TSTP Solution File: NUM494+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM494+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n005.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 08:45:06 EDT 2022
% Result : Theorem 6.47s 2.21s
% Output : Proof 13.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM494+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jul 7 08:12:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.55/0.59 ____ _
% 0.55/0.59 ___ / __ \_____(_)___ ________ __________
% 0.55/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.59
% 0.55/0.59 A Theorem Prover for First-Order Logic
% 0.61/0.59 (ePrincess v.1.0)
% 0.61/0.59
% 0.61/0.59 (c) Philipp Rümmer, 2009-2015
% 0.61/0.59 (c) Peter Backeman, 2014-2015
% 0.61/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.61/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.61/0.59 Bug reports to peter@backeman.se
% 0.61/0.59
% 0.61/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.61/0.59
% 0.61/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.95/1.01 Prover 0: Preprocessing ...
% 3.92/1.60 Prover 0: Constructing countermodel ...
% 6.47/2.21 Prover 0: proved (1564ms)
% 6.47/2.21
% 6.47/2.21 No countermodel exists, formula is valid
% 6.47/2.21 % SZS status Theorem for theBenchmark
% 6.47/2.21
% 6.47/2.21 Generating proof ... found it (size 164)
% 12.51/3.53
% 12.51/3.53 % SZS output start Proof for theBenchmark
% 12.51/3.53 Assumed formulas after preprocessing and simplification:
% 12.51/3.53 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (xr = xn) & ~ (xp = sz10) & ~ (xp = sz00) & ~ (sz10 = sz00) & sdtmndt0(xn, xp) = xr & sdtasdt0(xr, xm) = v3 & sdtasdt0(xp, v9) = v2 & sdtasdt0(xp, v6) = v3 & sdtasdt0(xn, xm) = v2 & sdtpldt0(v4, xp) = v5 & sdtpldt0(v0, xp) = v1 & sdtpldt0(xr, v7) = xn & sdtpldt0(xr, xm) = v4 & sdtpldt0(xp, v8) = xn & sdtpldt0(xp, xr) = xn & sdtpldt0(xn, xm) = v0 & isPrime0(xp) & doDivides0(xp, v3) & doDivides0(xp, v2) & sdtlseqdt0(xr, xn) & sdtlseqdt0(xp, xn) & aNaturalNumber0(v9) & aNaturalNumber0(v8) & aNaturalNumber0(v7) & aNaturalNumber0(v6) & aNaturalNumber0(xr) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ isPrime0(sz10) & ~ isPrime0(sz00) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v10 = sz00 | ~ (sdtsldt0(v14, v10) = v15) | ~ (sdtsldt0(v11, v10) = v12) | ~ (sdtasdt0(v13, v11) = v14) | ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v13) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtasdt0(v13, v12) = v15) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (sdtasdt0(v12, v10) = v14) | ~ (sdtasdt0(v11, v10) = v13) | ~ (sdtpldt0(v13, v14) = v15) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (sdtasdt0(v16, v10) = v15 & sdtasdt0(v10, v16) = v17 & sdtasdt0(v10, v12) = v19 & sdtasdt0(v10, v11) = v18 & sdtpldt0(v18, v19) = v17 & sdtpldt0(v11, v12) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (sdtasdt0(v10, v12) = v14) | ~ (sdtasdt0(v10, v11) = v13) | ~ (sdtpldt0(v13, v14) = v15) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (sdtasdt0(v16, v10) = v17 & sdtasdt0(v12, v10) = v19 & sdtasdt0(v11, v10) = v18 & sdtasdt0(v10, v16) = v15 & sdtpldt0(v18, v19) = v17 & sdtpldt0(v11, v12) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v12, v10) = v14) | ~ (sdtasdt0(v11, v10) = v13) | ~ sdtlseqdt0(v11, v12) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtlseqdt0(v13, v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v12, v10) = v14) | ~ (sdtasdt0(v11, v10) = v13) | ~ sdtlseqdt0(v11, v12) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v15) & sdtasdt0(v10, v12) = v16 & sdtasdt0(v10, v11) = v15 & sdtlseqdt0(v15, v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v12, v10) = v14) | ~ (sdtasdt0(v11, v10) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v15) & sdtasdt0(v10, v12) = v16 & sdtasdt0(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v12, v10) = v14) | ~ (sdtasdt0(v10, v11) = v13) | ~ sdtlseqdt0(v11, v12) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v14) & ~ (v15 = v13) & sdtasdt0(v11, v10) = v16 & sdtasdt0(v10, v12) = v15 & sdtlseqdt0(v16, v14) & sdtlseqdt0(v13, v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v12, v10) = v14) | ~ (sdtasdt0(v10, v11) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v14) & ~ (v15 = v13) & sdtasdt0(v11, v10) = v16 & sdtasdt0(v10, v12) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v11, v10) = v14) | ~ (sdtasdt0(v10, v12) = v13) | ~ sdtlseqdt0(v11, v12) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v14) & ~ (v15 = v13) & sdtasdt0(v12, v10) = v16 & sdtasdt0(v10, v11) = v15 & sdtlseqdt0(v15, v13) & sdtlseqdt0(v14, v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v11, v10) = v14) | ~ (sdtasdt0(v10, v12) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v14) & ~ (v15 = v13) & sdtasdt0(v12, v10) = v16 & sdtasdt0(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v10, v12) = v14) | ~ (sdtasdt0(v10, v11) = v13) | ~ sdtlseqdt0(v11, v12) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtlseqdt0(v13, v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v10, v12) = v14) | ~ (sdtasdt0(v10, v11) = v13) | ~ sdtlseqdt0(v11, v12) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v15) & sdtasdt0(v12, v10) = v16 & sdtasdt0(v11, v10) = v15 & sdtlseqdt0(v15, v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v10, v12) = v14) | ~ (sdtasdt0(v10, v11) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v15) & sdtasdt0(v12, v10) = v16 & sdtasdt0(v11, v10) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (sdtpldt0(v12, v10) = v14) | ~ (sdtpldt0(v11, v10) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v15) & sdtpldt0(v10, v12) = v16 & sdtpldt0(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (sdtpldt0(v12, v10) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v14) & ~ (v15 = v13) & sdtpldt0(v11, v10) = v16 & sdtpldt0(v10, v12) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (sdtpldt0(v11, v10) = v14) | ~ (sdtpldt0(v10, v12) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v14) & ~ (v15 = v13) & sdtpldt0(v12, v10) = v16 & sdtpldt0(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (sdtpldt0(v10, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v15) & sdtpldt0(v12, v10) = v16 & sdtpldt0(v11, v10) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = sz10 | v12 = sz00 | ~ (sdtpldt0(v13, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ iLess0(v14, v1) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v12, v11) | doDivides0(v12, v10) | ? [v15] : ? [v16] : ? [v17] : ((v17 = v12 & ~ (v15 = v12) & ~ (v15 = sz10) & sdtasdt0(v15, v16) = v12 & doDivides0(v15, v12) & aNaturalNumber0(v16) & aNaturalNumber0(v15)) | (sdtasdt0(v10, v11) = v15 & ~ doDivides0(v12, v15) & ! [v18] : ( ~ (sdtasdt0(v12, v18) = v15) | ~ aNaturalNumber0(v18))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = sz10 | v12 = sz00 | ~ (sdtpldt0(v13, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ iLess0(v14, v1) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v12, v11) | ? [v15] : ? [v16] : ? [v17] : ((v17 = v12 & ~ (v15 = v12) & ~ (v15 = sz10) & sdtasdt0(v15, v16) = v12 & doDivides0(v15, v12) & aNaturalNumber0(v16) & aNaturalNumber0(v15)) | (v16 = v10 & sdtasdt0(v12, v15) = v10 & aNaturalNumber0(v15)) | (sdtasdt0(v10, v11) = v15 & ~ doDivides0(v12, v15) & ! [v18] : ( ~ (sdtasdt0(v12, v18) = v15) | ~ aNaturalNumber0(v18))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = sz10 | v12 = sz00 | ~ (sdtpldt0(v13, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ iLess0(v14, v1) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v12, v10) | ? [v15] : ? [v16] : ? [v17] : ((v17 = v12 & ~ (v15 = v12) & ~ (v15 = sz10) & sdtasdt0(v15, v16) = v12 & doDivides0(v15, v12) & aNaturalNumber0(v16) & aNaturalNumber0(v15)) | (v16 = v11 & sdtasdt0(v12, v15) = v11 & aNaturalNumber0(v15)) | (sdtasdt0(v10, v11) = v15 & ~ doDivides0(v12, v15) & ! [v18] : ( ~ (sdtasdt0(v12, v18) = v15) | ~ aNaturalNumber0(v18))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = sz10 | v12 = sz00 | ~ (sdtpldt0(v13, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ iLess0(v14, v1) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ? [v17] : ((v17 = v12 & ~ (v15 = v12) & ~ (v15 = sz10) & sdtasdt0(v15, v16) = v12 & doDivides0(v15, v12) & aNaturalNumber0(v16) & aNaturalNumber0(v15)) | (v16 = v11 & sdtasdt0(v12, v15) = v11 & aNaturalNumber0(v15)) | (v16 = v10 & sdtasdt0(v12, v15) = v10 & aNaturalNumber0(v15)) | (sdtasdt0(v10, v11) = v15 & ~ doDivides0(v12, v15) & ! [v18] : ( ~ (sdtasdt0(v12, v18) = v15) | ~ aNaturalNumber0(v18))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = sz00 | ~ (sdtsldt0(v11, v10) = v12) | ~ (sdtasdt0(v13, v12) = v14) | ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v13) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : (sdtsldt0(v15, v10) = v14 & sdtasdt0(v13, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtasdt0(v13, v12) = v14) | ~ (sdtasdt0(v10, v11) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : (sdtasdt0(v11, v12) = v15 & sdtasdt0(v10, v15) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtasdt0(v13, v10) = v14) | ~ (sdtpldt0(v11, v12) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (sdtasdt0(v12, v10) = v19 & sdtasdt0(v11, v10) = v18 & sdtasdt0(v10, v13) = v15 & sdtasdt0(v10, v12) = v17 & sdtasdt0(v10, v11) = v16 & sdtpldt0(v18, v19) = v14 & sdtpldt0(v16, v17) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtasdt0(v11, v12) = v13) | ~ (sdtasdt0(v10, v13) = v14) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : (sdtasdt0(v15, v12) = v14 & sdtasdt0(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtasdt0(v10, v13) = v14) | ~ (sdtpldt0(v11, v12) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (sdtasdt0(v13, v10) = v17 & sdtasdt0(v12, v10) = v19 & sdtasdt0(v11, v10) = v18 & sdtasdt0(v10, v12) = v16 & sdtasdt0(v10, v11) = v15 & sdtpldt0(v18, v19) = v17 & sdtpldt0(v15, v16) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtpldt0(v13, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ isPrime0(v12) | ~ iLess0(v14, v1) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v12, v11) | doDivides0(v12, v10) | ? [v15] : (sdtasdt0(v10, v11) = v15 & ~ doDivides0(v12, v15) & ! [v16] : ( ~ (sdtasdt0(v12, v16) = v15) | ~ aNaturalNumber0(v16)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtpldt0(v13, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ isPrime0(v12) | ~ iLess0(v14, v1) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v12, v11) | ? [v15] : ? [v16] : ((v16 = v10 & sdtasdt0(v12, v15) = v10 & aNaturalNumber0(v15)) | (sdtasdt0(v10, v11) = v15 & ~ doDivides0(v12, v15) & ! [v17] : ( ~ (sdtasdt0(v12, v17) = v15) | ~ aNaturalNumber0(v17))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtpldt0(v13, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ isPrime0(v12) | ~ iLess0(v14, v1) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v12, v10) | ? [v15] : ? [v16] : ((v16 = v11 & sdtasdt0(v12, v15) = v11 & aNaturalNumber0(v15)) | (sdtasdt0(v10, v11) = v15 & ~ doDivides0(v12, v15) & ! [v17] : ( ~ (sdtasdt0(v12, v17) = v15) | ~ aNaturalNumber0(v17))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtpldt0(v13, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ isPrime0(v12) | ~ iLess0(v14, v1) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ((v16 = v11 & sdtasdt0(v12, v15) = v11 & aNaturalNumber0(v15)) | (v16 = v10 & sdtasdt0(v12, v15) = v10 & aNaturalNumber0(v15)) | (sdtasdt0(v10, v11) = v15 & ~ doDivides0(v12, v15) & ! [v17] : ( ~ (sdtasdt0(v12, v17) = v15) | ~ aNaturalNumber0(v17))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtpldt0(v13, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : (sdtpldt0(v11, v12) = v15 & sdtpldt0(v10, v15) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtpldt0(v11, v12) = v13) | ~ (sdtpldt0(v10, v13) = v14) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : (sdtpldt0(v15, v12) = v14 & sdtpldt0(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | v10 = sz00 | ~ (sdtsldt0(v11, v10) = v12) | ~ (sdtasdt0(v10, v13) = v11) | ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v13) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (sdtmndt0(v11, v10) = v12) | ~ (sdtpldt0(v10, v13) = v11) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v13) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | v10 = sz00 | ~ (sdtsldt0(v11, v10) = v12) | ~ (sdtasdt0(v10, v12) = v13) | ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (sdtmndt0(v11, v10) = v12) | ~ (sdtpldt0(v10, v12) = v13) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v12, v10) = v13) | ~ (sdtasdt0(v11, v10) = v13) | ~ sdtlseqdt0(v11, v12) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v12, v10) = v13) | ~ (sdtasdt0(v11, v10) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v10, v12) = v13) | ~ (sdtasdt0(v10, v11) = v13) | ~ sdtlseqdt0(v11, v12) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v10, v12) = v13) | ~ (sdtasdt0(v10, v11) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (sdtpldt0(v12, v10) = v13) | ~ (sdtpldt0(v11, v10) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (sdtpldt0(v10, v12) = v13) | ~ (sdtpldt0(v10, v11) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtsldt0(v13, v12) = v11) | ~ (sdtsldt0(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtmndt0(v13, v12) = v11) | ~ (sdtmndt0(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtasdt0(v13, v12) = v11) | ~ (sdtasdt0(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtpldt0(v13, v12) = v11) | ~ (sdtpldt0(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtpldt0(v12, v11) = v13) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v14] : ? [v15] : ? [v16] : ( ~ (v16 = v15) & ~ (v14 = v13) & sdtpldt0(v12, v10) = v14 & sdtpldt0(v11, v12) = v16 & sdtpldt0(v10, v12) = v15 & sdtlseqdt0(v15, v16) & sdtlseqdt0(v14, v13))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtpldt0(v12, v10) = v13) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v14] : ? [v15] : ? [v16] : ( ~ (v16 = v15) & ~ (v14 = v13) & sdtpldt0(v12, v11) = v14 & sdtpldt0(v11, v12) = v16 & sdtpldt0(v10, v12) = v15 & sdtlseqdt0(v15, v16) & sdtlseqdt0(v13, v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtpldt0(v11, v12) = v13) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v14] : ? [v15] : ? [v16] : ( ~ (v16 = v13) & ~ (v15 = v14) & sdtpldt0(v12, v11) = v15 & sdtpldt0(v12, v10) = v14 & sdtpldt0(v10, v12) = v16 & sdtlseqdt0(v16, v13) & sdtlseqdt0(v14, v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtpldt0(v10, v12) = v13) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v14] : ? [v15] : ? [v16] : ( ~ (v16 = v13) & ~ (v15 = v14) & sdtpldt0(v12, v11) = v15 & sdtpldt0(v12, v10) = v14 & sdtpldt0(v11, v12) = v16 & sdtlseqdt0(v14, v15) & sdtlseqdt0(v13, v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = sz00 | ~ (sdtsldt0(v11, v10) = v12) | ~ (sdtasdt0(v10, v12) = v13) | ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | aNaturalNumber0(v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtmndt0(v11, v10) = v12) | ~ (sdtpldt0(v10, v12) = v13) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | aNaturalNumber0(v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtpldt0(v11, v12) = v13) | ~ doDivides0(v10, v13) | ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtpldt0(v11, v12) = v13) | ~ doDivides0(v10, v12) | ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v10, v13)) & ! [v10] : ! [v11] : ! [v12] : (v10 = sz00 | ~ (sdtasdt0(v11, v10) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtlseqdt0(v11, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtasdt0(v11, v10) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtasdt0(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtasdt0(v10, v12) = v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtasdt0(v10, v11) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtasdt0(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtasdt0(v10, v11) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | aNaturalNumber0(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtpldt0(v11, v10) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtpldt0(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtpldt0(v10, v12) = v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtlseqdt0(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtpldt0(v10, v11) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtpldt0(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtpldt0(v10, v11) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | aNaturalNumber0(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ doDivides0(v11, v12) | ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ sdtlseqdt0(v11, v12) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtlseqdt0(v10, v12)) & ! [v10] : ! [v11] : (v11 = v10 | v11 = sz10 | ~ isPrime0(v10) | ~ doDivides0(v11, v10) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (sdtasdt0(v10, sz10) = v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (sdtasdt0(sz10, v10) = v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (sdtpldt0(v10, sz00) = v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (sdtpldt0(sz00, v10) = v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = v10 | ~ sdtlseqdt0(v11, v10) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = v10 | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | iLess0(v10, v11)) & ! [v10] : ! [v11] : (v11 = sz00 | v10 = sz00 | ~ (sdtasdt0(v10, v11) = sz00) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = sz00 | ~ (sdtasdt0(v10, sz00) = v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = sz00 | ~ (sdtasdt0(sz00, v10) = v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = sz00 | ~ (sdtpldt0(v10, v11) = sz00) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = sz00 | ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtlseqdt0(v10, v11)) & ! [v10] : ! [v11] : (v10 = xp | v10 = sz10 | ~ (sdtasdt0(v10, v11) = xp) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v10 = sz00 | ~ (sdtpldt0(v10, v11) = sz00) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ( ~ (sdtasdt0(v10, sz10) = v11) | ~ aNaturalNumber0(v10) | sdtasdt0(sz10, v10) = v10) & ! [v10] : ! [v11] : ( ~ (sdtasdt0(v10, sz00) = v11) | ~ aNaturalNumber0(v10) | sdtasdt0(sz00, v10) = sz00) & ! [v10] : ! [v11] : ( ~ (sdtasdt0(sz10, v10) = v11) | ~ aNaturalNumber0(v10) | sdtasdt0(v10, sz10) = v10) & ! [v10] : ! [v11] : ( ~ (sdtasdt0(sz00, v10) = v11) | ~ aNaturalNumber0(v10) | sdtasdt0(v10, sz00) = sz00) & ! [v10] : ! [v11] : ( ~ (sdtpldt0(v10, sz00) = v11) | ~ aNaturalNumber0(v10) | sdtpldt0(sz00, v10) = v10) & ! [v10] : ! [v11] : ( ~ (sdtpldt0(sz00, v10) = v11) | ~ aNaturalNumber0(v10) | sdtpldt0(v10, sz00) = v10) & ! [v10] : ! [v11] : ( ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v12] : (sdtasdt0(v10, v12) = v11 & aNaturalNumber0(v12))) & ! [v10] : ! [v11] : ( ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v12] : (sdtpldt0(v10, v12) = v11 & aNaturalNumber0(v12))) & ! [v10] : ! [v11] : ( ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtlseqdt0(v11, v10) | sdtlseqdt0(v10, v11)) & ! [v10] : (v10 = xp | v10 = sz10 | ~ doDivides0(v10, xp) | ~ aNaturalNumber0(v10)) & ! [v10] : (v10 = sz10 | v10 = sz00 | ~ aNaturalNumber0(v10) | isPrime0(v10) | ? [v11] : ( ~ (v11 = v10) & ~ (v11 = sz10) & doDivides0(v11, v10) & aNaturalNumber0(v11))) & ! [v10] : (v10 = sz10 | v10 = sz00 | ~ aNaturalNumber0(v10) | sdtlseqdt0(sz10, v10)) & ! [v10] : (v10 = sz10 | v10 = sz00 | ~ aNaturalNumber0(v10) | ? [v11] : (isPrime0(v11) & doDivides0(v11, v10) & aNaturalNumber0(v11))) & ! [v10] : ( ~ aNaturalNumber0(v10) | sdtlseqdt0(v10, v10)) & (v5 = v1 | ( ~ sdtlseqdt0(v5, v1) & ! [v10] : ( ~ aNaturalNumber0(v10) | ? [v11] : ( ~ (v11 = v1) & sdtpldt0(v5, v10) = v11)))))
% 12.63/3.60 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields:
% 12.63/3.60 | (1) ~ (xr = xn) & ~ (xp = sz10) & ~ (xp = sz00) & ~ (sz10 = sz00) & sdtmndt0(xn, xp) = xr & sdtasdt0(xr, xm) = all_0_6_6 & sdtasdt0(xp, all_0_0_0) = all_0_7_7 & sdtasdt0(xp, all_0_3_3) = all_0_6_6 & sdtasdt0(xn, xm) = all_0_7_7 & sdtpldt0(all_0_5_5, xp) = all_0_4_4 & sdtpldt0(all_0_9_9, xp) = all_0_8_8 & sdtpldt0(xr, all_0_2_2) = xn & sdtpldt0(xr, xm) = all_0_5_5 & sdtpldt0(xp, all_0_1_1) = xn & sdtpldt0(xp, xr) = xn & sdtpldt0(xn, xm) = all_0_9_9 & isPrime0(xp) & doDivides0(xp, all_0_6_6) & doDivides0(xp, all_0_7_7) & sdtlseqdt0(xr, xn) & sdtlseqdt0(xp, xn) & aNaturalNumber0(all_0_0_0) & aNaturalNumber0(all_0_1_1) & aNaturalNumber0(all_0_2_2) & aNaturalNumber0(all_0_3_3) & aNaturalNumber0(xr) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ isPrime0(sz10) & ~ isPrime0(sz00) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v3, v2) = v5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtlseqdt0(v6, v4) & sdtlseqdt0(v3, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v3) & sdtlseqdt0(v4, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtlseqdt0(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v0, v2) = v6 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v2) = v4) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtsldt0(v5, v0) = v4 & sdtasdt0(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v6, v7) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) | ? [v5] : (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v6] : ( ~ (sdtasdt0(v2, v6) = v5) | ~ aNaturalNumber0(v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5] : ? [v6] : ((v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ((v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ((v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v1) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v4, v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v0) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v1) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v1, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v0, v2) = v6 & sdtlseqdt0(v6, v3) & sdtlseqdt0(v4, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1)) & ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0] : ! [v1] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1) = xp) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0) & ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2))) & ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2))) & ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) & ! [v0] : (v0 = xp | v0 = sz10 | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0)) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1] : ( ~ (v1 = v0) & ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1))) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1))) & ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) & (all_0_4_4 = all_0_8_8 | ( ~ sdtlseqdt0(all_0_4_4, all_0_8_8) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_8_8) & sdtpldt0(all_0_4_4, v0) = v1))))
% 13.07/3.62 |
% 13.07/3.62 | Applying alpha-rule on (1) yields:
% 13.07/3.63 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.07/3.63 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 13.07/3.63 | (4) ! [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)))
% 13.07/3.63 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 13.07/3.63 | (6) aNaturalNumber0(all_0_3_3)
% 13.07/3.63 | (7) aNaturalNumber0(all_0_0_0)
% 13.07/3.63 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8)))))
% 13.07/3.63 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 13.07/3.63 | (10) ! [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))
% 13.07/3.63 | (11) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 13.07/3.63 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ((v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7)))))
% 13.07/3.63 | (13) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 13.07/3.63 | (14) ! [v0] : (v0 = xp | v0 = sz10 | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0))
% 13.07/3.63 | (15) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.07/3.63 | (16) sdtlseqdt0(xp, xn)
% 13.07/3.63 | (17) all_0_4_4 = all_0_8_8 | ( ~ sdtlseqdt0(all_0_4_4, all_0_8_8) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_8_8) & sdtpldt0(all_0_4_4, v0) = v1)))
% 13.07/3.63 | (18) sdtasdt0(xn, xm) = all_0_7_7
% 13.07/3.63 | (19) ! [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))
% 13.07/3.63 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 13.07/3.63 | (21) ! [v0] : ! [v1] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1) = xp) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.07/3.63 | (22) ~ (xr = xn)
% 13.07/3.63 | (23) ! [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))
% 13.07/3.63 | (24) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 13.07/3.63 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8)))))
% 13.07/3.63 | (26) sdtmndt0(xn, xp) = xr
% 13.07/3.63 | (27) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0)
% 13.07/3.63 | (28) ~ (xp = sz10)
% 13.07/3.63 | (29) ! [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))
% 13.07/3.63 | (30) aNaturalNumber0(all_0_1_1)
% 13.07/3.63 | (31) ! [v0] : ! [v1] : (v1 = sz00 | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 13.07/3.63 | (32) aNaturalNumber0(xp)
% 13.07/3.63 | (33) sdtpldt0(xr, xm) = all_0_5_5
% 13.07/3.63 | (34) isPrime0(xp)
% 13.07/3.63 | (35) sdtasdt0(xr, xm) = all_0_6_6
% 13.07/3.63 | (36) ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 13.07/3.63 | (37) ! [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))
% 13.07/3.63 | (38) ! [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)))
% 13.07/3.63 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.07/3.63 | (40) sdtpldt0(xn, xm) = all_0_9_9
% 13.07/3.63 | (41) ! [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))
% 13.07/3.63 | (42) sdtpldt0(xp, all_0_1_1) = xn
% 13.07/3.63 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2)
% 13.07/3.63 | (44) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 13.07/3.63 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5] : ? [v6] : ((v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7)))))
% 13.07/3.63 | (46) ~ (xp = sz00)
% 13.07/3.63 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 13.07/3.63 | (48) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.07/3.63 | (49) ! [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)))
% 13.07/3.64 | (50) ! [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))
% 13.07/3.64 | (51) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 13.07/3.64 | (52) ! [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))
% 13.07/3.64 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8)))))
% 13.07/3.64 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.07/3.64 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.07/3.64 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4))
% 13.07/3.64 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 13.07/3.64 | (58) sdtlseqdt0(xr, xn)
% 13.07/3.64 | (59) sdtpldt0(all_0_5_5, xp) = all_0_4_4
% 13.07/3.64 | (60) ! [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))
% 13.07/3.64 | (61) ~ isPrime0(sz00)
% 13.07/3.64 | (62) ! [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)
% 13.07/3.64 | (63) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0))
% 13.07/3.64 | (64) aNaturalNumber0(sz10)
% 13.07/3.64 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 13.07/3.64 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2)
% 13.07/3.64 | (67) ! [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))
% 13.07/3.64 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.07/3.64 | (69) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.07/3.64 | (70) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 13.07/3.64 | (71) ! [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))
% 13.07/3.64 | (72) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0))
% 13.07/3.64 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 13.07/3.64 | (74) ! [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))
% 13.07/3.64 | (75) sdtpldt0(all_0_9_9, xp) = all_0_8_8
% 13.07/3.64 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8)))))
% 13.07/3.64 | (77) ! [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)))
% 13.07/3.64 | (78) doDivides0(xp, all_0_6_6)
% 13.07/3.64 | (79) ! [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))
% 13.07/3.64 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.07/3.64 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 13.07/3.64 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ((v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7)))))
% 13.07/3.64 | (83) aNaturalNumber0(all_0_2_2)
% 13.07/3.64 | (84) ~ isPrime0(sz10)
% 13.07/3.64 | (85) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00)
% 13.07/3.64 | (86) sdtpldt0(xp, xr) = xn
% 13.07/3.64 | (87) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 13.07/3.64 | (88) sdtpldt0(xr, all_0_2_2) = xn
% 13.07/3.64 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 13.07/3.64 | (90) ! [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))
% 13.07/3.64 | (91) ! [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))
% 13.07/3.64 | (92) ! [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))
% 13.07/3.64 | (93) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.07/3.64 | (94) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1] : ( ~ (v1 = v0) & ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 13.07/3.64 | (95) ! [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)))
% 13.07/3.64 | (96) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 13.07/3.64 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.07/3.64 | (98) ! [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))
% 13.07/3.65 | (99) ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 13.07/3.65 | (100) sdtasdt0(xp, all_0_0_0) = all_0_7_7
% 13.07/3.65 | (101) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 13.07/3.65 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3))
% 13.07/3.65 | (103) ! [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)))
% 13.07/3.65 | (104) ~ (sz10 = sz00)
% 13.07/3.65 | (105) ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 13.07/3.65 | (106) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 13.07/3.65 | (107) ! [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)))
% 13.07/3.65 | (108) sdtasdt0(xp, all_0_3_3) = all_0_6_6
% 13.07/3.65 | (109) ! [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))
% 13.07/3.65 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 13.07/3.65 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 13.07/3.65 | (112) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 13.07/3.65 | (113) aNaturalNumber0(xm)
% 13.07/3.65 | (114) aNaturalNumber0(sz00)
% 13.07/3.65 | (115) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 13.07/3.65 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 13.07/3.65 | (117) aNaturalNumber0(xr)
% 13.07/3.65 | (118) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0)
% 13.07/3.65 | (119) aNaturalNumber0(xn)
% 13.07/3.65 | (120) ! [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))
% 13.07/3.65 | (121) ! [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))
% 13.07/3.65 | (122) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 13.07/3.65 | (123) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 13.07/3.65 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 13.07/3.65 | (125) doDivides0(xp, all_0_7_7)
% 13.07/3.65 | (126) ! [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))
% 13.07/3.65 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) | ? [v5] : (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v6] : ( ~ (sdtasdt0(v2, v6) = v5) | ~ aNaturalNumber0(v6))))
% 13.07/3.65 | (128) ! [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)))
% 13.07/3.65 |
% 13.07/3.65 | Instantiating formula (68) with all_0_1_1, xr, xn, xp and discharging atoms sdtmndt0(xn, xp) = xr, sdtpldt0(xp, all_0_1_1) = xn, sdtlseqdt0(xp, xn), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 13.07/3.65 | (129) all_0_1_1 = xr
% 13.07/3.65 |
% 13.07/3.65 | From (129) and (42) follows:
% 13.07/3.65 | (86) sdtpldt0(xp, xr) = xn
% 13.07/3.65 |
% 13.07/3.65 | From (129) and (30) follows:
% 13.07/3.65 | (117) aNaturalNumber0(xr)
% 13.07/3.65 |
% 13.07/3.65 | Instantiating formula (123) with all_0_2_2 and discharging atoms aNaturalNumber0(all_0_2_2), yields:
% 13.07/3.65 | (132) all_0_2_2 = sz10 | all_0_2_2 = sz00 | ? [v0] : (isPrime0(v0) & doDivides0(v0, all_0_2_2) & aNaturalNumber0(v0))
% 13.07/3.65 |
% 13.07/3.65 | Instantiating formula (66) with xn, xp, xr and discharging atoms sdtpldt0(xp, xr) = xn, aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 13.07/3.65 | (133) sdtpldt0(xr, xp) = xn
% 13.07/3.65 |
% 13.07/3.65 | Instantiating formula (44) with xp and discharging atoms aNaturalNumber0(xp), yields:
% 13.07/3.65 | (134) xp = sz10 | xp = sz00 | sdtlseqdt0(sz10, xp)
% 13.07/3.65 |
% 13.07/3.65 | Instantiating formula (123) with xp and discharging atoms aNaturalNumber0(xp), yields:
% 13.07/3.65 | (135) xp = sz10 | xp = sz00 | ? [v0] : (isPrime0(v0) & doDivides0(v0, xp) & aNaturalNumber0(v0))
% 13.07/3.65 |
% 13.07/3.65 | Instantiating formula (66) with all_0_5_5, xr, xm and discharging atoms sdtpldt0(xr, xm) = all_0_5_5, aNaturalNumber0(xr), aNaturalNumber0(xm), yields:
% 13.07/3.65 | (136) sdtpldt0(xm, xr) = all_0_5_5
% 13.07/3.65 |
% 13.07/3.65 | Instantiating formula (47) with all_0_5_5, xm, xr and discharging atoms sdtpldt0(xr, xm) = all_0_5_5, aNaturalNumber0(xr), aNaturalNumber0(xm), yields:
% 13.07/3.65 | (137) aNaturalNumber0(all_0_5_5)
% 13.07/3.65 |
% 13.07/3.65 | Instantiating formula (60) with all_0_9_9, xn, xm, xr, xp and discharging atoms sdtpldt0(xp, xr) = xn, sdtpldt0(xn, xm) = all_0_9_9, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 13.07/3.65 | (138) ? [v0] : (sdtpldt0(xr, xm) = v0 & sdtpldt0(xp, v0) = all_0_9_9)
% 13.07/3.65 |
% 13.07/3.65 | Instantiating formula (128) with all_0_5_5, xm, xn, xr and discharging atoms sdtpldt0(xr, xm) = all_0_5_5, sdtlseqdt0(xr, xn), aNaturalNumber0(xr), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 13.07/3.65 | (139) xr = xn | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_5_5) & ~ (v1 = v0) & sdtpldt0(xm, xr) = v0 & sdtpldt0(xm, xn) = v1 & sdtpldt0(xn, xm) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_5_5, v2))
% 13.07/3.65 |
% 13.07/3.65 | Instantiating formula (95) with all_0_9_9, xm, xn, xr and discharging atoms sdtpldt0(xn, xm) = all_0_9_9, sdtlseqdt0(xr, xn), aNaturalNumber0(xr), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 13.07/3.65 | (140) xr = xn | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_9_9) & ~ (v1 = v0) & sdtpldt0(xr, xm) = v2 & sdtpldt0(xm, xr) = v0 & sdtpldt0(xm, xn) = v1 & sdtlseqdt0(v2, all_0_9_9) & sdtlseqdt0(v0, v1))
% 13.07/3.65 |
% 13.07/3.65 | Instantiating formula (66) with all_0_9_9, xn, xm and discharging atoms sdtpldt0(xn, xm) = all_0_9_9, aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 13.07/3.65 | (141) sdtpldt0(xm, xn) = all_0_9_9
% 13.07/3.65 |
% 13.07/3.65 | Instantiating formula (47) with all_0_9_9, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_9_9, aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 13.07/3.65 | (142) aNaturalNumber0(all_0_9_9)
% 13.07/3.65 |
% 13.07/3.65 | Instantiating formula (13) with xn, xr and discharging atoms sdtlseqdt0(xr, xn), aNaturalNumber0(xr), aNaturalNumber0(xn), yields:
% 13.07/3.65 | (143) ? [v0] : (sdtpldt0(xr, v0) = xn & aNaturalNumber0(v0))
% 13.07/3.65 |
% 13.07/3.65 | Instantiating (143) with all_17_0_12 yields:
% 13.07/3.65 | (144) sdtpldt0(xr, all_17_0_12) = xn & aNaturalNumber0(all_17_0_12)
% 13.07/3.65 |
% 13.07/3.65 | Applying alpha-rule on (144) yields:
% 13.07/3.65 | (145) sdtpldt0(xr, all_17_0_12) = xn
% 13.07/3.65 | (146) aNaturalNumber0(all_17_0_12)
% 13.07/3.65 |
% 13.07/3.65 | Instantiating (138) with all_21_0_14 yields:
% 13.07/3.65 | (147) sdtpldt0(xr, xm) = all_21_0_14 & sdtpldt0(xp, all_21_0_14) = all_0_9_9
% 13.07/3.65 |
% 13.07/3.65 | Applying alpha-rule on (147) yields:
% 13.07/3.65 | (148) sdtpldt0(xr, xm) = all_21_0_14
% 13.07/3.65 | (149) sdtpldt0(xp, all_21_0_14) = all_0_9_9
% 13.07/3.65 |
% 13.07/3.65 +-Applying beta-rule and splitting (135), into two cases.
% 13.07/3.65 |-Branch one:
% 13.07/3.65 | (150) xp = sz00
% 13.07/3.66 |
% 13.07/3.66 | Equations (150) can reduce 46 to:
% 13.07/3.66 | (151) $false
% 13.07/3.66 |
% 13.07/3.66 |-The branch is then unsatisfiable
% 13.07/3.66 |-Branch two:
% 13.07/3.66 | (46) ~ (xp = sz00)
% 13.07/3.66 | (153) xp = sz10 | ? [v0] : (isPrime0(v0) & doDivides0(v0, xp) & aNaturalNumber0(v0))
% 13.07/3.66 |
% 13.07/3.66 +-Applying beta-rule and splitting (139), into two cases.
% 13.07/3.66 |-Branch one:
% 13.07/3.66 | (154) xr = xn
% 13.07/3.66 |
% 13.07/3.66 | Equations (154) can reduce 22 to:
% 13.07/3.66 | (151) $false
% 13.07/3.66 |
% 13.07/3.66 |-The branch is then unsatisfiable
% 13.07/3.66 |-Branch two:
% 13.07/3.66 | (22) ~ (xr = xn)
% 13.07/3.66 | (157) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_5_5) & ~ (v1 = v0) & sdtpldt0(xm, xr) = v0 & sdtpldt0(xm, xn) = v1 & sdtpldt0(xn, xm) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_5_5, v2))
% 13.07/3.66 |
% 13.07/3.66 | Instantiating (157) with all_40_0_26, all_40_1_27, all_40_2_28 yields:
% 13.07/3.66 | (158) ~ (all_40_0_26 = all_0_5_5) & ~ (all_40_1_27 = all_40_2_28) & sdtpldt0(xm, xr) = all_40_2_28 & sdtpldt0(xm, xn) = all_40_1_27 & sdtpldt0(xn, xm) = all_40_0_26 & sdtlseqdt0(all_40_2_28, all_40_1_27) & sdtlseqdt0(all_0_5_5, all_40_0_26)
% 13.07/3.66 |
% 13.07/3.66 | Applying alpha-rule on (158) yields:
% 13.07/3.66 | (159) ~ (all_40_0_26 = all_0_5_5)
% 13.07/3.66 | (160) ~ (all_40_1_27 = all_40_2_28)
% 13.07/3.66 | (161) sdtpldt0(xn, xm) = all_40_0_26
% 13.07/3.66 | (162) sdtlseqdt0(all_40_2_28, all_40_1_27)
% 13.07/3.66 | (163) sdtpldt0(xm, xr) = all_40_2_28
% 13.07/3.66 | (164) sdtlseqdt0(all_0_5_5, all_40_0_26)
% 13.07/3.66 | (165) sdtpldt0(xm, xn) = all_40_1_27
% 13.07/3.66 |
% 13.07/3.66 +-Applying beta-rule and splitting (140), into two cases.
% 13.07/3.66 |-Branch one:
% 13.07/3.66 | (154) xr = xn
% 13.07/3.66 |
% 13.07/3.66 | Equations (154) can reduce 22 to:
% 13.07/3.66 | (151) $false
% 13.07/3.66 |
% 13.07/3.66 |-The branch is then unsatisfiable
% 13.07/3.66 |-Branch two:
% 13.07/3.66 | (22) ~ (xr = xn)
% 13.07/3.66 | (169) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_9_9) & ~ (v1 = v0) & sdtpldt0(xr, xm) = v2 & sdtpldt0(xm, xr) = v0 & sdtpldt0(xm, xn) = v1 & sdtlseqdt0(v2, all_0_9_9) & sdtlseqdt0(v0, v1))
% 13.07/3.66 |
% 13.07/3.66 | Instantiating (169) with all_46_0_29, all_46_1_30, all_46_2_31 yields:
% 13.07/3.66 | (170) ~ (all_46_0_29 = all_0_9_9) & ~ (all_46_1_30 = all_46_2_31) & sdtpldt0(xr, xm) = all_46_0_29 & sdtpldt0(xm, xr) = all_46_2_31 & sdtpldt0(xm, xn) = all_46_1_30 & sdtlseqdt0(all_46_0_29, all_0_9_9) & sdtlseqdt0(all_46_2_31, all_46_1_30)
% 13.07/3.66 |
% 13.07/3.66 | Applying alpha-rule on (170) yields:
% 13.07/3.66 | (171) sdtlseqdt0(all_46_0_29, all_0_9_9)
% 13.07/3.66 | (172) sdtpldt0(xr, xm) = all_46_0_29
% 13.07/3.66 | (173) sdtlseqdt0(all_46_2_31, all_46_1_30)
% 13.07/3.66 | (174) sdtpldt0(xm, xr) = all_46_2_31
% 13.07/3.66 | (175) sdtpldt0(xm, xn) = all_46_1_30
% 13.07/3.66 | (176) ~ (all_46_0_29 = all_0_9_9)
% 13.07/3.66 | (177) ~ (all_46_1_30 = all_46_2_31)
% 13.07/3.66 |
% 13.07/3.66 +-Applying beta-rule and splitting (153), into two cases.
% 13.07/3.66 |-Branch one:
% 13.07/3.66 | (178) xp = sz10
% 13.07/3.66 |
% 13.07/3.66 | Equations (178) can reduce 28 to:
% 13.07/3.66 | (151) $false
% 13.07/3.66 |
% 13.07/3.66 |-The branch is then unsatisfiable
% 13.07/3.66 |-Branch two:
% 13.07/3.66 | (28) ~ (xp = sz10)
% 13.07/3.66 | (181) ? [v0] : (isPrime0(v0) & doDivides0(v0, xp) & aNaturalNumber0(v0))
% 13.07/3.66 |
% 13.07/3.66 +-Applying beta-rule and splitting (134), into two cases.
% 13.07/3.66 |-Branch one:
% 13.07/3.66 | (182) sdtlseqdt0(sz10, xp)
% 13.07/3.66 |
% 13.07/3.66 | Instantiating formula (89) with xr, xm, all_46_0_29, all_0_5_5 and discharging atoms sdtpldt0(xr, xm) = all_46_0_29, sdtpldt0(xr, xm) = all_0_5_5, yields:
% 13.07/3.66 | (183) all_46_0_29 = all_0_5_5
% 13.07/3.66 |
% 13.07/3.66 | Instantiating formula (89) with xr, xm, all_21_0_14, all_46_0_29 and discharging atoms sdtpldt0(xr, xm) = all_46_0_29, sdtpldt0(xr, xm) = all_21_0_14, yields:
% 13.07/3.66 | (184) all_46_0_29 = all_21_0_14
% 13.07/3.66 |
% 13.07/3.66 | Instantiating formula (89) with xm, xr, all_40_2_28, all_46_2_31 and discharging atoms sdtpldt0(xm, xr) = all_46_2_31, sdtpldt0(xm, xr) = all_40_2_28, yields:
% 13.07/3.66 | (185) all_46_2_31 = all_40_2_28
% 13.07/3.66 |
% 13.07/3.66 | Instantiating formula (89) with xm, xr, all_0_5_5, all_46_2_31 and discharging atoms sdtpldt0(xm, xr) = all_46_2_31, sdtpldt0(xm, xr) = all_0_5_5, yields:
% 13.07/3.66 | (186) all_46_2_31 = all_0_5_5
% 13.07/3.66 |
% 13.07/3.66 | Instantiating formula (89) with xm, xn, all_40_1_27, all_46_1_30 and discharging atoms sdtpldt0(xm, xn) = all_46_1_30, sdtpldt0(xm, xn) = all_40_1_27, yields:
% 13.07/3.66 | (187) all_46_1_30 = all_40_1_27
% 13.07/3.66 |
% 13.07/3.66 | Instantiating formula (89) with xm, xn, all_0_9_9, all_46_1_30 and discharging atoms sdtpldt0(xm, xn) = all_46_1_30, sdtpldt0(xm, xn) = all_0_9_9, yields:
% 13.07/3.66 | (188) all_46_1_30 = all_0_9_9
% 13.07/3.66 |
% 13.07/3.66 | Instantiating formula (89) with xn, xm, all_40_0_26, all_0_9_9 and discharging atoms sdtpldt0(xn, xm) = all_40_0_26, sdtpldt0(xn, xm) = all_0_9_9, yields:
% 13.07/3.66 | (189) all_40_0_26 = all_0_9_9
% 13.07/3.66 |
% 13.07/3.66 | Instantiating formula (54) with xn, all_0_2_2, all_17_0_12, xr and discharging atoms sdtpldt0(xr, all_17_0_12) = xn, sdtpldt0(xr, all_0_2_2) = xn, aNaturalNumber0(all_17_0_12), aNaturalNumber0(all_0_2_2), aNaturalNumber0(xr), yields:
% 13.07/3.66 | (190) all_17_0_12 = all_0_2_2
% 13.07/3.66 |
% 13.07/3.66 | Instantiating formula (54) with xn, all_17_0_12, xp, xr and discharging atoms sdtpldt0(xr, all_17_0_12) = xn, sdtpldt0(xr, xp) = xn, aNaturalNumber0(all_17_0_12), aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 13.07/3.66 | (191) all_17_0_12 = xp
% 13.07/3.66 |
% 13.07/3.66 | Combining equations (184,183) yields a new equation:
% 13.07/3.66 | (192) all_21_0_14 = all_0_5_5
% 13.07/3.66 |
% 13.07/3.66 | Simplifying 192 yields:
% 13.07/3.66 | (193) all_21_0_14 = all_0_5_5
% 13.07/3.66 |
% 13.07/3.66 | Combining equations (188,187) yields a new equation:
% 13.07/3.66 | (194) all_40_1_27 = all_0_9_9
% 13.07/3.66 |
% 13.07/3.66 | Combining equations (186,185) yields a new equation:
% 13.07/3.66 | (195) all_40_2_28 = all_0_5_5
% 13.07/3.66 |
% 13.07/3.66 | Combining equations (191,190) yields a new equation:
% 13.07/3.66 | (196) all_0_2_2 = xp
% 13.07/3.66 |
% 13.07/3.66 | Equations (194,195) can reduce 160 to:
% 13.07/3.66 | (197) ~ (all_0_5_5 = all_0_9_9)
% 13.07/3.66 |
% 13.07/3.66 | Simplifying 197 yields:
% 13.07/3.66 | (198) ~ (all_0_5_5 = all_0_9_9)
% 13.07/3.66 |
% 13.07/3.66 | From (193) and (149) follows:
% 13.07/3.66 | (199) sdtpldt0(xp, all_0_5_5) = all_0_9_9
% 13.07/3.66 |
% 13.07/3.66 | From (189) and (164) follows:
% 13.07/3.66 | (200) sdtlseqdt0(all_0_5_5, all_0_9_9)
% 13.07/3.66 |
% 13.07/3.66 | From (196) and (83) follows:
% 13.07/3.66 | (32) aNaturalNumber0(xp)
% 13.07/3.66 |
% 13.07/3.66 +-Applying beta-rule and splitting (132), into two cases.
% 13.07/3.66 |-Branch one:
% 13.07/3.66 | (202) all_0_2_2 = sz00
% 13.07/3.66 |
% 13.07/3.66 | Combining equations (202,196) yields a new equation:
% 13.07/3.66 | (150) xp = sz00
% 13.07/3.66 |
% 13.07/3.66 | Equations (150) can reduce 46 to:
% 13.07/3.66 | (151) $false
% 13.07/3.66 |
% 13.07/3.66 |-The branch is then unsatisfiable
% 13.07/3.66 |-Branch two:
% 13.07/3.66 | (205) ~ (all_0_2_2 = sz00)
% 13.07/3.66 | (206) all_0_2_2 = sz10 | ? [v0] : (isPrime0(v0) & doDivides0(v0, all_0_2_2) & aNaturalNumber0(v0))
% 13.07/3.66 |
% 13.07/3.66 +-Applying beta-rule and splitting (206), into two cases.
% 13.07/3.66 |-Branch one:
% 13.07/3.66 | (207) all_0_2_2 = sz10
% 13.07/3.66 |
% 13.07/3.66 | Combining equations (207,196) yields a new equation:
% 13.07/3.66 | (178) xp = sz10
% 13.07/3.66 |
% 13.07/3.66 | Equations (178) can reduce 28 to:
% 13.07/3.66 | (151) $false
% 13.07/3.66 |
% 13.07/3.66 |-The branch is then unsatisfiable
% 13.07/3.66 |-Branch two:
% 13.07/3.66 | (210) ~ (all_0_2_2 = sz10)
% 13.07/3.66 | (211) ? [v0] : (isPrime0(v0) & doDivides0(v0, all_0_2_2) & aNaturalNumber0(v0))
% 13.07/3.66 |
% 13.07/3.66 | Equations (196) can reduce 210 to:
% 13.07/3.66 | (28) ~ (xp = sz10)
% 13.07/3.66 |
% 13.07/3.66 | Instantiating formula (103) with all_0_4_4, all_0_5_5, xp, sz10 and discharging atoms sdtpldt0(all_0_5_5, xp) = all_0_4_4, sdtlseqdt0(sz10, xp), aNaturalNumber0(all_0_5_5), aNaturalNumber0(xp), aNaturalNumber0(sz10), yields:
% 13.07/3.66 | (213) xp = sz10 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = all_0_4_4) & sdtpldt0(all_0_5_5, sz10) = v0 & sdtpldt0(xp, all_0_5_5) = v2 & sdtpldt0(sz10, all_0_5_5) = v1 & sdtlseqdt0(v1, v2) & sdtlseqdt0(v0, all_0_4_4))
% 13.07/3.66 |
% 13.07/3.66 | Instantiating formula (60) with all_0_8_8, all_0_9_9, xp, all_0_5_5, xp and discharging atoms sdtpldt0(all_0_9_9, xp) = all_0_8_8, sdtpldt0(xp, all_0_5_5) = all_0_9_9, aNaturalNumber0(all_0_5_5), aNaturalNumber0(xp), yields:
% 13.07/3.66 | (214) ? [v0] : (sdtpldt0(all_0_5_5, xp) = v0 & sdtpldt0(xp, v0) = all_0_8_8)
% 13.07/3.66 |
% 13.07/3.66 | Instantiating formula (95) with all_0_9_9, all_0_5_5, xp, sz10 and discharging atoms sdtpldt0(xp, all_0_5_5) = all_0_9_9, sdtlseqdt0(sz10, xp), aNaturalNumber0(all_0_5_5), aNaturalNumber0(xp), aNaturalNumber0(sz10), yields:
% 13.07/3.66 | (215) xp = sz10 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_9_9) & ~ (v1 = v0) & sdtpldt0(all_0_5_5, xp) = v1 & sdtpldt0(all_0_5_5, sz10) = v0 & sdtpldt0(sz10, all_0_5_5) = v2 & sdtlseqdt0(v2, all_0_9_9) & sdtlseqdt0(v0, v1))
% 13.07/3.66 |
% 13.07/3.66 | Instantiating formula (66) with all_0_9_9, xp, all_0_5_5 and discharging atoms sdtpldt0(xp, all_0_5_5) = all_0_9_9, aNaturalNumber0(all_0_5_5), aNaturalNumber0(xp), yields:
% 13.07/3.66 | (216) sdtpldt0(all_0_5_5, xp) = all_0_9_9
% 13.07/3.66 |
% 13.07/3.66 | Instantiating formula (128) with all_0_4_4, xp, all_0_9_9, all_0_5_5 and discharging atoms sdtpldt0(all_0_5_5, xp) = all_0_4_4, sdtlseqdt0(all_0_5_5, all_0_9_9), aNaturalNumber0(all_0_5_5), aNaturalNumber0(all_0_9_9), aNaturalNumber0(xp), yields:
% 13.07/3.66 | (217) all_0_5_5 = all_0_9_9 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_4_4) & ~ (v1 = v0) & sdtpldt0(all_0_9_9, xp) = v2 & sdtpldt0(xp, all_0_5_5) = v0 & sdtpldt0(xp, all_0_9_9) = v1 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_4_4, v2))
% 13.07/3.66 |
% 13.07/3.66 | Instantiating formula (74) with all_0_8_8, all_0_4_4, all_0_9_9, all_0_5_5, xp and discharging atoms sdtpldt0(all_0_5_5, xp) = all_0_4_4, sdtpldt0(all_0_9_9, xp) = all_0_8_8, aNaturalNumber0(all_0_5_5), aNaturalNumber0(all_0_9_9), aNaturalNumber0(xp), yields:
% 13.07/3.66 | (218) all_0_5_5 = all_0_9_9 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xp, all_0_5_5) = v0 & sdtpldt0(xp, all_0_9_9) = v1)
% 13.07/3.66 |
% 13.07/3.66 | Instantiating formula (126) with all_0_8_8, all_0_9_9, all_0_9_9, all_0_5_5, xp and discharging atoms sdtpldt0(all_0_9_9, xp) = all_0_8_8, sdtpldt0(xp, all_0_5_5) = all_0_9_9, aNaturalNumber0(all_0_5_5), aNaturalNumber0(all_0_9_9), aNaturalNumber0(xp), yields:
% 13.07/3.66 | (219) all_0_5_5 = all_0_9_9 | ? [v0] : ? [v1] : ( ~ (v1 = all_0_8_8) & ~ (v0 = all_0_9_9) & sdtpldt0(all_0_5_5, xp) = v1 & sdtpldt0(xp, all_0_9_9) = v0)
% 13.07/3.66 |
% 13.07/3.66 | Instantiating formula (95) with all_0_8_8, xp, all_0_9_9, all_0_5_5 and discharging atoms sdtpldt0(all_0_9_9, xp) = all_0_8_8, sdtlseqdt0(all_0_5_5, all_0_9_9), aNaturalNumber0(all_0_5_5), aNaturalNumber0(all_0_9_9), aNaturalNumber0(xp), yields:
% 13.07/3.66 | (220) all_0_5_5 = all_0_9_9 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_8_8) & ~ (v1 = v0) & sdtpldt0(all_0_5_5, xp) = v2 & sdtpldt0(xp, all_0_5_5) = v0 & sdtpldt0(xp, all_0_9_9) = v1 & sdtlseqdt0(v2, all_0_8_8) & sdtlseqdt0(v0, v1))
% 13.07/3.66 |
% 13.07/3.67 | Instantiating formula (103) with all_0_8_8, all_0_9_9, xp, sz10 and discharging atoms sdtpldt0(all_0_9_9, xp) = all_0_8_8, sdtlseqdt0(sz10, xp), aNaturalNumber0(all_0_9_9), aNaturalNumber0(xp), aNaturalNumber0(sz10), yields:
% 13.07/3.67 | (221) xp = sz10 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = all_0_8_8) & sdtpldt0(all_0_9_9, sz10) = v0 & sdtpldt0(xp, all_0_9_9) = v2 & sdtpldt0(sz10, all_0_9_9) = v1 & sdtlseqdt0(v1, v2) & sdtlseqdt0(v0, all_0_8_8))
% 13.07/3.67 |
% 13.07/3.67 | Instantiating formula (66) with all_0_8_8, all_0_9_9, xp and discharging atoms sdtpldt0(all_0_9_9, xp) = all_0_8_8, aNaturalNumber0(all_0_9_9), aNaturalNumber0(xp), yields:
% 13.07/3.67 | (222) sdtpldt0(xp, all_0_9_9) = all_0_8_8
% 13.07/3.67 |
% 13.07/3.67 | Instantiating formula (77) with all_0_9_9, xp, all_0_9_9, all_0_5_5 and discharging atoms sdtpldt0(xp, all_0_5_5) = all_0_9_9, sdtlseqdt0(all_0_5_5, all_0_9_9), aNaturalNumber0(all_0_5_5), aNaturalNumber0(all_0_9_9), aNaturalNumber0(xp), yields:
% 13.07/3.67 | (223) all_0_5_5 = all_0_9_9 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = all_0_9_9) & sdtpldt0(all_0_5_5, xp) = v1 & sdtpldt0(all_0_9_9, xp) = v2 & sdtpldt0(xp, all_0_9_9) = v0 & sdtlseqdt0(v1, v2) & sdtlseqdt0(all_0_9_9, v0))
% 13.07/3.67 |
% 13.07/3.67 | Instantiating (214) with all_95_0_42 yields:
% 13.07/3.67 | (224) sdtpldt0(all_0_5_5, xp) = all_95_0_42 & sdtpldt0(xp, all_95_0_42) = all_0_8_8
% 13.07/3.67 |
% 13.07/3.67 | Applying alpha-rule on (224) yields:
% 13.07/3.67 | (225) sdtpldt0(all_0_5_5, xp) = all_95_0_42
% 13.07/3.67 | (226) sdtpldt0(xp, all_95_0_42) = all_0_8_8
% 13.07/3.67 |
% 13.07/3.67 +-Applying beta-rule and splitting (219), into two cases.
% 13.07/3.67 |-Branch one:
% 13.07/3.67 | (227) all_0_5_5 = all_0_9_9
% 13.07/3.67 |
% 13.07/3.67 | Equations (227) can reduce 198 to:
% 13.07/3.67 | (151) $false
% 13.07/3.67 |
% 13.07/3.67 |-The branch is then unsatisfiable
% 13.07/3.67 |-Branch two:
% 13.07/3.67 | (198) ~ (all_0_5_5 = all_0_9_9)
% 13.07/3.67 | (230) ? [v0] : ? [v1] : ( ~ (v1 = all_0_8_8) & ~ (v0 = all_0_9_9) & sdtpldt0(all_0_5_5, xp) = v1 & sdtpldt0(xp, all_0_9_9) = v0)
% 13.07/3.67 |
% 13.07/3.67 | Instantiating (230) with all_159_0_80, all_159_1_81 yields:
% 13.07/3.67 | (231) ~ (all_159_0_80 = all_0_8_8) & ~ (all_159_1_81 = all_0_9_9) & sdtpldt0(all_0_5_5, xp) = all_159_0_80 & sdtpldt0(xp, all_0_9_9) = all_159_1_81
% 13.07/3.67 |
% 13.07/3.67 | Applying alpha-rule on (231) yields:
% 13.07/3.67 | (232) ~ (all_159_0_80 = all_0_8_8)
% 13.07/3.67 | (233) ~ (all_159_1_81 = all_0_9_9)
% 13.07/3.67 | (234) sdtpldt0(all_0_5_5, xp) = all_159_0_80
% 13.07/3.67 | (235) sdtpldt0(xp, all_0_9_9) = all_159_1_81
% 13.07/3.67 |
% 13.07/3.67 +-Applying beta-rule and splitting (218), into two cases.
% 13.07/3.67 |-Branch one:
% 13.07/3.67 | (227) all_0_5_5 = all_0_9_9
% 13.07/3.67 |
% 13.07/3.67 | Equations (227) can reduce 198 to:
% 13.07/3.67 | (151) $false
% 13.07/3.67 |
% 13.07/3.67 |-The branch is then unsatisfiable
% 13.07/3.67 |-Branch two:
% 13.07/3.67 | (198) ~ (all_0_5_5 = all_0_9_9)
% 13.07/3.67 | (239) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xp, all_0_5_5) = v0 & sdtpldt0(xp, all_0_9_9) = v1)
% 13.07/3.67 |
% 13.07/3.67 | Instantiating (239) with all_165_0_82, all_165_1_83 yields:
% 13.07/3.67 | (240) ~ (all_165_0_82 = all_165_1_83) & sdtpldt0(xp, all_0_5_5) = all_165_1_83 & sdtpldt0(xp, all_0_9_9) = all_165_0_82
% 13.07/3.67 |
% 13.07/3.67 | Applying alpha-rule on (240) yields:
% 13.07/3.67 | (241) ~ (all_165_0_82 = all_165_1_83)
% 13.07/3.67 | (242) sdtpldt0(xp, all_0_5_5) = all_165_1_83
% 13.07/3.67 | (243) sdtpldt0(xp, all_0_9_9) = all_165_0_82
% 13.07/3.67 |
% 13.07/3.67 +-Applying beta-rule and splitting (223), into two cases.
% 13.07/3.67 |-Branch one:
% 13.07/3.67 | (227) all_0_5_5 = all_0_9_9
% 13.07/3.67 |
% 13.07/3.67 | Equations (227) can reduce 198 to:
% 13.07/3.67 | (151) $false
% 13.07/3.67 |
% 13.07/3.67 |-The branch is then unsatisfiable
% 13.07/3.67 |-Branch two:
% 13.07/3.67 | (198) ~ (all_0_5_5 = all_0_9_9)
% 13.07/3.67 | (247) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = all_0_9_9) & sdtpldt0(all_0_5_5, xp) = v1 & sdtpldt0(all_0_9_9, xp) = v2 & sdtpldt0(xp, all_0_9_9) = v0 & sdtlseqdt0(v1, v2) & sdtlseqdt0(all_0_9_9, v0))
% 13.07/3.67 |
% 13.07/3.67 | Instantiating (247) with all_171_0_84, all_171_1_85, all_171_2_86 yields:
% 13.07/3.67 | (248) ~ (all_171_0_84 = all_171_1_85) & ~ (all_171_2_86 = all_0_9_9) & sdtpldt0(all_0_5_5, xp) = all_171_1_85 & sdtpldt0(all_0_9_9, xp) = all_171_0_84 & sdtpldt0(xp, all_0_9_9) = all_171_2_86 & sdtlseqdt0(all_171_1_85, all_171_0_84) & sdtlseqdt0(all_0_9_9, all_171_2_86)
% 13.07/3.67 |
% 13.07/3.67 | Applying alpha-rule on (248) yields:
% 13.07/3.67 | (249) ~ (all_171_2_86 = all_0_9_9)
% 13.07/3.67 | (250) sdtlseqdt0(all_171_1_85, all_171_0_84)
% 13.07/3.67 | (251) sdtpldt0(all_0_5_5, xp) = all_171_1_85
% 13.07/3.67 | (252) sdtlseqdt0(all_0_9_9, all_171_2_86)
% 13.07/3.67 | (253) sdtpldt0(xp, all_0_9_9) = all_171_2_86
% 13.07/3.67 | (254) ~ (all_171_0_84 = all_171_1_85)
% 13.07/3.67 | (255) sdtpldt0(all_0_9_9, xp) = all_171_0_84
% 13.07/3.67 |
% 13.07/3.67 +-Applying beta-rule and splitting (215), into two cases.
% 13.07/3.67 |-Branch one:
% 13.07/3.67 | (178) xp = sz10
% 13.07/3.67 |
% 13.07/3.67 | Equations (178) can reduce 28 to:
% 13.07/3.67 | (151) $false
% 13.07/3.67 |
% 13.07/3.67 |-The branch is then unsatisfiable
% 13.07/3.67 |-Branch two:
% 13.07/3.67 | (28) ~ (xp = sz10)
% 13.07/3.67 | (259) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_9_9) & ~ (v1 = v0) & sdtpldt0(all_0_5_5, xp) = v1 & sdtpldt0(all_0_5_5, sz10) = v0 & sdtpldt0(sz10, all_0_5_5) = v2 & sdtlseqdt0(v2, all_0_9_9) & sdtlseqdt0(v0, v1))
% 13.07/3.67 |
% 13.07/3.67 | Instantiating (259) with all_184_0_87, all_184_1_88, all_184_2_89 yields:
% 13.07/3.67 | (260) ~ (all_184_0_87 = all_0_9_9) & ~ (all_184_1_88 = all_184_2_89) & sdtpldt0(all_0_5_5, xp) = all_184_1_88 & sdtpldt0(all_0_5_5, sz10) = all_184_2_89 & sdtpldt0(sz10, all_0_5_5) = all_184_0_87 & sdtlseqdt0(all_184_0_87, all_0_9_9) & sdtlseqdt0(all_184_2_89, all_184_1_88)
% 13.07/3.67 |
% 13.07/3.67 | Applying alpha-rule on (260) yields:
% 13.07/3.67 | (261) sdtlseqdt0(all_184_2_89, all_184_1_88)
% 13.07/3.67 | (262) sdtpldt0(all_0_5_5, xp) = all_184_1_88
% 13.07/3.67 | (263) ~ (all_184_1_88 = all_184_2_89)
% 13.07/3.67 | (264) sdtpldt0(sz10, all_0_5_5) = all_184_0_87
% 13.07/3.67 | (265) sdtpldt0(all_0_5_5, sz10) = all_184_2_89
% 13.07/3.67 | (266) sdtlseqdt0(all_184_0_87, all_0_9_9)
% 13.07/3.67 | (267) ~ (all_184_0_87 = all_0_9_9)
% 13.07/3.67 |
% 13.07/3.67 +-Applying beta-rule and splitting (213), into two cases.
% 13.07/3.67 |-Branch one:
% 13.07/3.67 | (178) xp = sz10
% 13.07/3.67 |
% 13.07/3.67 | Equations (178) can reduce 28 to:
% 13.07/3.67 | (151) $false
% 13.07/3.67 |
% 13.07/3.67 |-The branch is then unsatisfiable
% 13.07/3.67 |-Branch two:
% 13.07/3.67 | (28) ~ (xp = sz10)
% 13.07/3.67 | (271) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = all_0_4_4) & sdtpldt0(all_0_5_5, sz10) = v0 & sdtpldt0(xp, all_0_5_5) = v2 & sdtpldt0(sz10, all_0_5_5) = v1 & sdtlseqdt0(v1, v2) & sdtlseqdt0(v0, all_0_4_4))
% 13.07/3.67 |
% 13.07/3.67 +-Applying beta-rule and splitting (220), into two cases.
% 13.07/3.67 |-Branch one:
% 13.07/3.67 | (227) all_0_5_5 = all_0_9_9
% 13.07/3.67 |
% 13.07/3.67 | Equations (227) can reduce 198 to:
% 13.07/3.67 | (151) $false
% 13.07/3.67 |
% 13.07/3.67 |-The branch is then unsatisfiable
% 13.07/3.67 |-Branch two:
% 13.07/3.67 | (198) ~ (all_0_5_5 = all_0_9_9)
% 13.07/3.67 | (275) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_8_8) & ~ (v1 = v0) & sdtpldt0(all_0_5_5, xp) = v2 & sdtpldt0(xp, all_0_5_5) = v0 & sdtpldt0(xp, all_0_9_9) = v1 & sdtlseqdt0(v2, all_0_8_8) & sdtlseqdt0(v0, v1))
% 13.07/3.67 |
% 13.07/3.67 | Instantiating (275) with all_203_0_93, all_203_1_94, all_203_2_95 yields:
% 13.07/3.67 | (276) ~ (all_203_0_93 = all_0_8_8) & ~ (all_203_1_94 = all_203_2_95) & sdtpldt0(all_0_5_5, xp) = all_203_0_93 & sdtpldt0(xp, all_0_5_5) = all_203_2_95 & sdtpldt0(xp, all_0_9_9) = all_203_1_94 & sdtlseqdt0(all_203_0_93, all_0_8_8) & sdtlseqdt0(all_203_2_95, all_203_1_94)
% 13.07/3.67 |
% 13.07/3.67 | Applying alpha-rule on (276) yields:
% 13.07/3.67 | (277) sdtpldt0(xp, all_0_5_5) = all_203_2_95
% 13.07/3.67 | (278) sdtlseqdt0(all_203_2_95, all_203_1_94)
% 13.07/3.67 | (279) sdtpldt0(xp, all_0_9_9) = all_203_1_94
% 13.07/3.67 | (280) ~ (all_203_1_94 = all_203_2_95)
% 13.07/3.67 | (281) sdtpldt0(all_0_5_5, xp) = all_203_0_93
% 13.07/3.67 | (282) ~ (all_203_0_93 = all_0_8_8)
% 13.07/3.67 | (283) sdtlseqdt0(all_203_0_93, all_0_8_8)
% 13.07/3.67 |
% 13.07/3.67 +-Applying beta-rule and splitting (221), into two cases.
% 13.07/3.67 |-Branch one:
% 13.07/3.67 | (178) xp = sz10
% 13.07/3.67 |
% 13.07/3.67 | Equations (178) can reduce 28 to:
% 13.07/3.67 | (151) $false
% 13.07/3.67 |
% 13.07/3.67 |-The branch is then unsatisfiable
% 13.07/3.67 |-Branch two:
% 13.07/3.67 | (28) ~ (xp = sz10)
% 13.07/3.67 | (287) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = all_0_8_8) & sdtpldt0(all_0_9_9, sz10) = v0 & sdtpldt0(xp, all_0_9_9) = v2 & sdtpldt0(sz10, all_0_9_9) = v1 & sdtlseqdt0(v1, v2) & sdtlseqdt0(v0, all_0_8_8))
% 13.07/3.67 |
% 13.07/3.67 | Instantiating (287) with all_208_0_96, all_208_1_97, all_208_2_98 yields:
% 13.07/3.67 | (288) ~ (all_208_0_96 = all_208_1_97) & ~ (all_208_2_98 = all_0_8_8) & sdtpldt0(all_0_9_9, sz10) = all_208_2_98 & sdtpldt0(xp, all_0_9_9) = all_208_0_96 & sdtpldt0(sz10, all_0_9_9) = all_208_1_97 & sdtlseqdt0(all_208_1_97, all_208_0_96) & sdtlseqdt0(all_208_2_98, all_0_8_8)
% 13.07/3.67 |
% 13.07/3.67 | Applying alpha-rule on (288) yields:
% 13.07/3.67 | (289) sdtlseqdt0(all_208_1_97, all_208_0_96)
% 13.07/3.67 | (290) ~ (all_208_0_96 = all_208_1_97)
% 13.07/3.67 | (291) ~ (all_208_2_98 = all_0_8_8)
% 13.07/3.67 | (292) sdtlseqdt0(all_208_2_98, all_0_8_8)
% 13.07/3.67 | (293) sdtpldt0(xp, all_0_9_9) = all_208_0_96
% 13.07/3.67 | (294) sdtpldt0(all_0_9_9, sz10) = all_208_2_98
% 13.07/3.67 | (295) sdtpldt0(sz10, all_0_9_9) = all_208_1_97
% 13.07/3.67 |
% 13.07/3.67 +-Applying beta-rule and splitting (217), into two cases.
% 13.07/3.67 |-Branch one:
% 13.07/3.67 | (227) all_0_5_5 = all_0_9_9
% 13.07/3.67 |
% 13.07/3.67 | Equations (227) can reduce 198 to:
% 13.07/3.67 | (151) $false
% 13.07/3.67 |
% 13.07/3.67 |-The branch is then unsatisfiable
% 13.07/3.67 |-Branch two:
% 13.07/3.67 | (198) ~ (all_0_5_5 = all_0_9_9)
% 13.07/3.67 | (299) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_4_4) & ~ (v1 = v0) & sdtpldt0(all_0_9_9, xp) = v2 & sdtpldt0(xp, all_0_5_5) = v0 & sdtpldt0(xp, all_0_9_9) = v1 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_4_4, v2))
% 13.07/3.67 |
% 13.07/3.67 | Instantiating (299) with all_218_0_99, all_218_1_100, all_218_2_101 yields:
% 13.07/3.67 | (300) ~ (all_218_0_99 = all_0_4_4) & ~ (all_218_1_100 = all_218_2_101) & sdtpldt0(all_0_9_9, xp) = all_218_0_99 & sdtpldt0(xp, all_0_5_5) = all_218_2_101 & sdtpldt0(xp, all_0_9_9) = all_218_1_100 & sdtlseqdt0(all_218_2_101, all_218_1_100) & sdtlseqdt0(all_0_4_4, all_218_0_99)
% 13.07/3.67 |
% 13.07/3.67 | Applying alpha-rule on (300) yields:
% 13.07/3.67 | (301) sdtlseqdt0(all_218_2_101, all_218_1_100)
% 13.07/3.67 | (302) sdtlseqdt0(all_0_4_4, all_218_0_99)
% 13.07/3.67 | (303) ~ (all_218_0_99 = all_0_4_4)
% 13.07/3.67 | (304) ~ (all_218_1_100 = all_218_2_101)
% 13.07/3.67 | (305) sdtpldt0(xp, all_0_9_9) = all_218_1_100
% 13.07/3.67 | (306) sdtpldt0(xp, all_0_5_5) = all_218_2_101
% 13.07/3.67 | (307) sdtpldt0(all_0_9_9, xp) = all_218_0_99
% 13.07/3.67 |
% 13.07/3.67 | Instantiating formula (89) with all_0_5_5, xp, all_203_0_93, all_0_4_4 and discharging atoms sdtpldt0(all_0_5_5, xp) = all_203_0_93, sdtpldt0(all_0_5_5, xp) = all_0_4_4, yields:
% 13.07/3.67 | (308) all_203_0_93 = all_0_4_4
% 13.07/3.67 |
% 13.07/3.67 | Instantiating formula (89) with all_0_5_5, xp, all_171_1_85, all_203_0_93 and discharging atoms sdtpldt0(all_0_5_5, xp) = all_203_0_93, sdtpldt0(all_0_5_5, xp) = all_171_1_85, yields:
% 13.07/3.67 | (309) all_203_0_93 = all_171_1_85
% 13.07/3.67 |
% 13.07/3.67 | Instantiating formula (89) with all_0_5_5, xp, all_159_0_80, all_184_1_88 and discharging atoms sdtpldt0(all_0_5_5, xp) = all_184_1_88, sdtpldt0(all_0_5_5, xp) = all_159_0_80, yields:
% 13.07/3.67 | (310) all_184_1_88 = all_159_0_80
% 13.07/3.67 |
% 13.07/3.67 | Instantiating formula (89) with all_0_5_5, xp, all_159_0_80, all_171_1_85 and discharging atoms sdtpldt0(all_0_5_5, xp) = all_171_1_85, sdtpldt0(all_0_5_5, xp) = all_159_0_80, yields:
% 13.07/3.67 | (311) all_171_1_85 = all_159_0_80
% 13.07/3.67 |
% 13.07/3.67 | Instantiating formula (89) with all_0_5_5, xp, all_95_0_42, all_159_0_80 and discharging atoms sdtpldt0(all_0_5_5, xp) = all_159_0_80, sdtpldt0(all_0_5_5, xp) = all_95_0_42, yields:
% 13.07/3.67 | (312) all_159_0_80 = all_95_0_42
% 13.07/3.67 |
% 13.07/3.67 | Instantiating formula (89) with all_0_5_5, xp, all_0_9_9, all_184_1_88 and discharging atoms sdtpldt0(all_0_5_5, xp) = all_184_1_88, sdtpldt0(all_0_5_5, xp) = all_0_9_9, yields:
% 13.07/3.67 | (313) all_184_1_88 = all_0_9_9
% 13.07/3.67 |
% 13.07/3.67 | Instantiating formula (89) with xp, all_0_9_9, all_203_1_94, all_218_1_100 and discharging atoms sdtpldt0(xp, all_0_9_9) = all_218_1_100, sdtpldt0(xp, all_0_9_9) = all_203_1_94, yields:
% 13.07/3.67 | (314) all_218_1_100 = all_203_1_94
% 13.07/3.67 |
% 13.07/3.67 | Instantiating formula (89) with xp, all_0_9_9, all_171_2_86, all_203_1_94 and discharging atoms sdtpldt0(xp, all_0_9_9) = all_203_1_94, sdtpldt0(xp, all_0_9_9) = all_171_2_86, yields:
% 13.07/3.67 | (315) all_203_1_94 = all_171_2_86
% 13.07/3.67 |
% 13.07/3.67 | Instantiating formula (89) with xp, all_0_9_9, all_165_0_82, all_208_0_96 and discharging atoms sdtpldt0(xp, all_0_9_9) = all_208_0_96, sdtpldt0(xp, all_0_9_9) = all_165_0_82, yields:
% 13.07/3.67 | (316) all_208_0_96 = all_165_0_82
% 13.07/3.67 |
% 13.07/3.68 | Instantiating formula (89) with xp, all_0_9_9, all_165_0_82, all_203_1_94 and discharging atoms sdtpldt0(xp, all_0_9_9) = all_203_1_94, sdtpldt0(xp, all_0_9_9) = all_165_0_82, yields:
% 13.07/3.68 | (317) all_203_1_94 = all_165_0_82
% 13.07/3.68 |
% 13.07/3.68 | Instantiating formula (89) with xp, all_0_9_9, all_159_1_81, all_208_0_96 and discharging atoms sdtpldt0(xp, all_0_9_9) = all_208_0_96, sdtpldt0(xp, all_0_9_9) = all_159_1_81, yields:
% 13.07/3.68 | (318) all_208_0_96 = all_159_1_81
% 13.07/3.68 |
% 13.07/3.68 | Instantiating formula (89) with xp, all_0_9_9, all_0_8_8, all_218_1_100 and discharging atoms sdtpldt0(xp, all_0_9_9) = all_218_1_100, sdtpldt0(xp, all_0_9_9) = all_0_8_8, yields:
% 13.07/3.68 | (319) all_218_1_100 = all_0_8_8
% 13.07/3.68 |
% 13.07/3.68 | Combining equations (314,319) yields a new equation:
% 13.07/3.68 | (320) all_203_1_94 = all_0_8_8
% 13.07/3.68 |
% 13.07/3.68 | Simplifying 320 yields:
% 13.07/3.68 | (321) all_203_1_94 = all_0_8_8
% 13.07/3.68 |
% 13.07/3.68 | Combining equations (316,318) yields a new equation:
% 13.07/3.68 | (322) all_165_0_82 = all_159_1_81
% 13.07/3.68 |
% 13.07/3.68 | Simplifying 322 yields:
% 13.07/3.68 | (323) all_165_0_82 = all_159_1_81
% 13.07/3.68 |
% 13.07/3.68 | Combining equations (309,308) yields a new equation:
% 13.07/3.68 | (324) all_171_1_85 = all_0_4_4
% 13.07/3.68 |
% 13.07/3.68 | Simplifying 324 yields:
% 13.07/3.68 | (325) all_171_1_85 = all_0_4_4
% 13.07/3.68 |
% 13.07/3.68 | Combining equations (321,315) yields a new equation:
% 13.07/3.68 | (326) all_171_2_86 = all_0_8_8
% 13.07/3.68 |
% 13.07/3.68 | Combining equations (317,315) yields a new equation:
% 13.07/3.68 | (327) all_171_2_86 = all_165_0_82
% 13.07/3.68 |
% 13.07/3.68 | Combining equations (310,313) yields a new equation:
% 13.07/3.68 | (328) all_159_0_80 = all_0_9_9
% 13.07/3.68 |
% 13.07/3.68 | Simplifying 328 yields:
% 13.07/3.68 | (329) all_159_0_80 = all_0_9_9
% 13.07/3.68 |
% 13.07/3.68 | Combining equations (311,325) yields a new equation:
% 13.07/3.68 | (330) all_159_0_80 = all_0_4_4
% 13.07/3.68 |
% 13.07/3.68 | Simplifying 330 yields:
% 13.07/3.68 | (331) all_159_0_80 = all_0_4_4
% 13.07/3.68 |
% 13.07/3.68 | Combining equations (327,326) yields a new equation:
% 13.07/3.68 | (332) all_165_0_82 = all_0_8_8
% 13.07/3.68 |
% 13.07/3.68 | Simplifying 332 yields:
% 13.07/3.68 | (333) all_165_0_82 = all_0_8_8
% 13.07/3.68 |
% 13.07/3.68 | Combining equations (323,333) yields a new equation:
% 13.07/3.68 | (334) all_159_1_81 = all_0_8_8
% 13.07/3.68 |
% 13.07/3.68 | Simplifying 334 yields:
% 13.07/3.68 | (335) all_159_1_81 = all_0_8_8
% 13.07/3.68 |
% 13.07/3.68 | Combining equations (331,312) yields a new equation:
% 13.07/3.68 | (336) all_95_0_42 = all_0_4_4
% 13.07/3.68 |
% 13.07/3.68 | Combining equations (329,312) yields a new equation:
% 13.07/3.68 | (337) all_95_0_42 = all_0_9_9
% 13.07/3.68 |
% 13.07/3.68 | Combining equations (336,337) yields a new equation:
% 13.07/3.68 | (338) all_0_4_4 = all_0_9_9
% 13.07/3.68 |
% 13.07/3.68 | Simplifying 338 yields:
% 13.07/3.68 | (339) all_0_4_4 = all_0_9_9
% 13.07/3.68 |
% 13.07/3.68 | Equations (335) can reduce 233 to:
% 13.07/3.68 | (340) ~ (all_0_8_8 = all_0_9_9)
% 13.07/3.68 |
% 13.07/3.68 | From (326) and (252) follows:
% 13.07/3.68 | (341) sdtlseqdt0(all_0_9_9, all_0_8_8)
% 13.07/3.68 |
% 13.07/3.68 +-Applying beta-rule and splitting (17), into two cases.
% 13.07/3.68 |-Branch one:
% 13.07/3.68 | (342) all_0_4_4 = all_0_8_8
% 13.07/3.68 |
% 13.07/3.68 | Combining equations (339,342) yields a new equation:
% 13.07/3.68 | (343) all_0_8_8 = all_0_9_9
% 13.07/3.68 |
% 13.07/3.68 | Equations (343) can reduce 340 to:
% 13.07/3.68 | (151) $false
% 13.07/3.68 |
% 13.07/3.68 |-The branch is then unsatisfiable
% 13.07/3.68 |-Branch two:
% 13.07/3.68 | (345) ~ (all_0_4_4 = all_0_8_8)
% 13.07/3.68 | (346) ~ sdtlseqdt0(all_0_4_4, all_0_8_8) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_8_8) & sdtpldt0(all_0_4_4, v0) = v1))
% 13.07/3.68 |
% 13.07/3.68 | Applying alpha-rule on (346) yields:
% 13.07/3.68 | (347) ~ sdtlseqdt0(all_0_4_4, all_0_8_8)
% 13.07/3.68 | (348) ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_8_8) & sdtpldt0(all_0_4_4, v0) = v1))
% 13.07/3.68 |
% 13.07/3.68 | From (339) and (347) follows:
% 13.07/3.68 | (349) ~ sdtlseqdt0(all_0_9_9, all_0_8_8)
% 13.07/3.68 |
% 13.07/3.68 | Using (341) and (349) yields:
% 13.07/3.68 | (350) $false
% 13.07/3.68 |
% 13.07/3.68 |-The branch is then unsatisfiable
% 13.07/3.68 |-Branch two:
% 13.07/3.68 | (351) ~ sdtlseqdt0(sz10, xp)
% 13.07/3.68 | (352) xp = sz10 | xp = sz00
% 13.07/3.68 |
% 13.07/3.68 +-Applying beta-rule and splitting (352), into two cases.
% 13.07/3.68 |-Branch one:
% 13.07/3.68 | (150) xp = sz00
% 13.07/3.68 |
% 13.07/3.68 | Equations (150) can reduce 46 to:
% 13.07/3.68 | (151) $false
% 13.07/3.68 |
% 13.07/3.68 |-The branch is then unsatisfiable
% 13.07/3.68 |-Branch two:
% 13.07/3.68 | (46) ~ (xp = sz00)
% 13.07/3.68 | (178) xp = sz10
% 13.07/3.68 |
% 13.07/3.68 | Equations (178) can reduce 28 to:
% 13.07/3.68 | (151) $false
% 13.07/3.68 |
% 13.07/3.68 |-The branch is then unsatisfiable
% 13.07/3.68 % SZS output end Proof for theBenchmark
% 13.07/3.68
% 13.07/3.68 3076ms
%------------------------------------------------------------------------------