TSTP Solution File: NUM525+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM525+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n018.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 08:45:29 EDT 2022
% Result : Theorem 5.96s 1.99s
% Output : Proof 10.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM525+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n018.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 15:50:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.58 ____ _
% 0.19/0.58 ___ / __ \_____(_)___ ________ __________
% 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic
% 0.19/0.59 (ePrincess v.1.0)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2015
% 0.19/0.59 (c) Peter Backeman, 2014-2015
% 0.19/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.59 Bug reports to peter@backeman.se
% 0.19/0.59
% 0.19/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.96/1.02 Prover 0: Preprocessing ...
% 3.95/1.52 Prover 0: Constructing countermodel ...
% 5.96/1.99 Prover 0: proved (1326ms)
% 5.96/1.99
% 5.96/1.99 No countermodel exists, formula is valid
% 5.96/1.99 % SZS status Theorem for theBenchmark
% 5.96/1.99
% 5.96/1.99 Generating proof ... found it (size 89)
% 10.46/3.02
% 10.46/3.02 % SZS output start Proof for theBenchmark
% 10.46/3.02 Assumed formulas after preprocessing and simplification:
% 10.46/3.02 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v4 = v1) & ~ (xp = sz10) & ~ (xp = sz00) & ~ (xm = sz00) & ~ (xn = sz00) & ~ (sz10 = sz00) & sdtsldt0(xn, xp) = xq & sdtasdt0(xq, xq) = v2 & sdtasdt0(xp, v6) = v1 & sdtasdt0(xp, v5) = xn & sdtasdt0(xp, v3) = v4 & 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(v6) & aNaturalNumber0(v5) & aNaturalNumber0(xq) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ isPrime0(sz10) & ~ isPrime0(sz00) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v7 = sz00 | ~ (sdtsldt0(v11, v7) = v12) | ~ (sdtsldt0(v8, v7) = v9) | ~ (sdtasdt0(v10, v8) = v11) | ~ doDivides0(v7, v8) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtasdt0(v10, v9) = v12) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtasdt0(v9, v7) = v11) | ~ (sdtasdt0(v8, v7) = v10) | ~ (sdtpldt0(v10, v11) = v12) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (sdtasdt0(v13, v7) = v12 & sdtasdt0(v7, v13) = v14 & sdtasdt0(v7, v9) = v16 & sdtasdt0(v7, v8) = v15 & sdtpldt0(v15, v16) = v14 & sdtpldt0(v8, v9) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtasdt0(v7, v9) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ~ (sdtpldt0(v10, v11) = v12) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (sdtasdt0(v13, v7) = v14 & sdtasdt0(v9, v7) = v16 & sdtasdt0(v8, v7) = v15 & sdtasdt0(v7, v13) = v12 & sdtpldt0(v15, v16) = v14 & sdtpldt0(v8, v9) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v9, v7) = v11) | ~ (sdtasdt0(v8, v7) = v10) | ~ sdtlseqdt0(v8, v9) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtlseqdt0(v10, v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v9, v7) = v11) | ~ (sdtasdt0(v8, v7) = v10) | ~ sdtlseqdt0(v8, v9) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v12) & sdtasdt0(v7, v9) = v13 & sdtasdt0(v7, v8) = v12 & sdtlseqdt0(v12, v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v9, v7) = v11) | ~ (sdtasdt0(v8, v7) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v12) & sdtasdt0(v7, v9) = v13 & sdtasdt0(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v9, v7) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ~ sdtlseqdt0(v8, v9) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v11) & ~ (v12 = v10) & sdtasdt0(v8, v7) = v13 & sdtasdt0(v7, v9) = v12 & sdtlseqdt0(v13, v11) & sdtlseqdt0(v10, v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v9, v7) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v11) & ~ (v12 = v10) & sdtasdt0(v8, v7) = v13 & sdtasdt0(v7, v9) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v8, v7) = v11) | ~ (sdtasdt0(v7, v9) = v10) | ~ sdtlseqdt0(v8, v9) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v11) & ~ (v12 = v10) & sdtasdt0(v9, v7) = v13 & sdtasdt0(v7, v8) = v12 & sdtlseqdt0(v12, v10) & sdtlseqdt0(v11, v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v8, v7) = v11) | ~ (sdtasdt0(v7, v9) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v11) & ~ (v12 = v10) & sdtasdt0(v9, v7) = v13 & sdtasdt0(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v7, v9) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ~ sdtlseqdt0(v8, v9) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtlseqdt0(v10, v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v7, v9) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ~ sdtlseqdt0(v8, v9) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v12) & sdtasdt0(v9, v7) = v13 & sdtasdt0(v8, v7) = v12 & sdtlseqdt0(v12, v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v7, v9) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v12) & sdtasdt0(v9, v7) = v13 & sdtasdt0(v8, v7) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (sdtpldt0(v9, v7) = v11) | ~ (sdtpldt0(v8, v7) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v12) & sdtpldt0(v7, v9) = v13 & sdtpldt0(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (sdtpldt0(v9, v7) = v11) | ~ (sdtpldt0(v7, v8) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v11) & ~ (v12 = v10) & sdtpldt0(v8, v7) = v13 & sdtpldt0(v7, v9) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (sdtpldt0(v8, v7) = v11) | ~ (sdtpldt0(v7, v9) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v11) & ~ (v12 = v10) & sdtpldt0(v9, v7) = v13 & sdtpldt0(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (sdtpldt0(v7, v9) = v11) | ~ (sdtpldt0(v7, v8) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v12) & sdtpldt0(v9, v7) = v13 & sdtpldt0(v8, v7) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = sz10 | v9 = sz00 | v8 = sz00 | v7 = sz00 | ~ (sdtasdt0(v9, v10) = v11) | ~ (sdtasdt0(v8, v8) = v10) | ~ (sdtasdt0(v7, v7) = v11) | ~ iLess0(v7, xn) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v12 = v9) & ~ (v12 = sz10) & sdtasdt0(v12, v13) = v9 & doDivides0(v12, v9) & aNaturalNumber0(v13) & aNaturalNumber0(v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = sz00 | v8 = sz00 | v7 = sz00 | ~ (sdtasdt0(v9, v10) = v11) | ~ (sdtasdt0(v8, v8) = v10) | ~ (sdtasdt0(v7, v7) = v11) | ~ isPrime0(v9) | ~ iLess0(v7, xn) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v7 = sz00 | ~ (sdtsldt0(v8, v7) = v9) | ~ (sdtasdt0(v10, v9) = v11) | ~ doDivides0(v7, v8) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : (sdtsldt0(v12, v7) = v11 & sdtasdt0(v10, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v10, v9) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : (sdtasdt0(v8, v9) = v12 & sdtasdt0(v7, v12) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v10, v7) = v11) | ~ (sdtpldt0(v8, v9) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (sdtasdt0(v9, v7) = v16 & sdtasdt0(v8, v7) = v15 & sdtasdt0(v7, v10) = v12 & sdtasdt0(v7, v9) = v14 & sdtasdt0(v7, v8) = v13 & sdtpldt0(v15, v16) = v11 & sdtpldt0(v13, v14) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v8, v9) = v10) | ~ (sdtasdt0(v7, v10) = v11) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : (sdtasdt0(v12, v9) = v11 & sdtasdt0(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v7, v10) = v11) | ~ (sdtpldt0(v8, v9) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (sdtasdt0(v10, v7) = v14 & sdtasdt0(v9, v7) = v16 & sdtasdt0(v8, v7) = v15 & sdtasdt0(v7, v9) = v13 & sdtasdt0(v7, v8) = v12 & sdtpldt0(v15, v16) = v14 & sdtpldt0(v12, v13) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtpldt0(v10, v9) = v11) | ~ (sdtpldt0(v7, v8) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : (sdtpldt0(v8, v9) = v12 & sdtpldt0(v7, v12) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtpldt0(v8, v9) = v10) | ~ (sdtpldt0(v7, v10) = v11) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : (sdtpldt0(v12, v9) = v11 & sdtpldt0(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | v7 = sz00 | ~ (sdtsldt0(v8, v7) = v9) | ~ (sdtasdt0(v7, v10) = v8) | ~ doDivides0(v7, v8) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (sdtmndt0(v8, v7) = v9) | ~ (sdtpldt0(v7, v10) = v8) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | v7 = sz00 | ~ (sdtsldt0(v8, v7) = v9) | ~ (sdtasdt0(v7, v9) = v10) | ~ doDivides0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (sdtmndt0(v8, v7) = v9) | ~ (sdtpldt0(v7, v9) = v10) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v9, v7) = v10) | ~ (sdtasdt0(v8, v7) = v10) | ~ sdtlseqdt0(v8, v9) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v9, v7) = v10) | ~ (sdtasdt0(v8, v7) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v7, v9) = v10) | ~ (sdtasdt0(v7, v8) = v10) | ~ sdtlseqdt0(v8, v9) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v7, v9) = v10) | ~ (sdtasdt0(v7, v8) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (sdtpldt0(v9, v7) = v10) | ~ (sdtpldt0(v8, v7) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (sdtpldt0(v7, v9) = v10) | ~ (sdtpldt0(v7, v8) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtsldt0(v10, v9) = v8) | ~ (sdtsldt0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtmndt0(v10, v9) = v8) | ~ (sdtmndt0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtasdt0(v10, v9) = v8) | ~ (sdtasdt0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v10, v9) = v8) | ~ (sdtpldt0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v9, v8) = v10) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v11] : ? [v12] : ? [v13] : ( ~ (v13 = v12) & ~ (v11 = v10) & sdtpldt0(v9, v7) = v11 & sdtpldt0(v8, v9) = v13 & sdtpldt0(v7, v9) = v12 & sdtlseqdt0(v12, v13) & sdtlseqdt0(v11, v10))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v9, v7) = v10) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v11] : ? [v12] : ? [v13] : ( ~ (v13 = v12) & ~ (v11 = v10) & sdtpldt0(v9, v8) = v11 & sdtpldt0(v8, v9) = v13 & sdtpldt0(v7, v9) = v12 & sdtlseqdt0(v12, v13) & sdtlseqdt0(v10, v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v8, v9) = v10) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v11] : ? [v12] : ? [v13] : ( ~ (v13 = v10) & ~ (v12 = v11) & sdtpldt0(v9, v8) = v12 & sdtpldt0(v9, v7) = v11 & sdtpldt0(v7, v9) = v13 & sdtlseqdt0(v13, v10) & sdtlseqdt0(v11, v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v7, v9) = v10) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v11] : ? [v12] : ? [v13] : ( ~ (v13 = v10) & ~ (v12 = v11) & sdtpldt0(v9, v8) = v12 & sdtpldt0(v9, v7) = v11 & sdtpldt0(v8, v9) = v13 & sdtlseqdt0(v11, v12) & sdtlseqdt0(v10, v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = sz00 | ~ (sdtsldt0(v8, v7) = v9) | ~ (sdtasdt0(v7, v9) = v10) | ~ doDivides0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | aNaturalNumber0(v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtmndt0(v8, v7) = v9) | ~ (sdtpldt0(v7, v9) = v10) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | aNaturalNumber0(v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v7, v8) = v10) | ~ isPrime0(v9) | ~ doDivides0(v9, v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | doDivides0(v9, v8) | doDivides0(v9, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt0(v8, v9) = v10) | ~ doDivides0(v7, v10) | ~ doDivides0(v7, v8) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | doDivides0(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt0(v8, v9) = v10) | ~ doDivides0(v7, v9) | ~ doDivides0(v7, v8) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | doDivides0(v7, v10)) & ! [v7] : ! [v8] : ! [v9] : (v7 = sz00 | ~ (sdtasdt0(v8, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtlseqdt0(v8, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v8, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtasdt0(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v7, v9) = v8) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | doDivides0(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v7, v8) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtasdt0(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v7, v8) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | aNaturalNumber0(v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v8, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtpldt0(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v7, v9) = v8) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtlseqdt0(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v7, v8) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtpldt0(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v7, v8) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | aNaturalNumber0(v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ doDivides0(v8, v9) | ~ doDivides0(v7, v8) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | doDivides0(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ sdtlseqdt0(v8, v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtlseqdt0(v7, v9)) & ! [v7] : ! [v8] : (v8 = v7 | v8 = sz10 | ~ isPrime0(v7) | ~ doDivides0(v8, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (sdtasdt0(v7, sz10) = v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (sdtasdt0(sz10, v7) = v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (sdtpldt0(v7, sz00) = v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (sdtpldt0(sz00, v7) = v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v8 = v7 | ~ sdtlseqdt0(v8, v7) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v8 = v7 | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | iLess0(v7, v8)) & ! [v7] : ! [v8] : (v8 = sz00 | v7 = sz00 | ~ (sdtasdt0(v7, v8) = sz00) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v8 = sz00 | ~ (sdtasdt0(v7, sz00) = v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v8 = sz00 | ~ (sdtasdt0(sz00, v7) = v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v8 = sz00 | ~ (sdtpldt0(v7, v8) = sz00) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v8 = sz00 | ~ doDivides0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtlseqdt0(v7, v8)) & ! [v7] : ! [v8] : (v7 = xp | v7 = sz10 | ~ (sdtasdt0(v7, v8) = xp) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v7 = sz00 | ~ (sdtpldt0(v7, v8) = sz00) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ( ~ (sdtasdt0(v7, sz10) = v8) | ~ aNaturalNumber0(v7) | sdtasdt0(sz10, v7) = v7) & ! [v7] : ! [v8] : ( ~ (sdtasdt0(v7, sz00) = v8) | ~ aNaturalNumber0(v7) | sdtasdt0(sz00, v7) = sz00) & ! [v7] : ! [v8] : ( ~ (sdtasdt0(sz10, v7) = v8) | ~ aNaturalNumber0(v7) | sdtasdt0(v7, sz10) = v7) & ! [v7] : ! [v8] : ( ~ (sdtasdt0(sz00, v7) = v8) | ~ aNaturalNumber0(v7) | sdtasdt0(v7, sz00) = sz00) & ! [v7] : ! [v8] : ( ~ (sdtpldt0(v7, sz00) = v8) | ~ aNaturalNumber0(v7) | sdtpldt0(sz00, v7) = v7) & ! [v7] : ! [v8] : ( ~ (sdtpldt0(sz00, v7) = v8) | ~ aNaturalNumber0(v7) | sdtpldt0(v7, sz00) = v7) & ! [v7] : ! [v8] : ( ~ doDivides0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v9] : (sdtasdt0(v7, v9) = v8 & aNaturalNumber0(v9))) & ! [v7] : ! [v8] : ( ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v9] : (sdtpldt0(v7, v9) = v8 & aNaturalNumber0(v9))) & ! [v7] : ! [v8] : ( ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtlseqdt0(v8, v7) | sdtlseqdt0(v7, v8)) & ! [v7] : (v7 = xp | v7 = sz10 | ~ doDivides0(v7, xp) | ~ aNaturalNumber0(v7)) & ! [v7] : (v7 = sz10 | v7 = sz00 | ~ aNaturalNumber0(v7) | isPrime0(v7) | ? [v8] : ( ~ (v8 = v7) & ~ (v8 = sz10) & doDivides0(v8, v7) & aNaturalNumber0(v8))) & ! [v7] : (v7 = sz10 | v7 = sz00 | ~ aNaturalNumber0(v7) | sdtlseqdt0(sz10, v7)) & ! [v7] : (v7 = sz10 | v7 = sz00 | ~ aNaturalNumber0(v7) | ? [v8] : (isPrime0(v8) & doDivides0(v8, v7) & aNaturalNumber0(v8))) & ! [v7] : ( ~ aNaturalNumber0(v7) | sdtlseqdt0(v7, v7)))
% 10.46/3.08 | 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, all_0_6_6 yields:
% 10.46/3.08 | (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_4_4 & sdtasdt0(xp, all_0_0_0) = all_0_5_5 & sdtasdt0(xp, all_0_1_1) = xn & sdtasdt0(xp, all_0_3_3) = all_0_2_2 & sdtasdt0(xp, all_0_4_4) = all_0_3_3 & sdtasdt0(xp, all_0_6_6) = all_0_5_5 & sdtasdt0(xp, xq) = xn & sdtasdt0(xm, xm) = all_0_6_6 & sdtasdt0(xn, xn) = all_0_5_5 & isPrime0(xp) & doDivides0(xp, all_0_5_5) & 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))
% 10.46/3.10 |
% 10.46/3.10 | Applying alpha-rule on (1) yields:
% 10.46/3.10 | (2) ~ (xn = sz00)
% 10.46/3.10 | (3) ! [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))
% 10.46/3.10 | (4) ~ isPrime0(sz10)
% 10.46/3.10 | (5) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 10.93/3.10 | (6) ! [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))
% 10.93/3.10 | (7) ! [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))
% 10.93/3.10 | (8) aNaturalNumber0(all_0_0_0)
% 10.93/3.10 | (9) ! [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)))
% 10.93/3.11 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.93/3.11 | (11) ~ (sz10 = sz00)
% 10.93/3.11 | (12) aNaturalNumber0(xp)
% 10.93/3.11 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.93/3.11 | (14) ~ (xp = sz10)
% 10.93/3.11 | (15) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 10.93/3.11 | (16) doDivides0(xp, all_0_5_5)
% 10.93/3.11 | (17) ! [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))
% 10.93/3.11 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3))
% 10.93/3.11 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 10.93/3.11 | (20) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 10.93/3.11 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 10.93/3.11 | (22) ! [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))
% 10.93/3.11 | (23) sdtasdt0(xp, all_0_0_0) = all_0_5_5
% 10.93/3.11 | (24) doDivides0(xp, xn)
% 10.93/3.11 | (25) ~ (xp = sz00)
% 10.93/3.11 | (26) ! [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))
% 10.93/3.11 | (27) ! [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))
% 10.93/3.11 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2)
% 10.93/3.11 | (29) ! [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))
% 10.93/3.11 | (30) ~ isPrime0(sz00)
% 10.93/3.11 | (31) ! [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))
% 10.93/3.11 | (32) ! [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))
% 10.93/3.11 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 10.93/3.11 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 10.93/3.11 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 10.93/3.11 | (36) ! [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)))
% 10.93/3.12 | (37) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0))
% 10.93/3.12 | (38) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 10.93/3.12 | (39) ! [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))
% 10.93/3.12 | (40) ! [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))
% 10.93/3.12 | (41) sdtsldt0(xn, xp) = xq
% 10.93/3.12 | (42) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 10.93/3.12 | (43) aNaturalNumber0(all_0_1_1)
% 10.93/3.12 | (44) ! [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))
% 10.93/3.12 | (45) ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 10.93/3.12 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 10.93/3.12 | (47) sdtasdt0(xp, all_0_4_4) = all_0_3_3
% 10.93/3.12 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 10.93/3.12 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 10.93/3.12 | (50) ! [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))
% 10.93/3.12 | (51) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0)
% 10.93/3.12 | (52) ! [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))
% 10.93/3.12 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 10.93/3.12 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.93/3.12 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.93/3.12 | (56) ! [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))
% 10.93/3.12 | (57) isPrime0(xp)
% 10.93/3.12 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2)
% 10.93/3.12 | (59) aNaturalNumber0(xq)
% 10.93/3.12 | (60) ! [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))
% 10.93/3.12 | (61) ! [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))
% 10.93/3.12 | (62) ! [v0] : (v0 = xp | v0 = sz10 | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0))
% 10.93/3.12 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.93/3.12 | (64) aNaturalNumber0(xm)
% 10.93/3.12 | (65) sdtasdt0(xm, xm) = all_0_6_6
% 10.93/3.12 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.93/3.13 | (67) ! [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)))
% 10.93/3.13 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 10.93/3.13 | (69) sdtasdt0(xp, all_0_6_6) = all_0_5_5
% 10.93/3.13 | (70) ! [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))
% 10.93/3.13 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.93/3.13 | (72) ~ (xm = sz00)
% 10.93/3.13 | (73) ! [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))
% 10.93/3.13 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.93/3.13 | (75) ! [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)))
% 10.93/3.13 | (76) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 10.93/3.13 | (77) ! [v0] : ! [v1] : (v1 = sz00 | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 10.93/3.13 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.93/3.13 | (79) ! [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)))
% 10.93/3.13 | (80) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 10.93/3.13 | (81) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1] : ( ~ (v1 = v0) & ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 10.93/3.13 | (82) sdtasdt0(xp, all_0_3_3) = all_0_2_2
% 10.93/3.13 | (83) ! [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))
% 10.93/3.13 | (84) ! [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)))
% 10.93/3.13 | (85) ~ (all_0_2_2 = all_0_5_5)
% 10.93/3.13 | (86) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 10.93/3.13 | (87) aNaturalNumber0(xn)
% 10.93/3.13 | (88) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 10.93/3.13 | (89) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.93/3.13 | (90) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 10.93/3.13 | (91) sdtasdt0(xp, all_0_1_1) = xn
% 10.93/3.13 | (92) ! [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)
% 10.93/3.13 | (93) ! [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)))
% 10.93/3.13 | (94) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.93/3.13 | (95) ! [v0] : ! [v1] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1) = xp) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.93/3.13 | (96) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0))
% 10.93/3.13 | (97) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00)
% 10.93/3.13 | (98) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.93/3.13 | (99) ! [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))
% 10.93/3.13 | (100) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 10.93/3.13 | (101) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.93/3.14 | (102) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 10.93/3.14 | (103) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0)
% 10.93/3.14 | (104) aNaturalNumber0(sz00)
% 10.93/3.14 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 10.93/3.14 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.93/3.14 | (107) sdtasdt0(xp, xq) = xn
% 10.93/3.14 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.93/3.14 | (109) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 10.93/3.14 | (110) ! [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))
% 10.93/3.14 | (111) ! [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))
% 10.93/3.14 | (112) aNaturalNumber0(sz10)
% 10.93/3.14 | (113) ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 10.93/3.14 | (114) sdtasdt0(xq, xq) = all_0_4_4
% 10.93/3.14 | (115) ! [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)))
% 10.93/3.14 | (116) sdtasdt0(xn, xn) = all_0_5_5
% 10.93/3.14 | (117) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.93/3.14 | (118) ! [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)))
% 10.93/3.14 |
% 10.93/3.14 | Instantiating formula (27) 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:
% 10.93/3.14 | (119) all_0_1_1 = xq | xp = sz00
% 10.93/3.14 |
% 10.93/3.14 | Instantiating formula (50) with all_0_3_3, all_0_4_4, xq, xq, xp and discharging atoms sdtasdt0(xq, xq) = all_0_4_4, sdtasdt0(xp, all_0_4_4) = all_0_3_3, aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 10.93/3.14 | (120) ? [v0] : (sdtasdt0(v0, xq) = all_0_3_3 & sdtasdt0(xp, xq) = v0)
% 10.93/3.14 |
% 10.93/3.14 | Instantiating formula (58) 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:
% 10.93/3.14 | (121) sdtasdt0(all_0_1_1, xp) = xn
% 10.93/3.14 |
% 10.93/3.14 | Instantiating formula (5) with xp and discharging atoms aNaturalNumber0(xp), yields:
% 10.93/3.14 | (122) xp = sz10 | xp = sz00 | ? [v0] : (isPrime0(v0) & doDivides0(v0, xp) & aNaturalNumber0(v0))
% 10.93/3.14 |
% 10.93/3.14 | Instantiating formula (71) with all_0_6_6, xm, xm and discharging atoms sdtasdt0(xm, xm) = all_0_6_6, aNaturalNumber0(xm), yields:
% 10.93/3.14 | (123) aNaturalNumber0(all_0_6_6)
% 10.93/3.14 |
% 10.93/3.14 | Instantiating formula (73) with all_0_4_4, xq, xq, xn, xp and discharging atoms sdtsldt0(xn, xp) = xq, sdtasdt0(xq, xq) = all_0_4_4, doDivides0(xp, xn), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 10.93/3.14 | (124) xp = sz00 | ? [v0] : (sdtsldt0(v0, xp) = all_0_4_4 & sdtasdt0(xq, xn) = v0)
% 10.93/3.14 |
% 10.93/3.14 | Instantiating formula (73) 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:
% 10.93/3.14 | (125) xp = sz00 | ? [v0] : (sdtsldt0(v0, xp) = xn & sdtasdt0(xp, xn) = v0)
% 10.93/3.14 |
% 10.93/3.14 | Instantiating formula (71) with all_0_5_5, xn, xn and discharging atoms sdtasdt0(xn, xn) = all_0_5_5, aNaturalNumber0(xn), yields:
% 10.93/3.14 | (126) aNaturalNumber0(all_0_5_5)
% 10.93/3.14 |
% 10.93/3.14 | Instantiating formula (22) with all_0_5_5, xn, xn, all_0_1_1, xp and discharging atoms sdtasdt0(xp, all_0_1_1) = xn, sdtasdt0(xn, xn) = all_0_5_5, aNaturalNumber0(all_0_1_1), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 10.93/3.14 | (127) ? [v0] : (sdtasdt0(all_0_1_1, xn) = v0 & sdtasdt0(xp, v0) = all_0_5_5)
% 10.93/3.14 |
% 10.93/3.14 | Instantiating formula (22) with all_0_5_5, xn, xn, xq, xp and discharging atoms sdtasdt0(xp, xq) = xn, sdtasdt0(xn, xn) = all_0_5_5, aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 10.93/3.14 | (128) ? [v0] : (sdtasdt0(xq, xn) = v0 & sdtasdt0(xp, v0) = all_0_5_5)
% 10.93/3.14 |
% 10.93/3.14 | Instantiating formula (45) with xn, xp and discharging atoms doDivides0(xp, xn), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 10.93/3.14 | (129) ? [v0] : (sdtasdt0(xp, v0) = xn & aNaturalNumber0(v0))
% 10.93/3.14 |
% 10.93/3.14 | Instantiating (129) with all_11_0_8 yields:
% 10.93/3.14 | (130) sdtasdt0(xp, all_11_0_8) = xn & aNaturalNumber0(all_11_0_8)
% 10.93/3.14 |
% 10.93/3.14 | Applying alpha-rule on (130) yields:
% 10.93/3.14 | (131) sdtasdt0(xp, all_11_0_8) = xn
% 10.93/3.14 | (132) aNaturalNumber0(all_11_0_8)
% 10.93/3.14 |
% 10.93/3.14 | Instantiating (128) with all_17_0_11 yields:
% 10.93/3.14 | (133) sdtasdt0(xq, xn) = all_17_0_11 & sdtasdt0(xp, all_17_0_11) = all_0_5_5
% 10.93/3.14 |
% 10.93/3.14 | Applying alpha-rule on (133) yields:
% 10.93/3.14 | (134) sdtasdt0(xq, xn) = all_17_0_11
% 10.93/3.14 | (135) sdtasdt0(xp, all_17_0_11) = all_0_5_5
% 10.93/3.14 |
% 10.93/3.14 | Instantiating (127) with all_19_0_12 yields:
% 10.93/3.14 | (136) sdtasdt0(all_0_1_1, xn) = all_19_0_12 & sdtasdt0(xp, all_19_0_12) = all_0_5_5
% 10.93/3.14 |
% 10.93/3.14 | Applying alpha-rule on (136) yields:
% 10.93/3.14 | (137) sdtasdt0(all_0_1_1, xn) = all_19_0_12
% 10.93/3.14 | (138) sdtasdt0(xp, all_19_0_12) = all_0_5_5
% 10.93/3.14 |
% 10.93/3.14 | Instantiating (120) with all_21_0_13 yields:
% 10.93/3.14 | (139) sdtasdt0(all_21_0_13, xq) = all_0_3_3 & sdtasdt0(xp, xq) = all_21_0_13
% 10.93/3.14 |
% 10.93/3.14 | Applying alpha-rule on (139) yields:
% 10.93/3.14 | (140) sdtasdt0(all_21_0_13, xq) = all_0_3_3
% 10.93/3.14 | (141) sdtasdt0(xp, xq) = all_21_0_13
% 10.93/3.14 |
% 10.93/3.14 +-Applying beta-rule and splitting (119), into two cases.
% 10.93/3.14 |-Branch one:
% 10.93/3.14 | (142) xp = sz00
% 10.93/3.14 |
% 10.93/3.14 | Equations (142) can reduce 25 to:
% 10.93/3.14 | (143) $false
% 10.93/3.14 |
% 10.93/3.14 |-The branch is then unsatisfiable
% 10.93/3.14 |-Branch two:
% 10.93/3.14 | (25) ~ (xp = sz00)
% 10.93/3.14 | (145) all_0_1_1 = xq
% 10.93/3.14 |
% 10.93/3.14 | From (145) and (121) follows:
% 10.93/3.15 | (146) sdtasdt0(xq, xp) = xn
% 10.93/3.15 |
% 10.93/3.15 | From (145) and (137) follows:
% 10.93/3.15 | (147) sdtasdt0(xq, xn) = all_19_0_12
% 10.93/3.15 |
% 10.93/3.15 | From (145) and (91) follows:
% 10.93/3.15 | (107) sdtasdt0(xp, xq) = xn
% 10.93/3.15 |
% 10.93/3.15 +-Applying beta-rule and splitting (124), into two cases.
% 10.93/3.15 |-Branch one:
% 10.93/3.15 | (142) xp = sz00
% 10.93/3.15 |
% 10.93/3.15 | Equations (142) can reduce 25 to:
% 10.93/3.15 | (143) $false
% 10.93/3.15 |
% 10.93/3.15 |-The branch is then unsatisfiable
% 10.93/3.15 |-Branch two:
% 10.93/3.15 | (25) ~ (xp = sz00)
% 10.93/3.15 | (152) ? [v0] : (sdtsldt0(v0, xp) = all_0_4_4 & sdtasdt0(xq, xn) = v0)
% 10.93/3.15 |
% 10.93/3.15 | Instantiating (152) with all_39_0_14 yields:
% 10.93/3.15 | (153) sdtsldt0(all_39_0_14, xp) = all_0_4_4 & sdtasdt0(xq, xn) = all_39_0_14
% 10.93/3.15 |
% 10.93/3.15 | Applying alpha-rule on (153) yields:
% 10.93/3.15 | (154) sdtsldt0(all_39_0_14, xp) = all_0_4_4
% 10.93/3.15 | (155) sdtasdt0(xq, xn) = all_39_0_14
% 10.93/3.15 |
% 10.93/3.15 +-Applying beta-rule and splitting (125), into two cases.
% 10.93/3.15 |-Branch one:
% 10.93/3.15 | (142) xp = sz00
% 10.93/3.15 |
% 10.93/3.15 | Equations (142) can reduce 25 to:
% 10.93/3.15 | (143) $false
% 10.93/3.15 |
% 10.93/3.15 |-The branch is then unsatisfiable
% 10.93/3.15 |-Branch two:
% 10.93/3.15 | (25) ~ (xp = sz00)
% 10.93/3.15 | (159) ? [v0] : (sdtsldt0(v0, xp) = xn & sdtasdt0(xp, xn) = v0)
% 10.93/3.15 |
% 10.93/3.15 +-Applying beta-rule and splitting (122), into two cases.
% 10.93/3.15 |-Branch one:
% 10.93/3.15 | (142) xp = sz00
% 10.93/3.15 |
% 10.93/3.15 | Equations (142) can reduce 25 to:
% 10.93/3.15 | (143) $false
% 10.93/3.15 |
% 10.93/3.15 |-The branch is then unsatisfiable
% 10.93/3.15 |-Branch two:
% 10.93/3.15 | (25) ~ (xp = sz00)
% 10.93/3.15 | (163) xp = sz10 | ? [v0] : (isPrime0(v0) & doDivides0(v0, xp) & aNaturalNumber0(v0))
% 10.93/3.15 |
% 10.93/3.15 | Instantiating formula (34) with xq, xn, all_19_0_12, all_39_0_14 and discharging atoms sdtasdt0(xq, xn) = all_39_0_14, sdtasdt0(xq, xn) = all_19_0_12, yields:
% 10.93/3.15 | (164) all_39_0_14 = all_19_0_12
% 10.93/3.15 |
% 10.93/3.15 | Instantiating formula (34) with xq, xn, all_17_0_11, all_39_0_14 and discharging atoms sdtasdt0(xq, xn) = all_39_0_14, sdtasdt0(xq, xn) = all_17_0_11, yields:
% 10.93/3.15 | (165) all_39_0_14 = all_17_0_11
% 10.93/3.15 |
% 10.93/3.15 | Instantiating formula (34) with xp, xq, all_21_0_13, xn and discharging atoms sdtasdt0(xp, xq) = all_21_0_13, sdtasdt0(xp, xq) = xn, yields:
% 10.93/3.15 | (166) all_21_0_13 = xn
% 10.93/3.15 |
% 10.93/3.15 | Instantiating formula (27) with all_11_0_8, xq, xn, xp and discharging atoms sdtsldt0(xn, xp) = xq, sdtasdt0(xp, all_11_0_8) = xn, doDivides0(xp, xn), aNaturalNumber0(all_11_0_8), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 10.93/3.15 | (167) all_11_0_8 = xq | xp = sz00
% 10.93/3.15 |
% 10.93/3.15 | Instantiating formula (108) with all_0_5_5, all_0_0_0, all_0_6_6, xp and discharging atoms sdtasdt0(xp, all_0_0_0) = all_0_5_5, sdtasdt0(xp, all_0_6_6) = all_0_5_5, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_6_6), aNaturalNumber0(xp), yields:
% 10.93/3.15 | (168) all_0_0_0 = all_0_6_6 | xp = sz00
% 10.93/3.15 |
% 10.93/3.15 | Combining equations (164,165) yields a new equation:
% 10.93/3.15 | (169) all_19_0_12 = all_17_0_11
% 10.93/3.15 |
% 10.93/3.15 | Simplifying 169 yields:
% 10.93/3.15 | (170) all_19_0_12 = all_17_0_11
% 10.93/3.15 |
% 10.93/3.15 | From (166) and (140) follows:
% 10.93/3.15 | (171) sdtasdt0(xn, xq) = all_0_3_3
% 10.93/3.15 |
% 10.93/3.15 | From (170) and (147) follows:
% 10.93/3.15 | (134) sdtasdt0(xq, xn) = all_17_0_11
% 10.93/3.15 |
% 10.93/3.15 | From (170) and (138) follows:
% 10.93/3.15 | (135) sdtasdt0(xp, all_17_0_11) = all_0_5_5
% 10.93/3.15 |
% 10.93/3.15 +-Applying beta-rule and splitting (168), into two cases.
% 10.93/3.15 |-Branch one:
% 10.93/3.15 | (142) xp = sz00
% 10.93/3.15 |
% 10.93/3.15 | Equations (142) can reduce 25 to:
% 10.93/3.15 | (143) $false
% 10.93/3.15 |
% 10.93/3.15 |-The branch is then unsatisfiable
% 10.93/3.15 |-Branch two:
% 10.93/3.15 | (25) ~ (xp = sz00)
% 10.93/3.15 | (177) all_0_0_0 = all_0_6_6
% 10.93/3.15 |
% 10.93/3.15 | From (177) and (23) follows:
% 10.93/3.15 | (69) sdtasdt0(xp, all_0_6_6) = all_0_5_5
% 10.93/3.15 |
% 10.93/3.15 | From (177) and (8) follows:
% 10.93/3.15 | (123) aNaturalNumber0(all_0_6_6)
% 10.93/3.15 |
% 10.93/3.15 +-Applying beta-rule and splitting (167), into two cases.
% 10.93/3.15 |-Branch one:
% 10.93/3.15 | (142) xp = sz00
% 10.93/3.15 |
% 10.93/3.15 | Equations (142) can reduce 25 to:
% 10.93/3.15 | (143) $false
% 10.93/3.15 |
% 10.93/3.15 |-The branch is then unsatisfiable
% 10.93/3.15 |-Branch two:
% 10.93/3.15 | (25) ~ (xp = sz00)
% 10.93/3.15 | (183) all_11_0_8 = xq
% 10.93/3.15 |
% 10.93/3.15 | From (183) and (132) follows:
% 10.93/3.15 | (59) aNaturalNumber0(xq)
% 10.93/3.15 |
% 10.93/3.15 | Instantiating formula (50) with all_0_5_5, xn, xp, xq, xn and discharging atoms sdtasdt0(xq, xp) = xn, sdtasdt0(xn, xn) = all_0_5_5, aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 10.93/3.15 | (185) ? [v0] : (sdtasdt0(v0, xp) = all_0_5_5 & sdtasdt0(xn, xq) = v0)
% 10.93/3.15 |
% 10.93/3.15 | Instantiating formula (58) with all_17_0_11, xq, xn and discharging atoms sdtasdt0(xq, xn) = all_17_0_11, aNaturalNumber0(xq), aNaturalNumber0(xn), yields:
% 10.93/3.15 | (186) sdtasdt0(xn, xq) = all_17_0_11
% 10.93/3.15 |
% 10.93/3.15 | Instantiating formula (71) with all_17_0_11, xn, xq and discharging atoms sdtasdt0(xq, xn) = all_17_0_11, aNaturalNumber0(xq), aNaturalNumber0(xn), yields:
% 10.93/3.15 | (187) aNaturalNumber0(all_17_0_11)
% 10.93/3.15 |
% 10.93/3.15 | Instantiating formula (73) with all_0_3_3, xn, xq, xn, xp and discharging atoms sdtsldt0(xn, xp) = xq, sdtasdt0(xn, xq) = all_0_3_3, doDivides0(xp, xn), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 10.93/3.15 | (188) xp = sz00 | ? [v0] : (sdtsldt0(v0, xp) = all_0_3_3 & sdtasdt0(xn, xn) = v0)
% 10.93/3.15 |
% 10.93/3.15 | Instantiating formula (45) with all_0_5_5, xp and discharging atoms doDivides0(xp, all_0_5_5), aNaturalNumber0(all_0_5_5), aNaturalNumber0(xp), yields:
% 10.93/3.15 | (189) ? [v0] : (sdtasdt0(xp, v0) = all_0_5_5 & aNaturalNumber0(v0))
% 10.93/3.15 |
% 10.93/3.15 | Instantiating (189) with all_88_0_20 yields:
% 10.93/3.15 | (190) sdtasdt0(xp, all_88_0_20) = all_0_5_5 & aNaturalNumber0(all_88_0_20)
% 10.93/3.15 |
% 10.93/3.15 | Applying alpha-rule on (190) yields:
% 10.93/3.15 | (191) sdtasdt0(xp, all_88_0_20) = all_0_5_5
% 10.93/3.15 | (192) aNaturalNumber0(all_88_0_20)
% 10.93/3.15 |
% 10.93/3.15 | Instantiating (185) with all_120_0_36 yields:
% 10.93/3.15 | (193) sdtasdt0(all_120_0_36, xp) = all_0_5_5 & sdtasdt0(xn, xq) = all_120_0_36
% 10.93/3.15 |
% 10.93/3.15 | Applying alpha-rule on (193) yields:
% 10.93/3.15 | (194) sdtasdt0(all_120_0_36, xp) = all_0_5_5
% 10.93/3.15 | (195) sdtasdt0(xn, xq) = all_120_0_36
% 10.93/3.15 |
% 10.93/3.15 +-Applying beta-rule and splitting (188), into two cases.
% 10.93/3.15 |-Branch one:
% 10.93/3.15 | (142) xp = sz00
% 10.93/3.15 |
% 10.93/3.15 | Equations (142) can reduce 25 to:
% 10.93/3.15 | (143) $false
% 10.93/3.15 |
% 10.93/3.15 |-The branch is then unsatisfiable
% 10.93/3.15 |-Branch two:
% 10.93/3.15 | (25) ~ (xp = sz00)
% 10.93/3.15 | (199) ? [v0] : (sdtsldt0(v0, xp) = all_0_3_3 & sdtasdt0(xn, xn) = v0)
% 10.93/3.15 |
% 10.93/3.15 | Instantiating formula (34) with xn, xq, all_120_0_36, all_0_3_3 and discharging atoms sdtasdt0(xn, xq) = all_120_0_36, sdtasdt0(xn, xq) = all_0_3_3, yields:
% 10.93/3.15 | (200) all_120_0_36 = all_0_3_3
% 10.93/3.15 |
% 10.93/3.15 | Instantiating formula (34) with xn, xq, all_17_0_11, all_120_0_36 and discharging atoms sdtasdt0(xn, xq) = all_120_0_36, sdtasdt0(xn, xq) = all_17_0_11, yields:
% 10.93/3.15 | (201) all_120_0_36 = all_17_0_11
% 10.93/3.15 |
% 10.93/3.15 | Instantiating formula (108) with all_0_5_5, all_0_6_6, all_88_0_20, xp and discharging atoms sdtasdt0(xp, all_88_0_20) = all_0_5_5, sdtasdt0(xp, all_0_6_6) = all_0_5_5, aNaturalNumber0(all_88_0_20), aNaturalNumber0(all_0_6_6), aNaturalNumber0(xp), yields:
% 10.93/3.15 | (202) all_88_0_20 = all_0_6_6 | xp = sz00
% 10.93/3.15 |
% 10.93/3.15 | Instantiating formula (108) with all_0_5_5, all_17_0_11, all_88_0_20, xp and discharging atoms sdtasdt0(xp, all_88_0_20) = all_0_5_5, sdtasdt0(xp, all_17_0_11) = all_0_5_5, aNaturalNumber0(all_88_0_20), aNaturalNumber0(all_17_0_11), aNaturalNumber0(xp), yields:
% 10.93/3.15 | (203) all_88_0_20 = all_17_0_11 | xp = sz00
% 10.93/3.15 |
% 10.93/3.15 | Combining equations (201,200) yields a new equation:
% 10.93/3.15 | (204) all_17_0_11 = all_0_3_3
% 10.93/3.15 |
% 10.93/3.15 | Simplifying 204 yields:
% 10.93/3.15 | (205) all_17_0_11 = all_0_3_3
% 10.93/3.15 |
% 10.93/3.15 | From (205) and (135) follows:
% 10.93/3.15 | (206) sdtasdt0(xp, all_0_3_3) = all_0_5_5
% 10.93/3.15 |
% 10.93/3.15 +-Applying beta-rule and splitting (202), into two cases.
% 10.93/3.15 |-Branch one:
% 10.93/3.15 | (142) xp = sz00
% 10.93/3.15 |
% 10.93/3.15 | Equations (142) can reduce 25 to:
% 10.93/3.15 | (143) $false
% 10.93/3.15 |
% 10.93/3.15 |-The branch is then unsatisfiable
% 10.93/3.15 |-Branch two:
% 10.93/3.15 | (25) ~ (xp = sz00)
% 10.93/3.15 | (210) all_88_0_20 = all_0_6_6
% 10.93/3.15 |
% 10.93/3.15 +-Applying beta-rule and splitting (203), into two cases.
% 10.93/3.15 |-Branch one:
% 10.93/3.15 | (142) xp = sz00
% 10.93/3.15 |
% 10.93/3.15 | Equations (142) can reduce 25 to:
% 10.93/3.15 | (143) $false
% 10.93/3.15 |
% 10.93/3.15 |-The branch is then unsatisfiable
% 10.93/3.15 |-Branch two:
% 10.93/3.15 | (25) ~ (xp = sz00)
% 10.93/3.15 | (214) all_88_0_20 = all_17_0_11
% 10.93/3.15 |
% 10.93/3.15 | Combining equations (210,214) yields a new equation:
% 10.93/3.15 | (215) all_17_0_11 = all_0_6_6
% 10.93/3.15 |
% 10.93/3.15 | Combining equations (215,205) yields a new equation:
% 10.93/3.15 | (216) all_0_3_3 = all_0_6_6
% 10.93/3.15 |
% 10.93/3.15 | From (216) and (82) follows:
% 10.93/3.15 | (217) sdtasdt0(xp, all_0_6_6) = all_0_2_2
% 10.93/3.15 |
% 10.93/3.15 | From (216) and (206) follows:
% 10.93/3.15 | (69) sdtasdt0(xp, all_0_6_6) = all_0_5_5
% 10.93/3.15 |
% 10.93/3.15 | Instantiating formula (34) with xp, all_0_6_6, all_0_2_2, all_0_5_5 and discharging atoms sdtasdt0(xp, all_0_6_6) = all_0_2_2, sdtasdt0(xp, all_0_6_6) = all_0_5_5, yields:
% 10.93/3.15 | (219) all_0_2_2 = all_0_5_5
% 10.93/3.15 |
% 10.93/3.15 | Equations (219) can reduce 85 to:
% 10.93/3.15 | (143) $false
% 10.93/3.15 |
% 10.93/3.15 |-The branch is then unsatisfiable
% 10.93/3.15 % SZS output end Proof for theBenchmark
% 10.93/3.15
% 10.93/3.15 2549ms
%------------------------------------------------------------------------------