TSTP Solution File: NUM496+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM496+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n021.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 08:45:07 EDT 2022
% Result : Theorem 22.85s 6.47s
% Output : Proof 44.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM496+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n021.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 : Thu Jul 7 17:43:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.59 ____ _
% 0.20/0.59 ___ / __ \_____(_)___ ________ __________
% 0.20/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.20/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic
% 0.20/0.59 (ePrincess v.1.0)
% 0.20/0.59
% 0.20/0.59 (c) Philipp Rümmer, 2009-2015
% 0.20/0.59 (c) Peter Backeman, 2014-2015
% 0.20/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.59 Bug reports to peter@backeman.se
% 0.20/0.59
% 0.20/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.59
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.74/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.89/1.02 Prover 0: Preprocessing ...
% 3.85/1.53 Prover 0: Constructing countermodel ...
% 20.64/5.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 20.84/6.04 Prover 1: Preprocessing ...
% 21.53/6.18 Prover 1: Constructing countermodel ...
% 22.85/6.47 Prover 1: proved (532ms)
% 22.85/6.47 Prover 0: stopped
% 22.85/6.47
% 22.85/6.47 No countermodel exists, formula is valid
% 22.85/6.47 % SZS status Theorem for theBenchmark
% 22.85/6.47
% 22.85/6.47 Generating proof ... found it (size 690)
% 43.54/12.71
% 43.54/12.71 % SZS output start Proof for theBenchmark
% 43.54/12.71 Assumed formulas after preprocessing and simplification:
% 43.54/12.71 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (xr = xn) & ~ (sz10 = sz00) & isPrime0(xp) = 0 & doDivides0(xp, v3) = 0 & doDivides0(xp, v2) = 0 & doDivides0(xp, xr) = 0 & doDivides0(xp, xm) = v4 & doDivides0(xp, xn) = v5 & sdtmndt0(xn, xp) = xr & sdtlseqdt0(xr, xn) = 0 & sdtlseqdt0(xp, xn) = 0 & sdtasdt0(xr, xm) = v3 & sdtasdt0(xn, xm) = v2 & sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) = v0 & aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 & ~ (isPrime0(sz10) = 0) & ~ (isPrime0(sz00) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | v6 = sz00 | ~ (sdtlseqdt0(v9, v10) = v11) | ~ (sdtasdt0(v6, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (sdtlseqdt0(v16, v17) = v18 & sdtlseqdt0(v7, v8) = v15 & sdtasdt0(v8, v6) = v17 & sdtasdt0(v7, v6) = v16 & aNaturalNumber0(v8) = v14 & aNaturalNumber0(v7) = v13 & aNaturalNumber0(v6) = v12 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | (v18 = 0 & v11 = 0 & ~ (v17 = v16) & ~ (v10 = v9))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v7 = v6 | ~ (sdtlseqdt0(v9, v10) = v11) | ~ (sdtlseqdt0(v6, v7) = 0) | ~ (sdtpldt0(v7, v8) = v10) | ~ (sdtpldt0(v6, v8) = v9) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((sdtlseqdt0(v13, v14) = v15 & sdtpldt0(v8, v7) = v14 & sdtpldt0(v8, v6) = v13 & aNaturalNumber0(v8) = v12 & ( ~ (v12 = 0) | (v15 = 0 & v11 = 0 & ~ (v14 = v13) & ~ (v10 = v9)))) | (aNaturalNumber0(v7) = v13 & aNaturalNumber0(v6) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v6 = sz00 | ~ (sdtsldt0(v10, v6) = v11) | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v9, v7) = v10) | ? [v12] : ? [v13] : ? [v14] : ((doDivides0(v6, v7) = v14 & aNaturalNumber0(v7) = v13 & aNaturalNumber0(v6) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0))) | (sdtasdt0(v9, v8) = v13 & aNaturalNumber0(v9) = v12 & ( ~ (v12 = 0) | v13 = v11)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v6, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ (sdtpldt0(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (sdtasdt0(v15, v6) = v17 & sdtasdt0(v8, v6) = v19 & sdtasdt0(v7, v6) = v18 & sdtasdt0(v6, v15) = v16 & sdtpldt0(v18, v19) = v20 & sdtpldt0(v7, v8) = v15 & aNaturalNumber0(v8) = v14 & aNaturalNumber0(v7) = v13 & aNaturalNumber0(v6) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | (v20 = v17 & v16 = v11)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (doDivides0(v6, v9) = v10) | ~ (sdtpldt0(v7, v8) = v9) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (doDivides0(v6, v8) = v15 & doDivides0(v6, v7) = v14 & aNaturalNumber0(v8) = v13 & aNaturalNumber0(v7) = v12 & aNaturalNumber0(v6) = v11 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v6, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ (aNaturalNumber0(v6) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v8, v6) = v14 & sdtasdt0(v7, v6) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) | ( ~ (v14 = v13) & ~ (v10 = v9))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v6, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (sdtpldt0(v8, v6) = v15 & sdtpldt0(v7, v6) = v14 & aNaturalNumber0(v8) = v13 & aNaturalNumber0(v7) = v12 & aNaturalNumber0(v6) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ( ~ (v15 = v14) & ~ (v10 = v9))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v9, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (sdtasdt0(v7, v8) = v14 & sdtasdt0(v6, v14) = v15 & aNaturalNumber0(v8) = v13 & aNaturalNumber0(v7) = v12 & aNaturalNumber0(v6) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | v15 = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (sdtpldt0(v7, v8) = v14 & sdtpldt0(v6, v14) = v15 & aNaturalNumber0(v8) = v13 & aNaturalNumber0(v7) = v12 & aNaturalNumber0(v6) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | v15 = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | v6 = sz00 | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v6, v9) = v7) | ? [v10] : ? [v11] : ? [v12] : (( ~ (v10 = 0) & aNaturalNumber0(v9) = v10) | (doDivides0(v6, v7) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (sdtmndt0(v7, v6) = v8) | ~ (sdtpldt0(v6, v9) = v7) | ? [v10] : ? [v11] : ? [v12] : (( ~ (v10 = 0) & aNaturalNumber0(v9) = v10) | (sdtlseqdt0(v6, v7) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | v6 = sz00 | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v6, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (doDivides0(v6, v7) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (sdtmndt0(v7, v6) = v8) | ~ (sdtpldt0(v6, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (sdtlseqdt0(v6, v7) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v6 = sz00 | ~ (sdtlseqdt0(v7, v8) = v9) | ~ (sdtasdt0(v7, v6) = v8) | ? [v10] : ? [v11] : (aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (doDivides0(v6, v8) = v9) | ~ (doDivides0(v6, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (doDivides0(v7, v8) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (sdtlseqdt0(v6, v8) = v9) | ~ (sdtlseqdt0(v6, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (sdtlseqdt0(v7, v8) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (doDivides0(v6, v7) = v8) | ~ (sdtasdt0(v6, v9) = v7) | ? [v10] : ? [v11] : (( ~ (v10 = 0) & aNaturalNumber0(v9) = v10) | (aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (sdtlseqdt0(v6, v7) = v8) | ~ (sdtpldt0(v6, v9) = v7) | ? [v10] : ? [v11] : (( ~ (v10 = 0) & aNaturalNumber0(v9) = v10) | (aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtsldt0(v9, v8) = v7) | ~ (sdtsldt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (doDivides0(v9, v8) = v7) | ~ (doDivides0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (iLess0(v9, v8) = v7) | ~ (iLess0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtmndt0(v9, v8) = v7) | ~ (sdtmndt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtlseqdt0(v9, v8) = v7) | ~ (sdtlseqdt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtasdt0(v9, v8) = v7) | ~ (sdtasdt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v9, v8) = v7) | ~ (sdtpldt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = sz00 | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v6, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v10 = 0 & aNaturalNumber0(v8) = 0) | (doDivides0(v6, v7) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (doDivides0(v8, v9) = 0) | ~ (sdtasdt0(v6, v7) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (isPrime0(v8) = v13 & doDivides0(v8, v7) = v18 & doDivides0(v8, v6) = v17 & iLess0(v15, v1) = v16 & sdtpldt0(v14, v8) = v15 & sdtpldt0(v6, v7) = v14 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v16 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | v18 = 0 | v17 = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (doDivides0(v6, v9) = 0) | ~ (sdtpldt0(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (doDivides0(v6, v8) = v14 & doDivides0(v6, v7) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | v14 = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtmndt0(v7, v6) = v8) | ~ (sdtpldt0(v6, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v10 = 0 & aNaturalNumber0(v8) = 0) | (sdtlseqdt0(v6, v7) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0))))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = v6 | ~ (iLess0(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (sdtlseqdt0(v6, v7) = v11 & aNaturalNumber0(v7) = v10 & aNaturalNumber0(v6) = v9 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = sz00 | ~ (sdtlseqdt0(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (doDivides0(v6, v7) = v11 & aNaturalNumber0(v7) = v10 & aNaturalNumber0(v6) = v9 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (sdtlseqdt0(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (sdtlseqdt0(v7, v6) = v11 & aNaturalNumber0(v7) = v10 & aNaturalNumber0(v6) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | (v11 = 0 & ~ (v7 = v6))))) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (isPrime0(v8) = v7) | ~ (isPrime0(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (aNaturalNumber0(v8) = v7) | ~ (aNaturalNumber0(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (sdtasdt0(v7, v6) = v11 & aNaturalNumber0(v7) = v10 & aNaturalNumber0(v6) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = v8))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (aNaturalNumber0(v8) = v11 & aNaturalNumber0(v7) = v10 & aNaturalNumber0(v6) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = 0))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (sdtpldt0(v7, v6) = v11 & aNaturalNumber0(v7) = v10 & aNaturalNumber0(v6) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = v8))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (aNaturalNumber0(v8) = v11 & aNaturalNumber0(v7) = v10 & aNaturalNumber0(v6) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = 0))) & ! [v6] : ! [v7] : (v7 = v6 | v7 = sz10 | ~ (isPrime0(v6) = 0) | ~ (doDivides0(v7, v6) = 0) | ? [v8] : (( ~ (v8 = 0) & aNaturalNumber0(v7) = v8) | ( ~ (v8 = 0) & aNaturalNumber0(v6) = v8))) & ! [v6] : ! [v7] : (v7 = v6 | ~ (sdtlseqdt0(v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : (sdtlseqdt0(v7, v6) = v10 & aNaturalNumber0(v7) = v9 & aNaturalNumber0(v6) = v8 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v6] : ! [v7] : (v7 = sz00 | v6 = sz00 | ~ (sdtasdt0(v6, v7) = sz00) | ? [v8] : ? [v9] : (aNaturalNumber0(v7) = v9 & aNaturalNumber0(v6) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v6] : ! [v7] : (v7 = sz00 | ~ (sdtpldt0(v6, v7) = sz00) | ? [v8] : ? [v9] : (aNaturalNumber0(v7) = v9 & aNaturalNumber0(v6) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v6] : ! [v7] : (v7 = 0 | v6 = sz10 | v6 = sz00 | ~ (isPrime0(v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & ~ (v8 = v6) & ~ (v8 = sz10) & doDivides0(v8, v6) = 0 & aNaturalNumber0(v8) = 0) | ( ~ (v8 = 0) & aNaturalNumber0(v6) = v8))) & ! [v6] : ! [v7] : (v7 = 0 | v6 = sz10 | v6 = sz00 | ~ (sdtlseqdt0(sz10, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & aNaturalNumber0(v6) = v8)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (sdtlseqdt0(v6, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & aNaturalNumber0(v6) = v8)) & ! [v6] : ! [v7] : (v6 = sz00 | ~ (sdtpldt0(v6, v7) = sz00) | ? [v8] : ? [v9] : (aNaturalNumber0(v7) = v9 & aNaturalNumber0(v6) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v6] : ! [v7] : ( ~ (doDivides0(v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v10 = v7 & v9 = 0 & sdtasdt0(v6, v8) = v7 & aNaturalNumber0(v8) = 0) | (aNaturalNumber0(v7) = v9 & aNaturalNumber0(v6) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))) & ! [v6] : ! [v7] : ( ~ (sdtlseqdt0(v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v10 = v7 & v9 = 0 & sdtpldt0(v6, v8) = v7 & aNaturalNumber0(v8) = 0) | (aNaturalNumber0(v7) = v9 & aNaturalNumber0(v6) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))) & ! [v6] : ! [v7] : ( ~ (sdtasdt0(sz10, v6) = v7) | ? [v8] : ? [v9] : (sdtasdt0(v6, sz10) = v9 & aNaturalNumber0(v6) = v8 & ( ~ (v8 = 0) | (v9 = v6 & v7 = v6)))) & ! [v6] : ! [v7] : ( ~ (sdtasdt0(sz00, v6) = v7) | ? [v8] : ? [v9] : (sdtasdt0(v6, sz00) = v9 & aNaturalNumber0(v6) = v8 & ( ~ (v8 = 0) | (v9 = sz00 & v7 = sz00)))) & ! [v6] : ! [v7] : ( ~ (sdtpldt0(sz00, v6) = v7) | ? [v8] : ? [v9] : (sdtpldt0(v6, sz00) = v9 & aNaturalNumber0(v6) = v8 & ( ~ (v8 = 0) | (v9 = v6 & v7 = v6)))) & ! [v6] : (v6 = sz10 | v6 = sz00 | ~ (aNaturalNumber0(v6) = 0) | ? [v7] : (isPrime0(v7) = 0 & doDivides0(v7, v6) = 0 & aNaturalNumber0(v7) = 0)))
% 43.54/12.78 | 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 yields:
% 43.54/12.78 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & ~ (xr = xn) & ~ (sz10 = sz00) & isPrime0(xp) = 0 & doDivides0(xp, all_0_2_2) = 0 & doDivides0(xp, all_0_3_3) = 0 & doDivides0(xp, xr) = 0 & doDivides0(xp, xm) = all_0_1_1 & doDivides0(xp, xn) = all_0_0_0 & sdtmndt0(xn, xp) = xr & sdtlseqdt0(xr, xn) = 0 & sdtlseqdt0(xp, xn) = 0 & sdtasdt0(xr, xm) = all_0_2_2 & sdtasdt0(xn, xm) = all_0_3_3 & sdtpldt0(all_0_5_5, xp) = all_0_4_4 & sdtpldt0(xn, xm) = all_0_5_5 & 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_4_4) = 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 | v1 = sz00 | ~ (sdtlseqdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (doDivides0(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 | ~ (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))
% 43.90/12.80 |
% 43.90/12.80 | Applying alpha-rule on (1) yields:
% 43.90/12.80 | (2) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00))))
% 43.90/12.80 | (3) ! [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)))
% 43.90/12.80 | (4) ! [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))))
% 43.90/12.80 | (5) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 43.90/12.80 | (6) ! [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)))))
% 43.90/12.80 | (7) ! [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)))))
% 43.90/12.80 | (8) sdtasdt0(xn, xm) = all_0_3_3
% 43.90/12.80 | (9) ! [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)))))
% 43.90/12.80 | (10) ! [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))))
% 43.90/12.81 | (11) ! [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_4_4) = 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)))
% 43.90/12.81 | (12) doDivides0(xp, xr) = 0
% 43.90/12.81 | (13) ! [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)))
% 43.90/12.81 | (14) ! [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))))
% 43.90/12.81 | (15) ! [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))))
% 43.90/12.81 | (16) doDivides0(xp, all_0_3_3) = 0
% 43.90/12.81 | (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)))))
% 43.90/12.81 | (18) ~ (all_0_1_1 = 0)
% 43.90/12.81 | (19) ! [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)))
% 43.90/12.81 | (20) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 43.90/12.81 | (21) ! [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))))
% 43.90/12.81 | (22) sdtpldt0(all_0_5_5, xp) = all_0_4_4
% 43.90/12.81 | (23) ! [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)))))
% 43.90/12.81 | (24) aNaturalNumber0(xn) = 0
% 43.90/12.81 | (25) ~ (isPrime0(sz00) = 0)
% 43.90/12.81 | (26) ! [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))))
% 43.90/12.81 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0))
% 43.90/12.81 | (28) ! [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)))))
% 43.90/12.81 | (29) doDivides0(xp, all_0_2_2) = 0
% 43.90/12.81 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 43.90/12.81 | (31) ! [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)))
% 43.90/12.81 | (32) ! [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)))))
% 43.90/12.81 | (33) ! [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)))
% 43.90/12.81 | (34) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0))
% 43.90/12.81 | (35) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ (isPrime0(v0) = 0) | ~ (doDivides0(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 43.90/12.81 | (36) ! [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)))))
% 43.90/12.82 | (37) ! [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)))
% 43.90/12.82 | (38) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = sz00 | ~ (sdtlseqdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))))
% 43.90/12.82 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0))
% 43.90/12.82 | (40) ! [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)))))
% 43.90/12.82 | (41) sdtmndt0(xn, xp) = xr
% 43.90/12.82 | (42) ! [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))))
% 43.90/12.82 | (43) ~ (all_0_0_0 = 0)
% 43.90/12.82 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 43.90/12.82 | (45) aNaturalNumber0(xp) = 0
% 43.90/12.82 | (46) ! [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)))))
% 43.90/12.82 | (47) ! [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))))
% 43.90/12.82 | (48) isPrime0(xp) = 0
% 43.90/12.82 | (49) ! [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)))))
% 43.90/12.82 | (50) ~ (sz10 = sz00)
% 43.90/12.82 | (51) doDivides0(xp, xn) = all_0_0_0
% 43.90/12.82 | (52) ! [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)))))
% 43.90/12.82 | (53) ! [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))))
% 43.90/12.82 | (54) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 43.90/12.82 | (55) ! [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)))
% 43.90/12.82 | (56) doDivides0(xp, xm) = all_0_1_1
% 43.90/12.82 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 43.90/12.82 | (58) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 43.90/12.82 | (59) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0))
% 43.90/12.82 | (60) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0))
% 43.90/12.82 | (61) ~ (isPrime0(sz10) = 0)
% 43.90/12.82 | (62) sdtasdt0(xr, xm) = all_0_2_2
% 43.90/12.82 | (63) ! [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))))
% 43.90/12.82 | (64) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 43.90/12.82 | (65) sdtlseqdt0(xr, xn) = 0
% 43.90/12.82 | (66) aNaturalNumber0(sz10) = 0
% 43.90/12.82 | (67) ! [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)))
% 43.90/12.82 | (68) sdtpldt0(xn, xm) = all_0_5_5
% 43.90/12.82 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 43.90/12.82 | (70) ! [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)))))
% 43.90/12.83 | (71) sdtlseqdt0(xp, xn) = 0
% 43.90/12.83 | (72) aNaturalNumber0(xm) = 0
% 43.90/12.83 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0))
% 43.90/12.83 | (74) ~ (xr = xn)
% 43.90/12.83 | (75) ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 43.90/12.83 | (76) aNaturalNumber0(sz00) = 0
% 43.90/12.83 | (77) ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 43.90/12.83 |
% 43.90/12.83 | Using (48) and (61) yields:
% 43.90/12.83 | (78) ~ (xp = sz10)
% 43.90/12.83 |
% 43.90/12.83 | Using (48) and (25) yields:
% 43.90/12.83 | (79) ~ (xp = sz00)
% 43.90/12.83 |
% 43.90/12.83 | Instantiating formula (6) with all_0_3_3, xp and discharging atoms doDivides0(xp, all_0_3_3) = 0, yields:
% 43.90/12.83 | (80) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_3_3 & v1 = 0 & sdtasdt0(xp, v0) = all_0_3_3 & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 43.90/12.83 |
% 43.90/12.83 | Instantiating formula (21) with all_0_1_1, xm, all_0_2_2, xp and discharging atoms doDivides0(xp, all_0_2_2) = 0, doDivides0(xp, xm) = all_0_1_1, yields:
% 43.90/12.83 | (81) all_0_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_2_2, xm) = v3 & aNaturalNumber0(all_0_2_2) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 43.90/12.83 |
% 43.90/12.83 | Instantiating formula (21) with all_0_1_1, xm, all_0_3_3, xp and discharging atoms doDivides0(xp, all_0_3_3) = 0, doDivides0(xp, xm) = all_0_1_1, yields:
% 43.90/12.83 | (82) all_0_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_3_3, xm) = v3 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 43.90/12.83 |
% 43.90/12.83 | Instantiating formula (21) with all_0_1_1, xm, xr, xp and discharging atoms doDivides0(xp, xr) = 0, doDivides0(xp, xm) = all_0_1_1, yields:
% 43.90/12.83 | (83) all_0_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(xr, xm) = v3 & aNaturalNumber0(xr) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 43.90/12.83 |
% 43.90/12.83 | Instantiating formula (21) with all_0_0_0, xn, all_0_2_2, xp and discharging atoms doDivides0(xp, all_0_2_2) = 0, doDivides0(xp, xn) = all_0_0_0, yields:
% 43.90/12.83 | (84) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_2_2, xn) = v3 & aNaturalNumber0(all_0_2_2) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 43.90/12.83 |
% 43.90/12.83 | Instantiating formula (21) with all_0_0_0, xn, all_0_3_3, xp and discharging atoms doDivides0(xp, all_0_3_3) = 0, doDivides0(xp, xn) = all_0_0_0, yields:
% 43.90/12.83 | (85) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_3_3, xn) = v3 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 43.90/12.83 |
% 43.90/12.83 | Instantiating formula (21) with all_0_0_0, xn, xr, xp and discharging atoms doDivides0(xp, xr) = 0, doDivides0(xp, xn) = all_0_0_0, yields:
% 43.90/12.83 | (86) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(xr, xn) = v3 & aNaturalNumber0(xr) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 43.90/12.83 |
% 43.90/12.83 | Instantiating formula (42) with xn, xr and discharging atoms sdtlseqdt0(xr, xn) = 0, yields:
% 43.90/12.83 | (87) xr = xn | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xn, xr) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 43.90/12.83 |
% 43.90/12.83 | Instantiating formula (28) with xn, xp and discharging atoms sdtlseqdt0(xp, xn) = 0, yields:
% 43.90/12.83 | (88) ? [v0] : ? [v1] : ? [v2] : ((v2 = xn & v1 = 0 & sdtpldt0(xp, v0) = xn & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 43.90/12.83 |
% 43.90/12.83 | Instantiating formula (11) with all_0_2_2, xp, xm, xr and discharging atoms doDivides0(xp, all_0_2_2) = 0, sdtasdt0(xr, xm) = all_0_2_2, yields:
% 43.90/12.83 | (89) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, xr) = v7 & doDivides0(xp, xm) = v8 & iLess0(v5, all_0_4_4) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xr, xm) = v4 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 43.90/12.83 |
% 43.90/12.83 | Instantiating formula (67) with all_0_2_2, xm, xr and discharging atoms sdtasdt0(xr, xm) = all_0_2_2, yields:
% 43.90/12.83 | (90) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xm, xr) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_2_2))
% 43.90/12.83 |
% 43.90/12.83 | Instantiating formula (37) with all_0_2_2, xm, xr and discharging atoms sdtasdt0(xr, xm) = all_0_2_2, yields:
% 43.90/12.83 | (91) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_2_2) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 43.90/12.83 |
% 43.90/12.83 | Instantiating formula (11) with all_0_3_3, xp, xm, xn and discharging atoms doDivides0(xp, all_0_3_3) = 0, sdtasdt0(xn, xm) = all_0_3_3, yields:
% 43.90/12.83 | (92) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, xm) = v8 & doDivides0(xp, xn) = v7 & iLess0(v5, all_0_4_4) = 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))
% 43.90/12.83 |
% 43.90/12.83 | Instantiating formula (67) with all_0_3_3, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_3_3, yields:
% 43.90/12.83 | (93) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_3_3))
% 43.90/12.83 |
% 43.90/12.83 | Instantiating formula (37) with all_0_3_3, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_3_3, yields:
% 43.90/12.83 | (94) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_3_3) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 43.90/12.84 |
% 43.90/12.84 | Instantiating formula (55) with all_0_4_4, xp, all_0_5_5 and discharging atoms sdtpldt0(all_0_5_5, xp) = all_0_4_4, yields:
% 43.90/12.84 | (95) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, all_0_5_5) = v2 & aNaturalNumber0(all_0_5_5) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_4_4))
% 43.90/12.84 |
% 43.90/12.84 | Instantiating formula (13) with all_0_4_4, xp, all_0_5_5 and discharging atoms sdtpldt0(all_0_5_5, xp) = all_0_4_4, yields:
% 43.90/12.84 | (96) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_4_4) = v2 & aNaturalNumber0(all_0_5_5) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 43.90/12.84 |
% 43.90/12.84 | Instantiating formula (3) with all_0_4_4, all_0_5_5, xp, xm, xn and discharging atoms sdtpldt0(all_0_5_5, xp) = all_0_4_4, sdtpldt0(xn, xm) = all_0_5_5, yields:
% 43.90/12.84 | (97) ? [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_4_4))
% 43.90/12.84 |
% 43.90/12.84 | Instantiating formula (55) with all_0_5_5, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_5_5, yields:
% 43.90/12.84 | (98) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_5_5))
% 43.90/12.84 |
% 43.90/12.84 | Instantiating formula (13) with all_0_5_5, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_5_5, yields:
% 43.90/12.84 | (99) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_5_5) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 43.90/12.84 |
% 43.90/12.84 | Instantiating formula (34) with xp and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 43.90/12.84 | (100) xp = sz10 | xp = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 43.90/12.84 |
% 43.90/12.84 | Instantiating (99) with all_12_0_6, all_12_1_7, all_12_2_8 yields:
% 43.90/12.84 | (101) aNaturalNumber0(all_0_5_5) = all_12_0_6 & aNaturalNumber0(xm) = all_12_1_7 & aNaturalNumber0(xn) = all_12_2_8 & ( ~ (all_12_1_7 = 0) | ~ (all_12_2_8 = 0) | all_12_0_6 = 0)
% 43.90/12.84 |
% 43.90/12.84 | Applying alpha-rule on (101) yields:
% 43.90/12.84 | (102) aNaturalNumber0(all_0_5_5) = all_12_0_6
% 43.90/12.84 | (103) aNaturalNumber0(xm) = all_12_1_7
% 43.90/12.84 | (104) aNaturalNumber0(xn) = all_12_2_8
% 43.90/12.84 | (105) ~ (all_12_1_7 = 0) | ~ (all_12_2_8 = 0) | all_12_0_6 = 0
% 43.90/12.84 |
% 43.90/12.84 | Instantiating (92) with all_14_0_9, all_14_1_10, all_14_2_11, all_14_3_12, all_14_4_13, all_14_5_14, all_14_6_15, all_14_7_16, all_14_8_17 yields:
% 43.90/12.84 | (106) isPrime0(xp) = all_14_5_14 & doDivides0(xp, xm) = all_14_0_9 & doDivides0(xp, xn) = all_14_1_10 & iLess0(all_14_3_12, all_0_4_4) = all_14_2_11 & sdtpldt0(all_14_4_13, xp) = all_14_3_12 & sdtpldt0(xn, xm) = all_14_4_13 & aNaturalNumber0(xp) = all_14_6_15 & aNaturalNumber0(xm) = all_14_7_16 & aNaturalNumber0(xn) = all_14_8_17 & ( ~ (all_14_2_11 = 0) | ~ (all_14_5_14 = 0) | ~ (all_14_6_15 = 0) | ~ (all_14_7_16 = 0) | ~ (all_14_8_17 = 0) | all_14_0_9 = 0 | all_14_1_10 = 0)
% 43.90/12.84 |
% 43.90/12.84 | Applying alpha-rule on (106) yields:
% 43.90/12.84 | (107) ~ (all_14_2_11 = 0) | ~ (all_14_5_14 = 0) | ~ (all_14_6_15 = 0) | ~ (all_14_7_16 = 0) | ~ (all_14_8_17 = 0) | all_14_0_9 = 0 | all_14_1_10 = 0
% 43.90/12.84 | (108) aNaturalNumber0(xn) = all_14_8_17
% 43.90/12.84 | (109) iLess0(all_14_3_12, all_0_4_4) = all_14_2_11
% 43.90/12.84 | (110) sdtpldt0(xn, xm) = all_14_4_13
% 43.90/12.84 | (111) aNaturalNumber0(xm) = all_14_7_16
% 43.90/12.84 | (112) doDivides0(xp, xm) = all_14_0_9
% 43.90/12.84 | (113) aNaturalNumber0(xp) = all_14_6_15
% 43.90/12.84 | (114) sdtpldt0(all_14_4_13, xp) = all_14_3_12
% 43.90/12.84 | (115) isPrime0(xp) = all_14_5_14
% 43.90/12.84 | (116) doDivides0(xp, xn) = all_14_1_10
% 43.90/12.84 |
% 43.90/12.84 | Instantiating (89) with all_16_0_18, all_16_1_19, all_16_2_20, all_16_3_21, all_16_4_22, all_16_5_23, all_16_6_24, all_16_7_25, all_16_8_26 yields:
% 43.90/12.84 | (117) isPrime0(xp) = all_16_5_23 & doDivides0(xp, xr) = all_16_1_19 & doDivides0(xp, xm) = all_16_0_18 & iLess0(all_16_3_21, all_0_4_4) = all_16_2_20 & sdtpldt0(all_16_4_22, xp) = all_16_3_21 & sdtpldt0(xr, xm) = all_16_4_22 & aNaturalNumber0(xr) = all_16_8_26 & aNaturalNumber0(xp) = all_16_6_24 & aNaturalNumber0(xm) = all_16_7_25 & ( ~ (all_16_2_20 = 0) | ~ (all_16_5_23 = 0) | ~ (all_16_6_24 = 0) | ~ (all_16_7_25 = 0) | ~ (all_16_8_26 = 0) | all_16_0_18 = 0 | all_16_1_19 = 0)
% 43.90/12.84 |
% 43.90/12.84 | Applying alpha-rule on (117) yields:
% 43.90/12.84 | (118) ~ (all_16_2_20 = 0) | ~ (all_16_5_23 = 0) | ~ (all_16_6_24 = 0) | ~ (all_16_7_25 = 0) | ~ (all_16_8_26 = 0) | all_16_0_18 = 0 | all_16_1_19 = 0
% 43.90/12.84 | (119) sdtpldt0(all_16_4_22, xp) = all_16_3_21
% 43.90/12.84 | (120) aNaturalNumber0(xm) = all_16_7_25
% 43.90/12.84 | (121) sdtpldt0(xr, xm) = all_16_4_22
% 43.90/12.84 | (122) doDivides0(xp, xr) = all_16_1_19
% 43.90/12.84 | (123) doDivides0(xp, xm) = all_16_0_18
% 43.90/12.84 | (124) aNaturalNumber0(xr) = all_16_8_26
% 43.90/12.84 | (125) isPrime0(xp) = all_16_5_23
% 43.90/12.84 | (126) aNaturalNumber0(xp) = all_16_6_24
% 43.90/12.84 | (127) iLess0(all_16_3_21, all_0_4_4) = all_16_2_20
% 43.90/12.84 |
% 43.90/12.84 | Instantiating (88) with all_18_0_27, all_18_1_28, all_18_2_29 yields:
% 43.90/12.84 | (128) (all_18_0_27 = xn & all_18_1_28 = 0 & sdtpldt0(xp, all_18_2_29) = xn & aNaturalNumber0(all_18_2_29) = 0) | (aNaturalNumber0(xp) = all_18_2_29 & aNaturalNumber0(xn) = all_18_1_28 & ( ~ (all_18_1_28 = 0) | ~ (all_18_2_29 = 0)))
% 43.90/12.84 |
% 43.90/12.84 | Instantiating (98) with all_19_0_30, all_19_1_31, all_19_2_32 yields:
% 43.90/12.84 | (129) sdtpldt0(xm, xn) = all_19_0_30 & aNaturalNumber0(xm) = all_19_1_31 & aNaturalNumber0(xn) = all_19_2_32 & ( ~ (all_19_1_31 = 0) | ~ (all_19_2_32 = 0) | all_19_0_30 = all_0_5_5)
% 43.90/12.84 |
% 43.90/12.84 | Applying alpha-rule on (129) yields:
% 43.90/12.84 | (130) sdtpldt0(xm, xn) = all_19_0_30
% 43.90/12.84 | (131) aNaturalNumber0(xm) = all_19_1_31
% 43.90/12.84 | (132) aNaturalNumber0(xn) = all_19_2_32
% 43.90/12.84 | (133) ~ (all_19_1_31 = 0) | ~ (all_19_2_32 = 0) | all_19_0_30 = all_0_5_5
% 43.90/12.84 |
% 43.90/12.84 | Instantiating (96) with all_21_0_33, all_21_1_34, all_21_2_35 yields:
% 43.90/12.84 | (134) aNaturalNumber0(all_0_4_4) = all_21_0_33 & aNaturalNumber0(all_0_5_5) = all_21_2_35 & aNaturalNumber0(xp) = all_21_1_34 & ( ~ (all_21_1_34 = 0) | ~ (all_21_2_35 = 0) | all_21_0_33 = 0)
% 43.90/12.84 |
% 43.90/12.84 | Applying alpha-rule on (134) yields:
% 43.90/12.84 | (135) aNaturalNumber0(all_0_4_4) = all_21_0_33
% 43.90/12.84 | (136) aNaturalNumber0(all_0_5_5) = all_21_2_35
% 43.90/12.84 | (137) aNaturalNumber0(xp) = all_21_1_34
% 43.90/12.84 | (138) ~ (all_21_1_34 = 0) | ~ (all_21_2_35 = 0) | all_21_0_33 = 0
% 43.90/12.84 |
% 43.90/12.84 | Instantiating (94) with all_23_0_36, all_23_1_37, all_23_2_38 yields:
% 43.90/12.84 | (139) aNaturalNumber0(all_0_3_3) = all_23_0_36 & aNaturalNumber0(xm) = all_23_1_37 & aNaturalNumber0(xn) = all_23_2_38 & ( ~ (all_23_1_37 = 0) | ~ (all_23_2_38 = 0) | all_23_0_36 = 0)
% 43.90/12.84 |
% 43.90/12.84 | Applying alpha-rule on (139) yields:
% 43.90/12.84 | (140) aNaturalNumber0(all_0_3_3) = all_23_0_36
% 43.90/12.84 | (141) aNaturalNumber0(xm) = all_23_1_37
% 43.90/12.84 | (142) aNaturalNumber0(xn) = all_23_2_38
% 43.90/12.84 | (143) ~ (all_23_1_37 = 0) | ~ (all_23_2_38 = 0) | all_23_0_36 = 0
% 43.90/12.84 |
% 43.90/12.84 | Instantiating (93) with all_25_0_39, all_25_1_40, all_25_2_41 yields:
% 43.90/12.84 | (144) sdtasdt0(xm, xn) = all_25_0_39 & aNaturalNumber0(xm) = all_25_1_40 & aNaturalNumber0(xn) = all_25_2_41 & ( ~ (all_25_1_40 = 0) | ~ (all_25_2_41 = 0) | all_25_0_39 = all_0_3_3)
% 43.90/12.85 |
% 43.90/12.85 | Applying alpha-rule on (144) yields:
% 43.90/12.85 | (145) sdtasdt0(xm, xn) = all_25_0_39
% 43.90/12.85 | (146) aNaturalNumber0(xm) = all_25_1_40
% 43.90/12.85 | (147) aNaturalNumber0(xn) = all_25_2_41
% 43.90/12.85 | (148) ~ (all_25_1_40 = 0) | ~ (all_25_2_41 = 0) | all_25_0_39 = all_0_3_3
% 43.90/12.85 |
% 43.90/12.85 | Instantiating (91) with all_27_0_42, all_27_1_43, all_27_2_44 yields:
% 43.90/12.85 | (149) aNaturalNumber0(all_0_2_2) = all_27_0_42 & aNaturalNumber0(xr) = all_27_2_44 & aNaturalNumber0(xm) = all_27_1_43 & ( ~ (all_27_1_43 = 0) | ~ (all_27_2_44 = 0) | all_27_0_42 = 0)
% 43.90/12.85 |
% 43.90/12.85 | Applying alpha-rule on (149) yields:
% 43.90/12.85 | (150) aNaturalNumber0(all_0_2_2) = all_27_0_42
% 43.90/12.85 | (151) aNaturalNumber0(xr) = all_27_2_44
% 43.90/12.85 | (152) aNaturalNumber0(xm) = all_27_1_43
% 43.90/12.85 | (153) ~ (all_27_1_43 = 0) | ~ (all_27_2_44 = 0) | all_27_0_42 = 0
% 43.90/12.85 |
% 43.90/12.85 | Instantiating (90) with all_30_0_48, all_30_1_49, all_30_2_50 yields:
% 43.90/12.85 | (154) sdtasdt0(xm, xr) = all_30_0_48 & aNaturalNumber0(xr) = all_30_2_50 & aNaturalNumber0(xm) = all_30_1_49 & ( ~ (all_30_1_49 = 0) | ~ (all_30_2_50 = 0) | all_30_0_48 = all_0_2_2)
% 43.90/12.85 |
% 43.90/12.85 | Applying alpha-rule on (154) yields:
% 43.90/12.85 | (155) sdtasdt0(xm, xr) = all_30_0_48
% 43.90/12.85 | (156) aNaturalNumber0(xr) = all_30_2_50
% 43.90/12.85 | (157) aNaturalNumber0(xm) = all_30_1_49
% 43.90/12.85 | (158) ~ (all_30_1_49 = 0) | ~ (all_30_2_50 = 0) | all_30_0_48 = all_0_2_2
% 43.90/12.85 |
% 43.90/12.85 | Instantiating (95) with all_32_0_51, all_32_1_52, all_32_2_53 yields:
% 43.90/12.85 | (159) sdtpldt0(xp, all_0_5_5) = all_32_0_51 & aNaturalNumber0(all_0_5_5) = all_32_2_53 & aNaturalNumber0(xp) = all_32_1_52 & ( ~ (all_32_1_52 = 0) | ~ (all_32_2_53 = 0) | all_32_0_51 = all_0_4_4)
% 43.90/12.85 |
% 43.90/12.85 | Applying alpha-rule on (159) yields:
% 43.90/12.85 | (160) sdtpldt0(xp, all_0_5_5) = all_32_0_51
% 43.90/12.85 | (161) aNaturalNumber0(all_0_5_5) = all_32_2_53
% 43.90/12.85 | (162) aNaturalNumber0(xp) = all_32_1_52
% 43.90/12.85 | (163) ~ (all_32_1_52 = 0) | ~ (all_32_2_53 = 0) | all_32_0_51 = all_0_4_4
% 43.90/12.85 |
% 43.90/12.85 | Instantiating (97) with all_34_0_54, all_34_1_55, all_34_2_56, all_34_3_57, all_34_4_58 yields:
% 43.90/12.85 | (164) sdtpldt0(xm, xp) = all_34_1_55 & sdtpldt0(xn, all_34_1_55) = all_34_0_54 & aNaturalNumber0(xp) = all_34_2_56 & aNaturalNumber0(xm) = all_34_3_57 & aNaturalNumber0(xn) = all_34_4_58 & ( ~ (all_34_2_56 = 0) | ~ (all_34_3_57 = 0) | ~ (all_34_4_58 = 0) | all_34_0_54 = all_0_4_4)
% 43.90/12.85 |
% 43.90/12.85 | Applying alpha-rule on (164) yields:
% 43.90/12.85 | (165) aNaturalNumber0(xm) = all_34_3_57
% 43.90/12.85 | (166) sdtpldt0(xn, all_34_1_55) = all_34_0_54
% 43.90/12.85 | (167) aNaturalNumber0(xn) = all_34_4_58
% 43.90/12.85 | (168) aNaturalNumber0(xp) = all_34_2_56
% 43.90/12.85 | (169) sdtpldt0(xm, xp) = all_34_1_55
% 43.90/12.85 | (170) ~ (all_34_2_56 = 0) | ~ (all_34_3_57 = 0) | ~ (all_34_4_58 = 0) | all_34_0_54 = all_0_4_4
% 43.90/12.85 |
% 43.90/12.85 | Instantiating (80) with all_37_0_62, all_37_1_63, all_37_2_64 yields:
% 43.90/12.85 | (171) (all_37_0_62 = all_0_3_3 & all_37_1_63 = 0 & sdtasdt0(xp, all_37_2_64) = all_0_3_3 & aNaturalNumber0(all_37_2_64) = 0) | (aNaturalNumber0(all_0_3_3) = all_37_1_63 & aNaturalNumber0(xp) = all_37_2_64 & ( ~ (all_37_1_63 = 0) | ~ (all_37_2_64 = 0)))
% 43.90/12.85 |
% 43.90/12.85 +-Applying beta-rule and splitting (82), into two cases.
% 43.90/12.85 |-Branch one:
% 43.90/12.85 | (172) all_0_1_1 = 0
% 43.90/12.85 |
% 43.90/12.85 | Equations (172) can reduce 18 to:
% 43.90/12.85 | (173) $false
% 43.90/12.85 |
% 43.90/12.85 |-The branch is then unsatisfiable
% 43.90/12.85 |-Branch two:
% 43.90/12.85 | (18) ~ (all_0_1_1 = 0)
% 43.90/12.85 | (175) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_3_3, xm) = v3 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 43.90/12.85 |
% 43.90/12.85 | Instantiating (175) with all_43_0_68, all_43_1_69, all_43_2_70, all_43_3_71 yields:
% 43.90/12.85 | (176) doDivides0(all_0_3_3, xm) = all_43_0_68 & aNaturalNumber0(all_0_3_3) = all_43_2_70 & aNaturalNumber0(xp) = all_43_3_71 & aNaturalNumber0(xm) = all_43_1_69 & ( ~ (all_43_0_68 = 0) | ~ (all_43_1_69 = 0) | ~ (all_43_2_70 = 0) | ~ (all_43_3_71 = 0))
% 43.90/12.85 |
% 43.90/12.85 | Applying alpha-rule on (176) yields:
% 43.90/12.85 | (177) aNaturalNumber0(xp) = all_43_3_71
% 43.90/12.85 | (178) doDivides0(all_0_3_3, xm) = all_43_0_68
% 43.90/12.85 | (179) ~ (all_43_0_68 = 0) | ~ (all_43_1_69 = 0) | ~ (all_43_2_70 = 0) | ~ (all_43_3_71 = 0)
% 43.90/12.85 | (180) aNaturalNumber0(xm) = all_43_1_69
% 43.90/12.85 | (181) aNaturalNumber0(all_0_3_3) = all_43_2_70
% 43.90/12.85 |
% 43.90/12.85 +-Applying beta-rule and splitting (83), into two cases.
% 43.90/12.85 |-Branch one:
% 43.90/12.85 | (172) all_0_1_1 = 0
% 43.90/12.85 |
% 43.90/12.85 | Equations (172) can reduce 18 to:
% 43.90/12.85 | (173) $false
% 43.90/12.85 |
% 43.90/12.85 |-The branch is then unsatisfiable
% 43.90/12.85 |-Branch two:
% 43.90/12.85 | (18) ~ (all_0_1_1 = 0)
% 43.90/12.85 | (185) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(xr, xm) = v3 & aNaturalNumber0(xr) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 43.90/12.85 |
% 43.90/12.85 | Instantiating (185) with all_48_0_72, all_48_1_73, all_48_2_74, all_48_3_75 yields:
% 43.90/12.85 | (186) doDivides0(xr, xm) = all_48_0_72 & aNaturalNumber0(xr) = all_48_2_74 & aNaturalNumber0(xp) = all_48_3_75 & aNaturalNumber0(xm) = all_48_1_73 & ( ~ (all_48_0_72 = 0) | ~ (all_48_1_73 = 0) | ~ (all_48_2_74 = 0) | ~ (all_48_3_75 = 0))
% 43.90/12.85 |
% 43.90/12.85 | Applying alpha-rule on (186) yields:
% 43.90/12.85 | (187) ~ (all_48_0_72 = 0) | ~ (all_48_1_73 = 0) | ~ (all_48_2_74 = 0) | ~ (all_48_3_75 = 0)
% 43.90/12.85 | (188) aNaturalNumber0(xr) = all_48_2_74
% 43.90/12.85 | (189) doDivides0(xr, xm) = all_48_0_72
% 43.90/12.85 | (190) aNaturalNumber0(xm) = all_48_1_73
% 43.90/12.85 | (191) aNaturalNumber0(xp) = all_48_3_75
% 43.90/12.85 |
% 43.90/12.85 +-Applying beta-rule and splitting (84), into two cases.
% 43.90/12.85 |-Branch one:
% 43.90/12.85 | (192) all_0_0_0 = 0
% 43.90/12.85 |
% 43.90/12.85 | Equations (192) can reduce 43 to:
% 43.90/12.85 | (173) $false
% 43.90/12.85 |
% 43.90/12.85 |-The branch is then unsatisfiable
% 43.90/12.85 |-Branch two:
% 43.90/12.85 | (43) ~ (all_0_0_0 = 0)
% 43.90/12.85 | (195) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_2_2, xn) = v3 & aNaturalNumber0(all_0_2_2) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 43.90/12.86 |
% 43.90/12.86 | Instantiating (195) with all_53_0_76, all_53_1_77, all_53_2_78, all_53_3_79 yields:
% 43.90/12.86 | (196) doDivides0(all_0_2_2, xn) = all_53_0_76 & aNaturalNumber0(all_0_2_2) = all_53_2_78 & aNaturalNumber0(xp) = all_53_3_79 & aNaturalNumber0(xn) = all_53_1_77 & ( ~ (all_53_0_76 = 0) | ~ (all_53_1_77 = 0) | ~ (all_53_2_78 = 0) | ~ (all_53_3_79 = 0))
% 43.90/12.86 |
% 43.90/12.86 | Applying alpha-rule on (196) yields:
% 43.90/12.86 | (197) ~ (all_53_0_76 = 0) | ~ (all_53_1_77 = 0) | ~ (all_53_2_78 = 0) | ~ (all_53_3_79 = 0)
% 43.90/12.86 | (198) doDivides0(all_0_2_2, xn) = all_53_0_76
% 43.90/12.86 | (199) aNaturalNumber0(xn) = all_53_1_77
% 43.90/12.86 | (200) aNaturalNumber0(xp) = all_53_3_79
% 43.90/12.86 | (201) aNaturalNumber0(all_0_2_2) = all_53_2_78
% 43.90/12.86 |
% 43.90/12.86 +-Applying beta-rule and splitting (85), into two cases.
% 43.90/12.86 |-Branch one:
% 43.90/12.86 | (192) all_0_0_0 = 0
% 43.90/12.86 |
% 43.90/12.86 | Equations (192) can reduce 43 to:
% 43.90/12.86 | (173) $false
% 43.90/12.86 |
% 43.90/12.86 |-The branch is then unsatisfiable
% 43.90/12.86 |-Branch two:
% 43.90/12.86 | (43) ~ (all_0_0_0 = 0)
% 43.90/12.86 | (205) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_3_3, xn) = v3 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 43.90/12.86 |
% 43.90/12.86 | Instantiating (205) with all_58_0_80, all_58_1_81, all_58_2_82, all_58_3_83 yields:
% 43.90/12.86 | (206) doDivides0(all_0_3_3, xn) = all_58_0_80 & aNaturalNumber0(all_0_3_3) = all_58_2_82 & aNaturalNumber0(xp) = all_58_3_83 & aNaturalNumber0(xn) = all_58_1_81 & ( ~ (all_58_0_80 = 0) | ~ (all_58_1_81 = 0) | ~ (all_58_2_82 = 0) | ~ (all_58_3_83 = 0))
% 43.90/12.86 |
% 43.90/12.86 | Applying alpha-rule on (206) yields:
% 43.90/12.86 | (207) doDivides0(all_0_3_3, xn) = all_58_0_80
% 43.90/12.86 | (208) aNaturalNumber0(all_0_3_3) = all_58_2_82
% 43.90/12.86 | (209) ~ (all_58_0_80 = 0) | ~ (all_58_1_81 = 0) | ~ (all_58_2_82 = 0) | ~ (all_58_3_83 = 0)
% 43.90/12.86 | (210) aNaturalNumber0(xn) = all_58_1_81
% 43.90/12.86 | (211) aNaturalNumber0(xp) = all_58_3_83
% 43.90/12.86 |
% 43.90/12.86 +-Applying beta-rule and splitting (81), into two cases.
% 43.90/12.86 |-Branch one:
% 43.90/12.86 | (172) all_0_1_1 = 0
% 43.90/12.86 |
% 43.90/12.86 | Equations (172) can reduce 18 to:
% 43.90/12.86 | (173) $false
% 43.90/12.86 |
% 43.90/12.86 |-The branch is then unsatisfiable
% 43.90/12.86 |-Branch two:
% 43.90/12.86 | (18) ~ (all_0_1_1 = 0)
% 43.90/12.86 | (215) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_2_2, xm) = v3 & aNaturalNumber0(all_0_2_2) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 43.90/12.86 |
% 43.90/12.86 | Instantiating (215) with all_63_0_84, all_63_1_85, all_63_2_86, all_63_3_87 yields:
% 43.90/12.86 | (216) doDivides0(all_0_2_2, xm) = all_63_0_84 & aNaturalNumber0(all_0_2_2) = all_63_2_86 & aNaturalNumber0(xp) = all_63_3_87 & aNaturalNumber0(xm) = all_63_1_85 & ( ~ (all_63_0_84 = 0) | ~ (all_63_1_85 = 0) | ~ (all_63_2_86 = 0) | ~ (all_63_3_87 = 0))
% 43.90/12.86 |
% 43.90/12.86 | Applying alpha-rule on (216) yields:
% 43.90/12.86 | (217) doDivides0(all_0_2_2, xm) = all_63_0_84
% 43.90/12.86 | (218) aNaturalNumber0(xp) = all_63_3_87
% 43.90/12.86 | (219) aNaturalNumber0(all_0_2_2) = all_63_2_86
% 43.90/12.86 | (220) aNaturalNumber0(xm) = all_63_1_85
% 43.90/12.86 | (221) ~ (all_63_0_84 = 0) | ~ (all_63_1_85 = 0) | ~ (all_63_2_86 = 0) | ~ (all_63_3_87 = 0)
% 43.90/12.86 |
% 43.90/12.86 +-Applying beta-rule and splitting (86), into two cases.
% 43.90/12.86 |-Branch one:
% 43.90/12.86 | (192) all_0_0_0 = 0
% 43.90/12.86 |
% 43.90/12.86 | Equations (192) can reduce 43 to:
% 43.90/12.86 | (173) $false
% 43.90/12.86 |
% 43.90/12.86 |-The branch is then unsatisfiable
% 43.90/12.86 |-Branch two:
% 43.90/12.86 | (43) ~ (all_0_0_0 = 0)
% 43.90/12.86 | (225) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(xr, xn) = v3 & aNaturalNumber0(xr) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 43.90/12.86 |
% 43.90/12.86 | Instantiating (225) with all_68_0_88, all_68_1_89, all_68_2_90, all_68_3_91 yields:
% 43.90/12.86 | (226) doDivides0(xr, xn) = all_68_0_88 & aNaturalNumber0(xr) = all_68_2_90 & aNaturalNumber0(xp) = all_68_3_91 & aNaturalNumber0(xn) = all_68_1_89 & ( ~ (all_68_0_88 = 0) | ~ (all_68_1_89 = 0) | ~ (all_68_2_90 = 0) | ~ (all_68_3_91 = 0))
% 43.90/12.86 |
% 43.90/12.86 | Applying alpha-rule on (226) yields:
% 43.90/12.86 | (227) aNaturalNumber0(xr) = all_68_2_90
% 43.90/12.86 | (228) doDivides0(xr, xn) = all_68_0_88
% 43.90/12.86 | (229) aNaturalNumber0(xn) = all_68_1_89
% 43.90/12.86 | (230) ~ (all_68_0_88 = 0) | ~ (all_68_1_89 = 0) | ~ (all_68_2_90 = 0) | ~ (all_68_3_91 = 0)
% 43.90/12.86 | (231) aNaturalNumber0(xp) = all_68_3_91
% 43.90/12.86 |
% 43.90/12.86 +-Applying beta-rule and splitting (87), into two cases.
% 43.90/12.86 |-Branch one:
% 43.90/12.86 | (232) xr = xn
% 43.90/12.86 |
% 43.90/12.87 | Equations (232) can reduce 74 to:
% 43.90/12.87 | (173) $false
% 43.90/12.87 |
% 43.90/12.87 |-The branch is then unsatisfiable
% 43.90/12.87 |-Branch two:
% 43.90/12.87 | (74) ~ (xr = xn)
% 43.90/12.87 | (235) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xn, xr) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 43.90/12.87 |
% 43.90/12.87 | Instantiating (235) with all_73_0_92, all_73_1_93, all_73_2_94 yields:
% 43.90/12.87 | (236) sdtlseqdt0(xn, xr) = all_73_0_92 & aNaturalNumber0(xr) = all_73_2_94 & aNaturalNumber0(xn) = all_73_1_93 & ( ~ (all_73_0_92 = 0) | ~ (all_73_1_93 = 0) | ~ (all_73_2_94 = 0))
% 43.90/12.87 |
% 43.90/12.87 | Applying alpha-rule on (236) yields:
% 43.90/12.87 | (237) sdtlseqdt0(xn, xr) = all_73_0_92
% 43.90/12.87 | (238) aNaturalNumber0(xr) = all_73_2_94
% 43.90/12.87 | (239) aNaturalNumber0(xn) = all_73_1_93
% 43.90/12.87 | (240) ~ (all_73_0_92 = 0) | ~ (all_73_1_93 = 0) | ~ (all_73_2_94 = 0)
% 43.90/12.87 |
% 43.90/12.87 +-Applying beta-rule and splitting (100), into two cases.
% 43.90/12.87 |-Branch one:
% 43.90/12.87 | (241) xp = sz00
% 43.90/12.87 |
% 43.90/12.87 | Equations (241) can reduce 79 to:
% 43.90/12.87 | (173) $false
% 43.90/12.87 |
% 43.90/12.87 |-The branch is then unsatisfiable
% 43.90/12.87 |-Branch two:
% 43.90/12.87 | (79) ~ (xp = sz00)
% 43.90/12.87 | (244) xp = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 43.90/12.87 |
% 43.90/12.87 +-Applying beta-rule and splitting (244), into two cases.
% 43.90/12.87 |-Branch one:
% 43.90/12.87 | (245) xp = sz10
% 43.90/12.87 |
% 43.90/12.87 | Equations (245) can reduce 78 to:
% 43.90/12.87 | (173) $false
% 43.90/12.87 |
% 43.90/12.87 |-The branch is then unsatisfiable
% 43.90/12.87 |-Branch two:
% 43.90/12.87 | (78) ~ (xp = sz10)
% 43.90/12.87 | (248) ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 43.90/12.87 |
% 43.90/12.87 | Instantiating (248) with all_82_0_95 yields:
% 43.90/12.87 | (249) isPrime0(all_82_0_95) = 0 & doDivides0(all_82_0_95, xp) = 0 & aNaturalNumber0(all_82_0_95) = 0
% 43.90/12.87 |
% 43.90/12.87 | Applying alpha-rule on (249) yields:
% 43.90/12.87 | (250) isPrime0(all_82_0_95) = 0
% 43.90/12.87 | (251) doDivides0(all_82_0_95, xp) = 0
% 43.90/12.87 | (252) aNaturalNumber0(all_82_0_95) = 0
% 43.90/12.87 |
% 43.90/12.87 | Using (250) and (61) yields:
% 43.90/12.87 | (253) ~ (all_82_0_95 = sz10)
% 43.90/12.87 |
% 43.90/12.87 | Using (250) and (25) yields:
% 43.90/12.87 | (254) ~ (all_82_0_95 = sz00)
% 43.90/12.87 |
% 43.90/12.87 | Instantiating formula (59) with xp, all_16_5_23, 0 and discharging atoms isPrime0(xp) = all_16_5_23, isPrime0(xp) = 0, yields:
% 43.90/12.87 | (255) all_16_5_23 = 0
% 43.90/12.87 |
% 43.90/12.87 | Instantiating formula (59) with xp, all_14_5_14, all_16_5_23 and discharging atoms isPrime0(xp) = all_16_5_23, isPrime0(xp) = all_14_5_14, yields:
% 43.90/12.87 | (256) all_16_5_23 = all_14_5_14
% 43.90/12.87 |
% 43.90/12.87 | Instantiating formula (73) with xp, xr, all_16_1_19, 0 and discharging atoms doDivides0(xp, xr) = all_16_1_19, doDivides0(xp, xr) = 0, yields:
% 43.90/12.87 | (257) all_16_1_19 = 0
% 43.90/12.87 |
% 43.90/12.87 | Instantiating formula (73) with xp, xn, all_14_1_10, all_0_0_0 and discharging atoms doDivides0(xp, xn) = all_14_1_10, doDivides0(xp, xn) = all_0_0_0, yields:
% 43.90/12.87 | (258) all_14_1_10 = all_0_0_0
% 43.90/12.87 |
% 43.90/12.87 | Instantiating formula (69) with all_0_5_5, xp, all_14_3_12, all_0_4_4 and discharging atoms sdtpldt0(all_0_5_5, xp) = all_0_4_4, yields:
% 43.90/12.87 | (259) all_14_3_12 = all_0_4_4 | ~ (sdtpldt0(all_0_5_5, xp) = all_14_3_12)
% 43.90/12.87 |
% 43.90/12.87 | Instantiating formula (69) with xn, xm, all_14_4_13, all_0_5_5 and discharging atoms sdtpldt0(xn, xm) = all_14_4_13, sdtpldt0(xn, xm) = all_0_5_5, yields:
% 43.90/12.87 | (260) all_14_4_13 = all_0_5_5
% 43.90/12.87 |
% 43.90/12.87 | Instantiating formula (60) with all_0_2_2, all_53_2_78, all_63_2_86 and discharging atoms aNaturalNumber0(all_0_2_2) = all_63_2_86, aNaturalNumber0(all_0_2_2) = all_53_2_78, yields:
% 43.90/12.87 | (261) all_63_2_86 = all_53_2_78
% 43.90/12.87 |
% 43.90/12.87 | Instantiating formula (60) with all_0_2_2, all_27_0_42, all_63_2_86 and discharging atoms aNaturalNumber0(all_0_2_2) = all_63_2_86, aNaturalNumber0(all_0_2_2) = all_27_0_42, yields:
% 43.90/12.87 | (262) all_63_2_86 = all_27_0_42
% 43.90/12.87 |
% 43.90/12.87 | Instantiating formula (60) with all_0_3_3, all_43_2_70, all_58_2_82 and discharging atoms aNaturalNumber0(all_0_3_3) = all_58_2_82, aNaturalNumber0(all_0_3_3) = all_43_2_70, yields:
% 43.90/12.87 | (263) all_58_2_82 = all_43_2_70
% 43.90/12.87 |
% 43.90/12.87 | Instantiating formula (60) with all_0_3_3, all_23_0_36, all_58_2_82 and discharging atoms aNaturalNumber0(all_0_3_3) = all_58_2_82, aNaturalNumber0(all_0_3_3) = all_23_0_36, yields:
% 43.90/12.87 | (264) all_58_2_82 = all_23_0_36
% 43.90/12.87 |
% 43.90/12.87 | Instantiating formula (60) with xr, all_73_2_94, all_58_2_82 and discharging atoms aNaturalNumber0(xr) = all_73_2_94, yields:
% 43.90/12.87 | (265) all_73_2_94 = all_58_2_82 | ~ (aNaturalNumber0(xr) = all_58_2_82)
% 43.90/12.87 |
% 43.90/12.87 | Instantiating formula (60) with xr, all_68_2_90, all_73_2_94 and discharging atoms aNaturalNumber0(xr) = all_73_2_94, aNaturalNumber0(xr) = all_68_2_90, yields:
% 43.90/12.87 | (266) all_73_2_94 = all_68_2_90
% 43.90/12.87 |
% 43.90/12.87 | Instantiating formula (60) with xr, all_48_2_74, all_68_2_90 and discharging atoms aNaturalNumber0(xr) = all_68_2_90, aNaturalNumber0(xr) = all_48_2_74, yields:
% 43.90/12.87 | (267) all_68_2_90 = all_48_2_74
% 43.90/12.87 |
% 43.90/12.87 | Instantiating formula (60) with xr, all_30_2_50, all_73_2_94 and discharging atoms aNaturalNumber0(xr) = all_73_2_94, aNaturalNumber0(xr) = all_30_2_50, yields:
% 43.90/12.87 | (268) all_73_2_94 = all_30_2_50
% 43.90/12.87 |
% 43.90/12.87 | Instantiating formula (60) with xr, all_27_2_44, all_68_2_90 and discharging atoms aNaturalNumber0(xr) = all_68_2_90, aNaturalNumber0(xr) = all_27_2_44, yields:
% 43.90/12.87 | (269) all_68_2_90 = all_27_2_44
% 43.90/12.87 |
% 43.90/12.87 | Instantiating formula (60) with xr, all_16_8_26, all_68_2_90 and discharging atoms aNaturalNumber0(xr) = all_68_2_90, aNaturalNumber0(xr) = all_16_8_26, yields:
% 43.90/12.88 | (270) all_68_2_90 = all_16_8_26
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xp, all_63_3_87, all_68_3_91 and discharging atoms aNaturalNumber0(xp) = all_68_3_91, aNaturalNumber0(xp) = all_63_3_87, yields:
% 43.90/12.88 | (271) all_68_3_91 = all_63_3_87
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xp, all_53_3_79, all_63_3_87 and discharging atoms aNaturalNumber0(xp) = all_63_3_87, aNaturalNumber0(xp) = all_53_3_79, yields:
% 43.90/12.88 | (272) all_63_3_87 = all_53_3_79
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xp, all_53_3_79, all_58_3_83 and discharging atoms aNaturalNumber0(xp) = all_58_3_83, aNaturalNumber0(xp) = all_53_3_79, yields:
% 43.90/12.88 | (273) all_58_3_83 = all_53_3_79
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xp, all_48_3_75, all_68_3_91 and discharging atoms aNaturalNumber0(xp) = all_68_3_91, aNaturalNumber0(xp) = all_48_3_75, yields:
% 43.90/12.88 | (274) all_68_3_91 = all_48_3_75
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xp, all_43_3_71, all_63_3_87 and discharging atoms aNaturalNumber0(xp) = all_63_3_87, aNaturalNumber0(xp) = all_43_3_71, yields:
% 43.90/12.88 | (275) all_63_3_87 = all_43_3_71
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xp, all_34_2_56, all_58_3_83 and discharging atoms aNaturalNumber0(xp) = all_58_3_83, aNaturalNumber0(xp) = all_34_2_56, yields:
% 43.90/12.88 | (276) all_58_3_83 = all_34_2_56
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xp, all_32_1_52, all_43_3_71 and discharging atoms aNaturalNumber0(xp) = all_43_3_71, aNaturalNumber0(xp) = all_32_1_52, yields:
% 43.90/12.88 | (277) all_43_3_71 = all_32_1_52
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xp, all_21_1_34, 0 and discharging atoms aNaturalNumber0(xp) = all_21_1_34, aNaturalNumber0(xp) = 0, yields:
% 43.90/12.88 | (278) all_21_1_34 = 0
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xp, all_21_1_34, all_32_1_52 and discharging atoms aNaturalNumber0(xp) = all_32_1_52, aNaturalNumber0(xp) = all_21_1_34, yields:
% 43.90/12.88 | (279) all_32_1_52 = all_21_1_34
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xp, all_16_6_24, all_43_3_71 and discharging atoms aNaturalNumber0(xp) = all_43_3_71, aNaturalNumber0(xp) = all_16_6_24, yields:
% 43.90/12.88 | (280) all_43_3_71 = all_16_6_24
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xp, all_14_6_15, all_21_1_34 and discharging atoms aNaturalNumber0(xp) = all_21_1_34, aNaturalNumber0(xp) = all_14_6_15, yields:
% 43.90/12.88 | (281) all_21_1_34 = all_14_6_15
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xm, all_48_1_73, all_63_1_85 and discharging atoms aNaturalNumber0(xm) = all_63_1_85, aNaturalNumber0(xm) = all_48_1_73, yields:
% 43.90/12.88 | (282) all_63_1_85 = all_48_1_73
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xm, all_43_1_69, all_48_1_73 and discharging atoms aNaturalNumber0(xm) = all_48_1_73, aNaturalNumber0(xm) = all_43_1_69, yields:
% 43.90/12.88 | (283) all_48_1_73 = all_43_1_69
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xm, all_34_3_57, all_43_1_69 and discharging atoms aNaturalNumber0(xm) = all_43_1_69, aNaturalNumber0(xm) = all_34_3_57, yields:
% 43.90/12.88 | (284) all_43_1_69 = all_34_3_57
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xm, all_30_1_49, all_34_3_57 and discharging atoms aNaturalNumber0(xm) = all_34_3_57, aNaturalNumber0(xm) = all_30_1_49, yields:
% 43.90/12.88 | (285) all_34_3_57 = all_30_1_49
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xm, all_27_1_43, all_30_1_49 and discharging atoms aNaturalNumber0(xm) = all_30_1_49, aNaturalNumber0(xm) = all_27_1_43, yields:
% 43.90/12.88 | (286) all_30_1_49 = all_27_1_43
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xm, all_25_1_40, 0 and discharging atoms aNaturalNumber0(xm) = all_25_1_40, aNaturalNumber0(xm) = 0, yields:
% 43.90/12.88 | (287) all_25_1_40 = 0
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xm, all_25_1_40, all_27_1_43 and discharging atoms aNaturalNumber0(xm) = all_27_1_43, aNaturalNumber0(xm) = all_25_1_40, yields:
% 43.90/12.88 | (288) all_27_1_43 = all_25_1_40
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xm, all_23_1_37, all_63_1_85 and discharging atoms aNaturalNumber0(xm) = all_63_1_85, aNaturalNumber0(xm) = all_23_1_37, yields:
% 43.90/12.88 | (289) all_63_1_85 = all_23_1_37
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xm, all_19_1_31, all_25_1_40 and discharging atoms aNaturalNumber0(xm) = all_25_1_40, aNaturalNumber0(xm) = all_19_1_31, yields:
% 43.90/12.88 | (290) all_25_1_40 = all_19_1_31
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xm, all_16_7_25, all_25_1_40 and discharging atoms aNaturalNumber0(xm) = all_25_1_40, aNaturalNumber0(xm) = all_16_7_25, yields:
% 43.90/12.88 | (291) all_25_1_40 = all_16_7_25
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xm, all_14_7_16, all_25_1_40 and discharging atoms aNaturalNumber0(xm) = all_25_1_40, aNaturalNumber0(xm) = all_14_7_16, yields:
% 43.90/12.88 | (292) all_25_1_40 = all_14_7_16
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xm, all_12_1_7, all_25_1_40 and discharging atoms aNaturalNumber0(xm) = all_25_1_40, aNaturalNumber0(xm) = all_12_1_7, yields:
% 43.90/12.88 | (293) all_25_1_40 = all_12_1_7
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xn, all_58_1_81, all_68_1_89 and discharging atoms aNaturalNumber0(xn) = all_68_1_89, aNaturalNumber0(xn) = all_58_1_81, yields:
% 43.90/12.88 | (294) all_68_1_89 = all_58_1_81
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xn, all_53_1_77, 0 and discharging atoms aNaturalNumber0(xn) = all_53_1_77, aNaturalNumber0(xn) = 0, yields:
% 43.90/12.88 | (295) all_53_1_77 = 0
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xn, all_34_4_58, all_53_1_77 and discharging atoms aNaturalNumber0(xn) = all_53_1_77, aNaturalNumber0(xn) = all_34_4_58, yields:
% 43.90/12.88 | (296) all_53_1_77 = all_34_4_58
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xn, all_25_2_41, all_73_1_93 and discharging atoms aNaturalNumber0(xn) = all_73_1_93, aNaturalNumber0(xn) = all_25_2_41, yields:
% 43.90/12.88 | (297) all_73_1_93 = all_25_2_41
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xn, all_25_2_41, all_58_1_81 and discharging atoms aNaturalNumber0(xn) = all_58_1_81, aNaturalNumber0(xn) = all_25_2_41, yields:
% 43.90/12.88 | (298) all_58_1_81 = all_25_2_41
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xn, all_23_2_38, all_34_4_58 and discharging atoms aNaturalNumber0(xn) = all_34_4_58, aNaturalNumber0(xn) = all_23_2_38, yields:
% 43.90/12.88 | (299) all_34_4_58 = all_23_2_38
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xn, all_19_2_32, all_73_1_93 and discharging atoms aNaturalNumber0(xn) = all_73_1_93, aNaturalNumber0(xn) = all_19_2_32, yields:
% 43.90/12.88 | (300) all_73_1_93 = all_19_2_32
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xn, all_14_8_17, all_73_1_93 and discharging atoms aNaturalNumber0(xn) = all_73_1_93, aNaturalNumber0(xn) = all_14_8_17, yields:
% 43.90/12.88 | (301) all_73_1_93 = all_14_8_17
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xn, all_14_8_17, all_23_2_38 and discharging atoms aNaturalNumber0(xn) = all_23_2_38, aNaturalNumber0(xn) = all_14_8_17, yields:
% 43.90/12.88 | (302) all_23_2_38 = all_14_8_17
% 43.90/12.88 |
% 43.90/12.88 | Instantiating formula (60) with xn, all_12_2_8, all_68_1_89 and discharging atoms aNaturalNumber0(xn) = all_68_1_89, aNaturalNumber0(xn) = all_12_2_8, yields:
% 43.90/12.88 | (303) all_68_1_89 = all_12_2_8
% 43.90/12.88 |
% 43.90/12.88 | Combining equations (301,300) yields a new equation:
% 43.90/12.88 | (304) all_19_2_32 = all_14_8_17
% 43.90/12.88 |
% 43.90/12.88 | Combining equations (297,300) yields a new equation:
% 43.90/12.88 | (305) all_25_2_41 = all_19_2_32
% 43.90/12.88 |
% 43.90/12.88 | Simplifying 305 yields:
% 43.90/12.88 | (306) all_25_2_41 = all_19_2_32
% 43.90/12.88 |
% 43.90/12.88 | Combining equations (266,268) yields a new equation:
% 43.90/12.88 | (307) all_68_2_90 = all_30_2_50
% 43.90/12.88 |
% 43.90/12.88 | Simplifying 307 yields:
% 43.90/12.88 | (308) all_68_2_90 = all_30_2_50
% 43.90/12.88 |
% 43.90/12.88 | Combining equations (294,303) yields a new equation:
% 43.90/12.88 | (309) all_58_1_81 = all_12_2_8
% 43.90/12.88 |
% 43.90/12.88 | Simplifying 309 yields:
% 43.90/12.88 | (310) all_58_1_81 = all_12_2_8
% 43.90/12.88 |
% 43.90/12.88 | Combining equations (269,267) yields a new equation:
% 43.90/12.88 | (311) all_48_2_74 = all_27_2_44
% 43.90/12.88 |
% 43.90/12.88 | Combining equations (270,267) yields a new equation:
% 43.90/12.88 | (312) all_48_2_74 = all_16_8_26
% 43.90/12.88 |
% 43.90/12.88 | Combining equations (308,267) yields a new equation:
% 43.90/12.88 | (313) all_48_2_74 = all_30_2_50
% 43.90/12.88 |
% 43.90/12.88 | Combining equations (271,274) yields a new equation:
% 43.90/12.88 | (314) all_63_3_87 = all_48_3_75
% 43.90/12.88 |
% 43.90/12.88 | Simplifying 314 yields:
% 43.90/12.88 | (315) all_63_3_87 = all_48_3_75
% 43.90/12.88 |
% 43.90/12.88 | Combining equations (282,289) yields a new equation:
% 43.90/12.88 | (316) all_48_1_73 = all_23_1_37
% 43.90/12.88 |
% 43.90/12.88 | Simplifying 316 yields:
% 43.90/12.88 | (317) all_48_1_73 = all_23_1_37
% 43.90/12.88 |
% 43.90/12.88 | Combining equations (261,262) yields a new equation:
% 43.90/12.88 | (318) all_53_2_78 = all_27_0_42
% 43.90/12.88 |
% 43.90/12.88 | Simplifying 318 yields:
% 43.90/12.88 | (319) all_53_2_78 = all_27_0_42
% 43.90/12.88 |
% 43.90/12.88 | Combining equations (272,315) yields a new equation:
% 43.90/12.88 | (320) all_53_3_79 = all_48_3_75
% 43.90/12.88 |
% 43.90/12.88 | Simplifying 320 yields:
% 43.90/12.88 | (321) all_53_3_79 = all_48_3_75
% 43.90/12.88 |
% 43.90/12.88 | Combining equations (275,315) yields a new equation:
% 43.90/12.88 | (322) all_48_3_75 = all_43_3_71
% 43.90/12.88 |
% 43.90/12.88 | Combining equations (298,310) yields a new equation:
% 43.90/12.89 | (323) all_25_2_41 = all_12_2_8
% 43.90/12.89 |
% 43.90/12.89 | Simplifying 323 yields:
% 43.90/12.89 | (324) all_25_2_41 = all_12_2_8
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (263,264) yields a new equation:
% 43.90/12.89 | (325) all_43_2_70 = all_23_0_36
% 43.90/12.89 |
% 43.90/12.89 | Simplifying 325 yields:
% 43.90/12.89 | (326) all_43_2_70 = all_23_0_36
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (273,276) yields a new equation:
% 43.90/12.89 | (327) all_53_3_79 = all_34_2_56
% 43.90/12.89 |
% 43.90/12.89 | Simplifying 327 yields:
% 43.90/12.89 | (328) all_53_3_79 = all_34_2_56
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (296,295) yields a new equation:
% 43.90/12.89 | (329) all_34_4_58 = 0
% 43.90/12.89 |
% 43.90/12.89 | Simplifying 329 yields:
% 43.90/12.89 | (330) all_34_4_58 = 0
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (321,328) yields a new equation:
% 43.90/12.89 | (331) all_48_3_75 = all_34_2_56
% 43.90/12.89 |
% 43.90/12.89 | Simplifying 331 yields:
% 43.90/12.89 | (332) all_48_3_75 = all_34_2_56
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (283,317) yields a new equation:
% 43.90/12.89 | (333) all_43_1_69 = all_23_1_37
% 43.90/12.89 |
% 43.90/12.89 | Simplifying 333 yields:
% 43.90/12.89 | (334) all_43_1_69 = all_23_1_37
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (312,313) yields a new equation:
% 43.90/12.89 | (335) all_30_2_50 = all_16_8_26
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (311,313) yields a new equation:
% 43.90/12.89 | (336) all_30_2_50 = all_27_2_44
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (322,332) yields a new equation:
% 43.90/12.89 | (337) all_43_3_71 = all_34_2_56
% 43.90/12.89 |
% 43.90/12.89 | Simplifying 337 yields:
% 43.90/12.89 | (338) all_43_3_71 = all_34_2_56
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (284,334) yields a new equation:
% 43.90/12.89 | (339) all_34_3_57 = all_23_1_37
% 43.90/12.89 |
% 43.90/12.89 | Simplifying 339 yields:
% 43.90/12.89 | (340) all_34_3_57 = all_23_1_37
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (277,338) yields a new equation:
% 43.90/12.89 | (341) all_34_2_56 = all_32_1_52
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (280,338) yields a new equation:
% 43.90/12.89 | (342) all_34_2_56 = all_16_6_24
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (341,342) yields a new equation:
% 43.90/12.89 | (343) all_32_1_52 = all_16_6_24
% 43.90/12.89 |
% 43.90/12.89 | Simplifying 343 yields:
% 43.90/12.89 | (344) all_32_1_52 = all_16_6_24
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (285,340) yields a new equation:
% 43.90/12.89 | (345) all_30_1_49 = all_23_1_37
% 43.90/12.89 |
% 43.90/12.89 | Simplifying 345 yields:
% 43.90/12.89 | (346) all_30_1_49 = all_23_1_37
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (299,330) yields a new equation:
% 43.90/12.89 | (347) all_23_2_38 = 0
% 43.90/12.89 |
% 43.90/12.89 | Simplifying 347 yields:
% 43.90/12.89 | (348) all_23_2_38 = 0
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (279,344) yields a new equation:
% 43.90/12.89 | (349) all_21_1_34 = all_16_6_24
% 43.90/12.89 |
% 43.90/12.89 | Simplifying 349 yields:
% 43.90/12.89 | (350) all_21_1_34 = all_16_6_24
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (286,346) yields a new equation:
% 43.90/12.89 | (351) all_27_1_43 = all_23_1_37
% 43.90/12.89 |
% 43.90/12.89 | Simplifying 351 yields:
% 43.90/12.89 | (352) all_27_1_43 = all_23_1_37
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (335,336) yields a new equation:
% 43.90/12.89 | (353) all_27_2_44 = all_16_8_26
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (288,352) yields a new equation:
% 43.90/12.89 | (354) all_25_1_40 = all_23_1_37
% 43.90/12.89 |
% 43.90/12.89 | Simplifying 354 yields:
% 43.90/12.89 | (355) all_25_1_40 = all_23_1_37
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (290,355) yields a new equation:
% 43.90/12.89 | (356) all_23_1_37 = all_19_1_31
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (287,355) yields a new equation:
% 43.90/12.89 | (357) all_23_1_37 = 0
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (292,355) yields a new equation:
% 43.90/12.89 | (358) all_23_1_37 = all_14_7_16
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (291,355) yields a new equation:
% 43.90/12.89 | (359) all_23_1_37 = all_16_7_25
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (293,355) yields a new equation:
% 43.90/12.89 | (360) all_23_1_37 = all_12_1_7
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (306,324) yields a new equation:
% 43.90/12.89 | (361) all_19_2_32 = all_12_2_8
% 43.90/12.89 |
% 43.90/12.89 | Simplifying 361 yields:
% 43.90/12.89 | (362) all_19_2_32 = all_12_2_8
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (358,356) yields a new equation:
% 43.90/12.89 | (363) all_19_1_31 = all_14_7_16
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (359,356) yields a new equation:
% 43.90/12.89 | (364) all_19_1_31 = all_16_7_25
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (360,356) yields a new equation:
% 43.90/12.89 | (365) all_19_1_31 = all_12_1_7
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (357,356) yields a new equation:
% 43.90/12.89 | (366) all_19_1_31 = 0
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (302,348) yields a new equation:
% 43.90/12.89 | (367) all_14_8_17 = 0
% 43.90/12.89 |
% 43.90/12.89 | Simplifying 367 yields:
% 43.90/12.89 | (368) all_14_8_17 = 0
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (278,350) yields a new equation:
% 43.90/12.89 | (369) all_16_6_24 = 0
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (281,350) yields a new equation:
% 43.90/12.89 | (370) all_16_6_24 = all_14_6_15
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (365,364) yields a new equation:
% 43.90/12.89 | (371) all_16_7_25 = all_12_1_7
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (363,364) yields a new equation:
% 43.90/12.89 | (372) all_16_7_25 = all_14_7_16
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (366,364) yields a new equation:
% 43.90/12.89 | (373) all_16_7_25 = 0
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (304,362) yields a new equation:
% 43.90/12.89 | (374) all_14_8_17 = all_12_2_8
% 43.90/12.89 |
% 43.90/12.89 | Simplifying 374 yields:
% 43.90/12.89 | (375) all_14_8_17 = all_12_2_8
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (255,256) yields a new equation:
% 43.90/12.89 | (376) all_14_5_14 = 0
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (370,369) yields a new equation:
% 43.90/12.89 | (377) all_14_6_15 = 0
% 43.90/12.89 |
% 43.90/12.89 | Simplifying 377 yields:
% 43.90/12.89 | (378) all_14_6_15 = 0
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (371,372) yields a new equation:
% 43.90/12.89 | (379) all_14_7_16 = all_12_1_7
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (373,372) yields a new equation:
% 43.90/12.89 | (380) all_14_7_16 = 0
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (380,379) yields a new equation:
% 43.90/12.89 | (381) all_12_1_7 = 0
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (375,368) yields a new equation:
% 43.90/12.89 | (382) all_12_2_8 = 0
% 43.90/12.89 |
% 43.90/12.89 | Simplifying 382 yields:
% 43.90/12.89 | (383) all_12_2_8 = 0
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (381,379) yields a new equation:
% 43.90/12.89 | (380) all_14_7_16 = 0
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (380,372) yields a new equation:
% 43.90/12.89 | (373) all_16_7_25 = 0
% 43.90/12.89 |
% 43.90/12.89 | Combining equations (383,362) yields a new equation:
% 44.42/12.89 | (386) all_19_2_32 = 0
% 44.42/12.89 |
% 44.42/12.89 | Combining equations (373,364) yields a new equation:
% 44.42/12.89 | (366) all_19_1_31 = 0
% 44.42/12.89 |
% 44.42/12.89 | Combining equations (366,356) yields a new equation:
% 44.42/12.89 | (357) all_23_1_37 = 0
% 44.42/12.89 |
% 44.42/12.89 | Combining equations (353,336) yields a new equation:
% 44.42/12.89 | (335) all_30_2_50 = all_16_8_26
% 44.42/12.89 |
% 44.42/12.89 | Combining equations (357,346) yields a new equation:
% 44.42/12.89 | (390) all_30_1_49 = 0
% 44.42/12.89 |
% 44.42/12.89 | Combining equations (357,340) yields a new equation:
% 44.42/12.89 | (391) all_34_3_57 = 0
% 44.42/12.89 |
% 44.42/12.89 | Combining equations (369,342) yields a new equation:
% 44.42/12.89 | (392) all_34_2_56 = 0
% 44.42/12.89 |
% 44.42/12.89 | Combining equations (392,332) yields a new equation:
% 44.42/12.89 | (393) all_48_3_75 = 0
% 44.42/12.89 |
% 44.42/12.89 | Combining equations (335,313) yields a new equation:
% 44.42/12.89 | (312) all_48_2_74 = all_16_8_26
% 44.42/12.89 |
% 44.42/12.89 | Combining equations (392,328) yields a new equation:
% 44.42/12.89 | (395) all_53_3_79 = 0
% 44.42/12.89 |
% 44.42/12.89 | Combining equations (392,276) yields a new equation:
% 44.42/12.89 | (396) all_58_3_83 = 0
% 44.42/12.89 |
% 44.42/12.89 | Combining equations (383,310) yields a new equation:
% 44.42/12.89 | (397) all_58_1_81 = 0
% 44.42/12.89 |
% 44.42/12.89 | Combining equations (393,274) yields a new equation:
% 44.42/12.89 | (398) all_68_3_91 = 0
% 44.42/12.89 |
% 44.42/12.89 | Combining equations (312,267) yields a new equation:
% 44.42/12.89 | (270) all_68_2_90 = all_16_8_26
% 44.42/12.89 |
% 44.42/12.89 | Combining equations (383,303) yields a new equation:
% 44.42/12.89 | (400) all_68_1_89 = 0
% 44.42/12.89 |
% 44.42/12.89 | Combining equations (335,268) yields a new equation:
% 44.42/12.90 | (401) all_73_2_94 = all_16_8_26
% 44.42/12.90 |
% 44.42/12.90 | From (376) and (115) follows:
% 44.42/12.90 | (48) isPrime0(xp) = 0
% 44.42/12.90 |
% 44.42/12.90 | From (257) and (122) follows:
% 44.42/12.90 | (12) doDivides0(xp, xr) = 0
% 44.42/12.90 |
% 44.42/12.90 | From (258) and (116) follows:
% 44.42/12.90 | (51) doDivides0(xp, xn) = all_0_0_0
% 44.42/12.90 |
% 44.42/12.90 | From (260) and (114) follows:
% 44.42/12.90 | (405) sdtpldt0(all_0_5_5, xp) = all_14_3_12
% 44.42/12.90 |
% 44.42/12.90 | From (260) and (110) follows:
% 44.42/12.90 | (68) sdtpldt0(xn, xm) = all_0_5_5
% 44.42/12.90 |
% 44.42/12.90 | From (319) and (201) follows:
% 44.42/12.90 | (150) aNaturalNumber0(all_0_2_2) = all_27_0_42
% 44.42/12.90 |
% 44.42/12.90 | From (326) and (181) follows:
% 44.42/12.90 | (140) aNaturalNumber0(all_0_3_3) = all_23_0_36
% 44.42/12.90 |
% 44.42/12.90 | From (353) and (151) follows:
% 44.42/12.90 | (124) aNaturalNumber0(xr) = all_16_8_26
% 44.42/12.90 |
% 44.42/12.90 | From (378) and (113) follows:
% 44.42/12.90 | (45) aNaturalNumber0(xp) = 0
% 44.42/12.90 |
% 44.42/12.90 | From (381) and (103) follows:
% 44.42/12.90 | (72) aNaturalNumber0(xm) = 0
% 44.42/12.90 |
% 44.42/12.90 | From (383) and (104) follows:
% 44.42/12.90 | (24) aNaturalNumber0(xn) = 0
% 44.42/12.90 |
% 44.42/12.90 +-Applying beta-rule and splitting (133), into two cases.
% 44.42/12.90 |-Branch one:
% 44.42/12.90 | (413) ~ (all_19_1_31 = 0)
% 44.42/12.90 |
% 44.42/12.90 | Equations (366) can reduce 413 to:
% 44.42/12.90 | (173) $false
% 44.42/12.90 |
% 44.42/12.90 |-The branch is then unsatisfiable
% 44.42/12.90 |-Branch two:
% 44.42/12.90 | (366) all_19_1_31 = 0
% 44.42/12.90 | (416) ~ (all_19_2_32 = 0) | all_19_0_30 = all_0_5_5
% 44.42/12.90 |
% 44.42/12.90 +-Applying beta-rule and splitting (416), into two cases.
% 44.42/12.90 |-Branch one:
% 44.42/12.90 | (417) ~ (all_19_2_32 = 0)
% 44.42/12.90 |
% 44.42/12.90 | Equations (386) can reduce 417 to:
% 44.42/12.90 | (173) $false
% 44.42/12.90 |
% 44.42/12.90 |-The branch is then unsatisfiable
% 44.42/12.90 |-Branch two:
% 44.42/12.90 | (386) all_19_2_32 = 0
% 44.42/12.90 | (420) all_19_0_30 = all_0_5_5
% 44.42/12.90 |
% 44.42/12.90 | From (420) and (130) follows:
% 44.42/12.90 | (421) sdtpldt0(xm, xn) = all_0_5_5
% 44.42/12.90 |
% 44.42/12.90 +-Applying beta-rule and splitting (170), into two cases.
% 44.42/12.90 |-Branch one:
% 44.42/12.90 | (422) ~ (all_34_2_56 = 0)
% 44.42/12.90 |
% 44.42/12.90 | Equations (392) can reduce 422 to:
% 44.42/12.90 | (173) $false
% 44.42/12.90 |
% 44.42/12.90 |-The branch is then unsatisfiable
% 44.42/12.90 |-Branch two:
% 44.42/12.90 | (392) all_34_2_56 = 0
% 44.42/12.90 | (425) ~ (all_34_3_57 = 0) | ~ (all_34_4_58 = 0) | all_34_0_54 = all_0_4_4
% 44.42/12.90 |
% 44.42/12.90 +-Applying beta-rule and splitting (128), into two cases.
% 44.42/12.90 |-Branch one:
% 44.42/12.90 | (426) all_18_0_27 = xn & all_18_1_28 = 0 & sdtpldt0(xp, all_18_2_29) = xn & aNaturalNumber0(all_18_2_29) = 0
% 44.42/12.90 |
% 44.42/12.90 | Applying alpha-rule on (426) yields:
% 44.42/12.90 | (427) all_18_0_27 = xn
% 44.42/12.90 | (428) all_18_1_28 = 0
% 44.42/12.90 | (429) sdtpldt0(xp, all_18_2_29) = xn
% 44.42/12.90 | (430) aNaturalNumber0(all_18_2_29) = 0
% 44.42/12.90 |
% 44.42/12.90 +-Applying beta-rule and splitting (425), into two cases.
% 44.42/12.90 |-Branch one:
% 44.42/12.90 | (431) ~ (all_34_3_57 = 0)
% 44.42/12.90 |
% 44.42/12.90 | Equations (391) can reduce 431 to:
% 44.42/12.90 | (173) $false
% 44.42/12.90 |
% 44.42/12.90 |-The branch is then unsatisfiable
% 44.42/12.90 |-Branch two:
% 44.42/12.90 | (391) all_34_3_57 = 0
% 44.42/12.90 | (434) ~ (all_34_4_58 = 0) | all_34_0_54 = all_0_4_4
% 44.42/12.90 |
% 44.42/12.90 +-Applying beta-rule and splitting (434), into two cases.
% 44.42/12.90 |-Branch one:
% 44.42/12.90 | (435) ~ (all_34_4_58 = 0)
% 44.42/12.90 |
% 44.42/12.90 | Equations (330) can reduce 435 to:
% 44.42/12.90 | (173) $false
% 44.42/12.90 |
% 44.42/12.90 |-The branch is then unsatisfiable
% 44.42/12.90 |-Branch two:
% 44.42/12.90 | (330) all_34_4_58 = 0
% 44.42/12.90 | (438) all_34_0_54 = all_0_4_4
% 44.42/12.90 |
% 44.42/12.90 | From (438) and (166) follows:
% 44.42/12.90 | (439) sdtpldt0(xn, all_34_1_55) = all_0_4_4
% 44.42/12.90 |
% 44.42/12.90 +-Applying beta-rule and splitting (259), into two cases.
% 44.42/12.90 |-Branch one:
% 44.42/12.90 | (440) ~ (sdtpldt0(all_0_5_5, xp) = all_14_3_12)
% 44.42/12.90 |
% 44.42/12.90 | Using (405) and (440) yields:
% 44.42/12.90 | (441) $false
% 44.42/12.90 |
% 44.42/12.90 |-The branch is then unsatisfiable
% 44.42/12.90 |-Branch two:
% 44.42/12.90 | (405) sdtpldt0(all_0_5_5, xp) = all_14_3_12
% 44.42/12.90 | (443) all_14_3_12 = all_0_4_4
% 44.42/12.90 |
% 44.42/12.90 | From (443) and (405) follows:
% 44.42/12.90 | (22) sdtpldt0(all_0_5_5, xp) = all_0_4_4
% 44.42/12.90 |
% 44.42/12.90 +-Applying beta-rule and splitting (143), into two cases.
% 44.42/12.90 |-Branch one:
% 44.42/12.90 | (445) ~ (all_23_1_37 = 0)
% 44.42/12.90 |
% 44.42/12.90 | Equations (357) can reduce 445 to:
% 44.42/12.90 | (173) $false
% 44.42/12.90 |
% 44.42/12.90 |-The branch is then unsatisfiable
% 44.42/12.90 |-Branch two:
% 44.42/12.90 | (357) all_23_1_37 = 0
% 44.42/12.90 | (448) ~ (all_23_2_38 = 0) | all_23_0_36 = 0
% 44.42/12.90 |
% 44.42/12.90 +-Applying beta-rule and splitting (448), into two cases.
% 44.42/12.90 |-Branch one:
% 44.42/12.90 | (449) ~ (all_23_2_38 = 0)
% 44.42/12.90 |
% 44.42/12.90 | Equations (348) can reduce 449 to:
% 44.42/12.90 | (173) $false
% 44.42/12.90 |
% 44.42/12.90 |-The branch is then unsatisfiable
% 44.42/12.90 |-Branch two:
% 44.42/12.90 | (348) all_23_2_38 = 0
% 44.42/12.90 | (452) all_23_0_36 = 0
% 44.42/12.90 |
% 44.42/12.90 | Combining equations (452,264) yields a new equation:
% 44.42/12.90 | (453) all_58_2_82 = 0
% 44.42/12.90 |
% 44.42/12.90 | From (452) and (140) follows:
% 44.42/12.90 | (454) aNaturalNumber0(all_0_3_3) = 0
% 44.42/12.90 |
% 44.42/12.90 +-Applying beta-rule and splitting (171), into two cases.
% 44.42/12.90 |-Branch one:
% 44.42/12.90 | (455) all_37_0_62 = all_0_3_3 & all_37_1_63 = 0 & sdtasdt0(xp, all_37_2_64) = all_0_3_3 & aNaturalNumber0(all_37_2_64) = 0
% 44.42/12.90 |
% 44.42/12.90 | Applying alpha-rule on (455) yields:
% 44.42/12.90 | (456) all_37_0_62 = all_0_3_3
% 44.42/12.90 | (457) all_37_1_63 = 0
% 44.42/12.90 | (458) sdtasdt0(xp, all_37_2_64) = all_0_3_3
% 44.42/12.90 | (459) aNaturalNumber0(all_37_2_64) = 0
% 44.42/12.90 |
% 44.42/12.90 +-Applying beta-rule and splitting (209), into two cases.
% 44.42/12.90 |-Branch one:
% 44.42/12.90 | (460) ~ (all_58_0_80 = 0)
% 44.42/12.90 |
% 44.42/12.90 | Instantiating formula (35) with all_82_0_95, xp and discharging atoms isPrime0(xp) = 0, doDivides0(all_82_0_95, xp) = 0, yields:
% 44.42/12.90 | (461) all_82_0_95 = xp | all_82_0_95 = sz10 | ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_82_0_95) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0))
% 44.42/12.90 |
% 44.42/12.90 | Instantiating formula (11) with all_0_3_3, xp, all_37_2_64, xp and discharging atoms doDivides0(xp, all_0_3_3) = 0, sdtasdt0(xp, all_37_2_64) = all_0_3_3, yields:
% 44.42/12.90 | (462) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, all_37_2_64) = v8 & doDivides0(xp, xp) = v7 & iLess0(v5, all_0_4_4) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xp, all_37_2_64) = v4 & aNaturalNumber0(all_37_2_64) = v1 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 44.42/12.90 |
% 44.42/12.90 | Instantiating formula (67) with all_0_3_3, all_37_2_64, xp and discharging atoms sdtasdt0(xp, all_37_2_64) = all_0_3_3, yields:
% 44.42/12.90 | (463) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_37_2_64, xp) = v2 & aNaturalNumber0(all_37_2_64) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_3_3))
% 44.42/12.90 |
% 44.42/12.90 | Instantiating formula (11) with all_0_2_2, xp, xr, xm and discharging atoms doDivides0(xp, all_0_2_2) = 0, yields:
% 44.42/12.90 | (464) ~ (sdtasdt0(xm, xr) = all_0_2_2) | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, xr) = v8 & doDivides0(xp, xm) = v7 & iLess0(v5, all_0_4_4) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xm, xr) = v4 & aNaturalNumber0(xr) = v1 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 44.42/12.90 |
% 44.42/12.90 | Instantiating formula (67) with all_30_0_48, xr, xm and discharging atoms sdtasdt0(xm, xr) = all_30_0_48, yields:
% 44.42/12.90 | (465) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xr, xm) = v2 & aNaturalNumber0(xr) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_30_0_48))
% 44.42/12.90 |
% 44.42/12.90 | Instantiating formula (37) with all_30_0_48, xr, xm and discharging atoms sdtasdt0(xm, xr) = all_30_0_48, yields:
% 44.42/12.90 | (466) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_30_0_48) = v2 & aNaturalNumber0(xr) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 44.42/12.91 |
% 44.42/12.91 | Instantiating formula (3) with all_0_4_4, all_0_5_5, xp, xp, all_16_4_22 and discharging atoms sdtpldt0(all_0_5_5, xp) = all_0_4_4, yields:
% 44.42/12.91 | (467) ~ (sdtpldt0(all_16_4_22, xp) = all_0_5_5) | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_16_4_22, v3) = v4 & sdtpldt0(xp, xp) = v3 & aNaturalNumber0(all_16_4_22) = v0 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_4_4))
% 44.42/12.91 |
% 44.42/12.91 | Instantiating formula (55) with all_16_3_21, xp, all_16_4_22 and discharging atoms sdtpldt0(all_16_4_22, xp) = all_16_3_21, yields:
% 44.49/12.91 | (468) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, all_16_4_22) = v2 & aNaturalNumber0(all_16_4_22) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_16_3_21))
% 44.49/12.91 |
% 44.49/12.91 | Instantiating formula (13) with all_16_3_21, xp, all_16_4_22 and discharging atoms sdtpldt0(all_16_4_22, xp) = all_16_3_21, yields:
% 44.49/12.91 | (469) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_16_3_21) = v2 & aNaturalNumber0(all_16_4_22) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 44.49/12.91 |
% 44.49/12.91 | Instantiating formula (3) with all_16_3_21, all_16_4_22, xp, xm, xr and discharging atoms sdtpldt0(all_16_4_22, xp) = all_16_3_21, sdtpldt0(xr, xm) = all_16_4_22, yields:
% 44.49/12.91 | (470) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xr, v3) = v4 & sdtpldt0(xm, xp) = v3 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_16_3_21))
% 44.49/12.91 |
% 44.49/12.91 | Instantiating formula (55) with all_16_4_22, xm, xr and discharging atoms sdtpldt0(xr, xm) = all_16_4_22, yields:
% 44.49/12.91 | (471) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xm, xr) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_16_4_22))
% 44.49/12.91 |
% 44.49/12.91 | Instantiating formula (13) with all_16_4_22, xm, xr and discharging atoms sdtpldt0(xr, xm) = all_16_4_22, yields:
% 44.49/12.91 | (472) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_16_4_22) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 44.49/12.91 |
% 44.49/12.91 | Instantiating formula (47) with all_0_0_0, xn, all_18_2_29, xp, xp and discharging atoms doDivides0(xp, xn) = all_0_0_0, sdtpldt0(xp, all_18_2_29) = xn, yields:
% 44.49/12.91 | (473) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(xp, all_18_2_29) = v4 & doDivides0(xp, xp) = v3 & aNaturalNumber0(all_18_2_29) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 44.49/12.91 |
% 44.49/12.91 | Instantiating formula (47) with all_53_0_76, xn, all_18_2_29, xp, all_0_2_2 and discharging atoms doDivides0(all_0_2_2, xn) = all_53_0_76, sdtpldt0(xp, all_18_2_29) = xn, yields:
% 44.49/12.91 | (474) all_53_0_76 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(all_0_2_2, all_18_2_29) = v4 & doDivides0(all_0_2_2, xp) = v3 & aNaturalNumber0(all_18_2_29) = v2 & aNaturalNumber0(all_0_2_2) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 44.49/12.91 |
% 44.49/12.91 | Instantiating formula (47) with all_58_0_80, xn, all_18_2_29, xp, all_0_3_3 and discharging atoms doDivides0(all_0_3_3, xn) = all_58_0_80, sdtpldt0(xp, all_18_2_29) = xn, yields:
% 44.49/12.91 | (475) all_58_0_80 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(all_0_3_3, all_18_2_29) = v4 & doDivides0(all_0_3_3, xp) = v3 & aNaturalNumber0(all_18_2_29) = v2 & aNaturalNumber0(all_0_3_3) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 44.49/12.91 |
% 44.49/12.91 | Instantiating formula (47) with all_68_0_88, xn, all_18_2_29, xp, xr and discharging atoms doDivides0(xr, xn) = all_68_0_88, sdtpldt0(xp, all_18_2_29) = xn, yields:
% 44.49/12.91 | (476) all_68_0_88 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(xr, all_18_2_29) = v4 & doDivides0(xr, xp) = v3 & aNaturalNumber0(all_18_2_29) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 44.49/12.91 |
% 44.49/12.91 | Instantiating formula (3) with all_0_5_5, xn, xm, all_18_2_29, xp and discharging atoms sdtpldt0(xp, all_18_2_29) = xn, sdtpldt0(xn, xm) = all_0_5_5, yields:
% 44.49/12.91 | (477) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_18_2_29, xm) = v3 & sdtpldt0(xp, v3) = v4 & aNaturalNumber0(all_18_2_29) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_5_5))
% 44.49/12.91 |
% 44.49/12.91 | Instantiating formula (40) with all_18_2_29, xr, xn, xp and discharging atoms sdtmndt0(xn, xp) = xr, sdtpldt0(xp, all_18_2_29) = xn, yields:
% 44.49/12.91 | (478) all_18_2_29 = xr | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_18_2_29) = v0) | (sdtlseqdt0(xp, xn) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 44.49/12.91 |
% 44.49/12.91 | Instantiating formula (55) with xn, all_18_2_29, xp and discharging atoms sdtpldt0(xp, all_18_2_29) = xn, yields:
% 44.49/12.91 | (479) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_18_2_29, xp) = v2 & aNaturalNumber0(all_18_2_29) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xn))
% 44.49/12.91 |
% 44.49/12.91 | Instantiating formula (55) with all_34_1_55, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_34_1_55, yields:
% 44.49/12.91 | (480) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, xm) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_34_1_55))
% 44.49/12.91 |
% 44.49/12.91 | Instantiating formula (13) with all_34_1_55, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_34_1_55, yields:
% 44.49/12.91 | (481) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_34_1_55) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 44.49/12.91 |
% 44.49/12.91 | Instantiating formula (3) with all_0_4_4, all_0_5_5, xp, xn, xm and discharging atoms sdtpldt0(all_0_5_5, xp) = all_0_4_4, sdtpldt0(xm, xn) = all_0_5_5, yields:
% 44.49/12.91 | (482) ? [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_4_4))
% 44.49/12.91 |
% 44.49/12.91 | Instantiating formula (3) with all_0_4_4, xn, all_34_1_55, all_18_2_29, xp and discharging atoms sdtpldt0(xp, all_18_2_29) = xn, sdtpldt0(xn, all_34_1_55) = all_0_4_4, yields:
% 44.49/12.91 | (483) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_18_2_29, all_34_1_55) = v3 & sdtpldt0(xp, v3) = v4 & aNaturalNumber0(all_34_1_55) = v2 & aNaturalNumber0(all_18_2_29) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_4_4))
% 44.49/12.91 |
% 44.49/12.91 | Instantiating formula (55) with all_0_4_4, all_34_1_55, xn and discharging atoms sdtpldt0(xn, all_34_1_55) = all_0_4_4, yields:
% 44.49/12.91 | (484) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_34_1_55, xn) = v2 & aNaturalNumber0(all_34_1_55) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_4_4))
% 44.49/12.91 |
% 44.49/12.91 | Instantiating formula (13) with all_0_4_4, all_34_1_55, xn and discharging atoms sdtpldt0(xn, all_34_1_55) = all_0_4_4, yields:
% 44.49/12.91 | (485) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_34_1_55) = v1 & aNaturalNumber0(all_0_4_4) = v2 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 44.49/12.91 |
% 44.49/12.91 | Instantiating formula (34) with all_82_0_95 and discharging atoms aNaturalNumber0(all_82_0_95) = 0, yields:
% 44.49/12.91 | (486) all_82_0_95 = sz10 | all_82_0_95 = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_82_0_95) = 0 & aNaturalNumber0(v0) = 0)
% 44.49/12.91 |
% 44.49/12.91 | Instantiating (485) with all_185_0_96, all_185_1_97, all_185_2_98 yields:
% 44.49/12.91 | (487) aNaturalNumber0(all_34_1_55) = all_185_1_97 & aNaturalNumber0(all_0_4_4) = all_185_0_96 & aNaturalNumber0(xn) = all_185_2_98 & ( ~ (all_185_1_97 = 0) | ~ (all_185_2_98 = 0) | all_185_0_96 = 0)
% 44.49/12.91 |
% 44.49/12.91 | Applying alpha-rule on (487) yields:
% 44.49/12.91 | (488) aNaturalNumber0(all_34_1_55) = all_185_1_97
% 44.49/12.91 | (489) aNaturalNumber0(all_0_4_4) = all_185_0_96
% 44.49/12.91 | (490) aNaturalNumber0(xn) = all_185_2_98
% 44.49/12.91 | (491) ~ (all_185_1_97 = 0) | ~ (all_185_2_98 = 0) | all_185_0_96 = 0
% 44.49/12.91 |
% 44.49/12.91 | Instantiating (483) with all_187_0_99, all_187_1_100, all_187_2_101, all_187_3_102, all_187_4_103 yields:
% 44.49/12.91 | (492) sdtpldt0(all_18_2_29, all_34_1_55) = all_187_1_100 & sdtpldt0(xp, all_187_1_100) = all_187_0_99 & aNaturalNumber0(all_34_1_55) = all_187_2_101 & aNaturalNumber0(all_18_2_29) = all_187_3_102 & aNaturalNumber0(xp) = all_187_4_103 & ( ~ (all_187_2_101 = 0) | ~ (all_187_3_102 = 0) | ~ (all_187_4_103 = 0) | all_187_0_99 = all_0_4_4)
% 44.49/12.91 |
% 44.49/12.91 | Applying alpha-rule on (492) yields:
% 44.49/12.91 | (493) aNaturalNumber0(all_34_1_55) = all_187_2_101
% 44.49/12.91 | (494) aNaturalNumber0(xp) = all_187_4_103
% 44.49/12.91 | (495) aNaturalNumber0(all_18_2_29) = all_187_3_102
% 44.49/12.91 | (496) ~ (all_187_2_101 = 0) | ~ (all_187_3_102 = 0) | ~ (all_187_4_103 = 0) | all_187_0_99 = all_0_4_4
% 44.49/12.91 | (497) sdtpldt0(all_18_2_29, all_34_1_55) = all_187_1_100
% 44.49/12.91 | (498) sdtpldt0(xp, all_187_1_100) = all_187_0_99
% 44.49/12.91 |
% 44.49/12.91 | Instantiating (484) with all_189_0_104, all_189_1_105, all_189_2_106 yields:
% 44.49/12.91 | (499) sdtpldt0(all_34_1_55, xn) = all_189_0_104 & aNaturalNumber0(all_34_1_55) = all_189_1_105 & aNaturalNumber0(xn) = all_189_2_106 & ( ~ (all_189_1_105 = 0) | ~ (all_189_2_106 = 0) | all_189_0_104 = all_0_4_4)
% 44.49/12.91 |
% 44.49/12.91 | Applying alpha-rule on (499) yields:
% 44.49/12.91 | (500) sdtpldt0(all_34_1_55, xn) = all_189_0_104
% 44.49/12.91 | (501) aNaturalNumber0(all_34_1_55) = all_189_1_105
% 44.49/12.91 | (502) aNaturalNumber0(xn) = all_189_2_106
% 44.49/12.91 | (503) ~ (all_189_1_105 = 0) | ~ (all_189_2_106 = 0) | all_189_0_104 = all_0_4_4
% 44.49/12.91 |
% 44.49/12.91 | Instantiating (482) with all_191_0_107, all_191_1_108, all_191_2_109, all_191_3_110, all_191_4_111 yields:
% 44.49/12.91 | (504) sdtpldt0(xm, all_191_1_108) = all_191_0_107 & sdtpldt0(xn, xp) = all_191_1_108 & aNaturalNumber0(xp) = all_191_2_109 & aNaturalNumber0(xm) = all_191_4_111 & aNaturalNumber0(xn) = all_191_3_110 & ( ~ (all_191_2_109 = 0) | ~ (all_191_3_110 = 0) | ~ (all_191_4_111 = 0) | all_191_0_107 = all_0_4_4)
% 44.49/12.91 |
% 44.49/12.91 | Applying alpha-rule on (504) yields:
% 44.49/12.91 | (505) sdtpldt0(xm, all_191_1_108) = all_191_0_107
% 44.49/12.91 | (506) aNaturalNumber0(xp) = all_191_2_109
% 44.49/12.91 | (507) sdtpldt0(xn, xp) = all_191_1_108
% 44.49/12.91 | (508) aNaturalNumber0(xn) = all_191_3_110
% 44.49/12.91 | (509) aNaturalNumber0(xm) = all_191_4_111
% 44.49/12.91 | (510) ~ (all_191_2_109 = 0) | ~ (all_191_3_110 = 0) | ~ (all_191_4_111 = 0) | all_191_0_107 = all_0_4_4
% 44.49/12.92 |
% 44.49/12.92 | Instantiating (481) with all_193_0_112, all_193_1_113, all_193_2_114 yields:
% 44.49/12.92 | (511) aNaturalNumber0(all_34_1_55) = all_193_0_112 & aNaturalNumber0(xp) = all_193_1_113 & aNaturalNumber0(xm) = all_193_2_114 & ( ~ (all_193_1_113 = 0) | ~ (all_193_2_114 = 0) | all_193_0_112 = 0)
% 44.49/12.92 |
% 44.49/12.92 | Applying alpha-rule on (511) yields:
% 44.49/12.92 | (512) aNaturalNumber0(all_34_1_55) = all_193_0_112
% 44.49/12.92 | (513) aNaturalNumber0(xp) = all_193_1_113
% 44.49/12.92 | (514) aNaturalNumber0(xm) = all_193_2_114
% 44.49/12.92 | (515) ~ (all_193_1_113 = 0) | ~ (all_193_2_114 = 0) | all_193_0_112 = 0
% 44.49/12.92 |
% 44.49/12.92 | Instantiating (470) with all_195_0_115, all_195_1_116, all_195_2_117, all_195_3_118, all_195_4_119 yields:
% 44.49/12.92 | (516) sdtpldt0(xr, all_195_1_116) = all_195_0_115 & sdtpldt0(xm, xp) = all_195_1_116 & aNaturalNumber0(xr) = all_195_4_119 & aNaturalNumber0(xp) = all_195_2_117 & aNaturalNumber0(xm) = all_195_3_118 & ( ~ (all_195_2_117 = 0) | ~ (all_195_3_118 = 0) | ~ (all_195_4_119 = 0) | all_195_0_115 = all_16_3_21)
% 44.49/12.92 |
% 44.49/12.92 | Applying alpha-rule on (516) yields:
% 44.49/12.92 | (517) aNaturalNumber0(xm) = all_195_3_118
% 44.49/12.92 | (518) ~ (all_195_2_117 = 0) | ~ (all_195_3_118 = 0) | ~ (all_195_4_119 = 0) | all_195_0_115 = all_16_3_21
% 44.49/12.92 | (519) aNaturalNumber0(xp) = all_195_2_117
% 44.49/12.92 | (520) sdtpldt0(xr, all_195_1_116) = all_195_0_115
% 44.49/12.92 | (521) sdtpldt0(xm, xp) = all_195_1_116
% 44.49/12.92 | (522) aNaturalNumber0(xr) = all_195_4_119
% 44.49/12.92 |
% 44.49/12.92 | Instantiating (469) with all_197_0_120, all_197_1_121, all_197_2_122 yields:
% 44.49/12.92 | (523) aNaturalNumber0(all_16_3_21) = all_197_0_120 & aNaturalNumber0(all_16_4_22) = all_197_2_122 & aNaturalNumber0(xp) = all_197_1_121 & ( ~ (all_197_1_121 = 0) | ~ (all_197_2_122 = 0) | all_197_0_120 = 0)
% 44.49/12.92 |
% 44.49/12.92 | Applying alpha-rule on (523) yields:
% 44.49/12.92 | (524) aNaturalNumber0(all_16_3_21) = all_197_0_120
% 44.49/12.92 | (525) aNaturalNumber0(all_16_4_22) = all_197_2_122
% 44.49/12.92 | (526) aNaturalNumber0(xp) = all_197_1_121
% 44.49/12.92 | (527) ~ (all_197_1_121 = 0) | ~ (all_197_2_122 = 0) | all_197_0_120 = 0
% 44.49/12.92 |
% 44.49/12.92 | Instantiating (466) with all_199_0_123, all_199_1_124, all_199_2_125 yields:
% 44.49/12.92 | (528) aNaturalNumber0(all_30_0_48) = all_199_0_123 & aNaturalNumber0(xr) = all_199_1_124 & aNaturalNumber0(xm) = all_199_2_125 & ( ~ (all_199_1_124 = 0) | ~ (all_199_2_125 = 0) | all_199_0_123 = 0)
% 44.49/12.92 |
% 44.49/12.92 | Applying alpha-rule on (528) yields:
% 44.49/12.92 | (529) aNaturalNumber0(all_30_0_48) = all_199_0_123
% 44.49/12.92 | (530) aNaturalNumber0(xr) = all_199_1_124
% 44.49/12.92 | (531) aNaturalNumber0(xm) = all_199_2_125
% 44.49/12.92 | (532) ~ (all_199_1_124 = 0) | ~ (all_199_2_125 = 0) | all_199_0_123 = 0
% 44.49/12.92 |
% 44.49/12.92 | Instantiating (480) with all_201_0_126, all_201_1_127, all_201_2_128 yields:
% 44.49/12.92 | (533) sdtpldt0(xp, xm) = all_201_0_126 & aNaturalNumber0(xp) = all_201_1_127 & aNaturalNumber0(xm) = all_201_2_128 & ( ~ (all_201_1_127 = 0) | ~ (all_201_2_128 = 0) | all_201_0_126 = all_34_1_55)
% 44.49/12.92 |
% 44.49/12.92 | Applying alpha-rule on (533) yields:
% 44.49/12.92 | (534) sdtpldt0(xp, xm) = all_201_0_126
% 44.49/12.92 | (535) aNaturalNumber0(xp) = all_201_1_127
% 44.49/12.92 | (536) aNaturalNumber0(xm) = all_201_2_128
% 44.49/12.92 | (537) ~ (all_201_1_127 = 0) | ~ (all_201_2_128 = 0) | all_201_0_126 = all_34_1_55
% 44.49/12.92 |
% 44.49/12.92 | Instantiating (479) with all_203_0_129, all_203_1_130, all_203_2_131 yields:
% 44.49/12.92 | (538) sdtpldt0(all_18_2_29, xp) = all_203_0_129 & aNaturalNumber0(all_18_2_29) = all_203_1_130 & aNaturalNumber0(xp) = all_203_2_131 & ( ~ (all_203_1_130 = 0) | ~ (all_203_2_131 = 0) | all_203_0_129 = xn)
% 44.49/12.92 |
% 44.49/12.92 | Applying alpha-rule on (538) yields:
% 44.49/12.92 | (539) sdtpldt0(all_18_2_29, xp) = all_203_0_129
% 44.49/12.92 | (540) aNaturalNumber0(all_18_2_29) = all_203_1_130
% 44.49/12.92 | (541) aNaturalNumber0(xp) = all_203_2_131
% 44.49/12.92 | (542) ~ (all_203_1_130 = 0) | ~ (all_203_2_131 = 0) | all_203_0_129 = xn
% 44.49/12.92 |
% 44.49/12.92 | Instantiating (477) with all_205_0_132, all_205_1_133, all_205_2_134, all_205_3_135, all_205_4_136 yields:
% 44.49/12.92 | (543) sdtpldt0(all_18_2_29, xm) = all_205_1_133 & sdtpldt0(xp, all_205_1_133) = all_205_0_132 & aNaturalNumber0(all_18_2_29) = all_205_3_135 & aNaturalNumber0(xp) = all_205_4_136 & aNaturalNumber0(xm) = all_205_2_134 & ( ~ (all_205_2_134 = 0) | ~ (all_205_3_135 = 0) | ~ (all_205_4_136 = 0) | all_205_0_132 = all_0_5_5)
% 44.49/12.92 |
% 44.49/12.92 | Applying alpha-rule on (543) yields:
% 44.49/12.92 | (544) sdtpldt0(all_18_2_29, xm) = all_205_1_133
% 44.49/12.92 | (545) aNaturalNumber0(all_18_2_29) = all_205_3_135
% 44.49/12.92 | (546) aNaturalNumber0(xp) = all_205_4_136
% 44.49/12.92 | (547) sdtpldt0(xp, all_205_1_133) = all_205_0_132
% 44.49/12.92 | (548) aNaturalNumber0(xm) = all_205_2_134
% 44.49/12.92 | (549) ~ (all_205_2_134 = 0) | ~ (all_205_3_135 = 0) | ~ (all_205_4_136 = 0) | all_205_0_132 = all_0_5_5
% 44.49/12.92 |
% 44.49/12.92 | Instantiating (465) with all_207_0_137, all_207_1_138, all_207_2_139 yields:
% 44.49/12.92 | (550) sdtasdt0(xr, xm) = all_207_0_137 & aNaturalNumber0(xr) = all_207_1_138 & aNaturalNumber0(xm) = all_207_2_139 & ( ~ (all_207_1_138 = 0) | ~ (all_207_2_139 = 0) | all_207_0_137 = all_30_0_48)
% 44.49/12.92 |
% 44.49/12.92 | Applying alpha-rule on (550) yields:
% 44.49/12.92 | (551) sdtasdt0(xr, xm) = all_207_0_137
% 44.49/12.92 | (552) aNaturalNumber0(xr) = all_207_1_138
% 44.49/12.92 | (553) aNaturalNumber0(xm) = all_207_2_139
% 44.49/12.92 | (554) ~ (all_207_1_138 = 0) | ~ (all_207_2_139 = 0) | all_207_0_137 = all_30_0_48
% 44.49/12.92 |
% 44.49/12.92 | Instantiating (468) with all_209_0_140, all_209_1_141, all_209_2_142 yields:
% 44.49/12.92 | (555) sdtpldt0(xp, all_16_4_22) = all_209_0_140 & aNaturalNumber0(all_16_4_22) = all_209_2_142 & aNaturalNumber0(xp) = all_209_1_141 & ( ~ (all_209_1_141 = 0) | ~ (all_209_2_142 = 0) | all_209_0_140 = all_16_3_21)
% 44.49/12.92 |
% 44.49/12.92 | Applying alpha-rule on (555) yields:
% 44.49/12.92 | (556) sdtpldt0(xp, all_16_4_22) = all_209_0_140
% 44.49/12.92 | (557) aNaturalNumber0(all_16_4_22) = all_209_2_142
% 44.49/12.92 | (558) aNaturalNumber0(xp) = all_209_1_141
% 44.49/12.92 | (559) ~ (all_209_1_141 = 0) | ~ (all_209_2_142 = 0) | all_209_0_140 = all_16_3_21
% 44.49/12.92 |
% 44.49/12.92 | Instantiating (463) with all_211_0_143, all_211_1_144, all_211_2_145 yields:
% 44.49/12.92 | (560) sdtasdt0(all_37_2_64, xp) = all_211_0_143 & aNaturalNumber0(all_37_2_64) = all_211_1_144 & aNaturalNumber0(xp) = all_211_2_145 & ( ~ (all_211_1_144 = 0) | ~ (all_211_2_145 = 0) | all_211_0_143 = all_0_3_3)
% 44.49/12.92 |
% 44.49/12.92 | Applying alpha-rule on (560) yields:
% 44.49/12.92 | (561) sdtasdt0(all_37_2_64, xp) = all_211_0_143
% 44.49/12.92 | (562) aNaturalNumber0(all_37_2_64) = all_211_1_144
% 44.49/12.92 | (563) aNaturalNumber0(xp) = all_211_2_145
% 44.49/12.92 | (564) ~ (all_211_1_144 = 0) | ~ (all_211_2_145 = 0) | all_211_0_143 = all_0_3_3
% 44.49/12.92 |
% 44.49/12.92 | Instantiating (462) with all_214_0_149, all_214_1_150, all_214_2_151, all_214_3_152, all_214_4_153, all_214_5_154, all_214_6_155, all_214_7_156, all_214_8_157 yields:
% 44.49/12.92 | (565) isPrime0(xp) = all_214_5_154 & doDivides0(xp, all_37_2_64) = all_214_0_149 & doDivides0(xp, xp) = all_214_1_150 & iLess0(all_214_3_152, all_0_4_4) = all_214_2_151 & sdtpldt0(all_214_4_153, xp) = all_214_3_152 & sdtpldt0(xp, all_37_2_64) = all_214_4_153 & aNaturalNumber0(all_37_2_64) = all_214_7_156 & aNaturalNumber0(xp) = all_214_6_155 & aNaturalNumber0(xp) = all_214_8_157 & ( ~ (all_214_2_151 = 0) | ~ (all_214_5_154 = 0) | ~ (all_214_6_155 = 0) | ~ (all_214_7_156 = 0) | ~ (all_214_8_157 = 0) | all_214_0_149 = 0 | all_214_1_150 = 0)
% 44.49/12.92 |
% 44.49/12.92 | Applying alpha-rule on (565) yields:
% 44.49/12.92 | (566) doDivides0(xp, all_37_2_64) = all_214_0_149
% 44.49/12.92 | (567) sdtpldt0(all_214_4_153, xp) = all_214_3_152
% 44.49/12.92 | (568) aNaturalNumber0(all_37_2_64) = all_214_7_156
% 44.49/12.92 | (569) aNaturalNumber0(xp) = all_214_8_157
% 44.49/12.92 | (570) isPrime0(xp) = all_214_5_154
% 44.49/12.92 | (571) ~ (all_214_2_151 = 0) | ~ (all_214_5_154 = 0) | ~ (all_214_6_155 = 0) | ~ (all_214_7_156 = 0) | ~ (all_214_8_157 = 0) | all_214_0_149 = 0 | all_214_1_150 = 0
% 44.49/12.92 | (572) iLess0(all_214_3_152, all_0_4_4) = all_214_2_151
% 44.49/12.92 | (573) doDivides0(xp, xp) = all_214_1_150
% 44.49/12.92 | (574) aNaturalNumber0(xp) = all_214_6_155
% 44.49/12.92 | (575) sdtpldt0(xp, all_37_2_64) = all_214_4_153
% 44.49/12.92 |
% 44.49/12.92 | Instantiating (472) with all_216_0_158, all_216_1_159, all_216_2_160 yields:
% 44.49/12.92 | (576) aNaturalNumber0(all_16_4_22) = all_216_0_158 & aNaturalNumber0(xr) = all_216_2_160 & aNaturalNumber0(xm) = all_216_1_159 & ( ~ (all_216_1_159 = 0) | ~ (all_216_2_160 = 0) | all_216_0_158 = 0)
% 44.49/12.92 |
% 44.49/12.92 | Applying alpha-rule on (576) yields:
% 44.49/12.92 | (577) aNaturalNumber0(all_16_4_22) = all_216_0_158
% 44.49/12.92 | (578) aNaturalNumber0(xr) = all_216_2_160
% 44.49/12.92 | (579) aNaturalNumber0(xm) = all_216_1_159
% 44.49/12.92 | (580) ~ (all_216_1_159 = 0) | ~ (all_216_2_160 = 0) | all_216_0_158 = 0
% 44.49/12.92 |
% 44.49/12.92 | Instantiating (471) with all_218_0_161, all_218_1_162, all_218_2_163 yields:
% 44.49/12.92 | (581) sdtpldt0(xm, xr) = all_218_0_161 & aNaturalNumber0(xr) = all_218_2_163 & aNaturalNumber0(xm) = all_218_1_162 & ( ~ (all_218_1_162 = 0) | ~ (all_218_2_163 = 0) | all_218_0_161 = all_16_4_22)
% 44.49/12.92 |
% 44.49/12.92 | Applying alpha-rule on (581) yields:
% 44.49/12.92 | (582) sdtpldt0(xm, xr) = all_218_0_161
% 44.49/12.92 | (583) aNaturalNumber0(xr) = all_218_2_163
% 44.49/12.92 | (584) aNaturalNumber0(xm) = all_218_1_162
% 44.49/12.92 | (585) ~ (all_218_1_162 = 0) | ~ (all_218_2_163 = 0) | all_218_0_161 = all_16_4_22
% 44.49/12.92 |
% 44.49/12.92 +-Applying beta-rule and splitting (475), into two cases.
% 44.49/12.92 |-Branch one:
% 44.49/12.92 | (586) all_58_0_80 = 0
% 44.49/12.92 |
% 44.49/12.92 | Equations (586) can reduce 460 to:
% 44.49/12.92 | (173) $false
% 44.49/12.92 |
% 44.49/12.92 |-The branch is then unsatisfiable
% 44.49/12.92 |-Branch two:
% 44.49/12.92 | (460) ~ (all_58_0_80 = 0)
% 44.49/12.92 | (589) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(all_0_3_3, all_18_2_29) = v4 & doDivides0(all_0_3_3, xp) = v3 & aNaturalNumber0(all_18_2_29) = v2 & aNaturalNumber0(all_0_3_3) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 44.49/12.92 |
% 44.49/12.92 | Instantiating (589) with all_224_0_164, all_224_1_165, all_224_2_166, all_224_3_167, all_224_4_168 yields:
% 44.49/12.92 | (590) doDivides0(all_0_3_3, all_18_2_29) = all_224_0_164 & doDivides0(all_0_3_3, xp) = all_224_1_165 & aNaturalNumber0(all_18_2_29) = all_224_2_166 & aNaturalNumber0(all_0_3_3) = all_224_4_168 & aNaturalNumber0(xp) = all_224_3_167 & ( ~ (all_224_0_164 = 0) | ~ (all_224_1_165 = 0) | ~ (all_224_2_166 = 0) | ~ (all_224_3_167 = 0) | ~ (all_224_4_168 = 0))
% 44.49/12.92 |
% 44.49/12.92 | Applying alpha-rule on (590) yields:
% 44.49/12.92 | (591) aNaturalNumber0(xp) = all_224_3_167
% 44.49/12.92 | (592) aNaturalNumber0(all_18_2_29) = all_224_2_166
% 44.49/12.92 | (593) ~ (all_224_0_164 = 0) | ~ (all_224_1_165 = 0) | ~ (all_224_2_166 = 0) | ~ (all_224_3_167 = 0) | ~ (all_224_4_168 = 0)
% 44.49/12.92 | (594) doDivides0(all_0_3_3, all_18_2_29) = all_224_0_164
% 44.49/12.92 | (595) doDivides0(all_0_3_3, xp) = all_224_1_165
% 44.49/12.92 | (596) aNaturalNumber0(all_0_3_3) = all_224_4_168
% 44.49/12.92 |
% 44.49/12.92 +-Applying beta-rule and splitting (473), into two cases.
% 44.49/12.92 |-Branch one:
% 44.49/12.92 | (192) all_0_0_0 = 0
% 44.49/12.92 |
% 44.49/12.92 | Equations (192) can reduce 43 to:
% 44.49/12.92 | (173) $false
% 44.49/12.92 |
% 44.49/12.92 |-The branch is then unsatisfiable
% 44.49/12.92 |-Branch two:
% 44.49/12.92 | (43) ~ (all_0_0_0 = 0)
% 44.49/12.92 | (600) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(xp, all_18_2_29) = v4 & doDivides0(xp, xp) = v3 & aNaturalNumber0(all_18_2_29) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 44.49/12.92 |
% 44.49/12.92 | Instantiating (600) with all_229_0_169, all_229_1_170, all_229_2_171, all_229_3_172, all_229_4_173 yields:
% 44.49/12.92 | (601) doDivides0(xp, all_18_2_29) = all_229_0_169 & doDivides0(xp, xp) = all_229_1_170 & aNaturalNumber0(all_18_2_29) = all_229_2_171 & aNaturalNumber0(xp) = all_229_3_172 & aNaturalNumber0(xp) = all_229_4_173 & ( ~ (all_229_0_169 = 0) | ~ (all_229_1_170 = 0) | ~ (all_229_2_171 = 0) | ~ (all_229_3_172 = 0) | ~ (all_229_4_173 = 0))
% 44.49/12.92 |
% 44.49/12.92 | Applying alpha-rule on (601) yields:
% 44.49/12.92 | (602) doDivides0(xp, all_18_2_29) = all_229_0_169
% 44.49/12.92 | (603) ~ (all_229_0_169 = 0) | ~ (all_229_1_170 = 0) | ~ (all_229_2_171 = 0) | ~ (all_229_3_172 = 0) | ~ (all_229_4_173 = 0)
% 44.49/12.92 | (604) aNaturalNumber0(xp) = all_229_4_173
% 44.49/12.92 | (605) aNaturalNumber0(all_18_2_29) = all_229_2_171
% 44.49/12.92 | (606) aNaturalNumber0(xp) = all_229_3_172
% 44.49/12.92 | (607) doDivides0(xp, xp) = all_229_1_170
% 44.49/12.92 |
% 44.49/12.92 +-Applying beta-rule and splitting (486), into two cases.
% 44.49/12.92 |-Branch one:
% 44.49/12.92 | (608) all_82_0_95 = sz00
% 44.49/12.92 |
% 44.49/12.92 | Equations (608) can reduce 254 to:
% 44.49/12.92 | (173) $false
% 44.49/12.92 |
% 44.49/12.92 |-The branch is then unsatisfiable
% 44.49/12.92 |-Branch two:
% 44.49/12.92 | (254) ~ (all_82_0_95 = sz00)
% 44.49/12.92 | (611) all_82_0_95 = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_82_0_95) = 0 & aNaturalNumber0(v0) = 0)
% 44.49/12.93 |
% 44.49/12.93 +-Applying beta-rule and splitting (611), into two cases.
% 44.49/12.93 |-Branch one:
% 44.49/12.93 | (612) all_82_0_95 = sz10
% 44.49/12.93 |
% 44.49/12.93 | Equations (612) can reduce 253 to:
% 44.49/12.93 | (173) $false
% 44.49/12.93 |
% 44.49/12.93 |-The branch is then unsatisfiable
% 44.49/12.93 |-Branch two:
% 44.49/12.93 | (253) ~ (all_82_0_95 = sz10)
% 44.49/12.93 | (615) ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_82_0_95) = 0 & aNaturalNumber0(v0) = 0)
% 44.49/12.93 |
% 44.49/12.93 | Instantiating formula (73) with xp, xr, all_229_0_169, 0 and discharging atoms doDivides0(xp, xr) = 0, yields:
% 44.49/12.93 | (616) all_229_0_169 = 0 | ~ (doDivides0(xp, xr) = all_229_0_169)
% 44.49/12.93 |
% 44.49/12.93 | Instantiating formula (73) with xp, xp, all_214_1_150, 0 and discharging atoms doDivides0(xp, xp) = all_214_1_150, yields:
% 44.49/12.93 | (617) all_214_1_150 = 0 | ~ (doDivides0(xp, xp) = 0)
% 44.49/12.93 |
% 44.49/12.93 | Instantiating formula (73) with xp, xp, all_214_1_150, all_229_1_170 and discharging atoms doDivides0(xp, xp) = all_229_1_170, doDivides0(xp, xp) = all_214_1_150, yields:
% 44.49/12.93 | (618) all_229_1_170 = all_214_1_150
% 44.49/12.93 |
% 44.49/12.93 | Instantiating formula (69) with xr, xm, all_205_1_133, all_16_4_22 and discharging atoms sdtpldt0(xr, xm) = all_16_4_22, yields:
% 44.49/12.93 | (619) all_205_1_133 = all_16_4_22 | ~ (sdtpldt0(xr, xm) = all_205_1_133)
% 44.49/12.93 |
% 44.49/12.93 | Instantiating formula (69) with xp, all_16_4_22, all_209_0_140, all_205_0_132 and discharging atoms sdtpldt0(xp, all_16_4_22) = all_209_0_140, yields:
% 44.49/12.93 | (620) all_209_0_140 = all_205_0_132 | ~ (sdtpldt0(xp, all_16_4_22) = all_205_0_132)
% 44.49/12.93 |
% 44.49/12.93 | Instantiating formula (60) with all_0_2_2, all_199_0_123, all_27_0_42 and discharging atoms aNaturalNumber0(all_0_2_2) = all_27_0_42, yields:
% 44.49/12.93 | (621) all_199_0_123 = all_27_0_42 | ~ (aNaturalNumber0(all_0_2_2) = all_199_0_123)
% 44.49/12.93 |
% 44.49/12.93 | Instantiating formula (60) with all_18_2_29, all_224_2_166, 0 and discharging atoms aNaturalNumber0(all_18_2_29) = all_224_2_166, aNaturalNumber0(all_18_2_29) = 0, yields:
% 44.49/12.93 | (622) all_224_2_166 = 0
% 44.49/12.93 |
% 44.49/12.93 | Instantiating formula (60) with all_18_2_29, all_224_2_166, all_229_2_171 and discharging atoms aNaturalNumber0(all_18_2_29) = all_229_2_171, aNaturalNumber0(all_18_2_29) = all_224_2_166, yields:
% 44.49/12.93 | (623) all_229_2_171 = all_224_2_166
% 44.49/12.93 |
% 44.49/12.93 | Instantiating formula (60) with all_18_2_29, all_205_3_135, all_229_2_171 and discharging atoms aNaturalNumber0(all_18_2_29) = all_229_2_171, aNaturalNumber0(all_18_2_29) = all_205_3_135, yields:
% 44.49/12.93 | (624) all_229_2_171 = all_205_3_135
% 44.49/12.93 |
% 44.49/12.93 | Instantiating formula (60) with all_18_2_29, all_203_1_130, all_224_2_166 and discharging atoms aNaturalNumber0(all_18_2_29) = all_224_2_166, aNaturalNumber0(all_18_2_29) = all_203_1_130, yields:
% 44.49/12.93 | (625) all_224_2_166 = all_203_1_130
% 44.49/12.93 |
% 44.49/12.93 | Instantiating formula (60) with all_18_2_29, all_187_3_102, all_203_1_130 and discharging atoms aNaturalNumber0(all_18_2_29) = all_203_1_130, aNaturalNumber0(all_18_2_29) = all_187_3_102, yields:
% 44.49/12.93 | (626) all_203_1_130 = all_187_3_102
% 44.49/12.93 |
% 44.49/12.93 | Instantiating formula (60) with all_16_4_22, all_209_2_142, all_216_0_158 and discharging atoms aNaturalNumber0(all_16_4_22) = all_216_0_158, aNaturalNumber0(all_16_4_22) = all_209_2_142, yields:
% 44.49/12.93 | (627) all_216_0_158 = all_209_2_142
% 44.49/12.93 |
% 44.49/12.93 | Instantiating formula (60) with all_16_4_22, all_197_2_122, all_216_0_158 and discharging atoms aNaturalNumber0(all_16_4_22) = all_216_0_158, aNaturalNumber0(all_16_4_22) = all_197_2_122, yields:
% 44.49/12.93 | (628) all_216_0_158 = all_197_2_122
% 44.49/12.93 |
% 44.49/12.93 | Instantiating formula (60) with xr, all_216_2_160, all_218_2_163 and discharging atoms aNaturalNumber0(xr) = all_218_2_163, aNaturalNumber0(xr) = all_216_2_160, yields:
% 44.49/12.93 | (629) all_218_2_163 = all_216_2_160
% 44.49/12.93 |
% 44.49/12.93 | Instantiating formula (60) with xr, all_207_1_138, all_16_8_26 and discharging atoms aNaturalNumber0(xr) = all_207_1_138, aNaturalNumber0(xr) = all_16_8_26, yields:
% 44.49/12.93 | (630) all_207_1_138 = all_16_8_26
% 44.49/12.93 |
% 44.49/12.93 | Instantiating formula (60) with xr, all_207_1_138, all_216_2_160 and discharging atoms aNaturalNumber0(xr) = all_216_2_160, aNaturalNumber0(xr) = all_207_1_138, yields:
% 44.49/12.93 | (631) all_216_2_160 = all_207_1_138
% 44.49/12.93 |
% 44.49/12.93 | Instantiating formula (60) with xr, all_199_1_124, all_218_2_163 and discharging atoms aNaturalNumber0(xr) = all_218_2_163, aNaturalNumber0(xr) = all_199_1_124, yields:
% 44.60/12.93 | (632) all_218_2_163 = all_199_1_124
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xr, all_195_4_119, all_207_1_138 and discharging atoms aNaturalNumber0(xr) = all_207_1_138, aNaturalNumber0(xr) = all_195_4_119, yields:
% 44.60/12.93 | (633) all_207_1_138 = all_195_4_119
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xp, all_224_3_167, all_229_4_173 and discharging atoms aNaturalNumber0(xp) = all_229_4_173, aNaturalNumber0(xp) = all_224_3_167, yields:
% 44.60/12.93 | (634) all_229_4_173 = all_224_3_167
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xp, all_214_6_155, all_224_3_167 and discharging atoms aNaturalNumber0(xp) = all_224_3_167, aNaturalNumber0(xp) = all_214_6_155, yields:
% 44.60/12.93 | (635) all_224_3_167 = all_214_6_155
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xp, all_214_8_157, all_214_6_155 and discharging atoms aNaturalNumber0(xp) = all_214_6_155, aNaturalNumber0(xp) = all_214_8_157, yields:
% 44.60/12.93 | (636) all_214_6_155 = all_214_8_157
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xp, all_211_2_145, all_229_3_172 and discharging atoms aNaturalNumber0(xp) = all_229_3_172, aNaturalNumber0(xp) = all_211_2_145, yields:
% 44.60/12.93 | (637) all_229_3_172 = all_211_2_145
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xp, all_211_2_145, all_214_8_157 and discharging atoms aNaturalNumber0(xp) = all_214_8_157, aNaturalNumber0(xp) = all_211_2_145, yields:
% 44.60/12.93 | (638) all_214_8_157 = all_211_2_145
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xp, all_209_1_141, 0 and discharging atoms aNaturalNumber0(xp) = all_209_1_141, aNaturalNumber0(xp) = 0, yields:
% 44.60/12.93 | (639) all_209_1_141 = 0
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xp, all_203_2_131, all_229_3_172 and discharging atoms aNaturalNumber0(xp) = all_229_3_172, aNaturalNumber0(xp) = all_203_2_131, yields:
% 44.60/12.93 | (640) all_229_3_172 = all_203_2_131
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xp, all_201_1_127, all_229_3_172 and discharging atoms aNaturalNumber0(xp) = all_229_3_172, aNaturalNumber0(xp) = all_201_1_127, yields:
% 44.60/12.93 | (641) all_229_3_172 = all_201_1_127
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xp, all_201_1_127, all_205_4_136 and discharging atoms aNaturalNumber0(xp) = all_205_4_136, aNaturalNumber0(xp) = all_201_1_127, yields:
% 44.60/12.93 | (642) all_205_4_136 = all_201_1_127
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xp, all_197_1_121, all_205_4_136 and discharging atoms aNaturalNumber0(xp) = all_205_4_136, aNaturalNumber0(xp) = all_197_1_121, yields:
% 44.60/12.93 | (643) all_205_4_136 = all_197_1_121
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xp, all_195_2_117, all_209_1_141 and discharging atoms aNaturalNumber0(xp) = all_209_1_141, aNaturalNumber0(xp) = all_195_2_117, yields:
% 44.60/12.93 | (644) all_209_1_141 = all_195_2_117
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xp, all_195_2_117, all_205_4_136 and discharging atoms aNaturalNumber0(xp) = all_205_4_136, aNaturalNumber0(xp) = all_195_2_117, yields:
% 44.60/12.93 | (645) all_205_4_136 = all_195_2_117
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xp, all_193_1_113, all_209_1_141 and discharging atoms aNaturalNumber0(xp) = all_209_1_141, aNaturalNumber0(xp) = all_193_1_113, yields:
% 44.60/12.93 | (646) all_209_1_141 = all_193_1_113
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xp, all_191_2_109, all_229_4_173 and discharging atoms aNaturalNumber0(xp) = all_229_4_173, aNaturalNumber0(xp) = all_191_2_109, yields:
% 44.60/12.93 | (647) all_229_4_173 = all_191_2_109
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xp, all_187_4_103, all_209_1_141 and discharging atoms aNaturalNumber0(xp) = all_209_1_141, aNaturalNumber0(xp) = all_187_4_103, yields:
% 44.60/12.93 | (648) all_209_1_141 = all_187_4_103
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xm, all_216_1_159, all_218_1_162 and discharging atoms aNaturalNumber0(xm) = all_218_1_162, aNaturalNumber0(xm) = all_216_1_159, yields:
% 44.60/12.93 | (649) all_218_1_162 = all_216_1_159
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xm, all_207_2_139, all_216_1_159 and discharging atoms aNaturalNumber0(xm) = all_216_1_159, aNaturalNumber0(xm) = all_207_2_139, yields:
% 44.60/12.93 | (650) all_216_1_159 = all_207_2_139
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xm, all_205_2_134, all_207_2_139 and discharging atoms aNaturalNumber0(xm) = all_207_2_139, aNaturalNumber0(xm) = all_205_2_134, yields:
% 44.60/12.93 | (651) all_207_2_139 = all_205_2_134
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xm, all_201_2_128, all_205_2_134 and discharging atoms aNaturalNumber0(xm) = all_205_2_134, aNaturalNumber0(xm) = all_201_2_128, yields:
% 44.60/12.93 | (652) all_205_2_134 = all_201_2_128
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xm, all_199_2_125, all_218_1_162 and discharging atoms aNaturalNumber0(xm) = all_218_1_162, aNaturalNumber0(xm) = all_199_2_125, yields:
% 44.60/12.93 | (653) all_218_1_162 = all_199_2_125
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xm, all_195_3_118, 0 and discharging atoms aNaturalNumber0(xm) = all_195_3_118, aNaturalNumber0(xm) = 0, yields:
% 44.60/12.93 | (654) all_195_3_118 = 0
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xm, all_195_3_118, all_201_2_128 and discharging atoms aNaturalNumber0(xm) = all_201_2_128, aNaturalNumber0(xm) = all_195_3_118, yields:
% 44.60/12.93 | (655) all_201_2_128 = all_195_3_118
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xm, all_193_2_114, all_201_2_128 and discharging atoms aNaturalNumber0(xm) = all_201_2_128, aNaturalNumber0(xm) = all_193_2_114, yields:
% 44.60/12.93 | (656) all_201_2_128 = all_193_2_114
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xm, all_191_4_111, all_195_3_118 and discharging atoms aNaturalNumber0(xm) = all_195_3_118, aNaturalNumber0(xm) = all_191_4_111, yields:
% 44.60/12.93 | (657) all_195_3_118 = all_191_4_111
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xn, all_191_3_110, 0 and discharging atoms aNaturalNumber0(xn) = all_191_3_110, aNaturalNumber0(xn) = 0, yields:
% 44.60/12.93 | (658) all_191_3_110 = 0
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xn, all_189_2_106, all_191_3_110 and discharging atoms aNaturalNumber0(xn) = all_191_3_110, aNaturalNumber0(xn) = all_189_2_106, yields:
% 44.60/12.93 | (659) all_191_3_110 = all_189_2_106
% 44.60/12.93 |
% 44.60/12.93 | Instantiating formula (60) with xn, all_185_2_98, all_191_3_110 and discharging atoms aNaturalNumber0(xn) = all_191_3_110, aNaturalNumber0(xn) = all_185_2_98, yields:
% 44.60/12.93 | (660) all_191_3_110 = all_185_2_98
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (623,624) yields a new equation:
% 44.60/12.93 | (661) all_224_2_166 = all_205_3_135
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 661 yields:
% 44.60/12.93 | (662) all_224_2_166 = all_205_3_135
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (641,640) yields a new equation:
% 44.60/12.93 | (663) all_203_2_131 = all_201_1_127
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (637,640) yields a new equation:
% 44.60/12.93 | (664) all_211_2_145 = all_203_2_131
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 664 yields:
% 44.60/12.93 | (665) all_211_2_145 = all_203_2_131
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (634,647) yields a new equation:
% 44.60/12.93 | (666) all_224_3_167 = all_191_2_109
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 666 yields:
% 44.60/12.93 | (667) all_224_3_167 = all_191_2_109
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (625,662) yields a new equation:
% 44.60/12.93 | (668) all_205_3_135 = all_203_1_130
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (622,662) yields a new equation:
% 44.60/12.93 | (669) all_205_3_135 = 0
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (635,667) yields a new equation:
% 44.60/12.93 | (670) all_214_6_155 = all_191_2_109
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 670 yields:
% 44.60/12.93 | (671) all_214_6_155 = all_191_2_109
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (649,653) yields a new equation:
% 44.60/12.93 | (672) all_216_1_159 = all_199_2_125
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 672 yields:
% 44.60/12.93 | (673) all_216_1_159 = all_199_2_125
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (629,632) yields a new equation:
% 44.60/12.93 | (674) all_216_2_160 = all_199_1_124
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 674 yields:
% 44.60/12.93 | (675) all_216_2_160 = all_199_1_124
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (627,628) yields a new equation:
% 44.60/12.93 | (676) all_209_2_142 = all_197_2_122
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 676 yields:
% 44.60/12.93 | (677) all_209_2_142 = all_197_2_122
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (650,673) yields a new equation:
% 44.60/12.93 | (678) all_207_2_139 = all_199_2_125
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 678 yields:
% 44.60/12.93 | (679) all_207_2_139 = all_199_2_125
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (631,675) yields a new equation:
% 44.60/12.93 | (680) all_207_1_138 = all_199_1_124
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 680 yields:
% 44.60/12.93 | (681) all_207_1_138 = all_199_1_124
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (636,671) yields a new equation:
% 44.60/12.93 | (682) all_214_8_157 = all_191_2_109
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 682 yields:
% 44.60/12.93 | (683) all_214_8_157 = all_191_2_109
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (638,683) yields a new equation:
% 44.60/12.93 | (684) all_211_2_145 = all_191_2_109
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 684 yields:
% 44.60/12.93 | (685) all_211_2_145 = all_191_2_109
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (665,685) yields a new equation:
% 44.60/12.93 | (686) all_203_2_131 = all_191_2_109
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 686 yields:
% 44.60/12.93 | (687) all_203_2_131 = all_191_2_109
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (648,646) yields a new equation:
% 44.60/12.93 | (688) all_193_1_113 = all_187_4_103
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (644,646) yields a new equation:
% 44.60/12.93 | (689) all_195_2_117 = all_193_1_113
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 689 yields:
% 44.60/12.93 | (690) all_195_2_117 = all_193_1_113
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (639,646) yields a new equation:
% 44.60/12.93 | (691) all_193_1_113 = 0
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (633,681) yields a new equation:
% 44.60/12.93 | (692) all_199_1_124 = all_195_4_119
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (630,681) yields a new equation:
% 44.60/12.93 | (693) all_199_1_124 = all_16_8_26
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (651,679) yields a new equation:
% 44.60/12.93 | (694) all_205_2_134 = all_199_2_125
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 694 yields:
% 44.60/12.93 | (695) all_205_2_134 = all_199_2_125
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (652,695) yields a new equation:
% 44.60/12.93 | (696) all_201_2_128 = all_199_2_125
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 696 yields:
% 44.60/12.93 | (697) all_201_2_128 = all_199_2_125
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (668,669) yields a new equation:
% 44.60/12.93 | (698) all_203_1_130 = 0
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 698 yields:
% 44.60/12.93 | (699) all_203_1_130 = 0
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (645,643) yields a new equation:
% 44.60/12.93 | (700) all_197_1_121 = all_195_2_117
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (642,643) yields a new equation:
% 44.60/12.93 | (701) all_201_1_127 = all_197_1_121
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 701 yields:
% 44.60/12.93 | (702) all_201_1_127 = all_197_1_121
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (626,699) yields a new equation:
% 44.60/12.93 | (703) all_187_3_102 = 0
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 703 yields:
% 44.60/12.93 | (704) all_187_3_102 = 0
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (663,687) yields a new equation:
% 44.60/12.93 | (705) all_201_1_127 = all_191_2_109
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 705 yields:
% 44.60/12.93 | (706) all_201_1_127 = all_191_2_109
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (702,706) yields a new equation:
% 44.60/12.93 | (707) all_197_1_121 = all_191_2_109
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 707 yields:
% 44.60/12.93 | (708) all_197_1_121 = all_191_2_109
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (655,697) yields a new equation:
% 44.60/12.93 | (709) all_199_2_125 = all_195_3_118
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (656,697) yields a new equation:
% 44.60/12.93 | (710) all_199_2_125 = all_193_2_114
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (693,692) yields a new equation:
% 44.60/12.93 | (711) all_195_4_119 = all_16_8_26
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (709,710) yields a new equation:
% 44.60/12.93 | (712) all_195_3_118 = all_193_2_114
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 712 yields:
% 44.60/12.93 | (713) all_195_3_118 = all_193_2_114
% 44.60/12.93 |
% 44.60/12.93 | Combining equations (700,708) yields a new equation:
% 44.60/12.93 | (714) all_195_2_117 = all_191_2_109
% 44.60/12.93 |
% 44.60/12.93 | Simplifying 714 yields:
% 44.60/12.93 | (715) all_195_2_117 = all_191_2_109
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (690,715) yields a new equation:
% 44.60/12.94 | (716) all_193_1_113 = all_191_2_109
% 44.60/12.94 |
% 44.60/12.94 | Simplifying 716 yields:
% 44.60/12.94 | (717) all_193_1_113 = all_191_2_109
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (654,713) yields a new equation:
% 44.60/12.94 | (718) all_193_2_114 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (657,713) yields a new equation:
% 44.60/12.94 | (719) all_193_2_114 = all_191_4_111
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (691,717) yields a new equation:
% 44.60/12.94 | (720) all_191_2_109 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (688,717) yields a new equation:
% 44.60/12.94 | (721) all_191_2_109 = all_187_4_103
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (718,719) yields a new equation:
% 44.60/12.94 | (722) all_191_4_111 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (720,721) yields a new equation:
% 44.60/12.94 | (723) all_187_4_103 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (658,659) yields a new equation:
% 44.60/12.94 | (724) all_189_2_106 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (660,659) yields a new equation:
% 44.60/12.94 | (725) all_189_2_106 = all_185_2_98
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (725,724) yields a new equation:
% 44.60/12.94 | (726) all_185_2_98 = 0
% 44.60/12.94 |
% 44.60/12.94 | Simplifying 726 yields:
% 44.60/12.94 | (727) all_185_2_98 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (723,721) yields a new equation:
% 44.60/12.94 | (720) all_191_2_109 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (722,719) yields a new equation:
% 44.60/12.94 | (718) all_193_2_114 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (720,717) yields a new equation:
% 44.60/12.94 | (691) all_193_1_113 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (720,708) yields a new equation:
% 44.60/12.94 | (731) all_197_1_121 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (718,710) yields a new equation:
% 44.60/12.94 | (732) all_199_2_125 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (711,692) yields a new equation:
% 44.60/12.94 | (693) all_199_1_124 = all_16_8_26
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (720,687) yields a new equation:
% 44.60/12.94 | (734) all_203_2_131 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (731,643) yields a new equation:
% 44.60/12.94 | (735) all_205_4_136 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (732,695) yields a new equation:
% 44.60/12.94 | (736) all_205_2_134 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (691,646) yields a new equation:
% 44.60/12.94 | (639) all_209_1_141 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (693,675) yields a new equation:
% 44.60/12.94 | (738) all_216_2_160 = all_16_8_26
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (732,673) yields a new equation:
% 44.60/12.94 | (739) all_216_1_159 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (720,647) yields a new equation:
% 44.60/12.94 | (740) all_229_4_173 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (734,640) yields a new equation:
% 44.60/12.94 | (741) all_229_3_172 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (669,624) yields a new equation:
% 44.60/12.94 | (742) all_229_2_171 = 0
% 44.60/12.94 |
% 44.60/12.94 | From (704) and (495) follows:
% 44.60/12.94 | (430) aNaturalNumber0(all_18_2_29) = 0
% 44.60/12.94 |
% 44.60/12.94 | From (723) and (494) follows:
% 44.60/12.94 | (45) aNaturalNumber0(xp) = 0
% 44.60/12.94 |
% 44.60/12.94 | From (727) and (490) follows:
% 44.60/12.94 | (24) aNaturalNumber0(xn) = 0
% 44.60/12.94 |
% 44.60/12.94 +-Applying beta-rule and splitting (478), into two cases.
% 44.60/12.94 |-Branch one:
% 44.60/12.94 | (746) all_18_2_29 = xr
% 44.60/12.94 |
% 44.60/12.94 | From (746) and (602) follows:
% 44.60/12.94 | (747) doDivides0(xp, xr) = all_229_0_169
% 44.60/12.94 |
% 44.60/12.94 | From (746) and (544) follows:
% 44.60/12.94 | (748) sdtpldt0(xr, xm) = all_205_1_133
% 44.60/12.94 |
% 44.60/12.94 | From (746) and (430) follows:
% 44.60/12.94 | (749) aNaturalNumber0(xr) = 0
% 44.60/12.94 |
% 44.60/12.94 +-Applying beta-rule and splitting (265), into two cases.
% 44.60/12.94 |-Branch one:
% 44.60/12.94 | (750) ~ (aNaturalNumber0(xr) = all_58_2_82)
% 44.60/12.94 |
% 44.60/12.94 | From (453) and (750) follows:
% 44.60/12.94 | (751) ~ (aNaturalNumber0(xr) = 0)
% 44.60/12.94 |
% 44.60/12.94 | Using (749) and (751) yields:
% 44.60/12.94 | (441) $false
% 44.60/12.94 |
% 44.60/12.94 |-The branch is then unsatisfiable
% 44.60/12.94 |-Branch two:
% 44.60/12.94 | (753) aNaturalNumber0(xr) = all_58_2_82
% 44.60/12.94 | (754) all_73_2_94 = all_58_2_82
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (754,401) yields a new equation:
% 44.60/12.94 | (755) all_58_2_82 = all_16_8_26
% 44.60/12.94 |
% 44.60/12.94 | Simplifying 755 yields:
% 44.60/12.94 | (756) all_58_2_82 = all_16_8_26
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (453,756) yields a new equation:
% 44.60/12.94 | (757) all_16_8_26 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (757,335) yields a new equation:
% 44.60/12.94 | (758) all_30_2_50 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (757,270) yields a new equation:
% 44.60/12.94 | (759) all_68_2_90 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (757,693) yields a new equation:
% 44.60/12.94 | (760) all_199_1_124 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (757,738) yields a new equation:
% 44.60/12.94 | (761) all_216_2_160 = 0
% 44.60/12.94 |
% 44.60/12.94 +-Applying beta-rule and splitting (158), into two cases.
% 44.60/12.94 |-Branch one:
% 44.60/12.94 | (762) ~ (all_30_1_49 = 0)
% 44.60/12.94 |
% 44.60/12.94 | Equations (390) can reduce 762 to:
% 44.60/12.94 | (173) $false
% 44.60/12.94 |
% 44.60/12.94 |-The branch is then unsatisfiable
% 44.60/12.94 |-Branch two:
% 44.60/12.94 | (390) all_30_1_49 = 0
% 44.60/12.94 | (765) ~ (all_30_2_50 = 0) | all_30_0_48 = all_0_2_2
% 44.60/12.94 |
% 44.60/12.94 +-Applying beta-rule and splitting (765), into two cases.
% 44.60/12.94 |-Branch one:
% 44.60/12.94 | (766) ~ (all_30_2_50 = 0)
% 44.60/12.94 |
% 44.60/12.94 | Equations (758) can reduce 766 to:
% 44.60/12.94 | (173) $false
% 44.60/12.94 |
% 44.60/12.94 |-The branch is then unsatisfiable
% 44.60/12.94 |-Branch two:
% 44.60/12.94 | (758) all_30_2_50 = 0
% 44.60/12.94 | (769) all_30_0_48 = all_0_2_2
% 44.60/12.94 |
% 44.60/12.94 | From (769) and (155) follows:
% 44.60/12.94 | (770) sdtasdt0(xm, xr) = all_0_2_2
% 44.60/12.94 |
% 44.60/12.94 | From (769) and (529) follows:
% 44.60/12.94 | (771) aNaturalNumber0(all_0_2_2) = all_199_0_123
% 44.60/12.94 |
% 44.60/12.94 +-Applying beta-rule and splitting (464), into two cases.
% 44.60/12.94 |-Branch one:
% 44.60/12.94 | (772) ~ (sdtasdt0(xm, xr) = all_0_2_2)
% 44.60/12.94 |
% 44.60/12.94 | Using (770) and (772) yields:
% 44.60/12.94 | (441) $false
% 44.60/12.94 |
% 44.60/12.94 |-The branch is then unsatisfiable
% 44.60/12.94 |-Branch two:
% 44.60/12.94 | (770) sdtasdt0(xm, xr) = all_0_2_2
% 44.60/12.94 | (775) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, xr) = v8 & doDivides0(xp, xm) = v7 & iLess0(v5, all_0_4_4) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xm, xr) = v4 & aNaturalNumber0(xr) = v1 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 44.60/12.94 |
% 44.60/12.94 | Instantiating (775) with all_279_0_175, all_279_1_176, all_279_2_177, all_279_3_178, all_279_4_179, all_279_5_180, all_279_6_181, all_279_7_182, all_279_8_183 yields:
% 44.60/12.94 | (776) isPrime0(xp) = all_279_5_180 & doDivides0(xp, xr) = all_279_0_175 & doDivides0(xp, xm) = all_279_1_176 & iLess0(all_279_3_178, all_0_4_4) = all_279_2_177 & sdtpldt0(all_279_4_179, xp) = all_279_3_178 & sdtpldt0(xm, xr) = all_279_4_179 & aNaturalNumber0(xr) = all_279_7_182 & aNaturalNumber0(xp) = all_279_6_181 & aNaturalNumber0(xm) = all_279_8_183 & ( ~ (all_279_2_177 = 0) | ~ (all_279_5_180 = 0) | ~ (all_279_6_181 = 0) | ~ (all_279_7_182 = 0) | ~ (all_279_8_183 = 0) | all_279_0_175 = 0 | all_279_1_176 = 0)
% 44.60/12.94 |
% 44.60/12.94 | Applying alpha-rule on (776) yields:
% 44.60/12.94 | (777) sdtpldt0(xm, xr) = all_279_4_179
% 44.60/12.94 | (778) aNaturalNumber0(xr) = all_279_7_182
% 44.60/12.94 | (779) aNaturalNumber0(xp) = all_279_6_181
% 44.60/12.94 | (780) sdtpldt0(all_279_4_179, xp) = all_279_3_178
% 44.60/12.94 | (781) aNaturalNumber0(xm) = all_279_8_183
% 44.60/12.94 | (782) isPrime0(xp) = all_279_5_180
% 44.60/12.94 | (783) doDivides0(xp, xr) = all_279_0_175
% 44.60/12.94 | (784) doDivides0(xp, xm) = all_279_1_176
% 44.60/12.94 | (785) ~ (all_279_2_177 = 0) | ~ (all_279_5_180 = 0) | ~ (all_279_6_181 = 0) | ~ (all_279_7_182 = 0) | ~ (all_279_8_183 = 0) | all_279_0_175 = 0 | all_279_1_176 = 0
% 44.60/12.94 | (786) iLess0(all_279_3_178, all_0_4_4) = all_279_2_177
% 44.60/12.94 |
% 44.60/12.94 +-Applying beta-rule and splitting (580), into two cases.
% 44.60/12.94 |-Branch one:
% 44.60/12.94 | (787) ~ (all_216_1_159 = 0)
% 44.60/12.94 |
% 44.60/12.94 | Equations (739) can reduce 787 to:
% 44.60/12.94 | (173) $false
% 44.60/12.94 |
% 44.60/12.94 |-The branch is then unsatisfiable
% 44.60/12.94 |-Branch two:
% 44.60/12.94 | (739) all_216_1_159 = 0
% 44.60/12.94 | (790) ~ (all_216_2_160 = 0) | all_216_0_158 = 0
% 44.60/12.94 |
% 44.60/12.94 +-Applying beta-rule and splitting (230), into two cases.
% 44.60/12.94 |-Branch one:
% 44.60/12.94 | (791) ~ (all_68_0_88 = 0)
% 44.60/12.94 |
% 44.60/12.94 +-Applying beta-rule and splitting (621), into two cases.
% 44.60/12.94 |-Branch one:
% 44.60/12.94 | (792) ~ (aNaturalNumber0(all_0_2_2) = all_199_0_123)
% 44.60/12.94 |
% 44.60/12.94 | Using (771) and (792) yields:
% 44.60/12.94 | (441) $false
% 44.60/12.94 |
% 44.60/12.94 |-The branch is then unsatisfiable
% 44.60/12.94 |-Branch two:
% 44.60/12.94 | (771) aNaturalNumber0(all_0_2_2) = all_199_0_123
% 44.60/12.94 | (795) all_199_0_123 = all_27_0_42
% 44.60/12.94 |
% 44.60/12.94 +-Applying beta-rule and splitting (476), into two cases.
% 44.60/12.94 |-Branch one:
% 44.60/12.94 | (796) all_68_0_88 = 0
% 44.60/12.94 |
% 44.60/12.94 | Equations (796) can reduce 791 to:
% 44.60/12.94 | (173) $false
% 44.60/12.94 |
% 44.60/12.94 |-The branch is then unsatisfiable
% 44.60/12.94 |-Branch two:
% 44.60/12.94 | (791) ~ (all_68_0_88 = 0)
% 44.60/12.94 | (799) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(xr, all_18_2_29) = v4 & doDivides0(xr, xp) = v3 & aNaturalNumber0(all_18_2_29) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 44.60/12.94 |
% 44.60/12.94 | Instantiating (799) with all_296_0_184, all_296_1_185, all_296_2_186, all_296_3_187, all_296_4_188 yields:
% 44.60/12.94 | (800) doDivides0(xr, all_18_2_29) = all_296_0_184 & doDivides0(xr, xp) = all_296_1_185 & aNaturalNumber0(all_18_2_29) = all_296_2_186 & aNaturalNumber0(xr) = all_296_4_188 & aNaturalNumber0(xp) = all_296_3_187 & ( ~ (all_296_0_184 = 0) | ~ (all_296_1_185 = 0) | ~ (all_296_2_186 = 0) | ~ (all_296_3_187 = 0) | ~ (all_296_4_188 = 0))
% 44.60/12.94 |
% 44.60/12.94 | Applying alpha-rule on (800) yields:
% 44.60/12.94 | (801) aNaturalNumber0(xr) = all_296_4_188
% 44.60/12.94 | (802) aNaturalNumber0(xp) = all_296_3_187
% 44.60/12.94 | (803) doDivides0(xr, xp) = all_296_1_185
% 44.60/12.94 | (804) ~ (all_296_0_184 = 0) | ~ (all_296_1_185 = 0) | ~ (all_296_2_186 = 0) | ~ (all_296_3_187 = 0) | ~ (all_296_4_188 = 0)
% 44.60/12.94 | (805) doDivides0(xr, all_18_2_29) = all_296_0_184
% 44.60/12.94 | (806) aNaturalNumber0(all_18_2_29) = all_296_2_186
% 44.60/12.94 |
% 44.60/12.94 +-Applying beta-rule and splitting (790), into two cases.
% 44.60/12.94 |-Branch one:
% 44.60/12.94 | (807) ~ (all_216_2_160 = 0)
% 44.60/12.94 |
% 44.60/12.94 | Equations (761) can reduce 807 to:
% 44.60/12.94 | (173) $false
% 44.60/12.94 |
% 44.60/12.94 |-The branch is then unsatisfiable
% 44.60/12.94 |-Branch two:
% 44.60/12.94 | (761) all_216_2_160 = 0
% 44.60/12.94 | (810) all_216_0_158 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (810,628) yields a new equation:
% 44.60/12.94 | (811) all_197_2_122 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (811,677) yields a new equation:
% 44.60/12.94 | (812) all_209_2_142 = 0
% 44.60/12.94 |
% 44.60/12.94 +-Applying beta-rule and splitting (532), into two cases.
% 44.60/12.94 |-Branch one:
% 44.60/12.94 | (813) ~ (all_199_1_124 = 0)
% 44.60/12.94 |
% 44.60/12.94 | Equations (760) can reduce 813 to:
% 44.60/12.94 | (173) $false
% 44.60/12.94 |
% 44.60/12.94 |-The branch is then unsatisfiable
% 44.60/12.94 |-Branch two:
% 44.60/12.94 | (760) all_199_1_124 = 0
% 44.60/12.94 | (816) ~ (all_199_2_125 = 0) | all_199_0_123 = 0
% 44.60/12.94 |
% 44.60/12.94 +-Applying beta-rule and splitting (816), into two cases.
% 44.60/12.94 |-Branch one:
% 44.60/12.94 | (817) ~ (all_199_2_125 = 0)
% 44.60/12.94 |
% 44.60/12.94 | Equations (732) can reduce 817 to:
% 44.60/12.94 | (173) $false
% 44.60/12.94 |
% 44.60/12.94 |-The branch is then unsatisfiable
% 44.60/12.94 |-Branch two:
% 44.60/12.94 | (732) all_199_2_125 = 0
% 44.60/12.94 | (820) all_199_0_123 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (820,795) yields a new equation:
% 44.60/12.94 | (821) all_27_0_42 = 0
% 44.60/12.94 |
% 44.60/12.94 | Combining equations (821,319) yields a new equation:
% 44.60/12.94 | (822) all_53_2_78 = 0
% 44.60/12.94 |
% 44.60/12.94 +-Applying beta-rule and splitting (619), into two cases.
% 44.60/12.94 |-Branch one:
% 44.60/12.94 | (823) ~ (sdtpldt0(xr, xm) = all_205_1_133)
% 44.60/12.94 |
% 44.60/12.94 | Using (748) and (823) yields:
% 44.60/12.94 | (441) $false
% 44.60/12.94 |
% 44.60/12.94 |-The branch is then unsatisfiable
% 44.60/12.94 |-Branch two:
% 44.60/12.94 | (748) sdtpldt0(xr, xm) = all_205_1_133
% 44.60/12.94 | (826) all_205_1_133 = all_16_4_22
% 44.60/12.94 |
% 44.60/12.94 | From (826) and (547) follows:
% 44.60/12.94 | (827) sdtpldt0(xp, all_16_4_22) = all_205_0_132
% 44.60/12.94 |
% 44.60/12.94 +-Applying beta-rule and splitting (197), into two cases.
% 44.60/12.94 |-Branch one:
% 44.60/12.94 | (828) ~ (all_53_0_76 = 0)
% 44.60/12.94 |
% 44.60/12.94 +-Applying beta-rule and splitting (549), into two cases.
% 44.60/12.94 |-Branch one:
% 44.60/12.94 | (829) ~ (all_205_2_134 = 0)
% 44.60/12.94 |
% 44.60/12.94 | Equations (736) can reduce 829 to:
% 44.60/12.94 | (173) $false
% 44.60/12.94 |
% 44.60/12.94 |-The branch is then unsatisfiable
% 44.60/12.94 |-Branch two:
% 44.60/12.94 | (736) all_205_2_134 = 0
% 44.60/12.94 | (832) ~ (all_205_3_135 = 0) | ~ (all_205_4_136 = 0) | all_205_0_132 = all_0_5_5
% 44.60/12.94 |
% 44.60/12.94 +-Applying beta-rule and splitting (832), into two cases.
% 44.60/12.94 |-Branch one:
% 44.60/12.94 | (833) ~ (all_205_3_135 = 0)
% 44.60/12.94 |
% 44.60/12.94 | Equations (669) can reduce 833 to:
% 44.60/12.94 | (173) $false
% 44.60/12.94 |
% 44.60/12.94 |-The branch is then unsatisfiable
% 44.60/12.94 |-Branch two:
% 44.60/12.94 | (669) all_205_3_135 = 0
% 44.60/12.94 | (836) ~ (all_205_4_136 = 0) | all_205_0_132 = all_0_5_5
% 44.60/12.94 |
% 44.60/12.94 +-Applying beta-rule and splitting (836), into two cases.
% 44.60/12.94 |-Branch one:
% 44.60/12.94 | (837) ~ (all_205_4_136 = 0)
% 44.60/12.94 |
% 44.60/12.95 | Equations (735) can reduce 837 to:
% 44.60/12.95 | (173) $false
% 44.60/12.95 |
% 44.60/12.95 |-The branch is then unsatisfiable
% 44.60/12.95 |-Branch two:
% 44.60/12.95 | (735) all_205_4_136 = 0
% 44.60/12.95 | (840) all_205_0_132 = all_0_5_5
% 44.60/12.95 |
% 44.60/12.95 | From (840) and (827) follows:
% 44.60/12.95 | (841) sdtpldt0(xp, all_16_4_22) = all_0_5_5
% 44.60/12.95 |
% 44.60/12.95 +-Applying beta-rule and splitting (620), into two cases.
% 44.60/12.95 |-Branch one:
% 44.60/12.95 | (842) ~ (sdtpldt0(xp, all_16_4_22) = all_205_0_132)
% 44.60/12.95 |
% 44.60/12.95 | From (840) and (842) follows:
% 44.60/12.95 | (843) ~ (sdtpldt0(xp, all_16_4_22) = all_0_5_5)
% 44.60/12.95 |
% 44.60/12.95 | Using (841) and (843) yields:
% 44.60/12.95 | (441) $false
% 44.60/12.95 |
% 44.60/12.95 |-The branch is then unsatisfiable
% 44.60/12.95 |-Branch two:
% 44.60/12.95 | (827) sdtpldt0(xp, all_16_4_22) = all_205_0_132
% 44.60/12.95 | (846) all_209_0_140 = all_205_0_132
% 44.60/12.95 |
% 44.60/12.95 | Combining equations (840,846) yields a new equation:
% 44.60/12.95 | (847) all_209_0_140 = all_0_5_5
% 44.60/12.95 |
% 44.60/12.95 +-Applying beta-rule and splitting (474), into two cases.
% 44.60/12.95 |-Branch one:
% 44.60/12.95 | (848) all_53_0_76 = 0
% 44.60/12.95 |
% 44.60/12.95 | Equations (848) can reduce 828 to:
% 44.60/12.95 | (173) $false
% 44.60/12.95 |
% 44.60/12.95 |-The branch is then unsatisfiable
% 44.60/12.95 |-Branch two:
% 44.60/12.95 | (828) ~ (all_53_0_76 = 0)
% 44.60/12.95 | (851) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(all_0_2_2, all_18_2_29) = v4 & doDivides0(all_0_2_2, xp) = v3 & aNaturalNumber0(all_18_2_29) = v2 & aNaturalNumber0(all_0_2_2) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 44.60/12.95 |
% 44.60/12.95 | Instantiating (851) with all_377_0_189, all_377_1_190, all_377_2_191, all_377_3_192, all_377_4_193 yields:
% 44.60/12.95 | (852) doDivides0(all_0_2_2, all_18_2_29) = all_377_0_189 & doDivides0(all_0_2_2, xp) = all_377_1_190 & aNaturalNumber0(all_18_2_29) = all_377_2_191 & aNaturalNumber0(all_0_2_2) = all_377_4_193 & aNaturalNumber0(xp) = all_377_3_192 & ( ~ (all_377_0_189 = 0) | ~ (all_377_1_190 = 0) | ~ (all_377_2_191 = 0) | ~ (all_377_3_192 = 0) | ~ (all_377_4_193 = 0))
% 44.60/12.95 |
% 44.60/12.95 | Applying alpha-rule on (852) yields:
% 44.60/12.95 | (853) aNaturalNumber0(all_18_2_29) = all_377_2_191
% 44.60/12.95 | (854) aNaturalNumber0(all_0_2_2) = all_377_4_193
% 44.60/12.95 | (855) doDivides0(all_0_2_2, all_18_2_29) = all_377_0_189
% 44.60/12.95 | (856) ~ (all_377_0_189 = 0) | ~ (all_377_1_190 = 0) | ~ (all_377_2_191 = 0) | ~ (all_377_3_192 = 0) | ~ (all_377_4_193 = 0)
% 44.60/12.95 | (857) doDivides0(all_0_2_2, xp) = all_377_1_190
% 44.60/12.95 | (858) aNaturalNumber0(xp) = all_377_3_192
% 44.60/12.95 |
% 44.60/12.95 +-Applying beta-rule and splitting (559), into two cases.
% 44.60/12.95 |-Branch one:
% 44.60/12.95 | (859) ~ (all_209_1_141 = 0)
% 44.60/12.95 |
% 44.60/12.95 | Equations (639) can reduce 859 to:
% 44.60/12.95 | (173) $false
% 44.60/12.95 |
% 44.60/12.95 |-The branch is then unsatisfiable
% 44.60/12.95 |-Branch two:
% 44.60/12.95 | (639) all_209_1_141 = 0
% 44.60/12.95 | (862) ~ (all_209_2_142 = 0) | all_209_0_140 = all_16_3_21
% 44.60/12.95 |
% 44.60/12.95 +-Applying beta-rule and splitting (862), into two cases.
% 44.60/12.95 |-Branch one:
% 44.60/12.95 | (863) ~ (all_209_2_142 = 0)
% 44.60/12.95 |
% 44.60/12.95 | Equations (812) can reduce 863 to:
% 44.60/12.95 | (173) $false
% 44.60/12.95 |
% 44.60/12.95 |-The branch is then unsatisfiable
% 44.60/12.95 |-Branch two:
% 44.60/12.95 | (812) all_209_2_142 = 0
% 44.60/12.95 | (866) all_209_0_140 = all_16_3_21
% 44.60/12.95 |
% 44.60/12.95 | Combining equations (847,866) yields a new equation:
% 44.60/12.95 | (867) all_16_3_21 = all_0_5_5
% 44.60/12.95 |
% 44.60/12.95 | From (867) and (119) follows:
% 44.60/12.95 | (868) sdtpldt0(all_16_4_22, xp) = all_0_5_5
% 44.60/12.95 |
% 44.60/12.95 +-Applying beta-rule and splitting (467), into two cases.
% 44.60/12.95 |-Branch one:
% 44.60/12.95 | (869) ~ (sdtpldt0(all_16_4_22, xp) = all_0_5_5)
% 44.60/12.95 |
% 44.60/12.95 | Using (868) and (869) yields:
% 44.60/12.95 | (441) $false
% 44.60/12.95 |
% 44.60/12.95 |-The branch is then unsatisfiable
% 44.60/12.95 |-Branch two:
% 44.60/12.95 | (868) sdtpldt0(all_16_4_22, xp) = all_0_5_5
% 44.60/12.95 | (872) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_16_4_22, v3) = v4 & sdtpldt0(xp, xp) = v3 & aNaturalNumber0(all_16_4_22) = v0 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_4_4))
% 44.60/12.95 |
% 44.60/12.95 | Instantiating (872) with all_430_0_194, all_430_1_195, all_430_2_196, all_430_3_197, all_430_4_198 yields:
% 44.60/12.95 | (873) sdtpldt0(all_16_4_22, all_430_1_195) = all_430_0_194 & sdtpldt0(xp, xp) = all_430_1_195 & aNaturalNumber0(all_16_4_22) = all_430_4_198 & aNaturalNumber0(xp) = all_430_2_196 & aNaturalNumber0(xp) = all_430_3_197 & ( ~ (all_430_2_196 = 0) | ~ (all_430_3_197 = 0) | ~ (all_430_4_198 = 0) | all_430_0_194 = all_0_4_4)
% 44.60/12.95 |
% 44.60/12.95 | Applying alpha-rule on (873) yields:
% 44.60/12.95 | (874) sdtpldt0(all_16_4_22, all_430_1_195) = all_430_0_194
% 44.60/12.95 | (875) ~ (all_430_2_196 = 0) | ~ (all_430_3_197 = 0) | ~ (all_430_4_198 = 0) | all_430_0_194 = all_0_4_4
% 44.60/12.95 | (876) aNaturalNumber0(xp) = all_430_3_197
% 44.60/12.95 | (877) aNaturalNumber0(all_16_4_22) = all_430_4_198
% 44.60/12.95 | (878) sdtpldt0(xp, xp) = all_430_1_195
% 44.60/12.95 | (879) aNaturalNumber0(xp) = all_430_2_196
% 44.60/12.95 |
% 44.60/12.95 +-Applying beta-rule and splitting (616), into two cases.
% 44.60/12.95 |-Branch one:
% 44.60/12.95 | (880) ~ (doDivides0(xp, xr) = all_229_0_169)
% 44.60/12.95 |
% 44.60/12.95 | Using (747) and (880) yields:
% 44.60/12.95 | (441) $false
% 44.60/12.95 |
% 44.60/12.95 |-The branch is then unsatisfiable
% 44.60/12.95 |-Branch two:
% 44.60/12.95 | (747) doDivides0(xp, xr) = all_229_0_169
% 44.60/12.95 | (883) all_229_0_169 = 0
% 44.60/12.95 |
% 44.60/12.95 +-Applying beta-rule and splitting (603), into two cases.
% 44.60/12.95 |-Branch one:
% 44.60/12.95 | (884) ~ (all_229_0_169 = 0)
% 44.60/12.95 |
% 44.60/12.95 | Equations (883) can reduce 884 to:
% 44.60/12.95 | (173) $false
% 44.60/12.95 |
% 44.60/12.95 |-The branch is then unsatisfiable
% 44.60/12.95 |-Branch two:
% 44.60/12.95 | (883) all_229_0_169 = 0
% 44.60/12.95 | (887) ~ (all_229_1_170 = 0) | ~ (all_229_2_171 = 0) | ~ (all_229_3_172 = 0) | ~ (all_229_4_173 = 0)
% 44.60/12.95 |
% 44.60/12.95 +-Applying beta-rule and splitting (887), into two cases.
% 44.60/12.95 |-Branch one:
% 44.60/12.95 | (888) ~ (all_229_1_170 = 0)
% 44.60/12.95 |
% 44.60/12.95 | Equations (618) can reduce 888 to:
% 44.60/12.95 | (889) ~ (all_214_1_150 = 0)
% 44.60/12.95 |
% 44.60/12.95 | Instantiating formula (60) with xp, all_430_3_197, 0 and discharging atoms aNaturalNumber0(xp) = all_430_3_197, aNaturalNumber0(xp) = 0, yields:
% 44.60/12.95 | (890) all_430_3_197 = 0
% 44.60/12.95 |
% 44.60/12.95 | Instantiating formula (60) with xp, all_430_3_197, all_430_2_196 and discharging atoms aNaturalNumber0(xp) = all_430_2_196, aNaturalNumber0(xp) = all_430_3_197, yields:
% 44.60/12.95 | (891) all_430_2_196 = all_430_3_197
% 44.60/12.95 |
% 44.60/12.95 | Instantiating formula (60) with xp, all_377_3_192, all_430_2_196 and discharging atoms aNaturalNumber0(xp) = all_430_2_196, aNaturalNumber0(xp) = all_377_3_192, yields:
% 44.60/12.95 | (892) all_430_2_196 = all_377_3_192
% 44.60/12.95 |
% 44.60/12.95 | Instantiating formula (60) with xp, all_296_3_187, all_430_3_197 and discharging atoms aNaturalNumber0(xp) = all_430_3_197, aNaturalNumber0(xp) = all_296_3_187, yields:
% 44.60/12.95 | (893) all_430_3_197 = all_296_3_187
% 44.60/12.95 |
% 44.60/12.95 | Instantiating formula (60) with xp, all_279_6_181, all_296_3_187 and discharging atoms aNaturalNumber0(xp) = all_296_3_187, aNaturalNumber0(xp) = all_279_6_181, yields:
% 44.60/12.95 | (894) all_296_3_187 = all_279_6_181
% 44.60/12.95 |
% 44.60/12.95 | Combining equations (891,892) yields a new equation:
% 44.60/12.95 | (895) all_430_3_197 = all_377_3_192
% 44.60/12.95 |
% 44.60/12.95 | Simplifying 895 yields:
% 44.60/12.95 | (896) all_430_3_197 = all_377_3_192
% 44.60/12.95 |
% 44.60/12.95 | Combining equations (893,896) yields a new equation:
% 44.60/12.95 | (897) all_377_3_192 = all_296_3_187
% 44.60/12.95 |
% 44.60/12.95 | Combining equations (890,896) yields a new equation:
% 44.60/12.95 | (898) all_377_3_192 = 0
% 44.60/12.95 |
% 44.60/12.95 | Combining equations (897,898) yields a new equation:
% 44.60/12.95 | (899) all_296_3_187 = 0
% 44.60/12.95 |
% 44.60/12.95 | Simplifying 899 yields:
% 44.60/12.95 | (900) all_296_3_187 = 0
% 44.60/12.95 |
% 44.60/12.95 | Combining equations (900,894) yields a new equation:
% 44.60/12.95 | (901) all_279_6_181 = 0
% 44.60/12.95 |
% 44.60/12.95 | From (901) and (779) follows:
% 44.60/12.95 | (45) aNaturalNumber0(xp) = 0
% 44.60/12.95 |
% 44.60/12.95 +-Applying beta-rule and splitting (461), into two cases.
% 44.60/12.95 |-Branch one:
% 44.60/12.95 | (903) all_82_0_95 = xp
% 44.60/12.95 |
% 44.60/12.95 | From (903) and (251) follows:
% 44.60/12.95 | (904) doDivides0(xp, xp) = 0
% 44.60/12.95 |
% 44.60/12.95 +-Applying beta-rule and splitting (617), into two cases.
% 44.60/12.95 |-Branch one:
% 44.60/12.95 | (905) ~ (doDivides0(xp, xp) = 0)
% 44.60/12.95 |
% 44.60/12.95 | Using (904) and (905) yields:
% 44.60/12.95 | (441) $false
% 44.60/12.95 |
% 44.60/12.95 |-The branch is then unsatisfiable
% 44.60/12.95 |-Branch two:
% 44.60/12.95 | (904) doDivides0(xp, xp) = 0
% 44.60/12.95 | (908) all_214_1_150 = 0
% 44.60/12.95 |
% 44.60/12.95 | Equations (908) can reduce 889 to:
% 44.60/12.95 | (173) $false
% 44.60/12.95 |
% 44.60/12.95 |-The branch is then unsatisfiable
% 44.60/12.95 |-Branch two:
% 44.60/12.95 | (910) ~ (all_82_0_95 = xp)
% 44.60/12.95 | (911) all_82_0_95 = sz10 | ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_82_0_95) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0))
% 44.60/12.95 |
% 44.60/12.95 +-Applying beta-rule and splitting (911), into two cases.
% 44.60/12.95 |-Branch one:
% 44.60/12.95 | (612) all_82_0_95 = sz10
% 44.60/12.95 |
% 44.60/12.95 | Equations (612) can reduce 253 to:
% 44.60/12.95 | (173) $false
% 44.60/12.95 |
% 44.60/12.95 |-The branch is then unsatisfiable
% 44.60/12.95 |-Branch two:
% 44.60/12.95 | (253) ~ (all_82_0_95 = sz10)
% 44.60/12.95 | (915) ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_82_0_95) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0))
% 44.60/12.95 |
% 44.60/12.95 | Instantiating (915) with all_504_0_199 yields:
% 44.60/12.95 | (916) ( ~ (all_504_0_199 = 0) & aNaturalNumber0(all_82_0_95) = all_504_0_199) | ( ~ (all_504_0_199 = 0) & aNaturalNumber0(xp) = all_504_0_199)
% 44.60/12.95 |
% 44.60/12.95 +-Applying beta-rule and splitting (916), into two cases.
% 44.60/12.95 |-Branch one:
% 44.60/12.95 | (917) ~ (all_504_0_199 = 0) & aNaturalNumber0(all_82_0_95) = all_504_0_199
% 44.60/12.95 |
% 44.60/12.95 | Applying alpha-rule on (917) yields:
% 44.60/12.95 | (918) ~ (all_504_0_199 = 0)
% 44.60/12.95 | (919) aNaturalNumber0(all_82_0_95) = all_504_0_199
% 44.60/12.95 |
% 44.60/12.95 | Instantiating formula (60) with all_82_0_95, all_504_0_199, 0 and discharging atoms aNaturalNumber0(all_82_0_95) = all_504_0_199, aNaturalNumber0(all_82_0_95) = 0, yields:
% 44.60/12.95 | (920) all_504_0_199 = 0
% 44.60/12.95 |
% 44.60/12.95 | Equations (920) can reduce 918 to:
% 44.60/12.95 | (173) $false
% 44.60/12.95 |
% 44.60/12.95 |-The branch is then unsatisfiable
% 44.60/12.95 |-Branch two:
% 44.60/12.95 | (922) ~ (all_504_0_199 = 0) & aNaturalNumber0(xp) = all_504_0_199
% 44.60/12.95 |
% 44.60/12.95 | Applying alpha-rule on (922) yields:
% 44.60/12.95 | (918) ~ (all_504_0_199 = 0)
% 44.60/12.95 | (924) aNaturalNumber0(xp) = all_504_0_199
% 44.60/12.95 |
% 44.60/12.95 | Instantiating formula (60) with xp, all_504_0_199, 0 and discharging atoms aNaturalNumber0(xp) = all_504_0_199, aNaturalNumber0(xp) = 0, yields:
% 44.60/12.95 | (920) all_504_0_199 = 0
% 44.60/12.95 |
% 44.60/12.95 | Equations (920) can reduce 918 to:
% 44.60/12.95 | (173) $false
% 44.60/12.95 |
% 44.60/12.95 |-The branch is then unsatisfiable
% 44.60/12.95 |-Branch two:
% 44.60/12.95 | (927) all_229_1_170 = 0
% 44.60/12.95 | (928) ~ (all_229_2_171 = 0) | ~ (all_229_3_172 = 0) | ~ (all_229_4_173 = 0)
% 44.60/12.95 |
% 44.60/12.95 +-Applying beta-rule and splitting (928), into two cases.
% 44.60/12.95 |-Branch one:
% 44.60/12.95 | (929) ~ (all_229_2_171 = 0)
% 44.60/12.95 |
% 44.60/12.95 | Equations (742) can reduce 929 to:
% 44.60/12.95 | (173) $false
% 44.60/12.95 |
% 44.60/12.95 |-The branch is then unsatisfiable
% 44.60/12.95 |-Branch two:
% 44.60/12.95 | (742) all_229_2_171 = 0
% 44.60/12.95 | (932) ~ (all_229_3_172 = 0) | ~ (all_229_4_173 = 0)
% 44.60/12.95 |
% 44.60/12.95 +-Applying beta-rule and splitting (932), into two cases.
% 44.60/12.95 |-Branch one:
% 44.60/12.95 | (933) ~ (all_229_3_172 = 0)
% 44.60/12.95 |
% 44.60/12.95 | Equations (741) can reduce 933 to:
% 44.60/12.95 | (173) $false
% 44.60/12.95 |
% 44.60/12.95 |-The branch is then unsatisfiable
% 44.60/12.95 |-Branch two:
% 44.60/12.95 | (741) all_229_3_172 = 0
% 44.60/12.95 | (936) ~ (all_229_4_173 = 0)
% 44.60/12.95 |
% 44.60/12.95 | Equations (740) can reduce 936 to:
% 44.60/12.95 | (173) $false
% 44.60/12.95 |
% 44.60/12.95 |-The branch is then unsatisfiable
% 44.60/12.96 |-Branch two:
% 44.60/12.96 | (848) all_53_0_76 = 0
% 44.60/12.96 | (939) ~ (all_53_1_77 = 0) | ~ (all_53_2_78 = 0) | ~ (all_53_3_79 = 0)
% 44.60/12.96 |
% 44.60/12.96 +-Applying beta-rule and splitting (939), into two cases.
% 44.60/12.96 |-Branch one:
% 44.60/12.96 | (940) ~ (all_53_1_77 = 0)
% 44.60/12.96 |
% 44.60/12.96 | Equations (295) can reduce 940 to:
% 44.60/12.96 | (173) $false
% 44.60/12.96 |
% 44.60/12.96 |-The branch is then unsatisfiable
% 44.60/12.96 |-Branch two:
% 44.60/12.96 | (295) all_53_1_77 = 0
% 44.60/12.96 | (943) ~ (all_53_2_78 = 0) | ~ (all_53_3_79 = 0)
% 44.60/12.96 |
% 44.60/12.96 +-Applying beta-rule and splitting (943), into two cases.
% 44.60/12.96 |-Branch one:
% 44.60/12.96 | (944) ~ (all_53_2_78 = 0)
% 44.60/12.96 |
% 44.60/12.96 | Equations (822) can reduce 944 to:
% 44.60/12.96 | (173) $false
% 44.60/12.96 |
% 44.60/12.96 |-The branch is then unsatisfiable
% 44.60/12.96 |-Branch two:
% 44.60/12.96 | (822) all_53_2_78 = 0
% 44.60/12.96 | (947) ~ (all_53_3_79 = 0)
% 44.60/12.96 |
% 44.60/12.96 | Equations (395) can reduce 947 to:
% 44.60/12.96 | (173) $false
% 44.60/12.96 |
% 44.60/12.96 |-The branch is then unsatisfiable
% 44.60/12.96 |-Branch two:
% 44.60/12.96 | (796) all_68_0_88 = 0
% 44.60/12.96 | (950) ~ (all_68_1_89 = 0) | ~ (all_68_2_90 = 0) | ~ (all_68_3_91 = 0)
% 44.60/12.96 |
% 44.60/12.96 +-Applying beta-rule and splitting (950), into two cases.
% 44.60/12.96 |-Branch one:
% 44.60/12.96 | (951) ~ (all_68_1_89 = 0)
% 44.60/12.96 |
% 44.60/12.96 | Equations (400) can reduce 951 to:
% 44.60/12.96 | (173) $false
% 44.60/12.96 |
% 44.60/12.96 |-The branch is then unsatisfiable
% 44.60/12.96 |-Branch two:
% 44.60/12.96 | (400) all_68_1_89 = 0
% 44.60/12.96 | (954) ~ (all_68_2_90 = 0) | ~ (all_68_3_91 = 0)
% 44.60/12.96 |
% 44.60/12.96 +-Applying beta-rule and splitting (954), into two cases.
% 44.60/12.96 |-Branch one:
% 44.60/12.96 | (955) ~ (all_68_2_90 = 0)
% 44.60/12.96 |
% 44.60/12.96 | Equations (759) can reduce 955 to:
% 44.60/12.96 | (173) $false
% 44.60/12.96 |
% 44.60/12.96 |-The branch is then unsatisfiable
% 44.60/12.96 |-Branch two:
% 44.60/12.96 | (759) all_68_2_90 = 0
% 44.60/12.96 | (958) ~ (all_68_3_91 = 0)
% 44.60/12.96 |
% 44.60/12.96 | Equations (398) can reduce 958 to:
% 44.60/12.96 | (173) $false
% 44.60/12.96 |
% 44.60/12.96 |-The branch is then unsatisfiable
% 44.60/12.96 |-Branch two:
% 44.60/12.96 | (960) ~ (all_18_2_29 = xr)
% 44.60/12.96 | (961) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_18_2_29) = v0) | (sdtlseqdt0(xp, xn) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 44.60/12.96 |
% 44.60/12.96 | Instantiating (961) with all_252_0_215, all_252_1_216, all_252_2_217 yields:
% 44.60/12.96 | (962) ( ~ (all_252_2_217 = 0) & aNaturalNumber0(all_18_2_29) = all_252_2_217) | (sdtlseqdt0(xp, xn) = all_252_0_215 & aNaturalNumber0(xp) = all_252_2_217 & aNaturalNumber0(xn) = all_252_1_216 & ( ~ (all_252_0_215 = 0) | ~ (all_252_1_216 = 0) | ~ (all_252_2_217 = 0)))
% 44.60/12.96 |
% 44.60/12.96 +-Applying beta-rule and splitting (962), into two cases.
% 44.60/12.96 |-Branch one:
% 44.60/12.96 | (963) ~ (all_252_2_217 = 0) & aNaturalNumber0(all_18_2_29) = all_252_2_217
% 44.60/12.96 |
% 44.60/12.96 | Applying alpha-rule on (963) yields:
% 44.60/12.96 | (964) ~ (all_252_2_217 = 0)
% 44.60/12.96 | (965) aNaturalNumber0(all_18_2_29) = all_252_2_217
% 44.60/12.96 |
% 44.60/12.96 | Instantiating formula (60) with all_18_2_29, all_252_2_217, 0 and discharging atoms aNaturalNumber0(all_18_2_29) = all_252_2_217, aNaturalNumber0(all_18_2_29) = 0, yields:
% 44.60/12.96 | (966) all_252_2_217 = 0
% 44.60/12.96 |
% 44.60/12.96 | Equations (966) can reduce 964 to:
% 44.60/12.96 | (173) $false
% 44.60/12.96 |
% 44.60/12.96 |-The branch is then unsatisfiable
% 44.60/12.96 |-Branch two:
% 44.60/12.96 | (968) sdtlseqdt0(xp, xn) = all_252_0_215 & aNaturalNumber0(xp) = all_252_2_217 & aNaturalNumber0(xn) = all_252_1_216 & ( ~ (all_252_0_215 = 0) | ~ (all_252_1_216 = 0) | ~ (all_252_2_217 = 0))
% 44.60/12.96 |
% 44.60/12.96 | Applying alpha-rule on (968) yields:
% 44.60/12.96 | (969) sdtlseqdt0(xp, xn) = all_252_0_215
% 44.60/12.96 | (970) aNaturalNumber0(xp) = all_252_2_217
% 44.60/12.96 | (971) aNaturalNumber0(xn) = all_252_1_216
% 44.60/12.96 | (972) ~ (all_252_0_215 = 0) | ~ (all_252_1_216 = 0) | ~ (all_252_2_217 = 0)
% 44.60/12.96 |
% 44.60/12.96 | Instantiating formula (39) with xp, xn, all_252_0_215, 0 and discharging atoms sdtlseqdt0(xp, xn) = all_252_0_215, sdtlseqdt0(xp, xn) = 0, yields:
% 44.60/12.96 | (973) all_252_0_215 = 0
% 44.60/12.96 |
% 44.60/12.96 | Instantiating formula (60) with xp, all_252_2_217, 0 and discharging atoms aNaturalNumber0(xp) = all_252_2_217, aNaturalNumber0(xp) = 0, yields:
% 44.60/12.96 | (966) all_252_2_217 = 0
% 44.60/12.96 |
% 44.60/12.96 | Instantiating formula (60) with xn, all_252_1_216, 0 and discharging atoms aNaturalNumber0(xn) = all_252_1_216, aNaturalNumber0(xn) = 0, yields:
% 44.60/12.96 | (975) all_252_1_216 = 0
% 44.60/12.96 |
% 44.60/12.96 +-Applying beta-rule and splitting (972), into two cases.
% 44.60/12.96 |-Branch one:
% 44.60/12.96 | (976) ~ (all_252_0_215 = 0)
% 44.60/12.96 |
% 44.60/12.96 | Equations (973) can reduce 976 to:
% 44.60/12.96 | (173) $false
% 44.60/12.96 |
% 44.60/12.96 |-The branch is then unsatisfiable
% 44.60/12.96 |-Branch two:
% 44.60/12.96 | (973) all_252_0_215 = 0
% 44.60/12.96 | (979) ~ (all_252_1_216 = 0) | ~ (all_252_2_217 = 0)
% 44.60/12.96 |
% 44.60/12.96 +-Applying beta-rule and splitting (979), into two cases.
% 44.60/12.96 |-Branch one:
% 44.60/12.96 | (980) ~ (all_252_1_216 = 0)
% 44.60/12.96 |
% 44.60/12.96 | Equations (975) can reduce 980 to:
% 44.60/12.96 | (173) $false
% 44.60/12.96 |
% 44.60/12.96 |-The branch is then unsatisfiable
% 44.60/12.96 |-Branch two:
% 44.60/12.96 | (975) all_252_1_216 = 0
% 44.60/12.96 | (964) ~ (all_252_2_217 = 0)
% 44.60/12.96 |
% 44.60/12.96 | Equations (966) can reduce 964 to:
% 44.60/12.96 | (173) $false
% 44.60/12.96 |
% 44.60/12.96 |-The branch is then unsatisfiable
% 44.60/12.96 |-Branch two:
% 44.60/12.96 | (586) all_58_0_80 = 0
% 44.60/12.96 | (986) ~ (all_58_1_81 = 0) | ~ (all_58_2_82 = 0) | ~ (all_58_3_83 = 0)
% 44.60/12.96 |
% 44.60/12.96 +-Applying beta-rule and splitting (986), into two cases.
% 44.60/12.96 |-Branch one:
% 44.60/12.96 | (987) ~ (all_58_1_81 = 0)
% 44.60/12.96 |
% 44.60/12.96 | Equations (397) can reduce 987 to:
% 44.60/12.96 | (173) $false
% 44.60/12.96 |
% 44.60/12.96 |-The branch is then unsatisfiable
% 44.60/12.96 |-Branch two:
% 44.60/12.96 | (397) all_58_1_81 = 0
% 44.60/12.96 | (990) ~ (all_58_2_82 = 0) | ~ (all_58_3_83 = 0)
% 44.60/12.96 |
% 44.60/12.96 +-Applying beta-rule and splitting (990), into two cases.
% 44.60/12.96 |-Branch one:
% 44.60/12.96 | (991) ~ (all_58_2_82 = 0)
% 44.60/12.96 |
% 44.60/12.96 | Equations (453) can reduce 991 to:
% 44.60/12.96 | (173) $false
% 44.60/12.96 |
% 44.60/12.96 |-The branch is then unsatisfiable
% 44.60/12.96 |-Branch two:
% 44.60/12.96 | (453) all_58_2_82 = 0
% 44.60/12.96 | (994) ~ (all_58_3_83 = 0)
% 44.60/12.96 |
% 44.60/12.96 | Equations (396) can reduce 994 to:
% 44.60/12.96 | (173) $false
% 44.60/12.96 |
% 44.60/12.96 |-The branch is then unsatisfiable
% 44.60/12.96 |-Branch two:
% 44.60/12.96 | (996) aNaturalNumber0(all_0_3_3) = all_37_1_63 & aNaturalNumber0(xp) = all_37_2_64 & ( ~ (all_37_1_63 = 0) | ~ (all_37_2_64 = 0))
% 44.60/12.96 |
% 44.60/12.96 | Applying alpha-rule on (996) yields:
% 44.60/12.96 | (997) aNaturalNumber0(all_0_3_3) = all_37_1_63
% 44.60/12.96 | (998) aNaturalNumber0(xp) = all_37_2_64
% 44.60/12.96 | (999) ~ (all_37_1_63 = 0) | ~ (all_37_2_64 = 0)
% 44.60/12.96 |
% 44.60/12.96 | Instantiating formula (60) with all_0_3_3, all_37_1_63, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_37_1_63, aNaturalNumber0(all_0_3_3) = 0, yields:
% 44.60/12.96 | (457) all_37_1_63 = 0
% 44.60/12.96 |
% 44.60/12.96 | Instantiating formula (60) with xp, all_37_2_64, 0 and discharging atoms aNaturalNumber0(xp) = all_37_2_64, aNaturalNumber0(xp) = 0, yields:
% 44.60/12.96 | (1001) all_37_2_64 = 0
% 44.60/12.96 |
% 44.60/12.96 +-Applying beta-rule and splitting (999), into two cases.
% 44.60/12.96 |-Branch one:
% 44.60/12.96 | (1002) ~ (all_37_1_63 = 0)
% 44.60/12.96 |
% 44.60/12.96 | Equations (457) can reduce 1002 to:
% 44.60/12.96 | (173) $false
% 44.60/12.96 |
% 44.60/12.96 |-The branch is then unsatisfiable
% 44.60/12.96 |-Branch two:
% 44.60/12.96 | (457) all_37_1_63 = 0
% 44.60/12.96 | (1005) ~ (all_37_2_64 = 0)
% 44.60/12.96 |
% 44.60/12.96 | Equations (1001) can reduce 1005 to:
% 44.60/12.96 | (173) $false
% 44.60/12.96 |
% 44.60/12.96 |-The branch is then unsatisfiable
% 44.60/12.96 |-Branch two:
% 44.60/12.96 | (1007) aNaturalNumber0(xp) = all_18_2_29 & aNaturalNumber0(xn) = all_18_1_28 & ( ~ (all_18_1_28 = 0) | ~ (all_18_2_29 = 0))
% 44.60/12.96 |
% 44.60/12.96 | Applying alpha-rule on (1007) yields:
% 44.60/12.96 | (1008) aNaturalNumber0(xp) = all_18_2_29
% 44.60/12.96 | (1009) aNaturalNumber0(xn) = all_18_1_28
% 44.60/12.96 | (1010) ~ (all_18_1_28 = 0) | ~ (all_18_2_29 = 0)
% 44.60/12.96 |
% 44.60/12.96 | Instantiating formula (60) with xp, all_18_2_29, 0 and discharging atoms aNaturalNumber0(xp) = all_18_2_29, aNaturalNumber0(xp) = 0, yields:
% 44.60/12.96 | (1011) all_18_2_29 = 0
% 44.60/12.96 |
% 44.60/12.96 | Instantiating formula (60) with xn, all_18_1_28, 0 and discharging atoms aNaturalNumber0(xn) = all_18_1_28, aNaturalNumber0(xn) = 0, yields:
% 44.60/12.96 | (428) all_18_1_28 = 0
% 44.60/12.96 |
% 44.60/12.96 +-Applying beta-rule and splitting (1010), into two cases.
% 44.60/12.96 |-Branch one:
% 44.60/12.96 | (1013) ~ (all_18_1_28 = 0)
% 44.60/12.96 |
% 44.60/12.96 | Equations (428) can reduce 1013 to:
% 44.60/12.96 | (173) $false
% 44.60/12.96 |
% 44.60/12.96 |-The branch is then unsatisfiable
% 44.60/12.96 |-Branch two:
% 44.60/12.96 | (428) all_18_1_28 = 0
% 44.60/12.96 | (1016) ~ (all_18_2_29 = 0)
% 44.60/12.96 |
% 44.60/12.96 | Equations (1011) can reduce 1016 to:
% 44.60/12.96 | (173) $false
% 44.60/12.96 |
% 44.60/12.96 |-The branch is then unsatisfiable
% 44.60/12.96 % SZS output end Proof for theBenchmark
% 44.60/12.96
% 44.60/12.96 12357ms
%------------------------------------------------------------------------------