TSTP Solution File: NUM524+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM524+1 : 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 6.94s 2.29s
% Output : Proof 14.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM524+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % 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 03:10:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.59/0.59 ____ _
% 0.59/0.60 ___ / __ \_____(_)___ ________ __________
% 0.59/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.60
% 0.59/0.60 A Theorem Prover for First-Order Logic
% 0.59/0.60 (ePrincess v.1.0)
% 0.59/0.60
% 0.59/0.60 (c) Philipp Rümmer, 2009-2015
% 0.59/0.60 (c) Peter Backeman, 2014-2015
% 0.59/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.60 Bug reports to peter@backeman.se
% 0.59/0.60
% 0.59/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.60
% 0.59/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.81/1.00 Prover 0: Preprocessing ...
% 3.71/1.47 Prover 0: Constructing countermodel ...
% 6.94/2.28 Prover 0: proved (1637ms)
% 6.94/2.29
% 6.94/2.29 No countermodel exists, formula is valid
% 6.94/2.29 % SZS status Theorem for theBenchmark
% 6.94/2.29
% 6.94/2.29 Generating proof ... found it (size 98)
% 13.80/3.88
% 13.80/3.88 % SZS output start Proof for theBenchmark
% 13.80/3.88 Assumed formulas after preprocessing and simplification:
% 13.80/3.88 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v0) & ~ (xp = sz00) & ~ (xm = sz00) & ~ (xn = sz00) & ~ (sz10 = sz00) & sdtsldt0(xn, xp) = xq & sdtasdt0(xq, xq) = v2 & sdtasdt0(xp, v2) = v3 & sdtasdt0(xp, v0) = v1 & sdtasdt0(xm, xm) = v0 & sdtasdt0(xn, xn) = v1 & isPrime0(xp) & doDivides0(xp, v1) & doDivides0(xp, xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ isPrime0(sz10) & ~ isPrime0(sz00) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v4 = sz00 | ~ (sdtsldt0(v8, v4) = v9) | ~ (sdtsldt0(v5, v4) = v6) | ~ (sdtasdt0(v7, v5) = v8) | ~ doDivides0(v4, v5) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtasdt0(v7, v6) = v9) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v6, v4) = v8) | ~ (sdtasdt0(v5, v4) = v7) | ~ (sdtpldt0(v7, v8) = v9) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (sdtasdt0(v10, v4) = v9 & sdtasdt0(v4, v10) = v11 & sdtasdt0(v4, v6) = v13 & sdtasdt0(v4, v5) = v12 & sdtpldt0(v12, v13) = v11 & sdtpldt0(v5, v6) = v10)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v4, v6) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ (sdtpldt0(v7, v8) = v9) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (sdtasdt0(v10, v4) = v11 & sdtasdt0(v6, v4) = v13 & sdtasdt0(v5, v4) = v12 & sdtasdt0(v4, v10) = v9 & sdtpldt0(v12, v13) = v11 & sdtpldt0(v5, v6) = v10)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v8) | ~ (sdtasdt0(v5, v4) = v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v7, v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v8) | ~ (sdtasdt0(v5, v4) = v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtasdt0(v4, v6) = v10 & sdtasdt0(v4, v5) = v9 & sdtlseqdt0(v9, v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v8) | ~ (sdtasdt0(v5, v4) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtasdt0(v4, v6) = v10 & sdtasdt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtasdt0(v5, v4) = v10 & sdtasdt0(v4, v6) = v9 & sdtlseqdt0(v10, v8) & sdtlseqdt0(v7, v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtasdt0(v5, v4) = v10 & sdtasdt0(v4, v6) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v5, v4) = v8) | ~ (sdtasdt0(v4, v6) = v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtasdt0(v6, v4) = v10 & sdtasdt0(v4, v5) = v9 & sdtlseqdt0(v9, v7) & sdtlseqdt0(v8, v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v5, v4) = v8) | ~ (sdtasdt0(v4, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtasdt0(v6, v4) = v10 & sdtasdt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v4, v6) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v7, v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v4, v6) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtasdt0(v6, v4) = v10 & sdtasdt0(v5, v4) = v9 & sdtlseqdt0(v9, v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v4, v6) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtasdt0(v6, v4) = v10 & sdtasdt0(v5, v4) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v6, v4) = v8) | ~ (sdtpldt0(v5, v4) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtpldt0(v4, v6) = v10 & sdtpldt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v6, v4) = v8) | ~ (sdtpldt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtpldt0(v5, v4) = v10 & sdtpldt0(v4, v6) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v5, v4) = v8) | ~ (sdtpldt0(v4, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtpldt0(v6, v4) = v10 & sdtpldt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v4, v6) = v8) | ~ (sdtpldt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtpldt0(v6, v4) = v10 & sdtpldt0(v5, v4) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = sz00 | v5 = sz00 | v4 = sz00 | ~ (sdtasdt0(v6, v7) = v8) | ~ (sdtasdt0(v5, v5) = v7) | ~ (sdtasdt0(v4, v4) = v8) | ~ isPrime0(v6) | ~ iLess0(v4, xn) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v4 = sz00 | ~ (sdtsldt0(v5, v4) = v6) | ~ (sdtasdt0(v7, v6) = v8) | ~ doDivides0(v4, v5) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : (sdtsldt0(v9, v4) = v8 & sdtasdt0(v7, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v7, v6) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : (sdtasdt0(v5, v6) = v9 & sdtasdt0(v4, v9) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v7, v4) = v8) | ~ (sdtpldt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (sdtasdt0(v6, v4) = v13 & sdtasdt0(v5, v4) = v12 & sdtasdt0(v4, v7) = v9 & sdtasdt0(v4, v6) = v11 & sdtasdt0(v4, v5) = v10 & sdtpldt0(v12, v13) = v8 & sdtpldt0(v10, v11) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v5, v6) = v7) | ~ (sdtasdt0(v4, v7) = v8) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : (sdtasdt0(v9, v6) = v8 & sdtasdt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v4, v7) = v8) | ~ (sdtpldt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (sdtasdt0(v7, v4) = v11 & sdtasdt0(v6, v4) = v13 & sdtasdt0(v5, v4) = v12 & sdtasdt0(v4, v6) = v10 & sdtasdt0(v4, v5) = v9 & sdtpldt0(v12, v13) = v11 & sdtpldt0(v9, v10) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v7, v6) = v8) | ~ (sdtpldt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : (sdtpldt0(v5, v6) = v9 & sdtpldt0(v4, v9) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ (sdtpldt0(v4, v7) = v8) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : (sdtpldt0(v9, v6) = v8 & sdtpldt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | v4 = sz00 | ~ (sdtsldt0(v5, v4) = v6) | ~ (sdtasdt0(v4, v7) = v5) | ~ doDivides0(v4, v5) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (sdtmndt0(v5, v4) = v6) | ~ (sdtpldt0(v4, v7) = v5) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | v4 = sz00 | ~ (sdtsldt0(v5, v4) = v6) | ~ (sdtasdt0(v4, v6) = v7) | ~ doDivides0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (sdtmndt0(v5, v4) = v6) | ~ (sdtpldt0(v4, v6) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v7) | ~ (sdtasdt0(v5, v4) = v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v7) | ~ (sdtasdt0(v5, v4) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v4, v6) = v7) | ~ (sdtasdt0(v4, v5) = v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v4, v6) = v7) | ~ (sdtasdt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (sdtpldt0(v6, v4) = v7) | ~ (sdtpldt0(v5, v4) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (sdtpldt0(v4, v6) = v7) | ~ (sdtpldt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtsldt0(v7, v6) = v5) | ~ (sdtsldt0(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtmndt0(v7, v6) = v5) | ~ (sdtmndt0(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtasdt0(v7, v6) = v5) | ~ (sdtasdt0(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v7, v6) = v5) | ~ (sdtpldt0(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v6, v5) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = v9) & ~ (v8 = v7) & sdtpldt0(v6, v4) = v8 & sdtpldt0(v5, v6) = v10 & sdtpldt0(v4, v6) = v9 & sdtlseqdt0(v9, v10) & sdtlseqdt0(v8, v7))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v6, v4) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = v9) & ~ (v8 = v7) & sdtpldt0(v6, v5) = v8 & sdtpldt0(v5, v6) = v10 & sdtpldt0(v4, v6) = v9 & sdtlseqdt0(v9, v10) & sdtlseqdt0(v7, v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v5, v6) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = v7) & ~ (v9 = v8) & sdtpldt0(v6, v5) = v9 & sdtpldt0(v6, v4) = v8 & sdtpldt0(v4, v6) = v10 & sdtlseqdt0(v10, v7) & sdtlseqdt0(v8, v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v4, v6) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = v7) & ~ (v9 = v8) & sdtpldt0(v6, v5) = v9 & sdtpldt0(v6, v4) = v8 & sdtpldt0(v5, v6) = v10 & sdtlseqdt0(v8, v9) & sdtlseqdt0(v7, v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v4 = sz00 | ~ (sdtsldt0(v5, v4) = v6) | ~ (sdtasdt0(v4, v6) = v7) | ~ doDivides0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | aNaturalNumber0(v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtmndt0(v5, v4) = v6) | ~ (sdtpldt0(v4, v6) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | aNaturalNumber0(v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v4, v5) = v7) | ~ isPrime0(v6) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | doDivides0(v6, v5) | doDivides0(v6, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ doDivides0(v4, v7) | ~ doDivides0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | doDivides0(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ doDivides0(v4, v6) | ~ doDivides0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | doDivides0(v4, v7)) & ! [v4] : ! [v5] : ! [v6] : (v4 = sz00 | ~ (sdtasdt0(v5, v4) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v5, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, v4) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtasdt0(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v4, v6) = v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | doDivides0(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v4, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtasdt0(v5, v4) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v4, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | aNaturalNumber0(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v5, v4) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtpldt0(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v4, v6) = v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v4, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtpldt0(v5, v4) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v4, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | aNaturalNumber0(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ doDivides0(v5, v6) | ~ doDivides0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | doDivides0(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ sdtlseqdt0(v5, v6) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v4, v6)) & ! [v4] : ! [v5] : (v5 = v4 | v5 = sz10 | ~ isPrime0(v4) | ~ doDivides0(v5, v4) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtasdt0(v4, sz10) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtasdt0(sz10, v4) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtpldt0(v4, sz00) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtpldt0(sz00, v4) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ sdtlseqdt0(v5, v4) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | iLess0(v4, v5)) & ! [v4] : ! [v5] : (v5 = sz00 | v4 = sz00 | ~ (sdtasdt0(v4, v5) = sz00) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = sz00 | ~ (sdtasdt0(v4, sz00) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = sz00 | ~ (sdtasdt0(sz00, v4) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = sz00 | ~ (sdtpldt0(v4, v5) = sz00) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = sz00 | ~ doDivides0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v4, v5)) & ! [v4] : ! [v5] : (v4 = sz00 | ~ (sdtpldt0(v4, v5) = sz00) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ( ~ (sdtasdt0(v4, sz10) = v5) | ~ aNaturalNumber0(v4) | sdtasdt0(sz10, v4) = v4) & ! [v4] : ! [v5] : ( ~ (sdtasdt0(v4, sz00) = v5) | ~ aNaturalNumber0(v4) | sdtasdt0(sz00, v4) = sz00) & ! [v4] : ! [v5] : ( ~ (sdtasdt0(sz10, v4) = v5) | ~ aNaturalNumber0(v4) | sdtasdt0(v4, sz10) = v4) & ! [v4] : ! [v5] : ( ~ (sdtasdt0(sz00, v4) = v5) | ~ aNaturalNumber0(v4) | sdtasdt0(v4, sz00) = sz00) & ! [v4] : ! [v5] : ( ~ (sdtpldt0(v4, sz00) = v5) | ~ aNaturalNumber0(v4) | sdtpldt0(sz00, v4) = v4) & ! [v4] : ! [v5] : ( ~ (sdtpldt0(sz00, v4) = v5) | ~ aNaturalNumber0(v4) | sdtpldt0(v4, sz00) = v4) & ! [v4] : ! [v5] : ( ~ doDivides0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v6] : (sdtasdt0(v4, v6) = v5 & aNaturalNumber0(v6))) & ! [v4] : ! [v5] : ( ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v6] : (sdtpldt0(v4, v6) = v5 & aNaturalNumber0(v6))) & ! [v4] : ! [v5] : ( ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v5, v4) | sdtlseqdt0(v4, v5)) & ! [v4] : (v4 = sz10 | v4 = sz00 | ~ aNaturalNumber0(v4) | isPrime0(v4) | ? [v5] : ( ~ (v5 = v4) & ~ (v5 = sz10) & doDivides0(v5, v4) & aNaturalNumber0(v5))) & ! [v4] : (v4 = sz10 | v4 = sz00 | ~ aNaturalNumber0(v4) | sdtlseqdt0(sz10, v4)) & ! [v4] : (v4 = sz10 | v4 = sz00 | ~ aNaturalNumber0(v4) | ? [v5] : (isPrime0(v5) & doDivides0(v5, v4) & aNaturalNumber0(v5))) & ! [v4] : ( ~ aNaturalNumber0(v4) | sdtlseqdt0(v4, v4)))
% 14.06/3.95 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 14.06/3.95 | (1) ~ (all_0_0_0 = all_0_3_3) & ~ (xp = sz00) & ~ (xm = sz00) & ~ (xn = sz00) & ~ (sz10 = sz00) & sdtsldt0(xn, xp) = xq & sdtasdt0(xq, xq) = all_0_1_1 & sdtasdt0(xp, all_0_1_1) = all_0_0_0 & sdtasdt0(xp, all_0_3_3) = all_0_2_2 & sdtasdt0(xm, xm) = all_0_3_3 & sdtasdt0(xn, xn) = all_0_2_2 & isPrime0(xp) & doDivides0(xp, all_0_2_2) & doDivides0(xp, xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ isPrime0(sz10) & ~ isPrime0(sz00) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v3, v2) = v5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(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 = 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 = 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 = 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))
% 14.49/3.98 |
% 14.49/3.98 | Applying alpha-rule on (1) yields:
% 14.49/3.98 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 14.49/3.98 | (3) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 14.49/3.98 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2)
% 14.49/3.98 | (5) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 14.49/3.98 | (6) sdtsldt0(xn, xp) = xq
% 14.49/3.98 | (7) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 14.49/3.98 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3))
% 14.49/3.98 | (9) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 14.49/3.98 | (10) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 14.49/3.98 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 14.49/3.98 | (12) aNaturalNumber0(xn)
% 14.49/3.98 | (13) ~ isPrime0(sz00)
% 14.49/3.98 | (14) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 14.49/3.98 | (15) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00)
% 14.49/3.98 | (16) ! [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))
% 14.49/3.98 | (17) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 14.49/3.98 | (18) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 14.49/3.98 | (19) ! [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))
% 14.49/3.98 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 14.49/3.99 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 14.49/3.99 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0))
% 14.49/3.99 | (23) ! [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))
% 14.49/3.99 | (24) ~ (xm = sz00)
% 14.49/3.99 | (25) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 14.49/3.99 | (26) sdtasdt0(xm, xm) = all_0_3_3
% 14.49/3.99 | (27) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1] : ( ~ (v1 = v0) & ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 14.49/3.99 | (28) ! [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))
% 14.49/3.99 | (29) doDivides0(xp, xn)
% 14.49/3.99 | (30) isPrime0(xp)
% 14.49/3.99 | (31) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 14.59/3.99 | (32) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0)
% 14.59/3.99 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 14.59/3.99 | (34) ! [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)))
% 14.59/3.99 | (35) ! [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))
% 14.59/3.99 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 14.59/3.99 | (37) ! [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))
% 14.59/3.99 | (38) ! [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))
% 14.59/3.99 | (39) ~ (xn = sz00)
% 14.59/3.99 | (40) ! [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)))
% 14.59/3.99 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 14.59/3.99 | (42) sdtasdt0(xq, xq) = all_0_1_1
% 14.59/3.99 | (43) ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 14.59/3.99 | (44) doDivides0(xp, all_0_2_2)
% 14.59/3.99 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 14.59/3.99 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4))
% 14.59/4.00 | (47) ~ (xp = sz00)
% 14.59/4.00 | (48) ~ isPrime0(sz10)
% 14.59/4.00 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2)
% 14.59/4.00 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 14.59/4.00 | (51) ! [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))
% 14.59/4.00 | (52) ! [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))
% 14.59/4.00 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 14.59/4.00 | (54) aNaturalNumber0(sz00)
% 14.59/4.00 | (55) ! [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))
% 14.59/4.00 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 14.59/4.00 | (57) aNaturalNumber0(sz10)
% 14.59/4.00 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 14.59/4.00 | (59) ! [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))
% 14.59/4.00 | (60) aNaturalNumber0(xp)
% 14.59/4.00 | (61) ! [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)))
% 14.59/4.00 | (62) ~ (all_0_0_0 = all_0_3_3)
% 14.59/4.00 | (63) ! [v0] : ! [v1] : (v1 = sz00 | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 14.59/4.00 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 14.59/4.00 | (65) ! [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))
% 14.59/4.00 | (66) ! [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)))
% 14.59/4.00 | (67) ! [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)
% 14.59/4.00 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 14.59/4.00 | (69) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 14.59/4.00 | (70) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0)
% 14.59/4.00 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 14.59/4.00 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 14.59/4.01 | (73) ! [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))
% 14.59/4.01 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 14.59/4.01 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 14.59/4.01 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 14.59/4.01 | (77) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 14.59/4.01 | (78) ! [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))
% 14.59/4.01 | (79) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 14.59/4.01 | (80) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 14.59/4.01 | (81) ! [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)))
% 14.59/4.01 | (82) ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 14.59/4.01 | (83) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0))
% 14.59/4.01 | (84) aNaturalNumber0(xm)
% 14.59/4.01 | (85) ! [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))
% 14.59/4.01 | (86) ! [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))
% 14.59/4.01 | (87) ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 14.59/4.01 | (88) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 14.59/4.01 | (89) ! [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))
% 14.59/4.01 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 14.59/4.01 | (91) sdtasdt0(xp, all_0_3_3) = all_0_2_2
% 14.59/4.01 | (92) ! [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))
% 14.59/4.01 | (93) ! [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)))
% 14.59/4.01 | (94) ! [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))
% 14.59/4.01 | (95) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 14.59/4.01 | (96) ! [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))
% 14.59/4.02 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 14.59/4.02 | (98) ! [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))
% 14.59/4.02 | (99) ! [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))
% 14.59/4.02 | (100) ! [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)))
% 14.59/4.02 | (101) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 14.59/4.02 | (102) sdtasdt0(xn, xn) = all_0_2_2
% 14.59/4.02 | (103) sdtasdt0(xp, all_0_1_1) = all_0_0_0
% 14.59/4.02 | (104) ! [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)))
% 14.59/4.02 | (105) ~ (sz10 = sz00)
% 14.59/4.02 | (106) ! [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))
% 14.59/4.02 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 14.59/4.02 |
% 14.59/4.02 | Instantiating formula (88) with xp, xp and discharging atoms aNaturalNumber0(xp), yields:
% 14.59/4.02 | (108) sdtlseqdt0(xp, xp)
% 14.59/4.02 |
% 14.59/4.02 | Instantiating formula (20) with all_0_3_3, xm, xm and discharging atoms sdtasdt0(xm, xm) = all_0_3_3, aNaturalNumber0(xm), yields:
% 14.59/4.02 | (109) aNaturalNumber0(all_0_3_3)
% 14.59/4.02 |
% 14.59/4.02 | Instantiating formula (20) with all_0_2_2, xn, xn and discharging atoms sdtasdt0(xn, xn) = all_0_2_2, aNaturalNumber0(xn), yields:
% 14.59/4.02 | (110) aNaturalNumber0(all_0_2_2)
% 14.59/4.02 |
% 14.59/4.02 | Instantiating formula (63) with xn, xp and discharging atoms doDivides0(xp, xn), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 14.59/4.02 | (111) xn = sz00 | sdtlseqdt0(xp, xn)
% 14.59/4.02 |
% 14.59/4.02 | Instantiating formula (43) with xn, xp and discharging atoms doDivides0(xp, xn), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 14.59/4.02 | (112) ? [v0] : (sdtasdt0(xp, v0) = xn & aNaturalNumber0(v0))
% 14.59/4.02 |
% 14.59/4.02 | Instantiating formula (88) with xn, xn and discharging atoms aNaturalNumber0(xn), yields:
% 14.59/4.02 | (113) sdtlseqdt0(xn, xn)
% 14.59/4.02 |
% 14.59/4.02 | Instantiating (112) with all_9_0_4 yields:
% 14.59/4.02 | (114) sdtasdt0(xp, all_9_0_4) = xn & aNaturalNumber0(all_9_0_4)
% 14.59/4.02 |
% 14.59/4.02 | Applying alpha-rule on (114) yields:
% 14.59/4.02 | (115) sdtasdt0(xp, all_9_0_4) = xn
% 14.59/4.02 | (116) aNaturalNumber0(all_9_0_4)
% 14.59/4.02 |
% 14.59/4.02 +-Applying beta-rule and splitting (111), into two cases.
% 14.59/4.02 |-Branch one:
% 14.59/4.02 | (117) sdtlseqdt0(xp, xn)
% 14.59/4.02 |
% 14.59/4.02 | Instantiating formula (96) with all_9_0_4, xq, xn, xp and discharging atoms sdtsldt0(xn, xp) = xq, sdtasdt0(xp, all_9_0_4) = xn, doDivides0(xp, xn), aNaturalNumber0(all_9_0_4), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 14.59/4.02 | (118) all_9_0_4 = xq | xp = sz00
% 14.59/4.02 |
% 14.59/4.02 | Instantiating formula (101) with xp, xp and discharging atoms sdtlseqdt0(xp, xp), aNaturalNumber0(xp), yields:
% 14.59/4.02 | (119) ? [v0] : (sdtpldt0(xp, v0) = xp & aNaturalNumber0(v0))
% 14.59/4.02 |
% 14.59/4.02 | Instantiating formula (101) with xn, xp and discharging atoms sdtlseqdt0(xp, xn), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 14.59/4.02 | (120) ? [v0] : (sdtpldt0(xp, v0) = xn & aNaturalNumber0(v0))
% 14.59/4.02 |
% 14.59/4.02 | Instantiating formula (101) with xn, xn and discharging atoms sdtlseqdt0(xn, xn), aNaturalNumber0(xn), yields:
% 14.59/4.03 | (121) ? [v0] : (sdtpldt0(xn, v0) = xn & aNaturalNumber0(v0))
% 14.59/4.03 |
% 14.59/4.03 | Instantiating formula (94) with all_0_2_2, xn, xn, all_9_0_4, xp and discharging atoms sdtasdt0(xp, all_9_0_4) = xn, sdtasdt0(xn, xn) = all_0_2_2, aNaturalNumber0(all_9_0_4), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 14.59/4.03 | (122) ? [v0] : (sdtasdt0(all_9_0_4, xn) = v0 & sdtasdt0(xp, v0) = all_0_2_2)
% 14.59/4.03 |
% 14.59/4.03 | Instantiating formula (49) with xn, xp, all_9_0_4 and discharging atoms sdtasdt0(xp, all_9_0_4) = xn, aNaturalNumber0(all_9_0_4), aNaturalNumber0(xp), yields:
% 14.59/4.03 | (123) sdtasdt0(all_9_0_4, xp) = xn
% 14.59/4.03 |
% 14.59/4.03 | Instantiating formula (43) with all_0_2_2, xp and discharging atoms doDivides0(xp, all_0_2_2), aNaturalNumber0(all_0_2_2), aNaturalNumber0(xp), yields:
% 14.59/4.03 | (124) ? [v0] : (sdtasdt0(xp, v0) = all_0_2_2 & aNaturalNumber0(v0))
% 14.59/4.03 |
% 14.59/4.03 | Instantiating (124) with all_33_0_7 yields:
% 14.59/4.03 | (125) sdtasdt0(xp, all_33_0_7) = all_0_2_2 & aNaturalNumber0(all_33_0_7)
% 14.59/4.03 |
% 14.59/4.03 | Applying alpha-rule on (125) yields:
% 14.59/4.03 | (126) sdtasdt0(xp, all_33_0_7) = all_0_2_2
% 14.59/4.03 | (127) aNaturalNumber0(all_33_0_7)
% 14.59/4.03 |
% 14.59/4.03 | Instantiating (122) with all_39_0_10 yields:
% 14.59/4.03 | (128) sdtasdt0(all_9_0_4, xn) = all_39_0_10 & sdtasdt0(xp, all_39_0_10) = all_0_2_2
% 14.59/4.03 |
% 14.59/4.03 | Applying alpha-rule on (128) yields:
% 14.59/4.03 | (129) sdtasdt0(all_9_0_4, xn) = all_39_0_10
% 14.59/4.03 | (130) sdtasdt0(xp, all_39_0_10) = all_0_2_2
% 14.59/4.03 |
% 14.59/4.03 | Instantiating (119) with all_41_0_11 yields:
% 14.59/4.03 | (131) sdtpldt0(xp, all_41_0_11) = xp & aNaturalNumber0(all_41_0_11)
% 14.59/4.03 |
% 14.59/4.03 | Applying alpha-rule on (131) yields:
% 14.59/4.03 | (132) sdtpldt0(xp, all_41_0_11) = xp
% 14.59/4.03 | (133) aNaturalNumber0(all_41_0_11)
% 14.59/4.03 |
% 14.59/4.03 | Instantiating (121) with all_45_0_13 yields:
% 14.59/4.03 | (134) sdtpldt0(xn, all_45_0_13) = xn & aNaturalNumber0(all_45_0_13)
% 14.59/4.03 |
% 14.59/4.03 | Applying alpha-rule on (134) yields:
% 14.59/4.03 | (135) sdtpldt0(xn, all_45_0_13) = xn
% 14.59/4.03 | (136) aNaturalNumber0(all_45_0_13)
% 14.59/4.03 |
% 14.59/4.03 | Instantiating (120) with all_51_0_16 yields:
% 14.59/4.03 | (137) sdtpldt0(xp, all_51_0_16) = xn & aNaturalNumber0(all_51_0_16)
% 14.59/4.03 |
% 14.59/4.03 | Applying alpha-rule on (137) yields:
% 14.59/4.03 | (138) sdtpldt0(xp, all_51_0_16) = xn
% 14.59/4.03 | (139) aNaturalNumber0(all_51_0_16)
% 14.59/4.03 |
% 14.59/4.03 +-Applying beta-rule and splitting (118), into two cases.
% 14.59/4.03 |-Branch one:
% 14.59/4.03 | (140) xp = sz00
% 14.79/4.03 |
% 14.79/4.03 | Equations (140) can reduce 47 to:
% 14.79/4.03 | (141) $false
% 14.79/4.03 |
% 14.79/4.03 |-The branch is then unsatisfiable
% 14.79/4.03 |-Branch two:
% 14.79/4.03 | (47) ~ (xp = sz00)
% 14.79/4.03 | (143) all_9_0_4 = xq
% 14.79/4.03 |
% 14.79/4.03 | From (143) and (123) follows:
% 14.79/4.03 | (144) sdtasdt0(xq, xp) = xn
% 14.79/4.03 |
% 14.79/4.03 | From (143) and (129) follows:
% 14.79/4.03 | (145) sdtasdt0(xq, xn) = all_39_0_10
% 14.79/4.03 |
% 14.79/4.03 | From (143) and (115) follows:
% 14.79/4.03 | (146) sdtasdt0(xp, xq) = xn
% 14.79/4.03 |
% 14.79/4.03 | From (143) and (116) follows:
% 14.79/4.03 | (147) aNaturalNumber0(xq)
% 14.79/4.03 |
% 14.79/4.03 | Instantiating formula (64) with all_0_2_2, all_0_3_3, all_33_0_7, xp and discharging atoms sdtasdt0(xp, all_33_0_7) = all_0_2_2, sdtasdt0(xp, all_0_3_3) = all_0_2_2, aNaturalNumber0(all_33_0_7), aNaturalNumber0(all_0_3_3), aNaturalNumber0(xp), yields:
% 14.79/4.03 | (148) all_33_0_7 = all_0_3_3 | xp = sz00
% 14.79/4.03 |
% 14.79/4.03 +-Applying beta-rule and splitting (148), into two cases.
% 14.79/4.03 |-Branch one:
% 14.79/4.03 | (140) xp = sz00
% 14.79/4.03 |
% 14.79/4.03 | Equations (140) can reduce 47 to:
% 14.79/4.03 | (141) $false
% 14.79/4.03 |
% 14.79/4.03 |-The branch is then unsatisfiable
% 14.79/4.03 |-Branch two:
% 14.79/4.03 | (47) ~ (xp = sz00)
% 14.79/4.03 | (152) all_33_0_7 = all_0_3_3
% 14.79/4.03 |
% 14.79/4.03 | From (152) and (126) follows:
% 14.79/4.03 | (91) sdtasdt0(xp, all_0_3_3) = all_0_2_2
% 14.79/4.03 |
% 14.79/4.03 | From (152) and (127) follows:
% 14.79/4.03 | (109) aNaturalNumber0(all_0_3_3)
% 14.79/4.03 |
% 14.79/4.03 | Instantiating formula (78) 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:
% 14.79/4.03 | (155) xp = sz00 | ? [v0] : (sdtsldt0(v0, xp) = xn & sdtasdt0(xp, xn) = v0)
% 14.79/4.04 |
% 14.79/4.04 | Instantiating formula (78) with all_0_1_1, xq, xq, xn, xp and discharging atoms sdtsldt0(xn, xp) = xq, sdtasdt0(xq, xq) = all_0_1_1, doDivides0(xp, xn), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 14.79/4.04 | (156) xp = sz00 | ? [v0] : (sdtsldt0(v0, xp) = all_0_1_1 & sdtasdt0(xq, xn) = v0)
% 14.79/4.04 |
% 14.79/4.04 | Instantiating formula (98) with all_0_0_0, all_0_1_1, xq, xq, xp and discharging atoms sdtasdt0(xq, xq) = all_0_1_1, sdtasdt0(xp, all_0_1_1) = all_0_0_0, aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 14.79/4.04 | (157) ? [v0] : (sdtasdt0(v0, xq) = all_0_0_0 & sdtasdt0(xp, xq) = v0)
% 14.79/4.04 |
% 14.79/4.04 | Instantiating formula (98) with all_0_2_2, xn, xp, xq, xn and discharging atoms sdtasdt0(xq, xp) = xn, sdtasdt0(xn, xn) = all_0_2_2, aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 14.79/4.04 | (158) ? [v0] : (sdtasdt0(v0, xp) = all_0_2_2 & sdtasdt0(xn, xq) = v0)
% 14.79/4.04 |
% 14.79/4.04 | Instantiating formula (37) with xn, xp, all_41_0_11, xp, xq and discharging atoms sdtasdt0(xq, xp) = xn, sdtpldt0(xp, all_41_0_11) = xp, aNaturalNumber0(all_41_0_11), aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 14.79/4.04 | (159) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_41_0_11, xq) = v4 & sdtasdt0(xq, all_41_0_11) = v1 & sdtasdt0(xq, xp) = v0 & sdtasdt0(xp, xq) = v3 & sdtasdt0(xp, xq) = v2 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = xn)
% 14.79/4.04 |
% 14.79/4.04 | Instantiating formula (37) with all_39_0_10, xn, all_51_0_16, xp, xq and discharging atoms sdtasdt0(xq, xn) = all_39_0_10, sdtpldt0(xp, all_51_0_16) = xn, aNaturalNumber0(all_51_0_16), aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 14.79/4.04 | (160) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_51_0_16, xq) = v4 & sdtasdt0(xq, all_51_0_16) = v1 & sdtasdt0(xq, xp) = v0 & sdtasdt0(xp, xq) = v3 & sdtasdt0(xn, xq) = v2 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_39_0_10)
% 14.83/4.04 |
% 14.83/4.04 | Instantiating formula (37) with all_39_0_10, xn, all_45_0_13, xn, xq and discharging atoms sdtasdt0(xq, xn) = all_39_0_10, sdtpldt0(xn, all_45_0_13) = xn, aNaturalNumber0(all_45_0_13), aNaturalNumber0(xq), aNaturalNumber0(xn), yields:
% 14.83/4.04 | (161) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_45_0_13, xq) = v4 & sdtasdt0(xq, all_45_0_13) = v1 & sdtasdt0(xq, xn) = v0 & sdtasdt0(xn, xq) = v3 & sdtasdt0(xn, xq) = v2 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_39_0_10)
% 14.83/4.04 |
% 14.83/4.04 | Instantiating formula (49) with all_39_0_10, xq, xn and discharging atoms sdtasdt0(xq, xn) = all_39_0_10, aNaturalNumber0(xq), aNaturalNumber0(xn), yields:
% 14.83/4.04 | (162) sdtasdt0(xn, xq) = all_39_0_10
% 14.83/4.04 |
% 14.83/4.04 | Instantiating formula (20) with all_39_0_10, xn, xq and discharging atoms sdtasdt0(xq, xn) = all_39_0_10, aNaturalNumber0(xq), aNaturalNumber0(xn), yields:
% 14.83/4.04 | (163) aNaturalNumber0(all_39_0_10)
% 14.83/4.04 |
% 14.83/4.04 | Instantiating formula (65) with xn, xp, all_41_0_11, xp, xq and discharging atoms sdtasdt0(xp, xq) = xn, sdtpldt0(xp, all_41_0_11) = xp, aNaturalNumber0(all_41_0_11), aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 14.83/4.04 | (164) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_41_0_11, xq) = v4 & sdtasdt0(xq, all_41_0_11) = v2 & sdtasdt0(xq, xp) = v1 & sdtasdt0(xq, xp) = v0 & sdtasdt0(xp, xq) = v3 & sdtpldt0(v3, v4) = xn & sdtpldt0(v1, v2) = v0)
% 14.83/4.04 |
% 14.83/4.04 | Instantiating (161) with all_107_0_45, all_107_1_46, all_107_2_47, all_107_3_48, all_107_4_49 yields:
% 14.83/4.04 | (165) sdtasdt0(all_45_0_13, xq) = all_107_0_45 & sdtasdt0(xq, all_45_0_13) = all_107_3_48 & sdtasdt0(xq, xn) = all_107_4_49 & sdtasdt0(xn, xq) = all_107_1_46 & sdtasdt0(xn, xq) = all_107_2_47 & sdtpldt0(all_107_1_46, all_107_0_45) = all_107_2_47 & sdtpldt0(all_107_4_49, all_107_3_48) = all_39_0_10
% 14.83/4.04 |
% 14.83/4.04 | Applying alpha-rule on (165) yields:
% 14.83/4.04 | (166) sdtasdt0(xn, xq) = all_107_2_47
% 14.83/4.04 | (167) sdtasdt0(xq, xn) = all_107_4_49
% 14.83/4.04 | (168) sdtasdt0(xq, all_45_0_13) = all_107_3_48
% 14.83/4.04 | (169) sdtpldt0(all_107_4_49, all_107_3_48) = all_39_0_10
% 14.83/4.04 | (170) sdtasdt0(all_45_0_13, xq) = all_107_0_45
% 14.83/4.04 | (171) sdtpldt0(all_107_1_46, all_107_0_45) = all_107_2_47
% 14.83/4.04 | (172) sdtasdt0(xn, xq) = all_107_1_46
% 14.83/4.04 |
% 14.83/4.04 | Instantiating (160) with all_109_0_50, all_109_1_51, all_109_2_52, all_109_3_53, all_109_4_54 yields:
% 14.83/4.04 | (173) sdtasdt0(all_51_0_16, xq) = all_109_0_50 & sdtasdt0(xq, all_51_0_16) = all_109_3_53 & sdtasdt0(xq, xp) = all_109_4_54 & sdtasdt0(xp, xq) = all_109_1_51 & sdtasdt0(xn, xq) = all_109_2_52 & sdtpldt0(all_109_1_51, all_109_0_50) = all_109_2_52 & sdtpldt0(all_109_4_54, all_109_3_53) = all_39_0_10
% 14.83/4.04 |
% 14.83/4.04 | Applying alpha-rule on (173) yields:
% 14.83/4.04 | (174) sdtasdt0(xq, xp) = all_109_4_54
% 14.83/4.04 | (175) sdtasdt0(xp, xq) = all_109_1_51
% 14.83/4.04 | (176) sdtpldt0(all_109_1_51, all_109_0_50) = all_109_2_52
% 14.83/4.04 | (177) sdtasdt0(xn, xq) = all_109_2_52
% 14.83/4.04 | (178) sdtpldt0(all_109_4_54, all_109_3_53) = all_39_0_10
% 14.83/4.04 | (179) sdtasdt0(all_51_0_16, xq) = all_109_0_50
% 14.83/4.04 | (180) sdtasdt0(xq, all_51_0_16) = all_109_3_53
% 14.83/4.04 |
% 14.83/4.04 | Instantiating (164) with all_139_0_101, all_139_1_102, all_139_2_103, all_139_3_104, all_139_4_105 yields:
% 14.83/4.04 | (181) sdtasdt0(all_41_0_11, xq) = all_139_0_101 & sdtasdt0(xq, all_41_0_11) = all_139_2_103 & sdtasdt0(xq, xp) = all_139_3_104 & sdtasdt0(xq, xp) = all_139_4_105 & sdtasdt0(xp, xq) = all_139_1_102 & sdtpldt0(all_139_1_102, all_139_0_101) = xn & sdtpldt0(all_139_3_104, all_139_2_103) = all_139_4_105
% 14.83/4.04 |
% 14.83/4.04 | Applying alpha-rule on (181) yields:
% 14.83/4.04 | (182) sdtasdt0(xq, all_41_0_11) = all_139_2_103
% 14.83/4.04 | (183) sdtasdt0(xp, xq) = all_139_1_102
% 14.83/4.04 | (184) sdtpldt0(all_139_3_104, all_139_2_103) = all_139_4_105
% 14.83/4.04 | (185) sdtasdt0(xq, xp) = all_139_3_104
% 14.83/4.04 | (186) sdtpldt0(all_139_1_102, all_139_0_101) = xn
% 14.83/4.04 | (187) sdtasdt0(all_41_0_11, xq) = all_139_0_101
% 14.83/4.04 | (188) sdtasdt0(xq, xp) = all_139_4_105
% 14.83/4.04 |
% 14.83/4.04 | Instantiating (159) with all_157_0_138, all_157_1_139, all_157_2_140, all_157_3_141, all_157_4_142 yields:
% 14.83/4.04 | (189) sdtasdt0(all_41_0_11, xq) = all_157_0_138 & sdtasdt0(xq, all_41_0_11) = all_157_3_141 & sdtasdt0(xq, xp) = all_157_4_142 & sdtasdt0(xp, xq) = all_157_1_139 & sdtasdt0(xp, xq) = all_157_2_140 & sdtpldt0(all_157_1_139, all_157_0_138) = all_157_2_140 & sdtpldt0(all_157_4_142, all_157_3_141) = xn
% 14.83/4.05 |
% 14.83/4.05 | Applying alpha-rule on (189) yields:
% 14.83/4.05 | (190) sdtpldt0(all_157_4_142, all_157_3_141) = xn
% 14.83/4.05 | (191) sdtasdt0(xp, xq) = all_157_2_140
% 14.83/4.05 | (192) sdtasdt0(xq, all_41_0_11) = all_157_3_141
% 14.83/4.05 | (193) sdtasdt0(all_41_0_11, xq) = all_157_0_138
% 14.83/4.05 | (194) sdtasdt0(xp, xq) = all_157_1_139
% 14.83/4.05 | (195) sdtasdt0(xq, xp) = all_157_4_142
% 14.83/4.05 | (196) sdtpldt0(all_157_1_139, all_157_0_138) = all_157_2_140
% 14.83/4.05 |
% 14.83/4.05 | Instantiating (158) with all_159_0_143 yields:
% 14.83/4.05 | (197) sdtasdt0(all_159_0_143, xp) = all_0_2_2 & sdtasdt0(xn, xq) = all_159_0_143
% 14.83/4.05 |
% 14.83/4.05 | Applying alpha-rule on (197) yields:
% 14.83/4.05 | (198) sdtasdt0(all_159_0_143, xp) = all_0_2_2
% 14.83/4.05 | (199) sdtasdt0(xn, xq) = all_159_0_143
% 14.83/4.05 |
% 14.83/4.05 | Instantiating (157) with all_167_0_151 yields:
% 14.83/4.05 | (200) sdtasdt0(all_167_0_151, xq) = all_0_0_0 & sdtasdt0(xp, xq) = all_167_0_151
% 14.83/4.05 |
% 14.83/4.05 | Applying alpha-rule on (200) yields:
% 14.83/4.05 | (201) sdtasdt0(all_167_0_151, xq) = all_0_0_0
% 14.83/4.05 | (202) sdtasdt0(xp, xq) = all_167_0_151
% 14.83/4.05 |
% 14.83/4.05 +-Applying beta-rule and splitting (155), into two cases.
% 14.83/4.05 |-Branch one:
% 14.83/4.05 | (140) xp = sz00
% 14.83/4.05 |
% 14.83/4.05 | Equations (140) can reduce 47 to:
% 14.83/4.05 | (141) $false
% 14.83/4.05 |
% 14.83/4.05 |-The branch is then unsatisfiable
% 14.83/4.05 |-Branch two:
% 14.83/4.05 | (47) ~ (xp = sz00)
% 14.83/4.05 | (206) ? [v0] : (sdtsldt0(v0, xp) = xn & sdtasdt0(xp, xn) = v0)
% 14.83/4.05 |
% 14.83/4.05 +-Applying beta-rule and splitting (156), into two cases.
% 14.83/4.05 |-Branch one:
% 14.83/4.05 | (140) xp = sz00
% 14.83/4.05 |
% 14.83/4.05 | Equations (140) can reduce 47 to:
% 14.83/4.05 | (141) $false
% 14.83/4.05 |
% 14.83/4.05 |-The branch is then unsatisfiable
% 14.83/4.05 |-Branch two:
% 14.83/4.05 | (47) ~ (xp = sz00)
% 14.83/4.05 | (210) ? [v0] : (sdtsldt0(v0, xp) = all_0_1_1 & sdtasdt0(xq, xn) = v0)
% 14.83/4.05 |
% 14.83/4.05 | Instantiating formula (58) with xp, xq, all_157_2_140, xn and discharging atoms sdtasdt0(xp, xq) = all_157_2_140, sdtasdt0(xp, xq) = xn, yields:
% 14.83/4.05 | (211) all_157_2_140 = xn
% 14.83/4.05 |
% 14.83/4.05 | Instantiating formula (58) with xp, xq, all_157_2_140, all_167_0_151 and discharging atoms sdtasdt0(xp, xq) = all_167_0_151, sdtasdt0(xp, xq) = all_157_2_140, yields:
% 14.83/4.05 | (212) all_167_0_151 = all_157_2_140
% 14.83/4.05 |
% 14.83/4.05 | Instantiating formula (58) with xp, xq, all_139_1_102, all_167_0_151 and discharging atoms sdtasdt0(xp, xq) = all_167_0_151, sdtasdt0(xp, xq) = all_139_1_102, yields:
% 14.83/4.05 | (213) all_167_0_151 = all_139_1_102
% 14.83/4.05 |
% 14.83/4.05 | Instantiating formula (58) with xn, xq, all_109_2_52, all_159_0_143 and discharging atoms sdtasdt0(xn, xq) = all_159_0_143, sdtasdt0(xn, xq) = all_109_2_52, yields:
% 14.83/4.05 | (214) all_159_0_143 = all_109_2_52
% 14.83/4.05 |
% 14.83/4.05 | Instantiating formula (58) with xn, xq, all_107_1_46, all_109_2_52 and discharging atoms sdtasdt0(xn, xq) = all_109_2_52, sdtasdt0(xn, xq) = all_107_1_46, yields:
% 14.83/4.05 | (215) all_109_2_52 = all_107_1_46
% 14.83/4.05 |
% 14.83/4.05 | Instantiating formula (58) with xn, xq, all_107_2_47, all_159_0_143 and discharging atoms sdtasdt0(xn, xq) = all_159_0_143, sdtasdt0(xn, xq) = all_107_2_47, yields:
% 14.83/4.05 | (216) all_159_0_143 = all_107_2_47
% 14.83/4.05 |
% 14.83/4.05 | Instantiating formula (58) with xn, xq, all_39_0_10, all_109_2_52 and discharging atoms sdtasdt0(xn, xq) = all_109_2_52, sdtasdt0(xn, xq) = all_39_0_10, yields:
% 14.83/4.05 | (217) all_109_2_52 = all_39_0_10
% 14.83/4.05 |
% 14.83/4.05 | Instantiating formula (64) with all_0_2_2, all_39_0_10, all_0_3_3, xp and discharging atoms sdtasdt0(xp, all_39_0_10) = all_0_2_2, sdtasdt0(xp, all_0_3_3) = all_0_2_2, aNaturalNumber0(all_39_0_10), aNaturalNumber0(all_0_3_3), aNaturalNumber0(xp), yields:
% 14.83/4.05 | (218) all_39_0_10 = all_0_3_3 | xp = sz00
% 14.83/4.05 |
% 14.83/4.05 | Combining equations (212,213) yields a new equation:
% 14.83/4.05 | (219) all_157_2_140 = all_139_1_102
% 14.83/4.05 |
% 14.83/4.05 | Simplifying 219 yields:
% 14.83/4.05 | (220) all_157_2_140 = all_139_1_102
% 14.83/4.05 |
% 14.83/4.05 | Combining equations (214,216) yields a new equation:
% 14.83/4.05 | (221) all_109_2_52 = all_107_2_47
% 14.83/4.05 |
% 14.83/4.05 | Simplifying 221 yields:
% 14.83/4.05 | (222) all_109_2_52 = all_107_2_47
% 14.83/4.05 |
% 14.83/4.05 | Combining equations (220,211) yields a new equation:
% 14.83/4.05 | (223) all_139_1_102 = xn
% 14.83/4.05 |
% 14.83/4.05 | Simplifying 223 yields:
% 14.83/4.05 | (224) all_139_1_102 = xn
% 14.83/4.05 |
% 14.83/4.05 | Combining equations (217,215) yields a new equation:
% 14.83/4.05 | (225) all_107_1_46 = all_39_0_10
% 14.83/4.05 |
% 14.83/4.05 | Combining equations (222,215) yields a new equation:
% 14.83/4.05 | (226) all_107_1_46 = all_107_2_47
% 14.83/4.05 |
% 14.83/4.05 | Combining equations (225,226) yields a new equation:
% 14.83/4.05 | (227) all_107_2_47 = all_39_0_10
% 14.83/4.05 |
% 14.83/4.05 | Combining equations (224,213) yields a new equation:
% 14.83/4.05 | (228) all_167_0_151 = xn
% 14.83/4.05 |
% 14.83/4.05 | From (228) and (201) follows:
% 14.83/4.05 | (229) sdtasdt0(xn, xq) = all_0_0_0
% 14.83/4.05 |
% 14.83/4.05 | From (227) and (166) follows:
% 14.83/4.05 | (162) sdtasdt0(xn, xq) = all_39_0_10
% 14.83/4.05 |
% 14.83/4.05 +-Applying beta-rule and splitting (218), into two cases.
% 14.83/4.05 |-Branch one:
% 14.83/4.05 | (140) xp = sz00
% 14.83/4.05 |
% 14.83/4.05 | Equations (140) can reduce 47 to:
% 14.83/4.05 | (141) $false
% 14.83/4.05 |
% 14.83/4.05 |-The branch is then unsatisfiable
% 14.83/4.05 |-Branch two:
% 14.83/4.05 | (47) ~ (xp = sz00)
% 14.83/4.05 | (234) all_39_0_10 = all_0_3_3
% 14.83/4.05 |
% 14.83/4.05 | From (234) and (162) follows:
% 14.83/4.05 | (235) sdtasdt0(xn, xq) = all_0_3_3
% 14.83/4.05 |
% 14.83/4.05 | Instantiating formula (58) with xn, xq, all_0_3_3, all_0_0_0 and discharging atoms sdtasdt0(xn, xq) = all_0_0_0, sdtasdt0(xn, xq) = all_0_3_3, yields:
% 14.83/4.05 | (236) all_0_0_0 = all_0_3_3
% 14.83/4.05 |
% 14.83/4.05 | Equations (236) can reduce 62 to:
% 14.83/4.05 | (141) $false
% 14.83/4.05 |
% 14.83/4.05 |-The branch is then unsatisfiable
% 14.83/4.05 |-Branch two:
% 14.83/4.05 | (238) ~ sdtlseqdt0(xp, xn)
% 14.83/4.05 | (239) xn = sz00
% 14.83/4.05 |
% 14.83/4.05 | Equations (239) can reduce 39 to:
% 14.83/4.05 | (141) $false
% 14.83/4.05 |
% 14.83/4.05 |-The branch is then unsatisfiable
% 14.83/4.05 % SZS output end Proof for theBenchmark
% 14.83/4.05
% 14.83/4.05 3446ms
%------------------------------------------------------------------------------