TSTP Solution File: NUM524+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM524+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 08:45:28 EDT 2022
% Result : Theorem 6.26s 2.09s
% Output : Proof 10.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM524+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 : Tue Jul 5 21:30:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.49/0.57 ____ _
% 0.49/0.57 ___ / __ \_____(_)___ ________ __________
% 0.49/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.57
% 0.49/0.57 A Theorem Prover for First-Order Logic
% 0.49/0.57 (ePrincess v.1.0)
% 0.49/0.57
% 0.49/0.57 (c) Philipp Rümmer, 2009-2015
% 0.49/0.57 (c) Peter Backeman, 2014-2015
% 0.49/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.57 Bug reports to peter@backeman.se
% 0.49/0.57
% 0.49/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.57
% 0.49/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.49/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.90/1.03 Prover 0: Preprocessing ...
% 3.60/1.52 Prover 0: Constructing countermodel ...
% 6.26/2.09 Prover 0: proved (1465ms)
% 6.26/2.09
% 6.26/2.09 No countermodel exists, formula is valid
% 6.26/2.09 % SZS status Theorem for theBenchmark
% 6.26/2.09
% 6.26/2.09 Generating proof ... found it (size 85)
% 10.35/3.00
% 10.35/3.00 % SZS output start Proof for theBenchmark
% 10.35/3.00 Assumed formulas after preprocessing and simplification:
% 10.35/3.00 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v3 = v0) & ~ (xp = sz10) & ~ (xp = sz00) & ~ (xm = sz00) & ~ (xn = sz00) & ~ (sz10 = sz00) & sdtsldt0(xn, xp) = xq & sdtasdt0(xq, xq) = v2 & sdtasdt0(xp, v5) = v1 & sdtasdt0(xp, v4) = xn & sdtasdt0(xp, v2) = v3 & sdtasdt0(xp, v0) = v1 & sdtasdt0(xp, xq) = xn & sdtasdt0(xm, xm) = v0 & sdtasdt0(xn, xn) = v1 & isPrime0(xp) & doDivides0(xp, v1) & doDivides0(xp, xn) & aNaturalNumber0(v5) & aNaturalNumber0(v4) & aNaturalNumber0(xq) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ isPrime0(sz10) & ~ isPrime0(sz00) & ! [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 | v7 = sz00 | v6 = sz00 | ~ (sdtasdt0(v8, v9) = v10) | ~ (sdtasdt0(v7, v7) = v9) | ~ (sdtasdt0(v6, v6) = v10) | ~ iLess0(v6, xn) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v11 = v8) & ~ (v11 = sz10) & sdtasdt0(v11, v12) = v8 & doDivides0(v11, v8) & aNaturalNumber0(v12) & aNaturalNumber0(v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = sz00 | v7 = sz00 | v6 = sz00 | ~ (sdtasdt0(v8, v9) = v10) | ~ (sdtasdt0(v7, v7) = v9) | ~ (sdtasdt0(v6, v6) = v10) | ~ isPrime0(v8) | ~ iLess0(v6, xn) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [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) | ~ 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] : ( ~ (sdtasdt0(v6, v7) = v9) | ~ isPrime0(v8) | ~ doDivides0(v8, v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v8, v7) | doDivides0(v8, v6)) & ! [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 = 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] : ( ~ 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 | ~ 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] : ( ~ aNaturalNumber0(v6) | sdtlseqdt0(v6, v6)))
% 10.35/3.06 | 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:
% 10.35/3.06 | (1) ~ (all_0_2_2 = all_0_5_5) & ~ (xp = sz10) & ~ (xp = sz00) & ~ (xm = sz00) & ~ (xn = sz00) & ~ (sz10 = sz00) & sdtsldt0(xn, xp) = xq & sdtasdt0(xq, xq) = all_0_3_3 & sdtasdt0(xp, all_0_0_0) = all_0_4_4 & sdtasdt0(xp, all_0_1_1) = xn & sdtasdt0(xp, all_0_3_3) = all_0_2_2 & sdtasdt0(xp, all_0_5_5) = all_0_4_4 & sdtasdt0(xp, xq) = xn & sdtasdt0(xm, xm) = all_0_5_5 & sdtasdt0(xn, xn) = all_0_4_4 & isPrime0(xp) & doDivides0(xp, all_0_4_4) & doDivides0(xp, xn) & aNaturalNumber0(all_0_0_0) & aNaturalNumber0(all_0_1_1) & aNaturalNumber0(xq) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ isPrime0(sz10) & ~ isPrime0(sz00) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v3, v2) = v5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(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 | v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v2, v3) = v4) | ~ (sdtasdt0(v1, v1) = v3) | ~ (sdtasdt0(v0, v0) = v4) | ~ iLess0(v0, xn) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz00 | v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v2, v3) = v4) | ~ (sdtasdt0(v1, v1) = v3) | ~ (sdtasdt0(v0, v0) = v4) | ~ isPrime0(v2) | ~ iLess0(v0, xn) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [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) | ~ 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] : ( ~ (sdtasdt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ doDivides0(v2, v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0)) & ! [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 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0) & ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2))) & ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2))) & ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) & ! [v0] : (v0 = xp | v0 = sz10 | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0)) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1] : ( ~ (v1 = v0) & ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1))) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1))) & ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 10.76/3.08 |
% 10.76/3.08 | Applying alpha-rule on (1) yields:
% 10.76/3.08 | (2) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 10.76/3.08 | (3) sdtsldt0(xn, xp) = xq
% 10.76/3.08 | (4) ! [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))
% 10.76/3.09 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.76/3.09 | (6) ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 10.76/3.09 | (7) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1] : ( ~ (v1 = v0) & ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 10.76/3.09 | (8) sdtasdt0(xm, xm) = all_0_5_5
% 10.76/3.09 | (9) aNaturalNumber0(xq)
% 10.76/3.09 | (10) isPrime0(xp)
% 10.76/3.09 | (11) ! [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)))
% 10.76/3.09 | (12) ! [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))
% 10.76/3.09 | (13) ! [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)))
% 10.76/3.09 | (14) ! [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))
% 10.76/3.09 | (15) ~ (xn = sz00)
% 10.76/3.09 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.76/3.09 | (17) ~ isPrime0(sz10)
% 10.76/3.09 | (18) aNaturalNumber0(sz00)
% 10.76/3.09 | (19) ~ (xp = sz10)
% 10.76/3.09 | (20) aNaturalNumber0(all_0_0_0)
% 10.76/3.09 | (21) ! [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))
% 10.76/3.09 | (22) ! [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)))
% 10.76/3.09 | (23) ! [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)))
% 10.76/3.09 | (24) ~ (sz10 = sz00)
% 10.76/3.09 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.76/3.09 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 10.76/3.09 | (27) ! [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))
% 10.76/3.09 | (28) ! [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))
% 10.76/3.09 | (29) sdtasdt0(xn, xn) = all_0_4_4
% 10.76/3.09 | (30) aNaturalNumber0(all_0_1_1)
% 10.76/3.09 | (31) ! [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))
% 10.76/3.09 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 10.76/3.09 | (33) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 10.76/3.09 | (34) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.76/3.09 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 10.76/3.09 | (36) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0))
% 10.76/3.09 | (37) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 10.76/3.09 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v2, v3) = v4) | ~ (sdtasdt0(v1, v1) = v3) | ~ (sdtasdt0(v0, v0) = v4) | ~ iLess0(v0, xn) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)))
% 10.76/3.10 | (39) ! [v0] : ! [v1] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1) = xp) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.76/3.10 | (40) ! [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))
% 10.76/3.10 | (41) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00)
% 10.76/3.10 | (42) ! [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))
% 10.76/3.10 | (43) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 10.76/3.10 | (44) ! [v0] : ! [v1] : (v1 = sz00 | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 10.76/3.10 | (45) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 10.76/3.10 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz00 | v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v2, v3) = v4) | ~ (sdtasdt0(v1, v1) = v3) | ~ (sdtasdt0(v0, v0) = v4) | ~ isPrime0(v2) | ~ iLess0(v0, xn) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.76/3.10 | (47) ! [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))
% 10.76/3.10 | (48) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.76/3.10 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 10.76/3.10 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2)
% 10.76/3.10 | (51) ! [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)))
% 10.76/3.10 | (52) doDivides0(xp, xn)
% 10.76/3.10 | (53) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 10.76/3.10 | (54) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0)
% 10.76/3.10 | (55) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.76/3.10 | (56) ! [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))
% 10.76/3.10 | (57) aNaturalNumber0(xn)
% 10.76/3.10 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 10.76/3.10 | (59) ! [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)))
% 10.76/3.10 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.76/3.10 | (61) ~ (xm = sz00)
% 10.76/3.10 | (62) aNaturalNumber0(sz10)
% 10.76/3.10 | (63) ! [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))
% 10.76/3.10 | (64) ! [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)
% 10.76/3.10 | (65) sdtasdt0(xp, all_0_0_0) = all_0_4_4
% 10.76/3.10 | (66) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 10.76/3.10 | (67) ! [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))
% 10.76/3.10 | (68) sdtasdt0(xp, xq) = xn
% 10.76/3.10 | (69) ! [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))
% 10.76/3.10 | (70) ~ (all_0_2_2 = all_0_5_5)
% 10.76/3.10 | (71) ! [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))
% 10.76/3.10 | (72) aNaturalNumber0(xp)
% 10.76/3.10 | (73) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0))
% 10.76/3.10 | (74) sdtasdt0(xp, all_0_5_5) = all_0_4_4
% 10.76/3.10 | (75) aNaturalNumber0(xm)
% 10.76/3.10 | (76) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 10.76/3.11 | (77) ! [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))
% 10.76/3.11 | (78) ! [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))
% 10.76/3.11 | (79) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 10.76/3.11 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 10.76/3.11 | (81) ! [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))
% 10.76/3.11 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.76/3.11 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2)
% 10.76/3.11 | (84) sdtasdt0(xp, all_0_3_3) = all_0_2_2
% 10.76/3.11 | (85) doDivides0(xp, all_0_4_4)
% 10.76/3.11 | (86) ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 10.76/3.11 | (87) ! [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))
% 10.76/3.11 | (88) ! [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))
% 10.76/3.11 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 10.76/3.11 | (90) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 10.76/3.11 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.76/3.11 | (92) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 10.76/3.11 | (93) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.76/3.11 | (94) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.76/3.11 | (95) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 10.76/3.11 | (96) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 10.76/3.11 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.76/3.11 | (98) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 10.76/3.11 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3))
% 10.76/3.11 | (100) sdtasdt0(xp, all_0_1_1) = xn
% 10.76/3.11 | (101) ! [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))
% 10.76/3.11 | (102) ! [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)))
% 10.76/3.11 | (103) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 10.76/3.11 | (104) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 10.76/3.11 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.76/3.11 | (106) ! [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)))
% 10.76/3.11 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasdt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ doDivides0(v2, v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0))
% 10.76/3.11 | (108) ~ (xp = sz00)
% 10.76/3.11 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.76/3.11 | (110) ! [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))
% 10.76/3.11 | (111) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.76/3.11 | (112) ~ isPrime0(sz00)
% 10.76/3.12 | (113) ! [v0] : (v0 = xp | v0 = sz10 | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0))
% 10.76/3.12 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 10.76/3.12 | (115) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.76/3.12 | (116) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0)
% 10.76/3.12 | (117) sdtasdt0(xq, xq) = all_0_3_3
% 10.76/3.12 |
% 10.76/3.12 | Instantiating formula (40) with all_0_1_1, xq, xn, xp and discharging atoms sdtsldt0(xn, xp) = xq, sdtasdt0(xp, all_0_1_1) = xn, doDivides0(xp, xn), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 10.76/3.12 | (118) all_0_1_1 = xq | xp = sz00
% 10.76/3.12 |
% 10.76/3.12 | Instantiating formula (71) with all_0_2_2, all_0_3_3, xq, xq, xp and discharging atoms sdtasdt0(xq, xq) = all_0_3_3, sdtasdt0(xp, all_0_3_3) = all_0_2_2, aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 10.76/3.12 | (119) ? [v0] : (sdtasdt0(v0, xq) = all_0_2_2 & sdtasdt0(xp, xq) = v0)
% 10.76/3.12 |
% 10.76/3.12 | Instantiating formula (50) with xn, xp, all_0_1_1 and discharging atoms sdtasdt0(xp, all_0_1_1) = xn, aNaturalNumber0(all_0_1_1), aNaturalNumber0(xp), yields:
% 10.76/3.12 | (120) sdtasdt0(all_0_1_1, xp) = xn
% 10.76/3.12 |
% 10.76/3.12 | Instantiating formula (90) with xp and discharging atoms aNaturalNumber0(xp), yields:
% 10.76/3.12 | (121) xp = sz10 | xp = sz00 | ? [v0] : (isPrime0(v0) & doDivides0(v0, xp) & aNaturalNumber0(v0))
% 10.76/3.12 |
% 10.76/3.12 | Instantiating formula (93) with all_0_5_5, xm, xm and discharging atoms sdtasdt0(xm, xm) = all_0_5_5, aNaturalNumber0(xm), yields:
% 10.76/3.12 | (122) aNaturalNumber0(all_0_5_5)
% 10.76/3.12 |
% 10.76/3.12 | Instantiating formula (12) with all_0_3_3, xq, xq, xn, xp and discharging atoms sdtsldt0(xn, xp) = xq, sdtasdt0(xq, xq) = all_0_3_3, doDivides0(xp, xn), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 10.76/3.12 | (123) xp = sz00 | ? [v0] : (sdtsldt0(v0, xp) = all_0_3_3 & sdtasdt0(xq, xn) = v0)
% 10.76/3.12 |
% 10.76/3.12 | Instantiating formula (12) with xn, xp, xq, xn, xp and discharging atoms sdtsldt0(xn, xp) = xq, sdtasdt0(xp, xq) = xn, doDivides0(xp, xn), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 10.76/3.12 | (124) xp = sz00 | ? [v0] : (sdtsldt0(v0, xp) = xn & sdtasdt0(xp, xn) = v0)
% 10.76/3.12 |
% 10.76/3.12 | Instantiating formula (93) with all_0_4_4, xn, xn and discharging atoms sdtasdt0(xn, xn) = all_0_4_4, aNaturalNumber0(xn), yields:
% 10.76/3.12 | (125) aNaturalNumber0(all_0_4_4)
% 10.76/3.12 |
% 10.76/3.12 | Instantiating formula (81) with all_0_4_4, xn, xn, all_0_1_1, xp and discharging atoms sdtasdt0(xp, all_0_1_1) = xn, sdtasdt0(xn, xn) = all_0_4_4, aNaturalNumber0(all_0_1_1), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 10.76/3.12 | (126) ? [v0] : (sdtasdt0(all_0_1_1, xn) = v0 & sdtasdt0(xp, v0) = all_0_4_4)
% 10.76/3.12 |
% 10.76/3.12 | Instantiating formula (81) with all_0_4_4, xn, xn, xq, xp and discharging atoms sdtasdt0(xp, xq) = xn, sdtasdt0(xn, xn) = all_0_4_4, aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 10.76/3.12 | (127) ? [v0] : (sdtasdt0(xq, xn) = v0 & sdtasdt0(xp, v0) = all_0_4_4)
% 10.76/3.12 |
% 10.76/3.12 | Instantiating formula (6) with xn, xp and discharging atoms doDivides0(xp, xn), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 10.76/3.12 | (128) ? [v0] : (sdtasdt0(xp, v0) = xn & aNaturalNumber0(v0))
% 10.76/3.12 |
% 10.76/3.12 | Instantiating (128) with all_11_0_7 yields:
% 10.76/3.12 | (129) sdtasdt0(xp, all_11_0_7) = xn & aNaturalNumber0(all_11_0_7)
% 10.76/3.12 |
% 10.76/3.12 | Applying alpha-rule on (129) yields:
% 10.76/3.12 | (130) sdtasdt0(xp, all_11_0_7) = xn
% 10.76/3.12 | (131) aNaturalNumber0(all_11_0_7)
% 10.76/3.12 |
% 10.76/3.12 | Instantiating (127) with all_17_0_10 yields:
% 10.76/3.12 | (132) sdtasdt0(xq, xn) = all_17_0_10 & sdtasdt0(xp, all_17_0_10) = all_0_4_4
% 10.76/3.12 |
% 10.76/3.12 | Applying alpha-rule on (132) yields:
% 10.76/3.12 | (133) sdtasdt0(xq, xn) = all_17_0_10
% 10.76/3.12 | (134) sdtasdt0(xp, all_17_0_10) = all_0_4_4
% 10.76/3.12 |
% 10.76/3.12 | Instantiating (126) with all_19_0_11 yields:
% 10.76/3.12 | (135) sdtasdt0(all_0_1_1, xn) = all_19_0_11 & sdtasdt0(xp, all_19_0_11) = all_0_4_4
% 10.76/3.12 |
% 10.76/3.12 | Applying alpha-rule on (135) yields:
% 10.76/3.12 | (136) sdtasdt0(all_0_1_1, xn) = all_19_0_11
% 10.76/3.12 | (137) sdtasdt0(xp, all_19_0_11) = all_0_4_4
% 10.76/3.12 |
% 10.76/3.12 | Instantiating (119) with all_21_0_12 yields:
% 10.76/3.12 | (138) sdtasdt0(all_21_0_12, xq) = all_0_2_2 & sdtasdt0(xp, xq) = all_21_0_12
% 10.76/3.12 |
% 10.76/3.12 | Applying alpha-rule on (138) yields:
% 10.76/3.12 | (139) sdtasdt0(all_21_0_12, xq) = all_0_2_2
% 10.76/3.12 | (140) sdtasdt0(xp, xq) = all_21_0_12
% 10.76/3.12 |
% 10.76/3.12 +-Applying beta-rule and splitting (118), into two cases.
% 10.76/3.12 |-Branch one:
% 10.76/3.12 | (141) xp = sz00
% 10.76/3.12 |
% 10.76/3.12 | Equations (141) can reduce 108 to:
% 10.76/3.12 | (142) $false
% 10.76/3.12 |
% 10.76/3.12 |-The branch is then unsatisfiable
% 10.76/3.12 |-Branch two:
% 10.76/3.12 | (108) ~ (xp = sz00)
% 10.76/3.12 | (144) all_0_1_1 = xq
% 10.76/3.12 |
% 10.76/3.12 | From (144) and (120) follows:
% 10.76/3.12 | (145) sdtasdt0(xq, xp) = xn
% 10.76/3.12 |
% 10.76/3.12 | From (144) and (136) follows:
% 10.76/3.12 | (146) sdtasdt0(xq, xn) = all_19_0_11
% 10.76/3.12 |
% 10.76/3.12 | From (144) and (100) follows:
% 10.76/3.12 | (68) sdtasdt0(xp, xq) = xn
% 10.76/3.12 |
% 10.76/3.12 +-Applying beta-rule and splitting (123), into two cases.
% 10.76/3.12 |-Branch one:
% 10.76/3.12 | (141) xp = sz00
% 10.76/3.12 |
% 10.76/3.12 | Equations (141) can reduce 108 to:
% 10.76/3.12 | (142) $false
% 10.76/3.12 |
% 10.76/3.12 |-The branch is then unsatisfiable
% 10.76/3.12 |-Branch two:
% 10.76/3.12 | (108) ~ (xp = sz00)
% 10.76/3.12 | (151) ? [v0] : (sdtsldt0(v0, xp) = all_0_3_3 & sdtasdt0(xq, xn) = v0)
% 10.76/3.12 |
% 10.76/3.12 | Instantiating (151) with all_39_0_13 yields:
% 10.76/3.12 | (152) sdtsldt0(all_39_0_13, xp) = all_0_3_3 & sdtasdt0(xq, xn) = all_39_0_13
% 10.76/3.13 |
% 10.76/3.13 | Applying alpha-rule on (152) yields:
% 10.76/3.13 | (153) sdtsldt0(all_39_0_13, xp) = all_0_3_3
% 10.76/3.13 | (154) sdtasdt0(xq, xn) = all_39_0_13
% 10.76/3.13 |
% 10.76/3.13 +-Applying beta-rule and splitting (124), into two cases.
% 10.76/3.13 |-Branch one:
% 10.76/3.13 | (141) xp = sz00
% 10.76/3.13 |
% 10.76/3.13 | Equations (141) can reduce 108 to:
% 10.76/3.13 | (142) $false
% 10.76/3.13 |
% 10.76/3.13 |-The branch is then unsatisfiable
% 10.76/3.13 |-Branch two:
% 10.76/3.13 | (108) ~ (xp = sz00)
% 10.76/3.13 | (158) ? [v0] : (sdtsldt0(v0, xp) = xn & sdtasdt0(xp, xn) = v0)
% 10.76/3.13 |
% 10.76/3.13 +-Applying beta-rule and splitting (121), into two cases.
% 10.76/3.13 |-Branch one:
% 10.76/3.13 | (141) xp = sz00
% 10.76/3.13 |
% 10.76/3.13 | Equations (141) can reduce 108 to:
% 10.76/3.13 | (142) $false
% 10.76/3.13 |
% 10.76/3.13 |-The branch is then unsatisfiable
% 10.76/3.13 |-Branch two:
% 10.76/3.13 | (108) ~ (xp = sz00)
% 10.76/3.13 | (162) xp = sz10 | ? [v0] : (isPrime0(v0) & doDivides0(v0, xp) & aNaturalNumber0(v0))
% 10.76/3.13 |
% 10.76/3.13 | Instantiating formula (114) with xq, xn, all_19_0_11, all_39_0_13 and discharging atoms sdtasdt0(xq, xn) = all_39_0_13, sdtasdt0(xq, xn) = all_19_0_11, yields:
% 10.76/3.13 | (163) all_39_0_13 = all_19_0_11
% 10.76/3.13 |
% 10.76/3.13 | Instantiating formula (114) with xq, xn, all_17_0_10, all_39_0_13 and discharging atoms sdtasdt0(xq, xn) = all_39_0_13, sdtasdt0(xq, xn) = all_17_0_10, yields:
% 10.76/3.13 | (164) all_39_0_13 = all_17_0_10
% 10.76/3.13 |
% 10.76/3.13 | Instantiating formula (114) with xp, xq, all_21_0_12, xn and discharging atoms sdtasdt0(xp, xq) = all_21_0_12, sdtasdt0(xp, xq) = xn, yields:
% 10.76/3.13 | (165) all_21_0_12 = xn
% 10.76/3.13 |
% 10.76/3.13 | Instantiating formula (40) with all_11_0_7, xq, xn, xp and discharging atoms sdtsldt0(xn, xp) = xq, sdtasdt0(xp, all_11_0_7) = xn, doDivides0(xp, xn), aNaturalNumber0(all_11_0_7), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 10.76/3.13 | (166) all_11_0_7 = xq | xp = sz00
% 10.76/3.13 |
% 10.76/3.13 | Instantiating formula (91) with all_0_4_4, all_0_0_0, all_0_5_5, xp and discharging atoms sdtasdt0(xp, all_0_0_0) = all_0_4_4, sdtasdt0(xp, all_0_5_5) = all_0_4_4, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_5_5), aNaturalNumber0(xp), yields:
% 10.76/3.13 | (167) all_0_0_0 = all_0_5_5 | xp = sz00
% 10.76/3.13 |
% 10.76/3.13 | Combining equations (163,164) yields a new equation:
% 10.76/3.13 | (168) all_19_0_11 = all_17_0_10
% 10.76/3.13 |
% 10.76/3.13 | Simplifying 168 yields:
% 10.76/3.13 | (169) all_19_0_11 = all_17_0_10
% 10.76/3.13 |
% 10.76/3.13 | From (165) and (139) follows:
% 10.76/3.13 | (170) sdtasdt0(xn, xq) = all_0_2_2
% 10.76/3.13 |
% 10.76/3.13 | From (169) and (146) follows:
% 10.76/3.13 | (133) sdtasdt0(xq, xn) = all_17_0_10
% 10.76/3.13 |
% 10.76/3.13 | From (169) and (137) follows:
% 10.76/3.13 | (134) sdtasdt0(xp, all_17_0_10) = all_0_4_4
% 10.76/3.13 |
% 10.76/3.13 +-Applying beta-rule and splitting (167), into two cases.
% 10.76/3.13 |-Branch one:
% 10.76/3.13 | (141) xp = sz00
% 10.76/3.13 |
% 10.76/3.13 | Equations (141) can reduce 108 to:
% 10.76/3.13 | (142) $false
% 10.76/3.13 |
% 10.76/3.13 |-The branch is then unsatisfiable
% 10.76/3.13 |-Branch two:
% 10.76/3.13 | (108) ~ (xp = sz00)
% 10.76/3.13 | (176) all_0_0_0 = all_0_5_5
% 10.76/3.13 |
% 10.76/3.13 | From (176) and (65) follows:
% 10.76/3.13 | (74) sdtasdt0(xp, all_0_5_5) = all_0_4_4
% 10.76/3.13 |
% 10.76/3.13 | From (176) and (20) follows:
% 10.76/3.13 | (122) aNaturalNumber0(all_0_5_5)
% 10.76/3.13 |
% 10.76/3.13 +-Applying beta-rule and splitting (166), into two cases.
% 10.76/3.13 |-Branch one:
% 10.76/3.13 | (141) xp = sz00
% 10.76/3.13 |
% 10.76/3.13 | Equations (141) can reduce 108 to:
% 10.76/3.13 | (142) $false
% 10.76/3.13 |
% 10.76/3.13 |-The branch is then unsatisfiable
% 10.76/3.13 |-Branch two:
% 10.76/3.13 | (108) ~ (xp = sz00)
% 10.76/3.13 | (182) all_11_0_7 = xq
% 10.76/3.13 |
% 10.76/3.13 | From (182) and (131) follows:
% 10.76/3.13 | (9) aNaturalNumber0(xq)
% 10.76/3.13 |
% 10.76/3.13 | Instantiating formula (71) with all_0_4_4, xn, xp, xq, xn and discharging atoms sdtasdt0(xq, xp) = xn, sdtasdt0(xn, xn) = all_0_4_4, aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 10.76/3.13 | (184) ? [v0] : (sdtasdt0(v0, xp) = all_0_4_4 & sdtasdt0(xn, xq) = v0)
% 10.76/3.13 |
% 10.76/3.13 | Instantiating formula (50) with all_17_0_10, xq, xn and discharging atoms sdtasdt0(xq, xn) = all_17_0_10, aNaturalNumber0(xq), aNaturalNumber0(xn), yields:
% 10.76/3.13 | (185) sdtasdt0(xn, xq) = all_17_0_10
% 10.76/3.13 |
% 10.76/3.13 | Instantiating formula (93) with all_17_0_10, xn, xq and discharging atoms sdtasdt0(xq, xn) = all_17_0_10, aNaturalNumber0(xq), aNaturalNumber0(xn), yields:
% 10.76/3.13 | (186) aNaturalNumber0(all_17_0_10)
% 10.76/3.13 |
% 10.76/3.13 | Instantiating formula (12) with all_0_2_2, xn, xq, xn, xp and discharging atoms sdtsldt0(xn, xp) = xq, sdtasdt0(xn, xq) = all_0_2_2, doDivides0(xp, xn), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 10.76/3.13 | (187) xp = sz00 | ? [v0] : (sdtsldt0(v0, xp) = all_0_2_2 & sdtasdt0(xn, xn) = v0)
% 10.76/3.13 |
% 10.76/3.13 | Instantiating formula (6) with all_0_4_4, xp and discharging atoms doDivides0(xp, all_0_4_4), aNaturalNumber0(all_0_4_4), aNaturalNumber0(xp), yields:
% 10.76/3.13 | (188) ? [v0] : (sdtasdt0(xp, v0) = all_0_4_4 & aNaturalNumber0(v0))
% 10.76/3.13 |
% 10.76/3.13 | Instantiating (188) with all_104_0_27 yields:
% 10.76/3.13 | (189) sdtasdt0(xp, all_104_0_27) = all_0_4_4 & aNaturalNumber0(all_104_0_27)
% 10.76/3.13 |
% 10.76/3.13 | Applying alpha-rule on (189) yields:
% 10.76/3.13 | (190) sdtasdt0(xp, all_104_0_27) = all_0_4_4
% 10.76/3.13 | (191) aNaturalNumber0(all_104_0_27)
% 10.76/3.13 |
% 10.76/3.13 | Instantiating (184) with all_118_0_34 yields:
% 10.76/3.13 | (192) sdtasdt0(all_118_0_34, xp) = all_0_4_4 & sdtasdt0(xn, xq) = all_118_0_34
% 10.76/3.13 |
% 10.76/3.13 | Applying alpha-rule on (192) yields:
% 10.76/3.13 | (193) sdtasdt0(all_118_0_34, xp) = all_0_4_4
% 10.76/3.13 | (194) sdtasdt0(xn, xq) = all_118_0_34
% 10.76/3.13 |
% 10.76/3.13 +-Applying beta-rule and splitting (187), into two cases.
% 10.76/3.13 |-Branch one:
% 10.76/3.13 | (141) xp = sz00
% 10.76/3.13 |
% 10.76/3.13 | Equations (141) can reduce 108 to:
% 10.76/3.13 | (142) $false
% 10.76/3.13 |
% 10.76/3.13 |-The branch is then unsatisfiable
% 10.76/3.13 |-Branch two:
% 10.76/3.13 | (108) ~ (xp = sz00)
% 10.76/3.13 | (198) ? [v0] : (sdtsldt0(v0, xp) = all_0_2_2 & sdtasdt0(xn, xn) = v0)
% 10.76/3.13 |
% 10.76/3.13 | Instantiating formula (114) with xn, xq, all_118_0_34, all_0_2_2 and discharging atoms sdtasdt0(xn, xq) = all_118_0_34, sdtasdt0(xn, xq) = all_0_2_2, yields:
% 10.76/3.13 | (199) all_118_0_34 = all_0_2_2
% 10.76/3.13 |
% 10.76/3.13 | Instantiating formula (114) with xn, xq, all_17_0_10, all_118_0_34 and discharging atoms sdtasdt0(xn, xq) = all_118_0_34, sdtasdt0(xn, xq) = all_17_0_10, yields:
% 10.76/3.13 | (200) all_118_0_34 = all_17_0_10
% 10.76/3.13 |
% 10.76/3.13 | Instantiating formula (91) with all_0_4_4, all_17_0_10, all_0_5_5, xp and discharging atoms sdtasdt0(xp, all_17_0_10) = all_0_4_4, sdtasdt0(xp, all_0_5_5) = all_0_4_4, aNaturalNumber0(all_17_0_10), aNaturalNumber0(all_0_5_5), aNaturalNumber0(xp), yields:
% 10.76/3.13 | (201) all_17_0_10 = all_0_5_5 | xp = sz00
% 10.76/3.13 |
% 10.76/3.13 | Instantiating formula (91) with all_0_4_4, all_17_0_10, all_104_0_27, xp and discharging atoms sdtasdt0(xp, all_104_0_27) = all_0_4_4, sdtasdt0(xp, all_17_0_10) = all_0_4_4, aNaturalNumber0(all_104_0_27), aNaturalNumber0(all_17_0_10), aNaturalNumber0(xp), yields:
% 10.76/3.13 | (202) all_104_0_27 = all_17_0_10 | xp = sz00
% 10.76/3.13 |
% 10.76/3.13 | Combining equations (200,199) yields a new equation:
% 10.76/3.13 | (203) all_17_0_10 = all_0_2_2
% 10.76/3.13 |
% 10.76/3.13 | Simplifying 203 yields:
% 10.76/3.13 | (204) all_17_0_10 = all_0_2_2
% 10.76/3.13 |
% 10.76/3.13 +-Applying beta-rule and splitting (202), into two cases.
% 10.76/3.13 |-Branch one:
% 10.76/3.13 | (141) xp = sz00
% 10.76/3.13 |
% 10.76/3.13 | Equations (141) can reduce 108 to:
% 10.76/3.13 | (142) $false
% 10.76/3.13 |
% 10.76/3.13 |-The branch is then unsatisfiable
% 10.76/3.13 |-Branch two:
% 10.76/3.13 | (108) ~ (xp = sz00)
% 10.76/3.13 | (208) all_104_0_27 = all_17_0_10
% 10.76/3.13 |
% 10.76/3.13 +-Applying beta-rule and splitting (201), into two cases.
% 10.76/3.13 |-Branch one:
% 10.76/3.13 | (141) xp = sz00
% 10.76/3.13 |
% 10.76/3.13 | Equations (141) can reduce 108 to:
% 10.76/3.13 | (142) $false
% 10.76/3.13 |
% 10.76/3.13 |-The branch is then unsatisfiable
% 10.76/3.13 |-Branch two:
% 10.76/3.13 | (108) ~ (xp = sz00)
% 10.76/3.13 | (212) all_17_0_10 = all_0_5_5
% 10.76/3.13 |
% 10.76/3.13 | Combining equations (204,212) yields a new equation:
% 10.76/3.13 | (213) all_0_2_2 = all_0_5_5
% 10.76/3.13 |
% 10.76/3.13 | Simplifying 213 yields:
% 10.76/3.13 | (214) all_0_2_2 = all_0_5_5
% 10.76/3.13 |
% 10.76/3.13 | Equations (214) can reduce 70 to:
% 10.76/3.13 | (142) $false
% 10.76/3.13 |
% 10.76/3.13 |-The branch is then unsatisfiable
% 10.76/3.13 % SZS output end Proof for theBenchmark
% 10.76/3.14
% 10.76/3.14 2555ms
%------------------------------------------------------------------------------