385
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (65) with xk, sz10, all_220_3_368, all_282_2_396 and discharging atoms sdtasdt0(xk, sz10) = all_282_2_396, sdtasdt0(xk, sz10) = all_220_3_368, yields:
% 35.30/10.48 | (443) all_282_2_396 = all_220_3_368
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (65) with xk, sz10, all_181_2_318, all_266_0_386 and discharging atoms sdtasdt0(xk, sz10) = all_266_0_386, sdtasdt0(xk, sz10) = all_181_2_318, yields:
% 35.30/10.48 | (444) all_266_0_386 = all_181_2_318
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (65) with xk, sz10, xk, all_296_1_399 and discharging atoms sdtasdt0(xk, sz10) = all_296_1_399, sdtasdt0(xk, sz10) = xk, yields:
% 35.30/10.48 | (445) all_296_1_399 = xk
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (65) with sz10, xk, all_282_0_394, all_296_3_401 and discharging atoms sdtasdt0(sz10, xk) = all_296_3_401, sdtasdt0(sz10, xk) = all_282_0_394, yields:
% 35.30/10.48 | (446) all_296_3_401 = all_282_0_394
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (65) with sz10, xk, all_266_2_388, all_296_3_401 and discharging atoms sdtasdt0(sz10, xk) = all_296_3_401, sdtasdt0(sz10, xk) = all_266_2_388, yields:
% 35.30/10.48 | (447) all_296_3_401 = all_266_2_388
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (65) with sz10, xk, all_260_1_383, all_282_0_394 and discharging atoms sdtasdt0(sz10, xk) = all_282_0_394, sdtasdt0(sz10, xk) = all_260_1_383, yields:
% 35.30/10.48 | (448) all_282_0_394 = all_260_1_383
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (65) with sz10, xk, all_220_1_366, all_282_0_394 and discharging atoms sdtasdt0(sz10, xk) = all_282_0_394, sdtasdt0(sz10, xk) = all_220_1_366, yields:
% 35.30/10.48 | (449) all_282_0_394 = all_220_1_366
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (65) with sz10, xk, all_181_0_316, all_282_0_394 and discharging atoms sdtasdt0(sz10, xk) = all_282_0_394, sdtasdt0(sz10, xk) = all_181_0_316, yields:
% 35.30/10.48 | (450) all_282_0_394 = all_181_0_316
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (65) with sz10, xk, xk, all_220_1_366 and discharging atoms sdtasdt0(sz10, xk) = all_220_1_366, sdtasdt0(sz10, xk) = xk, yields:
% 35.30/10.48 | (451) all_220_1_366 = xk
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (102) with xk, sz10, all_191_1_321, all_254_2_380 and discharging atoms sdtpldt0(xk, sz10) = all_254_2_380, sdtpldt0(xk, sz10) = all_191_1_321, yields:
% 35.30/10.48 | (452) all_254_2_380 = all_191_1_321
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (102) with xk, sz10, all_171_2_232, all_191_1_321 and discharging atoms sdtpldt0(xk, sz10) = all_191_1_321, sdtpldt0(xk, sz10) = all_171_2_232, yields:
% 35.30/10.48 | (453) all_191_1_321 = all_171_2_232
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (102) with xk, sz10, all_117_3_197, all_171_2_232 and discharging atoms sdtpldt0(xk, sz10) = all_171_2_232, sdtpldt0(xk, sz10) = all_117_3_197, yields:
% 35.30/10.48 | (454) all_171_2_232 = all_117_3_197
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (102) with xk, sz10, all_117_3_197, all_165_0_226 and discharging atoms sdtpldt0(xk, sz10) = all_165_0_226, sdtpldt0(xk, sz10) = all_117_3_197, yields:
% 35.30/10.48 | (455) all_165_0_226 = all_117_3_197
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (102) with xk, sz10, all_112_0_190, all_165_0_226 and discharging atoms sdtpldt0(xk, sz10) = all_165_0_226, sdtpldt0(xk, sz10) = all_112_0_190, yields:
% 35.30/10.48 | (456) all_165_0_226 = all_112_0_190
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (102) with xk, sz10, all_107_1_187, all_254_2_380 and discharging atoms sdtpldt0(xk, sz10) = all_254_2_380, sdtpldt0(xk, sz10) = all_107_1_187, yields:
% 35.30/10.48 | (457) all_254_2_380 = all_107_1_187
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (102) with sz10, xk, all_171_0_230, all_191_3_323 and discharging atoms sdtpldt0(sz10, xk) = all_191_3_323, sdtpldt0(sz10, xk) = all_171_0_230, yields:
% 35.30/10.48 | (458) all_191_3_323 = all_171_0_230
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (102) with sz10, xk, all_165_2_228, all_171_0_230 and discharging atoms sdtpldt0(sz10, xk) = all_171_0_230, sdtpldt0(sz10, xk) = all_165_2_228, yields:
% 35.30/10.48 | (459) all_171_0_230 = all_165_2_228
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (102) with sz10, xk, all_117_1_195, all_254_0_378 and discharging atoms sdtpldt0(sz10, xk) = all_254_0_378, sdtpldt0(sz10, xk) = all_117_1_195, yields:
% 35.30/10.48 | (460) all_254_0_378 = all_117_1_195
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (102) with sz10, xk, all_117_1_195, all_165_2_228 and discharging atoms sdtpldt0(sz10, xk) = all_165_2_228, sdtpldt0(sz10, xk) = all_117_1_195, yields:
% 35.30/10.48 | (461) all_165_2_228 = all_117_1_195
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (102) with sz10, xk, all_112_2_192, all_254_0_378 and discharging atoms sdtpldt0(sz10, xk) = all_254_0_378, sdtpldt0(sz10, xk) = all_112_2_192, yields:
% 35.30/10.48 | (462) all_254_0_378 = all_112_2_192
% 35.30/10.48 |
% 35.30/10.48 | Instantiating formula (102) with sz10, xk, all_107_3_189, all_191_3_323 and discharging atoms sdtpldt0(sz10, xk) = all_191_3_323, sdtpldt0(sz10, xk) = all_107_3_189, yields:
% 35.30/10.48 | (463) all_191_3_323 = all_107_3_189
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (441,445) yields a new equation:
% 35.30/10.48 | (464) all_260_3_385 = xk
% 35.30/10.48 |
% 35.30/10.48 | Simplifying 464 yields:
% 35.30/10.48 | (465) all_260_3_385 = xk
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (446,447) yields a new equation:
% 35.30/10.48 | (466) all_282_0_394 = all_266_2_388
% 35.30/10.48 |
% 35.30/10.48 | Simplifying 466 yields:
% 35.30/10.48 | (467) all_282_0_394 = all_266_2_388
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (450,467) yields a new equation:
% 35.30/10.48 | (468) all_266_2_388 = all_181_0_316
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (449,467) yields a new equation:
% 35.30/10.48 | (469) all_266_2_388 = all_220_1_366
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (448,467) yields a new equation:
% 35.30/10.48 | (470) all_266_2_388 = all_260_1_383
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (440,443) yields a new equation:
% 35.30/10.48 | (471) all_266_0_386 = all_220_3_368
% 35.30/10.48 |
% 35.30/10.48 | Simplifying 471 yields:
% 35.30/10.48 | (472) all_266_0_386 = all_220_3_368
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (442,472) yields a new equation:
% 35.30/10.48 | (473) all_260_3_385 = all_220_3_368
% 35.30/10.48 |
% 35.30/10.48 | Simplifying 473 yields:
% 35.30/10.48 | (474) all_260_3_385 = all_220_3_368
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (444,472) yields a new equation:
% 35.30/10.48 | (475) all_220_3_368 = all_181_2_318
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (468,470) yields a new equation:
% 35.30/10.48 | (476) all_260_1_383 = all_181_0_316
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (469,470) yields a new equation:
% 35.30/10.48 | (477) all_260_1_383 = all_220_1_366
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (477,476) yields a new equation:
% 35.30/10.48 | (478) all_220_1_366 = all_181_0_316
% 35.30/10.48 |
% 35.30/10.48 | Simplifying 478 yields:
% 35.30/10.48 | (479) all_220_1_366 = all_181_0_316
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (474,465) yields a new equation:
% 35.30/10.48 | (480) all_220_3_368 = xk
% 35.30/10.48 |
% 35.30/10.48 | Simplifying 480 yields:
% 35.30/10.48 | (481) all_220_3_368 = xk
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (460,462) yields a new equation:
% 35.30/10.48 | (482) all_117_1_195 = all_112_2_192
% 35.30/10.48 |
% 35.30/10.48 | Simplifying 482 yields:
% 35.30/10.48 | (483) all_117_1_195 = all_112_2_192
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (452,457) yields a new equation:
% 35.30/10.48 | (484) all_191_1_321 = all_107_1_187
% 35.30/10.48 |
% 35.30/10.48 | Simplifying 484 yields:
% 35.30/10.48 | (485) all_191_1_321 = all_107_1_187
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (479,451) yields a new equation:
% 35.30/10.48 | (486) all_181_0_316 = xk
% 35.30/10.48 |
% 35.30/10.48 | Simplifying 486 yields:
% 35.30/10.48 | (487) all_181_0_316 = xk
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (475,481) yields a new equation:
% 35.30/10.48 | (488) all_181_2_318 = xk
% 35.30/10.48 |
% 35.30/10.48 | Simplifying 488 yields:
% 35.30/10.48 | (489) all_181_2_318 = xk
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (453,485) yields a new equation:
% 35.30/10.48 | (490) all_171_2_232 = all_107_1_187
% 35.30/10.48 |
% 35.30/10.48 | Simplifying 490 yields:
% 35.30/10.48 | (491) all_171_2_232 = all_107_1_187
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (458,463) yields a new equation:
% 35.30/10.48 | (492) all_171_0_230 = all_107_3_189
% 35.30/10.48 |
% 35.30/10.48 | Simplifying 492 yields:
% 35.30/10.48 | (493) all_171_0_230 = all_107_3_189
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (459,493) yields a new equation:
% 35.30/10.48 | (494) all_165_2_228 = all_107_3_189
% 35.30/10.48 |
% 35.30/10.48 | Simplifying 494 yields:
% 35.30/10.48 | (495) all_165_2_228 = all_107_3_189
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (454,491) yields a new equation:
% 35.30/10.48 | (496) all_117_3_197 = all_107_1_187
% 35.30/10.48 |
% 35.30/10.48 | Simplifying 496 yields:
% 35.30/10.48 | (497) all_117_3_197 = all_107_1_187
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (455,456) yields a new equation:
% 35.30/10.48 | (498) all_117_3_197 = all_112_0_190
% 35.30/10.48 |
% 35.30/10.48 | Simplifying 498 yields:
% 35.30/10.48 | (499) all_117_3_197 = all_112_0_190
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (461,495) yields a new equation:
% 35.30/10.48 | (500) all_117_1_195 = all_107_3_189
% 35.30/10.48 |
% 35.30/10.48 | Simplifying 500 yields:
% 35.30/10.48 | (501) all_117_1_195 = all_107_3_189
% 35.30/10.48 |
% 35.30/10.48 | Combining equations (501,483) yields a new equation:
% 35.30/10.48 | (502) all_112_2_192 = all_107_3_189
% 35.30/10.49 |
% 35.30/10.49 | Combining equations (499,497) yields a new equation:
% 35.30/10.49 | (503) all_112_0_190 = all_107_1_187
% 35.30/10.49 |
% 35.30/10.49 | Simplifying 503 yields:
% 35.30/10.49 | (504) all_112_0_190 = all_107_1_187
% 35.30/10.49 |
% 35.30/10.49 | Combining equations (439,438) yields a new equation:
% 35.30/10.49 | (505) all_75_0_76 = all_30_0_29
% 35.30/10.49 |
% 35.30/10.49 | Equations (505) can reduce 290 to:
% 35.30/10.49 | (182) ~ (all_30_0_29 = 0)
% 35.30/10.49 |
% 35.30/10.49 | From (505) and (291) follows:
% 35.30/10.49 | (188) doDivides0(xk, xk) = all_30_0_29
% 35.30/10.49 |
% 35.30/10.49 | From (489) and (302) follows:
% 35.30/10.49 | (148) sdtasdt0(xk, sz10) = xk
% 35.30/10.49 |
% 35.30/10.49 | From (487) and (301) follows:
% 35.30/10.49 | (149) sdtasdt0(sz10, xk) = xk
% 35.30/10.49 |
% 35.30/10.49 | From (504) and (220) follows:
% 35.30/10.49 | (207) sdtpldt0(xk, sz10) = all_107_1_187
% 35.30/10.49 |
% 35.30/10.49 | From (502) and (221) follows:
% 35.30/10.49 | (210) sdtpldt0(sz10, xk) = all_107_3_189
% 35.30/10.49 |
% 35.30/10.49 | Instantiating formula (48) with sz10, all_30_0_29, xk, xk and discharging atoms doDivides0(xk, xk) = all_30_0_29, aNaturalNumber0(sz10) = 0, yields:
% 35.30/10.49 | (512) all_30_0_29 = 0 | ? [v0] : (( ~ (v0 = xk) & sdtasdt0(xk, sz10) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xk) = v0))
% 35.30/10.49 |
% 35.30/10.49 | Instantiating formula (117) with all_107_1_187, sz10, xk, sz10, xk, sz10 and discharging atoms sdtasdt0(sz10, xk) = xk, sdtasdt0(sz10, sz10) = sz10, sdtpldt0(xk, sz10) = all_107_1_187, yields:
% 35.30/10.49 | (513) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = v2 & v1 = all_107_1_187 & sdtasdt0(v0, sz10) = v2 & sdtasdt0(xk, sz10) = v3 & sdtasdt0(sz10, v0) = all_107_1_187 & sdtasdt0(sz10, sz10) = v4 & sdtpldt0(v3, v4) = v2 & sdtpldt0(xk, sz10) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xk) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(sz10) = v0))
% 35.30/10.49 |
% 35.30/10.49 | Instantiating formula (117) with all_107_3_189, xk, sz10, xk, sz10, sz10 and discharging atoms sdtasdt0(sz10, xk) = xk, sdtasdt0(sz10, sz10) = sz10, sdtpldt0(sz10, xk) = all_107_3_189, yields:
% 35.30/10.49 | (514) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = v2 & v1 = all_107_3_189 & sdtasdt0(v0, sz10) = v2 & sdtasdt0(xk, sz10) = v4 & sdtasdt0(sz10, v0) = all_107_3_189 & sdtasdt0(sz10, sz10) = v3 & sdtpldt0(v3, v4) = v2 & sdtpldt0(sz10, xk) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xk) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(sz10) = v0))
% 35.30/10.49 |
% 35.30/10.49 | Instantiating (514) with all_324_0_427, all_324_1_428, all_324_2_429, all_324_3_430, all_324_4_431, all_324_5_432 yields:
% 35.30/10.49 | (515) (all_324_0_427 = all_324_3_430 & all_324_4_431 = all_107_3_189 & sdtasdt0(all_324_5_432, sz10) = all_324_3_430 & sdtasdt0(xk, sz10) = all_324_1_428 & sdtasdt0(sz10, all_324_5_432) = all_107_3_189 & sdtasdt0(sz10, sz10) = all_324_2_429 & sdtpldt0(all_324_2_429, all_324_1_428) = all_324_3_430 & sdtpldt0(sz10, xk) = all_324_5_432) | ( ~ (all_324_5_432 = 0) & aNaturalNumber0(xk) = all_324_5_432) | ( ~ (all_324_5_432 = 0) & aNaturalNumber0(sz10) = all_324_5_432)
% 35.30/10.49 |
% 35.30/10.49 | Instantiating (513) with all_326_0_439, all_326_1_440, all_326_2_441, all_326_3_442, all_326_4_443, all_326_5_444 yields:
% 35.30/10.49 | (516) (all_326_0_439 = all_326_3_442 & all_326_4_443 = all_107_1_187 & sdtasdt0(all_326_5_444, sz10) = all_326_3_442 & sdtasdt0(xk, sz10) = all_326_2_441 & sdtasdt0(sz10, all_326_5_444) = all_107_1_187 & sdtasdt0(sz10, sz10) = all_326_1_440 & sdtpldt0(all_326_2_441, all_326_1_440) = all_326_3_442 & sdtpldt0(xk, sz10) = all_326_5_444) | ( ~ (all_326_5_444 = 0) & aNaturalNumber0(xk) = all_326_5_444) | ( ~ (all_326_5_444 = 0) & aNaturalNumber0(sz10) = all_326_5_444)
% 35.30/10.49 |
% 35.30/10.49 +-Applying beta-rule and splitting (515), into two cases.
% 35.30/10.49 |-Branch one:
% 35.30/10.49 | (517) (all_324_0_427 = all_324_3_430 & all_324_4_431 = all_107_3_189 & sdtasdt0(all_324_5_432, sz10) = all_324_3_430 & sdtasdt0(xk, sz10) = all_324_1_428 & sdtasdt0(sz10, all_324_5_432) = all_107_3_189 & sdtasdt0(sz10, sz10) = all_324_2_429 & sdtpldt0(all_324_2_429, all_324_1_428) = all_324_3_430 & sdtpldt0(sz10, xk) = all_324_5_432) | ( ~ (all_324_5_432 = 0) & aNaturalNumber0(xk) = all_324_5_432)
% 35.30/10.49 |
% 35.30/10.49 +-Applying beta-rule and splitting (517), into two cases.
% 35.30/10.49 |-Branch one:
% 35.30/10.49 | (518) all_324_0_427 = all_324_3_430 & all_324_4_431 = all_107_3_189 & sdtasdt0(all_324_5_432, sz10) = all_324_3_430 & sdtasdt0(xk, sz10) = all_324_1_428 & sdtasdt0(sz10, all_324_5_432) = all_107_3_189 & sdtasdt0(sz10, sz10) = all_324_2_429 & sdtpldt0(all_324_2_429, all_324_1_428) = all_324_3_430 & sdtpldt0(sz10, xk) = all_324_5_432
% 35.30/10.49 |
% 35.30/10.49 | Applying alpha-rule on (518) yields:
% 35.30/10.49 | (519) all_324_4_431 = all_107_3_189
% 35.30/10.49 | (520) sdtpldt0(sz10, xk) = all_324_5_432
% 35.30/10.49 | (521) sdtasdt0(all_324_5_432, sz10) = all_324_3_430
% 35.30/10.49 | (522) sdtasdt0(sz10, sz10) = all_324_2_429
% 35.30/10.49 | (523) all_324_0_427 = all_324_3_430
% 35.30/10.49 | (524) sdtpldt0(all_324_2_429, all_324_1_428) = all_324_3_430
% 35.30/10.49 | (525) sdtasdt0(sz10, all_324_5_432) = all_107_3_189
% 35.30/10.49 | (526) sdtasdt0(xk, sz10) = all_324_1_428
% 35.30/10.49 |
% 35.30/10.49 +-Applying beta-rule and splitting (516), into two cases.
% 35.30/10.49 |-Branch one:
% 35.30/10.49 | (527) (all_326_0_439 = all_326_3_442 & all_326_4_443 = all_107_1_187 & sdtasdt0(all_326_5_444, sz10) = all_326_3_442 & sdtasdt0(xk, sz10) = all_326_2_441 & sdtasdt0(sz10, all_326_5_444) = all_107_1_187 & sdtasdt0(sz10, sz10) = all_326_1_440 & sdtpldt0(all_326_2_441, all_326_1_440) = all_326_3_442 & sdtpldt0(xk, sz10) = all_326_5_444) | ( ~ (all_326_5_444 = 0) & aNaturalNumber0(xk) = all_326_5_444)
% 35.30/10.49 |
% 35.30/10.49 +-Applying beta-rule and splitting (527), into two cases.
% 35.30/10.49 |-Branch one:
% 35.30/10.49 | (528) all_326_0_439 = all_326_3_442 & all_326_4_443 = all_107_1_187 & sdtasdt0(all_326_5_444, sz10) = all_326_3_442 & sdtasdt0(xk, sz10) = all_326_2_441 & sdtasdt0(sz10, all_326_5_444) = all_107_1_187 & sdtasdt0(sz10, sz10) = all_326_1_440 & sdtpldt0(all_326_2_441, all_326_1_440) = all_326_3_442 & sdtpldt0(xk, sz10) = all_326_5_444
% 35.30/10.49 |
% 35.30/10.49 | Applying alpha-rule on (528) yields:
% 35.30/10.49 | (529) sdtasdt0(all_326_5_444, sz10) = all_326_3_442
% 35.30/10.49 | (530) sdtasdt0(sz10, sz10) = all_326_1_440
% 35.30/10.49 | (531) all_326_0_439 = all_326_3_442
% 35.30/10.49 | (532) sdtpldt0(xk, sz10) = all_326_5_444
% 35.30/10.49 | (533) sdtasdt0(sz10, all_326_5_444) = all_107_1_187
% 35.30/10.49 | (534) sdtasdt0(xk, sz10) = all_326_2_441
% 35.30/10.49 | (535) all_326_4_443 = all_107_1_187
% 35.30/10.49 | (536) sdtpldt0(all_326_2_441, all_326_1_440) = all_326_3_442
% 35.30/10.49 |
% 35.30/10.49 +-Applying beta-rule and splitting (512), into two cases.
% 35.30/10.49 |-Branch one:
% 35.30/10.49 | (184) all_30_0_29 = 0
% 35.30/10.49 |
% 35.30/10.49 | Equations (184) can reduce 182 to:
% 35.30/10.49 | (185) $false
% 35.30/10.49 |
% 35.30/10.49 |-The branch is then unsatisfiable
% 35.30/10.49 |-Branch two:
% 35.30/10.49 | (182) ~ (all_30_0_29 = 0)
% 35.30/10.49 | (540) ? [v0] : (( ~ (v0 = xk) & sdtasdt0(xk, sz10) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xk) = v0))
% 35.30/10.49 |
% 35.30/10.49 | Instantiating (540) with all_468_0_839 yields:
% 35.30/10.49 | (541) ( ~ (all_468_0_839 = xk) & sdtasdt0(xk, sz10) = all_468_0_839) | ( ~ (all_468_0_839 = 0) & aNaturalNumber0(xk) = all_468_0_839)
% 35.30/10.49 |
% 35.30/10.49 +-Applying beta-rule and splitting (541), into two cases.
% 35.30/10.49 |-Branch one:
% 35.30/10.49 | (542) ~ (all_468_0_839 = xk) & sdtasdt0(xk, sz10) = all_468_0_839
% 35.30/10.49 |
% 35.30/10.49 | Applying alpha-rule on (542) yields:
% 35.30/10.49 | (543) ~ (all_468_0_839 = xk)
% 35.30/10.49 | (544) sdtasdt0(xk, sz10) = all_468_0_839
% 35.30/10.49 |
% 35.30/10.49 | Instantiating formula (65) with xk, sz10, all_326_2_441, xk and discharging atoms sdtasdt0(xk, sz10) = all_326_2_441, sdtasdt0(xk, sz10) = xk, yields:
% 35.30/10.49 | (545) all_326_2_441 = xk
% 35.30/10.49 |
% 35.30/10.49 | Instantiating formula (65) with xk, sz10, all_326_2_441, all_468_0_839 and discharging atoms sdtasdt0(xk, sz10) = all_468_0_839, sdtasdt0(xk, sz10) = all_326_2_441, yields:
% 35.30/10.49 | (546) all_468_0_839 = all_326_2_441
% 35.30/10.49 |
% 35.30/10.49 | Instantiating formula (65) with xk, sz10, all_324_1_428, all_468_0_839 and discharging atoms sdtasdt0(xk, sz10) = all_468_0_839, sdtasdt0(xk, sz10) = all_324_1_428, yields:
% 35.30/10.50 | (547) all_468_0_839 = all_324_1_428
% 35.30/10.50 |
% 35.30/10.50 | Combining equations (546,547) yields a new equation:
% 35.30/10.50 | (548) all_326_2_441 = all_324_1_428
% 35.30/10.50 |
% 35.30/10.50 | Simplifying 548 yields:
% 35.30/10.50 | (549) all_326_2_441 = all_324_1_428
% 35.30/10.50 |
% 35.30/10.50 | Combining equations (545,549) yields a new equation:
% 35.30/10.50 | (550) all_324_1_428 = xk
% 35.30/10.50 |
% 35.30/10.50 | Combining equations (550,547) yields a new equation:
% 35.30/10.50 | (551) all_468_0_839 = xk
% 35.30/10.50 |
% 35.30/10.50 | Equations (551) can reduce 543 to:
% 35.30/10.50 | (185) $false
% 35.30/10.50 |
% 35.30/10.50 |-The branch is then unsatisfiable
% 35.30/10.50 |-Branch two:
% 35.30/10.50 | (553) ~ (all_468_0_839 = 0) & aNaturalNumber0(xk) = all_468_0_839
% 35.30/10.50 |
% 35.30/10.50 | Applying alpha-rule on (553) yields:
% 35.30/10.50 | (554) ~ (all_468_0_839 = 0)
% 35.30/10.50 | (555) aNaturalNumber0(xk) = all_468_0_839
% 35.30/10.50 |
% 35.30/10.50 | Instantiating formula (140) with xk, all_468_0_839, 0 and discharging atoms aNaturalNumber0(xk) = all_468_0_839, aNaturalNumber0(xk) = 0, yields:
% 35.30/10.50 | (556) all_468_0_839 = 0
% 35.30/10.50 |
% 35.30/10.50 | Equations (556) can reduce 554 to:
% 35.30/10.50 | (185) $false
% 35.30/10.50 |
% 35.30/10.50 |-The branch is then unsatisfiable
% 35.30/10.50 |-Branch two:
% 35.30/10.50 | (558) ~ (all_326_5_444 = 0) & aNaturalNumber0(xk) = all_326_5_444
% 35.30/10.50 |
% 35.30/10.50 | Applying alpha-rule on (558) yields:
% 35.30/10.50 | (559) ~ (all_326_5_444 = 0)
% 35.44/10.50 | (560) aNaturalNumber0(xk) = all_326_5_444
% 35.44/10.50 |
% 35.44/10.50 | Instantiating formula (140) with xk, all_326_5_444, 0 and discharging atoms aNaturalNumber0(xk) = all_326_5_444, aNaturalNumber0(xk) = 0, yields:
% 35.44/10.50 | (561) all_326_5_444 = 0
% 35.44/10.50 |
% 35.44/10.50 | Equations (561) can reduce 559 to:
% 35.44/10.50 | (185) $false
% 35.44/10.50 |
% 35.44/10.50 |-The branch is then unsatisfiable
% 35.44/10.50 |-Branch two:
% 35.44/10.50 | (563) ~ (all_326_5_444 = 0) & aNaturalNumber0(sz10) = all_326_5_444
% 35.44/10.50 |
% 35.44/10.50 | Applying alpha-rule on (563) yields:
% 35.44/10.50 | (559) ~ (all_326_5_444 = 0)
% 35.44/10.50 | (565) aNaturalNumber0(sz10) = all_326_5_444
% 35.44/10.50 |
% 35.44/10.50 | Instantiating formula (140) with sz10, all_326_5_444, 0 and discharging atoms aNaturalNumber0(sz10) = all_326_5_444, aNaturalNumber0(sz10) = 0, yields:
% 35.44/10.50 | (561) all_326_5_444 = 0
% 35.44/10.50 |
% 35.44/10.50 | Equations (561) can reduce 559 to:
% 35.44/10.50 | (185) $false
% 35.44/10.50 |
% 35.44/10.50 |-The branch is then unsatisfiable
% 35.44/10.50 |-Branch two:
% 35.44/10.50 | (568) ~ (all_324_5_432 = 0) & aNaturalNumber0(xk) = all_324_5_432
% 35.44/10.50 |
% 35.44/10.50 | Applying alpha-rule on (568) yields:
% 35.44/10.50 | (569) ~ (all_324_5_432 = 0)
% 35.44/10.50 | (570) aNaturalNumber0(xk) = all_324_5_432
% 35.44/10.50 |
% 35.44/10.50 | Instantiating formula (140) with xk, all_324_5_432, 0 and discharging atoms aNaturalNumber0(xk) = all_324_5_432, aNaturalNumber0(xk) = 0, yields:
% 35.44/10.50 | (571) all_324_5_432 = 0
% 35.44/10.50 |
% 35.44/10.50 | Equations (571) can reduce 569 to:
% 35.44/10.50 | (185) $false
% 35.44/10.50 |
% 35.44/10.50 |-The branch is then unsatisfiable
% 35.44/10.50 |-Branch two:
% 35.44/10.50 | (573) ~ (all_324_5_432 = 0) & aNaturalNumber0(sz10) = all_324_5_432
% 35.44/10.50 |
% 35.44/10.50 | Applying alpha-rule on (573) yields:
% 35.44/10.50 | (569) ~ (all_324_5_432 = 0)
% 35.44/10.50 | (575) aNaturalNumber0(sz10) = all_324_5_432
% 35.44/10.50 |
% 35.44/10.50 | Instantiating formula (140) with sz10, all_324_5_432, 0 and discharging atoms aNaturalNumber0(sz10) = all_324_5_432, aNaturalNumber0(sz10) = 0, yields:
% 35.44/10.50 | (571) all_324_5_432 = 0
% 35.44/10.50 |
% 35.44/10.50 | Equations (571) can reduce 569 to:
% 35.44/10.50 | (185) $false
% 35.44/10.50 |
% 35.44/10.50 |-The branch is then unsatisfiable
% 35.44/10.50 |-Branch two:
% 35.44/10.50 | (578) ~ (all_80_0_80 = 0) & aNaturalNumber0(xk) = all_80_0_80
% 35.44/10.50 |
% 35.44/10.50 | Applying alpha-rule on (578) yields:
% 35.44/10.50 | (327) ~ (all_80_0_80 = 0)
% 35.44/10.50 | (580) aNaturalNumber0(xk) = all_80_0_80
% 35.44/10.50 |
% 35.44/10.50 | Instantiating formula (140) with xk, all_80_0_80, 0 and discharging atoms aNaturalNumber0(xk) = all_80_0_80, aNaturalNumber0(xk) = 0, yields:
% 35.44/10.50 | (581) all_80_0_80 = 0
% 35.44/10.50 |
% 35.44/10.50 | Equations (581) can reduce 327 to:
% 35.44/10.50 | (185) $false
% 35.44/10.50 |
% 35.44/10.50 |-The branch is then unsatisfiable
% 35.44/10.50 % SZS output end Proof for theBenchmark
% 35.44/10.50
% 35.44/10.50 9895ms
%------------------------------------------------------------------------------