TSTP Solution File: NUM525+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM525+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n019.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 6.25s 2.20s
% Output : Proof 13.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM525+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.33 % Computer : n019.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Thu Jul 7 15:00:08 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.55/0.58 ____ _
% 0.55/0.58 ___ / __ \_____(_)___ ________ __________
% 0.55/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.58
% 0.55/0.58 A Theorem Prover for First-Order Logic
% 0.55/0.58 (ePrincess v.1.0)
% 0.55/0.58
% 0.55/0.58 (c) Philipp Rümmer, 2009-2015
% 0.55/0.58 (c) Peter Backeman, 2014-2015
% 0.55/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.58 Bug reports to peter@backeman.se
% 0.55/0.58
% 0.55/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.58
% 0.55/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.60/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.96/1.02 Prover 0: Preprocessing ...
% 3.81/1.58 Prover 0: Constructing countermodel ...
% 6.25/2.20 Prover 0: proved (1570ms)
% 6.25/2.20
% 6.25/2.20 No countermodel exists, formula is valid
% 6.25/2.20 % SZS status Theorem for theBenchmark
% 6.25/2.20
% 6.25/2.20 Generating proof ... found it (size 101)
% 12.78/3.83
% 12.78/3.83 % SZS output start Proof for theBenchmark
% 12.78/3.83 Assumed formulas after preprocessing and simplification:
% 12.78/3.83 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = v1) & ~ (xp = sz00) & ~ (xm = sz00) & ~ (xn = sz00) & ~ (sz10 = sz00) & sdtsldt0(xn, xp) = xq & sdtasdt0(xq, xq) = v2 & sdtasdt0(xp, v3) = v4 & 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) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v5 = sz00 | ~ (sdtsldt0(v9, v5) = v10) | ~ (sdtsldt0(v6, v5) = v7) | ~ (sdtasdt0(v8, v6) = v9) | ~ doDivides0(v5, v6) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtasdt0(v8, v7) = v10) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v7, v5) = v9) | ~ (sdtasdt0(v6, v5) = v8) | ~ (sdtpldt0(v8, v9) = v10) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v11, v5) = v10 & sdtasdt0(v5, v11) = v12 & sdtasdt0(v5, v7) = v14 & sdtasdt0(v5, v6) = v13 & sdtpldt0(v13, v14) = v12 & sdtpldt0(v6, v7) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v5, v7) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ (sdtpldt0(v8, v9) = v10) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v11, v5) = v12 & sdtasdt0(v7, v5) = v14 & sdtasdt0(v6, v5) = v13 & sdtasdt0(v5, v11) = v10 & sdtpldt0(v13, v14) = v12 & sdtpldt0(v6, v7) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v9) | ~ (sdtasdt0(v6, v5) = v8) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtlseqdt0(v8, v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v9) | ~ (sdtasdt0(v6, v5) = v8) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtasdt0(v5, v7) = v11 & sdtasdt0(v5, v6) = v10 & sdtlseqdt0(v10, v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v9) | ~ (sdtasdt0(v6, v5) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtasdt0(v5, v7) = v11 & sdtasdt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtasdt0(v6, v5) = v11 & sdtasdt0(v5, v7) = v10 & sdtlseqdt0(v11, v9) & sdtlseqdt0(v8, v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtasdt0(v6, v5) = v11 & sdtasdt0(v5, v7) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v6, v5) = v9) | ~ (sdtasdt0(v5, v7) = v8) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtasdt0(v7, v5) = v11 & sdtasdt0(v5, v6) = v10 & sdtlseqdt0(v10, v8) & sdtlseqdt0(v9, v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v6, v5) = v9) | ~ (sdtasdt0(v5, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtasdt0(v7, v5) = v11 & sdtasdt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v5, v7) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtlseqdt0(v8, v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v5, v7) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtasdt0(v7, v5) = v11 & sdtasdt0(v6, v5) = v10 & sdtlseqdt0(v10, v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v5, v7) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtasdt0(v7, v5) = v11 & sdtasdt0(v6, v5) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v7, v5) = v9) | ~ (sdtpldt0(v6, v5) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtpldt0(v5, v7) = v11 & sdtpldt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v7, v5) = v9) | ~ (sdtpldt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtpldt0(v6, v5) = v11 & sdtpldt0(v5, v7) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v6, v5) = v9) | ~ (sdtpldt0(v5, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtpldt0(v7, v5) = v11 & sdtpldt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v5, v7) = v9) | ~ (sdtpldt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtpldt0(v7, v5) = v11 & sdtpldt0(v6, v5) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = sz00 | v6 = sz00 | v5 = sz00 | ~ (sdtasdt0(v7, v8) = v9) | ~ (sdtasdt0(v6, v6) = v8) | ~ (sdtasdt0(v5, v5) = v9) | ~ isPrime0(v7) | ~ iLess0(v5, xn) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v5 = sz00 | ~ (sdtsldt0(v6, v5) = v7) | ~ (sdtasdt0(v8, v7) = v9) | ~ doDivides0(v5, v6) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : (sdtsldt0(v10, v5) = v9 & sdtasdt0(v8, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v8, v7) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : (sdtasdt0(v6, v7) = v10 & sdtasdt0(v5, v10) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v8, v5) = v9) | ~ (sdtpldt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v7, v5) = v14 & sdtasdt0(v6, v5) = v13 & sdtasdt0(v5, v8) = v10 & sdtasdt0(v5, v7) = v12 & sdtasdt0(v5, v6) = v11 & sdtpldt0(v13, v14) = v9 & sdtpldt0(v11, v12) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v6, v7) = v8) | ~ (sdtasdt0(v5, v8) = v9) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : (sdtasdt0(v10, v7) = v9 & sdtasdt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v5, v8) = v9) | ~ (sdtpldt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v8, v5) = v12 & sdtasdt0(v7, v5) = v14 & sdtasdt0(v6, v5) = v13 & sdtasdt0(v5, v7) = v11 & sdtasdt0(v5, v6) = v10 & sdtpldt0(v13, v14) = v12 & sdtpldt0(v10, v11) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v8, v7) = v9) | ~ (sdtpldt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : (sdtpldt0(v6, v7) = v10 & sdtpldt0(v5, v10) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v6, v7) = v8) | ~ (sdtpldt0(v5, v8) = v9) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : (sdtpldt0(v10, v7) = v9 & sdtpldt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | v5 = sz00 | ~ (sdtsldt0(v6, v5) = v7) | ~ (sdtasdt0(v5, v8) = v6) | ~ doDivides0(v5, v6) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ (sdtmndt0(v6, v5) = v7) | ~ (sdtpldt0(v5, v8) = v6) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v6 | v5 = sz00 | ~ (sdtsldt0(v6, v5) = v7) | ~ (sdtasdt0(v5, v7) = v8) | ~ doDivides0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v6 | ~ (sdtmndt0(v6, v5) = v7) | ~ (sdtpldt0(v5, v7) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v8) | ~ (sdtasdt0(v6, v5) = v8) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v8) | ~ (sdtasdt0(v6, v5) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v5, v7) = v8) | ~ (sdtasdt0(v5, v6) = v8) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v5, v7) = v8) | ~ (sdtasdt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (sdtpldt0(v7, v5) = v8) | ~ (sdtpldt0(v6, v5) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (sdtpldt0(v5, v7) = v8) | ~ (sdtpldt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtsldt0(v8, v7) = v6) | ~ (sdtsldt0(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtmndt0(v8, v7) = v6) | ~ (sdtmndt0(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtasdt0(v8, v7) = v6) | ~ (sdtasdt0(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v8, v7) = v6) | ~ (sdtpldt0(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v7, v6) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = v10) & ~ (v9 = v8) & sdtpldt0(v7, v5) = v9 & sdtpldt0(v6, v7) = v11 & sdtpldt0(v5, v7) = v10 & sdtlseqdt0(v10, v11) & sdtlseqdt0(v9, v8))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v7, v5) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = v10) & ~ (v9 = v8) & sdtpldt0(v7, v6) = v9 & sdtpldt0(v6, v7) = v11 & sdtpldt0(v5, v7) = v10 & sdtlseqdt0(v10, v11) & sdtlseqdt0(v8, v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v6, v7) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = v8) & ~ (v10 = v9) & sdtpldt0(v7, v6) = v10 & sdtpldt0(v7, v5) = v9 & sdtpldt0(v5, v7) = v11 & sdtlseqdt0(v11, v8) & sdtlseqdt0(v9, v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v5, v7) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = v8) & ~ (v10 = v9) & sdtpldt0(v7, v6) = v10 & sdtpldt0(v7, v5) = v9 & sdtpldt0(v6, v7) = v11 & sdtlseqdt0(v9, v10) & sdtlseqdt0(v8, v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = sz00 | ~ (sdtsldt0(v6, v5) = v7) | ~ (sdtasdt0(v5, v7) = v8) | ~ doDivides0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | aNaturalNumber0(v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtmndt0(v6, v5) = v7) | ~ (sdtpldt0(v5, v7) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | aNaturalNumber0(v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v5, v6) = v8) | ~ isPrime0(v7) | ~ doDivides0(v7, v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | doDivides0(v7, v6) | doDivides0(v7, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v6, v7) = v8) | ~ doDivides0(v5, v8) | ~ doDivides0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | doDivides0(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v6, v7) = v8) | ~ doDivides0(v5, v7) | ~ doDivides0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | doDivides0(v5, v8)) & ! [v5] : ! [v6] : ! [v7] : (v5 = sz00 | ~ (sdtasdt0(v6, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtlseqdt0(v6, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v6, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtasdt0(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v5, v7) = v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | doDivides0(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtasdt0(v6, v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | aNaturalNumber0(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v6, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtpldt0(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v7) = v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtlseqdt0(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtpldt0(v6, v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | aNaturalNumber0(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ doDivides0(v6, v7) | ~ doDivides0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | doDivides0(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ sdtlseqdt0(v6, v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtlseqdt0(v5, v7)) & ! [v5] : ! [v6] : (v6 = v5 | v6 = sz10 | ~ isPrime0(v5) | ~ doDivides0(v6, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtasdt0(v5, sz10) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtasdt0(sz10, v5) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtpldt0(v5, sz00) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtpldt0(sz00, v5) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ sdtlseqdt0(v6, v5) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | iLess0(v5, v6)) & ! [v5] : ! [v6] : (v6 = sz00 | v5 = sz00 | ~ (sdtasdt0(v5, v6) = sz00) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = sz00 | ~ (sdtasdt0(v5, sz00) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = sz00 | ~ (sdtasdt0(sz00, v5) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = sz00 | ~ (sdtpldt0(v5, v6) = sz00) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = sz00 | ~ doDivides0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtlseqdt0(v5, v6)) & ! [v5] : ! [v6] : (v5 = sz00 | ~ (sdtpldt0(v5, v6) = sz00) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, sz10) = v6) | ~ aNaturalNumber0(v5) | sdtasdt0(sz10, v5) = v5) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, sz00) = v6) | ~ aNaturalNumber0(v5) | sdtasdt0(sz00, v5) = sz00) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(sz10, v5) = v6) | ~ aNaturalNumber0(v5) | sdtasdt0(v5, sz10) = v5) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(sz00, v5) = v6) | ~ aNaturalNumber0(v5) | sdtasdt0(v5, sz00) = sz00) & ! [v5] : ! [v6] : ( ~ (sdtpldt0(v5, sz00) = v6) | ~ aNaturalNumber0(v5) | sdtpldt0(sz00, v5) = v5) & ! [v5] : ! [v6] : ( ~ (sdtpldt0(sz00, v5) = v6) | ~ aNaturalNumber0(v5) | sdtpldt0(v5, sz00) = v5) & ! [v5] : ! [v6] : ( ~ doDivides0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v7] : (sdtasdt0(v5, v7) = v6 & aNaturalNumber0(v7))) & ! [v5] : ! [v6] : ( ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v7] : (sdtpldt0(v5, v7) = v6 & aNaturalNumber0(v7))) & ! [v5] : ! [v6] : ( ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtlseqdt0(v6, v5) | sdtlseqdt0(v5, v6)) & ! [v5] : (v5 = sz10 | v5 = sz00 | ~ aNaturalNumber0(v5) | isPrime0(v5) | ? [v6] : ( ~ (v6 = v5) & ~ (v6 = sz10) & doDivides0(v6, v5) & aNaturalNumber0(v6))) & ! [v5] : (v5 = sz10 | v5 = sz00 | ~ aNaturalNumber0(v5) | sdtlseqdt0(sz10, v5)) & ! [v5] : (v5 = sz10 | v5 = sz00 | ~ aNaturalNumber0(v5) | ? [v6] : (isPrime0(v6) & doDivides0(v6, v5) & aNaturalNumber0(v6))) & ! [v5] : ( ~ aNaturalNumber0(v5) | sdtlseqdt0(v5, v5)))
% 13.43/3.89 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 13.43/3.89 | (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_2_2 & sdtasdt0(xp, all_0_1_1) = all_0_0_0 & sdtasdt0(xp, all_0_2_2) = all_0_1_1 & sdtasdt0(xp, all_0_4_4) = all_0_3_3 & sdtasdt0(xm, xm) = all_0_4_4 & sdtasdt0(xn, xn) = all_0_3_3 & isPrime0(xp) & doDivides0(xp, all_0_3_3) & 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))
% 13.43/3.91 |
% 13.43/3.91 | Applying alpha-rule on (1) yields:
% 13.43/3.92 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.43/3.92 | (3) ! [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))
% 13.43/3.92 | (4) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 13.43/3.92 | (5) ! [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))
% 13.43/3.92 | (6) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.43/3.92 | (7) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 13.43/3.92 | (8) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 13.43/3.92 | (9) ! [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))
% 13.43/3.92 | (10) aNaturalNumber0(xn)
% 13.43/3.92 | (11) ! [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))
% 13.43/3.92 | (12) ~ isPrime0(sz00)
% 13.43/3.92 | (13) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 13.43/3.92 | (14) ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 13.43/3.92 | (15) ! [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))
% 13.43/3.92 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 13.43/3.92 | (17) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.43/3.92 | (18) ~ (xm = sz00)
% 13.43/3.92 | (19) sdtasdt0(xp, all_0_2_2) = all_0_1_1
% 13.43/3.92 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 13.43/3.92 | (21) ! [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)))
% 13.43/3.92 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 13.43/3.92 | (23) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 13.43/3.92 | (24) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1] : ( ~ (v1 = v0) & ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 13.43/3.92 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 13.43/3.92 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 13.43/3.92 | (27) doDivides0(xp, xn)
% 13.43/3.92 | (28) isPrime0(xp)
% 13.43/3.92 | (29) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 13.43/3.92 | (30) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00)
% 13.43/3.92 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 13.43/3.92 | (32) ! [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)))
% 13.43/3.92 | (33) sdtasdt0(xm, xm) = all_0_4_4
% 13.43/3.92 | (34) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 13.43/3.92 | (35) ! [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))
% 13.43/3.92 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 13.43/3.92 | (37) ! [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))
% 13.43/3.92 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.43/3.92 | (39) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0)
% 13.43/3.92 | (40) sdtasdt0(xn, xn) = all_0_3_3
% 13.43/3.92 | (41) ! [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))
% 13.43/3.93 | (42) ~ (xn = sz00)
% 13.43/3.93 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.43/3.93 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 13.43/3.93 | (45) ~ (all_0_0_0 = all_0_3_3)
% 13.43/3.93 | (46) ~ (xp = sz00)
% 13.43/3.93 | (47) ! [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))
% 13.43/3.93 | (48) ~ isPrime0(sz10)
% 13.43/3.93 | (49) ! [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))
% 13.43/3.93 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.43/3.93 | (51) ! [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))
% 13.43/3.93 | (52) ! [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)))
% 13.43/3.93 | (53) ! [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)))
% 13.43/3.93 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 13.43/3.93 | (55) ! [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))
% 13.43/3.93 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 13.43/3.93 | (57) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 13.43/3.93 | (58) aNaturalNumber0(sz00)
% 13.43/3.93 | (59) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0))
% 13.43/3.93 | (60) sdtasdt0(xp, all_0_4_4) = all_0_3_3
% 13.43/3.93 | (61) sdtasdt0(xq, xq) = all_0_2_2
% 13.43/3.93 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 13.43/3.93 | (63) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.43/3.93 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.43/3.93 | (65) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 13.43/3.93 | (66) aNaturalNumber0(sz10)
% 13.43/3.93 | (67) ! [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))
% 13.43/3.93 | (68) aNaturalNumber0(xp)
% 13.43/3.93 | (69) ! [v0] : ! [v1] : (v1 = sz00 | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 13.43/3.93 | (70) ! [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)))
% 13.43/3.93 | (71) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.43/3.93 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 13.43/3.93 | (73) sdtsldt0(xn, xp) = xq
% 13.43/3.93 | (74) ! [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))
% 13.43/3.93 | (75) doDivides0(xp, all_0_3_3)
% 13.43/3.93 | (76) ! [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)
% 13.43/3.93 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 13.43/3.93 | (78) ! [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))
% 13.43/3.93 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3))
% 13.43/3.94 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 13.43/3.94 | (81) ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 13.43/3.94 | (82) ! [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))
% 13.43/3.94 | (83) ! [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))
% 13.43/3.94 | (84) ! [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)))
% 13.43/3.94 | (85) ! [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))
% 13.43/3.94 | (86) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 13.43/3.94 | (87) ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 13.43/3.94 | (88) ! [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))
% 13.43/3.94 | (89) aNaturalNumber0(xm)
% 13.43/3.94 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 13.43/3.94 | (91) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0))
% 13.43/3.94 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.43/3.94 | (93) ! [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))
% 13.43/3.94 | (94) ! [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)))
% 13.43/3.94 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.43/3.94 | (96) ! [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))
% 13.43/3.94 | (97) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 13.43/3.94 | (98) ! [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))
% 13.43/3.94 | (99) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2)
% 13.43/3.94 | (100) ! [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))
% 13.43/3.94 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.43/3.94 | (102) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0)
% 13.43/3.94 | (103) ! [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)))
% 13.43/3.94 | (104) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2)
% 13.43/3.94 | (105) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 13.43/3.94 | (106) ! [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))
% 13.43/3.94 | (107) sdtasdt0(xp, all_0_1_1) = all_0_0_0
% 13.43/3.94 | (108) ~ (sz10 = sz00)
% 13.43/3.94 |
% 13.43/3.94 | Instantiating formula (97) with xp, xp and discharging atoms aNaturalNumber0(xp), yields:
% 13.43/3.94 | (109) sdtlseqdt0(xp, xp)
% 13.43/3.94 |
% 13.43/3.94 | Instantiating formula (62) with all_0_4_4, xm, xm and discharging atoms sdtasdt0(xm, xm) = all_0_4_4, aNaturalNumber0(xm), yields:
% 13.43/3.94 | (110) aNaturalNumber0(all_0_4_4)
% 13.43/3.94 |
% 13.43/3.94 | Instantiating formula (62) with all_0_3_3, xn, xn and discharging atoms sdtasdt0(xn, xn) = all_0_3_3, aNaturalNumber0(xn), yields:
% 13.43/3.94 | (111) aNaturalNumber0(all_0_3_3)
% 13.43/3.94 |
% 13.43/3.94 | Instantiating formula (69) with xn, xp and discharging atoms doDivides0(xp, xn), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 13.43/3.94 | (112) xn = sz00 | sdtlseqdt0(xp, xn)
% 13.43/3.95 |
% 13.43/3.95 | Instantiating formula (81) with xn, xp and discharging atoms doDivides0(xp, xn), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 13.43/3.95 | (113) ? [v0] : (sdtasdt0(xp, v0) = xn & aNaturalNumber0(v0))
% 13.43/3.95 |
% 13.43/3.95 | Instantiating formula (97) with xn, xn and discharging atoms aNaturalNumber0(xn), yields:
% 13.43/3.95 | (114) sdtlseqdt0(xn, xn)
% 13.43/3.95 |
% 13.43/3.95 | Instantiating (113) with all_9_0_5 yields:
% 13.43/3.95 | (115) sdtasdt0(xp, all_9_0_5) = xn & aNaturalNumber0(all_9_0_5)
% 13.43/3.95 |
% 13.43/3.95 | Applying alpha-rule on (115) yields:
% 13.43/3.95 | (116) sdtasdt0(xp, all_9_0_5) = xn
% 13.43/3.95 | (117) aNaturalNumber0(all_9_0_5)
% 13.43/3.95 |
% 13.43/3.95 +-Applying beta-rule and splitting (112), into two cases.
% 13.43/3.95 |-Branch one:
% 13.43/3.95 | (118) sdtlseqdt0(xp, xn)
% 13.43/3.95 |
% 13.43/3.95 | Instantiating formula (49) with all_9_0_5, xq, xn, xp and discharging atoms sdtsldt0(xn, xp) = xq, sdtasdt0(xp, all_9_0_5) = xn, doDivides0(xp, xn), aNaturalNumber0(all_9_0_5), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 13.43/3.95 | (119) all_9_0_5 = xq | xp = sz00
% 13.43/3.95 |
% 13.43/3.95 | Instantiating formula (8) with xp, xp and discharging atoms sdtlseqdt0(xp, xp), aNaturalNumber0(xp), yields:
% 13.43/3.95 | (120) ? [v0] : (sdtpldt0(xp, v0) = xp & aNaturalNumber0(v0))
% 13.43/3.95 |
% 13.43/3.95 | Instantiating formula (8) with xn, xp and discharging atoms sdtlseqdt0(xp, xn), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 13.43/3.95 | (121) ? [v0] : (sdtpldt0(xp, v0) = xn & aNaturalNumber0(v0))
% 13.43/3.95 |
% 13.43/3.95 | Instantiating formula (8) with xn, xn and discharging atoms sdtlseqdt0(xn, xn), aNaturalNumber0(xn), yields:
% 13.43/3.95 | (122) ? [v0] : (sdtpldt0(xn, v0) = xn & aNaturalNumber0(v0))
% 13.43/3.95 |
% 13.43/3.95 | Instantiating formula (98) with all_0_3_3, xn, xn, all_9_0_5, xp and discharging atoms sdtasdt0(xp, all_9_0_5) = xn, sdtasdt0(xn, xn) = all_0_3_3, aNaturalNumber0(all_9_0_5), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 13.43/3.95 | (123) ? [v0] : (sdtasdt0(all_9_0_5, xn) = v0 & sdtasdt0(xp, v0) = all_0_3_3)
% 13.43/3.95 |
% 13.43/3.95 | Instantiating formula (104) with xn, xp, all_9_0_5 and discharging atoms sdtasdt0(xp, all_9_0_5) = xn, aNaturalNumber0(all_9_0_5), aNaturalNumber0(xp), yields:
% 13.43/3.95 | (124) sdtasdt0(all_9_0_5, xp) = xn
% 13.43/3.95 |
% 13.43/3.95 | Instantiating formula (81) with all_0_3_3, xp and discharging atoms doDivides0(xp, all_0_3_3), aNaturalNumber0(all_0_3_3), aNaturalNumber0(xp), yields:
% 13.43/3.95 | (125) ? [v0] : (sdtasdt0(xp, v0) = all_0_3_3 & aNaturalNumber0(v0))
% 13.43/3.95 |
% 13.43/3.95 | Instantiating (125) with all_33_0_8 yields:
% 13.43/3.95 | (126) sdtasdt0(xp, all_33_0_8) = all_0_3_3 & aNaturalNumber0(all_33_0_8)
% 13.43/3.95 |
% 13.43/3.95 | Applying alpha-rule on (126) yields:
% 13.43/3.95 | (127) sdtasdt0(xp, all_33_0_8) = all_0_3_3
% 13.43/3.95 | (128) aNaturalNumber0(all_33_0_8)
% 13.43/3.95 |
% 13.43/3.95 | Instantiating (123) with all_39_0_11 yields:
% 13.43/3.95 | (129) sdtasdt0(all_9_0_5, xn) = all_39_0_11 & sdtasdt0(xp, all_39_0_11) = all_0_3_3
% 13.43/3.95 |
% 13.43/3.95 | Applying alpha-rule on (129) yields:
% 13.43/3.95 | (130) sdtasdt0(all_9_0_5, xn) = all_39_0_11
% 13.43/3.95 | (131) sdtasdt0(xp, all_39_0_11) = all_0_3_3
% 13.43/3.95 |
% 13.43/3.95 | Instantiating (120) with all_41_0_12 yields:
% 13.43/3.95 | (132) sdtpldt0(xp, all_41_0_12) = xp & aNaturalNumber0(all_41_0_12)
% 13.43/3.95 |
% 13.43/3.95 | Applying alpha-rule on (132) yields:
% 13.43/3.95 | (133) sdtpldt0(xp, all_41_0_12) = xp
% 13.43/3.95 | (134) aNaturalNumber0(all_41_0_12)
% 13.43/3.95 |
% 13.43/3.95 | Instantiating (122) with all_45_0_14 yields:
% 13.43/3.95 | (135) sdtpldt0(xn, all_45_0_14) = xn & aNaturalNumber0(all_45_0_14)
% 13.43/3.95 |
% 13.43/3.95 | Applying alpha-rule on (135) yields:
% 13.43/3.95 | (136) sdtpldt0(xn, all_45_0_14) = xn
% 13.43/3.95 | (137) aNaturalNumber0(all_45_0_14)
% 13.43/3.95 |
% 13.43/3.95 | Instantiating (121) with all_51_0_17 yields:
% 13.43/3.95 | (138) sdtpldt0(xp, all_51_0_17) = xn & aNaturalNumber0(all_51_0_17)
% 13.43/3.95 |
% 13.43/3.95 | Applying alpha-rule on (138) yields:
% 13.43/3.95 | (139) sdtpldt0(xp, all_51_0_17) = xn
% 13.43/3.95 | (140) aNaturalNumber0(all_51_0_17)
% 13.43/3.95 |
% 13.43/3.95 +-Applying beta-rule and splitting (119), into two cases.
% 13.43/3.95 |-Branch one:
% 13.43/3.95 | (141) xp = sz00
% 13.43/3.95 |
% 13.43/3.95 | Equations (141) can reduce 46 to:
% 13.43/3.95 | (142) $false
% 13.43/3.95 |
% 13.43/3.95 |-The branch is then unsatisfiable
% 13.43/3.95 |-Branch two:
% 13.43/3.95 | (46) ~ (xp = sz00)
% 13.43/3.95 | (144) all_9_0_5 = xq
% 13.43/3.95 |
% 13.43/3.95 | From (144) and (124) follows:
% 13.74/3.95 | (145) sdtasdt0(xq, xp) = xn
% 13.74/3.95 |
% 13.74/3.95 | From (144) and (130) follows:
% 13.74/3.95 | (146) sdtasdt0(xq, xn) = all_39_0_11
% 13.74/3.95 |
% 13.74/3.95 | From (144) and (116) follows:
% 13.74/3.95 | (147) sdtasdt0(xp, xq) = xn
% 13.74/3.95 |
% 13.74/3.95 | From (144) and (117) follows:
% 13.74/3.95 | (148) aNaturalNumber0(xq)
% 13.74/3.95 |
% 13.74/3.95 | Instantiating formula (38) with all_0_3_3, all_0_4_4, all_33_0_8, xp and discharging atoms sdtasdt0(xp, all_33_0_8) = all_0_3_3, sdtasdt0(xp, all_0_4_4) = all_0_3_3, aNaturalNumber0(all_33_0_8), aNaturalNumber0(all_0_4_4), aNaturalNumber0(xp), yields:
% 13.74/3.95 | (149) all_33_0_8 = all_0_4_4 | xp = sz00
% 13.74/3.95 |
% 13.74/3.95 +-Applying beta-rule and splitting (149), into two cases.
% 13.74/3.95 |-Branch one:
% 13.74/3.95 | (141) xp = sz00
% 13.74/3.95 |
% 13.74/3.95 | Equations (141) can reduce 46 to:
% 13.74/3.95 | (142) $false
% 13.74/3.95 |
% 13.74/3.95 |-The branch is then unsatisfiable
% 13.74/3.95 |-Branch two:
% 13.74/3.95 | (46) ~ (xp = sz00)
% 13.74/3.95 | (153) all_33_0_8 = all_0_4_4
% 13.74/3.95 |
% 13.74/3.95 | From (153) and (127) follows:
% 13.74/3.95 | (60) sdtasdt0(xp, all_0_4_4) = all_0_3_3
% 13.74/3.95 |
% 13.74/3.95 | From (153) and (128) follows:
% 13.74/3.95 | (110) aNaturalNumber0(all_0_4_4)
% 13.74/3.95 |
% 13.74/3.95 | Instantiating formula (9) 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:
% 13.74/3.95 | (156) xp = sz00 | ? [v0] : (sdtsldt0(v0, xp) = xn & sdtasdt0(xp, xn) = v0)
% 13.74/3.95 |
% 13.74/3.95 | Instantiating formula (9) with all_0_2_2, xq, xq, xn, xp and discharging atoms sdtsldt0(xn, xp) = xq, sdtasdt0(xq, xq) = all_0_2_2, doDivides0(xp, xn), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 13.74/3.95 | (157) xp = sz00 | ? [v0] : (sdtsldt0(v0, xp) = all_0_2_2 & sdtasdt0(xq, xn) = v0)
% 13.74/3.95 |
% 13.74/3.95 | Instantiating formula (37) with all_0_1_1, all_0_2_2, xq, xq, xp and discharging atoms sdtasdt0(xq, xq) = all_0_2_2, sdtasdt0(xp, all_0_2_2) = all_0_1_1, aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 13.74/3.95 | (158) ? [v0] : (sdtasdt0(v0, xq) = all_0_1_1 & sdtasdt0(xp, xq) = v0)
% 13.74/3.96 |
% 13.74/3.96 | Instantiating formula (37) with all_0_3_3, xn, xp, xq, xn and discharging atoms sdtasdt0(xq, xp) = xn, sdtasdt0(xn, xn) = all_0_3_3, aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 13.74/3.96 | (159) ? [v0] : (sdtasdt0(v0, xp) = all_0_3_3 & sdtasdt0(xn, xq) = v0)
% 13.74/3.96 |
% 13.74/3.96 | Instantiating formula (51) with xn, xp, all_41_0_12, xp, xq and discharging atoms sdtasdt0(xq, xp) = xn, sdtpldt0(xp, all_41_0_12) = xp, aNaturalNumber0(all_41_0_12), aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 13.74/3.96 | (160) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_41_0_12, xq) = v4 & sdtasdt0(xq, all_41_0_12) = v1 & sdtasdt0(xq, xp) = v0 & sdtasdt0(xp, xq) = v3 & sdtasdt0(xp, xq) = v2 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = xn)
% 13.74/3.96 |
% 13.74/3.96 | Instantiating formula (51) with all_39_0_11, xn, all_51_0_17, xp, xq and discharging atoms sdtasdt0(xq, xn) = all_39_0_11, sdtpldt0(xp, all_51_0_17) = xn, aNaturalNumber0(all_51_0_17), aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 13.74/3.96 | (161) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_51_0_17, xq) = v4 & sdtasdt0(xq, all_51_0_17) = v1 & sdtasdt0(xq, xp) = v0 & sdtasdt0(xp, xq) = v3 & sdtasdt0(xn, xq) = v2 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_39_0_11)
% 13.74/3.96 |
% 13.74/3.96 | Instantiating formula (51) with all_39_0_11, xn, all_45_0_14, xn, xq and discharging atoms sdtasdt0(xq, xn) = all_39_0_11, sdtpldt0(xn, all_45_0_14) = xn, aNaturalNumber0(all_45_0_14), aNaturalNumber0(xq), aNaturalNumber0(xn), yields:
% 13.74/3.96 | (162) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_45_0_14, xq) = v4 & sdtasdt0(xq, all_45_0_14) = v1 & sdtasdt0(xq, xn) = v0 & sdtasdt0(xn, xq) = v3 & sdtasdt0(xn, xq) = v2 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_39_0_11)
% 13.74/3.96 |
% 13.74/3.96 | Instantiating formula (104) with all_39_0_11, xq, xn and discharging atoms sdtasdt0(xq, xn) = all_39_0_11, aNaturalNumber0(xq), aNaturalNumber0(xn), yields:
% 13.74/3.96 | (163) sdtasdt0(xn, xq) = all_39_0_11
% 13.74/3.96 |
% 13.74/3.96 | Instantiating formula (62) with all_39_0_11, xn, xq and discharging atoms sdtasdt0(xq, xn) = all_39_0_11, aNaturalNumber0(xq), aNaturalNumber0(xn), yields:
% 13.74/3.96 | (164) aNaturalNumber0(all_39_0_11)
% 13.74/3.96 |
% 13.74/3.96 | Instantiating formula (5) with xn, xp, all_41_0_12, xp, xq and discharging atoms sdtasdt0(xp, xq) = xn, sdtpldt0(xp, all_41_0_12) = xp, aNaturalNumber0(all_41_0_12), aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 13.74/3.96 | (165) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_41_0_12, xq) = v4 & sdtasdt0(xq, all_41_0_12) = v2 & sdtasdt0(xq, xp) = v1 & sdtasdt0(xq, xp) = v0 & sdtasdt0(xp, xq) = v3 & sdtpldt0(v3, v4) = xn & sdtpldt0(v1, v2) = v0)
% 13.74/3.96 |
% 13.74/3.96 | Instantiating (162) with all_107_0_46, all_107_1_47, all_107_2_48, all_107_3_49, all_107_4_50 yields:
% 13.74/3.96 | (166) sdtasdt0(all_45_0_14, xq) = all_107_0_46 & sdtasdt0(xq, all_45_0_14) = all_107_3_49 & sdtasdt0(xq, xn) = all_107_4_50 & sdtasdt0(xn, xq) = all_107_1_47 & sdtasdt0(xn, xq) = all_107_2_48 & sdtpldt0(all_107_1_47, all_107_0_46) = all_107_2_48 & sdtpldt0(all_107_4_50, all_107_3_49) = all_39_0_11
% 13.74/3.96 |
% 13.74/3.96 | Applying alpha-rule on (166) yields:
% 13.74/3.96 | (167) sdtasdt0(xq, xn) = all_107_4_50
% 13.74/3.96 | (168) sdtasdt0(xn, xq) = all_107_2_48
% 13.74/3.96 | (169) sdtasdt0(all_45_0_14, xq) = all_107_0_46
% 13.74/3.96 | (170) sdtpldt0(all_107_4_50, all_107_3_49) = all_39_0_11
% 13.74/3.96 | (171) sdtasdt0(xn, xq) = all_107_1_47
% 13.74/3.96 | (172) sdtpldt0(all_107_1_47, all_107_0_46) = all_107_2_48
% 13.74/3.96 | (173) sdtasdt0(xq, all_45_0_14) = all_107_3_49
% 13.74/3.96 |
% 13.74/3.96 | Instantiating (161) with all_109_0_51, all_109_1_52, all_109_2_53, all_109_3_54, all_109_4_55 yields:
% 13.74/3.96 | (174) sdtasdt0(all_51_0_17, xq) = all_109_0_51 & sdtasdt0(xq, all_51_0_17) = all_109_3_54 & sdtasdt0(xq, xp) = all_109_4_55 & sdtasdt0(xp, xq) = all_109_1_52 & sdtasdt0(xn, xq) = all_109_2_53 & sdtpldt0(all_109_1_52, all_109_0_51) = all_109_2_53 & sdtpldt0(all_109_4_55, all_109_3_54) = all_39_0_11
% 13.74/3.96 |
% 13.74/3.96 | Applying alpha-rule on (174) yields:
% 13.74/3.96 | (175) sdtasdt0(xn, xq) = all_109_2_53
% 13.74/3.96 | (176) sdtasdt0(all_51_0_17, xq) = all_109_0_51
% 13.74/3.96 | (177) sdtpldt0(all_109_1_52, all_109_0_51) = all_109_2_53
% 13.74/3.96 | (178) sdtasdt0(xq, all_51_0_17) = all_109_3_54
% 13.74/3.96 | (179) sdtasdt0(xq, xp) = all_109_4_55
% 13.74/3.96 | (180) sdtasdt0(xp, xq) = all_109_1_52
% 13.74/3.96 | (181) sdtpldt0(all_109_4_55, all_109_3_54) = all_39_0_11
% 13.74/3.96 |
% 13.74/3.96 | Instantiating (165) with all_139_0_102, all_139_1_103, all_139_2_104, all_139_3_105, all_139_4_106 yields:
% 13.74/3.96 | (182) sdtasdt0(all_41_0_12, xq) = all_139_0_102 & sdtasdt0(xq, all_41_0_12) = all_139_2_104 & sdtasdt0(xq, xp) = all_139_3_105 & sdtasdt0(xq, xp) = all_139_4_106 & sdtasdt0(xp, xq) = all_139_1_103 & sdtpldt0(all_139_1_103, all_139_0_102) = xn & sdtpldt0(all_139_3_105, all_139_2_104) = all_139_4_106
% 13.74/3.96 |
% 13.74/3.96 | Applying alpha-rule on (182) yields:
% 13.74/3.96 | (183) sdtasdt0(xq, xp) = all_139_4_106
% 13.74/3.96 | (184) sdtasdt0(xp, xq) = all_139_1_103
% 13.74/3.96 | (185) sdtpldt0(all_139_1_103, all_139_0_102) = xn
% 13.79/3.96 | (186) sdtasdt0(xq, all_41_0_12) = all_139_2_104
% 13.79/3.96 | (187) sdtpldt0(all_139_3_105, all_139_2_104) = all_139_4_106
% 13.79/3.96 | (188) sdtasdt0(all_41_0_12, xq) = all_139_0_102
% 13.79/3.96 | (189) sdtasdt0(xq, xp) = all_139_3_105
% 13.79/3.96 |
% 13.79/3.96 | Instantiating (160) with all_157_0_139, all_157_1_140, all_157_2_141, all_157_3_142, all_157_4_143 yields:
% 13.79/3.96 | (190) sdtasdt0(all_41_0_12, xq) = all_157_0_139 & sdtasdt0(xq, all_41_0_12) = all_157_3_142 & sdtasdt0(xq, xp) = all_157_4_143 & sdtasdt0(xp, xq) = all_157_1_140 & sdtasdt0(xp, xq) = all_157_2_141 & sdtpldt0(all_157_1_140, all_157_0_139) = all_157_2_141 & sdtpldt0(all_157_4_143, all_157_3_142) = xn
% 13.79/3.96 |
% 13.79/3.96 | Applying alpha-rule on (190) yields:
% 13.79/3.96 | (191) sdtasdt0(xq, xp) = all_157_4_143
% 13.79/3.96 | (192) sdtpldt0(all_157_4_143, all_157_3_142) = xn
% 13.79/3.96 | (193) sdtasdt0(xp, xq) = all_157_1_140
% 13.79/3.96 | (194) sdtasdt0(xp, xq) = all_157_2_141
% 13.79/3.96 | (195) sdtasdt0(xq, all_41_0_12) = all_157_3_142
% 13.79/3.96 | (196) sdtpldt0(all_157_1_140, all_157_0_139) = all_157_2_141
% 13.79/3.96 | (197) sdtasdt0(all_41_0_12, xq) = all_157_0_139
% 13.79/3.96 |
% 13.79/3.96 | Instantiating (159) with all_159_0_144 yields:
% 13.79/3.96 | (198) sdtasdt0(all_159_0_144, xp) = all_0_3_3 & sdtasdt0(xn, xq) = all_159_0_144
% 13.79/3.96 |
% 13.79/3.96 | Applying alpha-rule on (198) yields:
% 13.79/3.96 | (199) sdtasdt0(all_159_0_144, xp) = all_0_3_3
% 13.79/3.96 | (200) sdtasdt0(xn, xq) = all_159_0_144
% 13.79/3.96 |
% 13.79/3.96 | Instantiating (158) with all_167_0_152 yields:
% 13.79/3.96 | (201) sdtasdt0(all_167_0_152, xq) = all_0_1_1 & sdtasdt0(xp, xq) = all_167_0_152
% 13.79/3.96 |
% 13.79/3.96 | Applying alpha-rule on (201) yields:
% 13.79/3.96 | (202) sdtasdt0(all_167_0_152, xq) = all_0_1_1
% 13.79/3.96 | (203) sdtasdt0(xp, xq) = all_167_0_152
% 13.79/3.96 |
% 13.79/3.96 +-Applying beta-rule and splitting (156), into two cases.
% 13.79/3.96 |-Branch one:
% 13.79/3.96 | (141) xp = sz00
% 13.79/3.96 |
% 13.79/3.96 | Equations (141) can reduce 46 to:
% 13.79/3.96 | (142) $false
% 13.79/3.96 |
% 13.79/3.96 |-The branch is then unsatisfiable
% 13.79/3.96 |-Branch two:
% 13.79/3.96 | (46) ~ (xp = sz00)
% 13.79/3.96 | (207) ? [v0] : (sdtsldt0(v0, xp) = xn & sdtasdt0(xp, xn) = v0)
% 13.79/3.96 |
% 13.79/3.96 +-Applying beta-rule and splitting (157), into two cases.
% 13.79/3.96 |-Branch one:
% 13.79/3.96 | (141) xp = sz00
% 13.79/3.96 |
% 13.79/3.96 | Equations (141) can reduce 46 to:
% 13.79/3.96 | (142) $false
% 13.79/3.96 |
% 13.79/3.96 |-The branch is then unsatisfiable
% 13.79/3.96 |-Branch two:
% 13.79/3.96 | (46) ~ (xp = sz00)
% 13.79/3.96 | (211) ? [v0] : (sdtsldt0(v0, xp) = all_0_2_2 & sdtasdt0(xq, xn) = v0)
% 13.79/3.96 |
% 13.79/3.96 | Instantiating formula (72) with xp, xq, all_157_2_141, xn and discharging atoms sdtasdt0(xp, xq) = all_157_2_141, sdtasdt0(xp, xq) = xn, yields:
% 13.79/3.96 | (212) all_157_2_141 = xn
% 13.79/3.96 |
% 13.79/3.96 | Instantiating formula (72) with xp, xq, all_157_2_141, all_167_0_152 and discharging atoms sdtasdt0(xp, xq) = all_167_0_152, sdtasdt0(xp, xq) = all_157_2_141, yields:
% 13.79/3.96 | (213) all_167_0_152 = all_157_2_141
% 13.79/3.96 |
% 13.79/3.96 | Instantiating formula (72) with xp, xq, all_139_1_103, all_167_0_152 and discharging atoms sdtasdt0(xp, xq) = all_167_0_152, sdtasdt0(xp, xq) = all_139_1_103, yields:
% 13.79/3.96 | (214) all_167_0_152 = all_139_1_103
% 13.79/3.96 |
% 13.79/3.96 | Instantiating formula (72) with xn, xq, all_109_2_53, all_159_0_144 and discharging atoms sdtasdt0(xn, xq) = all_159_0_144, sdtasdt0(xn, xq) = all_109_2_53, yields:
% 13.79/3.96 | (215) all_159_0_144 = all_109_2_53
% 13.79/3.96 |
% 13.79/3.96 | Instantiating formula (72) with xn, xq, all_107_1_47, all_109_2_53 and discharging atoms sdtasdt0(xn, xq) = all_109_2_53, sdtasdt0(xn, xq) = all_107_1_47, yields:
% 13.79/3.96 | (216) all_109_2_53 = all_107_1_47
% 13.79/3.96 |
% 13.79/3.96 | Instantiating formula (72) with xn, xq, all_107_2_48, all_159_0_144 and discharging atoms sdtasdt0(xn, xq) = all_159_0_144, sdtasdt0(xn, xq) = all_107_2_48, yields:
% 13.79/3.96 | (217) all_159_0_144 = all_107_2_48
% 13.79/3.96 |
% 13.79/3.96 | Instantiating formula (72) with xn, xq, all_39_0_11, all_109_2_53 and discharging atoms sdtasdt0(xn, xq) = all_109_2_53, sdtasdt0(xn, xq) = all_39_0_11, yields:
% 13.79/3.96 | (218) all_109_2_53 = all_39_0_11
% 13.79/3.96 |
% 13.79/3.96 | Instantiating formula (38) with all_0_3_3, all_39_0_11, all_0_4_4, xp and discharging atoms sdtasdt0(xp, all_39_0_11) = all_0_3_3, sdtasdt0(xp, all_0_4_4) = all_0_3_3, aNaturalNumber0(all_39_0_11), aNaturalNumber0(all_0_4_4), aNaturalNumber0(xp), yields:
% 13.79/3.96 | (219) all_39_0_11 = all_0_4_4 | xp = sz00
% 13.79/3.96 |
% 13.79/3.97 | Combining equations (213,214) yields a new equation:
% 13.79/3.97 | (220) all_157_2_141 = all_139_1_103
% 13.79/3.97 |
% 13.79/3.97 | Simplifying 220 yields:
% 13.79/3.97 | (221) all_157_2_141 = all_139_1_103
% 13.79/3.97 |
% 13.79/3.97 | Combining equations (215,217) yields a new equation:
% 13.79/3.97 | (222) all_109_2_53 = all_107_2_48
% 13.79/3.97 |
% 13.79/3.97 | Simplifying 222 yields:
% 13.79/3.97 | (223) all_109_2_53 = all_107_2_48
% 13.79/3.97 |
% 13.79/3.97 | Combining equations (221,212) yields a new equation:
% 13.79/3.97 | (224) all_139_1_103 = xn
% 13.79/3.97 |
% 13.79/3.97 | Simplifying 224 yields:
% 13.79/3.97 | (225) all_139_1_103 = xn
% 13.79/3.97 |
% 13.79/3.97 | Combining equations (218,216) yields a new equation:
% 13.79/3.97 | (226) all_107_1_47 = all_39_0_11
% 13.79/3.97 |
% 13.79/3.97 | Combining equations (223,216) yields a new equation:
% 13.79/3.97 | (227) all_107_1_47 = all_107_2_48
% 13.79/3.97 |
% 13.79/3.97 | Combining equations (226,227) yields a new equation:
% 13.79/3.97 | (228) all_107_2_48 = all_39_0_11
% 13.79/3.97 |
% 13.79/3.97 | Combining equations (225,214) yields a new equation:
% 13.79/3.97 | (229) all_167_0_152 = xn
% 13.79/3.97 |
% 13.79/3.97 | From (229) and (202) follows:
% 13.79/3.97 | (230) sdtasdt0(xn, xq) = all_0_1_1
% 13.79/3.97 |
% 13.79/3.97 | From (228) and (168) follows:
% 13.79/3.97 | (163) sdtasdt0(xn, xq) = all_39_0_11
% 13.79/3.97 |
% 13.79/3.97 +-Applying beta-rule and splitting (219), into two cases.
% 13.79/3.97 |-Branch one:
% 13.79/3.97 | (141) xp = sz00
% 13.79/3.97 |
% 13.79/3.97 | Equations (141) can reduce 46 to:
% 13.79/3.97 | (142) $false
% 13.79/3.97 |
% 13.79/3.97 |-The branch is then unsatisfiable
% 13.79/3.97 |-Branch two:
% 13.79/3.97 | (46) ~ (xp = sz00)
% 13.79/3.97 | (235) all_39_0_11 = all_0_4_4
% 13.79/3.97 |
% 13.79/3.97 | From (235) and (131) follows:
% 13.79/3.97 | (60) sdtasdt0(xp, all_0_4_4) = all_0_3_3
% 13.79/3.97 |
% 13.79/3.97 | From (235) and (163) follows:
% 13.79/3.97 | (237) sdtasdt0(xn, xq) = all_0_4_4
% 13.79/3.97 |
% 13.79/3.97 | Instantiating formula (72) with xn, xq, all_0_4_4, all_0_1_1 and discharging atoms sdtasdt0(xn, xq) = all_0_1_1, sdtasdt0(xn, xq) = all_0_4_4, yields:
% 13.79/3.97 | (238) all_0_1_1 = all_0_4_4
% 13.79/3.97 |
% 13.79/3.97 | From (238) and (107) follows:
% 13.79/3.97 | (239) sdtasdt0(xp, all_0_4_4) = all_0_0_0
% 13.79/3.97 |
% 13.79/3.97 | Instantiating formula (72) with xp, all_0_4_4, all_0_0_0, all_0_3_3 and discharging atoms sdtasdt0(xp, all_0_4_4) = all_0_0_0, sdtasdt0(xp, all_0_4_4) = all_0_3_3, yields:
% 13.79/3.97 | (240) all_0_0_0 = all_0_3_3
% 13.79/3.97 |
% 13.79/3.97 | Equations (240) can reduce 45 to:
% 13.79/3.97 | (142) $false
% 13.79/3.97 |
% 13.79/3.97 |-The branch is then unsatisfiable
% 13.79/3.97 |-Branch two:
% 13.79/3.97 | (242) ~ sdtlseqdt0(xp, xn)
% 13.79/3.97 | (243) xn = sz00
% 13.79/3.97 |
% 13.79/3.97 | Equations (243) can reduce 42 to:
% 13.79/3.97 | (142) $false
% 13.79/3.97 |
% 13.79/3.97 |-The branch is then unsatisfiable
% 13.79/3.97 % SZS output end Proof for theBenchmark
% 13.79/3.97
% 13.79/3.97 3378ms
%------------------------------------------------------------------------------