TSTP Solution File: NUM500+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM500+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 08:45:11 EDT 2022
% Result : Theorem 6.01s 1.98s
% Output : Proof 10.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM500+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n010.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 01:50:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.50/0.58 ____ _
% 0.50/0.58 ___ / __ \_____(_)___ ________ __________
% 0.50/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.58
% 0.50/0.58 A Theorem Prover for First-Order Logic
% 0.50/0.58 (ePrincess v.1.0)
% 0.50/0.58
% 0.50/0.58 (c) Philipp Rümmer, 2009-2015
% 0.50/0.58 (c) Peter Backeman, 2014-2015
% 0.50/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.58 Bug reports to peter@backeman.se
% 0.50/0.58
% 0.50/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.58
% 0.50/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.86/1.03 Prover 0: Preprocessing ...
% 4.14/1.58 Prover 0: Constructing countermodel ...
% 6.01/1.98 Prover 0: proved (1346ms)
% 6.01/1.98
% 6.01/1.98 No countermodel exists, formula is valid
% 6.01/1.98 % SZS status Theorem for theBenchmark
% 6.01/1.98
% 6.01/1.98 Generating proof ... found it (size 95)
% 9.34/2.82
% 9.34/2.82 % SZS output start Proof for theBenchmark
% 9.34/2.82 Assumed formulas after preprocessing and simplification:
% 9.34/2.82 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (xk = sz10) & ~ (xk = sz00) & ~ (xp = xm) & ~ (xp = xn) & ~ (xp = sz10) & ~ (xp = sz00) & ~ (sz10 = sz00) & sdtsldt0(v2, xp) = xk & sdtasdt0(xp, v5) = v2 & sdtasdt0(xp, xk) = v2 & sdtasdt0(xn, xm) = v2 & sdtpldt0(v0, xp) = v1 & sdtpldt0(xm, v3) = xp & sdtpldt0(xn, v4) = xp & sdtpldt0(xn, xm) = v0 & isPrime0(xp) & doDivides0(xp, v2) & sdtlseqdt0(xm, xp) & sdtlseqdt0(xn, xp) & aNaturalNumber0(v5) & aNaturalNumber0(v4) & aNaturalNumber0(v3) & aNaturalNumber0(xk) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ isPrime0(sz10) & ~ isPrime0(sz00) & ~ sdtlseqdt0(xp, xm) & ~ sdtlseqdt0(xp, xn) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v6 = sz00 | ~ (sdtsldt0(v10, v6) = v11) | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v9, v7) = v10) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtasdt0(v9, v8) = v11) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v8, v6) = v10) | ~ (sdtasdt0(v7, v6) = v9) | ~ (sdtpldt0(v9, v10) = v11) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (sdtasdt0(v12, v6) = v11 & sdtasdt0(v6, v12) = v13 & sdtasdt0(v6, v8) = v15 & sdtasdt0(v6, v7) = v14 & sdtpldt0(v14, v15) = v13 & sdtpldt0(v7, v8) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v6, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ (sdtpldt0(v9, v10) = v11) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (sdtasdt0(v12, v6) = v13 & sdtasdt0(v8, v6) = v15 & sdtasdt0(v7, v6) = v14 & sdtasdt0(v6, v12) = v11 & sdtpldt0(v14, v15) = v13 & sdtpldt0(v7, v8) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v8, v6) = v10) | ~ (sdtasdt0(v7, v6) = v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v9, v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v8, v6) = v10) | ~ (sdtasdt0(v7, v6) = v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v11) & sdtasdt0(v6, v8) = v12 & sdtasdt0(v6, v7) = v11 & sdtlseqdt0(v11, v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v8, v6) = v10) | ~ (sdtasdt0(v7, v6) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v11) & sdtasdt0(v6, v8) = v12 & sdtasdt0(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v8, v6) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v10) & ~ (v11 = v9) & sdtasdt0(v7, v6) = v12 & sdtasdt0(v6, v8) = v11 & sdtlseqdt0(v12, v10) & sdtlseqdt0(v9, v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v8, v6) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v10) & ~ (v11 = v9) & sdtasdt0(v7, v6) = v12 & sdtasdt0(v6, v8) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v7, v6) = v10) | ~ (sdtasdt0(v6, v8) = v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v10) & ~ (v11 = v9) & sdtasdt0(v8, v6) = v12 & sdtasdt0(v6, v7) = v11 & sdtlseqdt0(v11, v9) & sdtlseqdt0(v10, v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v7, v6) = v10) | ~ (sdtasdt0(v6, v8) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v10) & ~ (v11 = v9) & sdtasdt0(v8, v6) = v12 & sdtasdt0(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v6, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v9, v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v6, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v11) & sdtasdt0(v8, v6) = v12 & sdtasdt0(v7, v6) = v11 & sdtlseqdt0(v11, v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v6, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v11) & sdtasdt0(v8, v6) = v12 & sdtasdt0(v7, v6) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v8, v6) = v10) | ~ (sdtpldt0(v7, v6) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v11) & sdtpldt0(v6, v8) = v12 & sdtpldt0(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v8, v6) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v10) & ~ (v11 = v9) & sdtpldt0(v7, v6) = v12 & sdtpldt0(v6, v8) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v7, v6) = v10) | ~ (sdtpldt0(v6, v8) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v10) & ~ (v11 = v9) & sdtpldt0(v8, v6) = v12 & sdtpldt0(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v6, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v11) & sdtpldt0(v8, v6) = v12 & sdtpldt0(v7, v6) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = sz10 | v8 = sz00 | ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ iLess0(v10, v1) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v8, v7) | doDivides0(v8, v6) | ? [v11] : ? [v12] : ? [v13] : ((v13 = v8 & ~ (v11 = v8) & ~ (v11 = sz10) & sdtasdt0(v11, v12) = v8 & doDivides0(v11, v8) & aNaturalNumber0(v12) & aNaturalNumber0(v11)) | (sdtasdt0(v6, v7) = v11 & ~ doDivides0(v8, v11) & ! [v14] : ( ~ (sdtasdt0(v8, v14) = v11) | ~ aNaturalNumber0(v14))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = sz10 | v8 = sz00 | ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ iLess0(v10, v1) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v8, v7) | ? [v11] : ? [v12] : ? [v13] : ((v13 = v8 & ~ (v11 = v8) & ~ (v11 = sz10) & sdtasdt0(v11, v12) = v8 & doDivides0(v11, v8) & aNaturalNumber0(v12) & aNaturalNumber0(v11)) | (v12 = v6 & sdtasdt0(v8, v11) = v6 & aNaturalNumber0(v11)) | (sdtasdt0(v6, v7) = v11 & ~ doDivides0(v8, v11) & ! [v14] : ( ~ (sdtasdt0(v8, v14) = v11) | ~ aNaturalNumber0(v14))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = sz10 | v8 = sz00 | ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ iLess0(v10, v1) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v8, v6) | ? [v11] : ? [v12] : ? [v13] : ((v13 = v8 & ~ (v11 = v8) & ~ (v11 = sz10) & sdtasdt0(v11, v12) = v8 & doDivides0(v11, v8) & aNaturalNumber0(v12) & aNaturalNumber0(v11)) | (v12 = v7 & sdtasdt0(v8, v11) = v7 & aNaturalNumber0(v11)) | (sdtasdt0(v6, v7) = v11 & ~ doDivides0(v8, v11) & ! [v14] : ( ~ (sdtasdt0(v8, v14) = v11) | ~ aNaturalNumber0(v14))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = sz10 | v8 = sz00 | ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ iLess0(v10, v1) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ? [v13] : ((v13 = v8 & ~ (v11 = v8) & ~ (v11 = sz10) & sdtasdt0(v11, v12) = v8 & doDivides0(v11, v8) & aNaturalNumber0(v12) & aNaturalNumber0(v11)) | (v12 = v7 & sdtasdt0(v8, v11) = v7 & aNaturalNumber0(v11)) | (v12 = v6 & sdtasdt0(v8, v11) = v6 & aNaturalNumber0(v11)) | (sdtasdt0(v6, v7) = v11 & ~ doDivides0(v8, v11) & ! [v14] : ( ~ (sdtasdt0(v8, v14) = v11) | ~ aNaturalNumber0(v14))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v6 = sz00 | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v9, v8) = v10) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : (sdtsldt0(v11, v6) = v10 & sdtasdt0(v9, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v9, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : (sdtasdt0(v7, v8) = v11 & sdtasdt0(v6, v11) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v9, v6) = v10) | ~ (sdtpldt0(v7, v8) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (sdtasdt0(v8, v6) = v15 & sdtasdt0(v7, v6) = v14 & sdtasdt0(v6, v9) = v11 & sdtasdt0(v6, v8) = v13 & sdtasdt0(v6, v7) = v12 & sdtpldt0(v14, v15) = v10 & sdtpldt0(v12, v13) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v7, v8) = v9) | ~ (sdtasdt0(v6, v9) = v10) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : (sdtasdt0(v11, v8) = v10 & sdtasdt0(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v6, v9) = v10) | ~ (sdtpldt0(v7, v8) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (sdtasdt0(v9, v6) = v13 & sdtasdt0(v8, v6) = v15 & sdtasdt0(v7, v6) = v14 & sdtasdt0(v6, v8) = v12 & sdtasdt0(v6, v7) = v11 & sdtpldt0(v14, v15) = v13 & sdtpldt0(v11, v12) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ isPrime0(v8) | ~ iLess0(v10, v1) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v8, v7) | doDivides0(v8, v6) | ? [v11] : (sdtasdt0(v6, v7) = v11 & ~ doDivides0(v8, v11) & ! [v12] : ( ~ (sdtasdt0(v8, v12) = v11) | ~ aNaturalNumber0(v12)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ isPrime0(v8) | ~ iLess0(v10, v1) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v8, v7) | ? [v11] : ? [v12] : ((v12 = v6 & sdtasdt0(v8, v11) = v6 & aNaturalNumber0(v11)) | (sdtasdt0(v6, v7) = v11 & ~ doDivides0(v8, v11) & ! [v13] : ( ~ (sdtasdt0(v8, v13) = v11) | ~ aNaturalNumber0(v13))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ isPrime0(v8) | ~ iLess0(v10, v1) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v8, v6) | ? [v11] : ? [v12] : ((v12 = v7 & sdtasdt0(v8, v11) = v7 & aNaturalNumber0(v11)) | (sdtasdt0(v6, v7) = v11 & ~ doDivides0(v8, v11) & ! [v13] : ( ~ (sdtasdt0(v8, v13) = v11) | ~ aNaturalNumber0(v13))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ isPrime0(v8) | ~ iLess0(v10, v1) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ((v12 = v7 & sdtasdt0(v8, v11) = v7 & aNaturalNumber0(v11)) | (v12 = v6 & sdtasdt0(v8, v11) = v6 & aNaturalNumber0(v11)) | (sdtasdt0(v6, v7) = v11 & ~ doDivides0(v8, v11) & ! [v13] : ( ~ (sdtasdt0(v8, v13) = v11) | ~ aNaturalNumber0(v13))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : (sdtpldt0(v7, v8) = v11 & sdtpldt0(v6, v11) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt0(v7, v8) = v9) | ~ (sdtpldt0(v6, v9) = v10) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : (sdtpldt0(v11, v8) = v10 & sdtpldt0(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | v6 = sz00 | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v6, v9) = v7) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (sdtmndt0(v7, v6) = v8) | ~ (sdtpldt0(v6, v9) = v7) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | v6 = sz00 | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v6, v8) = v9) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (sdtmndt0(v7, v6) = v8) | ~ (sdtpldt0(v6, v8) = v9) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v8, v6) = v9) | ~ (sdtasdt0(v7, v6) = v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v8, v6) = v9) | ~ (sdtasdt0(v7, v6) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v6, v8) = v9) | ~ (sdtasdt0(v6, v7) = v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v6, v8) = v9) | ~ (sdtasdt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (sdtpldt0(v8, v6) = v9) | ~ (sdtpldt0(v7, v6) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (sdtpldt0(v6, v8) = v9) | ~ (sdtpldt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtsldt0(v9, v8) = v7) | ~ (sdtsldt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtmndt0(v9, v8) = v7) | ~ (sdtmndt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtasdt0(v9, v8) = v7) | ~ (sdtasdt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v9, v8) = v7) | ~ (sdtpldt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v8, v7) = v9) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = v11) & ~ (v10 = v9) & sdtpldt0(v8, v6) = v10 & sdtpldt0(v7, v8) = v12 & sdtpldt0(v6, v8) = v11 & sdtlseqdt0(v11, v12) & sdtlseqdt0(v10, v9))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v8, v6) = v9) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = v11) & ~ (v10 = v9) & sdtpldt0(v8, v7) = v10 & sdtpldt0(v7, v8) = v12 & sdtpldt0(v6, v8) = v11 & sdtlseqdt0(v11, v12) & sdtlseqdt0(v9, v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v7, v8) = v9) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = v9) & ~ (v11 = v10) & sdtpldt0(v8, v7) = v11 & sdtpldt0(v8, v6) = v10 & sdtpldt0(v6, v8) = v12 & sdtlseqdt0(v12, v9) & sdtlseqdt0(v10, v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v6, v8) = v9) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = v9) & ~ (v11 = v10) & sdtpldt0(v8, v7) = v11 & sdtpldt0(v8, v6) = v10 & sdtpldt0(v7, v8) = v12 & sdtlseqdt0(v10, v11) & sdtlseqdt0(v9, v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = sz00 | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v6, v8) = v9) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | aNaturalNumber0(v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtmndt0(v7, v6) = v8) | ~ (sdtpldt0(v6, v8) = v9) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | aNaturalNumber0(v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v7, v8) = v9) | ~ doDivides0(v6, v9) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v7, v8) = v9) | ~ doDivides0(v6, v8) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v6, v9)) & ! [v6] : ! [v7] : ! [v8] : (v6 = sz00 | ~ (sdtasdt0(v7, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v7, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v7, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtasdt0(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v6, v8) = v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtasdt0(v7, v6) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | aNaturalNumber0(v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v7, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtpldt0(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v6, v8) = v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtpldt0(v7, v6) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | aNaturalNumber0(v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ doDivides0(v7, v8) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ sdtlseqdt0(v7, v8) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v6, v8)) & ! [v6] : ! [v7] : (v7 = v6 | v7 = sz10 | ~ isPrime0(v6) | ~ doDivides0(v7, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (sdtasdt0(v6, sz10) = v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (sdtasdt0(sz10, v6) = v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (sdtpldt0(v6, sz00) = v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (sdtpldt0(sz00, v6) = v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ sdtlseqdt0(v7, v6) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | iLess0(v6, v7)) & ! [v6] : ! [v7] : (v7 = sz00 | v6 = sz00 | ~ (sdtasdt0(v6, v7) = sz00) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = sz00 | ~ (sdtasdt0(v6, sz00) = v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = sz00 | ~ (sdtasdt0(sz00, v6) = v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = sz00 | ~ (sdtpldt0(v6, v7) = sz00) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = sz00 | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v6, v7)) & ! [v6] : ! [v7] : (v6 = xp | v6 = sz10 | ~ (sdtasdt0(v6, v7) = xp) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v6 = sz10 | v6 = sz00 | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v8] : ? [v9] : ? [v10] : ((v10 = v6 & ~ (v8 = v6) & ~ (v8 = sz10) & sdtasdt0(v8, v9) = v6 & doDivides0(v8, v6) & aNaturalNumber0(v9) & aNaturalNumber0(v8)) | ( ~ (v8 = xk) & sdtasdt0(v6, v7) = v8))) & ! [v6] : ! [v7] : (v6 = sz00 | ~ (sdtpldt0(v6, v7) = sz00) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ( ~ (sdtasdt0(v6, sz10) = v7) | ~ aNaturalNumber0(v6) | sdtasdt0(sz10, v6) = v6) & ! [v6] : ! [v7] : ( ~ (sdtasdt0(v6, sz00) = v7) | ~ aNaturalNumber0(v6) | sdtasdt0(sz00, v6) = sz00) & ! [v6] : ! [v7] : ( ~ (sdtasdt0(sz10, v6) = v7) | ~ aNaturalNumber0(v6) | sdtasdt0(v6, sz10) = v6) & ! [v6] : ! [v7] : ( ~ (sdtasdt0(sz00, v6) = v7) | ~ aNaturalNumber0(v6) | sdtasdt0(v6, sz00) = sz00) & ! [v6] : ! [v7] : ( ~ (sdtpldt0(v6, sz00) = v7) | ~ aNaturalNumber0(v6) | sdtpldt0(sz00, v6) = v6) & ! [v6] : ! [v7] : ( ~ (sdtpldt0(sz00, v6) = v7) | ~ aNaturalNumber0(v6) | sdtpldt0(v6, sz00) = v6) & ! [v6] : ! [v7] : ( ~ isPrime0(v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v8] : ( ~ (v8 = xk) & sdtasdt0(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v8] : (sdtasdt0(v6, v8) = v7 & aNaturalNumber0(v8))) & ! [v6] : ! [v7] : ( ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v8] : (sdtpldt0(v6, v8) = v7 & aNaturalNumber0(v8))) & ! [v6] : ! [v7] : ( ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v7, v6) | sdtlseqdt0(v6, v7)) & ! [v6] : (v6 = xp | v6 = sz10 | ~ doDivides0(v6, xp) | ~ aNaturalNumber0(v6)) & ! [v6] : (v6 = sz10 | v6 = sz00 | ~ doDivides0(v6, xk) | ~ aNaturalNumber0(v6) | ? [v7] : ? [v8] : ( ~ (v7 = v6) & ~ (v7 = sz10) & sdtasdt0(v7, v8) = v6 & doDivides0(v7, v6) & aNaturalNumber0(v8) & aNaturalNumber0(v7))) & ! [v6] : (v6 = sz10 | v6 = sz00 | ~ aNaturalNumber0(v6) | isPrime0(v6) | ? [v7] : ( ~ (v7 = v6) & ~ (v7 = sz10) & doDivides0(v7, v6) & aNaturalNumber0(v7))) & ! [v6] : (v6 = sz10 | v6 = sz00 | ~ aNaturalNumber0(v6) | sdtlseqdt0(sz10, v6)) & ! [v6] : (v6 = sz10 | v6 = sz00 | ~ aNaturalNumber0(v6) | ? [v7] : (isPrime0(v7) & doDivides0(v7, v6) & aNaturalNumber0(v7))) & ! [v6] : ( ~ (sdtpldt0(xp, v6) = xm) | ~ aNaturalNumber0(v6)) & ! [v6] : ( ~ (sdtpldt0(xp, v6) = xn) | ~ aNaturalNumber0(v6)) & ! [v6] : ( ~ isPrime0(v6) | ~ doDivides0(v6, xk) | ~ aNaturalNumber0(v6)) & ! [v6] : ( ~ aNaturalNumber0(v6) | sdtlseqdt0(v6, v6)))
% 9.80/2.89 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 9.80/2.89 | (1) ~ (xk = sz10) & ~ (xk = sz00) & ~ (xp = xm) & ~ (xp = xn) & ~ (xp = sz10) & ~ (xp = sz00) & ~ (sz10 = sz00) & sdtsldt0(all_0_3_3, xp) = xk & sdtasdt0(xp, all_0_0_0) = all_0_3_3 & sdtasdt0(xp, xk) = all_0_3_3 & sdtasdt0(xn, xm) = all_0_3_3 & sdtpldt0(all_0_5_5, xp) = all_0_4_4 & sdtpldt0(xm, all_0_2_2) = xp & sdtpldt0(xn, all_0_1_1) = xp & sdtpldt0(xn, xm) = all_0_5_5 & isPrime0(xp) & doDivides0(xp, all_0_3_3) & sdtlseqdt0(xm, xp) & sdtlseqdt0(xn, xp) & aNaturalNumber0(all_0_0_0) & aNaturalNumber0(all_0_1_1) & aNaturalNumber0(all_0_2_2) & aNaturalNumber0(xk) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ isPrime0(sz10) & ~ isPrime0(sz00) & ~ sdtlseqdt0(xp, xm) & ~ sdtlseqdt0(xp, xn) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v3, v2) = v5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtlseqdt0(v6, v4) & sdtlseqdt0(v3, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v3) & sdtlseqdt0(v4, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtlseqdt0(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v0, v2) = v6 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v2) = v4) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtsldt0(v5, v0) = v4 & sdtasdt0(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v6, v7) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) | ? [v5] : (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v6] : ( ~ (sdtasdt0(v2, v6) = v5) | ~ aNaturalNumber0(v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5] : ? [v6] : ((v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ((v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ((v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v1) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v4, v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v0) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v1) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v1, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v0, v2) = v6 & sdtlseqdt0(v6, v3) & sdtlseqdt0(v4, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1)) & ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0] : ! [v1] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1) = xp) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & ~ (v2 = v0) & ~ (v2 = sz10) & sdtasdt0(v2, v3) = v0 & doDivides0(v2, v0) & aNaturalNumber0(v3) & aNaturalNumber0(v2)) | ( ~ (v2 = xk) & sdtasdt0(v0, v1) = v2))) & ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0) & ! [v0] : ! [v1] : ( ~ isPrime0(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : ( ~ (v2 = xk) & sdtasdt0(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2))) & ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2))) & ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) & ! [v0] : (v0 = xp | v0 = sz10 | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0)) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ doDivides0(v0, xk) | ~ aNaturalNumber0(v0) | ? [v1] : ? [v2] : ( ~ (v1 = v0) & ~ (v1 = sz10) & sdtasdt0(v1, v2) = v0 & doDivides0(v1, v0) & aNaturalNumber0(v2) & aNaturalNumber0(v1))) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1] : ( ~ (v1 = v0) & ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1))) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1))) & ! [v0] : ( ~ (sdtpldt0(xp, v0) = xm) | ~ aNaturalNumber0(v0)) & ! [v0] : ( ~ (sdtpldt0(xp, v0) = xn) | ~ aNaturalNumber0(v0)) & ! [v0] : ( ~ isPrime0(v0) | ~ doDivides0(v0, xk) | ~ aNaturalNumber0(v0)) & ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 10.13/2.92 |
% 10.13/2.92 | Applying alpha-rule on (1) yields:
% 10.13/2.92 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.13/2.92 | (3) sdtpldt0(xm, all_0_2_2) = xp
% 10.13/2.92 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.13/2.92 | (5) ~ (xk = sz10)
% 10.13/2.92 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3))
% 10.13/2.92 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6))
% 10.13/2.92 | (8) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 10.13/2.92 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) | ? [v5] : (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v6] : ( ~ (sdtasdt0(v2, v6) = v5) | ~ aNaturalNumber0(v6))))
% 10.13/2.92 | (10) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00)
% 10.13/2.92 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5))
% 10.13/2.92 | (12) ! [v0] : (v0 = xp | v0 = sz10 | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0))
% 10.13/2.92 | (13) ! [v0] : ( ~ (sdtpldt0(xp, v0) = xn) | ~ aNaturalNumber0(v0))
% 10.13/2.93 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 10.13/2.93 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4))
% 10.13/2.93 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.13/2.93 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 10.13/2.93 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 10.13/2.93 | (19) ! [v0] : ! [v1] : ( ~ isPrime0(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : ( ~ (v2 = xk) & sdtasdt0(v0, v1) = v2))
% 10.13/2.93 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.13/2.93 | (21) sdtlseqdt0(xn, xp)
% 10.13/2.93 | (22) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.13/2.93 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5))
% 10.13/2.93 | (24) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0)
% 10.13/2.93 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8)))))
% 10.13/2.93 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2)
% 10.13/2.93 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v3) & sdtlseqdt0(v4, v6)))
% 10.13/2.93 | (28) sdtpldt0(xn, xm) = all_0_5_5
% 10.13/2.93 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v6)))
% 10.13/2.93 | (30) ~ (xp = xm)
% 10.13/2.93 | (31) ~ (xp = sz10)
% 10.13/2.93 | (32) ! [v0] : ! [v1] : (v1 = sz00 | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 10.13/2.93 | (33) aNaturalNumber0(xp)
% 10.13/2.93 | (34) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 10.13/2.93 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v0) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v1) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v3, v4)))
% 10.13/2.93 | (36) isPrime0(xp)
% 10.13/2.93 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ((v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7)))))
% 10.13/2.93 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.13/2.93 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5))
% 10.13/2.93 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v6, v7) = v5))
% 10.13/2.93 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 10.13/2.93 | (42) aNaturalNumber0(all_0_2_2)
% 10.13/2.93 | (43) aNaturalNumber0(xk)
% 10.13/2.93 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v1) = v5))
% 10.13/2.93 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 10.13/2.93 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5] : ? [v6] : ((v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7)))))
% 10.13/2.93 | (47) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ doDivides0(v0, xk) | ~ aNaturalNumber0(v0) | ? [v1] : ? [v2] : ( ~ (v1 = v0) & ~ (v1 = sz10) & sdtasdt0(v1, v2) = v0 & doDivides0(v1, v0) & aNaturalNumber0(v2) & aNaturalNumber0(v1)))
% 10.13/2.94 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.13/2.94 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v0, v2) = v6 & sdtpldt0(v0, v1) = v5))
% 10.13/2.94 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6))
% 10.13/2.94 | (51) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 10.13/2.94 | (52) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 10.13/2.94 | (53) ~ (xp = sz00)
% 10.13/2.94 | (54) ! [v0] : ! [v1] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1) = xp) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.13/2.94 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5))
% 10.13/2.94 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.13/2.94 | (57) aNaturalNumber0(all_0_0_0)
% 10.13/2.94 | (58) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.13/2.94 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.13/2.94 | (60) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0))
% 10.13/2.94 | (61) sdtasdt0(xp, all_0_0_0) = all_0_3_3
% 10.13/2.94 | (62) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 10.13/2.94 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 10.13/2.94 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ((v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7)))))
% 10.13/2.94 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4))
% 10.13/2.94 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6)))
% 10.13/2.94 | (67) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.13/2.94 | (68) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 10.13/2.94 | (69) ~ isPrime0(sz00)
% 10.13/2.94 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 10.13/2.94 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2)
% 10.13/2.94 | (72) aNaturalNumber0(sz10)
% 10.13/2.94 | (73) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0))
% 10.13/2.94 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v1, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v0, v2) = v6 & sdtlseqdt0(v6, v3) & sdtlseqdt0(v4, v5)))
% 10.13/2.94 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5))
% 10.13/2.94 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5))
% 10.13/2.94 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8)))))
% 10.13/2.94 | (78) sdtsldt0(all_0_3_3, xp) = xk
% 10.13/2.94 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v3, v2) = v5)
% 10.13/2.94 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtlseqdt0(v6, v4) & sdtlseqdt0(v3, v5)))
% 10.13/2.94 | (81) doDivides0(xp, all_0_3_3)
% 10.13/2.94 | (82) sdtasdt0(xn, xm) = all_0_3_3
% 10.13/2.94 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4))
% 10.13/2.94 | (84) ~ isPrime0(sz10)
% 10.13/2.94 | (85) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 10.13/2.95 | (86) ~ (xk = sz00)
% 10.13/2.95 | (87) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 10.13/2.95 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.13/2.95 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.13/2.95 | (90) ~ sdtlseqdt0(xp, xm)
% 10.13/2.95 | (91) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.13/2.95 | (92) sdtpldt0(xn, all_0_1_1) = xp
% 10.13/2.95 | (93) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1] : ( ~ (v1 = v0) & ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 10.13/2.95 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.13/2.95 | (95) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 10.13/2.95 | (96) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 10.13/2.95 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.13/2.95 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.13/2.95 | (99) ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 10.13/2.95 | (100) ~ (sz10 = sz00)
% 10.13/2.95 | (101) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 10.13/2.95 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8)))))
% 10.13/2.95 | (103) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 10.13/2.95 | (104) ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 10.13/2.95 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtlseqdt0(v5, v6)))
% 10.13/2.95 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8)))))
% 10.13/2.95 | (107) sdtasdt0(xp, xk) = all_0_3_3
% 10.13/2.95 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.13/2.95 | (109) sdtpldt0(all_0_5_5, xp) = all_0_4_4
% 10.13/2.95 | (110) ~ sdtlseqdt0(xp, xn)
% 10.13/2.95 | (111) ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 10.13/2.95 | (112) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 10.13/2.95 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4))
% 10.13/2.95 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v2) = v4) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtsldt0(v5, v0) = v4 & sdtasdt0(v3, v1) = v5))
% 10.13/2.95 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5))
% 10.13/2.95 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v1) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v4, v3)))
% 10.13/2.95 | (117) ! [v0] : ( ~ isPrime0(v0) | ~ doDivides0(v0, xk) | ~ aNaturalNumber0(v0))
% 10.13/2.95 | (118) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0)
% 10.13/2.95 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 10.13/2.95 | (120) aNaturalNumber0(xm)
% 10.13/2.95 | (121) aNaturalNumber0(sz00)
% 10.13/2.95 | (122) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 10.13/2.95 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.13/2.95 | (124) aNaturalNumber0(xn)
% 10.13/2.95 | (125) aNaturalNumber0(all_0_1_1)
% 10.13/2.95 | (126) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 10.13/2.96 | (127) ~ (xp = xn)
% 10.13/2.96 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4))
% 10.13/2.96 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5))
% 10.13/2.96 | (130) ! [v0] : ! [v1] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & ~ (v2 = v0) & ~ (v2 = sz10) & sdtasdt0(v2, v3) = v0 & doDivides0(v2, v0) & aNaturalNumber0(v3) & aNaturalNumber0(v2)) | ( ~ (v2 = xk) & sdtasdt0(v0, v1) = v2)))
% 10.13/2.96 | (131) ! [v0] : ( ~ (sdtpldt0(xp, v0) = xm) | ~ aNaturalNumber0(v0))
% 10.13/2.96 | (132) sdtlseqdt0(xm, xp)
% 10.13/2.96 |
% 10.13/2.96 | Instantiating formula (4) with all_0_3_3, all_0_0_0, xk, xp and discharging atoms sdtasdt0(xp, all_0_0_0) = all_0_3_3, sdtasdt0(xp, xk) = all_0_3_3, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xk), aNaturalNumber0(xp), yields:
% 10.13/2.96 | (133) all_0_0_0 = xk | xp = sz00
% 10.13/2.96 |
% 10.13/2.96 | Instantiating formula (126) with all_0_0_0 and discharging atoms aNaturalNumber0(all_0_0_0), yields:
% 10.13/2.96 | (134) all_0_0_0 = sz10 | all_0_0_0 = sz00 | ? [v0] : (isPrime0(v0) & doDivides0(v0, all_0_0_0) & aNaturalNumber0(v0))
% 10.13/2.96 |
% 10.13/2.96 | Instantiating formula (130) with all_0_1_1, all_0_0_0 and discharging atoms aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_1_1), yields:
% 10.13/2.96 | (135) all_0_0_0 = sz10 | all_0_0_0 = sz00 | ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_0_0 & ~ (v0 = all_0_0_0) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = all_0_0_0 & doDivides0(v0, all_0_0_0) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(all_0_0_0, all_0_1_1) = v0))
% 10.13/2.96 |
% 10.13/2.96 | Instantiating formula (130) with all_0_2_2, all_0_0_0 and discharging atoms aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_2_2), yields:
% 10.13/2.96 | (136) all_0_0_0 = sz10 | all_0_0_0 = sz00 | ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_0_0 & ~ (v0 = all_0_0_0) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = all_0_0_0 & doDivides0(v0, all_0_0_0) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(all_0_0_0, all_0_2_2) = v0))
% 10.13/2.96 |
% 10.13/2.96 | Instantiating formula (130) with xk, all_0_0_0 and discharging atoms aNaturalNumber0(all_0_0_0), aNaturalNumber0(xk), yields:
% 10.13/2.96 | (137) all_0_0_0 = sz10 | all_0_0_0 = sz00 | ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_0_0 & ~ (v0 = all_0_0_0) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = all_0_0_0 & doDivides0(v0, all_0_0_0) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(all_0_0_0, xk) = v0))
% 10.13/2.96 |
% 10.13/2.96 | Instantiating formula (130) with all_0_0_0, xk and discharging atoms aNaturalNumber0(all_0_0_0), aNaturalNumber0(xk), yields:
% 10.13/2.96 | (138) xk = sz10 | xk = sz00 | ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & ~ (v0 = xk) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = xk & doDivides0(v0, xk) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(xk, all_0_0_0) = v0))
% 10.13/2.96 |
% 10.13/2.96 | Instantiating formula (130) with all_0_1_1, xk and discharging atoms aNaturalNumber0(all_0_1_1), aNaturalNumber0(xk), yields:
% 10.13/2.96 | (139) xk = sz10 | xk = sz00 | ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & ~ (v0 = xk) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = xk & doDivides0(v0, xk) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(xk, all_0_1_1) = v0))
% 10.13/2.96 |
% 10.13/2.96 | Instantiating formula (130) with xp, xk and discharging atoms aNaturalNumber0(xk), aNaturalNumber0(xp), yields:
% 10.13/2.96 | (140) xk = sz10 | xk = sz00 | ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & ~ (v0 = xk) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = xk & doDivides0(v0, xk) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(xk, xp) = v0))
% 10.13/2.96 |
% 10.13/2.96 | Instantiating formula (130) with xm, xk and discharging atoms aNaturalNumber0(xk), aNaturalNumber0(xm), yields:
% 10.13/2.96 | (141) xk = sz10 | xk = sz00 | ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & ~ (v0 = xk) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = xk & doDivides0(v0, xk) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(xk, xm) = v0))
% 10.13/2.96 |
% 10.13/2.96 | Instantiating formula (130) with xn, xk and discharging atoms aNaturalNumber0(xk), aNaturalNumber0(xn), yields:
% 10.13/2.96 | (142) xk = sz10 | xk = sz00 | ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & ~ (v0 = xk) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = xk & doDivides0(v0, xk) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(xk, xn) = v0))
% 10.13/2.96 |
% 10.13/2.96 | Instantiating formula (130) with sz10, xk and discharging atoms aNaturalNumber0(xk), aNaturalNumber0(sz10), yields:
% 10.13/2.96 | (143) xk = sz10 | xk = sz00 | ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & ~ (v0 = xk) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = xk & doDivides0(v0, xk) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(xk, sz10) = v0))
% 10.13/2.96 |
% 10.13/2.96 +-Applying beta-rule and splitting (133), into two cases.
% 10.13/2.96 |-Branch one:
% 10.13/2.96 | (144) xp = sz00
% 10.13/2.96 |
% 10.13/2.96 | Equations (144) can reduce 53 to:
% 10.13/2.96 | (145) $false
% 10.13/2.96 |
% 10.13/2.96 |-The branch is then unsatisfiable
% 10.13/2.96 |-Branch two:
% 10.13/2.96 | (53) ~ (xp = sz00)
% 10.13/2.96 | (147) all_0_0_0 = xk
% 10.13/2.96 |
% 10.13/2.96 +-Applying beta-rule and splitting (136), into two cases.
% 10.13/2.96 |-Branch one:
% 10.13/2.96 | (148) all_0_0_0 = sz00
% 10.13/2.96 |
% 10.13/2.96 | Combining equations (148,147) yields a new equation:
% 10.13/2.96 | (149) xk = sz00
% 10.13/2.96 |
% 10.13/2.96 | Equations (149) can reduce 86 to:
% 10.13/2.96 | (145) $false
% 10.13/2.96 |
% 10.13/2.96 |-The branch is then unsatisfiable
% 10.13/2.96 |-Branch two:
% 10.13/2.96 | (151) ~ (all_0_0_0 = sz00)
% 10.13/2.96 | (152) all_0_0_0 = sz10 | ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_0_0 & ~ (v0 = all_0_0_0) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = all_0_0_0 & doDivides0(v0, all_0_0_0) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(all_0_0_0, all_0_2_2) = v0))
% 10.13/2.96 |
% 10.13/2.96 | Equations (147) can reduce 151 to:
% 10.13/2.96 | (86) ~ (xk = sz00)
% 10.13/2.96 |
% 10.13/2.96 +-Applying beta-rule and splitting (142), into two cases.
% 10.13/2.96 |-Branch one:
% 10.13/2.96 | (149) xk = sz00
% 10.13/2.96 |
% 10.13/2.96 | Equations (149) can reduce 86 to:
% 10.13/2.96 | (145) $false
% 10.13/2.96 |
% 10.13/2.96 |-The branch is then unsatisfiable
% 10.13/2.96 |-Branch two:
% 10.13/2.96 | (86) ~ (xk = sz00)
% 10.13/2.96 | (157) xk = sz10 | ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & ~ (v0 = xk) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = xk & doDivides0(v0, xk) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(xk, xn) = v0))
% 10.13/2.97 |
% 10.13/2.97 +-Applying beta-rule and splitting (141), into two cases.
% 10.13/2.97 |-Branch one:
% 10.13/2.97 | (149) xk = sz00
% 10.13/2.97 |
% 10.13/2.97 | Equations (149) can reduce 86 to:
% 10.13/2.97 | (145) $false
% 10.13/2.97 |
% 10.13/2.97 |-The branch is then unsatisfiable
% 10.13/2.97 |-Branch two:
% 10.13/2.97 | (86) ~ (xk = sz00)
% 10.13/2.97 | (161) xk = sz10 | ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & ~ (v0 = xk) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = xk & doDivides0(v0, xk) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(xk, xm) = v0))
% 10.13/2.97 |
% 10.13/2.97 +-Applying beta-rule and splitting (140), into two cases.
% 10.13/2.97 |-Branch one:
% 10.13/2.97 | (149) xk = sz00
% 10.13/2.97 |
% 10.13/2.97 | Equations (149) can reduce 86 to:
% 10.13/2.97 | (145) $false
% 10.13/2.97 |
% 10.13/2.97 |-The branch is then unsatisfiable
% 10.13/2.97 |-Branch two:
% 10.13/2.97 | (86) ~ (xk = sz00)
% 10.13/2.97 | (165) xk = sz10 | ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & ~ (v0 = xk) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = xk & doDivides0(v0, xk) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(xk, xp) = v0))
% 10.13/2.97 |
% 10.13/2.97 +-Applying beta-rule and splitting (139), into two cases.
% 10.13/2.97 |-Branch one:
% 10.13/2.97 | (149) xk = sz00
% 10.13/2.97 |
% 10.13/2.97 | Equations (149) can reduce 86 to:
% 10.13/2.97 | (145) $false
% 10.13/2.97 |
% 10.13/2.97 |-The branch is then unsatisfiable
% 10.13/2.97 |-Branch two:
% 10.13/2.97 | (86) ~ (xk = sz00)
% 10.13/2.97 | (169) xk = sz10 | ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & ~ (v0 = xk) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = xk & doDivides0(v0, xk) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(xk, all_0_1_1) = v0))
% 10.36/2.97 |
% 10.36/2.97 +-Applying beta-rule and splitting (138), into two cases.
% 10.36/2.97 |-Branch one:
% 10.36/2.97 | (149) xk = sz00
% 10.36/2.97 |
% 10.36/2.97 | Equations (149) can reduce 86 to:
% 10.36/2.97 | (145) $false
% 10.36/2.97 |
% 10.36/2.97 |-The branch is then unsatisfiable
% 10.36/2.97 |-Branch two:
% 10.36/2.97 | (86) ~ (xk = sz00)
% 10.36/2.97 | (173) xk = sz10 | ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & ~ (v0 = xk) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = xk & doDivides0(v0, xk) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(xk, all_0_0_0) = v0))
% 10.36/2.97 |
% 10.36/2.97 +-Applying beta-rule and splitting (137), into two cases.
% 10.36/2.97 |-Branch one:
% 10.36/2.97 | (148) all_0_0_0 = sz00
% 10.36/2.97 |
% 10.36/2.97 | Combining equations (148,147) yields a new equation:
% 10.36/2.97 | (149) xk = sz00
% 10.36/2.97 |
% 10.36/2.97 | Equations (149) can reduce 86 to:
% 10.36/2.97 | (145) $false
% 10.36/2.97 |
% 10.36/2.97 |-The branch is then unsatisfiable
% 10.36/2.97 |-Branch two:
% 10.36/2.97 | (151) ~ (all_0_0_0 = sz00)
% 10.36/2.97 | (178) all_0_0_0 = sz10 | ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_0_0 & ~ (v0 = all_0_0_0) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = all_0_0_0 & doDivides0(v0, all_0_0_0) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(all_0_0_0, xk) = v0))
% 10.36/2.97 |
% 10.36/2.97 | Equations (147) can reduce 151 to:
% 10.36/2.97 | (86) ~ (xk = sz00)
% 10.36/2.97 |
% 10.36/2.97 +-Applying beta-rule and splitting (143), into two cases.
% 10.36/2.97 |-Branch one:
% 10.36/2.97 | (149) xk = sz00
% 10.36/2.97 |
% 10.36/2.97 | Equations (149) can reduce 86 to:
% 10.36/2.97 | (145) $false
% 10.36/2.97 |
% 10.36/2.97 |-The branch is then unsatisfiable
% 10.36/2.97 |-Branch two:
% 10.36/2.97 | (86) ~ (xk = sz00)
% 10.36/2.97 | (183) xk = sz10 | ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & ~ (v0 = xk) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = xk & doDivides0(v0, xk) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(xk, sz10) = v0))
% 10.36/2.97 |
% 10.36/2.97 +-Applying beta-rule and splitting (157), into two cases.
% 10.36/2.97 |-Branch one:
% 10.36/2.97 | (184) xk = sz10
% 10.36/2.97 |
% 10.36/2.97 | Equations (184) can reduce 5 to:
% 10.36/2.97 | (145) $false
% 10.36/2.97 |
% 10.36/2.97 |-The branch is then unsatisfiable
% 10.36/2.97 |-Branch two:
% 10.36/2.97 | (5) ~ (xk = sz10)
% 10.36/2.97 | (187) ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & ~ (v0 = xk) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = xk & doDivides0(v0, xk) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(xk, xn) = v0))
% 10.36/2.97 |
% 10.36/2.97 +-Applying beta-rule and splitting (135), into two cases.
% 10.36/2.97 |-Branch one:
% 10.36/2.97 | (148) all_0_0_0 = sz00
% 10.36/2.97 |
% 10.36/2.97 | Combining equations (148,147) yields a new equation:
% 10.36/2.97 | (149) xk = sz00
% 10.36/2.97 |
% 10.36/2.97 | Equations (149) can reduce 86 to:
% 10.36/2.97 | (145) $false
% 10.36/2.97 |
% 10.36/2.97 |-The branch is then unsatisfiable
% 10.36/2.97 |-Branch two:
% 10.36/2.97 | (151) ~ (all_0_0_0 = sz00)
% 10.36/2.97 | (192) all_0_0_0 = sz10 | ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_0_0 & ~ (v0 = all_0_0_0) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = all_0_0_0 & doDivides0(v0, all_0_0_0) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(all_0_0_0, all_0_1_1) = v0))
% 10.36/2.97 |
% 10.36/2.97 | Equations (147) can reduce 151 to:
% 10.36/2.97 | (86) ~ (xk = sz00)
% 10.36/2.97 |
% 10.36/2.97 +-Applying beta-rule and splitting (134), into two cases.
% 10.36/2.97 |-Branch one:
% 10.36/2.97 | (148) all_0_0_0 = sz00
% 10.36/2.97 |
% 10.36/2.97 | Combining equations (148,147) yields a new equation:
% 10.36/2.97 | (149) xk = sz00
% 10.36/2.97 |
% 10.36/2.97 | Equations (149) can reduce 86 to:
% 10.36/2.97 | (145) $false
% 10.36/2.97 |
% 10.36/2.97 |-The branch is then unsatisfiable
% 10.36/2.97 |-Branch two:
% 10.36/2.97 | (151) ~ (all_0_0_0 = sz00)
% 10.36/2.97 | (198) all_0_0_0 = sz10 | ? [v0] : (isPrime0(v0) & doDivides0(v0, all_0_0_0) & aNaturalNumber0(v0))
% 10.36/2.97 |
% 10.36/2.97 +-Applying beta-rule and splitting (165), into two cases.
% 10.36/2.97 |-Branch one:
% 10.36/2.97 | (184) xk = sz10
% 10.36/2.97 |
% 10.36/2.97 | Equations (184) can reduce 5 to:
% 10.36/2.97 | (145) $false
% 10.36/2.97 |
% 10.36/2.97 |-The branch is then unsatisfiable
% 10.36/2.97 |-Branch two:
% 10.36/2.97 | (5) ~ (xk = sz10)
% 10.36/2.97 | (202) ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & ~ (v0 = xk) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = xk & doDivides0(v0, xk) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(xk, xp) = v0))
% 10.36/2.97 |
% 10.36/2.97 +-Applying beta-rule and splitting (169), into two cases.
% 10.36/2.97 |-Branch one:
% 10.36/2.97 | (184) xk = sz10
% 10.36/2.97 |
% 10.36/2.97 | Equations (184) can reduce 5 to:
% 10.36/2.97 | (145) $false
% 10.36/2.97 |
% 10.36/2.97 |-The branch is then unsatisfiable
% 10.36/2.97 |-Branch two:
% 10.36/2.97 | (5) ~ (xk = sz10)
% 10.36/2.97 | (206) ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & ~ (v0 = xk) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = xk & doDivides0(v0, xk) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(xk, all_0_1_1) = v0))
% 10.36/2.97 |
% 10.36/2.97 +-Applying beta-rule and splitting (183), into two cases.
% 10.36/2.97 |-Branch one:
% 10.36/2.97 | (184) xk = sz10
% 10.36/2.97 |
% 10.36/2.97 | Equations (184) can reduce 5 to:
% 10.36/2.97 | (145) $false
% 10.36/2.97 |
% 10.36/2.97 |-The branch is then unsatisfiable
% 10.36/2.97 |-Branch two:
% 10.36/2.97 | (5) ~ (xk = sz10)
% 10.36/2.97 | (210) ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & ~ (v0 = xk) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = xk & doDivides0(v0, xk) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(xk, sz10) = v0))
% 10.36/2.97 |
% 10.36/2.97 +-Applying beta-rule and splitting (178), into two cases.
% 10.36/2.97 |-Branch one:
% 10.36/2.97 | (211) all_0_0_0 = sz10
% 10.36/2.97 |
% 10.36/2.97 | Combining equations (211,147) yields a new equation:
% 10.36/2.97 | (184) xk = sz10
% 10.36/2.97 |
% 10.36/2.97 | Equations (184) can reduce 5 to:
% 10.36/2.97 | (145) $false
% 10.36/2.97 |
% 10.36/2.97 |-The branch is then unsatisfiable
% 10.36/2.97 |-Branch two:
% 10.36/2.97 | (214) ~ (all_0_0_0 = sz10)
% 10.36/2.97 | (215) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_0_0 & ~ (v0 = all_0_0_0) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = all_0_0_0 & doDivides0(v0, all_0_0_0) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(all_0_0_0, xk) = v0))
% 10.36/2.97 |
% 10.36/2.97 | Equations (147) can reduce 214 to:
% 10.36/2.97 | (5) ~ (xk = sz10)
% 10.36/2.97 |
% 10.36/2.97 +-Applying beta-rule and splitting (152), into two cases.
% 10.36/2.97 |-Branch one:
% 10.36/2.97 | (211) all_0_0_0 = sz10
% 10.36/2.97 |
% 10.36/2.97 | Combining equations (211,147) yields a new equation:
% 10.36/2.97 | (184) xk = sz10
% 10.36/2.97 |
% 10.36/2.97 | Equations (184) can reduce 5 to:
% 10.36/2.97 | (145) $false
% 10.36/2.97 |
% 10.36/2.97 |-The branch is then unsatisfiable
% 10.36/2.97 |-Branch two:
% 10.36/2.97 | (214) ~ (all_0_0_0 = sz10)
% 10.36/2.97 | (221) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_0_0 & ~ (v0 = all_0_0_0) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = all_0_0_0 & doDivides0(v0, all_0_0_0) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(all_0_0_0, all_0_2_2) = v0))
% 10.36/2.97 |
% 10.36/2.97 | Equations (147) can reduce 214 to:
% 10.36/2.97 | (5) ~ (xk = sz10)
% 10.36/2.97 |
% 10.36/2.97 +-Applying beta-rule and splitting (161), into two cases.
% 10.36/2.97 |-Branch one:
% 10.36/2.98 | (184) xk = sz10
% 10.36/2.98 |
% 10.36/2.98 | Equations (184) can reduce 5 to:
% 10.36/2.98 | (145) $false
% 10.36/2.98 |
% 10.36/2.98 |-The branch is then unsatisfiable
% 10.36/2.98 |-Branch two:
% 10.36/2.98 | (5) ~ (xk = sz10)
% 10.36/2.98 | (226) ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & ~ (v0 = xk) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = xk & doDivides0(v0, xk) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(xk, xm) = v0))
% 10.36/2.98 |
% 10.36/2.98 +-Applying beta-rule and splitting (173), into two cases.
% 10.36/2.98 |-Branch one:
% 10.36/2.98 | (184) xk = sz10
% 10.36/2.98 |
% 10.36/2.98 | Equations (184) can reduce 5 to:
% 10.36/2.98 | (145) $false
% 10.36/2.98 |
% 10.36/2.98 |-The branch is then unsatisfiable
% 10.36/2.98 |-Branch two:
% 10.36/2.98 | (5) ~ (xk = sz10)
% 10.36/2.98 | (230) ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & ~ (v0 = xk) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = xk & doDivides0(v0, xk) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(xk, all_0_0_0) = v0))
% 10.36/2.98 |
% 10.36/2.98 +-Applying beta-rule and splitting (192), into two cases.
% 10.36/2.98 |-Branch one:
% 10.36/2.98 | (211) all_0_0_0 = sz10
% 10.36/2.98 |
% 10.36/2.98 | Combining equations (211,147) yields a new equation:
% 10.36/2.98 | (184) xk = sz10
% 10.36/2.98 |
% 10.36/2.98 | Equations (184) can reduce 5 to:
% 10.36/2.98 | (145) $false
% 10.36/2.98 |
% 10.36/2.98 |-The branch is then unsatisfiable
% 10.36/2.98 |-Branch two:
% 10.36/2.98 | (214) ~ (all_0_0_0 = sz10)
% 10.36/2.98 | (235) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_0_0 & ~ (v0 = all_0_0_0) & ~ (v0 = sz10) & sdtasdt0(v0, v1) = all_0_0_0 & doDivides0(v0, all_0_0_0) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) | ( ~ (v0 = xk) & sdtasdt0(all_0_0_0, all_0_1_1) = v0))
% 10.36/2.98 |
% 10.36/2.98 | Equations (147) can reduce 214 to:
% 10.36/2.98 | (5) ~ (xk = sz10)
% 10.36/2.98 |
% 10.36/2.98 +-Applying beta-rule and splitting (198), into two cases.
% 10.36/2.98 |-Branch one:
% 10.36/2.98 | (211) all_0_0_0 = sz10
% 10.36/2.98 |
% 10.36/2.98 | Combining equations (211,147) yields a new equation:
% 10.36/2.98 | (184) xk = sz10
% 10.36/2.98 |
% 10.36/2.98 | Equations (184) can reduce 5 to:
% 10.36/2.98 | (145) $false
% 10.36/2.98 |
% 10.36/2.98 |-The branch is then unsatisfiable
% 10.36/2.98 |-Branch two:
% 10.36/2.98 | (214) ~ (all_0_0_0 = sz10)
% 10.36/2.98 | (241) ? [v0] : (isPrime0(v0) & doDivides0(v0, all_0_0_0) & aNaturalNumber0(v0))
% 10.36/2.98 |
% 10.36/2.98 | Instantiating (241) with all_227_0_86 yields:
% 10.36/2.98 | (242) isPrime0(all_227_0_86) & doDivides0(all_227_0_86, all_0_0_0) & aNaturalNumber0(all_227_0_86)
% 10.36/2.98 |
% 10.36/2.98 | Applying alpha-rule on (242) yields:
% 10.36/2.98 | (243) isPrime0(all_227_0_86)
% 10.36/2.98 | (244) doDivides0(all_227_0_86, all_0_0_0)
% 10.36/2.98 | (245) aNaturalNumber0(all_227_0_86)
% 10.36/2.98 |
% 10.36/2.98 | From (147) and (244) follows:
% 10.36/2.98 | (246) doDivides0(all_227_0_86, xk)
% 10.36/2.98 |
% 10.36/2.98 | Instantiating formula (117) with all_227_0_86 and discharging atoms isPrime0(all_227_0_86), doDivides0(all_227_0_86, xk), aNaturalNumber0(all_227_0_86), yields:
% 10.36/2.98 | (247) $false
% 10.36/2.98 |
% 10.36/2.98 |-The branch is then unsatisfiable
% 10.36/2.98 % SZS output end Proof for theBenchmark
% 10.36/2.98
% 10.36/2.98 2385ms
%------------------------------------------------------------------------------