TSTP Solution File: NUM505+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM505+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n015.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 08:45:14 EDT 2022
% Result : Theorem 21.75s 6.50s
% Output : Proof 38.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM505+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 5 12:35:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.50/0.59 ____ _
% 0.50/0.59 ___ / __ \_____(_)___ ________ __________
% 0.50/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.59
% 0.50/0.59 A Theorem Prover for First-Order Logic
% 0.50/0.59 (ePrincess v.1.0)
% 0.50/0.59
% 0.50/0.59 (c) Philipp Rümmer, 2009-2015
% 0.50/0.59 (c) Peter Backeman, 2014-2015
% 0.50/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.59 Bug reports to peter@backeman.se
% 0.50/0.59
% 0.50/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.59
% 0.50/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.50/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.92/0.99 Prover 0: Preprocessing ...
% 3.96/1.50 Prover 0: Constructing countermodel ...
% 19.22/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.74/6.03 Prover 1: Preprocessing ...
% 20.49/6.19 Prover 1: Constructing countermodel ...
% 21.75/6.49 Prover 1: proved (565ms)
% 21.75/6.50 Prover 0: stopped
% 21.75/6.50
% 21.75/6.50 No countermodel exists, formula is valid
% 21.75/6.50 % SZS status Theorem for theBenchmark
% 21.75/6.50
% 21.75/6.50 Generating proof ... found it (size 509)
% 37.13/10.91
% 37.13/10.91 % SZS output start Proof for theBenchmark
% 37.13/10.91 Assumed formulas after preprocessing and simplification:
% 37.13/10.91 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = 0) & ~ (xk = sz10) & ~ (xk = sz00) & ~ (xp = xm) & ~ (xp = xn) & ~ (sz10 = sz00) & isPrime0(xr) = 0 & isPrime0(xp) = 0 & sdtsldt0(v2, xp) = xk & doDivides0(xr, v2) = 0 & doDivides0(xr, xk) = 0 & doDivides0(xp, v2) = 0 & sdtlseqdt0(xr, xk) = 0 & sdtlseqdt0(xk, xp) = v6 & sdtlseqdt0(xp, xk) = v5 & sdtlseqdt0(xp, xm) = v4 & sdtlseqdt0(xp, xn) = v3 & sdtlseqdt0(xm, xp) = 0 & sdtlseqdt0(xn, xp) = 0 & sdtasdt0(xn, xm) = v2 & sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) = v0 & aNaturalNumber0(xr) = 0 & aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 & ~ (isPrime0(sz10) = 0) & ~ (isPrime0(sz00) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | v7 = sz00 | ~ (sdtlseqdt0(v10, v11) = v12) | ~ (sdtasdt0(v7, v9) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (sdtlseqdt0(v17, v18) = v19 & sdtlseqdt0(v8, v9) = v16 & sdtasdt0(v9, v7) = v18 & sdtasdt0(v8, v7) = v17 & aNaturalNumber0(v9) = v15 & aNaturalNumber0(v8) = v14 & aNaturalNumber0(v7) = v13 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | (v19 = 0 & v12 = 0 & ~ (v18 = v17) & ~ (v11 = v10))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (sdtlseqdt0(v10, v11) = v12) | ~ (sdtlseqdt0(v7, v8) = 0) | ~ (sdtpldt0(v8, v9) = v11) | ~ (sdtpldt0(v7, v9) = v10) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((sdtlseqdt0(v14, v15) = v16 & sdtpldt0(v9, v8) = v15 & sdtpldt0(v9, v7) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v13 = 0) | (v16 = 0 & v12 = 0 & ~ (v15 = v14) & ~ (v11 = v10)))) | (aNaturalNumber0(v8) = v14 & aNaturalNumber0(v7) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v7 = sz00 | ~ (sdtsldt0(v11, v7) = v12) | ~ (sdtsldt0(v8, v7) = v9) | ~ (sdtasdt0(v10, v8) = v11) | ? [v13] : ? [v14] : ? [v15] : ((doDivides0(v7, v8) = v15 & aNaturalNumber0(v8) = v14 & aNaturalNumber0(v7) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0))) | (sdtasdt0(v10, v9) = v14 & aNaturalNumber0(v10) = v13 & ( ~ (v13 = 0) | v14 = v12)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtasdt0(v7, v9) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ~ (sdtpldt0(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (sdtasdt0(v16, v7) = v18 & sdtasdt0(v9, v7) = v20 & sdtasdt0(v8, v7) = v19 & sdtasdt0(v7, v16) = v17 & sdtpldt0(v19, v20) = v21 & sdtpldt0(v8, v9) = v16 & aNaturalNumber0(v9) = v15 & aNaturalNumber0(v8) = v14 & aNaturalNumber0(v7) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | (v21 = v18 & v17 = v12)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (doDivides0(v7, v10) = v11) | ~ (sdtpldt0(v8, v9) = v10) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (doDivides0(v7, v9) = v16 & doDivides0(v7, v8) = v15 & aNaturalNumber0(v9) = v14 & aNaturalNumber0(v8) = v13 & aNaturalNumber0(v7) = v12 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v7, v9) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ~ (aNaturalNumber0(v7) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (sdtasdt0(v9, v7) = v15 & sdtasdt0(v8, v7) = v14 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | ( ~ (v15 = v14) & ~ (v11 = v10))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (sdtpldt0(v7, v9) = v11) | ~ (sdtpldt0(v7, v8) = v10) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (sdtpldt0(v9, v7) = v16 & sdtpldt0(v8, v7) = v15 & aNaturalNumber0(v9) = v14 & aNaturalNumber0(v8) = v13 & aNaturalNumber0(v7) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ( ~ (v16 = v15) & ~ (v11 = v10))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v10, v9) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (sdtasdt0(v8, v9) = v15 & sdtasdt0(v7, v15) = v16 & aNaturalNumber0(v9) = v14 & aNaturalNumber0(v8) = v13 & aNaturalNumber0(v7) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | v16 = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtpldt0(v10, v9) = v11) | ~ (sdtpldt0(v7, v8) = v10) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (sdtpldt0(v8, v9) = v15 & sdtpldt0(v7, v15) = v16 & aNaturalNumber0(v9) = v14 & aNaturalNumber0(v8) = v13 & aNaturalNumber0(v7) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | v16 = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | v7 = sz00 | ~ (sdtsldt0(v8, v7) = v9) | ~ (sdtasdt0(v7, v10) = v8) | ? [v11] : ? [v12] : ? [v13] : (( ~ (v11 = 0) & aNaturalNumber0(v10) = v11) | (doDivides0(v7, v8) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (sdtmndt0(v8, v7) = v9) | ~ (sdtpldt0(v7, v10) = v8) | ? [v11] : ? [v12] : ? [v13] : (( ~ (v11 = 0) & aNaturalNumber0(v10) = v11) | (sdtlseqdt0(v7, v8) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | v7 = sz00 | ~ (sdtsldt0(v8, v7) = v9) | ~ (sdtasdt0(v7, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (doDivides0(v7, v8) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (sdtmndt0(v8, v7) = v9) | ~ (sdtpldt0(v7, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (sdtlseqdt0(v7, v8) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v7 = sz00 | ~ (sdtlseqdt0(v8, v9) = v10) | ~ (sdtasdt0(v8, v7) = v9) | ? [v11] : ? [v12] : (aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (doDivides0(v7, v9) = v10) | ~ (doDivides0(v7, v8) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (doDivides0(v8, v9) = v14 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (sdtlseqdt0(v7, v9) = v10) | ~ (sdtlseqdt0(v7, v8) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtlseqdt0(v8, v9) = v14 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (doDivides0(v7, v8) = v9) | ~ (sdtasdt0(v7, v10) = v8) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & aNaturalNumber0(v10) = v11) | (aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (sdtlseqdt0(v7, v8) = v9) | ~ (sdtpldt0(v7, v10) = v8) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & aNaturalNumber0(v10) = v11) | (aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtsldt0(v10, v9) = v8) | ~ (sdtsldt0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (doDivides0(v10, v9) = v8) | ~ (doDivides0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (iLess0(v10, v9) = v8) | ~ (iLess0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtmndt0(v10, v9) = v8) | ~ (sdtmndt0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtlseqdt0(v10, v9) = v8) | ~ (sdtlseqdt0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtasdt0(v10, v9) = v8) | ~ (sdtasdt0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v10, v9) = v8) | ~ (sdtpldt0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = sz00 | ~ (sdtsldt0(v8, v7) = v9) | ~ (sdtasdt0(v7, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v11 = 0 & aNaturalNumber0(v9) = 0) | (doDivides0(v7, v8) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (doDivides0(v9, v10) = 0) | ~ (sdtasdt0(v7, v8) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (isPrime0(v9) = v14 & doDivides0(v9, v8) = v19 & doDivides0(v9, v7) = v18 & iLess0(v16, v1) = v17 & sdtpldt0(v15, v9) = v16 & sdtpldt0(v7, v8) = v15 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v17 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | v19 = 0 | v18 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (doDivides0(v7, v10) = 0) | ~ (sdtpldt0(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (doDivides0(v7, v9) = v15 & doDivides0(v7, v8) = v14 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | v15 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtmndt0(v8, v7) = v9) | ~ (sdtpldt0(v7, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v11 = 0 & aNaturalNumber0(v9) = 0) | (sdtlseqdt0(v7, v8) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = v7 | ~ (iLess0(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (sdtlseqdt0(v7, v8) = v12 & aNaturalNumber0(v8) = v11 & aNaturalNumber0(v7) = v10 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (sdtlseqdt0(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (sdtlseqdt0(v8, v7) = v12 & aNaturalNumber0(v8) = v11 & aNaturalNumber0(v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | (v12 = 0 & ~ (v8 = v7))))) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (isPrime0(v9) = v8) | ~ (isPrime0(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (aNaturalNumber0(v9) = v8) | ~ (aNaturalNumber0(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (sdtasdt0(v8, v7) = v12 & aNaturalNumber0(v8) = v11 & aNaturalNumber0(v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | v12 = v9))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (aNaturalNumber0(v9) = v12 & aNaturalNumber0(v8) = v11 & aNaturalNumber0(v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | v12 = 0))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (sdtpldt0(v8, v7) = v12 & aNaturalNumber0(v8) = v11 & aNaturalNumber0(v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | v12 = v9))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (aNaturalNumber0(v9) = v12 & aNaturalNumber0(v8) = v11 & aNaturalNumber0(v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | v12 = 0))) & ! [v7] : ! [v8] : (v8 = v7 | v8 = sz10 | ~ (isPrime0(v7) = 0) | ~ (doDivides0(v8, v7) = 0) | ? [v9] : (( ~ (v9 = 0) & aNaturalNumber0(v8) = v9) | ( ~ (v9 = 0) & aNaturalNumber0(v7) = v9))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (sdtlseqdt0(v7, v8) = 0) | ? [v9] : ? [v10] : ? [v11] : (sdtlseqdt0(v8, v7) = v11 & aNaturalNumber0(v8) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : (v8 = sz00 | v7 = sz00 | ~ (sdtasdt0(v7, v8) = sz00) | ? [v9] : ? [v10] : (aNaturalNumber0(v8) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : (v8 = sz00 | ~ (doDivides0(v7, v8) = 0) | ? [v9] : ? [v10] : ? [v11] : (sdtlseqdt0(v7, v8) = v11 & aNaturalNumber0(v8) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = 0))) & ! [v7] : ! [v8] : (v8 = sz00 | ~ (sdtpldt0(v7, v8) = sz00) | ? [v9] : ? [v10] : (aNaturalNumber0(v8) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : (v8 = 0 | v7 = sz10 | v7 = sz00 | ~ (isPrime0(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & ~ (v9 = v7) & ~ (v9 = sz10) & doDivides0(v9, v7) = 0 & aNaturalNumber0(v9) = 0) | ( ~ (v9 = 0) & aNaturalNumber0(v7) = v9))) & ! [v7] : ! [v8] : (v8 = 0 | v7 = sz10 | v7 = sz00 | ~ (sdtlseqdt0(sz10, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & aNaturalNumber0(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (sdtlseqdt0(v7, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & aNaturalNumber0(v7) = v9)) & ! [v7] : ! [v8] : (v7 = sz00 | ~ (sdtpldt0(v7, v8) = sz00) | ? [v9] : ? [v10] : (aNaturalNumber0(v8) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : ( ~ (doDivides0(v7, v8) = 0) | ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & v10 = 0 & sdtasdt0(v7, v9) = v8 & aNaturalNumber0(v9) = 0) | (aNaturalNumber0(v8) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0))))) & ! [v7] : ! [v8] : ( ~ (sdtlseqdt0(v7, v8) = 0) | ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & v10 = 0 & sdtpldt0(v7, v9) = v8 & aNaturalNumber0(v9) = 0) | (aNaturalNumber0(v8) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0))))) & ! [v7] : ! [v8] : ( ~ (sdtasdt0(sz10, v7) = v8) | ? [v9] : ? [v10] : (sdtasdt0(v7, sz10) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v9 = 0) | (v10 = v7 & v8 = v7)))) & ! [v7] : ! [v8] : ( ~ (sdtasdt0(sz00, v7) = v8) | ? [v9] : ? [v10] : (sdtasdt0(v7, sz00) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v9 = 0) | (v10 = sz00 & v8 = sz00)))) & ! [v7] : ! [v8] : ( ~ (sdtpldt0(sz00, v7) = v8) | ? [v9] : ? [v10] : (sdtpldt0(v7, sz00) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v9 = 0) | (v10 = v7 & v8 = v7)))) & ! [v7] : (v7 = sz10 | v7 = sz00 | ~ (aNaturalNumber0(v7) = 0) | ? [v8] : (isPrime0(v8) = 0 & doDivides0(v8, v7) = 0 & aNaturalNumber0(v8) = 0)) & ( ~ (v6 = 0) | xk = xp))
% 37.30/10.99 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields:
% 37.30/10.99 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0) & ~ (all_0_3_3 = 0) & ~ (xk = sz10) & ~ (xk = sz00) & ~ (xp = xm) & ~ (xp = xn) & ~ (sz10 = sz00) & isPrime0(xr) = 0 & isPrime0(xp) = 0 & sdtsldt0(all_0_4_4, xp) = xk & doDivides0(xr, all_0_4_4) = 0 & doDivides0(xr, xk) = 0 & doDivides0(xp, all_0_4_4) = 0 & sdtlseqdt0(xr, xk) = 0 & sdtlseqdt0(xk, xp) = all_0_0_0 & sdtlseqdt0(xp, xk) = all_0_1_1 & sdtlseqdt0(xp, xm) = all_0_2_2 & sdtlseqdt0(xp, xn) = all_0_3_3 & sdtlseqdt0(xm, xp) = 0 & sdtlseqdt0(xn, xp) = 0 & sdtasdt0(xn, xm) = all_0_4_4 & sdtpldt0(all_0_6_6, xp) = all_0_5_5 & sdtpldt0(xn, xm) = all_0_6_6 & aNaturalNumber0(xr) = 0 & aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 & ~ (isPrime0(sz10) = 0) & ~ (isPrime0(sz00) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | v0 = sz00 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (sdtlseqdt0(v10, v11) = v12 & sdtlseqdt0(v1, v2) = v9 & sdtasdt0(v2, v0) = v11 & sdtasdt0(v1, v0) = v10 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v12 = 0 & v5 = 0 & ~ (v11 = v10) & ~ (v4 = v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtlseqdt0(v0, v1) = 0) | ~ (sdtpldt0(v1, v2) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((sdtlseqdt0(v7, v8) = v9 & sdtpldt0(v2, v1) = v8 & sdtpldt0(v2, v0) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0 & ~ (v8 = v7) & ~ (v4 = v3)))) | (aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ((doDivides0(v0, v1) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))) | (sdtasdt0(v3, v2) = v7 & aNaturalNumber0(v3) = v6 & ( ~ (v6 = 0) | v7 = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v9, v0) = v11 & sdtasdt0(v2, v0) = v13 & sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v9) = v10 & sdtpldt0(v12, v13) = v14 & sdtpldt0(v1, v2) = v9 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v14 = v11 & v10 = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (doDivides0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (doDivides0(v0, v2) = v9 & doDivides0(v0, v1) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v8 = v7) & ~ (v4 = v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtpldt0(v2, v0) = v9 & sdtpldt0(v1, v0) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v9 = v8) & ~ (v4 = v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtpldt0(v1, v2) = v8 & sdtpldt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v0 = sz00 | ~ (sdtlseqdt0(v1, v2) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ? [v4] : ? [v5] : (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (doDivides0(v0, v2) = v3) | ~ (doDivides0(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (doDivides0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (sdtlseqdt0(v0, v2) = v3) | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (sdtlseqdt0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (doDivides0(v0, v1) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(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] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (doDivides0(v2, v3) = 0) | ~ (sdtasdt0(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (isPrime0(v2) = v7 & doDivides0(v2, v1) = v12 & doDivides0(v2, v0) = v11 & iLess0(v9, all_0_5_5) = v10 & sdtpldt0(v8, v2) = v9 & sdtpldt0(v0, v1) = v8 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v10 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v12 = 0 | v11 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (doDivides0(v0, v3) = 0) | ~ (sdtpldt0(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (doDivides0(v0, v2) = v8 & doDivides0(v0, v1) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (iLess0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtlseqdt0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtlseqdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v5 = 0 & ~ (v1 = v0))))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ (isPrime0(v0) = 0) | ~ (doDivides0(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (sdtlseqdt0(v1, v0) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (doDivides0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (sdtlseqdt0(v0, v1) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0))) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (isPrime0(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & ~ (v2 = v0) & ~ (v2 = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)) & ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (doDivides0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ! [v0] : ! [v1] : ( ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00)))) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0)) & ( ~ (all_0_0_0 = 0) | xk = xp)
% 37.30/11.01 |
% 37.30/11.01 | Applying alpha-rule on (1) yields:
% 37.30/11.01 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0))
% 37.30/11.01 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v8 = v7) & ~ (v4 = v3)))))
% 37.30/11.01 | (4) sdtasdt0(xn, xm) = all_0_4_4
% 37.30/11.01 | (5) doDivides0(xr, xk) = 0
% 37.30/11.01 | (6) sdtpldt0(all_0_6_6, xp) = all_0_5_5
% 37.30/11.01 | (7) sdtlseqdt0(xp, xm) = all_0_2_2
% 37.30/11.01 | (8) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 37.30/11.01 | (9) doDivides0(xr, all_0_4_4) = 0
% 37.30/11.01 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (iLess0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtlseqdt0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))))
% 37.30/11.01 | (11) ~ (all_0_2_2 = 0)
% 37.30/11.01 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtlseqdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v5 = 0 & ~ (v1 = v0)))))
% 37.30/11.01 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 37.30/11.01 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 37.30/11.01 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v0 = sz00 | ~ (sdtlseqdt0(v1, v2) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ? [v4] : ? [v5] : (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))
% 37.30/11.01 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0))
% 37.30/11.01 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtlseqdt0(v0, v1) = 0) | ~ (sdtpldt0(v1, v2) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((sdtlseqdt0(v7, v8) = v9 & sdtpldt0(v2, v1) = v8 & sdtpldt0(v2, v0) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0 & ~ (v8 = v7) & ~ (v4 = v3)))) | (aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))))
% 37.30/11.01 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 37.30/11.01 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0))
% 37.30/11.01 | (20) isPrime0(xr) = 0
% 37.30/11.01 | (21) ! [v0] : ! [v1] : (v1 = sz00 | ~ (doDivides0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (sdtlseqdt0(v0, v1) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0)))
% 37.30/11.01 | (22) ~ (xk = sz00)
% 37.30/11.01 | (23) sdtlseqdt0(xp, xn) = all_0_3_3
% 37.30/11.01 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 37.30/11.01 | (25) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 37.30/11.01 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0))
% 37.30/11.01 | (27) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ (isPrime0(v0) = 0) | ~ (doDivides0(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 37.30/11.01 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 37.30/11.02 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (doDivides0(v0, v3) = 0) | ~ (sdtpldt0(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (doDivides0(v0, v2) = v8 & doDivides0(v0, v1) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v8 = 0)))
% 37.30/11.02 | (30) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00))))
% 37.30/11.02 | (31) ~ (isPrime0(sz00) = 0)
% 37.30/11.02 | (32) aNaturalNumber0(xr) = 0
% 37.30/11.02 | (33) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 37.30/11.02 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (doDivides0(v0, v2) = v3) | ~ (doDivides0(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (doDivides0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 37.30/11.02 | (35) doDivides0(xp, all_0_4_4) = 0
% 37.30/11.02 | (36) sdtsldt0(all_0_4_4, xp) = xk
% 37.30/11.02 | (37) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0))
% 37.30/11.02 | (38) sdtpldt0(xn, xm) = all_0_6_6
% 37.30/11.02 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 37.30/11.02 | (40) ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (isPrime0(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & ~ (v2 = v0) & ~ (v2 = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 37.30/11.02 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))))
% 37.30/11.02 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (sdtlseqdt0(v0, v2) = v3) | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (sdtlseqdt0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 37.30/11.02 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4)))
% 37.30/11.02 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))))
% 37.30/11.02 | (45) sdtlseqdt0(xn, xp) = 0
% 37.30/11.02 | (46) ~ (all_0_3_3 = 0)
% 37.30/11.02 | (47) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 37.30/11.02 | (48) sdtlseqdt0(xr, xk) = 0
% 37.30/11.02 | (49) sdtlseqdt0(xp, xk) = all_0_1_1
% 37.30/11.02 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (doDivides0(v0, v1) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 37.30/11.02 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))))
% 37.30/11.02 | (52) aNaturalNumber0(sz00) = 0
% 37.30/11.02 | (53) ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 37.30/11.02 | (54) ~ (all_0_1_1 = 0)
% 37.30/11.02 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (doDivides0(v2, v3) = 0) | ~ (sdtasdt0(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (isPrime0(v2) = v7 & doDivides0(v2, v1) = v12 & doDivides0(v2, v0) = v11 & iLess0(v9, all_0_5_5) = v10 & sdtpldt0(v8, v2) = v9 & sdtpldt0(v0, v1) = v8 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v10 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v12 = 0 | v11 = 0)))
% 37.30/11.02 | (56) aNaturalNumber0(xm) = 0
% 37.30/11.02 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 37.30/11.02 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtpldt0(v1, v2) = v8 & sdtpldt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4)))
% 37.30/11.02 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 37.30/11.02 | (60) ~ (sz10 = sz00)
% 37.30/11.02 | (61) sdtlseqdt0(xk, xp) = all_0_0_0
% 37.30/11.02 | (62) isPrime0(xp) = 0
% 37.30/11.02 | (63) aNaturalNumber0(xn) = 0
% 37.30/11.02 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v9, v0) = v11 & sdtasdt0(v2, v0) = v13 & sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v9) = v10 & sdtpldt0(v12, v13) = v14 & sdtpldt0(v1, v2) = v9 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v14 = v11 & v10 = v5))))
% 37.30/11.02 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 37.30/11.03 | (66) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (sdtlseqdt0(v1, v0) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0))))
% 37.30/11.03 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtpldt0(v2, v0) = v9 & sdtpldt0(v1, v0) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v9 = v8) & ~ (v4 = v3)))))
% 37.30/11.03 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | v0 = sz00 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (sdtlseqdt0(v10, v11) = v12 & sdtlseqdt0(v1, v2) = v9 & sdtasdt0(v2, v0) = v11 & sdtasdt0(v1, v0) = v10 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v12 = 0 & v5 = 0 & ~ (v11 = v10) & ~ (v4 = v3)))))
% 37.30/11.03 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (doDivides0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (doDivides0(v0, v2) = v9 & doDivides0(v0, v1) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0))))
% 37.30/11.03 | (70) ! [v0] : ! [v1] : ( ~ (doDivides0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))))
% 37.30/11.03 | (71) ~ (xk = sz10)
% 37.30/11.03 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ((doDivides0(v0, v1) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))) | (sdtasdt0(v3, v2) = v7 & aNaturalNumber0(v3) = v6 & ( ~ (v6 = 0) | v7 = v5))))
% 37.30/11.03 | (73) ~ (xp = xn)
% 37.30/11.03 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))))
% 37.30/11.03 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 37.30/11.03 | (76) ~ (isPrime0(sz10) = 0)
% 37.30/11.03 | (77) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0))
% 37.30/11.03 | (78) aNaturalNumber0(xp) = 0
% 37.30/11.03 | (79) ~ (all_0_0_0 = 0) | xk = xp
% 37.30/11.03 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 37.30/11.03 | (81) ~ (xp = xm)
% 37.30/11.03 | (82) aNaturalNumber0(sz10) = 0
% 37.30/11.03 | (83) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 37.30/11.03 | (84) ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 37.30/11.03 | (85) sdtlseqdt0(xm, xp) = 0
% 37.30/11.03 | (86) ! [v0] : ! [v1] : ( ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))))
% 37.30/11.03 |
% 37.30/11.03 | Using (20) and (76) yields:
% 37.30/11.03 | (87) ~ (xr = sz10)
% 37.30/11.03 |
% 37.30/11.03 | Using (62) and (76) yields:
% 37.30/11.03 | (88) ~ (xp = sz10)
% 37.30/11.03 |
% 37.30/11.03 | Using (20) and (31) yields:
% 37.30/11.03 | (89) ~ (xr = sz00)
% 37.30/11.03 |
% 37.30/11.03 | Using (62) and (31) yields:
% 37.30/11.03 | (90) ~ (xp = sz00)
% 37.30/11.03 |
% 37.30/11.03 | Instantiating formula (70) with all_0_4_4, xr and discharging atoms doDivides0(xr, all_0_4_4) = 0, yields:
% 37.30/11.03 | (91) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_4_4 & v1 = 0 & sdtasdt0(xr, v0) = all_0_4_4 & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 37.30/11.03 |
% 37.30/11.03 | Instantiating formula (21) with xk, xr and discharging atoms doDivides0(xr, xk) = 0, yields:
% 37.30/11.03 | (92) xk = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xr, xk) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 37.30/11.03 |
% 37.30/11.03 | Instantiating formula (70) with all_0_4_4, xp and discharging atoms doDivides0(xp, all_0_4_4) = 0, yields:
% 37.30/11.03 | (93) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_4_4 & v1 = 0 & sdtasdt0(xp, v0) = all_0_4_4 & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 37.30/11.03 |
% 37.30/11.03 | Instantiating formula (12) with all_0_0_0, xp, xk and discharging atoms sdtlseqdt0(xk, xp) = all_0_0_0, yields:
% 37.30/11.03 | (94) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, xk) = v2 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xk = xp))))
% 37.30/11.03 |
% 37.30/11.03 | Instantiating formula (53) with all_0_1_1, xp yields:
% 37.30/11.03 | (95) all_0_1_1 = 0 | ~ (sdtlseqdt0(xp, xp) = all_0_1_1) | ? [v0] : ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0)
% 37.30/11.03 |
% 37.30/11.03 | Instantiating formula (12) with all_0_1_1, xk, xp and discharging atoms sdtlseqdt0(xp, xk) = all_0_1_1, yields:
% 37.30/11.03 | (96) all_0_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xk, xp) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xk = xp))))
% 37.30/11.03 |
% 37.30/11.03 | Instantiating formula (86) with xp, xm and discharging atoms sdtlseqdt0(xm, xp) = 0, yields:
% 37.30/11.03 | (97) ? [v0] : ? [v1] : ? [v2] : ((v2 = xp & v1 = 0 & sdtpldt0(xm, v0) = xp & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 37.30/11.04 |
% 37.30/11.04 | Instantiating formula (86) with xp, xn and discharging atoms sdtlseqdt0(xn, xp) = 0, yields:
% 37.30/11.04 | (98) ? [v0] : ? [v1] : ? [v2] : ((v2 = xp & v1 = 0 & sdtpldt0(xn, v0) = xp & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xp) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 37.30/11.04 |
% 37.30/11.04 | Instantiating formula (55) with all_0_4_4, xr, xm, xn and discharging atoms doDivides0(xr, all_0_4_4) = 0, sdtasdt0(xn, xm) = all_0_4_4, yields:
% 37.30/11.04 | (99) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xr) = v3 & doDivides0(xr, xm) = v8 & doDivides0(xr, xn) = v7 & iLess0(v5, all_0_5_5) = v6 & sdtpldt0(v4, xr) = v5 & sdtpldt0(xn, xm) = v4 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 37.30/11.04 |
% 37.30/11.04 | Instantiating formula (55) with all_0_4_4, xp, xm, xn and discharging atoms doDivides0(xp, all_0_4_4) = 0, sdtasdt0(xn, xm) = all_0_4_4, yields:
% 37.30/11.04 | (100) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, xm) = v8 & doDivides0(xp, xn) = v7 & iLess0(v5, all_0_5_5) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xn, xm) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 37.30/11.04 |
% 37.30/11.04 | Instantiating formula (28) with all_0_4_4, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_4_4, yields:
% 37.30/11.04 | (101) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_4_4))
% 37.30/11.04 |
% 37.30/11.04 | Instantiating formula (18) with all_0_4_4, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_4_4, yields:
% 37.30/11.04 | (102) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_4_4) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 37.30/11.04 |
% 37.30/11.04 | Instantiating formula (75) with all_0_5_5, xp, all_0_6_6 and discharging atoms sdtpldt0(all_0_6_6, xp) = all_0_5_5, yields:
% 37.30/11.04 | (103) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, all_0_6_6) = v2 & aNaturalNumber0(all_0_6_6) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_5_5))
% 37.30/11.04 |
% 37.30/11.04 | Instantiating formula (57) with all_0_5_5, xp, all_0_6_6 and discharging atoms sdtpldt0(all_0_6_6, xp) = all_0_5_5, yields:
% 37.30/11.04 | (104) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_5_5) = v2 & aNaturalNumber0(all_0_6_6) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 37.30/11.04 |
% 37.30/11.04 | Instantiating formula (58) with all_0_5_5, all_0_6_6, xp, xm, xn and discharging atoms sdtpldt0(all_0_6_6, xp) = all_0_5_5, sdtpldt0(xn, xm) = all_0_6_6, yields:
% 37.30/11.04 | (105) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xm, xp) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_5_5))
% 37.30/11.04 |
% 37.30/11.04 | Instantiating formula (75) with all_0_6_6, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_6_6, yields:
% 37.30/11.04 | (106) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_6_6))
% 37.30/11.04 |
% 37.30/11.04 | Instantiating formula (57) with all_0_6_6, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_6_6, yields:
% 37.30/11.04 | (107) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_6_6) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 37.30/11.04 |
% 37.30/11.04 | Instantiating formula (37) with xr and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 37.78/11.04 | (108) xr = sz10 | xr = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xr) = 0 & aNaturalNumber0(v0) = 0)
% 37.78/11.04 |
% 37.78/11.04 | Instantiating formula (37) with xp and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 37.78/11.04 | (109) xp = sz10 | xp = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 37.78/11.04 |
% 37.78/11.04 | Instantiating (107) with all_12_0_7, all_12_1_8, all_12_2_9 yields:
% 37.78/11.04 | (110) aNaturalNumber0(all_0_6_6) = all_12_0_7 & aNaturalNumber0(xm) = all_12_1_8 & aNaturalNumber0(xn) = all_12_2_9 & ( ~ (all_12_1_8 = 0) | ~ (all_12_2_9 = 0) | all_12_0_7 = 0)
% 37.78/11.04 |
% 37.78/11.04 | Applying alpha-rule on (110) yields:
% 37.78/11.04 | (111) aNaturalNumber0(all_0_6_6) = all_12_0_7
% 37.78/11.04 | (112) aNaturalNumber0(xm) = all_12_1_8
% 37.78/11.04 | (113) aNaturalNumber0(xn) = all_12_2_9
% 37.78/11.04 | (114) ~ (all_12_1_8 = 0) | ~ (all_12_2_9 = 0) | all_12_0_7 = 0
% 37.78/11.04 |
% 37.78/11.04 | Instantiating (106) with all_14_0_10, all_14_1_11, all_14_2_12 yields:
% 37.78/11.04 | (115) sdtpldt0(xm, xn) = all_14_0_10 & aNaturalNumber0(xm) = all_14_1_11 & aNaturalNumber0(xn) = all_14_2_12 & ( ~ (all_14_1_11 = 0) | ~ (all_14_2_12 = 0) | all_14_0_10 = all_0_6_6)
% 37.78/11.04 |
% 37.78/11.04 | Applying alpha-rule on (115) yields:
% 37.78/11.04 | (116) sdtpldt0(xm, xn) = all_14_0_10
% 37.78/11.04 | (117) aNaturalNumber0(xm) = all_14_1_11
% 37.78/11.04 | (118) aNaturalNumber0(xn) = all_14_2_12
% 37.78/11.04 | (119) ~ (all_14_1_11 = 0) | ~ (all_14_2_12 = 0) | all_14_0_10 = all_0_6_6
% 37.78/11.04 |
% 37.78/11.04 | Instantiating (102) with all_16_0_13, all_16_1_14, all_16_2_15 yields:
% 37.78/11.04 | (120) aNaturalNumber0(all_0_4_4) = all_16_0_13 & aNaturalNumber0(xm) = all_16_1_14 & aNaturalNumber0(xn) = all_16_2_15 & ( ~ (all_16_1_14 = 0) | ~ (all_16_2_15 = 0) | all_16_0_13 = 0)
% 37.78/11.04 |
% 37.78/11.04 | Applying alpha-rule on (120) yields:
% 37.78/11.04 | (121) aNaturalNumber0(all_0_4_4) = all_16_0_13
% 37.78/11.04 | (122) aNaturalNumber0(xm) = all_16_1_14
% 37.78/11.04 | (123) aNaturalNumber0(xn) = all_16_2_15
% 37.78/11.04 | (124) ~ (all_16_1_14 = 0) | ~ (all_16_2_15 = 0) | all_16_0_13 = 0
% 37.78/11.04 |
% 37.78/11.04 | Instantiating (101) with all_18_0_16, all_18_1_17, all_18_2_18 yields:
% 37.78/11.04 | (125) sdtasdt0(xm, xn) = all_18_0_16 & aNaturalNumber0(xm) = all_18_1_17 & aNaturalNumber0(xn) = all_18_2_18 & ( ~ (all_18_1_17 = 0) | ~ (all_18_2_18 = 0) | all_18_0_16 = all_0_4_4)
% 37.78/11.04 |
% 37.78/11.04 | Applying alpha-rule on (125) yields:
% 37.78/11.04 | (126) sdtasdt0(xm, xn) = all_18_0_16
% 37.78/11.04 | (127) aNaturalNumber0(xm) = all_18_1_17
% 37.78/11.04 | (128) aNaturalNumber0(xn) = all_18_2_18
% 37.78/11.04 | (129) ~ (all_18_1_17 = 0) | ~ (all_18_2_18 = 0) | all_18_0_16 = all_0_4_4
% 37.78/11.04 |
% 37.78/11.04 | Instantiating (104) with all_20_0_19, all_20_1_20, all_20_2_21 yields:
% 37.78/11.04 | (130) aNaturalNumber0(all_0_5_5) = all_20_0_19 & aNaturalNumber0(all_0_6_6) = all_20_2_21 & aNaturalNumber0(xp) = all_20_1_20 & ( ~ (all_20_1_20 = 0) | ~ (all_20_2_21 = 0) | all_20_0_19 = 0)
% 37.78/11.04 |
% 37.78/11.04 | Applying alpha-rule on (130) yields:
% 37.78/11.04 | (131) aNaturalNumber0(all_0_5_5) = all_20_0_19
% 37.78/11.04 | (132) aNaturalNumber0(all_0_6_6) = all_20_2_21
% 37.78/11.04 | (133) aNaturalNumber0(xp) = all_20_1_20
% 37.78/11.04 | (134) ~ (all_20_1_20 = 0) | ~ (all_20_2_21 = 0) | all_20_0_19 = 0
% 37.78/11.04 |
% 37.78/11.04 | Instantiating (98) with all_22_0_22, all_22_1_23, all_22_2_24 yields:
% 37.78/11.04 | (135) (all_22_0_22 = xp & all_22_1_23 = 0 & sdtpldt0(xn, all_22_2_24) = xp & aNaturalNumber0(all_22_2_24) = 0) | (aNaturalNumber0(xp) = all_22_1_23 & aNaturalNumber0(xn) = all_22_2_24 & ( ~ (all_22_1_23 = 0) | ~ (all_22_2_24 = 0)))
% 37.78/11.04 |
% 37.78/11.04 | Instantiating (97) with all_23_0_25, all_23_1_26, all_23_2_27 yields:
% 37.78/11.04 | (136) (all_23_0_25 = xp & all_23_1_26 = 0 & sdtpldt0(xm, all_23_2_27) = xp & aNaturalNumber0(all_23_2_27) = 0) | (aNaturalNumber0(xp) = all_23_1_26 & aNaturalNumber0(xm) = all_23_2_27 & ( ~ (all_23_1_26 = 0) | ~ (all_23_2_27 = 0)))
% 37.78/11.04 |
% 37.78/11.04 | Instantiating (93) with all_24_0_28, all_24_1_29, all_24_2_30 yields:
% 37.78/11.04 | (137) (all_24_0_28 = all_0_4_4 & all_24_1_29 = 0 & sdtasdt0(xp, all_24_2_30) = all_0_4_4 & aNaturalNumber0(all_24_2_30) = 0) | (aNaturalNumber0(all_0_4_4) = all_24_1_29 & aNaturalNumber0(xp) = all_24_2_30 & ( ~ (all_24_1_29 = 0) | ~ (all_24_2_30 = 0)))
% 37.78/11.05 |
% 37.78/11.05 | Instantiating (103) with all_26_0_34, all_26_1_35, all_26_2_36 yields:
% 37.78/11.05 | (138) sdtpldt0(xp, all_0_6_6) = all_26_0_34 & aNaturalNumber0(all_0_6_6) = all_26_2_36 & aNaturalNumber0(xp) = all_26_1_35 & ( ~ (all_26_1_35 = 0) | ~ (all_26_2_36 = 0) | all_26_0_34 = all_0_5_5)
% 37.78/11.05 |
% 37.78/11.05 | Applying alpha-rule on (138) yields:
% 37.78/11.05 | (139) sdtpldt0(xp, all_0_6_6) = all_26_0_34
% 37.78/11.05 | (140) aNaturalNumber0(all_0_6_6) = all_26_2_36
% 37.78/11.05 | (141) aNaturalNumber0(xp) = all_26_1_35
% 37.78/11.05 | (142) ~ (all_26_1_35 = 0) | ~ (all_26_2_36 = 0) | all_26_0_34 = all_0_5_5
% 37.78/11.05 |
% 37.78/11.05 | Instantiating (91) with all_28_0_37, all_28_1_38, all_28_2_39 yields:
% 37.78/11.05 | (143) (all_28_0_37 = all_0_4_4 & all_28_1_38 = 0 & sdtasdt0(xr, all_28_2_39) = all_0_4_4 & aNaturalNumber0(all_28_2_39) = 0) | (aNaturalNumber0(all_0_4_4) = all_28_1_38 & aNaturalNumber0(xr) = all_28_2_39 & ( ~ (all_28_1_38 = 0) | ~ (all_28_2_39 = 0)))
% 37.78/11.05 |
% 37.78/11.05 | Instantiating (100) with all_29_0_40, all_29_1_41, all_29_2_42, all_29_3_43, all_29_4_44, all_29_5_45, all_29_6_46, all_29_7_47, all_29_8_48 yields:
% 37.78/11.05 | (144) isPrime0(xp) = all_29_5_45 & doDivides0(xp, xm) = all_29_0_40 & doDivides0(xp, xn) = all_29_1_41 & iLess0(all_29_3_43, all_0_5_5) = all_29_2_42 & sdtpldt0(all_29_4_44, xp) = all_29_3_43 & sdtpldt0(xn, xm) = all_29_4_44 & aNaturalNumber0(xp) = all_29_6_46 & aNaturalNumber0(xm) = all_29_7_47 & aNaturalNumber0(xn) = all_29_8_48 & ( ~ (all_29_2_42 = 0) | ~ (all_29_5_45 = 0) | ~ (all_29_6_46 = 0) | ~ (all_29_7_47 = 0) | ~ (all_29_8_48 = 0) | all_29_0_40 = 0 | all_29_1_41 = 0)
% 37.78/11.05 |
% 37.78/11.05 | Applying alpha-rule on (144) yields:
% 37.78/11.05 | (145) iLess0(all_29_3_43, all_0_5_5) = all_29_2_42
% 37.78/11.05 | (146) isPrime0(xp) = all_29_5_45
% 37.78/11.05 | (147) aNaturalNumber0(xn) = all_29_8_48
% 37.78/11.05 | (148) doDivides0(xp, xn) = all_29_1_41
% 37.78/11.05 | (149) ~ (all_29_2_42 = 0) | ~ (all_29_5_45 = 0) | ~ (all_29_6_46 = 0) | ~ (all_29_7_47 = 0) | ~ (all_29_8_48 = 0) | all_29_0_40 = 0 | all_29_1_41 = 0
% 37.78/11.05 | (150) sdtpldt0(xn, xm) = all_29_4_44
% 37.78/11.05 | (151) aNaturalNumber0(xp) = all_29_6_46
% 37.78/11.05 | (152) sdtpldt0(all_29_4_44, xp) = all_29_3_43
% 37.78/11.05 | (153) aNaturalNumber0(xm) = all_29_7_47
% 37.78/11.05 | (154) doDivides0(xp, xm) = all_29_0_40
% 37.78/11.05 |
% 37.78/11.05 | Instantiating (99) with all_31_0_49, all_31_1_50, all_31_2_51, all_31_3_52, all_31_4_53, all_31_5_54, all_31_6_55, all_31_7_56, all_31_8_57 yields:
% 37.78/11.05 | (155) isPrime0(xr) = all_31_5_54 & doDivides0(xr, xm) = all_31_0_49 & doDivides0(xr, xn) = all_31_1_50 & iLess0(all_31_3_52, all_0_5_5) = all_31_2_51 & sdtpldt0(all_31_4_53, xr) = all_31_3_52 & sdtpldt0(xn, xm) = all_31_4_53 & aNaturalNumber0(xr) = all_31_6_55 & aNaturalNumber0(xm) = all_31_7_56 & aNaturalNumber0(xn) = all_31_8_57 & ( ~ (all_31_2_51 = 0) | ~ (all_31_5_54 = 0) | ~ (all_31_6_55 = 0) | ~ (all_31_7_56 = 0) | ~ (all_31_8_57 = 0) | all_31_0_49 = 0 | all_31_1_50 = 0)
% 37.78/11.05 |
% 37.78/11.05 | Applying alpha-rule on (155) yields:
% 37.78/11.05 | (156) doDivides0(xr, xm) = all_31_0_49
% 37.78/11.05 | (157) sdtpldt0(all_31_4_53, xr) = all_31_3_52
% 37.78/11.05 | (158) iLess0(all_31_3_52, all_0_5_5) = all_31_2_51
% 37.78/11.05 | (159) aNaturalNumber0(xm) = all_31_7_56
% 37.78/11.05 | (160) aNaturalNumber0(xn) = all_31_8_57
% 37.78/11.05 | (161) aNaturalNumber0(xr) = all_31_6_55
% 37.78/11.05 | (162) ~ (all_31_2_51 = 0) | ~ (all_31_5_54 = 0) | ~ (all_31_6_55 = 0) | ~ (all_31_7_56 = 0) | ~ (all_31_8_57 = 0) | all_31_0_49 = 0 | all_31_1_50 = 0
% 37.78/11.05 | (163) isPrime0(xr) = all_31_5_54
% 37.78/11.05 | (164) doDivides0(xr, xn) = all_31_1_50
% 37.78/11.05 | (165) sdtpldt0(xn, xm) = all_31_4_53
% 37.78/11.05 |
% 37.78/11.05 | Instantiating (105) with all_33_0_58, all_33_1_59, all_33_2_60, all_33_3_61, all_33_4_62 yields:
% 37.78/11.05 | (166) sdtpldt0(xm, xp) = all_33_1_59 & sdtpldt0(xn, all_33_1_59) = all_33_0_58 & aNaturalNumber0(xp) = all_33_2_60 & aNaturalNumber0(xm) = all_33_3_61 & aNaturalNumber0(xn) = all_33_4_62 & ( ~ (all_33_2_60 = 0) | ~ (all_33_3_61 = 0) | ~ (all_33_4_62 = 0) | all_33_0_58 = all_0_5_5)
% 37.78/11.05 |
% 37.78/11.05 | Applying alpha-rule on (166) yields:
% 37.78/11.05 | (167) aNaturalNumber0(xn) = all_33_4_62
% 37.78/11.05 | (168) aNaturalNumber0(xm) = all_33_3_61
% 37.78/11.05 | (169) aNaturalNumber0(xp) = all_33_2_60
% 37.78/11.05 | (170) ~ (all_33_2_60 = 0) | ~ (all_33_3_61 = 0) | ~ (all_33_4_62 = 0) | all_33_0_58 = all_0_5_5
% 37.78/11.05 | (171) sdtpldt0(xm, xp) = all_33_1_59
% 37.78/11.05 | (172) sdtpldt0(xn, all_33_1_59) = all_33_0_58
% 37.78/11.05 |
% 37.78/11.05 +-Applying beta-rule and splitting (96), into two cases.
% 37.78/11.05 |-Branch one:
% 37.78/11.05 | (173) all_0_1_1 = 0
% 37.78/11.05 |
% 37.78/11.05 | Equations (173) can reduce 54 to:
% 37.78/11.05 | (174) $false
% 37.78/11.05 |
% 37.78/11.05 |-The branch is then unsatisfiable
% 37.78/11.05 |-Branch two:
% 37.78/11.05 | (54) ~ (all_0_1_1 = 0)
% 37.78/11.05 | (176) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xk, xp) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xk = xp))))
% 37.78/11.05 |
% 37.78/11.05 | Instantiating (176) with all_40_0_66, all_40_1_67, all_40_2_68 yields:
% 37.78/11.05 | (177) sdtlseqdt0(xk, xp) = all_40_0_66 & aNaturalNumber0(xk) = all_40_1_67 & aNaturalNumber0(xp) = all_40_2_68 & ( ~ (all_40_1_67 = 0) | ~ (all_40_2_68 = 0) | (all_40_0_66 = 0 & ~ (xk = xp)))
% 37.78/11.05 |
% 37.78/11.05 | Applying alpha-rule on (177) yields:
% 37.78/11.05 | (178) sdtlseqdt0(xk, xp) = all_40_0_66
% 37.78/11.05 | (179) aNaturalNumber0(xk) = all_40_1_67
% 37.78/11.05 | (180) aNaturalNumber0(xp) = all_40_2_68
% 37.78/11.05 | (181) ~ (all_40_1_67 = 0) | ~ (all_40_2_68 = 0) | (all_40_0_66 = 0 & ~ (xk = xp))
% 37.78/11.05 |
% 37.78/11.05 +-Applying beta-rule and splitting (92), into two cases.
% 37.78/11.05 |-Branch one:
% 37.78/11.05 | (182) xk = sz00
% 37.78/11.05 |
% 37.78/11.05 | Equations (182) can reduce 22 to:
% 37.78/11.05 | (174) $false
% 37.78/11.05 |
% 37.78/11.05 |-The branch is then unsatisfiable
% 37.78/11.05 |-Branch two:
% 37.78/11.05 | (22) ~ (xk = sz00)
% 37.78/11.06 | (185) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xr, xk) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 37.78/11.06 |
% 37.78/11.06 | Instantiating (185) with all_45_0_69, all_45_1_70, all_45_2_71 yields:
% 37.78/11.06 | (186) sdtlseqdt0(xr, xk) = all_45_0_69 & aNaturalNumber0(xr) = all_45_2_71 & aNaturalNumber0(xk) = all_45_1_70 & ( ~ (all_45_1_70 = 0) | ~ (all_45_2_71 = 0) | all_45_0_69 = 0)
% 37.78/11.06 |
% 37.78/11.06 | Applying alpha-rule on (186) yields:
% 37.78/11.06 | (187) sdtlseqdt0(xr, xk) = all_45_0_69
% 37.78/11.06 | (188) aNaturalNumber0(xr) = all_45_2_71
% 37.78/11.06 | (189) aNaturalNumber0(xk) = all_45_1_70
% 37.78/11.06 | (190) ~ (all_45_1_70 = 0) | ~ (all_45_2_71 = 0) | all_45_0_69 = 0
% 37.78/11.06 |
% 37.78/11.06 +-Applying beta-rule and splitting (108), into two cases.
% 37.78/11.06 |-Branch one:
% 37.78/11.06 | (191) xr = sz00
% 37.78/11.06 |
% 37.78/11.06 | Equations (191) can reduce 89 to:
% 37.78/11.06 | (174) $false
% 37.78/11.06 |
% 37.78/11.06 |-The branch is then unsatisfiable
% 37.78/11.06 |-Branch two:
% 37.78/11.06 | (89) ~ (xr = sz00)
% 37.78/11.06 | (194) xr = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xr) = 0 & aNaturalNumber0(v0) = 0)
% 37.78/11.06 |
% 37.78/11.06 +-Applying beta-rule and splitting (109), into two cases.
% 37.78/11.06 |-Branch one:
% 37.78/11.06 | (195) xp = sz00
% 37.78/11.06 |
% 37.78/11.06 | Equations (195) can reduce 90 to:
% 37.78/11.06 | (174) $false
% 37.78/11.06 |
% 37.78/11.06 |-The branch is then unsatisfiable
% 37.78/11.06 |-Branch two:
% 37.78/11.06 | (90) ~ (xp = sz00)
% 37.78/11.06 | (198) xp = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 37.78/11.06 |
% 37.78/11.06 +-Applying beta-rule and splitting (194), into two cases.
% 37.78/11.06 |-Branch one:
% 37.78/11.06 | (199) xr = sz10
% 37.78/11.06 |
% 37.78/11.06 | Equations (199) can reduce 87 to:
% 37.78/11.06 | (174) $false
% 37.78/11.06 |
% 37.78/11.06 |-The branch is then unsatisfiable
% 37.78/11.06 |-Branch two:
% 37.78/11.06 | (87) ~ (xr = sz10)
% 37.78/11.06 | (202) ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xr) = 0 & aNaturalNumber0(v0) = 0)
% 37.78/11.06 |
% 37.78/11.06 | Instantiating (202) with all_57_0_72 yields:
% 37.78/11.06 | (203) isPrime0(all_57_0_72) = 0 & doDivides0(all_57_0_72, xr) = 0 & aNaturalNumber0(all_57_0_72) = 0
% 37.78/11.06 |
% 37.78/11.06 | Applying alpha-rule on (203) yields:
% 37.78/11.06 | (204) isPrime0(all_57_0_72) = 0
% 37.78/11.06 | (205) doDivides0(all_57_0_72, xr) = 0
% 37.78/11.06 | (206) aNaturalNumber0(all_57_0_72) = 0
% 37.78/11.06 |
% 37.78/11.06 +-Applying beta-rule and splitting (198), into two cases.
% 37.78/11.06 |-Branch one:
% 37.78/11.06 | (207) xp = sz10
% 37.78/11.06 |
% 37.78/11.06 | Equations (207) can reduce 88 to:
% 37.78/11.06 | (174) $false
% 37.78/11.06 |
% 37.78/11.06 |-The branch is then unsatisfiable
% 37.78/11.06 |-Branch two:
% 37.78/11.06 | (88) ~ (xp = sz10)
% 37.78/11.06 | (210) ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 37.78/11.06 |
% 37.78/11.06 | Instantiating (210) with all_62_0_73 yields:
% 37.78/11.06 | (211) isPrime0(all_62_0_73) = 0 & doDivides0(all_62_0_73, xp) = 0 & aNaturalNumber0(all_62_0_73) = 0
% 37.78/11.06 |
% 37.78/11.06 | Applying alpha-rule on (211) yields:
% 37.78/11.06 | (212) isPrime0(all_62_0_73) = 0
% 37.78/11.06 | (213) doDivides0(all_62_0_73, xp) = 0
% 37.78/11.06 | (214) aNaturalNumber0(all_62_0_73) = 0
% 37.78/11.06 |
% 37.78/11.06 | Using (212) and (76) yields:
% 37.78/11.06 | (215) ~ (all_62_0_73 = sz10)
% 37.78/11.06 |
% 37.78/11.06 | Using (212) and (31) yields:
% 37.78/11.06 | (216) ~ (all_62_0_73 = sz00)
% 37.78/11.06 |
% 37.78/11.06 | Instantiating formula (77) with xp, all_29_5_45, 0 and discharging atoms isPrime0(xp) = all_29_5_45, isPrime0(xp) = 0, yields:
% 37.78/11.06 | (217) all_29_5_45 = 0
% 37.78/11.06 |
% 37.78/11.06 | Instantiating formula (26) with xk, xp, all_40_0_66, all_0_0_0 and discharging atoms sdtlseqdt0(xk, xp) = all_40_0_66, sdtlseqdt0(xk, xp) = all_0_0_0, yields:
% 37.78/11.06 | (218) all_40_0_66 = all_0_0_0
% 37.78/11.06 |
% 37.78/11.06 | Instantiating formula (14) with all_0_6_6, xp, all_29_3_43, all_0_5_5 and discharging atoms sdtpldt0(all_0_6_6, xp) = all_0_5_5, yields:
% 37.78/11.06 | (219) all_29_3_43 = all_0_5_5 | ~ (sdtpldt0(all_0_6_6, xp) = all_29_3_43)
% 37.78/11.06 |
% 37.78/11.06 | Instantiating formula (14) with xn, xm, all_31_4_53, all_0_6_6 and discharging atoms sdtpldt0(xn, xm) = all_31_4_53, sdtpldt0(xn, xm) = all_0_6_6, yields:
% 37.78/11.06 | (220) all_31_4_53 = all_0_6_6
% 37.78/11.06 |
% 37.78/11.06 | Instantiating formula (14) with xn, xm, all_29_4_44, all_31_4_53 and discharging atoms sdtpldt0(xn, xm) = all_31_4_53, sdtpldt0(xn, xm) = all_29_4_44, yields:
% 37.78/11.06 | (221) all_31_4_53 = all_29_4_44
% 37.78/11.06 |
% 37.78/11.06 | Instantiating formula (2) with all_0_6_6, all_20_2_21, all_26_2_36 and discharging atoms aNaturalNumber0(all_0_6_6) = all_26_2_36, aNaturalNumber0(all_0_6_6) = all_20_2_21, yields:
% 37.78/11.06 | (222) all_26_2_36 = all_20_2_21
% 37.78/11.06 |
% 37.78/11.06 | Instantiating formula (2) with all_0_6_6, all_12_0_7, all_26_2_36 and discharging atoms aNaturalNumber0(all_0_6_6) = all_26_2_36, aNaturalNumber0(all_0_6_6) = all_12_0_7, yields:
% 37.78/11.06 | (223) all_26_2_36 = all_12_0_7
% 37.78/11.06 |
% 37.78/11.06 | Instantiating formula (2) with xr, all_45_2_71, 0 and discharging atoms aNaturalNumber0(xr) = all_45_2_71, aNaturalNumber0(xr) = 0, yields:
% 37.78/11.06 | (224) all_45_2_71 = 0
% 37.78/11.06 |
% 37.78/11.06 | Instantiating formula (2) with xr, all_31_6_55, all_45_2_71 and discharging atoms aNaturalNumber0(xr) = all_45_2_71, aNaturalNumber0(xr) = all_31_6_55, yields:
% 37.78/11.06 | (225) all_45_2_71 = all_31_6_55
% 37.78/11.06 |
% 37.78/11.06 | Instantiating formula (2) with xk, all_40_1_67, all_45_1_70 and discharging atoms aNaturalNumber0(xk) = all_45_1_70, aNaturalNumber0(xk) = all_40_1_67, yields:
% 37.78/11.06 | (226) all_45_1_70 = all_40_1_67
% 37.78/11.06 |
% 37.78/11.06 | Instantiating formula (2) with xp, all_40_2_68, 0 and discharging atoms aNaturalNumber0(xp) = all_40_2_68, aNaturalNumber0(xp) = 0, yields:
% 37.78/11.06 | (227) all_40_2_68 = 0
% 37.78/11.06 |
% 37.78/11.06 | Instantiating formula (2) with xp, all_33_2_60, all_40_2_68 and discharging atoms aNaturalNumber0(xp) = all_40_2_68, aNaturalNumber0(xp) = all_33_2_60, yields:
% 37.78/11.06 | (228) all_40_2_68 = all_33_2_60
% 37.78/11.06 |
% 37.78/11.06 | Instantiating formula (2) with xp, all_29_6_46, all_33_2_60 and discharging atoms aNaturalNumber0(xp) = all_33_2_60, aNaturalNumber0(xp) = all_29_6_46, yields:
% 37.78/11.06 | (229) all_33_2_60 = all_29_6_46
% 37.78/11.06 |
% 37.78/11.06 | Instantiating formula (2) with xp, all_26_1_35, all_29_6_46 and discharging atoms aNaturalNumber0(xp) = all_29_6_46, aNaturalNumber0(xp) = all_26_1_35, yields:
% 37.78/11.06 | (230) all_29_6_46 = all_26_1_35
% 37.78/11.06 |
% 37.78/11.06 | Instantiating formula (2) with xp, all_20_1_20, all_29_6_46 and discharging atoms aNaturalNumber0(xp) = all_29_6_46, aNaturalNumber0(xp) = all_20_1_20, yields:
% 37.78/11.06 | (231) all_29_6_46 = all_20_1_20
% 37.78/11.06 |
% 37.78/11.06 | Instantiating formula (2) with xm, all_33_3_61, 0 and discharging atoms aNaturalNumber0(xm) = all_33_3_61, aNaturalNumber0(xm) = 0, yields:
% 37.78/11.06 | (232) all_33_3_61 = 0
% 37.78/11.06 |
% 37.78/11.06 | Instantiating formula (2) with xm, all_31_7_56, all_33_3_61 and discharging atoms aNaturalNumber0(xm) = all_33_3_61, aNaturalNumber0(xm) = all_31_7_56, yields:
% 37.78/11.07 | (233) all_33_3_61 = all_31_7_56
% 37.78/11.07 |
% 37.78/11.07 | Instantiating formula (2) with xm, all_29_7_47, all_40_1_67 and discharging atoms aNaturalNumber0(xm) = all_29_7_47, yields:
% 37.78/11.07 | (234) all_40_1_67 = all_29_7_47 | ~ (aNaturalNumber0(xm) = all_40_1_67)
% 37.78/11.07 |
% 37.78/11.07 | Instantiating formula (2) with xm, all_29_7_47, all_31_7_56 and discharging atoms aNaturalNumber0(xm) = all_31_7_56, aNaturalNumber0(xm) = all_29_7_47, yields:
% 37.78/11.07 | (235) all_31_7_56 = all_29_7_47
% 37.78/11.07 |
% 37.78/11.07 | Instantiating formula (2) with xm, all_18_1_17, all_29_7_47 and discharging atoms aNaturalNumber0(xm) = all_29_7_47, aNaturalNumber0(xm) = all_18_1_17, yields:
% 37.78/11.07 | (236) all_29_7_47 = all_18_1_17
% 37.78/11.07 |
% 37.78/11.07 | Instantiating formula (2) with xm, all_16_1_14, all_18_1_17 and discharging atoms aNaturalNumber0(xm) = all_18_1_17, aNaturalNumber0(xm) = all_16_1_14, yields:
% 37.78/11.07 | (237) all_18_1_17 = all_16_1_14
% 37.78/11.07 |
% 37.78/11.07 | Instantiating formula (2) with xm, all_14_1_11, all_16_1_14 and discharging atoms aNaturalNumber0(xm) = all_16_1_14, aNaturalNumber0(xm) = all_14_1_11, yields:
% 37.78/11.07 | (238) all_16_1_14 = all_14_1_11
% 37.78/11.07 |
% 37.78/11.07 | Instantiating formula (2) with xm, all_12_1_8, all_14_1_11 and discharging atoms aNaturalNumber0(xm) = all_14_1_11, aNaturalNumber0(xm) = all_12_1_8, yields:
% 37.78/11.07 | (239) all_14_1_11 = all_12_1_8
% 37.78/11.07 |
% 37.78/11.07 | Instantiating formula (2) with xn, all_29_8_48, all_31_8_57 and discharging atoms aNaturalNumber0(xn) = all_31_8_57, aNaturalNumber0(xn) = all_29_8_48, yields:
% 37.78/11.07 | (240) all_31_8_57 = all_29_8_48
% 37.78/11.07 |
% 37.78/11.07 | Instantiating formula (2) with xn, all_18_2_18, 0 and discharging atoms aNaturalNumber0(xn) = all_18_2_18, aNaturalNumber0(xn) = 0, yields:
% 37.78/11.07 | (241) all_18_2_18 = 0
% 37.78/11.07 |
% 37.78/11.07 | Instantiating formula (2) with xn, all_18_2_18, all_33_4_62 and discharging atoms aNaturalNumber0(xn) = all_33_4_62, aNaturalNumber0(xn) = all_18_2_18, yields:
% 37.78/11.07 | (242) all_33_4_62 = all_18_2_18
% 37.78/11.07 |
% 37.78/11.07 | Instantiating formula (2) with xn, all_18_2_18, all_29_8_48 and discharging atoms aNaturalNumber0(xn) = all_29_8_48, aNaturalNumber0(xn) = all_18_2_18, yields:
% 37.78/11.07 | (243) all_29_8_48 = all_18_2_18
% 37.78/11.07 |
% 37.78/11.07 | Instantiating formula (2) with xn, all_16_2_15, all_18_2_18 and discharging atoms aNaturalNumber0(xn) = all_18_2_18, aNaturalNumber0(xn) = all_16_2_15, yields:
% 37.78/11.07 | (244) all_18_2_18 = all_16_2_15
% 37.78/11.07 |
% 37.78/11.07 | Instantiating formula (2) with xn, all_14_2_12, all_31_8_57 and discharging atoms aNaturalNumber0(xn) = all_31_8_57, aNaturalNumber0(xn) = all_14_2_12, yields:
% 37.78/11.07 | (245) all_31_8_57 = all_14_2_12
% 37.78/11.07 |
% 37.78/11.07 | Instantiating formula (2) with xn, all_12_2_9, all_33_4_62 and discharging atoms aNaturalNumber0(xn) = all_33_4_62, aNaturalNumber0(xn) = all_12_2_9, yields:
% 37.78/11.07 | (246) all_33_4_62 = all_12_2_9
% 37.78/11.07 |
% 37.78/11.07 | Combining equations (224,225) yields a new equation:
% 37.78/11.07 | (247) all_31_6_55 = 0
% 37.78/11.07 |
% 37.78/11.07 | Combining equations (228,227) yields a new equation:
% 37.78/11.07 | (248) all_33_2_60 = 0
% 37.78/11.07 |
% 37.78/11.07 | Simplifying 248 yields:
% 37.78/11.07 | (249) all_33_2_60 = 0
% 37.78/11.07 |
% 37.78/11.07 | Combining equations (229,249) yields a new equation:
% 37.78/11.07 | (250) all_29_6_46 = 0
% 37.78/11.07 |
% 37.78/11.07 | Simplifying 250 yields:
% 37.78/11.07 | (251) all_29_6_46 = 0
% 37.78/11.07 |
% 37.78/11.07 | Combining equations (233,232) yields a new equation:
% 37.78/11.07 | (252) all_31_7_56 = 0
% 37.78/11.07 |
% 37.78/11.07 | Simplifying 252 yields:
% 37.78/11.07 | (253) all_31_7_56 = 0
% 37.78/11.07 |
% 37.78/11.07 | Combining equations (242,246) yields a new equation:
% 37.78/11.07 | (254) all_18_2_18 = all_12_2_9
% 37.78/11.07 |
% 37.78/11.07 | Simplifying 254 yields:
% 37.78/11.07 | (255) all_18_2_18 = all_12_2_9
% 37.78/11.07 |
% 37.78/11.07 | Combining equations (220,221) yields a new equation:
% 37.78/11.07 | (256) all_29_4_44 = all_0_6_6
% 37.78/11.07 |
% 37.78/11.07 | Combining equations (235,253) yields a new equation:
% 37.78/11.07 | (257) all_29_7_47 = 0
% 37.78/11.07 |
% 37.78/11.07 | Simplifying 257 yields:
% 37.78/11.07 | (258) all_29_7_47 = 0
% 37.78/11.07 |
% 37.78/11.07 | Combining equations (240,245) yields a new equation:
% 37.78/11.07 | (259) all_29_8_48 = all_14_2_12
% 37.78/11.07 |
% 37.78/11.07 | Simplifying 259 yields:
% 37.78/11.07 | (260) all_29_8_48 = all_14_2_12
% 37.78/11.07 |
% 37.78/11.07 | Combining equations (231,230) yields a new equation:
% 37.78/11.07 | (261) all_26_1_35 = all_20_1_20
% 37.78/11.07 |
% 37.78/11.07 | Combining equations (251,230) yields a new equation:
% 37.78/11.07 | (262) all_26_1_35 = 0
% 37.78/11.07 |
% 37.78/11.07 | Combining equations (236,258) yields a new equation:
% 37.78/11.07 | (263) all_18_1_17 = 0
% 37.78/11.07 |
% 37.78/11.07 | Simplifying 263 yields:
% 37.78/11.07 | (264) all_18_1_17 = 0
% 37.78/11.07 |
% 37.78/11.07 | Combining equations (243,260) yields a new equation:
% 37.78/11.07 | (265) all_18_2_18 = all_14_2_12
% 37.78/11.07 |
% 37.78/11.07 | Simplifying 265 yields:
% 37.78/11.07 | (266) all_18_2_18 = all_14_2_12
% 37.78/11.07 |
% 37.78/11.07 | Combining equations (261,262) yields a new equation:
% 37.78/11.07 | (267) all_20_1_20 = 0
% 37.78/11.07 |
% 37.78/11.07 | Simplifying 267 yields:
% 37.78/11.07 | (268) all_20_1_20 = 0
% 37.78/11.07 |
% 37.78/11.07 | Combining equations (223,222) yields a new equation:
% 37.78/11.07 | (269) all_20_2_21 = all_12_0_7
% 37.78/11.07 |
% 37.78/11.07 | Combining equations (237,264) yields a new equation:
% 37.78/11.07 | (270) all_16_1_14 = 0
% 37.78/11.07 |
% 37.78/11.07 | Simplifying 270 yields:
% 37.78/11.07 | (271) all_16_1_14 = 0
% 37.78/11.07 |
% 37.78/11.07 | Combining equations (255,244) yields a new equation:
% 37.78/11.07 | (272) all_16_2_15 = all_12_2_9
% 37.78/11.07 |
% 37.78/11.07 | Combining equations (241,244) yields a new equation:
% 37.78/11.07 | (273) all_16_2_15 = 0
% 37.78/11.07 |
% 37.78/11.07 | Combining equations (266,244) yields a new equation:
% 37.78/11.07 | (274) all_16_2_15 = all_14_2_12
% 37.78/11.07 |
% 37.78/11.08 | Combining equations (238,271) yields a new equation:
% 37.78/11.08 | (275) all_14_1_11 = 0
% 37.78/11.08 |
% 37.78/11.08 | Simplifying 275 yields:
% 37.78/11.08 | (276) all_14_1_11 = 0
% 37.78/11.08 |
% 37.78/11.08 | Combining equations (273,274) yields a new equation:
% 37.78/11.08 | (277) all_14_2_12 = 0
% 37.78/11.08 |
% 37.78/11.08 | Combining equations (272,274) yields a new equation:
% 37.78/11.08 | (278) all_14_2_12 = all_12_2_9
% 37.78/11.08 |
% 37.78/11.08 | Combining equations (239,276) yields a new equation:
% 37.78/11.08 | (279) all_12_1_8 = 0
% 37.78/11.08 |
% 37.78/11.08 | Simplifying 279 yields:
% 37.78/11.08 | (280) all_12_1_8 = 0
% 37.78/11.08 |
% 37.78/11.08 | Combining equations (277,278) yields a new equation:
% 37.78/11.08 | (281) all_12_2_9 = 0
% 37.78/11.08 |
% 37.78/11.08 | Combining equations (281,278) yields a new equation:
% 37.78/11.08 | (277) all_14_2_12 = 0
% 37.78/11.08 |
% 37.78/11.08 | Combining equations (277,274) yields a new equation:
% 37.78/11.08 | (273) all_16_2_15 = 0
% 37.78/11.08 |
% 37.78/11.08 | Combining equations (273,244) yields a new equation:
% 37.78/11.08 | (241) all_18_2_18 = 0
% 37.78/11.08 |
% 37.78/11.08 | Combining equations (269,222) yields a new equation:
% 37.78/11.08 | (223) all_26_2_36 = all_12_0_7
% 37.78/11.08 |
% 37.78/11.08 | Combining equations (256,221) yields a new equation:
% 37.78/11.08 | (220) all_31_4_53 = all_0_6_6
% 37.78/11.08 |
% 37.78/11.08 | From (217) and (146) follows:
% 37.78/11.08 | (62) isPrime0(xp) = 0
% 37.78/11.08 |
% 37.78/11.08 | From (220) and (157) follows:
% 37.78/11.08 | (288) sdtpldt0(all_0_6_6, xr) = all_31_3_52
% 37.78/11.08 |
% 37.78/11.08 | From (256) and (152) follows:
% 37.78/11.08 | (289) sdtpldt0(all_0_6_6, xp) = all_29_3_43
% 37.78/11.08 |
% 37.78/11.08 | From (256) and (150) follows:
% 37.78/11.08 | (38) sdtpldt0(xn, xm) = all_0_6_6
% 37.78/11.08 |
% 37.78/11.08 | From (247) and (161) follows:
% 37.78/11.08 | (32) aNaturalNumber0(xr) = 0
% 37.78/11.08 |
% 37.78/11.08 | From (226) and (189) follows:
% 37.78/11.08 | (179) aNaturalNumber0(xk) = all_40_1_67
% 37.78/11.08 |
% 37.78/11.08 | From (268) and (133) follows:
% 37.78/11.08 | (78) aNaturalNumber0(xp) = 0
% 37.78/11.08 |
% 37.78/11.08 | From (280) and (112) follows:
% 37.78/11.08 | (56) aNaturalNumber0(xm) = 0
% 37.78/11.08 |
% 37.78/11.08 | From (281) and (113) follows:
% 37.78/11.08 | (63) aNaturalNumber0(xn) = 0
% 37.78/11.08 |
% 37.78/11.08 +-Applying beta-rule and splitting (129), into two cases.
% 37.78/11.08 |-Branch one:
% 37.78/11.08 | (296) ~ (all_18_1_17 = 0)
% 37.78/11.08 |
% 37.78/11.08 | Equations (264) can reduce 296 to:
% 37.78/11.08 | (174) $false
% 37.78/11.08 |
% 37.78/11.08 |-The branch is then unsatisfiable
% 37.78/11.08 |-Branch two:
% 37.78/11.08 | (264) all_18_1_17 = 0
% 37.78/11.08 | (299) ~ (all_18_2_18 = 0) | all_18_0_16 = all_0_4_4
% 37.78/11.08 |
% 37.78/11.08 +-Applying beta-rule and splitting (299), into two cases.
% 37.78/11.08 |-Branch one:
% 37.78/11.08 | (300) ~ (all_18_2_18 = 0)
% 37.78/11.08 |
% 37.78/11.08 | Equations (241) can reduce 300 to:
% 37.78/11.08 | (174) $false
% 37.78/11.08 |
% 37.78/11.08 |-The branch is then unsatisfiable
% 37.78/11.08 |-Branch two:
% 37.78/11.08 | (241) all_18_2_18 = 0
% 37.78/11.08 | (303) all_18_0_16 = all_0_4_4
% 37.78/11.08 |
% 37.78/11.08 | From (303) and (126) follows:
% 37.78/11.08 | (304) sdtasdt0(xm, xn) = all_0_4_4
% 37.78/11.08 |
% 37.78/11.08 +-Applying beta-rule and splitting (135), into two cases.
% 37.78/11.08 |-Branch one:
% 37.78/11.08 | (305) all_22_0_22 = xp & all_22_1_23 = 0 & sdtpldt0(xn, all_22_2_24) = xp & aNaturalNumber0(all_22_2_24) = 0
% 37.78/11.08 |
% 37.78/11.08 | Applying alpha-rule on (305) yields:
% 37.78/11.08 | (306) all_22_0_22 = xp
% 37.78/11.08 | (307) all_22_1_23 = 0
% 37.78/11.08 | (308) sdtpldt0(xn, all_22_2_24) = xp
% 37.78/11.08 | (309) aNaturalNumber0(all_22_2_24) = 0
% 37.78/11.08 |
% 37.78/11.08 +-Applying beta-rule and splitting (219), into two cases.
% 37.78/11.08 |-Branch one:
% 37.78/11.08 | (310) ~ (sdtpldt0(all_0_6_6, xp) = all_29_3_43)
% 37.78/11.08 |
% 37.78/11.08 | Using (289) and (310) yields:
% 37.78/11.08 | (311) $false
% 37.78/11.08 |
% 37.78/11.08 |-The branch is then unsatisfiable
% 37.78/11.08 |-Branch two:
% 37.78/11.08 | (289) sdtpldt0(all_0_6_6, xp) = all_29_3_43
% 37.78/11.08 | (313) all_29_3_43 = all_0_5_5
% 37.78/11.08 |
% 37.78/11.08 | From (313) and (289) follows:
% 37.78/11.08 | (6) sdtpldt0(all_0_6_6, xp) = all_0_5_5
% 37.78/11.08 |
% 37.78/11.08 +-Applying beta-rule and splitting (124), into two cases.
% 37.78/11.08 |-Branch one:
% 37.78/11.08 | (315) ~ (all_16_1_14 = 0)
% 37.78/11.08 |
% 37.78/11.08 | Equations (271) can reduce 315 to:
% 37.78/11.08 | (174) $false
% 37.78/11.08 |
% 37.78/11.08 |-The branch is then unsatisfiable
% 37.78/11.08 |-Branch two:
% 37.78/11.08 | (271) all_16_1_14 = 0
% 37.78/11.08 | (318) ~ (all_16_2_15 = 0) | all_16_0_13 = 0
% 37.78/11.08 |
% 37.78/11.08 +-Applying beta-rule and splitting (318), into two cases.
% 37.78/11.08 |-Branch one:
% 37.78/11.08 | (319) ~ (all_16_2_15 = 0)
% 37.78/11.08 |
% 37.78/11.08 | Equations (273) can reduce 319 to:
% 37.78/11.08 | (174) $false
% 37.78/11.08 |
% 37.78/11.08 |-The branch is then unsatisfiable
% 37.78/11.08 |-Branch two:
% 37.78/11.08 | (273) all_16_2_15 = 0
% 37.78/11.08 | (322) all_16_0_13 = 0
% 37.78/11.08 |
% 37.78/11.08 | From (322) and (121) follows:
% 37.78/11.09 | (323) aNaturalNumber0(all_0_4_4) = 0
% 37.78/11.09 |
% 37.78/11.09 +-Applying beta-rule and splitting (136), into two cases.
% 37.78/11.09 |-Branch one:
% 37.78/11.09 | (324) all_23_0_25 = xp & all_23_1_26 = 0 & sdtpldt0(xm, all_23_2_27) = xp & aNaturalNumber0(all_23_2_27) = 0
% 37.78/11.09 |
% 37.78/11.09 | Applying alpha-rule on (324) yields:
% 37.78/11.09 | (325) all_23_0_25 = xp
% 37.78/11.09 | (326) all_23_1_26 = 0
% 37.78/11.09 | (327) sdtpldt0(xm, all_23_2_27) = xp
% 37.78/11.09 | (328) aNaturalNumber0(all_23_2_27) = 0
% 37.78/11.09 |
% 37.78/11.09 +-Applying beta-rule and splitting (95), into two cases.
% 37.78/11.09 |-Branch one:
% 37.78/11.09 | (329) ~ (sdtlseqdt0(xp, xp) = all_0_1_1)
% 37.78/11.09 |
% 37.78/11.09 +-Applying beta-rule and splitting (114), into two cases.
% 37.78/11.09 |-Branch one:
% 37.78/11.09 | (330) ~ (all_12_1_8 = 0)
% 37.78/11.09 |
% 37.78/11.09 | Equations (280) can reduce 330 to:
% 37.78/11.09 | (174) $false
% 37.78/11.09 |
% 37.78/11.09 |-The branch is then unsatisfiable
% 37.78/11.09 |-Branch two:
% 37.78/11.09 | (280) all_12_1_8 = 0
% 37.78/11.09 | (333) ~ (all_12_2_9 = 0) | all_12_0_7 = 0
% 37.78/11.09 |
% 37.78/11.09 +-Applying beta-rule and splitting (137), into two cases.
% 37.78/11.09 |-Branch one:
% 37.78/11.09 | (334) all_24_0_28 = all_0_4_4 & all_24_1_29 = 0 & sdtasdt0(xp, all_24_2_30) = all_0_4_4 & aNaturalNumber0(all_24_2_30) = 0
% 37.78/11.09 |
% 37.78/11.09 | Applying alpha-rule on (334) yields:
% 37.78/11.09 | (335) all_24_0_28 = all_0_4_4
% 37.78/11.09 | (336) all_24_1_29 = 0
% 37.78/11.09 | (337) sdtasdt0(xp, all_24_2_30) = all_0_4_4
% 37.78/11.09 | (338) aNaturalNumber0(all_24_2_30) = 0
% 37.78/11.09 |
% 37.78/11.09 +-Applying beta-rule and splitting (333), into two cases.
% 37.78/11.09 |-Branch one:
% 37.78/11.09 | (339) ~ (all_12_2_9 = 0)
% 37.78/11.09 |
% 37.78/11.09 | Equations (281) can reduce 339 to:
% 37.78/11.09 | (174) $false
% 37.78/11.09 |
% 37.78/11.09 |-The branch is then unsatisfiable
% 37.78/11.09 |-Branch two:
% 37.78/11.09 | (281) all_12_2_9 = 0
% 37.78/11.09 | (342) all_12_0_7 = 0
% 37.78/11.09 |
% 37.78/11.09 | Combining equations (342,223) yields a new equation:
% 37.78/11.09 | (343) all_26_2_36 = 0
% 37.78/11.09 |
% 37.78/11.09 +-Applying beta-rule and splitting (142), into two cases.
% 37.78/11.09 |-Branch one:
% 37.78/11.09 | (344) ~ (all_26_1_35 = 0)
% 37.78/11.09 |
% 37.78/11.09 | Equations (262) can reduce 344 to:
% 37.78/11.09 | (174) $false
% 37.78/11.09 |
% 37.78/11.09 |-The branch is then unsatisfiable
% 37.78/11.09 |-Branch two:
% 37.78/11.09 | (262) all_26_1_35 = 0
% 37.78/11.09 | (347) ~ (all_26_2_36 = 0) | all_26_0_34 = all_0_5_5
% 37.78/11.09 |
% 37.78/11.09 +-Applying beta-rule and splitting (347), into two cases.
% 37.78/11.09 |-Branch one:
% 37.78/11.09 | (348) ~ (all_26_2_36 = 0)
% 37.78/11.09 |
% 37.78/11.09 | Equations (343) can reduce 348 to:
% 37.78/11.09 | (174) $false
% 37.78/11.09 |
% 37.78/11.09 |-The branch is then unsatisfiable
% 37.78/11.09 |-Branch two:
% 37.78/11.09 | (343) all_26_2_36 = 0
% 37.78/11.09 | (351) all_26_0_34 = all_0_5_5
% 37.78/11.09 |
% 37.78/11.09 | From (351) and (139) follows:
% 37.78/11.09 | (352) sdtpldt0(xp, all_0_6_6) = all_0_5_5
% 37.78/11.09 |
% 37.78/11.09 +-Applying beta-rule and splitting (119), into two cases.
% 37.78/11.09 |-Branch one:
% 37.78/11.09 | (353) ~ (all_14_1_11 = 0)
% 37.78/11.09 |
% 37.78/11.09 | Equations (276) can reduce 353 to:
% 37.78/11.09 | (174) $false
% 37.78/11.09 |
% 37.78/11.09 |-The branch is then unsatisfiable
% 37.78/11.09 |-Branch two:
% 37.78/11.09 | (276) all_14_1_11 = 0
% 37.78/11.09 | (356) ~ (all_14_2_12 = 0) | all_14_0_10 = all_0_6_6
% 37.78/11.09 |
% 37.78/11.09 +-Applying beta-rule and splitting (143), into two cases.
% 37.78/11.09 |-Branch one:
% 37.78/11.09 | (357) all_28_0_37 = all_0_4_4 & all_28_1_38 = 0 & sdtasdt0(xr, all_28_2_39) = all_0_4_4 & aNaturalNumber0(all_28_2_39) = 0
% 37.78/11.09 |
% 37.78/11.09 | Applying alpha-rule on (357) yields:
% 37.78/11.09 | (358) all_28_0_37 = all_0_4_4
% 37.78/11.09 | (359) all_28_1_38 = 0
% 37.78/11.09 | (360) sdtasdt0(xr, all_28_2_39) = all_0_4_4
% 37.78/11.09 | (361) aNaturalNumber0(all_28_2_39) = 0
% 37.78/11.09 |
% 37.78/11.09 +-Applying beta-rule and splitting (356), into two cases.
% 37.78/11.09 |-Branch one:
% 37.78/11.09 | (362) ~ (all_14_2_12 = 0)
% 37.78/11.09 |
% 37.78/11.09 | Equations (277) can reduce 362 to:
% 37.78/11.09 | (174) $false
% 37.78/11.09 |
% 37.78/11.09 |-The branch is then unsatisfiable
% 37.78/11.09 |-Branch two:
% 37.78/11.09 | (277) all_14_2_12 = 0
% 37.78/11.09 | (365) all_14_0_10 = all_0_6_6
% 37.78/11.09 |
% 37.78/11.09 | From (365) and (116) follows:
% 37.78/11.09 | (366) sdtpldt0(xm, xn) = all_0_6_6
% 37.78/11.09 |
% 37.78/11.09 | Using (49) and (329) yields:
% 37.78/11.09 | (367) ~ (xk = xp)
% 37.78/11.09 |
% 37.78/11.09 +-Applying beta-rule and splitting (79), into two cases.
% 37.78/11.09 |-Branch one:
% 37.78/11.09 | (368) ~ (all_0_0_0 = 0)
% 37.78/11.09 |
% 37.78/11.09 +-Applying beta-rule and splitting (181), into two cases.
% 37.78/11.09 |-Branch one:
% 37.78/11.09 | (369) ~ (all_40_1_67 = 0)
% 37.78/11.09 |
% 37.78/11.09 | Instantiating formula (27) with all_62_0_73, xp and discharging atoms isPrime0(xp) = 0, doDivides0(all_62_0_73, xp) = 0, yields:
% 37.78/11.09 | (370) all_62_0_73 = xp | all_62_0_73 = sz10 | ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_62_0_73) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0))
% 37.78/11.09 |
% 37.78/11.09 | Instantiating formula (21) with xp, all_62_0_73 and discharging atoms doDivides0(all_62_0_73, xp) = 0, yields:
% 37.78/11.09 | (371) xp = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_62_0_73, xp) = v2 & aNaturalNumber0(all_62_0_73) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 37.78/11.09 |
% 37.78/11.09 | Instantiating formula (21) with xr, all_57_0_72 and discharging atoms doDivides0(all_57_0_72, xr) = 0, yields:
% 37.78/11.09 | (372) xr = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_57_0_72, xr) = v2 & aNaturalNumber0(all_57_0_72) = v0 & aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 37.78/11.09 |
% 37.78/11.09 | Instantiating formula (55) with all_0_4_4, xr, all_28_2_39, xr and discharging atoms doDivides0(xr, all_0_4_4) = 0, sdtasdt0(xr, all_28_2_39) = all_0_4_4, yields:
% 37.78/11.09 | (373) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xr) = v3 & doDivides0(xr, all_28_2_39) = v8 & doDivides0(xr, xr) = v7 & iLess0(v5, all_0_5_5) = v6 & sdtpldt0(v4, xr) = v5 & sdtpldt0(xr, all_28_2_39) = v4 & aNaturalNumber0(all_28_2_39) = v1 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xr) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 37.78/11.10 |
% 37.78/11.10 | Instantiating formula (55) with all_0_4_4, xp, all_28_2_39, xr and discharging atoms doDivides0(xp, all_0_4_4) = 0, sdtasdt0(xr, all_28_2_39) = all_0_4_4, yields:
% 37.78/11.10 | (374) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, all_28_2_39) = v8 & doDivides0(xp, xr) = v7 & iLess0(v5, all_0_5_5) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xr, all_28_2_39) = v4 & aNaturalNumber0(all_28_2_39) = v1 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xp) = v2 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 38.04/11.10 |
% 38.04/11.10 | Instantiating formula (28) with all_0_4_4, all_28_2_39, xr and discharging atoms sdtasdt0(xr, all_28_2_39) = all_0_4_4, yields:
% 38.04/11.10 | (375) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_28_2_39, xr) = v2 & aNaturalNumber0(all_28_2_39) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_4_4))
% 38.04/11.10 |
% 38.04/11.10 | Instantiating formula (74) with all_24_2_30, xk, all_0_4_4, xp and discharging atoms sdtsldt0(all_0_4_4, xp) = xk, sdtasdt0(xp, all_24_2_30) = all_0_4_4, yields:
% 38.04/11.10 | (376) all_24_2_30 = xk | xp = sz00 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_24_2_30) = v0) | (doDivides0(xp, all_0_4_4) = v2 & aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 38.04/11.10 |
% 38.04/11.10 | Instantiating formula (55) with all_0_4_4, xr, all_24_2_30, xp and discharging atoms doDivides0(xr, all_0_4_4) = 0, sdtasdt0(xp, all_24_2_30) = all_0_4_4, yields:
% 38.04/11.10 | (377) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xr) = v3 & doDivides0(xr, all_24_2_30) = v8 & doDivides0(xr, xp) = v7 & iLess0(v5, all_0_5_5) = v6 & sdtpldt0(v4, xr) = v5 & sdtpldt0(xp, all_24_2_30) = v4 & aNaturalNumber0(all_24_2_30) = v1 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 38.04/11.10 |
% 38.04/11.10 | Instantiating formula (55) with all_0_4_4, xp, all_24_2_30, xp and discharging atoms doDivides0(xp, all_0_4_4) = 0, sdtasdt0(xp, all_24_2_30) = all_0_4_4, yields:
% 38.04/11.10 | (378) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, all_24_2_30) = v8 & doDivides0(xp, xp) = v7 & iLess0(v5, all_0_5_5) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xp, all_24_2_30) = v4 & aNaturalNumber0(all_24_2_30) = v1 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 38.04/11.10 |
% 38.04/11.10 | Instantiating formula (28) with all_0_4_4, all_24_2_30, xp and discharging atoms sdtasdt0(xp, all_24_2_30) = all_0_4_4, yields:
% 38.04/11.10 | (379) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_24_2_30, xp) = v2 & aNaturalNumber0(all_24_2_30) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_4_4))
% 38.04/11.10 |
% 38.04/11.10 | Instantiating formula (55) with all_0_4_4, xr, xn, xm and discharging atoms doDivides0(xr, all_0_4_4) = 0, sdtasdt0(xm, xn) = all_0_4_4, yields:
% 38.04/11.10 | (380) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xr) = v3 & doDivides0(xr, xm) = v7 & doDivides0(xr, xn) = v8 & iLess0(v5, all_0_5_5) = v6 & sdtpldt0(v4, xr) = v5 & sdtpldt0(xm, xn) = v4 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 38.04/11.10 |
% 38.04/11.10 | Instantiating formula (55) with all_0_4_4, xp, xn, xm and discharging atoms doDivides0(xp, all_0_4_4) = 0, sdtasdt0(xm, xn) = all_0_4_4, yields:
% 38.04/11.10 | (381) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, xm) = v7 & doDivides0(xp, xn) = v8 & iLess0(v5, all_0_5_5) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xm, xn) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 38.04/11.10 |
% 38.04/11.10 | Instantiating formula (58) with all_31_3_52, all_0_6_6, xr, xm, xn and discharging atoms sdtpldt0(all_0_6_6, xr) = all_31_3_52, sdtpldt0(xn, xm) = all_0_6_6, yields:
% 38.04/11.10 | (382) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xm, xr) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_31_3_52))
% 38.04/11.10 |
% 38.04/11.10 | Instantiating formula (75) with all_31_3_52, xr, all_0_6_6 and discharging atoms sdtpldt0(all_0_6_6, xr) = all_31_3_52, yields:
% 38.04/11.10 | (383) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xr, all_0_6_6) = v2 & aNaturalNumber0(all_0_6_6) = v0 & aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_31_3_52))
% 38.04/11.10 |
% 38.04/11.10 | Instantiating formula (29) with xp, all_23_2_27, xm, all_62_0_73 and discharging atoms doDivides0(all_62_0_73, xp) = 0, sdtpldt0(xm, all_23_2_27) = xp, yields:
% 38.04/11.10 | (384) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(all_62_0_73, all_23_2_27) = v4 & doDivides0(all_62_0_73, xm) = v3 & aNaturalNumber0(all_62_0_73) = v0 & aNaturalNumber0(all_23_2_27) = v2 & aNaturalNumber0(xm) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 38.04/11.10 |
% 38.04/11.10 | Instantiating formula (58) with all_0_5_5, xp, all_0_6_6, all_23_2_27, xm and discharging atoms sdtpldt0(xp, all_0_6_6) = all_0_5_5, sdtpldt0(xm, all_23_2_27) = xp, yields:
% 38.04/11.10 | (385) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_23_2_27, all_0_6_6) = v3 & sdtpldt0(xm, v3) = v4 & aNaturalNumber0(all_23_2_27) = v1 & aNaturalNumber0(all_0_6_6) = v2 & aNaturalNumber0(xm) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_5_5))
% 38.04/11.10 |
% 38.04/11.10 | Instantiating formula (75) with xp, all_23_2_27, xm and discharging atoms sdtpldt0(xm, all_23_2_27) = xp, yields:
% 38.04/11.10 | (386) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_23_2_27, xm) = v2 & aNaturalNumber0(all_23_2_27) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xp))
% 38.04/11.10 |
% 38.04/11.10 | Instantiating formula (75) with all_33_1_59, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_33_1_59, yields:
% 38.04/11.10 | (387) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, xm) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_33_1_59))
% 38.04/11.10 |
% 38.04/11.10 | Instantiating formula (57) with all_33_1_59, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_33_1_59, yields:
% 38.04/11.10 | (388) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_33_1_59) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 38.04/11.10 |
% 38.04/11.10 | Instantiating formula (58) with all_0_5_5, all_0_6_6, xp, xn, xm and discharging atoms sdtpldt0(all_0_6_6, xp) = all_0_5_5, sdtpldt0(xm, xn) = all_0_6_6, yields:
% 38.04/11.10 | (389) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xm, v3) = v4 & sdtpldt0(xn, xp) = v3 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_5_5))
% 38.04/11.10 |
% 38.04/11.10 | Instantiating formula (58) with all_31_3_52, all_0_6_6, xr, xn, xm and discharging atoms sdtpldt0(all_0_6_6, xr) = all_31_3_52, sdtpldt0(xm, xn) = all_0_6_6, yields:
% 38.04/11.10 | (390) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xm, v3) = v4 & sdtpldt0(xn, xr) = v3 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_31_3_52))
% 38.04/11.10 |
% 38.04/11.10 | Instantiating formula (67) with all_0_6_6, all_33_1_59, xn, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_33_1_59, sdtpldt0(xm, xn) = all_0_6_6, yields:
% 38.04/11.10 | (391) xp = xn | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xp, xm) = v3 & sdtpldt0(xn, xm) = v4 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v4 = v3) & ~ (all_33_1_59 = all_0_6_6))))
% 38.04/11.10 |
% 38.04/11.10 | Instantiating formula (67) with all_33_1_59, all_0_6_6, xp, xn, xm and discharging atoms sdtpldt0(xm, xp) = all_33_1_59, sdtpldt0(xm, xn) = all_0_6_6, yields:
% 38.04/11.10 | (392) xp = xn | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xp, xm) = v4 & sdtpldt0(xn, xm) = v3 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v4 = v3) & ~ (all_33_1_59 = all_0_6_6))))
% 38.04/11.10 |
% 38.04/11.10 | Instantiating formula (29) with xp, all_22_2_24, xn, all_62_0_73 and discharging atoms doDivides0(all_62_0_73, xp) = 0, sdtpldt0(xn, all_22_2_24) = xp, yields:
% 38.04/11.10 | (393) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(all_62_0_73, all_22_2_24) = v4 & doDivides0(all_62_0_73, xn) = v3 & aNaturalNumber0(all_62_0_73) = v0 & aNaturalNumber0(all_22_2_24) = v2 & aNaturalNumber0(xn) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 38.04/11.11 |
% 38.04/11.11 | Instantiating formula (37) with all_62_0_73 and discharging atoms aNaturalNumber0(all_62_0_73) = 0, yields:
% 38.04/11.11 | (394) all_62_0_73 = sz10 | all_62_0_73 = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_62_0_73) = 0 & aNaturalNumber0(v0) = 0)
% 38.04/11.11 |
% 38.04/11.11 | Instantiating (393) with all_179_0_77, all_179_1_78, all_179_2_79, all_179_3_80, all_179_4_81 yields:
% 38.04/11.11 | (395) doDivides0(all_62_0_73, all_22_2_24) = all_179_0_77 & doDivides0(all_62_0_73, xn) = all_179_1_78 & aNaturalNumber0(all_62_0_73) = all_179_4_81 & aNaturalNumber0(all_22_2_24) = all_179_2_79 & aNaturalNumber0(xn) = all_179_3_80 & ( ~ (all_179_1_78 = 0) | ~ (all_179_2_79 = 0) | ~ (all_179_3_80 = 0) | ~ (all_179_4_81 = 0) | all_179_0_77 = 0)
% 38.04/11.11 |
% 38.04/11.11 | Applying alpha-rule on (395) yields:
% 38.04/11.11 | (396) doDivides0(all_62_0_73, xn) = all_179_1_78
% 38.04/11.11 | (397) aNaturalNumber0(all_62_0_73) = all_179_4_81
% 38.04/11.11 | (398) aNaturalNumber0(all_22_2_24) = all_179_2_79
% 38.04/11.11 | (399) ~ (all_179_1_78 = 0) | ~ (all_179_2_79 = 0) | ~ (all_179_3_80 = 0) | ~ (all_179_4_81 = 0) | all_179_0_77 = 0
% 38.04/11.11 | (400) aNaturalNumber0(xn) = all_179_3_80
% 38.04/11.11 | (401) doDivides0(all_62_0_73, all_22_2_24) = all_179_0_77
% 38.04/11.11 |
% 38.04/11.11 | Instantiating (383) with all_185_0_88, all_185_1_89, all_185_2_90 yields:
% 38.04/11.11 | (402) sdtpldt0(xr, all_0_6_6) = all_185_0_88 & aNaturalNumber0(all_0_6_6) = all_185_2_90 & aNaturalNumber0(xr) = all_185_1_89 & ( ~ (all_185_1_89 = 0) | ~ (all_185_2_90 = 0) | all_185_0_88 = all_31_3_52)
% 38.04/11.11 |
% 38.04/11.11 | Applying alpha-rule on (402) yields:
% 38.04/11.11 | (403) sdtpldt0(xr, all_0_6_6) = all_185_0_88
% 38.04/11.11 | (404) aNaturalNumber0(all_0_6_6) = all_185_2_90
% 38.04/11.11 | (405) aNaturalNumber0(xr) = all_185_1_89
% 38.04/11.11 | (406) ~ (all_185_1_89 = 0) | ~ (all_185_2_90 = 0) | all_185_0_88 = all_31_3_52
% 38.04/11.11 |
% 38.04/11.11 | Instantiating (375) with all_187_0_91, all_187_1_92, all_187_2_93 yields:
% 38.04/11.11 | (407) sdtasdt0(all_28_2_39, xr) = all_187_0_91 & aNaturalNumber0(all_28_2_39) = all_187_1_92 & aNaturalNumber0(xr) = all_187_2_93 & ( ~ (all_187_1_92 = 0) | ~ (all_187_2_93 = 0) | all_187_0_91 = all_0_4_4)
% 38.04/11.11 |
% 38.04/11.11 | Applying alpha-rule on (407) yields:
% 38.04/11.11 | (408) sdtasdt0(all_28_2_39, xr) = all_187_0_91
% 38.04/11.11 | (409) aNaturalNumber0(all_28_2_39) = all_187_1_92
% 38.04/11.11 | (410) aNaturalNumber0(xr) = all_187_2_93
% 38.04/11.11 | (411) ~ (all_187_1_92 = 0) | ~ (all_187_2_93 = 0) | all_187_0_91 = all_0_4_4
% 38.04/11.11 |
% 38.04/11.11 | Instantiating (374) with all_189_0_94, all_189_1_95, all_189_2_96, all_189_3_97, all_189_4_98, all_189_5_99, all_189_6_100, all_189_7_101, all_189_8_102 yields:
% 38.04/11.11 | (412) isPrime0(xp) = all_189_5_99 & doDivides0(xp, all_28_2_39) = all_189_0_94 & doDivides0(xp, xr) = all_189_1_95 & iLess0(all_189_3_97, all_0_5_5) = all_189_2_96 & sdtpldt0(all_189_4_98, xp) = all_189_3_97 & sdtpldt0(xr, all_28_2_39) = all_189_4_98 & aNaturalNumber0(all_28_2_39) = all_189_7_101 & aNaturalNumber0(xr) = all_189_8_102 & aNaturalNumber0(xp) = all_189_6_100 & ( ~ (all_189_2_96 = 0) | ~ (all_189_5_99 = 0) | ~ (all_189_6_100 = 0) | ~ (all_189_7_101 = 0) | ~ (all_189_8_102 = 0) | all_189_0_94 = 0 | all_189_1_95 = 0)
% 38.04/11.11 |
% 38.04/11.11 | Applying alpha-rule on (412) yields:
% 38.04/11.11 | (413) ~ (all_189_2_96 = 0) | ~ (all_189_5_99 = 0) | ~ (all_189_6_100 = 0) | ~ (all_189_7_101 = 0) | ~ (all_189_8_102 = 0) | all_189_0_94 = 0 | all_189_1_95 = 0
% 38.04/11.11 | (414) iLess0(all_189_3_97, all_0_5_5) = all_189_2_96
% 38.04/11.11 | (415) isPrime0(xp) = all_189_5_99
% 38.04/11.11 | (416) aNaturalNumber0(xr) = all_189_8_102
% 38.04/11.11 | (417) sdtpldt0(all_189_4_98, xp) = all_189_3_97
% 38.04/11.11 | (418) doDivides0(xp, xr) = all_189_1_95
% 38.04/11.11 | (419) sdtpldt0(xr, all_28_2_39) = all_189_4_98
% 38.04/11.11 | (420) doDivides0(xp, all_28_2_39) = all_189_0_94
% 38.04/11.11 | (421) aNaturalNumber0(all_28_2_39) = all_189_7_101
% 38.04/11.11 | (422) aNaturalNumber0(xp) = all_189_6_100
% 38.04/11.11 |
% 38.04/11.11 | Instantiating (373) with all_191_0_103, all_191_1_104, all_191_2_105, all_191_3_106, all_191_4_107, all_191_5_108, all_191_6_109, all_191_7_110, all_191_8_111 yields:
% 38.04/11.11 | (423) isPrime0(xr) = all_191_5_108 & doDivides0(xr, all_28_2_39) = all_191_0_103 & doDivides0(xr, xr) = all_191_1_104 & iLess0(all_191_3_106, all_0_5_5) = all_191_2_105 & sdtpldt0(all_191_4_107, xr) = all_191_3_106 & sdtpldt0(xr, all_28_2_39) = all_191_4_107 & aNaturalNumber0(all_28_2_39) = all_191_7_110 & aNaturalNumber0(xr) = all_191_6_109 & aNaturalNumber0(xr) = all_191_8_111 & ( ~ (all_191_2_105 = 0) | ~ (all_191_5_108 = 0) | ~ (all_191_6_109 = 0) | ~ (all_191_7_110 = 0) | ~ (all_191_8_111 = 0) | all_191_0_103 = 0 | all_191_1_104 = 0)
% 38.04/11.11 |
% 38.04/11.11 | Applying alpha-rule on (423) yields:
% 38.04/11.11 | (424) ~ (all_191_2_105 = 0) | ~ (all_191_5_108 = 0) | ~ (all_191_6_109 = 0) | ~ (all_191_7_110 = 0) | ~ (all_191_8_111 = 0) | all_191_0_103 = 0 | all_191_1_104 = 0
% 38.04/11.11 | (425) doDivides0(xr, all_28_2_39) = all_191_0_103
% 38.04/11.11 | (426) isPrime0(xr) = all_191_5_108
% 38.04/11.11 | (427) sdtpldt0(xr, all_28_2_39) = all_191_4_107
% 38.04/11.11 | (428) aNaturalNumber0(xr) = all_191_8_111
% 38.04/11.11 | (429) aNaturalNumber0(xr) = all_191_6_109
% 38.04/11.11 | (430) iLess0(all_191_3_106, all_0_5_5) = all_191_2_105
% 38.04/11.11 | (431) aNaturalNumber0(all_28_2_39) = all_191_7_110
% 38.04/11.11 | (432) sdtpldt0(all_191_4_107, xr) = all_191_3_106
% 38.04/11.11 | (433) doDivides0(xr, xr) = all_191_1_104
% 38.04/11.11 |
% 38.04/11.11 | Instantiating (382) with all_195_0_118, all_195_1_119, all_195_2_120, all_195_3_121, all_195_4_122 yields:
% 38.04/11.11 | (434) sdtpldt0(xm, xr) = all_195_1_119 & sdtpldt0(xn, all_195_1_119) = all_195_0_118 & aNaturalNumber0(xr) = all_195_2_120 & aNaturalNumber0(xm) = all_195_3_121 & aNaturalNumber0(xn) = all_195_4_122 & ( ~ (all_195_2_120 = 0) | ~ (all_195_3_121 = 0) | ~ (all_195_4_122 = 0) | all_195_0_118 = all_31_3_52)
% 38.04/11.11 |
% 38.04/11.11 | Applying alpha-rule on (434) yields:
% 38.04/11.11 | (435) sdtpldt0(xn, all_195_1_119) = all_195_0_118
% 38.04/11.11 | (436) aNaturalNumber0(xr) = all_195_2_120
% 38.04/11.11 | (437) aNaturalNumber0(xm) = all_195_3_121
% 38.04/11.11 | (438) sdtpldt0(xm, xr) = all_195_1_119
% 38.04/11.11 | (439) ~ (all_195_2_120 = 0) | ~ (all_195_3_121 = 0) | ~ (all_195_4_122 = 0) | all_195_0_118 = all_31_3_52
% 38.04/11.11 | (440) aNaturalNumber0(xn) = all_195_4_122
% 38.04/11.11 |
% 38.04/11.11 | Instantiating (381) with all_197_0_123, all_197_1_124, all_197_2_125, all_197_3_126, all_197_4_127, all_197_5_128, all_197_6_129, all_197_7_130, all_197_8_131 yields:
% 38.04/11.11 | (441) isPrime0(xp) = all_197_5_128 & doDivides0(xp, xm) = all_197_1_124 & doDivides0(xp, xn) = all_197_0_123 & iLess0(all_197_3_126, all_0_5_5) = all_197_2_125 & sdtpldt0(all_197_4_127, xp) = all_197_3_126 & sdtpldt0(xm, xn) = all_197_4_127 & aNaturalNumber0(xp) = all_197_6_129 & aNaturalNumber0(xm) = all_197_8_131 & aNaturalNumber0(xn) = all_197_7_130 & ( ~ (all_197_2_125 = 0) | ~ (all_197_5_128 = 0) | ~ (all_197_6_129 = 0) | ~ (all_197_7_130 = 0) | ~ (all_197_8_131 = 0) | all_197_0_123 = 0 | all_197_1_124 = 0)
% 38.04/11.11 |
% 38.04/11.11 | Applying alpha-rule on (441) yields:
% 38.04/11.11 | (442) sdtpldt0(all_197_4_127, xp) = all_197_3_126
% 38.04/11.12 | (443) doDivides0(xp, xm) = all_197_1_124
% 38.04/11.12 | (444) ~ (all_197_2_125 = 0) | ~ (all_197_5_128 = 0) | ~ (all_197_6_129 = 0) | ~ (all_197_7_130 = 0) | ~ (all_197_8_131 = 0) | all_197_0_123 = 0 | all_197_1_124 = 0
% 38.04/11.12 | (445) aNaturalNumber0(xn) = all_197_7_130
% 38.04/11.12 | (446) aNaturalNumber0(xp) = all_197_6_129
% 38.04/11.12 | (447) isPrime0(xp) = all_197_5_128
% 38.04/11.12 | (448) sdtpldt0(xm, xn) = all_197_4_127
% 38.04/11.12 | (449) aNaturalNumber0(xm) = all_197_8_131
% 38.04/11.12 | (450) doDivides0(xp, xn) = all_197_0_123
% 38.04/11.12 | (451) iLess0(all_197_3_126, all_0_5_5) = all_197_2_125
% 38.04/11.12 |
% 38.04/11.12 | Instantiating (380) with all_199_0_132, all_199_1_133, all_199_2_134, all_199_3_135, all_199_4_136, all_199_5_137, all_199_6_138, all_199_7_139, all_199_8_140 yields:
% 38.04/11.12 | (452) isPrime0(xr) = all_199_5_137 & doDivides0(xr, xm) = all_199_1_133 & doDivides0(xr, xn) = all_199_0_132 & iLess0(all_199_3_135, all_0_5_5) = all_199_2_134 & sdtpldt0(all_199_4_136, xr) = all_199_3_135 & sdtpldt0(xm, xn) = all_199_4_136 & aNaturalNumber0(xr) = all_199_6_138 & aNaturalNumber0(xm) = all_199_8_140 & aNaturalNumber0(xn) = all_199_7_139 & ( ~ (all_199_2_134 = 0) | ~ (all_199_5_137 = 0) | ~ (all_199_6_138 = 0) | ~ (all_199_7_139 = 0) | ~ (all_199_8_140 = 0) | all_199_0_132 = 0 | all_199_1_133 = 0)
% 38.04/11.12 |
% 38.04/11.12 | Applying alpha-rule on (452) yields:
% 38.04/11.12 | (453) aNaturalNumber0(xr) = all_199_6_138
% 38.04/11.12 | (454) doDivides0(xr, xn) = all_199_0_132
% 38.04/11.12 | (455) iLess0(all_199_3_135, all_0_5_5) = all_199_2_134
% 38.04/11.12 | (456) doDivides0(xr, xm) = all_199_1_133
% 38.04/11.12 | (457) sdtpldt0(all_199_4_136, xr) = all_199_3_135
% 38.04/11.12 | (458) aNaturalNumber0(xm) = all_199_8_140
% 38.04/11.12 | (459) sdtpldt0(xm, xn) = all_199_4_136
% 38.04/11.12 | (460) isPrime0(xr) = all_199_5_137
% 38.04/11.12 | (461) ~ (all_199_2_134 = 0) | ~ (all_199_5_137 = 0) | ~ (all_199_6_138 = 0) | ~ (all_199_7_139 = 0) | ~ (all_199_8_140 = 0) | all_199_0_132 = 0 | all_199_1_133 = 0
% 38.04/11.12 | (462) aNaturalNumber0(xn) = all_199_7_139
% 38.04/11.12 |
% 38.04/11.12 | Instantiating (390) with all_203_0_144, all_203_1_145, all_203_2_146, all_203_3_147, all_203_4_148 yields:
% 38.04/11.12 | (463) sdtpldt0(xm, all_203_1_145) = all_203_0_144 & sdtpldt0(xn, xr) = all_203_1_145 & aNaturalNumber0(xr) = all_203_2_146 & aNaturalNumber0(xm) = all_203_4_148 & aNaturalNumber0(xn) = all_203_3_147 & ( ~ (all_203_2_146 = 0) | ~ (all_203_3_147 = 0) | ~ (all_203_4_148 = 0) | all_203_0_144 = all_31_3_52)
% 38.04/11.12 |
% 38.04/11.12 | Applying alpha-rule on (463) yields:
% 38.04/11.12 | (464) sdtpldt0(xn, xr) = all_203_1_145
% 38.04/11.12 | (465) aNaturalNumber0(xr) = all_203_2_146
% 38.04/11.12 | (466) aNaturalNumber0(xn) = all_203_3_147
% 38.04/11.12 | (467) aNaturalNumber0(xm) = all_203_4_148
% 38.04/11.12 | (468) ~ (all_203_2_146 = 0) | ~ (all_203_3_147 = 0) | ~ (all_203_4_148 = 0) | all_203_0_144 = all_31_3_52
% 38.04/11.12 | (469) sdtpldt0(xm, all_203_1_145) = all_203_0_144
% 38.04/11.12 |
% 38.04/11.12 | Instantiating (379) with all_205_0_149, all_205_1_150, all_205_2_151 yields:
% 38.04/11.12 | (470) sdtasdt0(all_24_2_30, xp) = all_205_0_149 & aNaturalNumber0(all_24_2_30) = all_205_1_150 & aNaturalNumber0(xp) = all_205_2_151 & ( ~ (all_205_1_150 = 0) | ~ (all_205_2_151 = 0) | all_205_0_149 = all_0_4_4)
% 38.04/11.12 |
% 38.04/11.12 | Applying alpha-rule on (470) yields:
% 38.04/11.12 | (471) sdtasdt0(all_24_2_30, xp) = all_205_0_149
% 38.04/11.12 | (472) aNaturalNumber0(all_24_2_30) = all_205_1_150
% 38.04/11.12 | (473) aNaturalNumber0(xp) = all_205_2_151
% 38.04/11.12 | (474) ~ (all_205_1_150 = 0) | ~ (all_205_2_151 = 0) | all_205_0_149 = all_0_4_4
% 38.04/11.12 |
% 38.04/11.12 | Instantiating (377) with all_207_0_152, all_207_1_153, all_207_2_154, all_207_3_155, all_207_4_156, all_207_5_157, all_207_6_158, all_207_7_159, all_207_8_160 yields:
% 38.04/11.12 | (475) isPrime0(xr) = all_207_5_157 & doDivides0(xr, all_24_2_30) = all_207_0_152 & doDivides0(xr, xp) = all_207_1_153 & iLess0(all_207_3_155, all_0_5_5) = all_207_2_154 & sdtpldt0(all_207_4_156, xr) = all_207_3_155 & sdtpldt0(xp, all_24_2_30) = all_207_4_156 & aNaturalNumber0(all_24_2_30) = all_207_7_159 & aNaturalNumber0(xr) = all_207_6_158 & aNaturalNumber0(xp) = all_207_8_160 & ( ~ (all_207_2_154 = 0) | ~ (all_207_5_157 = 0) | ~ (all_207_6_158 = 0) | ~ (all_207_7_159 = 0) | ~ (all_207_8_160 = 0) | all_207_0_152 = 0 | all_207_1_153 = 0)
% 38.04/11.12 |
% 38.04/11.12 | Applying alpha-rule on (475) yields:
% 38.04/11.12 | (476) aNaturalNumber0(xr) = all_207_6_158
% 38.04/11.12 | (477) doDivides0(xr, all_24_2_30) = all_207_0_152
% 38.04/11.12 | (478) doDivides0(xr, xp) = all_207_1_153
% 38.04/11.12 | (479) sdtpldt0(xp, all_24_2_30) = all_207_4_156
% 38.04/11.12 | (480) ~ (all_207_2_154 = 0) | ~ (all_207_5_157 = 0) | ~ (all_207_6_158 = 0) | ~ (all_207_7_159 = 0) | ~ (all_207_8_160 = 0) | all_207_0_152 = 0 | all_207_1_153 = 0
% 38.04/11.12 | (481) aNaturalNumber0(xp) = all_207_8_160
% 38.04/11.12 | (482) isPrime0(xr) = all_207_5_157
% 38.04/11.12 | (483) sdtpldt0(all_207_4_156, xr) = all_207_3_155
% 38.04/11.12 | (484) iLess0(all_207_3_155, all_0_5_5) = all_207_2_154
% 38.04/11.12 | (485) aNaturalNumber0(all_24_2_30) = all_207_7_159
% 38.04/11.12 |
% 38.04/11.12 | Instantiating (389) with all_209_0_161, all_209_1_162, all_209_2_163, all_209_3_164, all_209_4_165 yields:
% 38.04/11.12 | (486) sdtpldt0(xm, all_209_1_162) = all_209_0_161 & sdtpldt0(xn, xp) = all_209_1_162 & aNaturalNumber0(xp) = all_209_2_163 & aNaturalNumber0(xm) = all_209_4_165 & aNaturalNumber0(xn) = all_209_3_164 & ( ~ (all_209_2_163 = 0) | ~ (all_209_3_164 = 0) | ~ (all_209_4_165 = 0) | all_209_0_161 = all_0_5_5)
% 38.04/11.12 |
% 38.04/11.12 | Applying alpha-rule on (486) yields:
% 38.04/11.12 | (487) aNaturalNumber0(xp) = all_209_2_163
% 38.04/11.12 | (488) ~ (all_209_2_163 = 0) | ~ (all_209_3_164 = 0) | ~ (all_209_4_165 = 0) | all_209_0_161 = all_0_5_5
% 38.04/11.12 | (489) aNaturalNumber0(xm) = all_209_4_165
% 38.04/11.12 | (490) sdtpldt0(xm, all_209_1_162) = all_209_0_161
% 38.04/11.12 | (491) sdtpldt0(xn, xp) = all_209_1_162
% 38.04/11.12 | (492) aNaturalNumber0(xn) = all_209_3_164
% 38.04/11.12 |
% 38.04/11.12 | Instantiating (378) with all_213_0_171, all_213_1_172, all_213_2_173, all_213_3_174, all_213_4_175, all_213_5_176, all_213_6_177, all_213_7_178, all_213_8_179 yields:
% 38.04/11.12 | (493) isPrime0(xp) = all_213_5_176 & doDivides0(xp, all_24_2_30) = all_213_0_171 & doDivides0(xp, xp) = all_213_1_172 & iLess0(all_213_3_174, all_0_5_5) = all_213_2_173 & sdtpldt0(all_213_4_175, xp) = all_213_3_174 & sdtpldt0(xp, all_24_2_30) = all_213_4_175 & aNaturalNumber0(all_24_2_30) = all_213_7_178 & aNaturalNumber0(xp) = all_213_6_177 & aNaturalNumber0(xp) = all_213_8_179 & ( ~ (all_213_2_173 = 0) | ~ (all_213_5_176 = 0) | ~ (all_213_6_177 = 0) | ~ (all_213_7_178 = 0) | ~ (all_213_8_179 = 0) | all_213_0_171 = 0 | all_213_1_172 = 0)
% 38.04/11.13 |
% 38.04/11.13 | Applying alpha-rule on (493) yields:
% 38.04/11.13 | (494) aNaturalNumber0(all_24_2_30) = all_213_7_178
% 38.04/11.13 | (495) iLess0(all_213_3_174, all_0_5_5) = all_213_2_173
% 38.04/11.13 | (496) aNaturalNumber0(xp) = all_213_6_177
% 38.04/11.13 | (497) isPrime0(xp) = all_213_5_176
% 38.04/11.13 | (498) sdtpldt0(all_213_4_175, xp) = all_213_3_174
% 38.04/11.13 | (499) sdtpldt0(xp, all_24_2_30) = all_213_4_175
% 38.04/11.13 | (500) ~ (all_213_2_173 = 0) | ~ (all_213_5_176 = 0) | ~ (all_213_6_177 = 0) | ~ (all_213_7_178 = 0) | ~ (all_213_8_179 = 0) | all_213_0_171 = 0 | all_213_1_172 = 0
% 38.04/11.13 | (501) aNaturalNumber0(xp) = all_213_8_179
% 38.04/11.13 | (502) doDivides0(xp, xp) = all_213_1_172
% 38.04/11.13 | (503) doDivides0(xp, all_24_2_30) = all_213_0_171
% 38.04/11.13 |
% 38.04/11.13 | Instantiating (388) with all_215_0_180, all_215_1_181, all_215_2_182 yields:
% 38.04/11.13 | (504) aNaturalNumber0(all_33_1_59) = all_215_0_180 & aNaturalNumber0(xp) = all_215_1_181 & aNaturalNumber0(xm) = all_215_2_182 & ( ~ (all_215_1_181 = 0) | ~ (all_215_2_182 = 0) | all_215_0_180 = 0)
% 38.04/11.13 |
% 38.04/11.13 | Applying alpha-rule on (504) yields:
% 38.04/11.13 | (505) aNaturalNumber0(all_33_1_59) = all_215_0_180
% 38.04/11.13 | (506) aNaturalNumber0(xp) = all_215_1_181
% 38.04/11.13 | (507) aNaturalNumber0(xm) = all_215_2_182
% 38.04/11.13 | (508) ~ (all_215_1_181 = 0) | ~ (all_215_2_182 = 0) | all_215_0_180 = 0
% 38.04/11.13 |
% 38.04/11.13 | Instantiating (386) with all_217_0_183, all_217_1_184, all_217_2_185 yields:
% 38.04/11.13 | (509) sdtpldt0(all_23_2_27, xm) = all_217_0_183 & aNaturalNumber0(all_23_2_27) = all_217_1_184 & aNaturalNumber0(xm) = all_217_2_185 & ( ~ (all_217_1_184 = 0) | ~ (all_217_2_185 = 0) | all_217_0_183 = xp)
% 38.04/11.13 |
% 38.04/11.13 | Applying alpha-rule on (509) yields:
% 38.04/11.13 | (510) sdtpldt0(all_23_2_27, xm) = all_217_0_183
% 38.04/11.13 | (511) aNaturalNumber0(all_23_2_27) = all_217_1_184
% 38.04/11.13 | (512) aNaturalNumber0(xm) = all_217_2_185
% 38.04/11.13 | (513) ~ (all_217_1_184 = 0) | ~ (all_217_2_185 = 0) | all_217_0_183 = xp
% 38.04/11.13 |
% 38.04/11.13 | Instantiating (385) with all_219_0_186, all_219_1_187, all_219_2_188, all_219_3_189, all_219_4_190 yields:
% 38.04/11.13 | (514) sdtpldt0(all_23_2_27, all_0_6_6) = all_219_1_187 & sdtpldt0(xm, all_219_1_187) = all_219_0_186 & aNaturalNumber0(all_23_2_27) = all_219_3_189 & aNaturalNumber0(all_0_6_6) = all_219_2_188 & aNaturalNumber0(xm) = all_219_4_190 & ( ~ (all_219_2_188 = 0) | ~ (all_219_3_189 = 0) | ~ (all_219_4_190 = 0) | all_219_0_186 = all_0_5_5)
% 38.04/11.13 |
% 38.04/11.13 | Applying alpha-rule on (514) yields:
% 38.04/11.13 | (515) ~ (all_219_2_188 = 0) | ~ (all_219_3_189 = 0) | ~ (all_219_4_190 = 0) | all_219_0_186 = all_0_5_5
% 38.04/11.13 | (516) aNaturalNumber0(all_23_2_27) = all_219_3_189
% 38.04/11.13 | (517) aNaturalNumber0(all_0_6_6) = all_219_2_188
% 38.04/11.13 | (518) sdtpldt0(all_23_2_27, all_0_6_6) = all_219_1_187
% 38.04/11.13 | (519) aNaturalNumber0(xm) = all_219_4_190
% 38.04/11.13 | (520) sdtpldt0(xm, all_219_1_187) = all_219_0_186
% 38.04/11.13 |
% 38.04/11.13 | Instantiating (387) with all_221_0_191, all_221_1_192, all_221_2_193 yields:
% 38.04/11.13 | (521) sdtpldt0(xp, xm) = all_221_0_191 & aNaturalNumber0(xp) = all_221_1_192 & aNaturalNumber0(xm) = all_221_2_193 & ( ~ (all_221_1_192 = 0) | ~ (all_221_2_193 = 0) | all_221_0_191 = all_33_1_59)
% 38.04/11.13 |
% 38.04/11.13 | Applying alpha-rule on (521) yields:
% 38.04/11.13 | (522) sdtpldt0(xp, xm) = all_221_0_191
% 38.04/11.13 | (523) aNaturalNumber0(xp) = all_221_1_192
% 38.04/11.13 | (524) aNaturalNumber0(xm) = all_221_2_193
% 38.04/11.13 | (525) ~ (all_221_1_192 = 0) | ~ (all_221_2_193 = 0) | all_221_0_191 = all_33_1_59
% 38.04/11.13 |
% 38.04/11.13 | Instantiating (384) with all_223_0_194, all_223_1_195, all_223_2_196, all_223_3_197, all_223_4_198 yields:
% 38.04/11.13 | (526) doDivides0(all_62_0_73, all_23_2_27) = all_223_0_194 & doDivides0(all_62_0_73, xm) = all_223_1_195 & aNaturalNumber0(all_62_0_73) = all_223_4_198 & aNaturalNumber0(all_23_2_27) = all_223_2_196 & aNaturalNumber0(xm) = all_223_3_197 & ( ~ (all_223_1_195 = 0) | ~ (all_223_2_196 = 0) | ~ (all_223_3_197 = 0) | ~ (all_223_4_198 = 0) | all_223_0_194 = 0)
% 38.04/11.13 |
% 38.04/11.13 | Applying alpha-rule on (526) yields:
% 38.04/11.13 | (527) doDivides0(all_62_0_73, xm) = all_223_1_195
% 38.04/11.13 | (528) doDivides0(all_62_0_73, all_23_2_27) = all_223_0_194
% 38.04/11.13 | (529) aNaturalNumber0(all_62_0_73) = all_223_4_198
% 38.04/11.13 | (530) ~ (all_223_1_195 = 0) | ~ (all_223_2_196 = 0) | ~ (all_223_3_197 = 0) | ~ (all_223_4_198 = 0) | all_223_0_194 = 0
% 38.04/11.13 | (531) aNaturalNumber0(xm) = all_223_3_197
% 38.04/11.13 | (532) aNaturalNumber0(all_23_2_27) = all_223_2_196
% 38.04/11.13 |
% 38.04/11.13 +-Applying beta-rule and splitting (234), into two cases.
% 38.04/11.13 |-Branch one:
% 38.04/11.13 | (533) ~ (aNaturalNumber0(xm) = all_40_1_67)
% 38.04/11.13 |
% 38.04/11.13 +-Applying beta-rule and splitting (371), into two cases.
% 38.04/11.13 |-Branch one:
% 38.04/11.13 | (195) xp = sz00
% 38.04/11.13 |
% 38.04/11.13 | Equations (195) can reduce 90 to:
% 38.04/11.13 | (174) $false
% 38.04/11.13 |
% 38.04/11.13 |-The branch is then unsatisfiable
% 38.04/11.13 |-Branch two:
% 38.04/11.13 | (90) ~ (xp = sz00)
% 38.04/11.13 | (537) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_62_0_73, xp) = v2 & aNaturalNumber0(all_62_0_73) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 38.04/11.13 |
% 38.04/11.13 | Instantiating (537) with all_236_0_199, all_236_1_200, all_236_2_201 yields:
% 38.04/11.13 | (538) sdtlseqdt0(all_62_0_73, xp) = all_236_0_199 & aNaturalNumber0(all_62_0_73) = all_236_2_201 & aNaturalNumber0(xp) = all_236_1_200 & ( ~ (all_236_1_200 = 0) | ~ (all_236_2_201 = 0) | all_236_0_199 = 0)
% 38.04/11.13 |
% 38.04/11.13 | Applying alpha-rule on (538) yields:
% 38.04/11.14 | (539) sdtlseqdt0(all_62_0_73, xp) = all_236_0_199
% 38.04/11.14 | (540) aNaturalNumber0(all_62_0_73) = all_236_2_201
% 38.04/11.14 | (541) aNaturalNumber0(xp) = all_236_1_200
% 38.04/11.14 | (542) ~ (all_236_1_200 = 0) | ~ (all_236_2_201 = 0) | all_236_0_199 = 0
% 38.04/11.14 |
% 38.04/11.14 +-Applying beta-rule and splitting (394), into two cases.
% 38.04/11.14 |-Branch one:
% 38.04/11.14 | (543) all_62_0_73 = sz00
% 38.04/11.14 |
% 38.04/11.14 | Equations (543) can reduce 216 to:
% 38.04/11.14 | (174) $false
% 38.04/11.14 |
% 38.04/11.14 |-The branch is then unsatisfiable
% 38.04/11.14 |-Branch two:
% 38.04/11.14 | (216) ~ (all_62_0_73 = sz00)
% 38.04/11.14 | (546) all_62_0_73 = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_62_0_73) = 0 & aNaturalNumber0(v0) = 0)
% 38.04/11.14 |
% 38.04/11.14 +-Applying beta-rule and splitting (372), into two cases.
% 38.04/11.14 |-Branch one:
% 38.04/11.14 | (191) xr = sz00
% 38.04/11.14 |
% 38.04/11.14 | Equations (191) can reduce 89 to:
% 38.04/11.14 | (174) $false
% 38.04/11.14 |
% 38.04/11.14 |-The branch is then unsatisfiable
% 38.04/11.14 |-Branch two:
% 38.04/11.14 | (89) ~ (xr = sz00)
% 38.04/11.14 | (550) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_57_0_72, xr) = v2 & aNaturalNumber0(all_57_0_72) = v0 & aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 38.04/11.14 |
% 38.04/11.14 | Instantiating (550) with all_251_0_202, all_251_1_203, all_251_2_204 yields:
% 38.04/11.14 | (551) sdtlseqdt0(all_57_0_72, xr) = all_251_0_202 & aNaturalNumber0(all_57_0_72) = all_251_2_204 & aNaturalNumber0(xr) = all_251_1_203 & ( ~ (all_251_1_203 = 0) | ~ (all_251_2_204 = 0) | all_251_0_202 = 0)
% 38.04/11.14 |
% 38.04/11.14 | Applying alpha-rule on (551) yields:
% 38.04/11.14 | (552) sdtlseqdt0(all_57_0_72, xr) = all_251_0_202
% 38.04/11.14 | (553) aNaturalNumber0(all_57_0_72) = all_251_2_204
% 38.04/11.14 | (554) aNaturalNumber0(xr) = all_251_1_203
% 38.04/11.14 | (555) ~ (all_251_1_203 = 0) | ~ (all_251_2_204 = 0) | all_251_0_202 = 0
% 38.04/11.14 |
% 38.04/11.14 +-Applying beta-rule and splitting (546), into two cases.
% 38.04/11.14 |-Branch one:
% 38.04/11.14 | (556) all_62_0_73 = sz10
% 38.04/11.14 |
% 38.04/11.14 | Equations (556) can reduce 215 to:
% 38.04/11.14 | (174) $false
% 38.04/11.14 |
% 38.04/11.14 |-The branch is then unsatisfiable
% 38.04/11.14 |-Branch two:
% 38.04/11.14 | (215) ~ (all_62_0_73 = sz10)
% 38.04/11.14 | (559) ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_62_0_73) = 0 & aNaturalNumber0(v0) = 0)
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with all_62_0_73, all_236_2_201, 0 and discharging atoms aNaturalNumber0(all_62_0_73) = all_236_2_201, aNaturalNumber0(all_62_0_73) = 0, yields:
% 38.04/11.14 | (560) all_236_2_201 = 0
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with all_62_0_73, all_223_4_198, all_236_2_201 and discharging atoms aNaturalNumber0(all_62_0_73) = all_236_2_201, aNaturalNumber0(all_62_0_73) = all_223_4_198, yields:
% 38.04/11.14 | (561) all_236_2_201 = all_223_4_198
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with all_62_0_73, all_179_4_81, all_236_2_201 and discharging atoms aNaturalNumber0(all_62_0_73) = all_236_2_201, aNaturalNumber0(all_62_0_73) = all_179_4_81, yields:
% 38.04/11.14 | (562) all_236_2_201 = all_179_4_81
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with all_24_2_30, all_213_7_178, 0 and discharging atoms aNaturalNumber0(all_24_2_30) = all_213_7_178, aNaturalNumber0(all_24_2_30) = 0, yields:
% 38.04/11.14 | (563) all_213_7_178 = 0
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with all_24_2_30, all_207_7_159, all_213_7_178 and discharging atoms aNaturalNumber0(all_24_2_30) = all_213_7_178, aNaturalNumber0(all_24_2_30) = all_207_7_159, yields:
% 38.04/11.14 | (564) all_213_7_178 = all_207_7_159
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with all_24_2_30, all_205_1_150, all_207_7_159 and discharging atoms aNaturalNumber0(all_24_2_30) = all_207_7_159, aNaturalNumber0(all_24_2_30) = all_205_1_150, yields:
% 38.04/11.14 | (565) all_207_7_159 = all_205_1_150
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xr, all_203_2_146, 0 and discharging atoms aNaturalNumber0(xr) = all_203_2_146, aNaturalNumber0(xr) = 0, yields:
% 38.04/11.14 | (566) all_203_2_146 = 0
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xk, all_199_6_138, all_40_1_67 and discharging atoms aNaturalNumber0(xk) = all_40_1_67, yields:
% 38.04/11.14 | (567) all_199_6_138 = all_40_1_67 | ~ (aNaturalNumber0(xk) = all_199_6_138)
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xr, all_199_6_138, all_251_1_203 and discharging atoms aNaturalNumber0(xr) = all_251_1_203, aNaturalNumber0(xr) = all_199_6_138, yields:
% 38.04/11.14 | (568) all_251_1_203 = all_199_6_138
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xr, all_195_2_120, all_207_6_158 and discharging atoms aNaturalNumber0(xr) = all_207_6_158, aNaturalNumber0(xr) = all_195_2_120, yields:
% 38.04/11.14 | (569) all_207_6_158 = all_195_2_120
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xr, all_191_6_109, all_207_6_158 and discharging atoms aNaturalNumber0(xr) = all_207_6_158, aNaturalNumber0(xr) = all_191_6_109, yields:
% 38.04/11.14 | (570) all_207_6_158 = all_191_6_109
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xr, all_191_6_109, all_203_2_146 and discharging atoms aNaturalNumber0(xr) = all_203_2_146, aNaturalNumber0(xr) = all_191_6_109, yields:
% 38.04/11.14 | (571) all_203_2_146 = all_191_6_109
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xr, all_191_8_111, all_251_1_203 and discharging atoms aNaturalNumber0(xr) = all_251_1_203, aNaturalNumber0(xr) = all_191_8_111, yields:
% 38.04/11.14 | (572) all_251_1_203 = all_191_8_111
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xr, all_189_8_102, all_207_6_158 and discharging atoms aNaturalNumber0(xr) = all_207_6_158, aNaturalNumber0(xr) = all_189_8_102, yields:
% 38.04/11.14 | (573) all_207_6_158 = all_189_8_102
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xr, all_187_2_93, all_207_6_158 and discharging atoms aNaturalNumber0(xr) = all_207_6_158, aNaturalNumber0(xr) = all_187_2_93, yields:
% 38.04/11.14 | (574) all_207_6_158 = all_187_2_93
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xr, all_187_2_93, all_191_8_111 and discharging atoms aNaturalNumber0(xr) = all_191_8_111, aNaturalNumber0(xr) = all_187_2_93, yields:
% 38.04/11.14 | (575) all_191_8_111 = all_187_2_93
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xr, all_185_1_89, all_251_1_203 and discharging atoms aNaturalNumber0(xr) = all_251_1_203, aNaturalNumber0(xr) = all_185_1_89, yields:
% 38.04/11.14 | (576) all_251_1_203 = all_185_1_89
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xp, all_221_1_192, all_236_1_200 and discharging atoms aNaturalNumber0(xp) = all_236_1_200, aNaturalNumber0(xp) = all_221_1_192, yields:
% 38.04/11.14 | (577) all_236_1_200 = all_221_1_192
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xp, all_213_6_177, all_215_1_181 and discharging atoms aNaturalNumber0(xp) = all_215_1_181, aNaturalNumber0(xp) = all_213_6_177, yields:
% 38.04/11.14 | (578) all_215_1_181 = all_213_6_177
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xp, all_213_8_179, all_221_1_192 and discharging atoms aNaturalNumber0(xp) = all_221_1_192, aNaturalNumber0(xp) = all_213_8_179, yields:
% 38.04/11.14 | (579) all_221_1_192 = all_213_8_179
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xp, all_209_2_163, all_213_8_179 and discharging atoms aNaturalNumber0(xp) = all_213_8_179, aNaturalNumber0(xp) = all_209_2_163, yields:
% 38.04/11.14 | (580) all_213_8_179 = all_209_2_163
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xp, all_207_8_160, 0 and discharging atoms aNaturalNumber0(xp) = all_207_8_160, aNaturalNumber0(xp) = 0, yields:
% 38.04/11.14 | (581) all_207_8_160 = 0
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xp, all_207_8_160, all_213_6_177 and discharging atoms aNaturalNumber0(xp) = all_213_6_177, aNaturalNumber0(xp) = all_207_8_160, yields:
% 38.04/11.14 | (582) all_213_6_177 = all_207_8_160
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xp, all_207_8_160, all_209_2_163 and discharging atoms aNaturalNumber0(xp) = all_209_2_163, aNaturalNumber0(xp) = all_207_8_160, yields:
% 38.04/11.14 | (583) all_209_2_163 = all_207_8_160
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xp, all_205_2_151, all_236_1_200 and discharging atoms aNaturalNumber0(xp) = all_236_1_200, aNaturalNumber0(xp) = all_205_2_151, yields:
% 38.04/11.14 | (584) all_236_1_200 = all_205_2_151
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xp, all_197_6_129, all_215_1_181 and discharging atoms aNaturalNumber0(xp) = all_215_1_181, aNaturalNumber0(xp) = all_197_6_129, yields:
% 38.04/11.14 | (585) all_215_1_181 = all_197_6_129
% 38.04/11.14 |
% 38.04/11.14 | Instantiating formula (2) with xp, all_189_6_100, all_213_6_177 and discharging atoms aNaturalNumber0(xp) = all_213_6_177, aNaturalNumber0(xp) = all_189_6_100, yields:
% 38.04/11.14 | (586) all_213_6_177 = all_189_6_100
% 38.04/11.15 |
% 38.04/11.15 | Instantiating formula (2) with xm, all_221_2_193, all_223_3_197 and discharging atoms aNaturalNumber0(xm) = all_223_3_197, aNaturalNumber0(xm) = all_221_2_193, yields:
% 38.04/11.15 | (587) all_223_3_197 = all_221_2_193
% 38.04/11.15 |
% 38.04/11.15 | Instantiating formula (2) with xm, all_219_4_190, all_221_2_193 and discharging atoms aNaturalNumber0(xm) = all_221_2_193, aNaturalNumber0(xm) = all_219_4_190, yields:
% 38.04/11.15 | (588) all_221_2_193 = all_219_4_190
% 38.04/11.15 |
% 38.04/11.15 | Instantiating formula (2) with xm, all_217_2_185, all_219_4_190 and discharging atoms aNaturalNumber0(xm) = all_219_4_190, aNaturalNumber0(xm) = all_217_2_185, yields:
% 38.04/11.15 | (589) all_219_4_190 = all_217_2_185
% 38.04/11.15 |
% 38.04/11.15 | Instantiating formula (2) with xm, all_215_2_182, all_217_2_185 and discharging atoms aNaturalNumber0(xm) = all_217_2_185, aNaturalNumber0(xm) = all_215_2_182, yields:
% 38.04/11.15 | (590) all_217_2_185 = all_215_2_182
% 38.04/11.15 |
% 38.04/11.15 | Instantiating formula (2) with xm, all_209_4_165, 0 and discharging atoms aNaturalNumber0(xm) = all_209_4_165, aNaturalNumber0(xm) = 0, yields:
% 38.04/11.15 | (591) all_209_4_165 = 0
% 38.04/11.15 |
% 38.04/11.15 | Instantiating formula (2) with xm, all_209_4_165, all_215_2_182 and discharging atoms aNaturalNumber0(xm) = all_215_2_182, aNaturalNumber0(xm) = all_209_4_165, yields:
% 38.04/11.15 | (592) all_215_2_182 = all_209_4_165
% 38.04/11.15 |
% 38.04/11.15 | Instantiating formula (2) with xm, all_203_4_148, all_223_3_197 and discharging atoms aNaturalNumber0(xm) = all_223_3_197, aNaturalNumber0(xm) = all_203_4_148, yields:
% 38.04/11.15 | (593) all_223_3_197 = all_203_4_148
% 38.04/11.15 |
% 38.04/11.15 | Instantiating formula (2) with xm, all_199_8_140, all_209_4_165 and discharging atoms aNaturalNumber0(xm) = all_209_4_165, aNaturalNumber0(xm) = all_199_8_140, yields:
% 38.04/11.15 | (594) all_209_4_165 = all_199_8_140
% 38.04/11.15 |
% 38.04/11.15 | Instantiating formula (2) with xm, all_197_8_131, all_199_8_140 and discharging atoms aNaturalNumber0(xm) = all_199_8_140, aNaturalNumber0(xm) = all_197_8_131, yields:
% 38.04/11.15 | (595) all_199_8_140 = all_197_8_131
% 38.04/11.15 |
% 38.04/11.15 | Instantiating formula (2) with xm, all_195_3_121, all_197_8_131 and discharging atoms aNaturalNumber0(xm) = all_197_8_131, aNaturalNumber0(xm) = all_195_3_121, yields:
% 38.04/11.15 | (596) all_197_8_131 = all_195_3_121
% 38.04/11.15 |
% 38.04/11.15 | Combining equations (576,568) yields a new equation:
% 38.04/11.15 | (597) all_199_6_138 = all_185_1_89
% 38.04/11.15 |
% 38.04/11.15 | Combining equations (572,568) yields a new equation:
% 38.04/11.15 | (598) all_199_6_138 = all_191_8_111
% 38.04/11.15 |
% 38.04/11.15 | Combining equations (577,584) yields a new equation:
% 38.04/11.15 | (599) all_221_1_192 = all_205_2_151
% 38.04/11.15 |
% 38.04/11.15 | Simplifying 599 yields:
% 38.04/11.15 | (600) all_221_1_192 = all_205_2_151
% 38.04/11.15 |
% 38.04/11.15 | Combining equations (562,561) yields a new equation:
% 38.04/11.15 | (601) all_223_4_198 = all_179_4_81
% 38.04/11.15 |
% 38.04/11.15 | Combining equations (560,561) yields a new equation:
% 38.04/11.15 | (602) all_223_4_198 = 0
% 38.04/11.15 |
% 38.04/11.15 | Combining equations (587,593) yields a new equation:
% 38.04/11.15 | (603) all_221_2_193 = all_203_4_148
% 38.04/11.15 |
% 38.04/11.15 | Simplifying 603 yields:
% 38.04/11.15 | (604) all_221_2_193 = all_203_4_148
% 38.04/11.15 |
% 38.04/11.15 | Combining equations (602,601) yields a new equation:
% 38.04/11.15 | (605) all_179_4_81 = 0
% 38.04/11.15 |
% 38.04/11.15 | Combining equations (579,600) yields a new equation:
% 38.04/11.15 | (606) all_213_8_179 = all_205_2_151
% 38.04/11.15 |
% 38.04/11.15 | Simplifying 606 yields:
% 38.04/11.15 | (607) all_213_8_179 = all_205_2_151
% 38.04/11.15 |
% 38.04/11.15 | Combining equations (588,604) yields a new equation:
% 38.04/11.15 | (608) all_219_4_190 = all_203_4_148
% 38.04/11.15 |
% 38.04/11.15 | Simplifying 608 yields:
% 38.04/11.15 | (609) all_219_4_190 = all_203_4_148
% 38.04/11.15 |
% 38.04/11.15 | Combining equations (589,609) yields a new equation:
% 38.04/11.15 | (610) all_217_2_185 = all_203_4_148
% 38.04/11.15 |
% 38.04/11.15 | Simplifying 610 yields:
% 38.04/11.15 | (611) all_217_2_185 = all_203_4_148
% 38.04/11.15 |
% 38.04/11.15 | Combining equations (590,611) yields a new equation:
% 38.31/11.15 | (612) all_215_2_182 = all_203_4_148
% 38.31/11.15 |
% 38.31/11.15 | Simplifying 612 yields:
% 38.31/11.15 | (613) all_215_2_182 = all_203_4_148
% 38.31/11.15 |
% 38.31/11.15 | Combining equations (578,585) yields a new equation:
% 38.31/11.15 | (614) all_213_6_177 = all_197_6_129
% 38.31/11.15 |
% 38.31/11.15 | Simplifying 614 yields:
% 38.31/11.15 | (615) all_213_6_177 = all_197_6_129
% 38.31/11.15 |
% 38.31/11.15 | Combining equations (592,613) yields a new equation:
% 38.31/11.15 | (616) all_209_4_165 = all_203_4_148
% 38.31/11.15 |
% 38.31/11.15 | Simplifying 616 yields:
% 38.31/11.15 | (617) all_209_4_165 = all_203_4_148
% 38.31/11.15 |
% 38.31/11.15 | Combining equations (582,615) yields a new equation:
% 38.31/11.15 | (618) all_207_8_160 = all_197_6_129
% 38.31/11.15 |
% 38.31/11.16 | Simplifying 618 yields:
% 38.31/11.16 | (619) all_207_8_160 = all_197_6_129
% 38.31/11.16 |
% 38.31/11.16 | Combining equations (586,615) yields a new equation:
% 38.31/11.16 | (620) all_197_6_129 = all_189_6_100
% 38.31/11.16 |
% 38.31/11.16 | Combining equations (564,563) yields a new equation:
% 38.31/11.16 | (621) all_207_7_159 = 0
% 38.31/11.16 |
% 38.31/11.16 | Simplifying 621 yields:
% 38.31/11.16 | (622) all_207_7_159 = 0
% 38.31/11.16 |
% 38.31/11.16 | Combining equations (580,607) yields a new equation:
% 38.31/11.16 | (623) all_209_2_163 = all_205_2_151
% 38.31/11.16 |
% 38.31/11.16 | Simplifying 623 yields:
% 38.31/11.16 | (624) all_209_2_163 = all_205_2_151
% 38.31/11.16 |
% 38.31/11.16 | Combining equations (583,624) yields a new equation:
% 38.31/11.16 | (625) all_207_8_160 = all_205_2_151
% 38.31/11.16 |
% 38.31/11.16 | Simplifying 625 yields:
% 38.31/11.16 | (626) all_207_8_160 = all_205_2_151
% 38.31/11.16 |
% 38.31/11.16 | Combining equations (591,617) yields a new equation:
% 38.31/11.16 | (627) all_203_4_148 = 0
% 38.31/11.16 |
% 38.31/11.16 | Combining equations (594,617) yields a new equation:
% 38.31/11.16 | (628) all_203_4_148 = all_199_8_140
% 38.31/11.16 |
% 38.31/11.16 | Combining equations (573,569) yields a new equation:
% 38.31/11.16 | (629) all_195_2_120 = all_189_8_102
% 38.31/11.16 |
% 38.31/11.16 | Combining equations (574,569) yields a new equation:
% 38.31/11.16 | (630) all_195_2_120 = all_187_2_93
% 38.31/11.16 |
% 38.31/11.16 | Combining equations (570,569) yields a new equation:
% 38.31/11.16 | (631) all_195_2_120 = all_191_6_109
% 38.31/11.16 |
% 38.31/11.16 | Combining equations (565,622) yields a new equation:
% 38.31/11.16 | (632) all_205_1_150 = 0
% 38.31/11.16 |
% 38.31/11.16 | Simplifying 632 yields:
% 38.31/11.16 | (633) all_205_1_150 = 0
% 38.31/11.16 |
% 38.31/11.16 | Combining equations (619,626) yields a new equation:
% 38.31/11.16 | (634) all_205_2_151 = all_197_6_129
% 38.31/11.16 |
% 38.31/11.16 | Combining equations (581,626) yields a new equation:
% 38.31/11.16 | (635) all_205_2_151 = 0
% 38.31/11.16 |
% 38.31/11.16 | Combining equations (634,635) yields a new equation:
% 38.31/11.16 | (636) all_197_6_129 = 0
% 38.31/11.16 |
% 38.31/11.16 | Simplifying 636 yields:
% 38.31/11.16 | (637) all_197_6_129 = 0
% 38.31/11.16 |
% 38.31/11.16 | Combining equations (571,566) yields a new equation:
% 38.31/11.16 | (638) all_191_6_109 = 0
% 38.31/11.16 |
% 38.31/11.16 | Simplifying 638 yields:
% 38.31/11.16 | (639) all_191_6_109 = 0
% 38.31/11.16 |
% 38.31/11.16 | Combining equations (628,627) yields a new equation:
% 38.31/11.16 | (640) all_199_8_140 = 0
% 38.31/11.16 |
% 38.31/11.16 | Simplifying 640 yields:
% 38.31/11.16 | (641) all_199_8_140 = 0
% 38.31/11.16 |
% 38.31/11.16 | Combining equations (598,597) yields a new equation:
% 38.31/11.16 | (642) all_191_8_111 = all_185_1_89
% 38.31/11.16 |
% 38.31/11.16 | Simplifying 642 yields:
% 38.31/11.16 | (643) all_191_8_111 = all_185_1_89
% 38.31/11.16 |
% 38.31/11.16 | Combining equations (595,641) yields a new equation:
% 38.31/11.16 | (644) all_197_8_131 = 0
% 38.31/11.16 |
% 38.31/11.16 | Simplifying 644 yields:
% 38.31/11.16 | (645) all_197_8_131 = 0
% 38.31/11.16 |
% 38.31/11.17 | Combining equations (620,637) yields a new equation:
% 38.31/11.17 | (646) all_189_6_100 = 0
% 38.31/11.17 |
% 38.31/11.17 | Simplifying 646 yields:
% 38.31/11.17 | (647) all_189_6_100 = 0
% 38.31/11.17 |
% 38.31/11.17 | Combining equations (596,645) yields a new equation:
% 38.31/11.17 | (648) all_195_3_121 = 0
% 38.31/11.17 |
% 38.31/11.17 | Simplifying 648 yields:
% 38.31/11.17 | (649) all_195_3_121 = 0
% 38.31/11.17 |
% 38.31/11.17 | Combining equations (630,629) yields a new equation:
% 38.31/11.17 | (650) all_189_8_102 = all_187_2_93
% 38.31/11.17 |
% 38.31/11.17 | Combining equations (631,629) yields a new equation:
% 38.31/11.17 | (651) all_191_6_109 = all_189_8_102
% 38.31/11.17 |
% 38.31/11.17 | Simplifying 651 yields:
% 38.31/11.17 | (652) all_191_6_109 = all_189_8_102
% 38.31/11.17 |
% 38.31/11.17 | Combining equations (652,639) yields a new equation:
% 38.31/11.17 | (653) all_189_8_102 = 0
% 38.31/11.17 |
% 38.31/11.17 | Simplifying 653 yields:
% 38.31/11.17 | (654) all_189_8_102 = 0
% 38.31/11.17 |
% 38.31/11.17 | Combining equations (575,643) yields a new equation:
% 38.31/11.17 | (655) all_187_2_93 = all_185_1_89
% 38.31/11.17 |
% 38.31/11.17 | Simplifying 655 yields:
% 38.31/11.17 | (656) all_187_2_93 = all_185_1_89
% 38.31/11.17 |
% 38.31/11.17 | Combining equations (650,654) yields a new equation:
% 38.31/11.17 | (657) all_187_2_93 = 0
% 38.31/11.17 |
% 38.31/11.17 | Simplifying 657 yields:
% 38.31/11.17 | (658) all_187_2_93 = 0
% 38.31/11.17 |
% 38.31/11.17 | Combining equations (658,656) yields a new equation:
% 38.31/11.17 | (659) all_185_1_89 = 0
% 38.31/11.17 |
% 38.31/11.17 | Combining equations (659,597) yields a new equation:
% 38.31/11.17 | (660) all_199_6_138 = 0
% 38.31/11.17 |
% 38.31/11.17 | From (605) and (397) follows:
% 38.31/11.17 | (214) aNaturalNumber0(all_62_0_73) = 0
% 38.31/11.17 |
% 38.31/11.17 | From (633) and (472) follows:
% 38.31/11.17 | (338) aNaturalNumber0(all_24_2_30) = 0
% 38.31/11.17 |
% 38.31/11.17 | From (647) and (422) follows:
% 38.31/11.17 | (78) aNaturalNumber0(xp) = 0
% 38.31/11.17 |
% 38.31/11.17 | From (649) and (437) follows:
% 38.31/11.17 | (56) aNaturalNumber0(xm) = 0
% 38.31/11.17 |
% 38.31/11.17 +-Applying beta-rule and splitting (391), into two cases.
% 38.31/11.17 |-Branch one:
% 38.31/11.17 | (665) xp = xn
% 38.31/11.17 |
% 38.31/11.17 | Equations (665) can reduce 73 to:
% 38.31/11.17 | (174) $false
% 38.31/11.17 |
% 38.31/11.17 |-The branch is then unsatisfiable
% 38.31/11.17 |-Branch two:
% 38.31/11.17 | (73) ~ (xp = xn)
% 38.31/11.17 | (668) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xp, xm) = v3 & sdtpldt0(xn, xm) = v4 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v4 = v3) & ~ (all_33_1_59 = all_0_6_6))))
% 38.31/11.17 |
% 38.31/11.17 | Instantiating (668) with all_284_0_207, all_284_1_208, all_284_2_209, all_284_3_210, all_284_4_211 yields:
% 38.31/11.17 | (669) sdtpldt0(xp, xm) = all_284_1_208 & sdtpldt0(xn, xm) = all_284_0_207 & aNaturalNumber0(xp) = all_284_3_210 & aNaturalNumber0(xm) = all_284_4_211 & aNaturalNumber0(xn) = all_284_2_209 & ( ~ (all_284_2_209 = 0) | ~ (all_284_3_210 = 0) | ~ (all_284_4_211 = 0) | ( ~ (all_284_0_207 = all_284_1_208) & ~ (all_33_1_59 = all_0_6_6)))
% 38.31/11.17 |
% 38.31/11.17 | Applying alpha-rule on (669) yields:
% 38.31/11.17 | (670) aNaturalNumber0(xm) = all_284_4_211
% 38.31/11.17 | (671) aNaturalNumber0(xn) = all_284_2_209
% 38.31/11.17 | (672) aNaturalNumber0(xp) = all_284_3_210
% 38.31/11.17 | (673) ~ (all_284_2_209 = 0) | ~ (all_284_3_210 = 0) | ~ (all_284_4_211 = 0) | ( ~ (all_284_0_207 = all_284_1_208) & ~ (all_33_1_59 = all_0_6_6))
% 38.31/11.17 | (674) sdtpldt0(xn, xm) = all_284_0_207
% 38.31/11.17 | (675) sdtpldt0(xp, xm) = all_284_1_208
% 38.31/11.17 |
% 38.31/11.17 | Instantiating formula (2) with xp, all_284_3_210, 0 and discharging atoms aNaturalNumber0(xp) = all_284_3_210, aNaturalNumber0(xp) = 0, yields:
% 38.31/11.17 | (676) all_284_3_210 = 0
% 38.31/11.17 |
% 38.31/11.17 | Instantiating formula (2) with xm, all_284_4_211, 0 and discharging atoms aNaturalNumber0(xm) = all_284_4_211, aNaturalNumber0(xm) = 0, yields:
% 38.31/11.17 | (677) all_284_4_211 = 0
% 38.31/11.17 |
% 38.31/11.17 | From (676) and (672) follows:
% 38.31/11.17 | (78) aNaturalNumber0(xp) = 0
% 38.31/11.17 |
% 38.31/11.17 | From (677) and (670) follows:
% 38.31/11.17 | (56) aNaturalNumber0(xm) = 0
% 38.31/11.17 |
% 38.31/11.18 +-Applying beta-rule and splitting (376), into two cases.
% 38.31/11.18 |-Branch one:
% 38.31/11.18 | (195) xp = sz00
% 38.31/11.18 |
% 38.31/11.18 | Equations (195) can reduce 90 to:
% 38.31/11.18 | (174) $false
% 38.31/11.18 |
% 38.31/11.18 |-The branch is then unsatisfiable
% 38.31/11.18 |-Branch two:
% 38.31/11.18 | (90) ~ (xp = sz00)
% 38.31/11.18 | (683) all_24_2_30 = xk | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_24_2_30) = v0) | (doDivides0(xp, all_0_4_4) = v2 & aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 38.31/11.18 |
% 38.31/11.18 +-Applying beta-rule and splitting (392), into two cases.
% 38.31/11.18 |-Branch one:
% 38.31/11.18 | (665) xp = xn
% 38.31/11.18 |
% 38.31/11.18 | Equations (665) can reduce 73 to:
% 38.31/11.18 | (174) $false
% 38.31/11.18 |
% 38.31/11.18 |-The branch is then unsatisfiable
% 38.31/11.18 |-Branch two:
% 38.31/11.18 | (73) ~ (xp = xn)
% 38.31/11.18 | (687) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xp, xm) = v4 & sdtpldt0(xn, xm) = v3 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v4 = v3) & ~ (all_33_1_59 = all_0_6_6))))
% 38.31/11.18 |
% 38.31/11.18 | Instantiating (687) with all_466_0_212, all_466_1_213, all_466_2_214, all_466_3_215, all_466_4_216 yields:
% 38.31/11.18 | (688) sdtpldt0(xp, xm) = all_466_0_212 & sdtpldt0(xn, xm) = all_466_1_213 & aNaturalNumber0(xp) = all_466_2_214 & aNaturalNumber0(xm) = all_466_4_216 & aNaturalNumber0(xn) = all_466_3_215 & ( ~ (all_466_2_214 = 0) | ~ (all_466_3_215 = 0) | ~ (all_466_4_216 = 0) | ( ~ (all_466_0_212 = all_466_1_213) & ~ (all_33_1_59 = all_0_6_6)))
% 38.31/11.18 |
% 38.31/11.18 | Applying alpha-rule on (688) yields:
% 38.31/11.18 | (689) ~ (all_466_2_214 = 0) | ~ (all_466_3_215 = 0) | ~ (all_466_4_216 = 0) | ( ~ (all_466_0_212 = all_466_1_213) & ~ (all_33_1_59 = all_0_6_6))
% 38.31/11.18 | (690) sdtpldt0(xn, xm) = all_466_1_213
% 38.31/11.18 | (691) aNaturalNumber0(xm) = all_466_4_216
% 38.31/11.18 | (692) sdtpldt0(xp, xm) = all_466_0_212
% 38.31/11.18 | (693) aNaturalNumber0(xp) = all_466_2_214
% 38.31/11.18 | (694) aNaturalNumber0(xn) = all_466_3_215
% 38.31/11.18 |
% 38.31/11.18 | Instantiating formula (2) with xp, all_466_2_214, 0 and discharging atoms aNaturalNumber0(xp) = all_466_2_214, aNaturalNumber0(xp) = 0, yields:
% 38.31/11.18 | (695) all_466_2_214 = 0
% 38.31/11.18 |
% 38.31/11.18 | Instantiating formula (2) with xm, all_466_4_216, 0 and discharging atoms aNaturalNumber0(xm) = all_466_4_216, aNaturalNumber0(xm) = 0, yields:
% 38.31/11.18 | (696) all_466_4_216 = 0
% 38.31/11.18 |
% 38.31/11.18 | Using (691) and (533) yields:
% 38.31/11.18 | (697) ~ (all_466_4_216 = all_40_1_67)
% 38.31/11.18 |
% 38.31/11.18 | Equations (696) can reduce 697 to:
% 38.31/11.18 | (698) ~ (all_40_1_67 = 0)
% 38.31/11.18 |
% 38.31/11.18 | Simplifying 698 yields:
% 38.31/11.18 | (369) ~ (all_40_1_67 = 0)
% 38.31/11.18 |
% 38.31/11.18 | From (695) and (693) follows:
% 38.31/11.18 | (78) aNaturalNumber0(xp) = 0
% 38.31/11.18 |
% 38.31/11.18 +-Applying beta-rule and splitting (370), into two cases.
% 38.31/11.18 |-Branch one:
% 38.31/11.18 | (701) all_62_0_73 = xp
% 38.31/11.18 |
% 38.31/11.18 | From (701) and (214) follows:
% 38.31/11.18 | (78) aNaturalNumber0(xp) = 0
% 38.31/11.18 |
% 38.31/11.18 +-Applying beta-rule and splitting (683), into two cases.
% 38.31/11.18 |-Branch one:
% 38.31/11.18 | (703) all_24_2_30 = xk
% 38.31/11.18 |
% 38.31/11.18 | From (703) and (338) follows:
% 38.31/11.18 | (704) aNaturalNumber0(xk) = 0
% 38.31/11.18 |
% 38.31/11.18 +-Applying beta-rule and splitting (567), into two cases.
% 38.31/11.18 |-Branch one:
% 38.31/11.18 | (705) ~ (aNaturalNumber0(xk) = all_199_6_138)
% 38.31/11.18 |
% 38.31/11.18 | From (660) and (705) follows:
% 38.31/11.18 | (706) ~ (aNaturalNumber0(xk) = 0)
% 38.31/11.18 |
% 38.31/11.18 | Using (704) and (706) yields:
% 38.31/11.18 | (311) $false
% 38.31/11.18 |
% 38.31/11.18 |-The branch is then unsatisfiable
% 38.31/11.18 |-Branch two:
% 38.31/11.18 | (708) aNaturalNumber0(xk) = all_199_6_138
% 38.31/11.18 | (709) all_199_6_138 = all_40_1_67
% 38.31/11.18 |
% 38.31/11.18 | Combining equations (709,660) yields a new equation:
% 38.31/11.18 | (710) all_40_1_67 = 0
% 38.31/11.18 |
% 38.31/11.18 | Simplifying 710 yields:
% 38.31/11.18 | (711) all_40_1_67 = 0
% 38.31/11.18 |
% 38.31/11.18 | Equations (711) can reduce 369 to:
% 38.31/11.18 | (174) $false
% 38.31/11.18 |
% 38.31/11.18 |-The branch is then unsatisfiable
% 38.31/11.18 |-Branch two:
% 38.31/11.18 | (713) ~ (all_24_2_30 = xk)
% 38.31/11.18 | (714) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_24_2_30) = v0) | (doDivides0(xp, all_0_4_4) = v2 & aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 38.31/11.18 |
% 38.31/11.18 | Instantiating (714) with all_516_0_217, all_516_1_218, all_516_2_219 yields:
% 38.31/11.19 | (715) ( ~ (all_516_2_219 = 0) & aNaturalNumber0(all_24_2_30) = all_516_2_219) | (doDivides0(xp, all_0_4_4) = all_516_0_217 & aNaturalNumber0(all_0_4_4) = all_516_1_218 & aNaturalNumber0(xp) = all_516_2_219 & ( ~ (all_516_0_217 = 0) | ~ (all_516_1_218 = 0) | ~ (all_516_2_219 = 0)))
% 38.31/11.19 |
% 38.31/11.19 +-Applying beta-rule and splitting (715), into two cases.
% 38.31/11.19 |-Branch one:
% 38.31/11.19 | (716) ~ (all_516_2_219 = 0) & aNaturalNumber0(all_24_2_30) = all_516_2_219
% 38.31/11.19 |
% 38.31/11.19 | Applying alpha-rule on (716) yields:
% 38.31/11.19 | (717) ~ (all_516_2_219 = 0)
% 38.31/11.19 | (718) aNaturalNumber0(all_24_2_30) = all_516_2_219
% 38.31/11.19 |
% 38.31/11.19 | Instantiating formula (2) with all_24_2_30, all_516_2_219, 0 and discharging atoms aNaturalNumber0(all_24_2_30) = all_516_2_219, aNaturalNumber0(all_24_2_30) = 0, yields:
% 38.31/11.19 | (719) all_516_2_219 = 0
% 38.31/11.19 |
% 38.31/11.19 | Equations (719) can reduce 717 to:
% 38.31/11.19 | (174) $false
% 38.31/11.19 |
% 38.31/11.19 |-The branch is then unsatisfiable
% 38.31/11.19 |-Branch two:
% 38.31/11.19 | (721) doDivides0(xp, all_0_4_4) = all_516_0_217 & aNaturalNumber0(all_0_4_4) = all_516_1_218 & aNaturalNumber0(xp) = all_516_2_219 & ( ~ (all_516_0_217 = 0) | ~ (all_516_1_218 = 0) | ~ (all_516_2_219 = 0))
% 38.31/11.19 |
% 38.31/11.19 | Applying alpha-rule on (721) yields:
% 38.31/11.19 | (722) doDivides0(xp, all_0_4_4) = all_516_0_217
% 38.31/11.19 | (723) aNaturalNumber0(all_0_4_4) = all_516_1_218
% 38.31/11.19 | (724) aNaturalNumber0(xp) = all_516_2_219
% 38.31/11.19 | (725) ~ (all_516_0_217 = 0) | ~ (all_516_1_218 = 0) | ~ (all_516_2_219 = 0)
% 38.31/11.19 |
% 38.31/11.19 | Instantiating formula (19) with xp, all_0_4_4, all_516_0_217, 0 and discharging atoms doDivides0(xp, all_0_4_4) = all_516_0_217, doDivides0(xp, all_0_4_4) = 0, yields:
% 38.31/11.19 | (726) all_516_0_217 = 0
% 38.31/11.19 |
% 38.31/11.19 | Instantiating formula (2) with all_0_4_4, all_516_1_218, 0 and discharging atoms aNaturalNumber0(all_0_4_4) = all_516_1_218, aNaturalNumber0(all_0_4_4) = 0, yields:
% 38.31/11.19 | (727) all_516_1_218 = 0
% 38.31/11.19 |
% 38.31/11.19 | Instantiating formula (2) with xp, all_516_2_219, 0 and discharging atoms aNaturalNumber0(xp) = all_516_2_219, aNaturalNumber0(xp) = 0, yields:
% 38.31/11.19 | (719) all_516_2_219 = 0
% 38.31/11.19 |
% 38.31/11.19 +-Applying beta-rule and splitting (725), into two cases.
% 38.31/11.19 |-Branch one:
% 38.31/11.19 | (729) ~ (all_516_0_217 = 0)
% 38.31/11.19 |
% 38.31/11.19 | Equations (726) can reduce 729 to:
% 38.31/11.19 | (174) $false
% 38.31/11.19 |
% 38.31/11.19 |-The branch is then unsatisfiable
% 38.31/11.19 |-Branch two:
% 38.31/11.19 | (726) all_516_0_217 = 0
% 38.31/11.19 | (732) ~ (all_516_1_218 = 0) | ~ (all_516_2_219 = 0)
% 38.31/11.19 |
% 38.31/11.19 +-Applying beta-rule and splitting (732), into two cases.
% 38.31/11.19 |-Branch one:
% 38.31/11.19 | (733) ~ (all_516_1_218 = 0)
% 38.31/11.19 |
% 38.31/11.19 | Equations (727) can reduce 733 to:
% 38.31/11.19 | (174) $false
% 38.31/11.19 |
% 38.31/11.19 |-The branch is then unsatisfiable
% 38.31/11.19 |-Branch two:
% 38.31/11.19 | (727) all_516_1_218 = 0
% 38.31/11.19 | (717) ~ (all_516_2_219 = 0)
% 38.31/11.19 |
% 38.31/11.19 | Equations (719) can reduce 717 to:
% 38.31/11.19 | (174) $false
% 38.31/11.19 |
% 38.31/11.19 |-The branch is then unsatisfiable
% 38.31/11.19 |-Branch two:
% 38.31/11.19 | (738) ~ (all_62_0_73 = xp)
% 38.31/11.19 | (739) all_62_0_73 = sz10 | ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_62_0_73) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0))
% 38.31/11.19 |
% 38.31/11.19 +-Applying beta-rule and splitting (739), into two cases.
% 38.31/11.19 |-Branch one:
% 38.31/11.19 | (556) all_62_0_73 = sz10
% 38.31/11.19 |
% 38.31/11.19 | Equations (556) can reduce 215 to:
% 38.31/11.19 | (174) $false
% 38.31/11.19 |
% 38.31/11.19 |-The branch is then unsatisfiable
% 38.31/11.19 |-Branch two:
% 38.31/11.19 | (215) ~ (all_62_0_73 = sz10)
% 38.31/11.19 | (743) ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_62_0_73) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0))
% 38.31/11.19 |
% 38.31/11.19 | Instantiating (743) with all_496_0_220 yields:
% 38.31/11.19 | (744) ( ~ (all_496_0_220 = 0) & aNaturalNumber0(all_62_0_73) = all_496_0_220) | ( ~ (all_496_0_220 = 0) & aNaturalNumber0(xp) = all_496_0_220)
% 38.31/11.19 |
% 38.31/11.19 +-Applying beta-rule and splitting (744), into two cases.
% 38.31/11.19 |-Branch one:
% 38.31/11.19 | (745) ~ (all_496_0_220 = 0) & aNaturalNumber0(all_62_0_73) = all_496_0_220
% 38.31/11.19 |
% 38.31/11.19 | Applying alpha-rule on (745) yields:
% 38.31/11.19 | (746) ~ (all_496_0_220 = 0)
% 38.31/11.19 | (747) aNaturalNumber0(all_62_0_73) = all_496_0_220
% 38.31/11.19 |
% 38.31/11.19 | Instantiating formula (2) with all_62_0_73, all_496_0_220, 0 and discharging atoms aNaturalNumber0(all_62_0_73) = all_496_0_220, aNaturalNumber0(all_62_0_73) = 0, yields:
% 38.31/11.19 | (748) all_496_0_220 = 0
% 38.31/11.19 |
% 38.31/11.19 | Equations (748) can reduce 746 to:
% 38.31/11.20 | (174) $false
% 38.31/11.20 |
% 38.31/11.20 |-The branch is then unsatisfiable
% 38.31/11.20 |-Branch two:
% 38.31/11.20 | (750) ~ (all_496_0_220 = 0) & aNaturalNumber0(xp) = all_496_0_220
% 38.31/11.20 |
% 38.31/11.20 | Applying alpha-rule on (750) yields:
% 38.31/11.20 | (746) ~ (all_496_0_220 = 0)
% 38.31/11.20 | (752) aNaturalNumber0(xp) = all_496_0_220
% 38.31/11.20 |
% 38.31/11.20 | Instantiating formula (2) with xp, all_496_0_220, 0 and discharging atoms aNaturalNumber0(xp) = all_496_0_220, aNaturalNumber0(xp) = 0, yields:
% 38.31/11.20 | (748) all_496_0_220 = 0
% 38.31/11.20 |
% 38.31/11.20 | Equations (748) can reduce 746 to:
% 38.31/11.20 | (174) $false
% 38.31/11.20 |
% 38.31/11.20 |-The branch is then unsatisfiable
% 38.49/11.20 |-Branch two:
% 38.49/11.20 | (755) aNaturalNumber0(xm) = all_40_1_67
% 38.49/11.20 | (756) all_40_1_67 = all_29_7_47
% 38.49/11.20 |
% 38.49/11.20 | Combining equations (258,756) yields a new equation:
% 38.49/11.20 | (711) all_40_1_67 = 0
% 38.49/11.20 |
% 38.49/11.20 | Equations (711) can reduce 369 to:
% 38.49/11.20 | (174) $false
% 38.49/11.20 |
% 38.49/11.20 |-The branch is then unsatisfiable
% 38.49/11.20 |-Branch two:
% 38.49/11.20 | (711) all_40_1_67 = 0
% 38.49/11.20 | (760) ~ (all_40_2_68 = 0) | (all_40_0_66 = 0 & ~ (xk = xp))
% 38.49/11.20 |
% 38.49/11.20 +-Applying beta-rule and splitting (94), into two cases.
% 38.49/11.20 |-Branch one:
% 38.49/11.20 | (761) all_0_0_0 = 0
% 38.49/11.20 |
% 38.49/11.20 | Equations (761) can reduce 368 to:
% 38.49/11.20 | (174) $false
% 38.49/11.20 |
% 38.49/11.20 |-The branch is then unsatisfiable
% 38.49/11.20 |-Branch two:
% 38.49/11.20 | (368) ~ (all_0_0_0 = 0)
% 38.49/11.20 | (764) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, xk) = v2 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xk = xp))))
% 38.49/11.20 |
% 38.49/11.20 +-Applying beta-rule and splitting (760), into two cases.
% 38.49/11.20 |-Branch one:
% 38.49/11.20 | (765) ~ (all_40_2_68 = 0)
% 38.49/11.20 |
% 38.49/11.20 | Equations (227) can reduce 765 to:
% 38.49/11.20 | (174) $false
% 38.49/11.20 |
% 38.49/11.20 |-The branch is then unsatisfiable
% 38.49/11.20 |-Branch two:
% 38.49/11.20 | (227) all_40_2_68 = 0
% 38.49/11.20 | (768) all_40_0_66 = 0 & ~ (xk = xp)
% 38.49/11.20 |
% 38.49/11.20 | Applying alpha-rule on (768) yields:
% 38.49/11.20 | (769) all_40_0_66 = 0
% 38.49/11.20 | (367) ~ (xk = xp)
% 38.49/11.20 |
% 38.49/11.20 | Combining equations (769,218) yields a new equation:
% 38.49/11.20 | (761) all_0_0_0 = 0
% 38.49/11.20 |
% 38.49/11.20 | Equations (761) can reduce 368 to:
% 38.49/11.20 | (174) $false
% 38.49/11.20 |
% 38.49/11.20 |-The branch is then unsatisfiable
% 38.49/11.20 |-Branch two:
% 38.49/11.20 | (761) all_0_0_0 = 0
% 38.49/11.20 | (774) xk = xp
% 38.49/11.20 |
% 38.49/11.20 | Equations (774) can reduce 367 to:
% 38.49/11.20 | (174) $false
% 38.49/11.20 |
% 38.49/11.20 |-The branch is then unsatisfiable
% 38.49/11.20 |-Branch two:
% 38.49/11.20 | (776) aNaturalNumber0(all_0_4_4) = all_28_1_38 & aNaturalNumber0(xr) = all_28_2_39 & ( ~ (all_28_1_38 = 0) | ~ (all_28_2_39 = 0))
% 38.49/11.20 |
% 38.49/11.20 | Applying alpha-rule on (776) yields:
% 38.49/11.20 | (777) aNaturalNumber0(all_0_4_4) = all_28_1_38
% 38.49/11.20 | (778) aNaturalNumber0(xr) = all_28_2_39
% 38.49/11.20 | (779) ~ (all_28_1_38 = 0) | ~ (all_28_2_39 = 0)
% 38.49/11.20 |
% 38.49/11.20 | Instantiating formula (2) with all_0_4_4, all_28_1_38, 0 and discharging atoms aNaturalNumber0(all_0_4_4) = all_28_1_38, aNaturalNumber0(all_0_4_4) = 0, yields:
% 38.49/11.20 | (359) all_28_1_38 = 0
% 38.49/11.20 |
% 38.49/11.20 | Instantiating formula (2) with xr, all_28_2_39, 0 and discharging atoms aNaturalNumber0(xr) = all_28_2_39, aNaturalNumber0(xr) = 0, yields:
% 38.49/11.20 | (781) all_28_2_39 = 0
% 38.49/11.20 |
% 38.49/11.20 +-Applying beta-rule and splitting (779), into two cases.
% 38.49/11.20 |-Branch one:
% 38.49/11.20 | (782) ~ (all_28_1_38 = 0)
% 38.49/11.20 |
% 38.49/11.20 | Equations (359) can reduce 782 to:
% 38.49/11.20 | (174) $false
% 38.49/11.20 |
% 38.49/11.20 |-The branch is then unsatisfiable
% 38.49/11.20 |-Branch two:
% 38.49/11.20 | (359) all_28_1_38 = 0
% 38.49/11.20 | (785) ~ (all_28_2_39 = 0)
% 38.49/11.20 |
% 38.49/11.20 | Equations (781) can reduce 785 to:
% 38.49/11.20 | (174) $false
% 38.49/11.20 |
% 38.49/11.20 |-The branch is then unsatisfiable
% 38.49/11.20 |-Branch two:
% 38.49/11.20 | (787) aNaturalNumber0(all_0_4_4) = all_24_1_29 & aNaturalNumber0(xp) = all_24_2_30 & ( ~ (all_24_1_29 = 0) | ~ (all_24_2_30 = 0))
% 38.49/11.20 |
% 38.49/11.20 | Applying alpha-rule on (787) yields:
% 38.49/11.20 | (788) aNaturalNumber0(all_0_4_4) = all_24_1_29
% 38.49/11.20 | (789) aNaturalNumber0(xp) = all_24_2_30
% 38.49/11.20 | (790) ~ (all_24_1_29 = 0) | ~ (all_24_2_30 = 0)
% 38.49/11.20 |
% 38.49/11.20 | Instantiating formula (2) with all_0_4_4, all_24_1_29, 0 and discharging atoms aNaturalNumber0(all_0_4_4) = all_24_1_29, aNaturalNumber0(all_0_4_4) = 0, yields:
% 38.49/11.20 | (336) all_24_1_29 = 0
% 38.49/11.20 |
% 38.49/11.20 | Instantiating formula (2) with xp, all_24_2_30, 0 and discharging atoms aNaturalNumber0(xp) = all_24_2_30, aNaturalNumber0(xp) = 0, yields:
% 38.49/11.20 | (792) all_24_2_30 = 0
% 38.49/11.20 |
% 38.49/11.20 +-Applying beta-rule and splitting (790), into two cases.
% 38.49/11.20 |-Branch one:
% 38.49/11.20 | (793) ~ (all_24_1_29 = 0)
% 38.49/11.20 |
% 38.49/11.20 | Equations (336) can reduce 793 to:
% 38.49/11.20 | (174) $false
% 38.49/11.20 |
% 38.49/11.20 |-The branch is then unsatisfiable
% 38.49/11.20 |-Branch two:
% 38.49/11.20 | (336) all_24_1_29 = 0
% 38.49/11.20 | (796) ~ (all_24_2_30 = 0)
% 38.49/11.20 |
% 38.49/11.20 | Equations (792) can reduce 796 to:
% 38.49/11.20 | (174) $false
% 38.49/11.20 |
% 38.49/11.20 |-The branch is then unsatisfiable
% 38.49/11.20 |-Branch two:
% 38.49/11.20 | (798) sdtlseqdt0(xp, xp) = all_0_1_1
% 38.49/11.20 | (799) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0)
% 38.49/11.20 |
% 38.49/11.20 +-Applying beta-rule and splitting (799), into two cases.
% 38.49/11.20 |-Branch one:
% 38.49/11.20 | (173) all_0_1_1 = 0
% 38.49/11.20 |
% 38.49/11.20 | Equations (173) can reduce 54 to:
% 38.49/11.20 | (174) $false
% 38.49/11.20 |
% 38.49/11.20 |-The branch is then unsatisfiable
% 38.49/11.20 |-Branch two:
% 38.49/11.20 | (54) ~ (all_0_1_1 = 0)
% 38.49/11.20 | (803) ? [v0] : ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0)
% 38.49/11.20 |
% 38.49/11.20 | Instantiating (803) with all_152_0_230 yields:
% 38.49/11.20 | (804) ~ (all_152_0_230 = 0) & aNaturalNumber0(xp) = all_152_0_230
% 38.49/11.20 |
% 38.49/11.20 | Applying alpha-rule on (804) yields:
% 38.49/11.20 | (805) ~ (all_152_0_230 = 0)
% 38.49/11.20 | (806) aNaturalNumber0(xp) = all_152_0_230
% 38.49/11.20 |
% 38.49/11.20 | Instantiating formula (2) with xp, all_152_0_230, 0 and discharging atoms aNaturalNumber0(xp) = all_152_0_230, aNaturalNumber0(xp) = 0, yields:
% 38.49/11.20 | (807) all_152_0_230 = 0
% 38.49/11.20 |
% 38.49/11.20 | Equations (807) can reduce 805 to:
% 38.49/11.20 | (174) $false
% 38.49/11.20 |
% 38.49/11.20 |-The branch is then unsatisfiable
% 38.49/11.20 |-Branch two:
% 38.49/11.20 | (809) aNaturalNumber0(xp) = all_23_1_26 & aNaturalNumber0(xm) = all_23_2_27 & ( ~ (all_23_1_26 = 0) | ~ (all_23_2_27 = 0))
% 38.49/11.21 |
% 38.49/11.21 | Applying alpha-rule on (809) yields:
% 38.49/11.21 | (810) aNaturalNumber0(xp) = all_23_1_26
% 38.49/11.21 | (811) aNaturalNumber0(xm) = all_23_2_27
% 38.49/11.21 | (812) ~ (all_23_1_26 = 0) | ~ (all_23_2_27 = 0)
% 38.49/11.21 |
% 38.49/11.21 | Instantiating formula (2) with xp, all_23_1_26, 0 and discharging atoms aNaturalNumber0(xp) = all_23_1_26, aNaturalNumber0(xp) = 0, yields:
% 38.49/11.21 | (326) all_23_1_26 = 0
% 38.49/11.21 |
% 38.49/11.21 | Instantiating formula (2) with xm, all_23_2_27, 0 and discharging atoms aNaturalNumber0(xm) = all_23_2_27, aNaturalNumber0(xm) = 0, yields:
% 38.49/11.21 | (814) all_23_2_27 = 0
% 38.49/11.21 |
% 38.49/11.21 +-Applying beta-rule and splitting (812), into two cases.
% 38.49/11.21 |-Branch one:
% 38.49/11.21 | (815) ~ (all_23_1_26 = 0)
% 38.49/11.21 |
% 38.49/11.21 | Equations (326) can reduce 815 to:
% 38.49/11.21 | (174) $false
% 38.49/11.21 |
% 38.49/11.21 |-The branch is then unsatisfiable
% 38.49/11.21 |-Branch two:
% 38.49/11.21 | (326) all_23_1_26 = 0
% 38.49/11.21 | (818) ~ (all_23_2_27 = 0)
% 38.49/11.21 |
% 38.49/11.21 | Equations (814) can reduce 818 to:
% 38.49/11.21 | (174) $false
% 38.49/11.21 |
% 38.49/11.21 |-The branch is then unsatisfiable
% 38.49/11.21 |-Branch two:
% 38.49/11.21 | (820) aNaturalNumber0(xp) = all_22_1_23 & aNaturalNumber0(xn) = all_22_2_24 & ( ~ (all_22_1_23 = 0) | ~ (all_22_2_24 = 0))
% 38.49/11.21 |
% 38.49/11.21 | Applying alpha-rule on (820) yields:
% 38.49/11.21 | (821) aNaturalNumber0(xp) = all_22_1_23
% 38.49/11.21 | (822) aNaturalNumber0(xn) = all_22_2_24
% 38.49/11.21 | (823) ~ (all_22_1_23 = 0) | ~ (all_22_2_24 = 0)
% 38.49/11.21 |
% 38.49/11.21 | Instantiating formula (2) with xp, all_22_1_23, 0 and discharging atoms aNaturalNumber0(xp) = all_22_1_23, aNaturalNumber0(xp) = 0, yields:
% 38.49/11.21 | (307) all_22_1_23 = 0
% 38.49/11.21 |
% 38.49/11.21 | Instantiating formula (2) with xn, all_22_2_24, 0 and discharging atoms aNaturalNumber0(xn) = all_22_2_24, aNaturalNumber0(xn) = 0, yields:
% 38.49/11.21 | (825) all_22_2_24 = 0
% 38.49/11.21 |
% 38.49/11.21 +-Applying beta-rule and splitting (823), into two cases.
% 38.49/11.21 |-Branch one:
% 38.49/11.21 | (826) ~ (all_22_1_23 = 0)
% 38.49/11.21 |
% 38.49/11.21 | Equations (307) can reduce 826 to:
% 38.49/11.21 | (174) $false
% 38.49/11.21 |
% 38.49/11.21 |-The branch is then unsatisfiable
% 38.49/11.21 |-Branch two:
% 38.49/11.21 | (307) all_22_1_23 = 0
% 38.49/11.21 | (829) ~ (all_22_2_24 = 0)
% 38.49/11.21 |
% 38.49/11.21 | Equations (825) can reduce 829 to:
% 38.49/11.21 | (174) $false
% 38.49/11.21 |
% 38.49/11.21 |-The branch is then unsatisfiable
% 38.49/11.21 % SZS output end Proof for theBenchmark
% 38.49/11.21
% 38.49/11.21 10608ms
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