TSTP Solution File: NUM512+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM512+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.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 08:45:19 EDT 2022
% Result : Theorem 23.82s 6.72s
% Output : Proof 67.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM512+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n020.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 05:20:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.54/0.58 ____ _
% 0.54/0.58 ___ / __ \_____(_)___ ________ __________
% 0.54/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.58
% 0.54/0.58 A Theorem Prover for First-Order Logic
% 0.54/0.58 (ePrincess v.1.0)
% 0.54/0.58
% 0.54/0.59 (c) Philipp Rümmer, 2009-2015
% 0.54/0.59 (c) Peter Backeman, 2014-2015
% 0.54/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.59 Bug reports to peter@backeman.se
% 0.54/0.59
% 0.54/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.59
% 0.54/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.98/1.03 Prover 0: Preprocessing ...
% 3.91/1.51 Prover 0: Constructing countermodel ...
% 20.36/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 20.36/6.02 Prover 1: Preprocessing ...
% 21.23/6.17 Prover 1: Constructing countermodel ...
% 23.82/6.72 Prover 1: proved (794ms)
% 23.82/6.72 Prover 0: stopped
% 23.82/6.72
% 23.82/6.72 No countermodel exists, formula is valid
% 23.82/6.72 % SZS status Theorem for theBenchmark
% 23.82/6.72
% 23.82/6.72 Generating proof ... found it (size 904)
% 65.93/30.88
% 65.93/30.88 % SZS output start Proof for theBenchmark
% 65.93/30.88 Assumed formulas after preprocessing and simplification:
% 65.93/30.88 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v6 = xn) & ~ (v4 = 0) & ~ (v3 = 0) & ~ (xk = xp) & ~ (xk = sz10) & ~ (xk = sz00) & ~ (xp = xm) & ~ (xp = xn) & ~ (sz10 = sz00) & isPrime0(xr) = 0 & isPrime0(xp) = 0 & sdtsldt0(v9, xr) = v10 & sdtsldt0(v2, xp) = xk & sdtsldt0(xn, xr) = v6 & doDivides0(xr, v2) = 0 & doDivides0(xr, xk) = 0 & doDivides0(xr, xm) = v5 & doDivides0(xr, xn) = 0 & doDivides0(xp, v2) = 0 & sdtlseqdt0(v6, xn) = 0 & sdtlseqdt0(xr, xk) = 0 & sdtlseqdt0(xk, xp) = 0 & sdtlseqdt0(xp, xm) = v4 & sdtlseqdt0(xp, xn) = v3 & sdtlseqdt0(xm, xp) = 0 & sdtlseqdt0(xn, xp) = 0 & sdtasdt0(v10, xr) = v11 & sdtasdt0(v7, xr) = v8 & sdtasdt0(v6, xm) = v7 & sdtasdt0(xp, xk) = v9 & sdtasdt0(xn, xm) = v2 & sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) = v0 & aNaturalNumber0(xr) = 0 & aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 & ~ (isPrime0(sz10) = 0) & ~ (isPrime0(sz00) = 0) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v14 = v13 | v12 = sz00 | ~ (sdtlseqdt0(v15, v16) = v17) | ~ (sdtasdt0(v12, v14) = v16) | ~ (sdtasdt0(v12, v13) = v15) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (sdtlseqdt0(v22, v23) = v24 & sdtlseqdt0(v13, v14) = v21 & sdtasdt0(v14, v12) = v23 & sdtasdt0(v13, v12) = v22 & aNaturalNumber0(v14) = v20 & aNaturalNumber0(v13) = v19 & aNaturalNumber0(v12) = v18 & ( ~ (v21 = 0) | ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | (v24 = 0 & v17 = 0 & ~ (v23 = v22) & ~ (v16 = v15))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v13 = v12 | ~ (sdtlseqdt0(v15, v16) = v17) | ~ (sdtlseqdt0(v12, v13) = 0) | ~ (sdtpldt0(v13, v14) = v16) | ~ (sdtpldt0(v12, v14) = v15) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ((sdtlseqdt0(v19, v20) = v21 & sdtpldt0(v14, v13) = v20 & sdtpldt0(v14, v12) = v19 & aNaturalNumber0(v14) = v18 & ( ~ (v18 = 0) | (v21 = 0 & v17 = 0 & ~ (v20 = v19) & ~ (v16 = v15)))) | (aNaturalNumber0(v13) = v19 & aNaturalNumber0(v12) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v12 = sz00 | ~ (sdtsldt0(v16, v12) = v17) | ~ (sdtsldt0(v13, v12) = v14) | ~ (sdtasdt0(v15, v13) = v16) | ? [v18] : ? [v19] : ? [v20] : ((doDivides0(v12, v13) = v20 & aNaturalNumber0(v13) = v19 & aNaturalNumber0(v12) = v18 & ( ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0))) | (sdtasdt0(v15, v14) = v19 & aNaturalNumber0(v15) = v18 & ( ~ (v18 = 0) | v19 = v17)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (sdtasdt0(v12, v14) = v16) | ~ (sdtasdt0(v12, v13) = v15) | ~ (sdtpldt0(v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (sdtasdt0(v21, v12) = v23 & sdtasdt0(v14, v12) = v25 & sdtasdt0(v13, v12) = v24 & sdtasdt0(v12, v21) = v22 & sdtpldt0(v24, v25) = v26 & sdtpldt0(v13, v14) = v21 & aNaturalNumber0(v14) = v20 & aNaturalNumber0(v13) = v19 & aNaturalNumber0(v12) = v18 & ( ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | (v26 = v23 & v22 = v17)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (doDivides0(v12, v15) = v16) | ~ (sdtpldt0(v13, v14) = v15) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (doDivides0(v12, v14) = v21 & doDivides0(v12, v13) = v20 & aNaturalNumber0(v14) = v19 & aNaturalNumber0(v13) = v18 & aNaturalNumber0(v12) = v17 & ( ~ (v21 = 0) | ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | v12 = sz00 | ~ (sdtasdt0(v12, v14) = v16) | ~ (sdtasdt0(v12, v13) = v15) | ~ (aNaturalNumber0(v12) = 0) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (sdtasdt0(v14, v12) = v20 & sdtasdt0(v13, v12) = v19 & aNaturalNumber0(v14) = v18 & aNaturalNumber0(v13) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0) | ( ~ (v20 = v19) & ~ (v16 = v15))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (sdtpldt0(v12, v14) = v16) | ~ (sdtpldt0(v12, v13) = v15) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (sdtpldt0(v14, v12) = v21 & sdtpldt0(v13, v12) = v20 & aNaturalNumber0(v14) = v19 & aNaturalNumber0(v13) = v18 & aNaturalNumber0(v12) = v17 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | ( ~ (v21 = v20) & ~ (v16 = v15))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (sdtasdt0(v15, v14) = v16) | ~ (sdtasdt0(v12, v13) = v15) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (sdtasdt0(v13, v14) = v20 & sdtasdt0(v12, v20) = v21 & aNaturalNumber0(v14) = v19 & aNaturalNumber0(v13) = v18 & aNaturalNumber0(v12) = v17 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | v21 = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (sdtpldt0(v15, v14) = v16) | ~ (sdtpldt0(v12, v13) = v15) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (isPrime0(v14) = v20 & doDivides0(v14, v21) = v22 & doDivides0(v14, v13) = v25 & doDivides0(v14, v12) = v24 & iLess0(v16, v1) = v23 & sdtasdt0(v12, v13) = v21 & aNaturalNumber0(v14) = v19 & aNaturalNumber0(v13) = v18 & aNaturalNumber0(v12) = v17 & ( ~ (v23 = 0) | ~ (v22 = 0) | ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | v25 = 0 | v24 = 0))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (sdtpldt0(v15, v14) = v16) | ~ (sdtpldt0(v12, v13) = v15) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (sdtpldt0(v13, v14) = v20 & sdtpldt0(v12, v20) = v21 & aNaturalNumber0(v14) = v19 & aNaturalNumber0(v13) = v18 & aNaturalNumber0(v12) = v17 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | v21 = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | v12 = sz00 | ~ (sdtsldt0(v13, v12) = v14) | ~ (sdtasdt0(v12, v15) = v13) | ? [v16] : ? [v17] : ? [v18] : (( ~ (v16 = 0) & aNaturalNumber0(v15) = v16) | (doDivides0(v12, v13) = v18 & aNaturalNumber0(v13) = v17 & aNaturalNumber0(v12) = v16 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | ~ (sdtmndt0(v13, v12) = v14) | ~ (sdtpldt0(v12, v15) = v13) | ? [v16] : ? [v17] : ? [v18] : (( ~ (v16 = 0) & aNaturalNumber0(v15) = v16) | (sdtlseqdt0(v12, v13) = v18 & aNaturalNumber0(v13) = v17 & aNaturalNumber0(v12) = v16 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v13 | v12 = sz00 | ~ (sdtsldt0(v13, v12) = v14) | ~ (sdtasdt0(v12, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : (doDivides0(v12, v13) = v18 & aNaturalNumber0(v13) = v17 & aNaturalNumber0(v12) = v16 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (sdtmndt0(v13, v12) = v14) | ~ (sdtpldt0(v12, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : (sdtlseqdt0(v12, v13) = v18 & aNaturalNumber0(v13) = v17 & aNaturalNumber0(v12) = v16 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v12 = sz00 | ~ (sdtlseqdt0(v13, v14) = v15) | ~ (sdtasdt0(v13, v12) = v14) | ? [v16] : ? [v17] : (aNaturalNumber0(v13) = v17 & aNaturalNumber0(v12) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (doDivides0(v12, v14) = v15) | ~ (doDivides0(v12, v13) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (doDivides0(v13, v14) = v19 & aNaturalNumber0(v14) = v18 & aNaturalNumber0(v13) = v17 & aNaturalNumber0(v12) = v16 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (sdtlseqdt0(v12, v14) = v15) | ~ (sdtlseqdt0(v12, v13) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (sdtlseqdt0(v13, v14) = v19 & aNaturalNumber0(v14) = v18 & aNaturalNumber0(v13) = v17 & aNaturalNumber0(v12) = v16 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (doDivides0(v12, v13) = v14) | ~ (sdtasdt0(v12, v15) = v13) | ? [v16] : ? [v17] : (( ~ (v16 = 0) & aNaturalNumber0(v15) = v16) | (aNaturalNumber0(v13) = v17 & aNaturalNumber0(v12) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (sdtlseqdt0(v12, v13) = v14) | ~ (sdtpldt0(v12, v15) = v13) | ? [v16] : ? [v17] : (( ~ (v16 = 0) & aNaturalNumber0(v15) = v16) | (aNaturalNumber0(v13) = v17 & aNaturalNumber0(v12) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (sdtsldt0(v15, v14) = v13) | ~ (sdtsldt0(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (doDivides0(v15, v14) = v13) | ~ (doDivides0(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (iLess0(v15, v14) = v13) | ~ (iLess0(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (sdtmndt0(v15, v14) = v13) | ~ (sdtmndt0(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (sdtlseqdt0(v15, v14) = v13) | ~ (sdtlseqdt0(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (sdtasdt0(v15, v14) = v13) | ~ (sdtasdt0(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (sdtpldt0(v15, v14) = v13) | ~ (sdtpldt0(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = sz00 | ~ (sdtsldt0(v13, v12) = v14) | ~ (sdtasdt0(v12, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v16 = 0 & aNaturalNumber0(v14) = 0) | (doDivides0(v12, v13) = v18 & aNaturalNumber0(v13) = v17 & aNaturalNumber0(v12) = v16 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (doDivides0(v12, v15) = 0) | ~ (sdtpldt0(v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (doDivides0(v12, v14) = v20 & doDivides0(v12, v13) = v19 & aNaturalNumber0(v14) = v18 & aNaturalNumber0(v13) = v17 & aNaturalNumber0(v12) = v16 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0) | v20 = 0))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (sdtmndt0(v13, v12) = v14) | ~ (sdtpldt0(v12, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v16 = 0 & aNaturalNumber0(v14) = 0) | (sdtlseqdt0(v12, v13) = v18 & aNaturalNumber0(v13) = v17 & aNaturalNumber0(v12) = v16 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0))))) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = v12 | ~ (iLess0(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (sdtlseqdt0(v12, v13) = v17 & aNaturalNumber0(v13) = v16 & aNaturalNumber0(v12) = v15 & ( ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (sdtlseqdt0(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (sdtlseqdt0(v13, v12) = v17 & aNaturalNumber0(v13) = v16 & aNaturalNumber0(v12) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | (v17 = 0 & ~ (v13 = v12))))) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (isPrime0(v14) = v13) | ~ (isPrime0(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (aNaturalNumber0(v14) = v13) | ~ (aNaturalNumber0(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtasdt0(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (sdtasdt0(v13, v12) = v17 & aNaturalNumber0(v13) = v16 & aNaturalNumber0(v12) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v17 = v14))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtasdt0(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (aNaturalNumber0(v14) = v17 & aNaturalNumber0(v13) = v16 & aNaturalNumber0(v12) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v17 = 0))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtpldt0(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (sdtpldt0(v13, v12) = v17 & aNaturalNumber0(v13) = v16 & aNaturalNumber0(v12) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v17 = v14))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtpldt0(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (aNaturalNumber0(v14) = v17 & aNaturalNumber0(v13) = v16 & aNaturalNumber0(v12) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v17 = 0))) & ! [v12] : ! [v13] : (v13 = v12 | v13 = sz10 | ~ (isPrime0(v12) = 0) | ~ (doDivides0(v13, v12) = 0) | ? [v14] : (( ~ (v14 = 0) & aNaturalNumber0(v13) = v14) | ( ~ (v14 = 0) & aNaturalNumber0(v12) = v14))) & ! [v12] : ! [v13] : (v13 = v12 | ~ (sdtlseqdt0(v12, v13) = 0) | ? [v14] : ? [v15] : ? [v16] : (sdtlseqdt0(v13, v12) = v16 & aNaturalNumber0(v13) = v15 & aNaturalNumber0(v12) = v14 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v12] : ! [v13] : (v13 = sz00 | v12 = sz00 | ~ (sdtasdt0(v12, v13) = sz00) | ? [v14] : ? [v15] : (aNaturalNumber0(v13) = v15 & aNaturalNumber0(v12) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v12] : ! [v13] : (v13 = sz00 | ~ (doDivides0(v12, v13) = 0) | ? [v14] : ? [v15] : ? [v16] : (sdtlseqdt0(v12, v13) = v16 & aNaturalNumber0(v13) = v15 & aNaturalNumber0(v12) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | v16 = 0))) & ! [v12] : ! [v13] : (v13 = sz00 | ~ (sdtpldt0(v12, v13) = sz00) | ? [v14] : ? [v15] : (aNaturalNumber0(v13) = v15 & aNaturalNumber0(v12) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v12] : ! [v13] : (v13 = 0 | v12 = sz10 | v12 = sz00 | ~ (isPrime0(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & ~ (v14 = v12) & ~ (v14 = sz10) & doDivides0(v14, v12) = 0 & aNaturalNumber0(v14) = 0) | ( ~ (v14 = 0) & aNaturalNumber0(v12) = v14))) & ! [v12] : ! [v13] : (v13 = 0 | v12 = sz10 | v12 = sz00 | ~ (sdtlseqdt0(sz10, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & aNaturalNumber0(v12) = v14)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (sdtlseqdt0(v12, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & aNaturalNumber0(v12) = v14)) & ! [v12] : ! [v13] : (v12 = sz00 | ~ (sdtpldt0(v12, v13) = sz00) | ? [v14] : ? [v15] : (aNaturalNumber0(v13) = v15 & aNaturalNumber0(v12) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v12] : ! [v13] : ( ~ (doDivides0(v12, v13) = 0) | ? [v14] : ? [v15] : ? [v16] : ((v16 = v13 & v15 = 0 & sdtasdt0(v12, v14) = v13 & aNaturalNumber0(v14) = 0) | (aNaturalNumber0(v13) = v15 & aNaturalNumber0(v12) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0))))) & ! [v12] : ! [v13] : ( ~ (sdtlseqdt0(v12, v13) = 0) | ? [v14] : ? [v15] : ? [v16] : ((v16 = v13 & v15 = 0 & sdtpldt0(v12, v14) = v13 & aNaturalNumber0(v14) = 0) | (aNaturalNumber0(v13) = v15 & aNaturalNumber0(v12) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0))))) & ! [v12] : ! [v13] : ( ~ (sdtasdt0(sz10, v12) = v13) | ? [v14] : ? [v15] : (sdtasdt0(v12, sz10) = v15 & aNaturalNumber0(v12) = v14 & ( ~ (v14 = 0) | (v15 = v12 & v13 = v12)))) & ! [v12] : ! [v13] : ( ~ (sdtasdt0(sz00, v12) = v13) | ? [v14] : ? [v15] : (sdtasdt0(v12, sz00) = v15 & aNaturalNumber0(v12) = v14 & ( ~ (v14 = 0) | (v15 = sz00 & v13 = sz00)))) & ! [v12] : ! [v13] : ( ~ (sdtpldt0(sz00, v12) = v13) | ? [v14] : ? [v15] : (sdtpldt0(v12, sz00) = v15 & aNaturalNumber0(v12) = v14 & ( ~ (v14 = 0) | (v15 = v12 & v13 = v12)))) & ! [v12] : (v12 = sz10 | v12 = sz00 | ~ (aNaturalNumber0(v12) = 0) | ? [v13] : (isPrime0(v13) = 0 & doDivides0(v13, v12) = 0 & aNaturalNumber0(v13) = 0)) & ( ~ (v11 = v2) | ~ (v8 = v2)))
% 66.20/30.96 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11 yields:
% 66.20/30.96 | (1) ~ (all_0_5_5 = xn) & ~ (all_0_7_7 = 0) & ~ (all_0_8_8 = 0) & ~ (xk = xp) & ~ (xk = sz10) & ~ (xk = sz00) & ~ (xp = xm) & ~ (xp = xn) & ~ (sz10 = sz00) & isPrime0(xr) = 0 & isPrime0(xp) = 0 & sdtsldt0(all_0_2_2, xr) = all_0_1_1 & sdtsldt0(all_0_9_9, xp) = xk & sdtsldt0(xn, xr) = all_0_5_5 & doDivides0(xr, all_0_9_9) = 0 & doDivides0(xr, xk) = 0 & doDivides0(xr, xm) = all_0_6_6 & doDivides0(xr, xn) = 0 & doDivides0(xp, all_0_9_9) = 0 & sdtlseqdt0(all_0_5_5, xn) = 0 & sdtlseqdt0(xr, xk) = 0 & sdtlseqdt0(xk, xp) = 0 & sdtlseqdt0(xp, xm) = all_0_7_7 & sdtlseqdt0(xp, xn) = all_0_8_8 & sdtlseqdt0(xm, xp) = 0 & sdtlseqdt0(xn, xp) = 0 & sdtasdt0(all_0_1_1, xr) = all_0_0_0 & sdtasdt0(all_0_4_4, xr) = all_0_3_3 & sdtasdt0(all_0_5_5, xm) = all_0_4_4 & sdtasdt0(xp, xk) = all_0_2_2 & sdtasdt0(xn, xm) = all_0_9_9 & sdtpldt0(all_0_11_11, xp) = all_0_10_10 & sdtpldt0(xn, xm) = all_0_11_11 & aNaturalNumber0(xr) = 0 & aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 & ~ (isPrime0(sz10) = 0) & ~ (isPrime0(sz00) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | v0 = sz00 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (sdtlseqdt0(v10, v11) = v12 & sdtlseqdt0(v1, v2) = v9 & sdtasdt0(v2, v0) = v11 & sdtasdt0(v1, v0) = v10 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v12 = 0 & v5 = 0 & ~ (v11 = v10) & ~ (v4 = v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtlseqdt0(v0, v1) = 0) | ~ (sdtpldt0(v1, v2) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((sdtlseqdt0(v7, v8) = v9 & sdtpldt0(v2, v1) = v8 & sdtpldt0(v2, v0) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0 & ~ (v8 = v7) & ~ (v4 = v3)))) | (aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ((doDivides0(v0, v1) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))) | (sdtasdt0(v3, v2) = v7 & aNaturalNumber0(v3) = v6 & ( ~ (v6 = 0) | v7 = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v9, v0) = v11 & sdtasdt0(v2, v0) = v13 & sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v9) = v10 & sdtpldt0(v12, v13) = v14 & sdtpldt0(v1, v2) = v9 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v14 = v11 & v10 = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (doDivides0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (doDivides0(v0, v2) = v9 & doDivides0(v0, v1) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v8 = v7) & ~ (v4 = v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtpldt0(v2, v0) = v9 & sdtpldt0(v1, v0) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v9 = v8) & ~ (v4 = v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (isPrime0(v2) = v8 & doDivides0(v2, v9) = v10 & doDivides0(v2, v1) = v13 & doDivides0(v2, v0) = v12 & iLess0(v4, all_0_10_10) = v11 & sdtasdt0(v0, v1) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v13 = 0 | v12 = 0))) & ! [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(v0, v3) = 0) | ~ (sdtpldt0(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (doDivides0(v0, v2) = v8 & doDivides0(v0, v1) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (iLess0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtlseqdt0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtlseqdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v5 = 0 & ~ (v1 = v0))))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ (isPrime0(v0) = 0) | ~ (doDivides0(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (sdtlseqdt0(v1, v0) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (doDivides0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (sdtlseqdt0(v0, v1) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0))) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (isPrime0(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & ~ (v2 = v0) & ~ (v2 = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)) & ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (doDivides0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ! [v0] : ! [v1] : ( ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00)))) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0)) & ( ~ (all_0_0_0 = all_0_9_9) | ~ (all_0_3_3 = all_0_9_9))
% 66.20/30.99 |
% 66.20/30.99 | Applying alpha-rule on (1) yields:
% 66.20/30.99 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 66.20/30.99 | (3) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0))
% 66.20/30.99 | (4) aNaturalNumber0(sz10) = 0
% 66.20/30.99 | (5) ~ (all_0_5_5 = xn)
% 66.20/30.99 | (6) ! [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))))
% 66.20/30.99 | (7) ! [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))))
% 66.20/30.99 | (8) ! [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)))))
% 66.20/30.99 | (9) ~ (xk = sz10)
% 66.20/30.99 | (10) ! [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))))
% 66.47/30.99 | (11) ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 66.47/30.99 | (12) ! [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)))
% 66.47/31.00 | (13) ! [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)))))
% 66.47/31.00 | (14) sdtlseqdt0(xm, xp) = 0
% 66.47/31.00 | (15) ~ (isPrime0(sz00) = 0)
% 66.47/31.00 | (16) ! [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)))
% 66.47/31.00 | (17) sdtpldt0(all_0_11_11, xp) = all_0_10_10
% 66.47/31.00 | (18) aNaturalNumber0(xn) = 0
% 66.47/31.00 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0))
% 66.47/31.00 | (20) ~ (all_0_0_0 = all_0_9_9) | ~ (all_0_3_3 = all_0_9_9)
% 66.47/31.00 | (21) sdtlseqdt0(xk, xp) = 0
% 66.47/31.00 | (22) ~ (isPrime0(sz10) = 0)
% 66.47/31.00 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0))
% 66.47/31.00 | (24) ! [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)))
% 66.47/31.00 | (25) ! [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)))))
% 66.47/31.00 | (26) ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 66.47/31.00 | (27) ! [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)))))
% 66.47/31.00 | (28) ! [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))))
% 66.47/31.00 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0))
% 66.47/31.00 | (30) ! [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)))))
% 66.47/31.00 | (31) ~ (xk = sz00)
% 66.47/31.00 | (32) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 66.47/31.00 | (33) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 66.47/31.00 | (34) ! [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)))
% 66.47/31.00 | (35) ! [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)))
% 66.47/31.00 | (36) sdtlseqdt0(all_0_5_5, xn) = 0
% 66.47/31.00 | (37) ! [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))))
% 66.47/31.00 | (38) ! [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)))
% 66.47/31.01 | (39) sdtasdt0(all_0_1_1, xr) = all_0_0_0
% 66.47/31.01 | (40) doDivides0(xr, xm) = all_0_6_6
% 66.47/31.01 | (41) aNaturalNumber0(xp) = 0
% 66.47/31.01 | (42) ! [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))))
% 66.47/31.01 | (43) sdtlseqdt0(xp, xm) = all_0_7_7
% 66.47/31.01 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 66.47/31.01 | (45) doDivides0(xr, all_0_9_9) = 0
% 66.47/31.01 | (46) ~ (xp = xm)
% 66.47/31.01 | (47) sdtlseqdt0(xr, xk) = 0
% 66.47/31.01 | (48) ~ (all_0_8_8 = 0)
% 66.47/31.01 | (49) sdtsldt0(xn, xr) = all_0_5_5
% 66.47/31.01 | (50) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 66.47/31.01 | (51) ! [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))))
% 66.47/31.01 | (52) ! [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)))))
% 66.47/31.01 | (53) sdtasdt0(all_0_4_4, xr) = all_0_3_3
% 66.47/31.01 | (54) ~ (xp = xn)
% 66.47/31.01 | (55) aNaturalNumber0(xm) = 0
% 66.47/31.01 | (56) ! [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)))))
% 66.47/31.01 | (57) ~ (sz10 = sz00)
% 66.47/31.01 | (58) ! [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)))))
% 66.47/31.01 | (59) sdtsldt0(all_0_9_9, xp) = xk
% 66.47/31.01 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 66.47/31.01 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (isPrime0(v2) = v8 & doDivides0(v2, v9) = v10 & doDivides0(v2, v1) = v13 & doDivides0(v2, v0) = v12 & iLess0(v4, all_0_10_10) = v11 & sdtasdt0(v0, v1) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v13 = 0 | v12 = 0)))
% 66.47/31.01 | (62) aNaturalNumber0(xr) = 0
% 66.47/31.01 | (63) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0))
% 66.47/31.01 | (64) ! [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)))))
% 66.47/31.01 | (65) ! [v0] : ! [v1] : (v1 = sz00 | ~ (doDivides0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (sdtlseqdt0(v0, v1) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0)))
% 66.47/31.01 | (66) ! [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)))))
% 66.47/31.01 | (67) ! [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)))))
% 66.47/31.02 | (68) sdtasdt0(xp, xk) = all_0_2_2
% 66.47/31.02 | (69) doDivides0(xr, xk) = 0
% 66.47/31.02 | (70) doDivides0(xp, all_0_9_9) = 0
% 66.47/31.02 | (71) ! [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))))
% 66.47/31.02 | (72) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 66.47/31.02 | (73) sdtlseqdt0(xn, xp) = 0
% 66.47/31.02 | (74) aNaturalNumber0(sz00) = 0
% 66.47/31.02 | (75) ! [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)))))
% 66.47/31.02 | (76) sdtpldt0(xn, xm) = all_0_11_11
% 66.47/31.02 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 66.47/31.02 | (78) ! [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))))
% 66.47/31.02 | (79) sdtasdt0(all_0_5_5, xm) = all_0_4_4
% 66.47/31.02 | (80) ~ (xk = xp)
% 66.47/31.02 | (81) ~ (all_0_7_7 = 0)
% 66.47/31.02 | (82) sdtsldt0(all_0_2_2, xr) = all_0_1_1
% 66.47/31.02 | (83) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ (isPrime0(v0) = 0) | ~ (doDivides0(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 66.47/31.02 | (84) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 66.47/31.02 | (85) isPrime0(xp) = 0
% 66.47/31.02 | (86) ! [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))))
% 66.47/31.02 | (87) doDivides0(xr, xn) = 0
% 66.47/31.02 | (88) isPrime0(xr) = 0
% 66.47/31.02 | (89) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00))))
% 66.47/31.02 | (90) sdtasdt0(xn, xm) = all_0_9_9
% 66.47/31.02 | (91) sdtlseqdt0(xp, xn) = all_0_8_8
% 66.47/31.02 | (92) ! [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)))
% 66.47/31.02 | (93) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0))
% 66.47/31.02 | (94) ! [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)))
% 66.47/31.02 | (95) ! [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)))))
% 66.47/31.02 |
% 66.47/31.02 | Using (88) and (22) yields:
% 66.47/31.02 | (96) ~ (xr = sz10)
% 66.47/31.02 |
% 66.47/31.02 | Using (85) and (22) yields:
% 66.47/31.02 | (97) ~ (xp = sz10)
% 66.47/31.03 |
% 66.47/31.03 | Using (88) and (15) yields:
% 66.47/31.03 | (98) ~ (xr = sz00)
% 66.47/31.03 |
% 66.47/31.03 | Using (85) and (15) yields:
% 66.47/31.03 | (99) ~ (xp = sz00)
% 66.47/31.03 |
% 66.47/31.03 | Instantiating formula (65) with all_0_9_9, xr and discharging atoms doDivides0(xr, all_0_9_9) = 0, yields:
% 66.47/31.03 | (100) all_0_9_9 = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xr, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.47/31.03 |
% 66.47/31.03 | Instantiating formula (66) with all_0_9_9, xr and discharging atoms doDivides0(xr, all_0_9_9) = 0, yields:
% 66.47/31.03 | (101) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_9_9 & v1 = 0 & sdtasdt0(xr, v0) = all_0_9_9 & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 66.47/31.03 |
% 66.47/31.03 | Instantiating formula (66) with xk, xr and discharging atoms doDivides0(xr, xk) = 0, yields:
% 66.47/31.03 | (102) ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & v1 = 0 & sdtasdt0(xr, v0) = xk & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 66.47/31.03 |
% 66.47/31.03 | Instantiating formula (65) with xn, xr and discharging atoms doDivides0(xr, xn) = 0, yields:
% 66.47/31.03 | (103) xn = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xr, xn) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.47/31.03 |
% 66.47/31.03 | Instantiating formula (66) with xn, xr and discharging atoms doDivides0(xr, xn) = 0, yields:
% 66.47/31.03 | (104) ? [v0] : ? [v1] : ? [v2] : ((v2 = xn & v1 = 0 & sdtasdt0(xr, v0) = xn & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 66.47/31.03 |
% 66.47/31.03 | Instantiating formula (65) with all_0_9_9, xp and discharging atoms doDivides0(xp, all_0_9_9) = 0, yields:
% 66.47/31.03 | (105) all_0_9_9 = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.47/31.03 |
% 66.47/31.03 | Instantiating formula (28) with xn, all_0_5_5 and discharging atoms sdtlseqdt0(all_0_5_5, xn) = 0, yields:
% 66.47/31.03 | (106) all_0_5_5 = xn | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xn, all_0_5_5) = v2 & aNaturalNumber0(all_0_5_5) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 66.47/31.03 |
% 66.47/31.03 | Instantiating formula (56) with xk, xr and discharging atoms sdtlseqdt0(xr, xk) = 0, yields:
% 66.47/31.03 | (107) ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & v1 = 0 & sdtpldt0(xr, v0) = xk & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 66.47/31.03 |
% 66.47/31.03 | Instantiating formula (28) with xp, xk and discharging atoms sdtlseqdt0(xk, xp) = 0, yields:
% 66.47/31.03 | (108) xk = xp | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, xk) = v2 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 66.47/31.03 |
% 66.47/31.03 | Instantiating formula (56) with xp, xk and discharging atoms sdtlseqdt0(xk, xp) = 0, yields:
% 66.47/31.03 | (109) ? [v0] : ? [v1] : ? [v2] : ((v2 = xp & v1 = 0 & sdtpldt0(xk, v0) = xp & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 66.47/31.03 |
% 66.47/31.03 | Instantiating formula (56) with xp, xm and discharging atoms sdtlseqdt0(xm, xp) = 0, yields:
% 66.47/31.03 | (110) ? [v0] : ? [v1] : ? [v2] : ((v2 = xp & v1 = 0 & sdtpldt0(xm, v0) = xp & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 66.47/31.03 |
% 66.47/31.03 | Instantiating formula (56) with xp, xn and discharging atoms sdtlseqdt0(xn, xp) = 0, yields:
% 66.47/31.03 | (111) ? [v0] : ? [v1] : ? [v2] : ((v2 = xp & v1 = 0 & sdtpldt0(xn, v0) = xp & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xp) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 66.47/31.03 |
% 66.47/31.03 | Instantiating formula (35) with all_0_0_0, xr, all_0_1_1 and discharging atoms sdtasdt0(all_0_1_1, xr) = all_0_0_0, yields:
% 66.47/31.03 | (112) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xr, all_0_1_1) = v2 & aNaturalNumber0(all_0_1_1) = v0 & aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_0_0))
% 66.47/31.03 |
% 66.47/31.03 | Instantiating formula (16) with all_0_0_0, xr, all_0_1_1 and discharging atoms sdtasdt0(all_0_1_1, xr) = all_0_0_0, yields:
% 66.47/31.03 | (113) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_0_0) = v2 & aNaturalNumber0(all_0_1_1) = v0 & aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.47/31.03 |
% 66.47/31.03 | Instantiating formula (35) with all_0_3_3, xr, all_0_4_4 and discharging atoms sdtasdt0(all_0_4_4, xr) = all_0_3_3, yields:
% 66.47/31.03 | (114) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xr, all_0_4_4) = v2 & aNaturalNumber0(all_0_4_4) = v0 & aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_3_3))
% 66.47/31.03 |
% 66.47/31.03 | Instantiating formula (16) with all_0_3_3, xr, all_0_4_4 and discharging atoms sdtasdt0(all_0_4_4, xr) = all_0_3_3, yields:
% 66.47/31.03 | (115) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_3_3) = v2 & aNaturalNumber0(all_0_4_4) = v0 & aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.47/31.03 |
% 66.47/31.03 | Instantiating formula (24) with all_0_3_3, all_0_4_4, xr, xm, all_0_5_5 and discharging atoms sdtasdt0(all_0_4_4, xr) = all_0_3_3, sdtasdt0(all_0_5_5, xm) = all_0_4_4, yields:
% 66.47/31.03 | (116) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_5_5, v3) = v4 & sdtasdt0(xm, xr) = v3 & aNaturalNumber0(all_0_5_5) = v0 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xm) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_3_3))
% 66.47/31.04 |
% 66.47/31.04 | Instantiating formula (35) with all_0_4_4, xm, all_0_5_5 and discharging atoms sdtasdt0(all_0_5_5, xm) = all_0_4_4, yields:
% 66.47/31.04 | (117) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xm, all_0_5_5) = v2 & aNaturalNumber0(all_0_5_5) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_4_4))
% 66.47/31.04 |
% 66.47/31.04 | Instantiating formula (16) with all_0_4_4, xm, all_0_5_5 and discharging atoms sdtasdt0(all_0_5_5, xm) = all_0_4_4, yields:
% 66.47/31.04 | (118) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_4_4) = v2 & aNaturalNumber0(all_0_5_5) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.47/31.04 |
% 66.47/31.04 | Instantiating formula (10) with all_0_7_7, xm, xp, xk and discharging atoms sdtlseqdt0(xp, xm) = all_0_7_7, yields:
% 66.47/31.04 | (119) all_0_7_7 = 0 | xk = sz00 | ~ (sdtasdt0(xp, xk) = xm) | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 66.47/31.04 |
% 66.47/31.04 | Instantiating formula (42) with all_0_2_2, xk, all_0_9_9, xp and discharging atoms sdtsldt0(all_0_9_9, xp) = xk, sdtasdt0(xp, xk) = all_0_2_2, yields:
% 66.47/31.04 | (120) all_0_2_2 = all_0_9_9 | xp = sz00 | ? [v0] : ? [v1] : ? [v2] : (doDivides0(xp, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 66.47/31.04 |
% 66.47/31.04 | Instantiating formula (13) with all_0_2_2, xk, all_0_9_9, xp and discharging atoms sdtsldt0(all_0_9_9, xp) = xk, sdtasdt0(xp, xk) = all_0_2_2, yields:
% 66.47/31.04 | (121) xp = sz00 | ? [v0] : ? [v1] : ? [v2] : ((v0 = 0 & aNaturalNumber0(xk) = 0) | (doDivides0(xp, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 66.47/31.04 |
% 66.47/31.04 | Instantiating formula (50) with xk, xp yields:
% 66.47/31.04 | (122) xk = sz00 | xp = sz00 | ~ (sdtasdt0(xp, xk) = sz00) | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 66.47/31.04 |
% 66.47/31.04 | Instantiating formula (35) with all_0_2_2, xk, xp and discharging atoms sdtasdt0(xp, xk) = all_0_2_2, yields:
% 66.47/31.04 | (123) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xk, xp) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_2_2))
% 66.47/31.04 |
% 66.47/31.04 | Instantiating formula (16) with all_0_2_2, xk, xp and discharging atoms sdtasdt0(xp, xk) = all_0_2_2, yields:
% 66.47/31.04 | (124) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_2_2) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.47/31.04 |
% 66.47/31.04 | Instantiating formula (32) with all_0_9_9, xm yields:
% 66.47/31.04 | (125) ~ (sdtasdt0(sz10, xm) = all_0_9_9) | ? [v0] : ? [v1] : (sdtasdt0(xm, sz10) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v0 = 0) | (v1 = xm & all_0_9_9 = xm)))
% 66.47/31.04 |
% 66.47/31.04 | Instantiating formula (89) with all_0_9_9, xm yields:
% 66.47/31.04 | (126) ~ (sdtasdt0(sz00, xm) = all_0_9_9) | ? [v0] : ? [v1] : (sdtasdt0(xm, sz00) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v0 = 0) | (v1 = sz00 & all_0_9_9 = sz00)))
% 66.47/31.04 |
% 66.47/31.04 | Instantiating formula (35) with all_0_9_9, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_9_9, yields:
% 66.47/31.04 | (127) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_9_9))
% 66.47/31.04 |
% 66.47/31.04 | Instantiating formula (16) with all_0_9_9, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_9_9, yields:
% 66.47/31.04 | (128) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_9_9) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.47/31.04 |
% 66.47/31.04 | Instantiating formula (38) with all_0_10_10, xp, all_0_11_11 and discharging atoms sdtpldt0(all_0_11_11, xp) = all_0_10_10, yields:
% 66.47/31.04 | (129) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, all_0_11_11) = v2 & aNaturalNumber0(all_0_11_11) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_10_10))
% 66.47/31.04 |
% 66.47/31.04 | Instantiating formula (34) with all_0_10_10, xp, all_0_11_11 and discharging atoms sdtpldt0(all_0_11_11, xp) = all_0_10_10, yields:
% 66.47/31.04 | (130) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_10_10) = v2 & aNaturalNumber0(all_0_11_11) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.47/31.04 |
% 66.47/31.04 | Instantiating formula (61) with all_0_10_10, all_0_11_11, xp, xm, xn and discharging atoms sdtpldt0(all_0_11_11, xp) = all_0_10_10, sdtpldt0(xn, xm) = all_0_11_11, yields:
% 66.47/31.04 | (131) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, v4) = v5 & doDivides0(xp, xm) = v8 & doDivides0(xp, xn) = v7 & iLess0(all_0_10_10, all_0_10_10) = v6 & sdtasdt0(xn, xm) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 66.47/31.04 |
% 66.47/31.04 | Instantiating formula (12) with all_0_10_10, all_0_11_11, xp, xm, xn and discharging atoms sdtpldt0(all_0_11_11, xp) = all_0_10_10, sdtpldt0(xn, xm) = all_0_11_11, yields:
% 66.47/31.04 | (132) ? [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_10_10))
% 66.47/31.04 |
% 66.47/31.04 | Instantiating formula (38) with all_0_11_11, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_11_11, yields:
% 66.47/31.04 | (133) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_11_11))
% 66.47/31.04 |
% 66.47/31.04 | Instantiating formula (34) with all_0_11_11, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_11_11, yields:
% 66.47/31.04 | (134) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_11_11) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.47/31.05 |
% 66.47/31.05 | Instantiating formula (3) with xr and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 66.47/31.05 | (135) xr = sz10 | xr = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xr) = 0 & aNaturalNumber0(v0) = 0)
% 66.47/31.05 |
% 66.47/31.05 | Instantiating formula (3) with xp and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 66.47/31.05 | (136) xp = sz10 | xp = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 66.47/31.05 |
% 66.47/31.05 | Instantiating formula (3) with xn and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 66.47/31.05 | (137) xn = sz10 | xn = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xn) = 0 & aNaturalNumber0(v0) = 0)
% 66.47/31.05 |
% 66.47/31.05 | Instantiating (134) with all_12_0_12, all_12_1_13, all_12_2_14 yields:
% 66.47/31.05 | (138) aNaturalNumber0(all_0_11_11) = all_12_0_12 & aNaturalNumber0(xm) = all_12_1_13 & aNaturalNumber0(xn) = all_12_2_14 & ( ~ (all_12_1_13 = 0) | ~ (all_12_2_14 = 0) | all_12_0_12 = 0)
% 66.47/31.05 |
% 66.47/31.05 | Applying alpha-rule on (138) yields:
% 66.47/31.05 | (139) aNaturalNumber0(all_0_11_11) = all_12_0_12
% 66.47/31.05 | (140) aNaturalNumber0(xm) = all_12_1_13
% 66.47/31.05 | (141) aNaturalNumber0(xn) = all_12_2_14
% 66.47/31.05 | (142) ~ (all_12_1_13 = 0) | ~ (all_12_2_14 = 0) | all_12_0_12 = 0
% 66.47/31.05 |
% 66.47/31.05 | Instantiating (130) with all_14_0_15, all_14_1_16, all_14_2_17 yields:
% 66.47/31.05 | (143) aNaturalNumber0(all_0_10_10) = all_14_0_15 & aNaturalNumber0(all_0_11_11) = all_14_2_17 & aNaturalNumber0(xp) = all_14_1_16 & ( ~ (all_14_1_16 = 0) | ~ (all_14_2_17 = 0) | all_14_0_15 = 0)
% 66.47/31.05 |
% 66.47/31.05 | Applying alpha-rule on (143) yields:
% 66.47/31.05 | (144) aNaturalNumber0(all_0_10_10) = all_14_0_15
% 66.47/31.05 | (145) aNaturalNumber0(all_0_11_11) = all_14_2_17
% 66.47/31.05 | (146) aNaturalNumber0(xp) = all_14_1_16
% 66.47/31.05 | (147) ~ (all_14_1_16 = 0) | ~ (all_14_2_17 = 0) | all_14_0_15 = 0
% 66.47/31.05 |
% 66.47/31.05 | Instantiating (118) with all_16_0_18, all_16_1_19, all_16_2_20 yields:
% 66.47/31.05 | (148) aNaturalNumber0(all_0_4_4) = all_16_0_18 & aNaturalNumber0(all_0_5_5) = all_16_2_20 & aNaturalNumber0(xm) = all_16_1_19 & ( ~ (all_16_1_19 = 0) | ~ (all_16_2_20 = 0) | all_16_0_18 = 0)
% 66.47/31.05 |
% 66.47/31.05 | Applying alpha-rule on (148) yields:
% 66.47/31.05 | (149) aNaturalNumber0(all_0_4_4) = all_16_0_18
% 66.47/31.05 | (150) aNaturalNumber0(all_0_5_5) = all_16_2_20
% 66.47/31.05 | (151) aNaturalNumber0(xm) = all_16_1_19
% 66.47/31.05 | (152) ~ (all_16_1_19 = 0) | ~ (all_16_2_20 = 0) | all_16_0_18 = 0
% 66.47/31.05 |
% 66.47/31.05 | Instantiating (117) with all_18_0_21, all_18_1_22, all_18_2_23 yields:
% 66.47/31.05 | (153) sdtasdt0(xm, all_0_5_5) = all_18_0_21 & aNaturalNumber0(all_0_5_5) = all_18_2_23 & aNaturalNumber0(xm) = all_18_1_22 & ( ~ (all_18_1_22 = 0) | ~ (all_18_2_23 = 0) | all_18_0_21 = all_0_4_4)
% 66.47/31.05 |
% 66.47/31.05 | Applying alpha-rule on (153) yields:
% 66.47/31.05 | (154) sdtasdt0(xm, all_0_5_5) = all_18_0_21
% 66.47/31.05 | (155) aNaturalNumber0(all_0_5_5) = all_18_2_23
% 66.47/31.05 | (156) aNaturalNumber0(xm) = all_18_1_22
% 66.47/31.05 | (157) ~ (all_18_1_22 = 0) | ~ (all_18_2_23 = 0) | all_18_0_21 = all_0_4_4
% 66.47/31.05 |
% 66.47/31.05 | Instantiating (116) with all_20_0_24, all_20_1_25, all_20_2_26, all_20_3_27, all_20_4_28 yields:
% 66.47/31.05 | (158) sdtasdt0(all_0_5_5, all_20_1_25) = all_20_0_24 & sdtasdt0(xm, xr) = all_20_1_25 & aNaturalNumber0(all_0_5_5) = all_20_4_28 & aNaturalNumber0(xr) = all_20_2_26 & aNaturalNumber0(xm) = all_20_3_27 & ( ~ (all_20_2_26 = 0) | ~ (all_20_3_27 = 0) | ~ (all_20_4_28 = 0) | all_20_0_24 = all_0_3_3)
% 66.47/31.05 |
% 66.47/31.05 | Applying alpha-rule on (158) yields:
% 66.47/31.05 | (159) aNaturalNumber0(all_0_5_5) = all_20_4_28
% 66.47/31.05 | (160) aNaturalNumber0(xr) = all_20_2_26
% 66.47/31.05 | (161) ~ (all_20_2_26 = 0) | ~ (all_20_3_27 = 0) | ~ (all_20_4_28 = 0) | all_20_0_24 = all_0_3_3
% 66.47/31.05 | (162) sdtasdt0(xm, xr) = all_20_1_25
% 66.47/31.05 | (163) aNaturalNumber0(xm) = all_20_3_27
% 66.47/31.05 | (164) sdtasdt0(all_0_5_5, all_20_1_25) = all_20_0_24
% 66.47/31.05 |
% 66.47/31.05 | Instantiating (115) with all_22_0_29, all_22_1_30, all_22_2_31 yields:
% 66.47/31.05 | (165) aNaturalNumber0(all_0_3_3) = all_22_0_29 & aNaturalNumber0(all_0_4_4) = all_22_2_31 & aNaturalNumber0(xr) = all_22_1_30 & ( ~ (all_22_1_30 = 0) | ~ (all_22_2_31 = 0) | all_22_0_29 = 0)
% 66.47/31.05 |
% 66.47/31.05 | Applying alpha-rule on (165) yields:
% 66.47/31.05 | (166) aNaturalNumber0(all_0_3_3) = all_22_0_29
% 66.47/31.05 | (167) aNaturalNumber0(all_0_4_4) = all_22_2_31
% 66.47/31.05 | (168) aNaturalNumber0(xr) = all_22_1_30
% 66.47/31.05 | (169) ~ (all_22_1_30 = 0) | ~ (all_22_2_31 = 0) | all_22_0_29 = 0
% 66.47/31.05 |
% 66.47/31.05 | Instantiating (114) with all_24_0_32, all_24_1_33, all_24_2_34 yields:
% 66.47/31.05 | (170) sdtasdt0(xr, all_0_4_4) = all_24_0_32 & aNaturalNumber0(all_0_4_4) = all_24_2_34 & aNaturalNumber0(xr) = all_24_1_33 & ( ~ (all_24_1_33 = 0) | ~ (all_24_2_34 = 0) | all_24_0_32 = all_0_3_3)
% 66.47/31.05 |
% 66.47/31.05 | Applying alpha-rule on (170) yields:
% 66.47/31.05 | (171) sdtasdt0(xr, all_0_4_4) = all_24_0_32
% 66.47/31.05 | (172) aNaturalNumber0(all_0_4_4) = all_24_2_34
% 66.47/31.05 | (173) aNaturalNumber0(xr) = all_24_1_33
% 66.47/31.05 | (174) ~ (all_24_1_33 = 0) | ~ (all_24_2_34 = 0) | all_24_0_32 = all_0_3_3
% 66.47/31.05 |
% 66.47/31.05 | Instantiating (113) with all_26_0_35, all_26_1_36, all_26_2_37 yields:
% 66.47/31.05 | (175) aNaturalNumber0(all_0_0_0) = all_26_0_35 & aNaturalNumber0(all_0_1_1) = all_26_2_37 & aNaturalNumber0(xr) = all_26_1_36 & ( ~ (all_26_1_36 = 0) | ~ (all_26_2_37 = 0) | all_26_0_35 = 0)
% 66.47/31.05 |
% 66.47/31.05 | Applying alpha-rule on (175) yields:
% 66.47/31.05 | (176) aNaturalNumber0(all_0_0_0) = all_26_0_35
% 66.47/31.05 | (177) aNaturalNumber0(all_0_1_1) = all_26_2_37
% 66.47/31.05 | (178) aNaturalNumber0(xr) = all_26_1_36
% 66.47/31.05 | (179) ~ (all_26_1_36 = 0) | ~ (all_26_2_37 = 0) | all_26_0_35 = 0
% 66.47/31.06 |
% 66.47/31.06 | Instantiating (112) with all_28_0_38, all_28_1_39, all_28_2_40 yields:
% 66.47/31.06 | (180) sdtasdt0(xr, all_0_1_1) = all_28_0_38 & aNaturalNumber0(all_0_1_1) = all_28_2_40 & aNaturalNumber0(xr) = all_28_1_39 & ( ~ (all_28_1_39 = 0) | ~ (all_28_2_40 = 0) | all_28_0_38 = all_0_0_0)
% 66.47/31.06 |
% 66.47/31.06 | Applying alpha-rule on (180) yields:
% 66.47/31.06 | (181) sdtasdt0(xr, all_0_1_1) = all_28_0_38
% 66.47/31.06 | (182) aNaturalNumber0(all_0_1_1) = all_28_2_40
% 66.47/31.06 | (183) aNaturalNumber0(xr) = all_28_1_39
% 66.47/31.06 | (184) ~ (all_28_1_39 = 0) | ~ (all_28_2_40 = 0) | all_28_0_38 = all_0_0_0
% 66.47/31.06 |
% 66.47/31.06 | Instantiating (109) with all_30_0_41, all_30_1_42, all_30_2_43 yields:
% 66.47/31.06 | (185) (all_30_0_41 = xp & all_30_1_42 = 0 & sdtpldt0(xk, all_30_2_43) = xp & aNaturalNumber0(all_30_2_43) = 0) | (aNaturalNumber0(xk) = all_30_2_43 & aNaturalNumber0(xp) = all_30_1_42 & ( ~ (all_30_1_42 = 0) | ~ (all_30_2_43 = 0)))
% 66.47/31.06 |
% 66.47/31.06 | Instantiating (107) with all_31_0_44, all_31_1_45, all_31_2_46 yields:
% 66.47/31.06 | (186) (all_31_0_44 = xk & all_31_1_45 = 0 & sdtpldt0(xr, all_31_2_46) = xk & aNaturalNumber0(all_31_2_46) = 0) | (aNaturalNumber0(xr) = all_31_2_46 & aNaturalNumber0(xk) = all_31_1_45 & ( ~ (all_31_1_45 = 0) | ~ (all_31_2_46 = 0)))
% 66.47/31.06 |
% 66.47/31.06 | Instantiating (104) with all_33_0_50, all_33_1_51, all_33_2_52 yields:
% 66.47/31.06 | (187) (all_33_0_50 = xn & all_33_1_51 = 0 & sdtasdt0(xr, all_33_2_52) = xn & aNaturalNumber0(all_33_2_52) = 0) | (aNaturalNumber0(xr) = all_33_2_52 & aNaturalNumber0(xn) = all_33_1_51 & ( ~ (all_33_1_51 = 0) | ~ (all_33_2_52 = 0)))
% 66.47/31.06 |
% 66.47/31.06 | Instantiating (129) with all_35_0_56, all_35_1_57, all_35_2_58 yields:
% 66.47/31.06 | (188) sdtpldt0(xp, all_0_11_11) = all_35_0_56 & aNaturalNumber0(all_0_11_11) = all_35_2_58 & aNaturalNumber0(xp) = all_35_1_57 & ( ~ (all_35_1_57 = 0) | ~ (all_35_2_58 = 0) | all_35_0_56 = all_0_10_10)
% 66.47/31.06 |
% 66.47/31.06 | Applying alpha-rule on (188) yields:
% 66.47/31.06 | (189) sdtpldt0(xp, all_0_11_11) = all_35_0_56
% 66.47/31.06 | (190) aNaturalNumber0(all_0_11_11) = all_35_2_58
% 66.47/31.06 | (191) aNaturalNumber0(xp) = all_35_1_57
% 66.47/31.06 | (192) ~ (all_35_1_57 = 0) | ~ (all_35_2_58 = 0) | all_35_0_56 = all_0_10_10
% 66.47/31.06 |
% 66.47/31.06 | Instantiating (102) with all_37_0_59, all_37_1_60, all_37_2_61 yields:
% 66.47/31.06 | (193) (all_37_0_59 = xk & all_37_1_60 = 0 & sdtasdt0(xr, all_37_2_61) = xk & aNaturalNumber0(all_37_2_61) = 0) | (aNaturalNumber0(xr) = all_37_2_61 & aNaturalNumber0(xk) = all_37_1_60 & ( ~ (all_37_1_60 = 0) | ~ (all_37_2_61 = 0)))
% 66.47/31.06 |
% 66.47/31.06 | Instantiating (101) with all_38_0_62, all_38_1_63, all_38_2_64 yields:
% 66.47/31.06 | (194) (all_38_0_62 = all_0_9_9 & all_38_1_63 = 0 & sdtasdt0(xr, all_38_2_64) = all_0_9_9 & aNaturalNumber0(all_38_2_64) = 0) | (aNaturalNumber0(all_0_9_9) = all_38_1_63 & aNaturalNumber0(xr) = all_38_2_64 & ( ~ (all_38_1_63 = 0) | ~ (all_38_2_64 = 0)))
% 66.47/31.06 |
% 66.47/31.06 | Instantiating (133) with all_39_0_65, all_39_1_66, all_39_2_67 yields:
% 66.47/31.06 | (195) sdtpldt0(xm, xn) = all_39_0_65 & aNaturalNumber0(xm) = all_39_1_66 & aNaturalNumber0(xn) = all_39_2_67 & ( ~ (all_39_1_66 = 0) | ~ (all_39_2_67 = 0) | all_39_0_65 = all_0_11_11)
% 66.47/31.06 |
% 66.47/31.06 | Applying alpha-rule on (195) yields:
% 66.47/31.06 | (196) sdtpldt0(xm, xn) = all_39_0_65
% 66.47/31.06 | (197) aNaturalNumber0(xm) = all_39_1_66
% 66.47/31.06 | (198) aNaturalNumber0(xn) = all_39_2_67
% 66.47/31.06 | (199) ~ (all_39_1_66 = 0) | ~ (all_39_2_67 = 0) | all_39_0_65 = all_0_11_11
% 66.47/31.06 |
% 66.47/31.06 | Instantiating (132) with all_41_0_68, all_41_1_69, all_41_2_70, all_41_3_71, all_41_4_72 yields:
% 66.47/31.06 | (200) sdtpldt0(xm, xp) = all_41_1_69 & sdtpldt0(xn, all_41_1_69) = all_41_0_68 & aNaturalNumber0(xp) = all_41_2_70 & aNaturalNumber0(xm) = all_41_3_71 & aNaturalNumber0(xn) = all_41_4_72 & ( ~ (all_41_2_70 = 0) | ~ (all_41_3_71 = 0) | ~ (all_41_4_72 = 0) | all_41_0_68 = all_0_10_10)
% 66.47/31.06 |
% 66.47/31.06 | Applying alpha-rule on (200) yields:
% 66.47/31.06 | (201) sdtpldt0(xn, all_41_1_69) = all_41_0_68
% 66.47/31.06 | (202) sdtpldt0(xm, xp) = all_41_1_69
% 66.47/31.06 | (203) aNaturalNumber0(xn) = all_41_4_72
% 66.47/31.06 | (204) ~ (all_41_2_70 = 0) | ~ (all_41_3_71 = 0) | ~ (all_41_4_72 = 0) | all_41_0_68 = all_0_10_10
% 66.47/31.06 | (205) aNaturalNumber0(xp) = all_41_2_70
% 66.47/31.06 | (206) aNaturalNumber0(xm) = all_41_3_71
% 66.47/31.06 |
% 66.47/31.06 | Instantiating (128) with all_43_0_73, all_43_1_74, all_43_2_75 yields:
% 66.47/31.06 | (207) aNaturalNumber0(all_0_9_9) = all_43_0_73 & aNaturalNumber0(xm) = all_43_1_74 & aNaturalNumber0(xn) = all_43_2_75 & ( ~ (all_43_1_74 = 0) | ~ (all_43_2_75 = 0) | all_43_0_73 = 0)
% 66.47/31.06 |
% 66.47/31.06 | Applying alpha-rule on (207) yields:
% 66.47/31.06 | (208) aNaturalNumber0(all_0_9_9) = all_43_0_73
% 66.47/31.06 | (209) aNaturalNumber0(xm) = all_43_1_74
% 66.47/31.06 | (210) aNaturalNumber0(xn) = all_43_2_75
% 66.47/31.06 | (211) ~ (all_43_1_74 = 0) | ~ (all_43_2_75 = 0) | all_43_0_73 = 0
% 66.47/31.06 |
% 66.47/31.06 | Instantiating (111) with all_45_0_76, all_45_1_77, all_45_2_78 yields:
% 66.47/31.06 | (212) (all_45_0_76 = xp & all_45_1_77 = 0 & sdtpldt0(xn, all_45_2_78) = xp & aNaturalNumber0(all_45_2_78) = 0) | (aNaturalNumber0(xp) = all_45_1_77 & aNaturalNumber0(xn) = all_45_2_78 & ( ~ (all_45_1_77 = 0) | ~ (all_45_2_78 = 0)))
% 66.47/31.06 |
% 66.47/31.06 | Instantiating (110) with all_46_0_79, all_46_1_80, all_46_2_81 yields:
% 66.47/31.06 | (213) (all_46_0_79 = xp & all_46_1_80 = 0 & sdtpldt0(xm, all_46_2_81) = xp & aNaturalNumber0(all_46_2_81) = 0) | (aNaturalNumber0(xp) = all_46_1_80 & aNaturalNumber0(xm) = all_46_2_81 & ( ~ (all_46_1_80 = 0) | ~ (all_46_2_81 = 0)))
% 66.47/31.06 |
% 66.47/31.06 | Instantiating (127) with all_47_0_82, all_47_1_83, all_47_2_84 yields:
% 66.47/31.06 | (214) sdtasdt0(xm, xn) = all_47_0_82 & aNaturalNumber0(xm) = all_47_1_83 & aNaturalNumber0(xn) = all_47_2_84 & ( ~ (all_47_1_83 = 0) | ~ (all_47_2_84 = 0) | all_47_0_82 = all_0_9_9)
% 66.47/31.06 |
% 66.47/31.06 | Applying alpha-rule on (214) yields:
% 66.47/31.06 | (215) sdtasdt0(xm, xn) = all_47_0_82
% 66.47/31.06 | (216) aNaturalNumber0(xm) = all_47_1_83
% 66.47/31.06 | (217) aNaturalNumber0(xn) = all_47_2_84
% 66.47/31.06 | (218) ~ (all_47_1_83 = 0) | ~ (all_47_2_84 = 0) | all_47_0_82 = all_0_9_9
% 66.47/31.06 |
% 66.47/31.06 | Instantiating (124) with all_49_0_85, all_49_1_86, all_49_2_87 yields:
% 66.47/31.06 | (219) aNaturalNumber0(all_0_2_2) = all_49_0_85 & aNaturalNumber0(xk) = all_49_1_86 & aNaturalNumber0(xp) = all_49_2_87 & ( ~ (all_49_1_86 = 0) | ~ (all_49_2_87 = 0) | all_49_0_85 = 0)
% 66.47/31.06 |
% 66.47/31.06 | Applying alpha-rule on (219) yields:
% 66.47/31.06 | (220) aNaturalNumber0(all_0_2_2) = all_49_0_85
% 66.47/31.06 | (221) aNaturalNumber0(xk) = all_49_1_86
% 66.82/31.06 | (222) aNaturalNumber0(xp) = all_49_2_87
% 66.82/31.06 | (223) ~ (all_49_1_86 = 0) | ~ (all_49_2_87 = 0) | all_49_0_85 = 0
% 66.82/31.06 |
% 66.82/31.06 | Instantiating (123) with all_51_0_88, all_51_1_89, all_51_2_90 yields:
% 66.82/31.06 | (224) sdtasdt0(xk, xp) = all_51_0_88 & aNaturalNumber0(xk) = all_51_1_89 & aNaturalNumber0(xp) = all_51_2_90 & ( ~ (all_51_1_89 = 0) | ~ (all_51_2_90 = 0) | all_51_0_88 = all_0_2_2)
% 66.82/31.06 |
% 66.82/31.06 | Applying alpha-rule on (224) yields:
% 66.82/31.06 | (225) sdtasdt0(xk, xp) = all_51_0_88
% 66.82/31.06 | (226) aNaturalNumber0(xk) = all_51_1_89
% 66.82/31.07 | (227) aNaturalNumber0(xp) = all_51_2_90
% 66.82/31.07 | (228) ~ (all_51_1_89 = 0) | ~ (all_51_2_90 = 0) | all_51_0_88 = all_0_2_2
% 66.82/31.07 |
% 66.82/31.07 | Instantiating (131) with all_53_0_91, all_53_1_92, all_53_2_93, all_53_3_94, all_53_4_95, all_53_5_96, all_53_6_97, all_53_7_98, all_53_8_99 yields:
% 66.82/31.07 | (229) isPrime0(xp) = all_53_5_96 & doDivides0(xp, all_53_4_95) = all_53_3_94 & doDivides0(xp, xm) = all_53_0_91 & doDivides0(xp, xn) = all_53_1_92 & iLess0(all_0_10_10, all_0_10_10) = all_53_2_93 & sdtasdt0(xn, xm) = all_53_4_95 & aNaturalNumber0(xp) = all_53_6_97 & aNaturalNumber0(xm) = all_53_7_98 & aNaturalNumber0(xn) = all_53_8_99 & ( ~ (all_53_2_93 = 0) | ~ (all_53_3_94 = 0) | ~ (all_53_5_96 = 0) | ~ (all_53_6_97 = 0) | ~ (all_53_7_98 = 0) | ~ (all_53_8_99 = 0) | all_53_0_91 = 0 | all_53_1_92 = 0)
% 66.82/31.07 |
% 66.82/31.07 | Applying alpha-rule on (229) yields:
% 66.82/31.07 | (230) sdtasdt0(xn, xm) = all_53_4_95
% 66.82/31.07 | (231) ~ (all_53_2_93 = 0) | ~ (all_53_3_94 = 0) | ~ (all_53_5_96 = 0) | ~ (all_53_6_97 = 0) | ~ (all_53_7_98 = 0) | ~ (all_53_8_99 = 0) | all_53_0_91 = 0 | all_53_1_92 = 0
% 66.82/31.07 | (232) isPrime0(xp) = all_53_5_96
% 66.82/31.07 | (233) doDivides0(xp, xn) = all_53_1_92
% 66.82/31.07 | (234) aNaturalNumber0(xn) = all_53_8_99
% 66.82/31.07 | (235) doDivides0(xp, all_53_4_95) = all_53_3_94
% 66.82/31.07 | (236) iLess0(all_0_10_10, all_0_10_10) = all_53_2_93
% 66.82/31.07 | (237) aNaturalNumber0(xm) = all_53_7_98
% 66.83/31.07 | (238) doDivides0(xp, xm) = all_53_0_91
% 66.83/31.07 | (239) aNaturalNumber0(xp) = all_53_6_97
% 66.83/31.07 |
% 66.83/31.07 +-Applying beta-rule and splitting (108), into two cases.
% 66.83/31.07 |-Branch one:
% 66.83/31.07 | (240) xk = xp
% 66.83/31.07 |
% 66.83/31.07 | Equations (240) can reduce 80 to:
% 66.83/31.07 | (241) $false
% 66.83/31.07 |
% 66.83/31.07 |-The branch is then unsatisfiable
% 66.83/31.07 |-Branch two:
% 66.83/31.07 | (80) ~ (xk = xp)
% 66.83/31.07 | (243) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, xk) = v2 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 66.83/31.07 |
% 66.83/31.07 | Instantiating (243) with all_59_0_100, all_59_1_101, all_59_2_102 yields:
% 66.83/31.07 | (244) sdtlseqdt0(xp, xk) = all_59_0_100 & aNaturalNumber0(xk) = all_59_2_102 & aNaturalNumber0(xp) = all_59_1_101 & ( ~ (all_59_0_100 = 0) | ~ (all_59_1_101 = 0) | ~ (all_59_2_102 = 0))
% 66.83/31.07 |
% 66.83/31.07 | Applying alpha-rule on (244) yields:
% 66.83/31.07 | (245) sdtlseqdt0(xp, xk) = all_59_0_100
% 66.83/31.07 | (246) aNaturalNumber0(xk) = all_59_2_102
% 66.83/31.07 | (247) aNaturalNumber0(xp) = all_59_1_101
% 66.83/31.07 | (248) ~ (all_59_0_100 = 0) | ~ (all_59_1_101 = 0) | ~ (all_59_2_102 = 0)
% 66.83/31.07 |
% 66.83/31.07 +-Applying beta-rule and splitting (106), into two cases.
% 66.83/31.07 |-Branch one:
% 66.83/31.07 | (249) all_0_5_5 = xn
% 66.83/31.07 |
% 66.83/31.07 | Equations (249) can reduce 5 to:
% 66.83/31.07 | (241) $false
% 66.83/31.07 |
% 66.83/31.07 |-The branch is then unsatisfiable
% 66.83/31.07 |-Branch two:
% 66.83/31.07 | (5) ~ (all_0_5_5 = xn)
% 66.83/31.07 | (252) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xn, all_0_5_5) = v2 & aNaturalNumber0(all_0_5_5) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 66.83/31.07 |
% 66.83/31.07 | Instantiating (252) with all_64_0_103, all_64_1_104, all_64_2_105 yields:
% 66.83/31.07 | (253) sdtlseqdt0(xn, all_0_5_5) = all_64_0_103 & aNaturalNumber0(all_0_5_5) = all_64_2_105 & aNaturalNumber0(xn) = all_64_1_104 & ( ~ (all_64_0_103 = 0) | ~ (all_64_1_104 = 0) | ~ (all_64_2_105 = 0))
% 66.83/31.07 |
% 66.83/31.07 | Applying alpha-rule on (253) yields:
% 66.83/31.07 | (254) sdtlseqdt0(xn, all_0_5_5) = all_64_0_103
% 66.83/31.07 | (255) aNaturalNumber0(all_0_5_5) = all_64_2_105
% 66.83/31.07 | (256) aNaturalNumber0(xn) = all_64_1_104
% 66.83/31.07 | (257) ~ (all_64_0_103 = 0) | ~ (all_64_1_104 = 0) | ~ (all_64_2_105 = 0)
% 66.83/31.07 |
% 66.83/31.07 +-Applying beta-rule and splitting (121), into two cases.
% 66.83/31.07 |-Branch one:
% 66.83/31.07 | (258) xp = sz00
% 66.83/31.07 |
% 66.83/31.07 | Equations (258) can reduce 99 to:
% 66.83/31.07 | (241) $false
% 66.83/31.07 |
% 66.83/31.07 |-The branch is then unsatisfiable
% 66.83/31.07 |-Branch two:
% 66.83/31.07 | (99) ~ (xp = sz00)
% 66.83/31.07 | (261) ? [v0] : ? [v1] : ? [v2] : ((v0 = 0 & aNaturalNumber0(xk) = 0) | (doDivides0(xp, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 66.83/31.07 |
% 66.83/31.07 | Instantiating (261) with all_69_0_106, all_69_1_107, all_69_2_108 yields:
% 66.83/31.07 | (262) (all_69_2_108 = 0 & aNaturalNumber0(xk) = 0) | (doDivides0(xp, all_0_9_9) = all_69_0_106 & aNaturalNumber0(all_0_9_9) = all_69_1_107 & aNaturalNumber0(xp) = all_69_2_108 & ( ~ (all_69_0_106 = 0) | ~ (all_69_1_107 = 0) | ~ (all_69_2_108 = 0)))
% 66.83/31.07 |
% 66.83/31.07 +-Applying beta-rule and splitting (135), into two cases.
% 66.83/31.07 |-Branch one:
% 66.83/31.07 | (263) xr = sz00
% 66.83/31.07 |
% 66.83/31.07 | Equations (263) can reduce 98 to:
% 66.83/31.07 | (241) $false
% 66.83/31.07 |
% 66.83/31.07 |-The branch is then unsatisfiable
% 66.83/31.07 |-Branch two:
% 66.83/31.07 | (98) ~ (xr = sz00)
% 66.83/31.07 | (266) xr = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xr) = 0 & aNaturalNumber0(v0) = 0)
% 66.83/31.07 |
% 66.83/31.07 +-Applying beta-rule and splitting (136), into two cases.
% 66.83/31.07 |-Branch one:
% 66.83/31.07 | (258) xp = sz00
% 66.83/31.07 |
% 66.83/31.07 | Equations (258) can reduce 99 to:
% 66.83/31.07 | (241) $false
% 66.83/31.07 |
% 66.83/31.07 |-The branch is then unsatisfiable
% 66.83/31.07 |-Branch two:
% 66.83/31.07 | (99) ~ (xp = sz00)
% 66.83/31.07 | (270) xp = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 66.83/31.07 |
% 66.83/31.07 +-Applying beta-rule and splitting (266), into two cases.
% 66.83/31.07 |-Branch one:
% 66.83/31.07 | (271) xr = sz10
% 66.83/31.07 |
% 66.83/31.07 | Equations (271) can reduce 96 to:
% 66.83/31.07 | (241) $false
% 66.83/31.07 |
% 66.83/31.07 |-The branch is then unsatisfiable
% 66.83/31.07 |-Branch two:
% 66.83/31.07 | (96) ~ (xr = sz10)
% 66.83/31.07 | (274) ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xr) = 0 & aNaturalNumber0(v0) = 0)
% 66.83/31.07 |
% 66.83/31.07 | Instantiating (274) with all_80_0_109 yields:
% 66.83/31.07 | (275) isPrime0(all_80_0_109) = 0 & doDivides0(all_80_0_109, xr) = 0 & aNaturalNumber0(all_80_0_109) = 0
% 66.83/31.07 |
% 66.83/31.07 | Applying alpha-rule on (275) yields:
% 66.83/31.07 | (276) isPrime0(all_80_0_109) = 0
% 66.83/31.07 | (277) doDivides0(all_80_0_109, xr) = 0
% 66.83/31.07 | (278) aNaturalNumber0(all_80_0_109) = 0
% 66.83/31.07 |
% 66.83/31.07 +-Applying beta-rule and splitting (270), into two cases.
% 66.83/31.07 |-Branch one:
% 66.83/31.07 | (279) xp = sz10
% 66.83/31.07 |
% 66.83/31.07 | Equations (279) can reduce 97 to:
% 66.83/31.07 | (241) $false
% 66.83/31.07 |
% 66.83/31.07 |-The branch is then unsatisfiable
% 66.83/31.07 |-Branch two:
% 66.83/31.07 | (97) ~ (xp = sz10)
% 66.83/31.07 | (282) ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 66.83/31.07 |
% 66.83/31.07 | Instantiating (282) with all_85_0_110 yields:
% 66.83/31.07 | (283) isPrime0(all_85_0_110) = 0 & doDivides0(all_85_0_110, xp) = 0 & aNaturalNumber0(all_85_0_110) = 0
% 66.83/31.07 |
% 66.83/31.07 | Applying alpha-rule on (283) yields:
% 66.83/31.07 | (284) isPrime0(all_85_0_110) = 0
% 66.83/31.07 | (285) doDivides0(all_85_0_110, xp) = 0
% 66.83/31.07 | (286) aNaturalNumber0(all_85_0_110) = 0
% 66.83/31.07 |
% 66.83/31.07 | Instantiating formula (19) with xp, all_0_9_9, all_53_3_94, 0 and discharging atoms doDivides0(xp, all_0_9_9) = 0, yields:
% 66.83/31.07 | (287) all_53_3_94 = 0 | ~ (doDivides0(xp, all_0_9_9) = all_53_3_94)
% 66.83/31.07 |
% 66.83/31.07 | Instantiating formula (77) with xn, xm, all_53_4_95, all_0_9_9 and discharging atoms sdtasdt0(xn, xm) = all_53_4_95, sdtasdt0(xn, xm) = all_0_9_9, yields:
% 66.83/31.08 | (288) all_53_4_95 = all_0_9_9
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with all_0_2_2, all_49_0_85, 0 and discharging atoms aNaturalNumber0(all_0_2_2) = all_49_0_85, yields:
% 66.83/31.08 | (289) all_49_0_85 = 0 | ~ (aNaturalNumber0(all_0_2_2) = 0)
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with all_0_4_4, all_22_2_31, all_24_2_34 and discharging atoms aNaturalNumber0(all_0_4_4) = all_24_2_34, aNaturalNumber0(all_0_4_4) = all_22_2_31, yields:
% 66.83/31.08 | (290) all_24_2_34 = all_22_2_31
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with all_0_4_4, all_16_0_18, all_24_2_34 and discharging atoms aNaturalNumber0(all_0_4_4) = all_24_2_34, aNaturalNumber0(all_0_4_4) = all_16_0_18, yields:
% 66.83/31.08 | (291) all_24_2_34 = all_16_0_18
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with all_0_5_5, all_20_4_28, all_64_2_105 and discharging atoms aNaturalNumber0(all_0_5_5) = all_64_2_105, aNaturalNumber0(all_0_5_5) = all_20_4_28, yields:
% 66.83/31.08 | (292) all_64_2_105 = all_20_4_28
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with all_0_5_5, all_18_2_23, all_64_2_105 and discharging atoms aNaturalNumber0(all_0_5_5) = all_64_2_105, aNaturalNumber0(all_0_5_5) = all_18_2_23, yields:
% 66.83/31.08 | (293) all_64_2_105 = all_18_2_23
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with all_0_5_5, all_16_2_20, all_64_2_105 and discharging atoms aNaturalNumber0(all_0_5_5) = all_64_2_105, aNaturalNumber0(all_0_5_5) = all_16_2_20, yields:
% 66.83/31.08 | (294) all_64_2_105 = all_16_2_20
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with all_0_11_11, all_12_0_12, all_35_2_58 and discharging atoms aNaturalNumber0(all_0_11_11) = all_35_2_58, aNaturalNumber0(all_0_11_11) = all_12_0_12, yields:
% 66.83/31.08 | (295) all_35_2_58 = all_12_0_12
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xr, all_28_1_39, 0 and discharging atoms aNaturalNumber0(xr) = all_28_1_39, aNaturalNumber0(xr) = 0, yields:
% 66.83/31.08 | (296) all_28_1_39 = 0
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xr, all_26_1_36, all_28_1_39 and discharging atoms aNaturalNumber0(xr) = all_28_1_39, aNaturalNumber0(xr) = all_26_1_36, yields:
% 66.83/31.08 | (297) all_28_1_39 = all_26_1_36
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xr, all_24_1_33, all_28_1_39 and discharging atoms aNaturalNumber0(xr) = all_28_1_39, aNaturalNumber0(xr) = all_24_1_33, yields:
% 66.83/31.08 | (298) all_28_1_39 = all_24_1_33
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xr, all_22_1_30, all_28_1_39 and discharging atoms aNaturalNumber0(xr) = all_28_1_39, aNaturalNumber0(xr) = all_22_1_30, yields:
% 66.83/31.08 | (299) all_28_1_39 = all_22_1_30
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xr, all_20_2_26, all_24_1_33 and discharging atoms aNaturalNumber0(xr) = all_24_1_33, aNaturalNumber0(xr) = all_20_2_26, yields:
% 66.83/31.08 | (300) all_24_1_33 = all_20_2_26
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xk, all_59_2_102, all_28_1_39 and discharging atoms aNaturalNumber0(xk) = all_59_2_102, yields:
% 66.83/31.08 | (301) all_59_2_102 = all_28_1_39 | ~ (aNaturalNumber0(xk) = all_28_1_39)
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xk, all_51_1_89, all_59_2_102 and discharging atoms aNaturalNumber0(xk) = all_59_2_102, aNaturalNumber0(xk) = all_51_1_89, yields:
% 66.83/31.08 | (302) all_59_2_102 = all_51_1_89
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xk, all_49_1_86, all_59_2_102 and discharging atoms aNaturalNumber0(xk) = all_59_2_102, aNaturalNumber0(xk) = all_49_1_86, yields:
% 66.83/31.08 | (303) all_59_2_102 = all_49_1_86
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xp, all_53_6_97, all_59_1_101 and discharging atoms aNaturalNumber0(xp) = all_59_1_101, aNaturalNumber0(xp) = all_53_6_97, yields:
% 66.83/31.08 | (304) all_59_1_101 = all_53_6_97
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xp, all_51_2_90, all_59_1_101 and discharging atoms aNaturalNumber0(xp) = all_59_1_101, aNaturalNumber0(xp) = all_51_2_90, yields:
% 66.83/31.08 | (305) all_59_1_101 = all_51_2_90
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xp, all_49_2_87, 0 and discharging atoms aNaturalNumber0(xp) = all_49_2_87, aNaturalNumber0(xp) = 0, yields:
% 66.83/31.08 | (306) all_49_2_87 = 0
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xp, all_49_2_87, all_53_6_97 and discharging atoms aNaturalNumber0(xp) = all_53_6_97, aNaturalNumber0(xp) = all_49_2_87, yields:
% 66.83/31.08 | (307) all_53_6_97 = all_49_2_87
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xp, all_41_2_70, all_53_6_97 and discharging atoms aNaturalNumber0(xp) = all_53_6_97, aNaturalNumber0(xp) = all_41_2_70, yields:
% 66.83/31.08 | (308) all_53_6_97 = all_41_2_70
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xp, all_35_1_57, all_53_6_97 and discharging atoms aNaturalNumber0(xp) = all_53_6_97, aNaturalNumber0(xp) = all_35_1_57, yields:
% 66.83/31.08 | (309) all_53_6_97 = all_35_1_57
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xp, all_14_1_16, all_35_1_57 and discharging atoms aNaturalNumber0(xp) = all_35_1_57, aNaturalNumber0(xp) = all_14_1_16, yields:
% 66.83/31.08 | (310) all_35_1_57 = all_14_1_16
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xm, all_53_7_98, 0 and discharging atoms aNaturalNumber0(xm) = all_53_7_98, aNaturalNumber0(xm) = 0, yields:
% 66.83/31.08 | (311) all_53_7_98 = 0
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xm, all_47_1_83, all_53_7_98 and discharging atoms aNaturalNumber0(xm) = all_53_7_98, aNaturalNumber0(xm) = all_47_1_83, yields:
% 66.83/31.08 | (312) all_53_7_98 = all_47_1_83
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xm, all_43_1_74, all_53_7_98 and discharging atoms aNaturalNumber0(xm) = all_53_7_98, aNaturalNumber0(xm) = all_43_1_74, yields:
% 66.83/31.08 | (313) all_53_7_98 = all_43_1_74
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xm, all_41_3_71, all_43_1_74 and discharging atoms aNaturalNumber0(xm) = all_43_1_74, aNaturalNumber0(xm) = all_41_3_71, yields:
% 66.83/31.08 | (314) all_43_1_74 = all_41_3_71
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xm, all_39_1_66, all_43_1_74 and discharging atoms aNaturalNumber0(xm) = all_43_1_74, aNaturalNumber0(xm) = all_39_1_66, yields:
% 66.83/31.08 | (315) all_43_1_74 = all_39_1_66
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xm, all_20_3_27, all_39_1_66 and discharging atoms aNaturalNumber0(xm) = all_39_1_66, aNaturalNumber0(xm) = all_20_3_27, yields:
% 66.83/31.08 | (316) all_39_1_66 = all_20_3_27
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xm, all_18_1_22, all_20_3_27 and discharging atoms aNaturalNumber0(xm) = all_20_3_27, aNaturalNumber0(xm) = all_18_1_22, yields:
% 66.83/31.08 | (317) all_20_3_27 = all_18_1_22
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xm, all_16_1_19, all_18_1_22 and discharging atoms aNaturalNumber0(xm) = all_18_1_22, aNaturalNumber0(xm) = all_16_1_19, yields:
% 66.83/31.08 | (318) all_18_1_22 = all_16_1_19
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xm, all_12_1_13, all_16_1_19 and discharging atoms aNaturalNumber0(xm) = all_16_1_19, aNaturalNumber0(xm) = all_12_1_13, yields:
% 66.83/31.08 | (319) all_16_1_19 = all_12_1_13
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xn, all_53_8_99, all_64_1_104 and discharging atoms aNaturalNumber0(xn) = all_64_1_104, aNaturalNumber0(xn) = all_53_8_99, yields:
% 66.83/31.08 | (320) all_64_1_104 = all_53_8_99
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xn, all_47_2_84, all_64_1_104 and discharging atoms aNaturalNumber0(xn) = all_64_1_104, aNaturalNumber0(xn) = all_47_2_84, yields:
% 66.83/31.08 | (321) all_64_1_104 = all_47_2_84
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xn, all_43_2_75, all_64_1_104 and discharging atoms aNaturalNumber0(xn) = all_64_1_104, aNaturalNumber0(xn) = all_43_2_75, yields:
% 66.83/31.08 | (322) all_64_1_104 = all_43_2_75
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xn, all_41_4_72, 0 and discharging atoms aNaturalNumber0(xn) = all_41_4_72, aNaturalNumber0(xn) = 0, yields:
% 66.83/31.08 | (323) all_41_4_72 = 0
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xn, all_41_4_72, all_64_1_104 and discharging atoms aNaturalNumber0(xn) = all_64_1_104, aNaturalNumber0(xn) = all_41_4_72, yields:
% 66.83/31.08 | (324) all_64_1_104 = all_41_4_72
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xn, all_39_2_67, all_64_1_104 and discharging atoms aNaturalNumber0(xn) = all_64_1_104, aNaturalNumber0(xn) = all_39_2_67, yields:
% 66.83/31.08 | (325) all_64_1_104 = all_39_2_67
% 66.83/31.08 |
% 66.83/31.08 | Instantiating formula (63) with xn, all_12_2_14, all_41_4_72 and discharging atoms aNaturalNumber0(xn) = all_41_4_72, aNaturalNumber0(xn) = all_12_2_14, yields:
% 66.83/31.08 | (326) all_41_4_72 = all_12_2_14
% 66.83/31.08 |
% 66.83/31.08 | Combining equations (324,320) yields a new equation:
% 66.83/31.08 | (327) all_53_8_99 = all_41_4_72
% 66.83/31.08 |
% 66.83/31.08 | Combining equations (325,320) yields a new equation:
% 66.83/31.08 | (328) all_53_8_99 = all_39_2_67
% 66.83/31.08 |
% 66.83/31.08 | Combining equations (321,320) yields a new equation:
% 66.83/31.08 | (329) all_53_8_99 = all_47_2_84
% 66.83/31.08 |
% 66.83/31.08 | Combining equations (322,320) yields a new equation:
% 66.83/31.08 | (330) all_53_8_99 = all_43_2_75
% 66.83/31.08 |
% 66.83/31.08 | Combining equations (294,292) yields a new equation:
% 66.83/31.08 | (331) all_20_4_28 = all_16_2_20
% 66.83/31.08 |
% 66.83/31.08 | Combining equations (293,292) yields a new equation:
% 66.83/31.08 | (332) all_20_4_28 = all_18_2_23
% 66.83/31.08 |
% 66.83/31.08 | Combining equations (304,305) yields a new equation:
% 66.83/31.08 | (333) all_53_6_97 = all_51_2_90
% 66.83/31.08 |
% 66.83/31.08 | Simplifying 333 yields:
% 66.83/31.08 | (334) all_53_6_97 = all_51_2_90
% 66.83/31.08 |
% 66.83/31.08 | Combining equations (302,303) yields a new equation:
% 66.83/31.08 | (335) all_51_1_89 = all_49_1_86
% 66.83/31.08 |
% 66.83/31.08 | Simplifying 335 yields:
% 66.83/31.08 | (336) all_51_1_89 = all_49_1_86
% 66.83/31.08 |
% 66.83/31.08 | Combining equations (308,334) yields a new equation:
% 66.83/31.08 | (337) all_51_2_90 = all_41_2_70
% 66.83/31.08 |
% 66.83/31.08 | Combining equations (309,334) yields a new equation:
% 66.83/31.08 | (338) all_51_2_90 = all_35_1_57
% 66.83/31.08 |
% 66.83/31.08 | Combining equations (307,334) yields a new equation:
% 66.83/31.08 | (339) all_51_2_90 = all_49_2_87
% 66.83/31.08 |
% 66.83/31.08 | Combining equations (313,312) yields a new equation:
% 66.83/31.08 | (340) all_47_1_83 = all_43_1_74
% 66.83/31.08 |
% 66.83/31.08 | Combining equations (311,312) yields a new equation:
% 66.83/31.08 | (341) all_47_1_83 = 0
% 66.83/31.08 |
% 66.83/31.08 | Combining equations (328,329) yields a new equation:
% 66.83/31.08 | (342) all_47_2_84 = all_39_2_67
% 66.83/31.08 |
% 66.83/31.08 | Combining equations (330,329) yields a new equation:
% 66.83/31.08 | (343) all_47_2_84 = all_43_2_75
% 66.83/31.08 |
% 66.83/31.08 | Combining equations (327,329) yields a new equation:
% 66.83/31.08 | (344) all_47_2_84 = all_41_4_72
% 66.83/31.08 |
% 66.83/31.08 | Combining equations (338,337) yields a new equation:
% 66.83/31.08 | (345) all_41_2_70 = all_35_1_57
% 66.83/31.08 |
% 66.83/31.08 | Combining equations (339,337) yields a new equation:
% 66.83/31.08 | (346) all_49_2_87 = all_41_2_70
% 66.83/31.08 |
% 66.83/31.08 | Simplifying 346 yields:
% 66.83/31.08 | (347) all_49_2_87 = all_41_2_70
% 66.83/31.08 |
% 66.83/31.09 | Combining equations (347,306) yields a new equation:
% 66.83/31.09 | (348) all_41_2_70 = 0
% 66.83/31.09 |
% 66.83/31.09 | Simplifying 348 yields:
% 66.83/31.09 | (349) all_41_2_70 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (340,341) yields a new equation:
% 66.83/31.09 | (350) all_43_1_74 = 0
% 66.83/31.09 |
% 66.83/31.09 | Simplifying 350 yields:
% 66.83/31.09 | (351) all_43_1_74 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (344,343) yields a new equation:
% 66.83/31.09 | (352) all_43_2_75 = all_41_4_72
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (342,343) yields a new equation:
% 66.83/31.09 | (353) all_43_2_75 = all_39_2_67
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (315,314) yields a new equation:
% 66.83/31.09 | (354) all_41_3_71 = all_39_1_66
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (351,314) yields a new equation:
% 66.83/31.09 | (355) all_41_3_71 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (352,353) yields a new equation:
% 66.83/31.09 | (356) all_41_4_72 = all_39_2_67
% 66.83/31.09 |
% 66.83/31.09 | Simplifying 356 yields:
% 66.83/31.09 | (357) all_41_4_72 = all_39_2_67
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (345,349) yields a new equation:
% 66.83/31.09 | (358) all_35_1_57 = 0
% 66.83/31.09 |
% 66.83/31.09 | Simplifying 358 yields:
% 66.83/31.09 | (359) all_35_1_57 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (354,355) yields a new equation:
% 66.83/31.09 | (360) all_39_1_66 = 0
% 66.83/31.09 |
% 66.83/31.09 | Simplifying 360 yields:
% 66.83/31.09 | (361) all_39_1_66 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (323,357) yields a new equation:
% 66.83/31.09 | (362) all_39_2_67 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (326,357) yields a new equation:
% 66.83/31.09 | (363) all_39_2_67 = all_12_2_14
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (316,361) yields a new equation:
% 66.83/31.09 | (364) all_20_3_27 = 0
% 66.83/31.09 |
% 66.83/31.09 | Simplifying 364 yields:
% 66.83/31.09 | (365) all_20_3_27 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (362,363) yields a new equation:
% 66.83/31.09 | (366) all_12_2_14 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (310,359) yields a new equation:
% 66.83/31.09 | (367) all_14_1_16 = 0
% 66.83/31.09 |
% 66.83/31.09 | Simplifying 367 yields:
% 66.83/31.09 | (368) all_14_1_16 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (298,297) yields a new equation:
% 66.83/31.09 | (369) all_26_1_36 = all_24_1_33
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (296,297) yields a new equation:
% 66.83/31.09 | (370) all_26_1_36 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (299,297) yields a new equation:
% 66.83/31.09 | (371) all_26_1_36 = all_22_1_30
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (369,371) yields a new equation:
% 66.83/31.09 | (372) all_24_1_33 = all_22_1_30
% 66.83/31.09 |
% 66.83/31.09 | Simplifying 372 yields:
% 66.83/31.09 | (373) all_24_1_33 = all_22_1_30
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (370,371) yields a new equation:
% 66.83/31.09 | (374) all_22_1_30 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (373,300) yields a new equation:
% 66.83/31.09 | (375) all_22_1_30 = all_20_2_26
% 66.83/31.09 |
% 66.83/31.09 | Simplifying 375 yields:
% 66.83/31.09 | (376) all_22_1_30 = all_20_2_26
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (291,290) yields a new equation:
% 66.83/31.09 | (377) all_22_2_31 = all_16_0_18
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (374,376) yields a new equation:
% 66.83/31.09 | (378) all_20_2_26 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (317,365) yields a new equation:
% 66.83/31.09 | (379) all_18_1_22 = 0
% 66.83/31.09 |
% 66.83/31.09 | Simplifying 379 yields:
% 66.83/31.09 | (380) all_18_1_22 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (331,332) yields a new equation:
% 66.83/31.09 | (381) all_18_2_23 = all_16_2_20
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (318,380) yields a new equation:
% 66.83/31.09 | (382) all_16_1_19 = 0
% 66.83/31.09 |
% 66.83/31.09 | Simplifying 382 yields:
% 66.83/31.09 | (383) all_16_1_19 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (319,383) yields a new equation:
% 66.83/31.09 | (384) all_12_1_13 = 0
% 66.83/31.09 |
% 66.83/31.09 | Simplifying 384 yields:
% 66.83/31.09 | (385) all_12_1_13 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (378,376) yields a new equation:
% 66.83/31.09 | (374) all_22_1_30 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (377,290) yields a new equation:
% 66.83/31.09 | (291) all_24_2_34 = all_16_0_18
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (378,300) yields a new equation:
% 66.83/31.09 | (388) all_24_1_33 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (374,371) yields a new equation:
% 66.83/31.09 | (370) all_26_1_36 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (370,297) yields a new equation:
% 66.83/31.09 | (296) all_28_1_39 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (366,363) yields a new equation:
% 66.83/31.09 | (362) all_39_2_67 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (362,357) yields a new equation:
% 66.83/31.09 | (323) all_41_4_72 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (362,353) yields a new equation:
% 66.83/31.09 | (393) all_43_2_75 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (355,314) yields a new equation:
% 66.83/31.09 | (351) all_43_1_74 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (393,343) yields a new equation:
% 66.83/31.09 | (395) all_47_2_84 = 0
% 66.83/31.09 |
% 66.83/31.09 | Combining equations (349,337) yields a new equation:
% 66.83/31.09 | (396) all_51_2_90 = 0
% 66.83/31.09 |
% 66.83/31.09 | From (288) and (235) follows:
% 66.83/31.09 | (397) doDivides0(xp, all_0_9_9) = all_53_3_94
% 66.83/31.09 |
% 66.83/31.09 | From (288) and (230) follows:
% 66.83/31.09 | (90) sdtasdt0(xn, xm) = all_0_9_9
% 66.83/31.09 |
% 66.83/31.09 | From (381) and (155) follows:
% 66.83/31.09 | (150) aNaturalNumber0(all_0_5_5) = all_16_2_20
% 66.83/31.09 |
% 66.83/31.09 | From (378) and (160) follows:
% 66.83/31.09 | (62) aNaturalNumber0(xr) = 0
% 66.83/31.09 |
% 66.83/31.09 | From (368) and (146) follows:
% 66.83/31.09 | (41) aNaturalNumber0(xp) = 0
% 66.83/31.09 |
% 66.83/31.09 | From (385) and (140) follows:
% 66.83/31.09 | (55) aNaturalNumber0(xm) = 0
% 66.83/31.09 |
% 66.83/31.09 | From (366) and (141) follows:
% 66.83/31.09 | (18) aNaturalNumber0(xn) = 0
% 66.83/31.09 |
% 66.83/31.09 +-Applying beta-rule and splitting (218), into two cases.
% 66.83/31.09 |-Branch one:
% 66.83/31.09 | (404) ~ (all_47_1_83 = 0)
% 66.83/31.09 |
% 66.83/31.09 | Equations (341) can reduce 404 to:
% 66.83/31.09 | (241) $false
% 66.83/31.09 |
% 66.83/31.09 |-The branch is then unsatisfiable
% 66.83/31.09 |-Branch two:
% 66.83/31.09 | (341) all_47_1_83 = 0
% 66.83/31.09 | (407) ~ (all_47_2_84 = 0) | all_47_0_82 = all_0_9_9
% 66.83/31.09 |
% 66.83/31.09 +-Applying beta-rule and splitting (407), into two cases.
% 66.83/31.09 |-Branch one:
% 66.83/31.09 | (408) ~ (all_47_2_84 = 0)
% 66.83/31.09 |
% 66.83/31.09 | Equations (395) can reduce 408 to:
% 66.83/31.09 | (241) $false
% 66.83/31.09 |
% 66.83/31.09 |-The branch is then unsatisfiable
% 66.83/31.09 |-Branch two:
% 66.83/31.09 | (395) all_47_2_84 = 0
% 66.83/31.09 | (411) all_47_0_82 = all_0_9_9
% 66.83/31.09 |
% 66.83/31.09 | From (411) and (215) follows:
% 66.83/31.09 | (412) sdtasdt0(xm, xn) = all_0_9_9
% 66.83/31.09 |
% 66.83/31.09 +-Applying beta-rule and splitting (213), into two cases.
% 66.83/31.09 |-Branch one:
% 66.83/31.09 | (413) all_46_0_79 = xp & all_46_1_80 = 0 & sdtpldt0(xm, all_46_2_81) = xp & aNaturalNumber0(all_46_2_81) = 0
% 66.83/31.09 |
% 66.83/31.09 | Applying alpha-rule on (413) yields:
% 66.83/31.09 | (414) all_46_0_79 = xp
% 66.83/31.09 | (415) all_46_1_80 = 0
% 66.83/31.09 | (416) sdtpldt0(xm, all_46_2_81) = xp
% 66.83/31.09 | (417) aNaturalNumber0(all_46_2_81) = 0
% 66.83/31.09 |
% 66.83/31.09 +-Applying beta-rule and splitting (212), into two cases.
% 66.83/31.09 |-Branch one:
% 66.83/31.09 | (418) all_45_0_76 = xp & all_45_1_77 = 0 & sdtpldt0(xn, all_45_2_78) = xp & aNaturalNumber0(all_45_2_78) = 0
% 66.83/31.09 |
% 66.83/31.09 | Applying alpha-rule on (418) yields:
% 66.83/31.09 | (419) all_45_0_76 = xp
% 66.83/31.09 | (420) all_45_1_77 = 0
% 66.83/31.09 | (421) sdtpldt0(xn, all_45_2_78) = xp
% 66.83/31.09 | (422) aNaturalNumber0(all_45_2_78) = 0
% 66.83/31.09 |
% 66.83/31.09 +-Applying beta-rule and splitting (287), into two cases.
% 66.83/31.09 |-Branch one:
% 66.83/31.09 | (423) ~ (doDivides0(xp, all_0_9_9) = all_53_3_94)
% 66.83/31.09 |
% 66.83/31.09 | Using (397) and (423) yields:
% 66.83/31.09 | (424) $false
% 66.83/31.09 |
% 66.83/31.09 |-The branch is then unsatisfiable
% 66.83/31.09 |-Branch two:
% 66.83/31.09 | (397) doDivides0(xp, all_0_9_9) = all_53_3_94
% 66.83/31.09 | (426) all_53_3_94 = 0
% 66.83/31.09 |
% 66.83/31.09 | From (426) and (397) follows:
% 66.83/31.09 | (70) doDivides0(xp, all_0_9_9) = 0
% 66.83/31.09 |
% 66.83/31.09 +-Applying beta-rule and splitting (211), into two cases.
% 66.83/31.09 |-Branch one:
% 66.83/31.09 | (428) ~ (all_43_1_74 = 0)
% 66.83/31.09 |
% 66.83/31.09 | Equations (351) can reduce 428 to:
% 66.83/31.09 | (241) $false
% 66.83/31.09 |
% 66.83/31.09 |-The branch is then unsatisfiable
% 66.83/31.09 |-Branch two:
% 66.83/31.09 | (351) all_43_1_74 = 0
% 66.83/31.09 | (431) ~ (all_43_2_75 = 0) | all_43_0_73 = 0
% 66.83/31.09 |
% 66.83/31.09 +-Applying beta-rule and splitting (199), into two cases.
% 66.83/31.09 |-Branch one:
% 66.83/31.09 | (432) ~ (all_39_1_66 = 0)
% 66.83/31.09 |
% 66.83/31.09 | Equations (361) can reduce 432 to:
% 66.83/31.09 | (241) $false
% 66.83/31.09 |
% 66.83/31.09 |-The branch is then unsatisfiable
% 66.83/31.09 |-Branch two:
% 66.83/31.09 | (361) all_39_1_66 = 0
% 66.83/31.09 | (435) ~ (all_39_2_67 = 0) | all_39_0_65 = all_0_11_11
% 66.83/31.09 |
% 66.83/31.09 +-Applying beta-rule and splitting (142), into two cases.
% 66.83/31.09 |-Branch one:
% 66.83/31.09 | (436) ~ (all_12_1_13 = 0)
% 66.83/31.10 |
% 66.83/31.10 | Equations (385) can reduce 436 to:
% 66.83/31.10 | (241) $false
% 66.83/31.10 |
% 66.83/31.10 |-The branch is then unsatisfiable
% 66.83/31.10 |-Branch two:
% 66.83/31.10 | (385) all_12_1_13 = 0
% 66.83/31.10 | (439) ~ (all_12_2_14 = 0) | all_12_0_12 = 0
% 66.83/31.10 |
% 66.83/31.10 +-Applying beta-rule and splitting (439), into two cases.
% 66.83/31.10 |-Branch one:
% 66.83/31.10 | (440) ~ (all_12_2_14 = 0)
% 66.83/31.10 |
% 66.83/31.10 | Equations (366) can reduce 440 to:
% 66.83/31.10 | (241) $false
% 66.83/31.10 |
% 66.83/31.10 |-The branch is then unsatisfiable
% 66.83/31.10 |-Branch two:
% 66.83/31.10 | (366) all_12_2_14 = 0
% 66.83/31.10 | (443) all_12_0_12 = 0
% 66.83/31.10 |
% 66.83/31.10 | Combining equations (443,295) yields a new equation:
% 66.83/31.10 | (444) all_35_2_58 = 0
% 66.83/31.10 |
% 66.83/31.10 +-Applying beta-rule and splitting (431), into two cases.
% 66.83/31.10 |-Branch one:
% 66.83/31.10 | (445) ~ (all_43_2_75 = 0)
% 66.83/31.10 |
% 66.83/31.10 | Equations (393) can reduce 445 to:
% 66.83/31.10 | (241) $false
% 66.83/31.10 |
% 66.83/31.10 |-The branch is then unsatisfiable
% 66.83/31.10 |-Branch two:
% 66.83/31.10 | (393) all_43_2_75 = 0
% 66.83/31.10 | (448) all_43_0_73 = 0
% 66.83/31.10 |
% 66.83/31.10 | From (448) and (208) follows:
% 66.83/31.10 | (449) aNaturalNumber0(all_0_9_9) = 0
% 66.83/31.10 |
% 66.83/31.10 +-Applying beta-rule and splitting (192), into two cases.
% 66.83/31.10 |-Branch one:
% 66.83/31.10 | (450) ~ (all_35_1_57 = 0)
% 66.83/31.10 |
% 66.83/31.10 | Equations (359) can reduce 450 to:
% 66.83/31.10 | (241) $false
% 66.83/31.10 |
% 66.83/31.10 |-The branch is then unsatisfiable
% 66.83/31.10 |-Branch two:
% 66.83/31.10 | (359) all_35_1_57 = 0
% 66.83/31.10 | (453) ~ (all_35_2_58 = 0) | all_35_0_56 = all_0_10_10
% 66.83/31.10 |
% 66.83/31.10 +-Applying beta-rule and splitting (453), into two cases.
% 66.83/31.10 |-Branch one:
% 66.83/31.10 | (454) ~ (all_35_2_58 = 0)
% 66.83/31.10 |
% 66.83/31.10 | Equations (444) can reduce 454 to:
% 66.83/31.10 | (241) $false
% 66.83/31.10 |
% 66.83/31.10 |-The branch is then unsatisfiable
% 66.83/31.10 |-Branch two:
% 66.83/31.10 | (444) all_35_2_58 = 0
% 66.83/31.10 | (457) all_35_0_56 = all_0_10_10
% 66.83/31.10 |
% 66.83/31.10 | From (457) and (189) follows:
% 66.83/31.10 | (458) sdtpldt0(xp, all_0_11_11) = all_0_10_10
% 66.83/31.10 |
% 66.83/31.10 +-Applying beta-rule and splitting (435), into two cases.
% 66.83/31.10 |-Branch one:
% 66.83/31.10 | (459) ~ (all_39_2_67 = 0)
% 66.83/31.10 |
% 66.83/31.10 | Equations (362) can reduce 459 to:
% 66.83/31.10 | (241) $false
% 66.83/31.10 |
% 66.83/31.10 |-The branch is then unsatisfiable
% 66.83/31.10 |-Branch two:
% 66.83/31.10 | (362) all_39_2_67 = 0
% 66.83/31.10 | (462) all_39_0_65 = all_0_11_11
% 66.83/31.10 |
% 66.83/31.10 | From (462) and (196) follows:
% 66.83/31.10 | (463) sdtpldt0(xm, xn) = all_0_11_11
% 66.83/31.10 |
% 66.83/31.10 +-Applying beta-rule and splitting (204), into two cases.
% 66.83/31.10 |-Branch one:
% 66.83/31.10 | (464) ~ (all_41_2_70 = 0)
% 66.83/31.10 |
% 66.83/31.10 | Equations (349) can reduce 464 to:
% 66.83/31.10 | (241) $false
% 66.83/31.10 |
% 66.83/31.10 |-The branch is then unsatisfiable
% 66.83/31.10 |-Branch two:
% 66.83/31.10 | (349) all_41_2_70 = 0
% 66.83/31.10 | (467) ~ (all_41_3_71 = 0) | ~ (all_41_4_72 = 0) | all_41_0_68 = all_0_10_10
% 66.83/31.10 |
% 66.83/31.10 +-Applying beta-rule and splitting (467), into two cases.
% 66.83/31.10 |-Branch one:
% 66.83/31.10 | (468) ~ (all_41_3_71 = 0)
% 66.83/31.10 |
% 66.83/31.10 | Equations (355) can reduce 468 to:
% 66.83/31.10 | (241) $false
% 66.83/31.10 |
% 66.83/31.10 |-The branch is then unsatisfiable
% 66.83/31.10 |-Branch two:
% 66.83/31.10 | (355) all_41_3_71 = 0
% 66.83/31.10 | (471) ~ (all_41_4_72 = 0) | all_41_0_68 = all_0_10_10
% 66.83/31.10 |
% 66.83/31.10 +-Applying beta-rule and splitting (194), into two cases.
% 66.83/31.10 |-Branch one:
% 66.83/31.10 | (472) all_38_0_62 = all_0_9_9 & all_38_1_63 = 0 & sdtasdt0(xr, all_38_2_64) = all_0_9_9 & aNaturalNumber0(all_38_2_64) = 0
% 66.83/31.10 |
% 66.83/31.10 | Applying alpha-rule on (472) yields:
% 66.83/31.10 | (473) all_38_0_62 = all_0_9_9
% 66.83/31.10 | (474) all_38_1_63 = 0
% 66.83/31.10 | (475) sdtasdt0(xr, all_38_2_64) = all_0_9_9
% 66.83/31.10 | (476) aNaturalNumber0(all_38_2_64) = 0
% 66.83/31.10 |
% 66.83/31.10 +-Applying beta-rule and splitting (120), into two cases.
% 66.83/31.10 |-Branch one:
% 66.83/31.10 | (258) xp = sz00
% 66.83/31.10 |
% 66.83/31.10 | Equations (258) can reduce 99 to:
% 66.83/31.10 | (241) $false
% 66.83/31.10 |
% 66.83/31.10 |-The branch is then unsatisfiable
% 66.83/31.10 |-Branch two:
% 66.83/31.10 | (99) ~ (xp = sz00)
% 66.83/31.10 | (480) all_0_2_2 = all_0_9_9 | ? [v0] : ? [v1] : ? [v2] : (doDivides0(xp, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 66.99/31.10 |
% 66.99/31.10 +-Applying beta-rule and splitting (262), into two cases.
% 66.99/31.10 |-Branch one:
% 66.99/31.10 | (481) all_69_2_108 = 0 & aNaturalNumber0(xk) = 0
% 66.99/31.10 |
% 66.99/31.10 | Applying alpha-rule on (481) yields:
% 66.99/31.10 | (482) all_69_2_108 = 0
% 66.99/31.10 | (483) aNaturalNumber0(xk) = 0
% 66.99/31.10 |
% 66.99/31.10 +-Applying beta-rule and splitting (301), into two cases.
% 66.99/31.10 |-Branch one:
% 66.99/31.10 | (484) ~ (aNaturalNumber0(xk) = all_28_1_39)
% 66.99/31.10 |
% 66.99/31.10 | From (296) and (484) follows:
% 66.99/31.10 | (485) ~ (aNaturalNumber0(xk) = 0)
% 66.99/31.10 |
% 66.99/31.10 | Using (483) and (485) yields:
% 66.99/31.10 | (424) $false
% 66.99/31.10 |
% 66.99/31.10 |-The branch is then unsatisfiable
% 66.99/31.10 |-Branch two:
% 66.99/31.10 | (487) aNaturalNumber0(xk) = all_28_1_39
% 66.99/31.10 | (488) all_59_2_102 = all_28_1_39
% 66.99/31.10 |
% 66.99/31.10 | Combining equations (488,303) yields a new equation:
% 66.99/31.10 | (489) all_49_1_86 = all_28_1_39
% 66.99/31.10 |
% 66.99/31.10 | Combining equations (296,489) yields a new equation:
% 66.99/31.10 | (490) all_49_1_86 = 0
% 66.99/31.10 |
% 66.99/31.10 | Combining equations (490,336) yields a new equation:
% 66.99/31.10 | (491) all_51_1_89 = 0
% 66.99/31.10 |
% 66.99/31.10 | From (296) and (487) follows:
% 66.99/31.10 | (483) aNaturalNumber0(xk) = 0
% 66.99/31.10 |
% 66.99/31.10 +-Applying beta-rule and splitting (193), into two cases.
% 66.99/31.10 |-Branch one:
% 66.99/31.10 | (493) all_37_0_59 = xk & all_37_1_60 = 0 & sdtasdt0(xr, all_37_2_61) = xk & aNaturalNumber0(all_37_2_61) = 0
% 66.99/31.10 |
% 66.99/31.10 | Applying alpha-rule on (493) yields:
% 66.99/31.10 | (494) all_37_0_59 = xk
% 66.99/31.10 | (495) all_37_1_60 = 0
% 66.99/31.10 | (496) sdtasdt0(xr, all_37_2_61) = xk
% 66.99/31.10 | (497) aNaturalNumber0(all_37_2_61) = 0
% 66.99/31.10 |
% 66.99/31.10 +-Applying beta-rule and splitting (186), into two cases.
% 66.99/31.10 |-Branch one:
% 66.99/31.10 | (498) all_31_0_44 = xk & all_31_1_45 = 0 & sdtpldt0(xr, all_31_2_46) = xk & aNaturalNumber0(all_31_2_46) = 0
% 66.99/31.10 |
% 66.99/31.10 | Applying alpha-rule on (498) yields:
% 66.99/31.10 | (499) all_31_0_44 = xk
% 66.99/31.10 | (500) all_31_1_45 = 0
% 66.99/31.10 | (501) sdtpldt0(xr, all_31_2_46) = xk
% 66.99/31.10 | (502) aNaturalNumber0(all_31_2_46) = 0
% 66.99/31.10 |
% 66.99/31.10 +-Applying beta-rule and splitting (122), into two cases.
% 66.99/31.10 |-Branch one:
% 66.99/31.10 | (503) ~ (sdtasdt0(xp, xk) = sz00)
% 66.99/31.10 |
% 66.99/31.10 +-Applying beta-rule and splitting (119), into two cases.
% 66.99/31.10 |-Branch one:
% 66.99/31.10 | (504) ~ (sdtasdt0(xp, xk) = xm)
% 66.99/31.10 |
% 66.99/31.10 +-Applying beta-rule and splitting (480), into two cases.
% 66.99/31.10 |-Branch one:
% 66.99/31.10 | (505) all_0_2_2 = all_0_9_9
% 66.99/31.10 |
% 66.99/31.10 | From (505) and (82) follows:
% 66.99/31.10 | (506) sdtsldt0(all_0_9_9, xr) = all_0_1_1
% 66.99/31.10 |
% 66.99/31.10 | From (505) and (68) follows:
% 66.99/31.10 | (507) sdtasdt0(xp, xk) = all_0_9_9
% 66.99/31.10 |
% 66.99/31.10 | From (505) and (220) follows:
% 66.99/31.10 | (508) aNaturalNumber0(all_0_9_9) = all_49_0_85
% 66.99/31.10 |
% 66.99/31.10 +-Applying beta-rule and splitting (289), into two cases.
% 66.99/31.10 |-Branch one:
% 66.99/31.10 | (509) ~ (aNaturalNumber0(all_0_2_2) = 0)
% 66.99/31.10 |
% 66.99/31.10 | From (505) and (509) follows:
% 66.99/31.10 | (510) ~ (aNaturalNumber0(all_0_9_9) = 0)
% 66.99/31.10 |
% 66.99/31.10 | Using (449) and (510) yields:
% 66.99/31.10 | (424) $false
% 66.99/31.10 |
% 66.99/31.10 |-The branch is then unsatisfiable
% 66.99/31.10 |-Branch two:
% 66.99/31.10 | (512) aNaturalNumber0(all_0_2_2) = 0
% 66.99/31.10 | (513) all_49_0_85 = 0
% 66.99/31.10 |
% 66.99/31.10 | From (513) and (508) follows:
% 66.99/31.10 | (449) aNaturalNumber0(all_0_9_9) = 0
% 66.99/31.10 |
% 66.99/31.10 +-Applying beta-rule and splitting (185), into two cases.
% 66.99/31.10 |-Branch one:
% 66.99/31.10 | (515) all_30_0_41 = xp & all_30_1_42 = 0 & sdtpldt0(xk, all_30_2_43) = xp & aNaturalNumber0(all_30_2_43) = 0
% 66.99/31.10 |
% 66.99/31.10 | Applying alpha-rule on (515) yields:
% 66.99/31.10 | (516) all_30_0_41 = xp
% 66.99/31.10 | (517) all_30_1_42 = 0
% 66.99/31.10 | (518) sdtpldt0(xk, all_30_2_43) = xp
% 66.99/31.10 | (519) aNaturalNumber0(all_30_2_43) = 0
% 66.99/31.10 |
% 66.99/31.10 +-Applying beta-rule and splitting (471), into two cases.
% 66.99/31.10 |-Branch one:
% 66.99/31.10 | (520) ~ (all_41_4_72 = 0)
% 66.99/31.10 |
% 66.99/31.10 | Equations (323) can reduce 520 to:
% 66.99/31.10 | (241) $false
% 66.99/31.10 |
% 66.99/31.10 |-The branch is then unsatisfiable
% 66.99/31.10 |-Branch two:
% 66.99/31.10 | (323) all_41_4_72 = 0
% 66.99/31.10 | (523) all_41_0_68 = all_0_10_10
% 66.99/31.10 |
% 66.99/31.10 | From (523) and (201) follows:
% 66.99/31.10 | (524) sdtpldt0(xn, all_41_1_69) = all_0_10_10
% 66.99/31.10 |
% 66.99/31.10 +-Applying beta-rule and splitting (187), into two cases.
% 66.99/31.10 |-Branch one:
% 66.99/31.10 | (525) all_33_0_50 = xn & all_33_1_51 = 0 & sdtasdt0(xr, all_33_2_52) = xn & aNaturalNumber0(all_33_2_52) = 0
% 66.99/31.10 |
% 66.99/31.10 | Applying alpha-rule on (525) yields:
% 66.99/31.10 | (526) all_33_0_50 = xn
% 66.99/31.10 | (527) all_33_1_51 = 0
% 66.99/31.10 | (528) sdtasdt0(xr, all_33_2_52) = xn
% 66.99/31.10 | (529) aNaturalNumber0(all_33_2_52) = 0
% 66.99/31.10 |
% 66.99/31.10 +-Applying beta-rule and splitting (228), into two cases.
% 66.99/31.10 |-Branch one:
% 66.99/31.10 | (530) ~ (all_51_1_89 = 0)
% 66.99/31.10 |
% 66.99/31.10 | Equations (491) can reduce 530 to:
% 66.99/31.10 | (241) $false
% 66.99/31.10 |
% 66.99/31.10 |-The branch is then unsatisfiable
% 66.99/31.10 |-Branch two:
% 66.99/31.10 | (491) all_51_1_89 = 0
% 66.99/31.10 | (533) ~ (all_51_2_90 = 0) | all_51_0_88 = all_0_2_2
% 66.99/31.10 |
% 66.99/31.10 +-Applying beta-rule and splitting (533), into two cases.
% 66.99/31.10 |-Branch one:
% 66.99/31.10 | (534) ~ (all_51_2_90 = 0)
% 66.99/31.10 |
% 66.99/31.10 | Equations (396) can reduce 534 to:
% 66.99/31.10 | (241) $false
% 66.99/31.10 |
% 66.99/31.10 |-The branch is then unsatisfiable
% 66.99/31.10 |-Branch two:
% 66.99/31.10 | (396) all_51_2_90 = 0
% 66.99/31.10 | (537) all_51_0_88 = all_0_2_2
% 66.99/31.10 |
% 66.99/31.10 | Combining equations (505,537) yields a new equation:
% 66.99/31.10 | (538) all_51_0_88 = all_0_9_9
% 66.99/31.10 |
% 66.99/31.10 | From (538) and (225) follows:
% 66.99/31.11 | (539) sdtasdt0(xk, xp) = all_0_9_9
% 66.99/31.11 |
% 66.99/31.11 | Instantiating formula (77) with xr, all_0_4_4, all_0_9_9, all_24_0_32 and discharging atoms sdtasdt0(xr, all_0_4_4) = all_24_0_32, yields:
% 66.99/31.11 | (540) all_24_0_32 = all_0_9_9 | ~ (sdtasdt0(xr, all_0_4_4) = all_0_9_9)
% 66.99/31.11 |
% 66.99/31.11 | Using (507) and (504) yields:
% 66.99/31.11 | (541) ~ (all_0_9_9 = xm)
% 66.99/31.11 |
% 66.99/31.11 | Using (507) and (503) yields:
% 66.99/31.11 | (542) ~ (all_0_9_9 = sz00)
% 66.99/31.11 |
% 66.99/31.11 +-Applying beta-rule and splitting (126), into two cases.
% 66.99/31.11 |-Branch one:
% 66.99/31.11 | (543) ~ (sdtasdt0(sz00, xm) = all_0_9_9)
% 66.99/31.11 |
% 66.99/31.11 +-Applying beta-rule and splitting (100), into two cases.
% 66.99/31.11 |-Branch one:
% 66.99/31.11 | (544) all_0_9_9 = sz00
% 66.99/31.11 |
% 66.99/31.11 | Equations (544) can reduce 542 to:
% 66.99/31.11 | (241) $false
% 66.99/31.11 |
% 66.99/31.11 |-The branch is then unsatisfiable
% 66.99/31.11 |-Branch two:
% 66.99/31.11 | (542) ~ (all_0_9_9 = sz00)
% 66.99/31.11 | (547) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xr, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.99/31.11 |
% 66.99/31.11 | Instantiating (547) with all_247_0_111, all_247_1_112, all_247_2_113 yields:
% 66.99/31.11 | (548) sdtlseqdt0(xr, all_0_9_9) = all_247_0_111 & aNaturalNumber0(all_0_9_9) = all_247_1_112 & aNaturalNumber0(xr) = all_247_2_113 & ( ~ (all_247_1_112 = 0) | ~ (all_247_2_113 = 0) | all_247_0_111 = 0)
% 66.99/31.11 |
% 66.99/31.11 | Applying alpha-rule on (548) yields:
% 66.99/31.11 | (549) sdtlseqdt0(xr, all_0_9_9) = all_247_0_111
% 66.99/31.11 | (550) aNaturalNumber0(all_0_9_9) = all_247_1_112
% 66.99/31.11 | (551) aNaturalNumber0(xr) = all_247_2_113
% 66.99/31.11 | (552) ~ (all_247_1_112 = 0) | ~ (all_247_2_113 = 0) | all_247_0_111 = 0
% 66.99/31.11 |
% 66.99/31.11 +-Applying beta-rule and splitting (125), into two cases.
% 66.99/31.11 |-Branch one:
% 66.99/31.11 | (553) ~ (sdtasdt0(sz10, xm) = all_0_9_9)
% 66.99/31.11 |
% 66.99/31.11 +-Applying beta-rule and splitting (105), into two cases.
% 66.99/31.11 |-Branch one:
% 66.99/31.11 | (544) all_0_9_9 = sz00
% 66.99/31.11 |
% 66.99/31.11 | Equations (544) can reduce 542 to:
% 66.99/31.11 | (241) $false
% 66.99/31.11 |
% 66.99/31.11 |-The branch is then unsatisfiable
% 66.99/31.11 |-Branch two:
% 66.99/31.11 | (542) ~ (all_0_9_9 = sz00)
% 66.99/31.11 | (557) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.99/31.11 |
% 66.99/31.11 | Instantiating (557) with all_257_0_114, all_257_1_115, all_257_2_116 yields:
% 66.99/31.11 | (558) sdtlseqdt0(xp, all_0_9_9) = all_257_0_114 & aNaturalNumber0(all_0_9_9) = all_257_1_115 & aNaturalNumber0(xp) = all_257_2_116 & ( ~ (all_257_1_115 = 0) | ~ (all_257_2_116 = 0) | all_257_0_114 = 0)
% 66.99/31.11 |
% 66.99/31.11 | Applying alpha-rule on (558) yields:
% 66.99/31.11 | (559) sdtlseqdt0(xp, all_0_9_9) = all_257_0_114
% 66.99/31.11 | (560) aNaturalNumber0(all_0_9_9) = all_257_1_115
% 66.99/31.11 | (561) aNaturalNumber0(xp) = all_257_2_116
% 66.99/31.11 | (562) ~ (all_257_1_115 = 0) | ~ (all_257_2_116 = 0) | all_257_0_114 = 0
% 66.99/31.11 |
% 66.99/31.11 | Instantiating formula (63) with all_0_9_9, all_257_1_115, 0 and discharging atoms aNaturalNumber0(all_0_9_9) = all_257_1_115, aNaturalNumber0(all_0_9_9) = 0, yields:
% 66.99/31.11 | (563) all_257_1_115 = 0
% 66.99/31.11 |
% 66.99/31.11 | Instantiating formula (63) with all_0_9_9, all_247_1_112, all_257_1_115 and discharging atoms aNaturalNumber0(all_0_9_9) = all_257_1_115, aNaturalNumber0(all_0_9_9) = all_247_1_112, yields:
% 66.99/31.11 | (564) all_257_1_115 = all_247_1_112
% 66.99/31.11 |
% 66.99/31.11 | Instantiating formula (63) with xr, all_247_2_113, 0 and discharging atoms aNaturalNumber0(xr) = all_247_2_113, aNaturalNumber0(xr) = 0, yields:
% 66.99/31.11 | (565) all_247_2_113 = 0
% 66.99/31.11 |
% 66.99/31.11 | Instantiating formula (63) with xp, all_257_2_116, 0 and discharging atoms aNaturalNumber0(xp) = all_257_2_116, aNaturalNumber0(xp) = 0, yields:
% 66.99/31.11 | (566) all_257_2_116 = 0
% 66.99/31.11 |
% 66.99/31.11 | Using (90) and (553) yields:
% 66.99/31.11 | (567) ~ (xn = sz10)
% 66.99/31.11 |
% 66.99/31.11 | Using (90) and (543) yields:
% 66.99/31.11 | (568) ~ (xn = sz00)
% 66.99/31.11 |
% 66.99/31.11 | Combining equations (563,564) yields a new equation:
% 66.99/31.11 | (569) all_247_1_112 = 0
% 66.99/31.11 |
% 66.99/31.11 | Combining equations (569,564) yields a new equation:
% 66.99/31.11 | (563) all_257_1_115 = 0
% 66.99/31.11 |
% 66.99/31.11 | From (565) and (551) follows:
% 66.99/31.11 | (62) aNaturalNumber0(xr) = 0
% 66.99/31.11 |
% 66.99/31.11 +-Applying beta-rule and splitting (562), into two cases.
% 66.99/31.11 |-Branch one:
% 66.99/31.11 | (572) ~ (all_257_1_115 = 0)
% 66.99/31.11 |
% 66.99/31.11 | Equations (563) can reduce 572 to:
% 66.99/31.11 | (241) $false
% 66.99/31.11 |
% 66.99/31.11 |-The branch is then unsatisfiable
% 66.99/31.11 |-Branch two:
% 66.99/31.11 | (563) all_257_1_115 = 0
% 66.99/31.11 | (575) ~ (all_257_2_116 = 0) | all_257_0_114 = 0
% 66.99/31.11 |
% 66.99/31.11 +-Applying beta-rule and splitting (137), into two cases.
% 66.99/31.11 |-Branch one:
% 66.99/31.11 | (576) xn = sz00
% 66.99/31.11 |
% 66.99/31.11 | Equations (576) can reduce 568 to:
% 66.99/31.11 | (241) $false
% 66.99/31.11 |
% 66.99/31.11 |-The branch is then unsatisfiable
% 66.99/31.11 |-Branch two:
% 66.99/31.11 | (568) ~ (xn = sz00)
% 66.99/31.11 | (579) xn = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xn) = 0 & aNaturalNumber0(v0) = 0)
% 66.99/31.11 |
% 66.99/31.11 +-Applying beta-rule and splitting (575), into two cases.
% 66.99/31.11 |-Branch one:
% 66.99/31.11 | (580) ~ (all_257_2_116 = 0)
% 66.99/31.11 |
% 66.99/31.11 | Equations (566) can reduce 580 to:
% 66.99/31.11 | (241) $false
% 66.99/31.11 |
% 66.99/31.11 |-The branch is then unsatisfiable
% 66.99/31.11 |-Branch two:
% 66.99/31.11 | (566) all_257_2_116 = 0
% 66.99/31.11 | (583) all_257_0_114 = 0
% 66.99/31.11 |
% 66.99/31.11 | From (583) and (559) follows:
% 66.99/31.11 | (584) sdtlseqdt0(xp, all_0_9_9) = 0
% 66.99/31.11 |
% 66.99/31.11 +-Applying beta-rule and splitting (579), into two cases.
% 66.99/31.11 |-Branch one:
% 66.99/31.11 | (585) xn = sz10
% 66.99/31.11 |
% 66.99/31.11 | Equations (585) can reduce 567 to:
% 66.99/31.11 | (241) $false
% 66.99/31.11 |
% 66.99/31.11 |-The branch is then unsatisfiable
% 66.99/31.11 |-Branch two:
% 66.99/31.11 | (567) ~ (xn = sz10)
% 66.99/31.11 | (588) ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xn) = 0 & aNaturalNumber0(v0) = 0)
% 66.99/31.11 |
% 66.99/31.11 | Instantiating (588) with all_285_0_117 yields:
% 66.99/31.11 | (589) isPrime0(all_285_0_117) = 0 & doDivides0(all_285_0_117, xn) = 0 & aNaturalNumber0(all_285_0_117) = 0
% 66.99/31.11 |
% 66.99/31.11 | Applying alpha-rule on (589) yields:
% 66.99/31.11 | (590) isPrime0(all_285_0_117) = 0
% 66.99/31.11 | (591) doDivides0(all_285_0_117, xn) = 0
% 66.99/31.11 | (592) aNaturalNumber0(all_285_0_117) = 0
% 66.99/31.11 |
% 66.99/31.11 +-Applying beta-rule and splitting (103), into two cases.
% 66.99/31.11 |-Branch one:
% 66.99/31.11 | (576) xn = sz00
% 66.99/31.11 |
% 66.99/31.11 | Equations (576) can reduce 568 to:
% 66.99/31.11 | (241) $false
% 66.99/31.11 |
% 66.99/31.11 |-The branch is then unsatisfiable
% 66.99/31.11 |-Branch two:
% 66.99/31.11 | (568) ~ (xn = sz00)
% 66.99/31.11 | (596) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xr, xn) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.99/31.11 |
% 66.99/31.11 | Instantiating (596) with all_295_0_118, all_295_1_119, all_295_2_120 yields:
% 66.99/31.11 | (597) sdtlseqdt0(xr, xn) = all_295_0_118 & aNaturalNumber0(xr) = all_295_2_120 & aNaturalNumber0(xn) = all_295_1_119 & ( ~ (all_295_1_119 = 0) | ~ (all_295_2_120 = 0) | all_295_0_118 = 0)
% 66.99/31.11 |
% 66.99/31.11 | Applying alpha-rule on (597) yields:
% 66.99/31.11 | (598) sdtlseqdt0(xr, xn) = all_295_0_118
% 66.99/31.11 | (599) aNaturalNumber0(xr) = all_295_2_120
% 66.99/31.11 | (600) aNaturalNumber0(xn) = all_295_1_119
% 66.99/31.11 | (601) ~ (all_295_1_119 = 0) | ~ (all_295_2_120 = 0) | all_295_0_118 = 0
% 66.99/31.11 |
% 66.99/31.11 | Instantiating formula (63) with xr, all_295_2_120, 0 and discharging atoms aNaturalNumber0(xr) = all_295_2_120, aNaturalNumber0(xr) = 0, yields:
% 66.99/31.11 | (602) all_295_2_120 = 0
% 66.99/31.11 |
% 66.99/31.11 | Instantiating formula (63) with xn, all_295_1_119, 0 and discharging atoms aNaturalNumber0(xn) = all_295_1_119, aNaturalNumber0(xn) = 0, yields:
% 66.99/31.11 | (603) all_295_1_119 = 0
% 66.99/31.11 |
% 66.99/31.11 | From (602) and (599) follows:
% 66.99/31.11 | (62) aNaturalNumber0(xr) = 0
% 66.99/31.11 |
% 66.99/31.11 | From (603) and (600) follows:
% 66.99/31.11 | (18) aNaturalNumber0(xn) = 0
% 66.99/31.11 |
% 66.99/31.11 | Instantiating formula (65) with xn, all_285_0_117 and discharging atoms doDivides0(all_285_0_117, xn) = 0, yields:
% 66.99/31.11 | (606) xn = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_285_0_117, xn) = v2 & aNaturalNumber0(all_285_0_117) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.99/31.11 |
% 66.99/31.11 | Instantiating formula (65) with xr, all_80_0_109 and discharging atoms doDivides0(all_80_0_109, xr) = 0, yields:
% 66.99/31.11 | (607) xr = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_80_0_109, xr) = v2 & aNaturalNumber0(all_80_0_109) = v0 & aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.99/31.11 |
% 66.99/31.11 | Instantiating formula (78) with all_0_7_7, xm, all_0_9_9, xp and discharging atoms sdtlseqdt0(xp, all_0_9_9) = 0, sdtlseqdt0(xp, xm) = all_0_7_7, yields:
% 66.99/31.11 | (608) all_0_7_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtlseqdt0(all_0_9_9, xm) = v3 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 66.99/31.11 |
% 66.99/31.11 | Instantiating formula (78) with all_0_8_8, xn, all_0_9_9, xp and discharging atoms sdtlseqdt0(xp, all_0_9_9) = 0, sdtlseqdt0(xp, xn) = all_0_8_8, yields:
% 66.99/31.11 | (609) all_0_8_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtlseqdt0(all_0_9_9, xn) = v3 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 66.99/31.11 |
% 66.99/31.11 | Instantiating formula (35) with all_20_0_24, all_20_1_25, all_0_5_5 and discharging atoms sdtasdt0(all_0_5_5, all_20_1_25) = all_20_0_24, yields:
% 66.99/31.11 | (610) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_20_1_25, all_0_5_5) = v2 & aNaturalNumber0(all_20_1_25) = v1 & aNaturalNumber0(all_0_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_20_0_24))
% 66.99/31.11 |
% 66.99/31.11 | Instantiating formula (16) with all_20_0_24, all_20_1_25, all_0_5_5 and discharging atoms sdtasdt0(all_0_5_5, all_20_1_25) = all_20_0_24, yields:
% 66.99/31.11 | (611) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_20_0_24) = v2 & aNaturalNumber0(all_20_1_25) = v1 & aNaturalNumber0(all_0_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.99/31.11 |
% 66.99/31.11 | Instantiating formula (35) with all_0_9_9, all_38_2_64, xr and discharging atoms sdtasdt0(xr, all_38_2_64) = all_0_9_9, yields:
% 66.99/31.11 | (612) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_38_2_64, xr) = v2 & aNaturalNumber0(all_38_2_64) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_9_9))
% 66.99/31.11 |
% 66.99/31.11 | Instantiating formula (35) with xk, all_37_2_61, xr and discharging atoms sdtasdt0(xr, all_37_2_61) = xk, yields:
% 66.99/31.11 | (613) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_37_2_61, xr) = v2 & aNaturalNumber0(all_37_2_61) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xk))
% 66.99/31.11 |
% 66.99/31.11 | Instantiating formula (27) with all_33_2_52, all_0_5_5, xn, xr and discharging atoms sdtsldt0(xn, xr) = all_0_5_5, sdtasdt0(xr, all_33_2_52) = xn, yields:
% 66.99/31.11 | (614) all_33_2_52 = all_0_5_5 | xr = sz00 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_33_2_52) = v0) | (doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (24) with all_0_9_9, xn, xm, all_33_2_52, xr and discharging atoms sdtasdt0(xr, all_33_2_52) = xn, sdtasdt0(xn, xm) = all_0_9_9, yields:
% 66.99/31.12 | (615) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_33_2_52, xm) = v3 & sdtasdt0(xr, v3) = v4 & aNaturalNumber0(all_33_2_52) = v1 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_9_9))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (35) with xn, all_33_2_52, xr and discharging atoms sdtasdt0(xr, all_33_2_52) = xn, yields:
% 66.99/31.12 | (616) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_33_2_52, xr) = v2 & aNaturalNumber0(all_33_2_52) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xn))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (13) with all_28_0_38, all_0_1_1, all_0_9_9, xr and discharging atoms sdtsldt0(all_0_9_9, xr) = all_0_1_1, sdtasdt0(xr, all_0_1_1) = all_28_0_38, yields:
% 66.99/31.12 | (617) xr = sz00 | ? [v0] : ? [v1] : ? [v2] : ((v0 = 0 & aNaturalNumber0(all_0_1_1) = 0) | (doDivides0(xr, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (35) with all_28_0_38, all_0_1_1, xr and discharging atoms sdtasdt0(xr, all_0_1_1) = all_28_0_38, yields:
% 66.99/31.12 | (618) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_0_1_1, xr) = v2 & aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_28_0_38))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (16) with all_28_0_38, all_0_1_1, xr and discharging atoms sdtasdt0(xr, all_0_1_1) = all_28_0_38, yields:
% 66.99/31.12 | (619) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_28_0_38) = v2 & aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (35) with all_24_0_32, all_0_4_4, xr and discharging atoms sdtasdt0(xr, all_0_4_4) = all_24_0_32, yields:
% 66.99/31.12 | (620) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_0_4_4, xr) = v2 & aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_24_0_32))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (16) with all_24_0_32, all_0_4_4, xr and discharging atoms sdtasdt0(xr, all_0_4_4) = all_24_0_32, yields:
% 66.99/31.12 | (621) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_24_0_32) = v2 & aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (24) with all_0_9_9, xk, xp, all_37_2_61, xr and discharging atoms sdtasdt0(xr, all_37_2_61) = xk, sdtasdt0(xk, xp) = all_0_9_9, yields:
% 66.99/31.12 | (622) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_37_2_61, xp) = v3 & sdtasdt0(xr, v3) = v4 & aNaturalNumber0(all_37_2_61) = v1 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xp) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_9_9))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (35) with all_18_0_21, all_0_5_5, xm and discharging atoms sdtasdt0(xm, all_0_5_5) = all_18_0_21, yields:
% 66.99/31.12 | (623) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_0_5_5, xm) = v2 & aNaturalNumber0(all_0_5_5) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_18_0_21))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (16) with all_18_0_21, all_0_5_5, xm and discharging atoms sdtasdt0(xm, all_0_5_5) = all_18_0_21, yields:
% 66.99/31.12 | (624) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_18_0_21) = v2 & aNaturalNumber0(all_0_5_5) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (35) with all_20_1_25, xr, xm and discharging atoms sdtasdt0(xm, xr) = all_20_1_25, yields:
% 66.99/31.12 | (625) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xr, xm) = v2 & aNaturalNumber0(xr) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_20_1_25))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (16) with all_20_1_25, xr, xm and discharging atoms sdtasdt0(xm, xr) = all_20_1_25, yields:
% 66.99/31.12 | (626) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_20_1_25) = v2 & aNaturalNumber0(xr) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (86) with all_0_1_1, all_0_9_9, xm, all_0_5_5, xn, xr and discharging atoms sdtsldt0(all_0_9_9, xr) = all_0_1_1, sdtsldt0(xn, xr) = all_0_5_5, sdtasdt0(xm, xn) = all_0_9_9, yields:
% 66.99/31.12 | (627) xr = sz00 | ? [v0] : ? [v1] : ? [v2] : ((doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) | (sdtasdt0(xm, all_0_5_5) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v0 = 0) | v1 = all_0_1_1)))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (92) with xk, all_31_2_46, xr, xr and discharging atoms doDivides0(xr, xk) = 0, sdtpldt0(xr, all_31_2_46) = xk, yields:
% 66.99/31.12 | (628) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(xr, all_31_2_46) = v4 & doDivides0(xr, xr) = v3 & aNaturalNumber0(all_31_2_46) = v2 & aNaturalNumber0(xr) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (38) with xk, all_31_2_46, xr and discharging atoms sdtpldt0(xr, all_31_2_46) = xk, yields:
% 66.99/31.12 | (629) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_31_2_46, xr) = v2 & aNaturalNumber0(all_31_2_46) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xk))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (61) with xp, xk, all_30_2_43, all_31_2_46, xr and discharging atoms sdtpldt0(xr, all_31_2_46) = xk, sdtpldt0(xk, all_30_2_43) = xp, yields:
% 66.99/31.12 | (630) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(all_30_2_43) = v3 & doDivides0(all_30_2_43, v4) = v5 & doDivides0(all_30_2_43, all_31_2_46) = v8 & doDivides0(all_30_2_43, xr) = v7 & iLess0(xp, all_0_10_10) = v6 & sdtasdt0(xr, all_31_2_46) = v4 & aNaturalNumber0(all_31_2_46) = v1 & aNaturalNumber0(all_30_2_43) = v2 & aNaturalNumber0(xr) = v0 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (12) with xp, xk, all_30_2_43, all_31_2_46, xr and discharging atoms sdtpldt0(xr, all_31_2_46) = xk, sdtpldt0(xk, all_30_2_43) = xp, yields:
% 66.99/31.12 | (631) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_31_2_46, all_30_2_43) = v3 & sdtpldt0(xr, v3) = v4 & aNaturalNumber0(all_31_2_46) = v1 & aNaturalNumber0(all_30_2_43) = v2 & aNaturalNumber0(xr) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = xp))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (92) with xp, all_46_2_81, xm, all_85_0_110 and discharging atoms doDivides0(all_85_0_110, xp) = 0, sdtpldt0(xm, all_46_2_81) = xp, yields:
% 66.99/31.12 | (632) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(all_85_0_110, all_46_2_81) = v4 & doDivides0(all_85_0_110, xm) = v3 & aNaturalNumber0(all_85_0_110) = v0 & aNaturalNumber0(all_46_2_81) = v2 & aNaturalNumber0(xm) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (61) with all_0_10_10, xp, all_0_11_11, all_46_2_81, xm and discharging atoms sdtpldt0(xp, all_0_11_11) = all_0_10_10, sdtpldt0(xm, all_46_2_81) = xp, yields:
% 66.99/31.12 | (633) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(all_0_11_11) = v3 & doDivides0(all_0_11_11, v4) = v5 & doDivides0(all_0_11_11, all_46_2_81) = v8 & doDivides0(all_0_11_11, xm) = v7 & iLess0(all_0_10_10, all_0_10_10) = v6 & sdtasdt0(xm, all_46_2_81) = v4 & aNaturalNumber0(all_46_2_81) = v1 & aNaturalNumber0(all_0_11_11) = v2 & aNaturalNumber0(xm) = v0 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (12) with all_0_10_10, xp, all_0_11_11, all_46_2_81, xm and discharging atoms sdtpldt0(xp, all_0_11_11) = all_0_10_10, sdtpldt0(xm, all_46_2_81) = xp, yields:
% 66.99/31.12 | (634) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_46_2_81, all_0_11_11) = v3 & sdtpldt0(xm, v3) = v4 & aNaturalNumber0(all_46_2_81) = v1 & aNaturalNumber0(all_0_11_11) = v2 & aNaturalNumber0(xm) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_10_10))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (38) with xp, all_46_2_81, xm and discharging atoms sdtpldt0(xm, all_46_2_81) = xp, yields:
% 66.99/31.12 | (635) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_46_2_81, xm) = v2 & aNaturalNumber0(all_46_2_81) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xp))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (38) with all_41_1_69, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_41_1_69, yields:
% 66.99/31.12 | (636) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, xm) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_41_1_69))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (34) with all_41_1_69, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_41_1_69, yields:
% 66.99/31.12 | (637) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_41_1_69) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (61) with all_0_10_10, all_0_11_11, xp, xn, xm and discharging atoms sdtpldt0(all_0_11_11, xp) = all_0_10_10, sdtpldt0(xm, xn) = all_0_11_11, yields:
% 66.99/31.12 | (638) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, v4) = v5 & doDivides0(xp, xm) = v7 & doDivides0(xp, xn) = v8 & iLess0(all_0_10_10, all_0_10_10) = v6 & sdtasdt0(xm, xn) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (12) with all_0_10_10, all_0_11_11, xp, xn, xm and discharging atoms sdtpldt0(all_0_11_11, xp) = all_0_10_10, sdtpldt0(xm, xn) = all_0_11_11, yields:
% 66.99/31.12 | (639) ? [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_10_10))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (92) with xp, all_45_2_78, xn, all_85_0_110 and discharging atoms doDivides0(all_85_0_110, xp) = 0, sdtpldt0(xn, all_45_2_78) = xp, yields:
% 66.99/31.12 | (640) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(all_85_0_110, all_45_2_78) = v4 & doDivides0(all_85_0_110, xn) = v3 & aNaturalNumber0(all_85_0_110) = v0 & aNaturalNumber0(all_45_2_78) = v2 & aNaturalNumber0(xn) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (61) with all_0_10_10, xp, all_0_11_11, all_45_2_78, xn and discharging atoms sdtpldt0(xp, all_0_11_11) = all_0_10_10, sdtpldt0(xn, all_45_2_78) = xp, yields:
% 66.99/31.12 | (641) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(all_0_11_11) = v3 & doDivides0(all_0_11_11, v4) = v5 & doDivides0(all_0_11_11, all_45_2_78) = v8 & doDivides0(all_0_11_11, xn) = v7 & iLess0(all_0_10_10, all_0_10_10) = v6 & sdtasdt0(xn, all_45_2_78) = v4 & aNaturalNumber0(all_45_2_78) = v1 & aNaturalNumber0(all_0_11_11) = v2 & aNaturalNumber0(xn) = v0 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (12) with all_0_10_10, xp, all_0_11_11, all_45_2_78, xn and discharging atoms sdtpldt0(xp, all_0_11_11) = all_0_10_10, sdtpldt0(xn, all_45_2_78) = xp, yields:
% 66.99/31.12 | (642) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_45_2_78, all_0_11_11) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(all_45_2_78) = v1 & aNaturalNumber0(all_0_11_11) = v2 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_10_10))
% 66.99/31.12 |
% 66.99/31.12 | Instantiating formula (38) with xp, all_45_2_78, xn and discharging atoms sdtpldt0(xn, all_45_2_78) = xp, yields:
% 66.99/31.13 | (643) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_45_2_78, xn) = v2 & aNaturalNumber0(all_45_2_78) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xp))
% 66.99/31.13 |
% 66.99/31.13 | Instantiating formula (38) with all_0_10_10, all_41_1_69, xn and discharging atoms sdtpldt0(xn, all_41_1_69) = all_0_10_10, yields:
% 66.99/31.13 | (644) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_41_1_69, xn) = v2 & aNaturalNumber0(all_41_1_69) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_10_10))
% 66.99/31.13 |
% 66.99/31.13 | Instantiating formula (34) with all_0_10_10, all_41_1_69, xn and discharging atoms sdtpldt0(xn, all_41_1_69) = all_0_10_10, yields:
% 66.99/31.13 | (645) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_41_1_69) = v1 & aNaturalNumber0(all_0_10_10) = v2 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.99/31.13 |
% 66.99/31.13 | Instantiating (645) with all_314_0_121, all_314_1_122, all_314_2_123 yields:
% 66.99/31.13 | (646) aNaturalNumber0(all_41_1_69) = all_314_1_122 & aNaturalNumber0(all_0_10_10) = all_314_0_121 & aNaturalNumber0(xn) = all_314_2_123 & ( ~ (all_314_1_122 = 0) | ~ (all_314_2_123 = 0) | all_314_0_121 = 0)
% 66.99/31.13 |
% 66.99/31.13 | Applying alpha-rule on (646) yields:
% 66.99/31.13 | (647) aNaturalNumber0(all_41_1_69) = all_314_1_122
% 66.99/31.13 | (648) aNaturalNumber0(all_0_10_10) = all_314_0_121
% 66.99/31.13 | (649) aNaturalNumber0(xn) = all_314_2_123
% 66.99/31.13 | (650) ~ (all_314_1_122 = 0) | ~ (all_314_2_123 = 0) | all_314_0_121 = 0
% 66.99/31.13 |
% 66.99/31.13 | Instantiating (644) with all_316_0_124, all_316_1_125, all_316_2_126 yields:
% 66.99/31.13 | (651) sdtpldt0(all_41_1_69, xn) = all_316_0_124 & aNaturalNumber0(all_41_1_69) = all_316_1_125 & aNaturalNumber0(xn) = all_316_2_126 & ( ~ (all_316_1_125 = 0) | ~ (all_316_2_126 = 0) | all_316_0_124 = all_0_10_10)
% 66.99/31.13 |
% 66.99/31.13 | Applying alpha-rule on (651) yields:
% 66.99/31.13 | (652) sdtpldt0(all_41_1_69, xn) = all_316_0_124
% 66.99/31.13 | (653) aNaturalNumber0(all_41_1_69) = all_316_1_125
% 66.99/31.13 | (654) aNaturalNumber0(xn) = all_316_2_126
% 66.99/31.13 | (655) ~ (all_316_1_125 = 0) | ~ (all_316_2_126 = 0) | all_316_0_124 = all_0_10_10
% 66.99/31.13 |
% 66.99/31.13 | Instantiating (632) with all_318_0_127, all_318_1_128, all_318_2_129, all_318_3_130, all_318_4_131 yields:
% 66.99/31.13 | (656) doDivides0(all_85_0_110, all_46_2_81) = all_318_0_127 & doDivides0(all_85_0_110, xm) = all_318_1_128 & aNaturalNumber0(all_85_0_110) = all_318_4_131 & aNaturalNumber0(all_46_2_81) = all_318_2_129 & aNaturalNumber0(xm) = all_318_3_130 & ( ~ (all_318_1_128 = 0) | ~ (all_318_2_129 = 0) | ~ (all_318_3_130 = 0) | ~ (all_318_4_131 = 0) | all_318_0_127 = 0)
% 66.99/31.13 |
% 66.99/31.13 | Applying alpha-rule on (656) yields:
% 66.99/31.13 | (657) ~ (all_318_1_128 = 0) | ~ (all_318_2_129 = 0) | ~ (all_318_3_130 = 0) | ~ (all_318_4_131 = 0) | all_318_0_127 = 0
% 66.99/31.13 | (658) aNaturalNumber0(all_85_0_110) = all_318_4_131
% 66.99/31.13 | (659) aNaturalNumber0(all_46_2_81) = all_318_2_129
% 66.99/31.13 | (660) aNaturalNumber0(xm) = all_318_3_130
% 66.99/31.13 | (661) doDivides0(all_85_0_110, all_46_2_81) = all_318_0_127
% 66.99/31.13 | (662) doDivides0(all_85_0_110, xm) = all_318_1_128
% 66.99/31.13 |
% 66.99/31.13 | Instantiating (629) with all_322_0_137, all_322_1_138, all_322_2_139 yields:
% 66.99/31.13 | (663) sdtpldt0(all_31_2_46, xr) = all_322_0_137 & aNaturalNumber0(all_31_2_46) = all_322_1_138 & aNaturalNumber0(xr) = all_322_2_139 & ( ~ (all_322_1_138 = 0) | ~ (all_322_2_139 = 0) | all_322_0_137 = xk)
% 66.99/31.13 |
% 66.99/31.13 | Applying alpha-rule on (663) yields:
% 66.99/31.13 | (664) sdtpldt0(all_31_2_46, xr) = all_322_0_137
% 66.99/31.13 | (665) aNaturalNumber0(all_31_2_46) = all_322_1_138
% 66.99/31.13 | (666) aNaturalNumber0(xr) = all_322_2_139
% 66.99/31.13 | (667) ~ (all_322_1_138 = 0) | ~ (all_322_2_139 = 0) | all_322_0_137 = xk
% 66.99/31.13 |
% 66.99/31.13 | Instantiating (621) with all_324_0_140, all_324_1_141, all_324_2_142 yields:
% 66.99/31.13 | (668) aNaturalNumber0(all_24_0_32) = all_324_0_140 & aNaturalNumber0(all_0_4_4) = all_324_1_141 & aNaturalNumber0(xr) = all_324_2_142 & ( ~ (all_324_1_141 = 0) | ~ (all_324_2_142 = 0) | all_324_0_140 = 0)
% 66.99/31.13 |
% 66.99/31.13 | Applying alpha-rule on (668) yields:
% 66.99/31.13 | (669) aNaturalNumber0(all_24_0_32) = all_324_0_140
% 66.99/31.13 | (670) aNaturalNumber0(all_0_4_4) = all_324_1_141
% 66.99/31.13 | (671) aNaturalNumber0(xr) = all_324_2_142
% 66.99/31.13 | (672) ~ (all_324_1_141 = 0) | ~ (all_324_2_142 = 0) | all_324_0_140 = 0
% 66.99/31.13 |
% 66.99/31.13 | Instantiating (620) with all_326_0_143, all_326_1_144, all_326_2_145 yields:
% 66.99/31.13 | (673) sdtasdt0(all_0_4_4, xr) = all_326_0_143 & aNaturalNumber0(all_0_4_4) = all_326_1_144 & aNaturalNumber0(xr) = all_326_2_145 & ( ~ (all_326_1_144 = 0) | ~ (all_326_2_145 = 0) | all_326_0_143 = all_24_0_32)
% 66.99/31.13 |
% 66.99/31.13 | Applying alpha-rule on (673) yields:
% 66.99/31.13 | (674) sdtasdt0(all_0_4_4, xr) = all_326_0_143
% 66.99/31.13 | (675) aNaturalNumber0(all_0_4_4) = all_326_1_144
% 66.99/31.13 | (676) aNaturalNumber0(xr) = all_326_2_145
% 66.99/31.13 | (677) ~ (all_326_1_144 = 0) | ~ (all_326_2_145 = 0) | all_326_0_143 = all_24_0_32
% 66.99/31.13 |
% 66.99/31.13 | Instantiating (613) with all_328_0_146, all_328_1_147, all_328_2_148 yields:
% 66.99/31.13 | (678) sdtasdt0(all_37_2_61, xr) = all_328_0_146 & aNaturalNumber0(all_37_2_61) = all_328_1_147 & aNaturalNumber0(xr) = all_328_2_148 & ( ~ (all_328_1_147 = 0) | ~ (all_328_2_148 = 0) | all_328_0_146 = xk)
% 67.13/31.13 |
% 67.13/31.13 | Applying alpha-rule on (678) yields:
% 67.13/31.13 | (679) sdtasdt0(all_37_2_61, xr) = all_328_0_146
% 67.13/31.13 | (680) aNaturalNumber0(all_37_2_61) = all_328_1_147
% 67.13/31.13 | (681) aNaturalNumber0(xr) = all_328_2_148
% 67.13/31.13 | (682) ~ (all_328_1_147 = 0) | ~ (all_328_2_148 = 0) | all_328_0_146 = xk
% 67.13/31.13 |
% 67.13/31.13 | Instantiating (612) with all_332_0_155, all_332_1_156, all_332_2_157 yields:
% 67.13/31.13 | (683) sdtasdt0(all_38_2_64, xr) = all_332_0_155 & aNaturalNumber0(all_38_2_64) = all_332_1_156 & aNaturalNumber0(xr) = all_332_2_157 & ( ~ (all_332_1_156 = 0) | ~ (all_332_2_157 = 0) | all_332_0_155 = all_0_9_9)
% 67.13/31.13 |
% 67.13/31.13 | Applying alpha-rule on (683) yields:
% 67.13/31.13 | (684) sdtasdt0(all_38_2_64, xr) = all_332_0_155
% 67.13/31.13 | (685) aNaturalNumber0(all_38_2_64) = all_332_1_156
% 67.13/31.13 | (686) aNaturalNumber0(xr) = all_332_2_157
% 67.13/31.13 | (687) ~ (all_332_1_156 = 0) | ~ (all_332_2_157 = 0) | all_332_0_155 = all_0_9_9
% 67.13/31.13 |
% 67.13/31.13 | Instantiating (611) with all_334_0_158, all_334_1_159, all_334_2_160 yields:
% 67.13/31.13 | (688) aNaturalNumber0(all_20_0_24) = all_334_0_158 & aNaturalNumber0(all_20_1_25) = all_334_1_159 & aNaturalNumber0(all_0_5_5) = all_334_2_160 & ( ~ (all_334_1_159 = 0) | ~ (all_334_2_160 = 0) | all_334_0_158 = 0)
% 67.13/31.13 |
% 67.13/31.13 | Applying alpha-rule on (688) yields:
% 67.13/31.13 | (689) aNaturalNumber0(all_20_0_24) = all_334_0_158
% 67.13/31.13 | (690) aNaturalNumber0(all_20_1_25) = all_334_1_159
% 67.13/31.13 | (691) aNaturalNumber0(all_0_5_5) = all_334_2_160
% 67.13/31.13 | (692) ~ (all_334_1_159 = 0) | ~ (all_334_2_160 = 0) | all_334_0_158 = 0
% 67.13/31.13 |
% 67.13/31.13 | Instantiating (610) with all_339_0_170, all_339_1_171, all_339_2_172 yields:
% 67.13/31.13 | (693) sdtasdt0(all_20_1_25, all_0_5_5) = all_339_0_170 & aNaturalNumber0(all_20_1_25) = all_339_1_171 & aNaturalNumber0(all_0_5_5) = all_339_2_172 & ( ~ (all_339_1_171 = 0) | ~ (all_339_2_172 = 0) | all_339_0_170 = all_20_0_24)
% 67.13/31.13 |
% 67.13/31.13 | Applying alpha-rule on (693) yields:
% 67.13/31.13 | (694) sdtasdt0(all_20_1_25, all_0_5_5) = all_339_0_170
% 67.13/31.13 | (695) aNaturalNumber0(all_20_1_25) = all_339_1_171
% 67.13/31.13 | (696) aNaturalNumber0(all_0_5_5) = all_339_2_172
% 67.13/31.13 | (697) ~ (all_339_1_171 = 0) | ~ (all_339_2_172 = 0) | all_339_0_170 = all_20_0_24
% 67.13/31.13 |
% 67.13/31.13 | Instantiating (619) with all_342_0_176, all_342_1_177, all_342_2_178 yields:
% 67.13/31.13 | (698) aNaturalNumber0(all_28_0_38) = all_342_0_176 & aNaturalNumber0(all_0_1_1) = all_342_1_177 & aNaturalNumber0(xr) = all_342_2_178 & ( ~ (all_342_1_177 = 0) | ~ (all_342_2_178 = 0) | all_342_0_176 = 0)
% 67.13/31.13 |
% 67.13/31.13 | Applying alpha-rule on (698) yields:
% 67.13/31.13 | (699) aNaturalNumber0(all_28_0_38) = all_342_0_176
% 67.13/31.13 | (700) aNaturalNumber0(all_0_1_1) = all_342_1_177
% 67.13/31.13 | (701) aNaturalNumber0(xr) = all_342_2_178
% 67.13/31.13 | (702) ~ (all_342_1_177 = 0) | ~ (all_342_2_178 = 0) | all_342_0_176 = 0
% 67.13/31.13 |
% 67.13/31.13 | Instantiating (618) with all_344_0_179, all_344_1_180, all_344_2_181 yields:
% 67.13/31.13 | (703) sdtasdt0(all_0_1_1, xr) = all_344_0_179 & aNaturalNumber0(all_0_1_1) = all_344_1_180 & aNaturalNumber0(xr) = all_344_2_181 & ( ~ (all_344_1_180 = 0) | ~ (all_344_2_181 = 0) | all_344_0_179 = all_28_0_38)
% 67.13/31.13 |
% 67.13/31.13 | Applying alpha-rule on (703) yields:
% 67.13/31.13 | (704) sdtasdt0(all_0_1_1, xr) = all_344_0_179
% 67.13/31.13 | (705) aNaturalNumber0(all_0_1_1) = all_344_1_180
% 67.13/31.13 | (706) aNaturalNumber0(xr) = all_344_2_181
% 67.13/31.13 | (707) ~ (all_344_1_180 = 0) | ~ (all_344_2_181 = 0) | all_344_0_179 = all_28_0_38
% 67.13/31.13 |
% 67.13/31.13 | Instantiating (616) with all_346_0_182, all_346_1_183, all_346_2_184 yields:
% 67.13/31.13 | (708) sdtasdt0(all_33_2_52, xr) = all_346_0_182 & aNaturalNumber0(all_33_2_52) = all_346_1_183 & aNaturalNumber0(xr) = all_346_2_184 & ( ~ (all_346_1_183 = 0) | ~ (all_346_2_184 = 0) | all_346_0_182 = xn)
% 67.13/31.13 |
% 67.13/31.13 | Applying alpha-rule on (708) yields:
% 67.13/31.13 | (709) sdtasdt0(all_33_2_52, xr) = all_346_0_182
% 67.13/31.13 | (710) aNaturalNumber0(all_33_2_52) = all_346_1_183
% 67.13/31.13 | (711) aNaturalNumber0(xr) = all_346_2_184
% 67.13/31.13 | (712) ~ (all_346_1_183 = 0) | ~ (all_346_2_184 = 0) | all_346_0_182 = xn
% 67.13/31.13 |
% 67.13/31.13 | Instantiating (615) with all_348_0_185, all_348_1_186, all_348_2_187, all_348_3_188, all_348_4_189 yields:
% 67.13/31.13 | (713) sdtasdt0(all_33_2_52, xm) = all_348_1_186 & sdtasdt0(xr, all_348_1_186) = all_348_0_185 & aNaturalNumber0(all_33_2_52) = all_348_3_188 & aNaturalNumber0(xr) = all_348_4_189 & aNaturalNumber0(xm) = all_348_2_187 & ( ~ (all_348_2_187 = 0) | ~ (all_348_3_188 = 0) | ~ (all_348_4_189 = 0) | all_348_0_185 = all_0_9_9)
% 67.13/31.13 |
% 67.13/31.13 | Applying alpha-rule on (713) yields:
% 67.13/31.13 | (714) ~ (all_348_2_187 = 0) | ~ (all_348_3_188 = 0) | ~ (all_348_4_189 = 0) | all_348_0_185 = all_0_9_9
% 67.13/31.13 | (715) aNaturalNumber0(xm) = all_348_2_187
% 67.13/31.13 | (716) aNaturalNumber0(all_33_2_52) = all_348_3_188
% 67.13/31.13 | (717) sdtasdt0(xr, all_348_1_186) = all_348_0_185
% 67.13/31.13 | (718) aNaturalNumber0(xr) = all_348_4_189
% 67.13/31.13 | (719) sdtasdt0(all_33_2_52, xm) = all_348_1_186
% 67.13/31.13 |
% 67.13/31.13 | Instantiating (628) with all_350_0_190, all_350_1_191, all_350_2_192, all_350_3_193, all_350_4_194 yields:
% 67.13/31.13 | (720) doDivides0(xr, all_31_2_46) = all_350_0_190 & doDivides0(xr, xr) = all_350_1_191 & aNaturalNumber0(all_31_2_46) = all_350_2_192 & aNaturalNumber0(xr) = all_350_3_193 & aNaturalNumber0(xr) = all_350_4_194 & ( ~ (all_350_1_191 = 0) | ~ (all_350_2_192 = 0) | ~ (all_350_3_193 = 0) | ~ (all_350_4_194 = 0) | all_350_0_190 = 0)
% 67.13/31.13 |
% 67.13/31.13 | Applying alpha-rule on (720) yields:
% 67.13/31.13 | (721) aNaturalNumber0(xr) = all_350_4_194
% 67.13/31.13 | (722) doDivides0(xr, xr) = all_350_1_191
% 67.13/31.13 | (723) aNaturalNumber0(all_31_2_46) = all_350_2_192
% 67.13/31.14 | (724) ~ (all_350_1_191 = 0) | ~ (all_350_2_192 = 0) | ~ (all_350_3_193 = 0) | ~ (all_350_4_194 = 0) | all_350_0_190 = 0
% 67.13/31.14 | (725) aNaturalNumber0(xr) = all_350_3_193
% 67.13/31.14 | (726) doDivides0(xr, all_31_2_46) = all_350_0_190
% 67.13/31.14 |
% 67.13/31.14 | Instantiating (626) with all_354_0_200, all_354_1_201, all_354_2_202 yields:
% 67.13/31.14 | (727) aNaturalNumber0(all_20_1_25) = all_354_0_200 & aNaturalNumber0(xr) = all_354_1_201 & aNaturalNumber0(xm) = all_354_2_202 & ( ~ (all_354_1_201 = 0) | ~ (all_354_2_202 = 0) | all_354_0_200 = 0)
% 67.13/31.14 |
% 67.13/31.14 | Applying alpha-rule on (727) yields:
% 67.13/31.14 | (728) aNaturalNumber0(all_20_1_25) = all_354_0_200
% 67.13/31.14 | (729) aNaturalNumber0(xr) = all_354_1_201
% 67.13/31.14 | (730) aNaturalNumber0(xm) = all_354_2_202
% 67.13/31.14 | (731) ~ (all_354_1_201 = 0) | ~ (all_354_2_202 = 0) | all_354_0_200 = 0
% 67.13/31.14 |
% 67.13/31.14 | Instantiating (625) with all_356_0_203, all_356_1_204, all_356_2_205 yields:
% 67.13/31.14 | (732) sdtasdt0(xr, xm) = all_356_0_203 & aNaturalNumber0(xr) = all_356_1_204 & aNaturalNumber0(xm) = all_356_2_205 & ( ~ (all_356_1_204 = 0) | ~ (all_356_2_205 = 0) | all_356_0_203 = all_20_1_25)
% 67.13/31.14 |
% 67.13/31.14 | Applying alpha-rule on (732) yields:
% 67.13/31.14 | (733) sdtasdt0(xr, xm) = all_356_0_203
% 67.13/31.14 | (734) aNaturalNumber0(xr) = all_356_1_204
% 67.13/31.14 | (735) aNaturalNumber0(xm) = all_356_2_205
% 67.13/31.14 | (736) ~ (all_356_1_204 = 0) | ~ (all_356_2_205 = 0) | all_356_0_203 = all_20_1_25
% 67.13/31.14 |
% 67.13/31.14 | Instantiating (624) with all_360_0_209, all_360_1_210, all_360_2_211 yields:
% 67.13/31.14 | (737) aNaturalNumber0(all_18_0_21) = all_360_0_209 & aNaturalNumber0(all_0_5_5) = all_360_1_210 & aNaturalNumber0(xm) = all_360_2_211 & ( ~ (all_360_1_210 = 0) | ~ (all_360_2_211 = 0) | all_360_0_209 = 0)
% 67.13/31.14 |
% 67.13/31.14 | Applying alpha-rule on (737) yields:
% 67.13/31.14 | (738) aNaturalNumber0(all_18_0_21) = all_360_0_209
% 67.13/31.14 | (739) aNaturalNumber0(all_0_5_5) = all_360_1_210
% 67.13/31.14 | (740) aNaturalNumber0(xm) = all_360_2_211
% 67.13/31.14 | (741) ~ (all_360_1_210 = 0) | ~ (all_360_2_211 = 0) | all_360_0_209 = 0
% 67.13/31.14 |
% 67.13/31.14 | Instantiating (631) with all_366_0_224, all_366_1_225, all_366_2_226, all_366_3_227, all_366_4_228 yields:
% 67.13/31.14 | (742) sdtpldt0(all_31_2_46, all_30_2_43) = all_366_1_225 & sdtpldt0(xr, all_366_1_225) = all_366_0_224 & aNaturalNumber0(all_31_2_46) = all_366_3_227 & aNaturalNumber0(all_30_2_43) = all_366_2_226 & aNaturalNumber0(xr) = all_366_4_228 & ( ~ (all_366_2_226 = 0) | ~ (all_366_3_227 = 0) | ~ (all_366_4_228 = 0) | all_366_0_224 = xp)
% 67.13/31.14 |
% 67.13/31.14 | Applying alpha-rule on (742) yields:
% 67.13/31.14 | (743) aNaturalNumber0(xr) = all_366_4_228
% 67.13/31.14 | (744) aNaturalNumber0(all_30_2_43) = all_366_2_226
% 67.13/31.14 | (745) aNaturalNumber0(all_31_2_46) = all_366_3_227
% 67.13/31.14 | (746) sdtpldt0(all_31_2_46, all_30_2_43) = all_366_1_225
% 67.13/31.14 | (747) ~ (all_366_2_226 = 0) | ~ (all_366_3_227 = 0) | ~ (all_366_4_228 = 0) | all_366_0_224 = xp
% 67.13/31.14 | (748) sdtpldt0(xr, all_366_1_225) = all_366_0_224
% 67.13/31.14 |
% 67.13/31.14 | Instantiating (642) with all_368_0_229, all_368_1_230, all_368_2_231, all_368_3_232, all_368_4_233 yields:
% 67.13/31.14 | (749) sdtpldt0(all_45_2_78, all_0_11_11) = all_368_1_230 & sdtpldt0(xn, all_368_1_230) = all_368_0_229 & aNaturalNumber0(all_45_2_78) = all_368_3_232 & aNaturalNumber0(all_0_11_11) = all_368_2_231 & aNaturalNumber0(xn) = all_368_4_233 & ( ~ (all_368_2_231 = 0) | ~ (all_368_3_232 = 0) | ~ (all_368_4_233 = 0) | all_368_0_229 = all_0_10_10)
% 67.13/31.14 |
% 67.13/31.14 | Applying alpha-rule on (749) yields:
% 67.13/31.14 | (750) aNaturalNumber0(all_45_2_78) = all_368_3_232
% 67.13/31.14 | (751) sdtpldt0(all_45_2_78, all_0_11_11) = all_368_1_230
% 67.13/31.14 | (752) aNaturalNumber0(xn) = all_368_4_233
% 67.13/31.14 | (753) aNaturalNumber0(all_0_11_11) = all_368_2_231
% 67.13/31.14 | (754) sdtpldt0(xn, all_368_1_230) = all_368_0_229
% 67.13/31.14 | (755) ~ (all_368_2_231 = 0) | ~ (all_368_3_232 = 0) | ~ (all_368_4_233 = 0) | all_368_0_229 = all_0_10_10
% 67.13/31.14 |
% 67.13/31.14 | Instantiating (641) with all_370_0_234, all_370_1_235, all_370_2_236, all_370_3_237, all_370_4_238, all_370_5_239, all_370_6_240, all_370_7_241, all_370_8_242 yields:
% 67.13/31.14 | (756) isPrime0(all_0_11_11) = all_370_5_239 & doDivides0(all_0_11_11, all_370_4_238) = all_370_3_237 & doDivides0(all_0_11_11, all_45_2_78) = all_370_0_234 & doDivides0(all_0_11_11, xn) = all_370_1_235 & iLess0(all_0_10_10, all_0_10_10) = all_370_2_236 & sdtasdt0(xn, all_45_2_78) = all_370_4_238 & aNaturalNumber0(all_45_2_78) = all_370_7_241 & aNaturalNumber0(all_0_11_11) = all_370_6_240 & aNaturalNumber0(xn) = all_370_8_242 & ( ~ (all_370_2_236 = 0) | ~ (all_370_3_237 = 0) | ~ (all_370_5_239 = 0) | ~ (all_370_6_240 = 0) | ~ (all_370_7_241 = 0) | ~ (all_370_8_242 = 0) | all_370_0_234 = 0 | all_370_1_235 = 0)
% 67.13/31.14 |
% 67.13/31.14 | Applying alpha-rule on (756) yields:
% 67.13/31.14 | (757) ~ (all_370_2_236 = 0) | ~ (all_370_3_237 = 0) | ~ (all_370_5_239 = 0) | ~ (all_370_6_240 = 0) | ~ (all_370_7_241 = 0) | ~ (all_370_8_242 = 0) | all_370_0_234 = 0 | all_370_1_235 = 0
% 67.13/31.14 | (758) sdtasdt0(xn, all_45_2_78) = all_370_4_238
% 67.13/31.14 | (759) aNaturalNumber0(all_45_2_78) = all_370_7_241
% 67.13/31.14 | (760) aNaturalNumber0(xn) = all_370_8_242
% 67.13/31.14 | (761) doDivides0(all_0_11_11, xn) = all_370_1_235
% 67.13/31.14 | (762) aNaturalNumber0(all_0_11_11) = all_370_6_240
% 67.13/31.14 | (763) iLess0(all_0_10_10, all_0_10_10) = all_370_2_236
% 67.13/31.14 | (764) doDivides0(all_0_11_11, all_370_4_238) = all_370_3_237
% 67.13/31.14 | (765) doDivides0(all_0_11_11, all_45_2_78) = all_370_0_234
% 67.13/31.14 | (766) isPrime0(all_0_11_11) = all_370_5_239
% 67.13/31.14 |
% 67.13/31.14 | Instantiating (637) with all_372_0_243, all_372_1_244, all_372_2_245 yields:
% 67.13/31.14 | (767) aNaturalNumber0(all_41_1_69) = all_372_0_243 & aNaturalNumber0(xp) = all_372_1_244 & aNaturalNumber0(xm) = all_372_2_245 & ( ~ (all_372_1_244 = 0) | ~ (all_372_2_245 = 0) | all_372_0_243 = 0)
% 67.13/31.14 |
% 67.13/31.14 | Applying alpha-rule on (767) yields:
% 67.13/31.14 | (768) aNaturalNumber0(all_41_1_69) = all_372_0_243
% 67.13/31.14 | (769) aNaturalNumber0(xp) = all_372_1_244
% 67.13/31.14 | (770) aNaturalNumber0(xm) = all_372_2_245
% 67.13/31.14 | (771) ~ (all_372_1_244 = 0) | ~ (all_372_2_245 = 0) | all_372_0_243 = 0
% 67.13/31.14 |
% 67.13/31.14 | Instantiating (635) with all_374_0_246, all_374_1_247, all_374_2_248 yields:
% 67.13/31.14 | (772) sdtpldt0(all_46_2_81, xm) = all_374_0_246 & aNaturalNumber0(all_46_2_81) = all_374_1_247 & aNaturalNumber0(xm) = all_374_2_248 & ( ~ (all_374_1_247 = 0) | ~ (all_374_2_248 = 0) | all_374_0_246 = xp)
% 67.13/31.14 |
% 67.13/31.14 | Applying alpha-rule on (772) yields:
% 67.13/31.14 | (773) sdtpldt0(all_46_2_81, xm) = all_374_0_246
% 67.13/31.14 | (774) aNaturalNumber0(all_46_2_81) = all_374_1_247
% 67.13/31.14 | (775) aNaturalNumber0(xm) = all_374_2_248
% 67.13/31.14 | (776) ~ (all_374_1_247 = 0) | ~ (all_374_2_248 = 0) | all_374_0_246 = xp
% 67.13/31.14 |
% 67.13/31.14 | Instantiating (634) with all_376_0_249, all_376_1_250, all_376_2_251, all_376_3_252, all_376_4_253 yields:
% 67.13/31.14 | (777) sdtpldt0(all_46_2_81, all_0_11_11) = all_376_1_250 & sdtpldt0(xm, all_376_1_250) = all_376_0_249 & aNaturalNumber0(all_46_2_81) = all_376_3_252 & aNaturalNumber0(all_0_11_11) = all_376_2_251 & aNaturalNumber0(xm) = all_376_4_253 & ( ~ (all_376_2_251 = 0) | ~ (all_376_3_252 = 0) | ~ (all_376_4_253 = 0) | all_376_0_249 = all_0_10_10)
% 67.13/31.14 |
% 67.13/31.14 | Applying alpha-rule on (777) yields:
% 67.13/31.14 | (778) sdtpldt0(xm, all_376_1_250) = all_376_0_249
% 67.13/31.14 | (779) aNaturalNumber0(all_46_2_81) = all_376_3_252
% 67.13/31.14 | (780) aNaturalNumber0(all_0_11_11) = all_376_2_251
% 67.13/31.14 | (781) aNaturalNumber0(xm) = all_376_4_253
% 67.13/31.14 | (782) ~ (all_376_2_251 = 0) | ~ (all_376_3_252 = 0) | ~ (all_376_4_253 = 0) | all_376_0_249 = all_0_10_10
% 67.13/31.14 | (783) sdtpldt0(all_46_2_81, all_0_11_11) = all_376_1_250
% 67.13/31.14 |
% 67.13/31.14 | Instantiating (636) with all_378_0_254, all_378_1_255, all_378_2_256 yields:
% 67.13/31.14 | (784) sdtpldt0(xp, xm) = all_378_0_254 & aNaturalNumber0(xp) = all_378_1_255 & aNaturalNumber0(xm) = all_378_2_256 & ( ~ (all_378_1_255 = 0) | ~ (all_378_2_256 = 0) | all_378_0_254 = all_41_1_69)
% 67.13/31.14 |
% 67.13/31.14 | Applying alpha-rule on (784) yields:
% 67.13/31.14 | (785) sdtpldt0(xp, xm) = all_378_0_254
% 67.13/31.14 | (786) aNaturalNumber0(xp) = all_378_1_255
% 67.13/31.14 | (787) aNaturalNumber0(xm) = all_378_2_256
% 67.13/31.14 | (788) ~ (all_378_1_255 = 0) | ~ (all_378_2_256 = 0) | all_378_0_254 = all_41_1_69
% 67.13/31.14 |
% 67.13/31.14 | Instantiating (640) with all_380_0_257, all_380_1_258, all_380_2_259, all_380_3_260, all_380_4_261 yields:
% 67.13/31.14 | (789) doDivides0(all_85_0_110, all_45_2_78) = all_380_0_257 & doDivides0(all_85_0_110, xn) = all_380_1_258 & aNaturalNumber0(all_85_0_110) = all_380_4_261 & aNaturalNumber0(all_45_2_78) = all_380_2_259 & aNaturalNumber0(xn) = all_380_3_260 & ( ~ (all_380_1_258 = 0) | ~ (all_380_2_259 = 0) | ~ (all_380_3_260 = 0) | ~ (all_380_4_261 = 0) | all_380_0_257 = 0)
% 67.13/31.14 |
% 67.13/31.14 | Applying alpha-rule on (789) yields:
% 67.13/31.14 | (790) doDivides0(all_85_0_110, xn) = all_380_1_258
% 67.13/31.14 | (791) ~ (all_380_1_258 = 0) | ~ (all_380_2_259 = 0) | ~ (all_380_3_260 = 0) | ~ (all_380_4_261 = 0) | all_380_0_257 = 0
% 67.13/31.14 | (792) aNaturalNumber0(all_45_2_78) = all_380_2_259
% 67.13/31.14 | (793) doDivides0(all_85_0_110, all_45_2_78) = all_380_0_257
% 67.13/31.14 | (794) aNaturalNumber0(all_85_0_110) = all_380_4_261
% 67.13/31.14 | (795) aNaturalNumber0(xn) = all_380_3_260
% 67.13/31.14 |
% 67.13/31.14 | Instantiating (639) with all_382_0_262, all_382_1_263, all_382_2_264, all_382_3_265, all_382_4_266 yields:
% 67.13/31.14 | (796) sdtpldt0(xm, all_382_1_263) = all_382_0_262 & sdtpldt0(xn, xp) = all_382_1_263 & aNaturalNumber0(xp) = all_382_2_264 & aNaturalNumber0(xm) = all_382_4_266 & aNaturalNumber0(xn) = all_382_3_265 & ( ~ (all_382_2_264 = 0) | ~ (all_382_3_265 = 0) | ~ (all_382_4_266 = 0) | all_382_0_262 = all_0_10_10)
% 67.13/31.14 |
% 67.13/31.14 | Applying alpha-rule on (796) yields:
% 67.13/31.14 | (797) aNaturalNumber0(xp) = all_382_2_264
% 67.13/31.14 | (798) aNaturalNumber0(xm) = all_382_4_266
% 67.13/31.14 | (799) sdtpldt0(xn, xp) = all_382_1_263
% 67.13/31.14 | (800) aNaturalNumber0(xn) = all_382_3_265
% 67.13/31.14 | (801) sdtpldt0(xm, all_382_1_263) = all_382_0_262
% 67.13/31.14 | (802) ~ (all_382_2_264 = 0) | ~ (all_382_3_265 = 0) | ~ (all_382_4_266 = 0) | all_382_0_262 = all_0_10_10
% 67.13/31.14 |
% 67.13/31.14 | Instantiating (643) with all_384_0_267, all_384_1_268, all_384_2_269 yields:
% 67.13/31.14 | (803) sdtpldt0(all_45_2_78, xn) = all_384_0_267 & aNaturalNumber0(all_45_2_78) = all_384_1_268 & aNaturalNumber0(xn) = all_384_2_269 & ( ~ (all_384_1_268 = 0) | ~ (all_384_2_269 = 0) | all_384_0_267 = xp)
% 67.13/31.14 |
% 67.13/31.14 | Applying alpha-rule on (803) yields:
% 67.13/31.14 | (804) sdtpldt0(all_45_2_78, xn) = all_384_0_267
% 67.13/31.14 | (805) aNaturalNumber0(all_45_2_78) = all_384_1_268
% 67.13/31.14 | (806) aNaturalNumber0(xn) = all_384_2_269
% 67.13/31.14 | (807) ~ (all_384_1_268 = 0) | ~ (all_384_2_269 = 0) | all_384_0_267 = xp
% 67.13/31.14 |
% 67.13/31.14 | Instantiating (630) with all_386_0_270, all_386_1_271, all_386_2_272, all_386_3_273, all_386_4_274, all_386_5_275, all_386_6_276, all_386_7_277, all_386_8_278 yields:
% 67.13/31.14 | (808) isPrime0(all_30_2_43) = all_386_5_275 & doDivides0(all_30_2_43, all_386_4_274) = all_386_3_273 & doDivides0(all_30_2_43, all_31_2_46) = all_386_0_270 & doDivides0(all_30_2_43, xr) = all_386_1_271 & iLess0(xp, all_0_10_10) = all_386_2_272 & sdtasdt0(xr, all_31_2_46) = all_386_4_274 & aNaturalNumber0(all_31_2_46) = all_386_7_277 & aNaturalNumber0(all_30_2_43) = all_386_6_276 & aNaturalNumber0(xr) = all_386_8_278 & ( ~ (all_386_2_272 = 0) | ~ (all_386_3_273 = 0) | ~ (all_386_5_275 = 0) | ~ (all_386_6_276 = 0) | ~ (all_386_7_277 = 0) | ~ (all_386_8_278 = 0) | all_386_0_270 = 0 | all_386_1_271 = 0)
% 67.13/31.15 |
% 67.13/31.15 | Applying alpha-rule on (808) yields:
% 67.13/31.15 | (809) doDivides0(all_30_2_43, all_31_2_46) = all_386_0_270
% 67.13/31.15 | (810) ~ (all_386_2_272 = 0) | ~ (all_386_3_273 = 0) | ~ (all_386_5_275 = 0) | ~ (all_386_6_276 = 0) | ~ (all_386_7_277 = 0) | ~ (all_386_8_278 = 0) | all_386_0_270 = 0 | all_386_1_271 = 0
% 67.13/31.15 | (811) aNaturalNumber0(all_31_2_46) = all_386_7_277
% 67.13/31.15 | (812) isPrime0(all_30_2_43) = all_386_5_275
% 67.13/31.15 | (813) doDivides0(all_30_2_43, all_386_4_274) = all_386_3_273
% 67.13/31.15 | (814) sdtasdt0(xr, all_31_2_46) = all_386_4_274
% 67.13/31.15 | (815) aNaturalNumber0(all_30_2_43) = all_386_6_276
% 67.13/31.15 | (816) aNaturalNumber0(xr) = all_386_8_278
% 67.13/31.15 | (817) iLess0(xp, all_0_10_10) = all_386_2_272
% 67.13/31.15 | (818) doDivides0(all_30_2_43, xr) = all_386_1_271
% 67.13/31.15 |
% 67.13/31.15 | Instantiating (638) with all_388_0_279, all_388_1_280, all_388_2_281, all_388_3_282, all_388_4_283, all_388_5_284, all_388_6_285, all_388_7_286, all_388_8_287 yields:
% 67.13/31.15 | (819) isPrime0(xp) = all_388_5_284 & doDivides0(xp, all_388_4_283) = all_388_3_282 & doDivides0(xp, xm) = all_388_1_280 & doDivides0(xp, xn) = all_388_0_279 & iLess0(all_0_10_10, all_0_10_10) = all_388_2_281 & sdtasdt0(xm, xn) = all_388_4_283 & aNaturalNumber0(xp) = all_388_6_285 & aNaturalNumber0(xm) = all_388_8_287 & aNaturalNumber0(xn) = all_388_7_286 & ( ~ (all_388_2_281 = 0) | ~ (all_388_3_282 = 0) | ~ (all_388_5_284 = 0) | ~ (all_388_6_285 = 0) | ~ (all_388_7_286 = 0) | ~ (all_388_8_287 = 0) | all_388_0_279 = 0 | all_388_1_280 = 0)
% 67.13/31.15 |
% 67.13/31.15 | Applying alpha-rule on (819) yields:
% 67.13/31.15 | (820) aNaturalNumber0(xp) = all_388_6_285
% 67.13/31.15 | (821) aNaturalNumber0(xm) = all_388_8_287
% 67.13/31.15 | (822) doDivides0(xp, all_388_4_283) = all_388_3_282
% 67.13/31.15 | (823) aNaturalNumber0(xn) = all_388_7_286
% 67.13/31.15 | (824) doDivides0(xp, xm) = all_388_1_280
% 67.13/31.15 | (825) isPrime0(xp) = all_388_5_284
% 67.13/31.15 | (826) doDivides0(xp, xn) = all_388_0_279
% 67.13/31.15 | (827) sdtasdt0(xm, xn) = all_388_4_283
% 67.13/31.15 | (828) ~ (all_388_2_281 = 0) | ~ (all_388_3_282 = 0) | ~ (all_388_5_284 = 0) | ~ (all_388_6_285 = 0) | ~ (all_388_7_286 = 0) | ~ (all_388_8_287 = 0) | all_388_0_279 = 0 | all_388_1_280 = 0
% 67.13/31.15 | (829) iLess0(all_0_10_10, all_0_10_10) = all_388_2_281
% 67.13/31.15 |
% 67.13/31.15 | Instantiating (623) with all_390_0_288, all_390_1_289, all_390_2_290 yields:
% 67.13/31.15 | (830) sdtasdt0(all_0_5_5, xm) = all_390_0_288 & aNaturalNumber0(all_0_5_5) = all_390_1_289 & aNaturalNumber0(xm) = all_390_2_290 & ( ~ (all_390_1_289 = 0) | ~ (all_390_2_290 = 0) | all_390_0_288 = all_18_0_21)
% 67.13/31.15 |
% 67.13/31.15 | Applying alpha-rule on (830) yields:
% 67.13/31.15 | (831) sdtasdt0(all_0_5_5, xm) = all_390_0_288
% 67.13/31.15 | (832) aNaturalNumber0(all_0_5_5) = all_390_1_289
% 67.13/31.15 | (833) aNaturalNumber0(xm) = all_390_2_290
% 67.13/31.15 | (834) ~ (all_390_1_289 = 0) | ~ (all_390_2_290 = 0) | all_390_0_288 = all_18_0_21
% 67.13/31.15 |
% 67.13/31.15 | Instantiating (633) with all_392_0_291, all_392_1_292, all_392_2_293, all_392_3_294, all_392_4_295, all_392_5_296, all_392_6_297, all_392_7_298, all_392_8_299 yields:
% 67.13/31.15 | (835) isPrime0(all_0_11_11) = all_392_5_296 & doDivides0(all_0_11_11, all_392_4_295) = all_392_3_294 & doDivides0(all_0_11_11, all_46_2_81) = all_392_0_291 & doDivides0(all_0_11_11, xm) = all_392_1_292 & iLess0(all_0_10_10, all_0_10_10) = all_392_2_293 & sdtasdt0(xm, all_46_2_81) = all_392_4_295 & aNaturalNumber0(all_46_2_81) = all_392_7_298 & aNaturalNumber0(all_0_11_11) = all_392_6_297 & aNaturalNumber0(xm) = all_392_8_299 & ( ~ (all_392_2_293 = 0) | ~ (all_392_3_294 = 0) | ~ (all_392_5_296 = 0) | ~ (all_392_6_297 = 0) | ~ (all_392_7_298 = 0) | ~ (all_392_8_299 = 0) | all_392_0_291 = 0 | all_392_1_292 = 0)
% 67.13/31.15 |
% 67.13/31.15 | Applying alpha-rule on (835) yields:
% 67.13/31.15 | (836) ~ (all_392_2_293 = 0) | ~ (all_392_3_294 = 0) | ~ (all_392_5_296 = 0) | ~ (all_392_6_297 = 0) | ~ (all_392_7_298 = 0) | ~ (all_392_8_299 = 0) | all_392_0_291 = 0 | all_392_1_292 = 0
% 67.13/31.15 | (837) aNaturalNumber0(all_0_11_11) = all_392_6_297
% 67.13/31.15 | (838) isPrime0(all_0_11_11) = all_392_5_296
% 67.13/31.15 | (839) sdtasdt0(xm, all_46_2_81) = all_392_4_295
% 67.13/31.15 | (840) iLess0(all_0_10_10, all_0_10_10) = all_392_2_293
% 67.13/31.15 | (841) doDivides0(all_0_11_11, all_46_2_81) = all_392_0_291
% 67.13/31.15 | (842) aNaturalNumber0(all_46_2_81) = all_392_7_298
% 67.13/31.15 | (843) doDivides0(all_0_11_11, xm) = all_392_1_292
% 67.13/31.15 | (844) aNaturalNumber0(xm) = all_392_8_299
% 67.13/31.15 | (845) doDivides0(all_0_11_11, all_392_4_295) = all_392_3_294
% 67.13/31.15 |
% 67.13/31.15 | Instantiating (622) with all_394_0_300, all_394_1_301, all_394_2_302, all_394_3_303, all_394_4_304 yields:
% 67.13/31.15 | (846) sdtasdt0(all_37_2_61, xp) = all_394_1_301 & sdtasdt0(xr, all_394_1_301) = all_394_0_300 & aNaturalNumber0(all_37_2_61) = all_394_3_303 & aNaturalNumber0(xr) = all_394_4_304 & aNaturalNumber0(xp) = all_394_2_302 & ( ~ (all_394_2_302 = 0) | ~ (all_394_3_303 = 0) | ~ (all_394_4_304 = 0) | all_394_0_300 = all_0_9_9)
% 67.13/31.15 |
% 67.13/31.15 | Applying alpha-rule on (846) yields:
% 67.13/31.15 | (847) ~ (all_394_2_302 = 0) | ~ (all_394_3_303 = 0) | ~ (all_394_4_304 = 0) | all_394_0_300 = all_0_9_9
% 67.13/31.15 | (848) sdtasdt0(all_37_2_61, xp) = all_394_1_301
% 67.13/31.15 | (849) aNaturalNumber0(xp) = all_394_2_302
% 67.13/31.15 | (850) aNaturalNumber0(all_37_2_61) = all_394_3_303
% 67.13/31.15 | (851) sdtasdt0(xr, all_394_1_301) = all_394_0_300
% 67.13/31.15 | (852) aNaturalNumber0(xr) = all_394_4_304
% 67.13/31.15 |
% 67.13/31.15 +-Applying beta-rule and splitting (606), into two cases.
% 67.13/31.15 |-Branch one:
% 67.13/31.15 | (576) xn = sz00
% 67.13/31.15 |
% 67.13/31.15 | Equations (576) can reduce 568 to:
% 67.13/31.15 | (241) $false
% 67.13/31.15 |
% 67.13/31.15 |-The branch is then unsatisfiable
% 67.13/31.15 |-Branch two:
% 67.13/31.15 | (568) ~ (xn = sz00)
% 67.13/31.15 | (856) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_285_0_117, xn) = v2 & aNaturalNumber0(all_285_0_117) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 67.13/31.15 |
% 67.13/31.15 | Instantiating (856) with all_400_0_305, all_400_1_306, all_400_2_307 yields:
% 67.13/31.15 | (857) sdtlseqdt0(all_285_0_117, xn) = all_400_0_305 & aNaturalNumber0(all_285_0_117) = all_400_2_307 & aNaturalNumber0(xn) = all_400_1_306 & ( ~ (all_400_1_306 = 0) | ~ (all_400_2_307 = 0) | all_400_0_305 = 0)
% 67.13/31.15 |
% 67.13/31.15 | Applying alpha-rule on (857) yields:
% 67.13/31.15 | (858) sdtlseqdt0(all_285_0_117, xn) = all_400_0_305
% 67.13/31.15 | (859) aNaturalNumber0(all_285_0_117) = all_400_2_307
% 67.13/31.15 | (860) aNaturalNumber0(xn) = all_400_1_306
% 67.13/31.15 | (861) ~ (all_400_1_306 = 0) | ~ (all_400_2_307 = 0) | all_400_0_305 = 0
% 67.13/31.15 |
% 67.13/31.15 +-Applying beta-rule and splitting (608), into two cases.
% 67.13/31.15 |-Branch one:
% 67.13/31.15 | (862) all_0_7_7 = 0
% 67.13/31.15 |
% 67.13/31.15 | Equations (862) can reduce 81 to:
% 67.13/31.15 | (241) $false
% 67.13/31.15 |
% 67.13/31.15 |-The branch is then unsatisfiable
% 67.13/31.15 |-Branch two:
% 67.13/31.15 | (81) ~ (all_0_7_7 = 0)
% 67.13/31.15 | (865) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtlseqdt0(all_0_9_9, xm) = v3 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 67.13/31.15 |
% 67.13/31.15 | Instantiating (865) with all_410_0_312, all_410_1_313, all_410_2_314, all_410_3_315 yields:
% 67.13/31.15 | (866) sdtlseqdt0(all_0_9_9, xm) = all_410_0_312 & aNaturalNumber0(all_0_9_9) = all_410_2_314 & aNaturalNumber0(xp) = all_410_3_315 & aNaturalNumber0(xm) = all_410_1_313 & ( ~ (all_410_0_312 = 0) | ~ (all_410_1_313 = 0) | ~ (all_410_2_314 = 0) | ~ (all_410_3_315 = 0))
% 67.13/31.15 |
% 67.13/31.15 | Applying alpha-rule on (866) yields:
% 67.13/31.15 | (867) aNaturalNumber0(xm) = all_410_1_313
% 67.13/31.15 | (868) sdtlseqdt0(all_0_9_9, xm) = all_410_0_312
% 67.13/31.15 | (869) ~ (all_410_0_312 = 0) | ~ (all_410_1_313 = 0) | ~ (all_410_2_314 = 0) | ~ (all_410_3_315 = 0)
% 67.13/31.15 | (870) aNaturalNumber0(xp) = all_410_3_315
% 67.13/31.15 | (871) aNaturalNumber0(all_0_9_9) = all_410_2_314
% 67.13/31.15 |
% 67.13/31.15 +-Applying beta-rule and splitting (609), into two cases.
% 67.13/31.15 |-Branch one:
% 67.13/31.15 | (872) all_0_8_8 = 0
% 67.13/31.15 |
% 67.13/31.15 | Equations (872) can reduce 48 to:
% 67.13/31.15 | (241) $false
% 67.13/31.15 |
% 67.13/31.15 |-The branch is then unsatisfiable
% 67.13/31.15 |-Branch two:
% 67.13/31.15 | (48) ~ (all_0_8_8 = 0)
% 67.13/31.15 | (875) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtlseqdt0(all_0_9_9, xn) = v3 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 67.13/31.15 |
% 67.13/31.15 | Instantiating (875) with all_415_0_316, all_415_1_317, all_415_2_318, all_415_3_319 yields:
% 67.13/31.15 | (876) sdtlseqdt0(all_0_9_9, xn) = all_415_0_316 & aNaturalNumber0(all_0_9_9) = all_415_2_318 & aNaturalNumber0(xp) = all_415_3_319 & aNaturalNumber0(xn) = all_415_1_317 & ( ~ (all_415_0_316 = 0) | ~ (all_415_1_317 = 0) | ~ (all_415_2_318 = 0) | ~ (all_415_3_319 = 0))
% 67.13/31.15 |
% 67.13/31.15 | Applying alpha-rule on (876) yields:
% 67.13/31.15 | (877) sdtlseqdt0(all_0_9_9, xn) = all_415_0_316
% 67.13/31.15 | (878) aNaturalNumber0(xp) = all_415_3_319
% 67.13/31.15 | (879) aNaturalNumber0(xn) = all_415_1_317
% 67.13/31.15 | (880) ~ (all_415_0_316 = 0) | ~ (all_415_1_317 = 0) | ~ (all_415_2_318 = 0) | ~ (all_415_3_319 = 0)
% 67.13/31.15 | (881) aNaturalNumber0(all_0_9_9) = all_415_2_318
% 67.13/31.15 |
% 67.13/31.15 +-Applying beta-rule and splitting (607), into two cases.
% 67.13/31.15 |-Branch one:
% 67.13/31.15 | (263) xr = sz00
% 67.13/31.15 |
% 67.13/31.15 | Equations (263) can reduce 98 to:
% 67.13/31.15 | (241) $false
% 67.13/31.15 |
% 67.13/31.15 |-The branch is then unsatisfiable
% 67.13/31.15 |-Branch two:
% 67.13/31.15 | (98) ~ (xr = sz00)
% 67.13/31.15 | (885) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_80_0_109, xr) = v2 & aNaturalNumber0(all_80_0_109) = v0 & aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 67.13/31.15 |
% 67.13/31.15 | Instantiating (885) with all_420_0_320, all_420_1_321, all_420_2_322 yields:
% 67.13/31.15 | (886) sdtlseqdt0(all_80_0_109, xr) = all_420_0_320 & aNaturalNumber0(all_80_0_109) = all_420_2_322 & aNaturalNumber0(xr) = all_420_1_321 & ( ~ (all_420_1_321 = 0) | ~ (all_420_2_322 = 0) | all_420_0_320 = 0)
% 67.13/31.15 |
% 67.13/31.15 | Applying alpha-rule on (886) yields:
% 67.13/31.15 | (887) sdtlseqdt0(all_80_0_109, xr) = all_420_0_320
% 67.13/31.15 | (888) aNaturalNumber0(all_80_0_109) = all_420_2_322
% 67.13/31.16 | (889) aNaturalNumber0(xr) = all_420_1_321
% 67.13/31.16 | (890) ~ (all_420_1_321 = 0) | ~ (all_420_2_322 = 0) | all_420_0_320 = 0
% 67.13/31.16 |
% 67.13/31.16 +-Applying beta-rule and splitting (617), into two cases.
% 67.13/31.16 |-Branch one:
% 67.13/31.16 | (263) xr = sz00
% 67.13/31.16 |
% 67.13/31.16 | Equations (263) can reduce 98 to:
% 67.13/31.16 | (241) $false
% 67.13/31.16 |
% 67.13/31.16 |-The branch is then unsatisfiable
% 67.13/31.16 |-Branch two:
% 67.13/31.16 | (98) ~ (xr = sz00)
% 67.13/31.16 | (894) ? [v0] : ? [v1] : ? [v2] : ((v0 = 0 & aNaturalNumber0(all_0_1_1) = 0) | (doDivides0(xr, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 67.13/31.16 |
% 67.13/31.16 +-Applying beta-rule and splitting (627), into two cases.
% 67.13/31.16 |-Branch one:
% 67.13/31.16 | (263) xr = sz00
% 67.13/31.16 |
% 67.13/31.16 | Equations (263) can reduce 98 to:
% 67.13/31.16 | (241) $false
% 67.13/31.16 |
% 67.13/31.16 |-The branch is then unsatisfiable
% 67.13/31.16 |-Branch two:
% 67.13/31.16 | (98) ~ (xr = sz00)
% 67.13/31.16 | (898) ? [v0] : ? [v1] : ? [v2] : ((doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) | (sdtasdt0(xm, all_0_5_5) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v0 = 0) | v1 = all_0_1_1)))
% 67.13/31.16 |
% 67.13/31.16 | Instantiating (898) with all_434_0_329, all_434_1_330, all_434_2_331 yields:
% 67.13/31.16 | (899) (doDivides0(xr, xn) = all_434_0_329 & aNaturalNumber0(xr) = all_434_2_331 & aNaturalNumber0(xn) = all_434_1_330 & ( ~ (all_434_0_329 = 0) | ~ (all_434_1_330 = 0) | ~ (all_434_2_331 = 0))) | (sdtasdt0(xm, all_0_5_5) = all_434_1_330 & aNaturalNumber0(xm) = all_434_2_331 & ( ~ (all_434_2_331 = 0) | all_434_1_330 = all_0_1_1))
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (77) with all_0_1_1, xr, all_344_0_179, all_0_0_0 and discharging atoms sdtasdt0(all_0_1_1, xr) = all_344_0_179, sdtasdt0(all_0_1_1, xr) = all_0_0_0, yields:
% 67.13/31.16 | (900) all_344_0_179 = all_0_0_0
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (77) with all_0_4_4, xr, all_326_0_143, all_0_0_0 and discharging atoms sdtasdt0(all_0_4_4, xr) = all_326_0_143, yields:
% 67.13/31.16 | (901) all_326_0_143 = all_0_0_0 | ~ (sdtasdt0(all_0_4_4, xr) = all_0_0_0)
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (77) with all_0_4_4, xr, all_326_0_143, all_0_3_3 and discharging atoms sdtasdt0(all_0_4_4, xr) = all_326_0_143, sdtasdt0(all_0_4_4, xr) = all_0_3_3, yields:
% 67.13/31.16 | (902) all_326_0_143 = all_0_3_3
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (77) with all_0_5_5, xm, all_390_0_288, all_0_4_4 and discharging atoms sdtasdt0(all_0_5_5, xm) = all_390_0_288, sdtasdt0(all_0_5_5, xm) = all_0_4_4, yields:
% 67.13/31.16 | (903) all_390_0_288 = all_0_4_4
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (77) with all_0_5_5, xm, all_390_0_288, all_348_1_186 and discharging atoms sdtasdt0(all_0_5_5, xm) = all_390_0_288, yields:
% 67.13/31.16 | (904) all_390_0_288 = all_348_1_186 | ~ (sdtasdt0(all_0_5_5, xm) = all_348_1_186)
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with all_285_0_117, all_400_2_307, 0 and discharging atoms aNaturalNumber0(all_285_0_117) = all_400_2_307, aNaturalNumber0(all_285_0_117) = 0, yields:
% 67.13/31.16 | (905) all_400_2_307 = 0
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with all_33_2_52, all_348_3_188, 0 and discharging atoms aNaturalNumber0(all_33_2_52) = all_348_3_188, aNaturalNumber0(all_33_2_52) = 0, yields:
% 67.13/31.16 | (906) all_348_3_188 = 0
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with all_33_2_52, all_346_1_183, all_348_3_188 and discharging atoms aNaturalNumber0(all_33_2_52) = all_348_3_188, aNaturalNumber0(all_33_2_52) = all_346_1_183, yields:
% 67.13/31.16 | (907) all_348_3_188 = all_346_1_183
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with all_0_5_5, all_390_1_289, all_16_2_20 and discharging atoms aNaturalNumber0(all_0_5_5) = all_390_1_289, aNaturalNumber0(all_0_5_5) = all_16_2_20, yields:
% 67.13/31.16 | (908) all_390_1_289 = all_16_2_20
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with all_0_5_5, all_360_1_210, all_390_1_289 and discharging atoms aNaturalNumber0(all_0_5_5) = all_390_1_289, aNaturalNumber0(all_0_5_5) = all_360_1_210, yields:
% 67.13/31.16 | (909) all_390_1_289 = all_360_1_210
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with all_0_5_5, all_339_2_172, all_360_1_210 and discharging atoms aNaturalNumber0(all_0_5_5) = all_360_1_210, aNaturalNumber0(all_0_5_5) = all_339_2_172, yields:
% 67.13/31.16 | (910) all_360_1_210 = all_339_2_172
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with all_0_5_5, all_334_2_160, all_400_2_307 and discharging atoms aNaturalNumber0(all_0_5_5) = all_334_2_160, yields:
% 67.13/31.16 | (911) all_400_2_307 = all_334_2_160 | ~ (aNaturalNumber0(all_0_5_5) = all_400_2_307)
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with all_0_5_5, all_334_2_160, all_339_2_172 and discharging atoms aNaturalNumber0(all_0_5_5) = all_339_2_172, aNaturalNumber0(all_0_5_5) = all_334_2_160, yields:
% 67.13/31.16 | (912) all_339_2_172 = all_334_2_160
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xr, all_394_4_304, all_420_1_321 and discharging atoms aNaturalNumber0(xr) = all_420_1_321, aNaturalNumber0(xr) = all_394_4_304, yields:
% 67.13/31.16 | (913) all_420_1_321 = all_394_4_304
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xr, all_386_8_278, all_394_4_304 and discharging atoms aNaturalNumber0(xr) = all_394_4_304, aNaturalNumber0(xr) = all_386_8_278, yields:
% 67.13/31.16 | (914) all_394_4_304 = all_386_8_278
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xr, all_354_1_201, all_386_8_278 and discharging atoms aNaturalNumber0(xr) = all_386_8_278, aNaturalNumber0(xr) = all_354_1_201, yields:
% 67.13/31.16 | (915) all_386_8_278 = all_354_1_201
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xr, all_350_3_193, all_354_1_201 and discharging atoms aNaturalNumber0(xr) = all_354_1_201, aNaturalNumber0(xr) = all_350_3_193, yields:
% 67.13/31.16 | (916) all_354_1_201 = all_350_3_193
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xr, all_350_4_194, all_366_4_228 and discharging atoms aNaturalNumber0(xr) = all_366_4_228, aNaturalNumber0(xr) = all_350_4_194, yields:
% 67.13/31.16 | (917) all_366_4_228 = all_350_4_194
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xr, all_350_4_194, all_350_3_193 and discharging atoms aNaturalNumber0(xr) = all_350_3_193, aNaturalNumber0(xr) = all_350_4_194, yields:
% 67.13/31.16 | (918) all_350_3_193 = all_350_4_194
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xr, all_348_4_189, all_366_4_228 and discharging atoms aNaturalNumber0(xr) = all_366_4_228, aNaturalNumber0(xr) = all_348_4_189, yields:
% 67.13/31.16 | (919) all_366_4_228 = all_348_4_189
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xr, all_346_2_184, all_350_4_194 and discharging atoms aNaturalNumber0(xr) = all_350_4_194, aNaturalNumber0(xr) = all_346_2_184, yields:
% 67.13/31.16 | (920) all_350_4_194 = all_346_2_184
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xr, all_342_2_178, 0 and discharging atoms aNaturalNumber0(xr) = all_342_2_178, aNaturalNumber0(xr) = 0, yields:
% 67.13/31.16 | (921) all_342_2_178 = 0
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xr, all_342_2_178, all_346_2_184 and discharging atoms aNaturalNumber0(xr) = all_346_2_184, aNaturalNumber0(xr) = all_342_2_178, yields:
% 67.13/31.16 | (922) all_346_2_184 = all_342_2_178
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xr, all_342_2_178, all_344_2_181 and discharging atoms aNaturalNumber0(xr) = all_344_2_181, aNaturalNumber0(xr) = all_342_2_178, yields:
% 67.13/31.16 | (923) all_344_2_181 = all_342_2_178
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xr, all_332_2_157, all_420_1_321 and discharging atoms aNaturalNumber0(xr) = all_420_1_321, aNaturalNumber0(xr) = all_332_2_157, yields:
% 67.13/31.16 | (924) all_420_1_321 = all_332_2_157
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xr, all_328_2_148, all_344_2_181 and discharging atoms aNaturalNumber0(xr) = all_344_2_181, aNaturalNumber0(xr) = all_328_2_148, yields:
% 67.13/31.16 | (925) all_344_2_181 = all_328_2_148
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xr, all_326_2_145, all_356_1_204 and discharging atoms aNaturalNumber0(xr) = all_356_1_204, aNaturalNumber0(xr) = all_326_2_145, yields:
% 67.13/31.16 | (926) all_356_1_204 = all_326_2_145
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xr, all_326_2_145, all_342_2_178 and discharging atoms aNaturalNumber0(xr) = all_342_2_178, aNaturalNumber0(xr) = all_326_2_145, yields:
% 67.13/31.16 | (927) all_342_2_178 = all_326_2_145
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xr, all_324_2_142, all_356_1_204 and discharging atoms aNaturalNumber0(xr) = all_356_1_204, aNaturalNumber0(xr) = all_324_2_142, yields:
% 67.13/31.16 | (928) all_356_1_204 = all_324_2_142
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xr, all_322_2_139, all_326_2_145 and discharging atoms aNaturalNumber0(xr) = all_326_2_145, aNaturalNumber0(xr) = all_322_2_139, yields:
% 67.13/31.16 | (929) all_326_2_145 = all_322_2_139
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xm, all_390_2_290, all_410_1_313 and discharging atoms aNaturalNumber0(xm) = all_410_1_313, aNaturalNumber0(xm) = all_390_2_290, yields:
% 67.13/31.16 | (930) all_410_1_313 = all_390_2_290
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xm, all_390_2_290, all_392_8_299 and discharging atoms aNaturalNumber0(xm) = all_392_8_299, aNaturalNumber0(xm) = all_390_2_290, yields:
% 67.13/31.16 | (931) all_392_8_299 = all_390_2_290
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xm, all_382_4_266, all_410_1_313 and discharging atoms aNaturalNumber0(xm) = all_410_1_313, aNaturalNumber0(xm) = all_382_4_266, yields:
% 67.13/31.16 | (932) all_410_1_313 = all_382_4_266
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xm, all_378_2_256, all_410_1_313 and discharging atoms aNaturalNumber0(xm) = all_410_1_313, aNaturalNumber0(xm) = all_378_2_256, yields:
% 67.13/31.16 | (933) all_410_1_313 = all_378_2_256
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xm, all_376_4_253, all_388_8_287 and discharging atoms aNaturalNumber0(xm) = all_388_8_287, aNaturalNumber0(xm) = all_376_4_253, yields:
% 67.13/31.16 | (934) all_388_8_287 = all_376_4_253
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xm, all_376_4_253, all_378_2_256 and discharging atoms aNaturalNumber0(xm) = all_378_2_256, aNaturalNumber0(xm) = all_376_4_253, yields:
% 67.13/31.16 | (935) all_378_2_256 = all_376_4_253
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xm, all_374_2_248, all_378_2_256 and discharging atoms aNaturalNumber0(xm) = all_378_2_256, aNaturalNumber0(xm) = all_374_2_248, yields:
% 67.13/31.16 | (936) all_378_2_256 = all_374_2_248
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xm, all_372_2_245, all_388_8_287 and discharging atoms aNaturalNumber0(xm) = all_388_8_287, aNaturalNumber0(xm) = all_372_2_245, yields:
% 67.13/31.16 | (937) all_388_8_287 = all_372_2_245
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xm, all_360_2_211, all_376_4_253 and discharging atoms aNaturalNumber0(xm) = all_376_4_253, aNaturalNumber0(xm) = all_360_2_211, yields:
% 67.13/31.16 | (938) all_376_4_253 = all_360_2_211
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xm, all_356_2_205, all_360_2_211 and discharging atoms aNaturalNumber0(xm) = all_360_2_211, aNaturalNumber0(xm) = all_356_2_205, yields:
% 67.13/31.16 | (939) all_360_2_211 = all_356_2_205
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xm, all_354_2_202, 0 and discharging atoms aNaturalNumber0(xm) = all_354_2_202, aNaturalNumber0(xm) = 0, yields:
% 67.13/31.16 | (940) all_354_2_202 = 0
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xm, all_354_2_202, all_360_2_211 and discharging atoms aNaturalNumber0(xm) = all_360_2_211, aNaturalNumber0(xm) = all_354_2_202, yields:
% 67.13/31.16 | (941) all_360_2_211 = all_354_2_202
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xm, all_348_2_187, all_392_8_299 and discharging atoms aNaturalNumber0(xm) = all_392_8_299, aNaturalNumber0(xm) = all_348_2_187, yields:
% 67.13/31.16 | (942) all_392_8_299 = all_348_2_187
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xm, all_318_3_130, all_356_2_205 and discharging atoms aNaturalNumber0(xm) = all_356_2_205, aNaturalNumber0(xm) = all_318_3_130, yields:
% 67.13/31.16 | (943) all_356_2_205 = all_318_3_130
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xn, all_415_1_317, 0 and discharging atoms aNaturalNumber0(xn) = all_415_1_317, aNaturalNumber0(xn) = 0, yields:
% 67.13/31.16 | (944) all_415_1_317 = 0
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xn, all_388_7_286, all_400_1_306 and discharging atoms aNaturalNumber0(xn) = all_400_1_306, aNaturalNumber0(xn) = all_388_7_286, yields:
% 67.13/31.16 | (945) all_400_1_306 = all_388_7_286
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xn, all_384_2_269, all_388_7_286 and discharging atoms aNaturalNumber0(xn) = all_388_7_286, aNaturalNumber0(xn) = all_384_2_269, yields:
% 67.13/31.16 | (946) all_388_7_286 = all_384_2_269
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xn, all_382_3_265, all_400_1_306 and discharging atoms aNaturalNumber0(xn) = all_400_1_306, aNaturalNumber0(xn) = all_382_3_265, yields:
% 67.13/31.16 | (947) all_400_1_306 = all_382_3_265
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xn, all_380_3_260, all_415_1_317 and discharging atoms aNaturalNumber0(xn) = all_415_1_317, aNaturalNumber0(xn) = all_380_3_260, yields:
% 67.13/31.16 | (948) all_415_1_317 = all_380_3_260
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xn, all_370_8_242, all_384_2_269 and discharging atoms aNaturalNumber0(xn) = all_384_2_269, aNaturalNumber0(xn) = all_370_8_242, yields:
% 67.13/31.16 | (949) all_384_2_269 = all_370_8_242
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xn, all_368_4_233, all_384_2_269 and discharging atoms aNaturalNumber0(xn) = all_384_2_269, aNaturalNumber0(xn) = all_368_4_233, yields:
% 67.13/31.16 | (950) all_384_2_269 = all_368_4_233
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xn, all_316_2_126, all_415_1_317 and discharging atoms aNaturalNumber0(xn) = all_415_1_317, aNaturalNumber0(xn) = all_316_2_126, yields:
% 67.13/31.16 | (951) all_415_1_317 = all_316_2_126
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xn, all_316_2_126, all_370_8_242 and discharging atoms aNaturalNumber0(xn) = all_370_8_242, aNaturalNumber0(xn) = all_316_2_126, yields:
% 67.13/31.16 | (952) all_370_8_242 = all_316_2_126
% 67.13/31.16 |
% 67.13/31.16 | Instantiating formula (63) with xn, all_314_2_123, all_370_8_242 and discharging atoms aNaturalNumber0(xn) = all_370_8_242, aNaturalNumber0(xn) = all_314_2_123, yields:
% 67.13/31.16 | (953) all_370_8_242 = all_314_2_123
% 67.13/31.16 |
% 67.13/31.16 | Combining equations (913,924) yields a new equation:
% 67.13/31.16 | (954) all_394_4_304 = all_332_2_157
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 954 yields:
% 67.13/31.17 | (955) all_394_4_304 = all_332_2_157
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (944,948) yields a new equation:
% 67.13/31.17 | (956) all_380_3_260 = 0
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (951,948) yields a new equation:
% 67.13/31.17 | (957) all_380_3_260 = all_316_2_126
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (933,932) yields a new equation:
% 67.13/31.17 | (958) all_382_4_266 = all_378_2_256
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (930,932) yields a new equation:
% 67.13/31.17 | (959) all_390_2_290 = all_382_4_266
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 959 yields:
% 67.13/31.17 | (960) all_390_2_290 = all_382_4_266
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (945,947) yields a new equation:
% 67.13/31.17 | (961) all_388_7_286 = all_382_3_265
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 961 yields:
% 67.13/31.17 | (962) all_388_7_286 = all_382_3_265
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (914,955) yields a new equation:
% 67.13/31.17 | (963) all_386_8_278 = all_332_2_157
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 963 yields:
% 67.13/31.17 | (964) all_386_8_278 = all_332_2_157
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (931,942) yields a new equation:
% 67.13/31.17 | (965) all_390_2_290 = all_348_2_187
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 965 yields:
% 67.13/31.17 | (966) all_390_2_290 = all_348_2_187
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (909,908) yields a new equation:
% 67.13/31.17 | (967) all_360_1_210 = all_16_2_20
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 967 yields:
% 67.13/31.17 | (968) all_360_1_210 = all_16_2_20
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (960,966) yields a new equation:
% 67.13/31.17 | (969) all_382_4_266 = all_348_2_187
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 969 yields:
% 67.13/31.17 | (970) all_382_4_266 = all_348_2_187
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (946,962) yields a new equation:
% 67.13/31.17 | (971) all_384_2_269 = all_382_3_265
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 971 yields:
% 67.13/31.17 | (972) all_384_2_269 = all_382_3_265
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (934,937) yields a new equation:
% 67.13/31.17 | (973) all_376_4_253 = all_372_2_245
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 973 yields:
% 67.13/31.17 | (974) all_376_4_253 = all_372_2_245
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (915,964) yields a new equation:
% 67.13/31.17 | (975) all_354_1_201 = all_332_2_157
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 975 yields:
% 67.13/31.17 | (976) all_354_1_201 = all_332_2_157
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (950,972) yields a new equation:
% 67.13/31.17 | (977) all_382_3_265 = all_368_4_233
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (949,972) yields a new equation:
% 67.13/31.17 | (978) all_382_3_265 = all_370_8_242
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (978,977) yields a new equation:
% 67.13/31.17 | (979) all_370_8_242 = all_368_4_233
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 979 yields:
% 67.13/31.17 | (980) all_370_8_242 = all_368_4_233
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (958,970) yields a new equation:
% 67.13/31.17 | (981) all_378_2_256 = all_348_2_187
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 981 yields:
% 67.13/31.17 | (982) all_378_2_256 = all_348_2_187
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (957,956) yields a new equation:
% 67.13/31.17 | (983) all_316_2_126 = 0
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 983 yields:
% 67.13/31.17 | (984) all_316_2_126 = 0
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (935,936) yields a new equation:
% 67.13/31.17 | (985) all_376_4_253 = all_374_2_248
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 985 yields:
% 67.13/31.17 | (986) all_376_4_253 = all_374_2_248
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (982,936) yields a new equation:
% 67.13/31.17 | (987) all_374_2_248 = all_348_2_187
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (938,974) yields a new equation:
% 67.13/31.17 | (988) all_372_2_245 = all_360_2_211
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (986,974) yields a new equation:
% 67.13/31.17 | (989) all_374_2_248 = all_372_2_245
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 989 yields:
% 67.13/31.17 | (990) all_374_2_248 = all_372_2_245
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (990,987) yields a new equation:
% 67.13/31.17 | (991) all_372_2_245 = all_348_2_187
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 991 yields:
% 67.13/31.17 | (992) all_372_2_245 = all_348_2_187
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (988,992) yields a new equation:
% 67.13/31.17 | (993) all_360_2_211 = all_348_2_187
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 993 yields:
% 67.13/31.17 | (994) all_360_2_211 = all_348_2_187
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (953,980) yields a new equation:
% 67.13/31.17 | (995) all_368_4_233 = all_314_2_123
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (952,980) yields a new equation:
% 67.13/31.17 | (996) all_368_4_233 = all_316_2_126
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (996,995) yields a new equation:
% 67.13/31.17 | (997) all_316_2_126 = all_314_2_123
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 997 yields:
% 67.13/31.17 | (998) all_316_2_126 = all_314_2_123
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (917,919) yields a new equation:
% 67.13/31.17 | (999) all_350_4_194 = all_348_4_189
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 999 yields:
% 67.13/31.17 | (1000) all_350_4_194 = all_348_4_189
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (910,968) yields a new equation:
% 67.13/31.17 | (1001) all_339_2_172 = all_16_2_20
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 1001 yields:
% 67.13/31.17 | (1002) all_339_2_172 = all_16_2_20
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (939,994) yields a new equation:
% 67.13/31.17 | (1003) all_356_2_205 = all_348_2_187
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 1003 yields:
% 67.13/31.17 | (1004) all_356_2_205 = all_348_2_187
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (941,994) yields a new equation:
% 67.13/31.17 | (1005) all_354_2_202 = all_348_2_187
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 1005 yields:
% 67.13/31.17 | (1006) all_354_2_202 = all_348_2_187
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (926,928) yields a new equation:
% 67.13/31.17 | (1007) all_326_2_145 = all_324_2_142
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 1007 yields:
% 67.13/31.17 | (1008) all_326_2_145 = all_324_2_142
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (1004,943) yields a new equation:
% 67.13/31.17 | (1009) all_348_2_187 = all_318_3_130
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 1009 yields:
% 67.13/31.17 | (1010) all_348_2_187 = all_318_3_130
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (916,976) yields a new equation:
% 67.13/31.17 | (1011) all_350_3_193 = all_332_2_157
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 1011 yields:
% 67.13/31.17 | (1012) all_350_3_193 = all_332_2_157
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (1006,940) yields a new equation:
% 67.13/31.17 | (1013) all_348_2_187 = 0
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 1013 yields:
% 67.13/31.17 | (1014) all_348_2_187 = 0
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (918,1012) yields a new equation:
% 67.13/31.17 | (1015) all_350_4_194 = all_332_2_157
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 1015 yields:
% 67.13/31.17 | (1016) all_350_4_194 = all_332_2_157
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (1016,1000) yields a new equation:
% 67.13/31.17 | (1017) all_348_4_189 = all_332_2_157
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (920,1000) yields a new equation:
% 67.13/31.17 | (1018) all_348_4_189 = all_346_2_184
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (1014,1010) yields a new equation:
% 67.13/31.17 | (1019) all_318_3_130 = 0
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (906,907) yields a new equation:
% 67.13/31.17 | (1020) all_346_1_183 = 0
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (1018,1017) yields a new equation:
% 67.13/31.17 | (1021) all_346_2_184 = all_332_2_157
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 1021 yields:
% 67.13/31.17 | (1022) all_346_2_184 = all_332_2_157
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (922,1022) yields a new equation:
% 67.13/31.17 | (1023) all_342_2_178 = all_332_2_157
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 1023 yields:
% 67.13/31.17 | (1024) all_342_2_178 = all_332_2_157
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (923,925) yields a new equation:
% 67.13/31.17 | (1025) all_342_2_178 = all_328_2_148
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 1025 yields:
% 67.13/31.17 | (1026) all_342_2_178 = all_328_2_148
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (927,1024) yields a new equation:
% 67.13/31.17 | (1027) all_332_2_157 = all_326_2_145
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (1026,1024) yields a new equation:
% 67.13/31.17 | (1028) all_332_2_157 = all_328_2_148
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (921,1024) yields a new equation:
% 67.13/31.17 | (1029) all_332_2_157 = 0
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (1002,912) yields a new equation:
% 67.13/31.17 | (1030) all_334_2_160 = all_16_2_20
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (1027,1028) yields a new equation:
% 67.13/31.17 | (1031) all_328_2_148 = all_326_2_145
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (1029,1028) yields a new equation:
% 67.13/31.17 | (1032) all_328_2_148 = 0
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (1031,1032) yields a new equation:
% 67.13/31.17 | (1033) all_326_2_145 = 0
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 1033 yields:
% 67.13/31.17 | (1034) all_326_2_145 = 0
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (929,1008) yields a new equation:
% 67.13/31.17 | (1035) all_324_2_142 = all_322_2_139
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (1034,1008) yields a new equation:
% 67.13/31.17 | (1036) all_324_2_142 = 0
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (1035,1036) yields a new equation:
% 67.13/31.17 | (1037) all_322_2_139 = 0
% 67.13/31.17 |
% 67.13/31.17 | Simplifying 1037 yields:
% 67.13/31.17 | (1038) all_322_2_139 = 0
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (984,998) yields a new equation:
% 67.13/31.17 | (1039) all_314_2_123 = 0
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (1032,1028) yields a new equation:
% 67.13/31.17 | (1029) all_332_2_157 = 0
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (1029,1017) yields a new equation:
% 67.13/31.17 | (1041) all_348_4_189 = 0
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (1020,907) yields a new equation:
% 67.13/31.17 | (906) all_348_3_188 = 0
% 67.13/31.17 |
% 67.13/31.17 | Combining equations (1019,1010) yields a new equation:
% 67.13/31.18 | (1014) all_348_2_187 = 0
% 67.13/31.18 |
% 67.13/31.18 | Combining equations (1039,995) yields a new equation:
% 67.13/31.18 | (1044) all_368_4_233 = 0
% 67.13/31.18 |
% 67.13/31.18 | Combining equations (1044,977) yields a new equation:
% 67.13/31.18 | (1045) all_382_3_265 = 0
% 67.13/31.18 |
% 67.13/31.18 | Combining equations (1014,966) yields a new equation:
% 67.13/31.18 | (1046) all_390_2_290 = 0
% 67.13/31.18 |
% 67.13/31.18 | Combining equations (1045,947) yields a new equation:
% 67.13/31.18 | (1047) all_400_1_306 = 0
% 67.13/31.18 |
% 67.13/31.18 | From (900) and (704) follows:
% 67.13/31.18 | (39) sdtasdt0(all_0_1_1, xr) = all_0_0_0
% 67.13/31.18 |
% 67.13/31.18 | From (1020) and (710) follows:
% 67.13/31.18 | (529) aNaturalNumber0(all_33_2_52) = 0
% 67.13/31.18 |
% 67.13/31.18 | From (1038) and (666) follows:
% 67.13/31.18 | (62) aNaturalNumber0(xr) = 0
% 67.13/31.18 |
% 67.13/31.18 | From (1019) and (660) follows:
% 67.13/31.18 | (55) aNaturalNumber0(xm) = 0
% 67.13/31.18 |
% 67.13/31.18 | From (1039) and (649) follows:
% 67.13/31.18 | (18) aNaturalNumber0(xn) = 0
% 67.13/31.18 |
% 67.13/31.18 +-Applying beta-rule and splitting (899), into two cases.
% 67.13/31.18 |-Branch one:
% 67.13/31.18 | (1053) doDivides0(xr, xn) = all_434_0_329 & aNaturalNumber0(xr) = all_434_2_331 & aNaturalNumber0(xn) = all_434_1_330 & ( ~ (all_434_0_329 = 0) | ~ (all_434_1_330 = 0) | ~ (all_434_2_331 = 0))
% 67.13/31.18 |
% 67.13/31.18 | Applying alpha-rule on (1053) yields:
% 67.13/31.18 | (1054) doDivides0(xr, xn) = all_434_0_329
% 67.13/31.18 | (1055) aNaturalNumber0(xr) = all_434_2_331
% 67.13/31.18 | (1056) aNaturalNumber0(xn) = all_434_1_330
% 67.13/31.18 | (1057) ~ (all_434_0_329 = 0) | ~ (all_434_1_330 = 0) | ~ (all_434_2_331 = 0)
% 67.13/31.18 |
% 67.13/31.18 | Instantiating formula (19) with xr, xn, all_434_0_329, 0 and discharging atoms doDivides0(xr, xn) = all_434_0_329, doDivides0(xr, xn) = 0, yields:
% 67.13/31.18 | (1058) all_434_0_329 = 0
% 67.13/31.18 |
% 67.13/31.18 | Instantiating formula (63) with xr, all_434_2_331, 0 and discharging atoms aNaturalNumber0(xr) = all_434_2_331, aNaturalNumber0(xr) = 0, yields:
% 67.13/31.18 | (1059) all_434_2_331 = 0
% 67.13/31.18 |
% 67.13/31.18 | Instantiating formula (63) with xn, all_434_1_330, 0 and discharging atoms aNaturalNumber0(xn) = all_434_1_330, aNaturalNumber0(xn) = 0, yields:
% 67.13/31.18 | (1060) all_434_1_330 = 0
% 67.13/31.18 |
% 67.13/31.18 +-Applying beta-rule and splitting (1057), into two cases.
% 67.13/31.18 |-Branch one:
% 67.13/31.18 | (1061) ~ (all_434_0_329 = 0)
% 67.13/31.18 |
% 67.13/31.18 | Equations (1058) can reduce 1061 to:
% 67.13/31.18 | (241) $false
% 67.13/31.18 |
% 67.13/31.18 |-The branch is then unsatisfiable
% 67.13/31.18 |-Branch two:
% 67.13/31.18 | (1058) all_434_0_329 = 0
% 67.13/31.18 | (1064) ~ (all_434_1_330 = 0) | ~ (all_434_2_331 = 0)
% 67.13/31.18 |
% 67.13/31.18 +-Applying beta-rule and splitting (1064), into two cases.
% 67.13/31.18 |-Branch one:
% 67.13/31.18 | (1065) ~ (all_434_1_330 = 0)
% 67.13/31.18 |
% 67.13/31.18 | Equations (1060) can reduce 1065 to:
% 67.13/31.18 | (241) $false
% 67.13/31.18 |
% 67.13/31.18 |-The branch is then unsatisfiable
% 67.13/31.18 |-Branch two:
% 67.13/31.18 | (1060) all_434_1_330 = 0
% 67.13/31.18 | (1068) ~ (all_434_2_331 = 0)
% 67.13/31.18 |
% 67.13/31.18 | Equations (1059) can reduce 1068 to:
% 67.13/31.18 | (241) $false
% 67.13/31.18 |
% 67.13/31.18 |-The branch is then unsatisfiable
% 67.13/31.18 |-Branch two:
% 67.13/31.18 | (1070) sdtasdt0(xm, all_0_5_5) = all_434_1_330 & aNaturalNumber0(xm) = all_434_2_331 & ( ~ (all_434_2_331 = 0) | all_434_1_330 = all_0_1_1)
% 67.13/31.18 |
% 67.13/31.18 | Applying alpha-rule on (1070) yields:
% 67.13/31.18 | (1071) sdtasdt0(xm, all_0_5_5) = all_434_1_330
% 67.13/31.18 | (1072) aNaturalNumber0(xm) = all_434_2_331
% 67.13/31.18 | (1073) ~ (all_434_2_331 = 0) | all_434_1_330 = all_0_1_1
% 67.13/31.18 |
% 67.13/31.18 +-Applying beta-rule and splitting (861), into two cases.
% 67.13/31.18 |-Branch one:
% 67.13/31.18 | (1074) ~ (all_400_1_306 = 0)
% 67.13/31.18 |
% 67.13/31.18 | Equations (1047) can reduce 1074 to:
% 67.13/31.18 | (241) $false
% 67.13/31.18 |
% 67.13/31.18 |-The branch is then unsatisfiable
% 67.13/31.18 |-Branch two:
% 67.13/31.18 | (1047) all_400_1_306 = 0
% 67.13/31.18 | (1077) ~ (all_400_2_307 = 0) | all_400_0_305 = 0
% 67.13/31.18 |
% 67.13/31.18 +-Applying beta-rule and splitting (1077), into two cases.
% 67.13/31.18 |-Branch one:
% 67.13/31.18 | (1078) ~ (all_400_2_307 = 0)
% 67.13/31.18 |
% 67.13/31.18 | Equations (905) can reduce 1078 to:
% 67.13/31.18 | (241) $false
% 67.13/31.18 |
% 67.13/31.18 |-The branch is then unsatisfiable
% 67.13/31.18 |-Branch two:
% 67.13/31.18 | (905) all_400_2_307 = 0
% 67.13/31.18 | (1081) all_400_0_305 = 0
% 67.13/31.18 |
% 67.13/31.18 +-Applying beta-rule and splitting (714), into two cases.
% 67.13/31.18 |-Branch one:
% 67.13/31.18 | (1082) ~ (all_348_2_187 = 0)
% 67.13/31.18 |
% 67.13/31.18 | Equations (1014) can reduce 1082 to:
% 67.13/31.18 | (241) $false
% 67.13/31.18 |
% 67.13/31.18 |-The branch is then unsatisfiable
% 67.13/31.18 |-Branch two:
% 67.13/31.18 | (1014) all_348_2_187 = 0
% 67.13/31.18 | (1085) ~ (all_348_3_188 = 0) | ~ (all_348_4_189 = 0) | all_348_0_185 = all_0_9_9
% 67.13/31.18 |
% 67.13/31.18 +-Applying beta-rule and splitting (1085), into two cases.
% 67.13/31.18 |-Branch one:
% 67.13/31.18 | (1086) ~ (all_348_3_188 = 0)
% 67.13/31.18 |
% 67.13/31.18 | Equations (906) can reduce 1086 to:
% 67.13/31.18 | (241) $false
% 67.13/31.18 |
% 67.13/31.18 |-The branch is then unsatisfiable
% 67.13/31.18 |-Branch two:
% 67.13/31.18 | (906) all_348_3_188 = 0
% 67.13/31.18 | (1089) ~ (all_348_4_189 = 0) | all_348_0_185 = all_0_9_9
% 67.13/31.18 |
% 67.13/31.18 +-Applying beta-rule and splitting (1089), into two cases.
% 67.13/31.18 |-Branch one:
% 67.13/31.18 | (1090) ~ (all_348_4_189 = 0)
% 67.13/31.18 |
% 67.13/31.18 | Equations (1041) can reduce 1090 to:
% 67.13/31.18 | (241) $false
% 67.13/31.18 |
% 67.13/31.18 |-The branch is then unsatisfiable
% 67.13/31.18 |-Branch two:
% 67.13/31.18 | (1041) all_348_4_189 = 0
% 67.13/31.18 | (1093) all_348_0_185 = all_0_9_9
% 67.13/31.18 |
% 67.13/31.18 | From (1093) and (717) follows:
% 67.13/31.18 | (1094) sdtasdt0(xr, all_348_1_186) = all_0_9_9
% 67.13/31.18 |
% 67.13/31.18 +-Applying beta-rule and splitting (614), into two cases.
% 67.13/31.18 |-Branch one:
% 67.13/31.18 | (263) xr = sz00
% 67.13/31.18 |
% 67.13/31.18 | Equations (263) can reduce 98 to:
% 67.13/31.18 | (241) $false
% 67.13/31.18 |
% 67.13/31.18 |-The branch is then unsatisfiable
% 67.13/31.18 |-Branch two:
% 67.13/31.18 | (98) ~ (xr = sz00)
% 67.13/31.18 | (1098) all_33_2_52 = all_0_5_5 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_33_2_52) = v0) | (doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 67.13/31.18 |
% 67.13/31.18 +-Applying beta-rule and splitting (1098), into two cases.
% 67.13/31.18 |-Branch one:
% 67.13/31.18 | (1099) all_33_2_52 = all_0_5_5
% 67.13/31.18 |
% 67.13/31.18 | From (1099) and (719) follows:
% 67.13/31.18 | (1100) sdtasdt0(all_0_5_5, xm) = all_348_1_186
% 67.13/31.18 |
% 67.13/31.18 | From (1099) and (529) follows:
% 67.13/31.18 | (1101) aNaturalNumber0(all_0_5_5) = 0
% 67.13/31.18 |
% 67.13/31.18 +-Applying beta-rule and splitting (911), into two cases.
% 67.13/31.18 |-Branch one:
% 67.13/31.18 | (1102) ~ (aNaturalNumber0(all_0_5_5) = all_400_2_307)
% 67.13/31.18 |
% 67.13/31.18 | From (905) and (1102) follows:
% 67.13/31.18 | (1103) ~ (aNaturalNumber0(all_0_5_5) = 0)
% 67.13/31.18 |
% 67.13/31.18 | Using (1101) and (1103) yields:
% 67.13/31.18 | (424) $false
% 67.13/31.18 |
% 67.13/31.18 |-The branch is then unsatisfiable
% 67.13/31.18 |-Branch two:
% 67.13/31.18 | (1105) aNaturalNumber0(all_0_5_5) = all_400_2_307
% 67.13/31.18 | (1106) all_400_2_307 = all_334_2_160
% 67.13/31.18 |
% 67.13/31.18 | Combining equations (1106,905) yields a new equation:
% 67.13/31.18 | (1107) all_334_2_160 = 0
% 67.13/31.18 |
% 67.13/31.18 | Simplifying 1107 yields:
% 67.13/31.18 | (1108) all_334_2_160 = 0
% 67.13/31.18 |
% 67.13/31.18 | Combining equations (1030,1108) yields a new equation:
% 67.13/31.18 | (1109) all_16_2_20 = 0
% 67.13/31.18 |
% 67.13/31.18 | Simplifying 1109 yields:
% 67.13/31.18 | (1110) all_16_2_20 = 0
% 67.13/31.18 |
% 67.13/31.18 | Combining equations (1110,908) yields a new equation:
% 67.13/31.18 | (1111) all_390_1_289 = 0
% 67.13/31.18 |
% 67.13/31.18 +-Applying beta-rule and splitting (834), into two cases.
% 67.13/31.18 |-Branch one:
% 67.13/31.18 | (1112) ~ (all_390_1_289 = 0)
% 67.13/31.18 |
% 67.13/31.18 | Equations (1111) can reduce 1112 to:
% 67.13/31.18 | (241) $false
% 67.13/31.18 |
% 67.13/31.18 |-The branch is then unsatisfiable
% 67.13/31.18 |-Branch two:
% 67.13/31.18 | (1111) all_390_1_289 = 0
% 67.13/31.18 | (1115) ~ (all_390_2_290 = 0) | all_390_0_288 = all_18_0_21
% 67.13/31.18 |
% 67.13/31.18 +-Applying beta-rule and splitting (152), into two cases.
% 67.13/31.18 |-Branch one:
% 67.13/31.18 | (1116) ~ (all_16_1_19 = 0)
% 67.13/31.18 |
% 67.13/31.18 | Equations (383) can reduce 1116 to:
% 67.13/31.18 | (241) $false
% 67.13/31.18 |
% 67.13/31.18 |-The branch is then unsatisfiable
% 67.13/31.18 |-Branch two:
% 67.13/31.18 | (383) all_16_1_19 = 0
% 67.13/31.18 | (1119) ~ (all_16_2_20 = 0) | all_16_0_18 = 0
% 67.13/31.18 |
% 67.13/31.18 +-Applying beta-rule and splitting (1119), into two cases.
% 67.13/31.18 |-Branch one:
% 67.13/31.18 | (1120) ~ (all_16_2_20 = 0)
% 67.13/31.18 |
% 67.13/31.18 | Equations (1110) can reduce 1120 to:
% 67.13/31.18 | (241) $false
% 67.13/31.18 |
% 67.13/31.18 |-The branch is then unsatisfiable
% 67.13/31.18 |-Branch two:
% 67.13/31.18 | (1110) all_16_2_20 = 0
% 67.13/31.18 | (1123) all_16_0_18 = 0
% 67.13/31.18 |
% 67.13/31.18 | Combining equations (1123,291) yields a new equation:
% 67.13/31.18 | (1124) all_24_2_34 = 0
% 67.13/31.18 |
% 67.13/31.18 +-Applying beta-rule and splitting (174), into two cases.
% 67.13/31.18 |-Branch one:
% 67.13/31.18 | (1125) ~ (all_24_1_33 = 0)
% 67.13/31.18 |
% 67.13/31.18 | Equations (388) can reduce 1125 to:
% 67.13/31.18 | (241) $false
% 67.13/31.18 |
% 67.13/31.18 |-The branch is then unsatisfiable
% 67.13/31.18 |-Branch two:
% 67.13/31.18 | (388) all_24_1_33 = 0
% 67.13/31.18 | (1128) ~ (all_24_2_34 = 0) | all_24_0_32 = all_0_3_3
% 67.13/31.18 |
% 67.13/31.18 +-Applying beta-rule and splitting (1128), into two cases.
% 67.13/31.18 |-Branch one:
% 67.13/31.18 | (1129) ~ (all_24_2_34 = 0)
% 67.13/31.18 |
% 67.13/31.18 | Equations (1124) can reduce 1129 to:
% 67.13/31.18 | (241) $false
% 67.13/31.18 |
% 67.13/31.18 |-The branch is then unsatisfiable
% 67.13/31.18 |-Branch two:
% 67.13/31.18 | (1124) all_24_2_34 = 0
% 67.13/31.18 | (1132) all_24_0_32 = all_0_3_3
% 67.13/31.19 |
% 67.13/31.19 +-Applying beta-rule and splitting (904), into two cases.
% 67.13/31.19 |-Branch one:
% 67.13/31.19 | (1133) ~ (sdtasdt0(all_0_5_5, xm) = all_348_1_186)
% 67.13/31.19 |
% 67.13/31.19 | Using (1100) and (1133) yields:
% 67.13/31.19 | (424) $false
% 67.13/31.19 |
% 67.13/31.19 |-The branch is then unsatisfiable
% 67.13/31.19 |-Branch two:
% 67.13/31.19 | (1100) sdtasdt0(all_0_5_5, xm) = all_348_1_186
% 67.13/31.19 | (1136) all_390_0_288 = all_348_1_186
% 67.13/31.19 |
% 67.13/31.19 | Combining equations (1136,903) yields a new equation:
% 67.13/31.19 | (1137) all_348_1_186 = all_0_4_4
% 67.13/31.19 |
% 67.13/31.19 | Simplifying 1137 yields:
% 67.13/31.19 | (1138) all_348_1_186 = all_0_4_4
% 67.13/31.19 |
% 67.13/31.19 | From (1138) and (1094) follows:
% 67.13/31.19 | (1139) sdtasdt0(xr, all_0_4_4) = all_0_9_9
% 67.13/31.19 |
% 67.13/31.19 +-Applying beta-rule and splitting (1115), into two cases.
% 67.13/31.19 |-Branch one:
% 67.13/31.19 | (1140) ~ (all_390_2_290 = 0)
% 67.13/31.19 |
% 67.13/31.19 | Equations (1046) can reduce 1140 to:
% 67.13/31.19 | (241) $false
% 67.13/31.19 |
% 67.13/31.19 |-The branch is then unsatisfiable
% 67.13/31.19 |-Branch two:
% 67.13/31.19 | (1046) all_390_2_290 = 0
% 67.13/31.19 | (1143) all_390_0_288 = all_18_0_21
% 67.13/31.19 |
% 67.13/31.19 | Combining equations (1143,903) yields a new equation:
% 67.13/31.19 | (1144) all_18_0_21 = all_0_4_4
% 67.13/31.19 |
% 67.13/31.19 | Simplifying 1144 yields:
% 67.13/31.19 | (1145) all_18_0_21 = all_0_4_4
% 67.13/31.19 |
% 67.13/31.19 | From (1145) and (154) follows:
% 67.13/31.19 | (1146) sdtasdt0(xm, all_0_5_5) = all_0_4_4
% 67.13/31.19 |
% 67.13/31.19 +-Applying beta-rule and splitting (540), into two cases.
% 67.13/31.19 |-Branch one:
% 67.13/31.19 | (1147) ~ (sdtasdt0(xr, all_0_4_4) = all_0_9_9)
% 67.13/31.19 |
% 67.13/31.19 | Using (1139) and (1147) yields:
% 67.13/31.19 | (424) $false
% 67.13/31.19 |
% 67.13/31.19 |-The branch is then unsatisfiable
% 67.13/31.19 |-Branch two:
% 67.13/31.19 | (1139) sdtasdt0(xr, all_0_4_4) = all_0_9_9
% 67.13/31.19 | (1150) all_24_0_32 = all_0_9_9
% 67.13/31.19 |
% 67.13/31.19 | Combining equations (1132,1150) yields a new equation:
% 67.13/31.19 | (1151) all_0_3_3 = all_0_9_9
% 67.13/31.19 |
% 67.13/31.19 | Simplifying 1151 yields:
% 67.13/31.19 | (1152) all_0_3_3 = all_0_9_9
% 67.13/31.19 |
% 67.13/31.19 | Combining equations (1152,902) yields a new equation:
% 67.13/31.19 | (1153) all_326_0_143 = all_0_9_9
% 67.13/31.19 |
% 67.13/31.19 +-Applying beta-rule and splitting (20), into two cases.
% 67.13/31.19 |-Branch one:
% 67.13/31.19 | (1154) ~ (all_0_0_0 = all_0_9_9)
% 67.13/31.19 |
% 67.13/31.19 +-Applying beta-rule and splitting (901), into two cases.
% 67.13/31.19 |-Branch one:
% 67.13/31.19 | (1155) ~ (sdtasdt0(all_0_4_4, xr) = all_0_0_0)
% 67.13/31.19 |
% 67.13/31.19 | Instantiating formula (77) with xm, all_0_5_5, all_0_4_4, all_434_1_330 and discharging atoms sdtasdt0(xm, all_0_5_5) = all_434_1_330, sdtasdt0(xm, all_0_5_5) = all_0_4_4, yields:
% 67.13/31.19 | (1156) all_434_1_330 = all_0_4_4
% 67.13/31.19 |
% 67.13/31.19 | Instantiating formula (63) with xm, all_434_2_331, 0 and discharging atoms aNaturalNumber0(xm) = all_434_2_331, aNaturalNumber0(xm) = 0, yields:
% 67.13/31.19 | (1059) all_434_2_331 = 0
% 67.13/31.19 |
% 67.13/31.19 | Using (39) and (1155) yields:
% 67.13/31.19 | (1158) ~ (all_0_1_1 = all_0_4_4)
% 67.13/31.19 |
% 67.13/31.19 +-Applying beta-rule and splitting (1073), into two cases.
% 67.13/31.19 |-Branch one:
% 67.13/31.19 | (1068) ~ (all_434_2_331 = 0)
% 67.13/31.19 |
% 67.13/31.19 | Equations (1059) can reduce 1068 to:
% 67.13/31.19 | (241) $false
% 67.13/31.19 |
% 67.13/31.19 |-The branch is then unsatisfiable
% 67.13/31.19 |-Branch two:
% 67.13/31.19 | (1059) all_434_2_331 = 0
% 67.13/31.19 | (1162) all_434_1_330 = all_0_1_1
% 67.13/31.19 |
% 67.13/31.19 | Combining equations (1162,1156) yields a new equation:
% 67.13/31.19 | (1163) all_0_1_1 = all_0_4_4
% 67.13/31.19 |
% 67.13/31.19 | Simplifying 1163 yields:
% 67.13/31.19 | (1164) all_0_1_1 = all_0_4_4
% 67.13/31.19 |
% 67.13/31.19 | Equations (1164) can reduce 1158 to:
% 67.13/31.19 | (241) $false
% 67.13/31.19 |
% 67.13/31.19 |-The branch is then unsatisfiable
% 67.13/31.19 |-Branch two:
% 67.13/31.19 | (1166) sdtasdt0(all_0_4_4, xr) = all_0_0_0
% 67.13/31.19 | (1167) all_326_0_143 = all_0_0_0
% 67.13/31.19 |
% 67.13/31.19 | Combining equations (1153,1167) yields a new equation:
% 67.13/31.19 | (1168) all_0_0_0 = all_0_9_9
% 67.13/31.19 |
% 67.13/31.19 | Equations (1168) can reduce 1154 to:
% 67.13/31.19 | (241) $false
% 67.13/31.19 |
% 67.13/31.19 |-The branch is then unsatisfiable
% 67.13/31.19 |-Branch two:
% 67.13/31.19 | (1168) all_0_0_0 = all_0_9_9
% 67.13/31.19 | (1171) ~ (all_0_3_3 = all_0_9_9)
% 67.13/31.19 |
% 67.13/31.19 | Equations (1152) can reduce 1171 to:
% 67.13/31.19 | (241) $false
% 67.13/31.19 |
% 67.13/31.19 |-The branch is then unsatisfiable
% 67.13/31.19 |-Branch two:
% 67.13/31.19 | (1173) ~ (all_33_2_52 = all_0_5_5)
% 67.13/31.19 | (1174) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_33_2_52) = v0) | (doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 67.13/31.19 |
% 67.13/31.19 | Instantiating (1174) with all_580_0_392, all_580_1_393, all_580_2_394 yields:
% 67.13/31.19 | (1175) ( ~ (all_580_2_394 = 0) & aNaturalNumber0(all_33_2_52) = all_580_2_394) | (doDivides0(xr, xn) = all_580_0_392 & aNaturalNumber0(xr) = all_580_2_394 & aNaturalNumber0(xn) = all_580_1_393 & ( ~ (all_580_0_392 = 0) | ~ (all_580_1_393 = 0) | ~ (all_580_2_394 = 0)))
% 67.13/31.19 |
% 67.13/31.19 +-Applying beta-rule and splitting (1175), into two cases.
% 67.13/31.19 |-Branch one:
% 67.13/31.19 | (1176) ~ (all_580_2_394 = 0) & aNaturalNumber0(all_33_2_52) = all_580_2_394
% 67.13/31.19 |
% 67.13/31.19 | Applying alpha-rule on (1176) yields:
% 67.13/31.19 | (1177) ~ (all_580_2_394 = 0)
% 67.13/31.19 | (1178) aNaturalNumber0(all_33_2_52) = all_580_2_394
% 67.13/31.19 |
% 67.13/31.19 | Instantiating formula (63) with all_33_2_52, all_580_2_394, 0 and discharging atoms aNaturalNumber0(all_33_2_52) = all_580_2_394, aNaturalNumber0(all_33_2_52) = 0, yields:
% 67.13/31.19 | (1179) all_580_2_394 = 0
% 67.13/31.19 |
% 67.13/31.19 | Equations (1179) can reduce 1177 to:
% 67.13/31.19 | (241) $false
% 67.13/31.19 |
% 67.13/31.19 |-The branch is then unsatisfiable
% 67.13/31.19 |-Branch two:
% 67.13/31.19 | (1181) doDivides0(xr, xn) = all_580_0_392 & aNaturalNumber0(xr) = all_580_2_394 & aNaturalNumber0(xn) = all_580_1_393 & ( ~ (all_580_0_392 = 0) | ~ (all_580_1_393 = 0) | ~ (all_580_2_394 = 0))
% 67.13/31.19 |
% 67.13/31.19 | Applying alpha-rule on (1181) yields:
% 67.13/31.19 | (1182) doDivides0(xr, xn) = all_580_0_392
% 67.13/31.19 | (1183) aNaturalNumber0(xr) = all_580_2_394
% 67.13/31.19 | (1184) aNaturalNumber0(xn) = all_580_1_393
% 67.13/31.19 | (1185) ~ (all_580_0_392 = 0) | ~ (all_580_1_393 = 0) | ~ (all_580_2_394 = 0)
% 67.13/31.19 |
% 67.13/31.19 | Instantiating formula (19) with xr, xn, all_580_0_392, 0 and discharging atoms doDivides0(xr, xn) = all_580_0_392, doDivides0(xr, xn) = 0, yields:
% 67.13/31.19 | (1186) all_580_0_392 = 0
% 67.13/31.19 |
% 67.13/31.19 | Instantiating formula (63) with xr, all_580_2_394, 0 and discharging atoms aNaturalNumber0(xr) = all_580_2_394, aNaturalNumber0(xr) = 0, yields:
% 67.13/31.19 | (1179) all_580_2_394 = 0
% 67.13/31.19 |
% 67.13/31.19 | Instantiating formula (63) with xn, all_580_1_393, 0 and discharging atoms aNaturalNumber0(xn) = all_580_1_393, aNaturalNumber0(xn) = 0, yields:
% 67.13/31.19 | (1188) all_580_1_393 = 0
% 67.13/31.19 |
% 67.13/31.19 +-Applying beta-rule and splitting (1185), into two cases.
% 67.13/31.19 |-Branch one:
% 67.13/31.19 | (1189) ~ (all_580_0_392 = 0)
% 67.13/31.19 |
% 67.13/31.19 | Equations (1186) can reduce 1189 to:
% 67.13/31.19 | (241) $false
% 67.13/31.19 |
% 67.13/31.19 |-The branch is then unsatisfiable
% 67.13/31.19 |-Branch two:
% 67.13/31.19 | (1186) all_580_0_392 = 0
% 67.13/31.19 | (1192) ~ (all_580_1_393 = 0) | ~ (all_580_2_394 = 0)
% 67.13/31.19 |
% 67.13/31.19 +-Applying beta-rule and splitting (1192), into two cases.
% 67.13/31.19 |-Branch one:
% 67.13/31.19 | (1193) ~ (all_580_1_393 = 0)
% 67.13/31.19 |
% 67.13/31.19 | Equations (1188) can reduce 1193 to:
% 67.13/31.19 | (241) $false
% 67.13/31.19 |
% 67.13/31.19 |-The branch is then unsatisfiable
% 67.13/31.19 |-Branch two:
% 67.13/31.19 | (1188) all_580_1_393 = 0
% 67.13/31.19 | (1177) ~ (all_580_2_394 = 0)
% 67.13/31.19 |
% 67.13/31.19 | Equations (1179) can reduce 1177 to:
% 67.13/31.19 | (241) $false
% 67.13/31.19 |
% 67.13/31.19 |-The branch is then unsatisfiable
% 67.13/31.19 |-Branch two:
% 67.13/31.19 | (1198) sdtasdt0(sz10, xm) = all_0_9_9
% 67.13/31.19 | (1199) ? [v0] : ? [v1] : (sdtasdt0(xm, sz10) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v0 = 0) | (v1 = xm & all_0_9_9 = xm)))
% 67.13/31.19 |
% 67.13/31.19 | Instantiating (1199) with all_253_0_397, all_253_1_398 yields:
% 67.13/31.19 | (1200) sdtasdt0(xm, sz10) = all_253_0_397 & aNaturalNumber0(xm) = all_253_1_398 & ( ~ (all_253_1_398 = 0) | (all_253_0_397 = xm & all_0_9_9 = xm))
% 67.13/31.19 |
% 67.13/31.19 | Applying alpha-rule on (1200) yields:
% 67.13/31.19 | (1201) sdtasdt0(xm, sz10) = all_253_0_397
% 67.13/31.19 | (1202) aNaturalNumber0(xm) = all_253_1_398
% 67.13/31.19 | (1203) ~ (all_253_1_398 = 0) | (all_253_0_397 = xm & all_0_9_9 = xm)
% 67.13/31.19 |
% 67.13/31.19 +-Applying beta-rule and splitting (1203), into two cases.
% 67.13/31.19 |-Branch one:
% 67.13/31.19 | (1204) ~ (all_253_1_398 = 0)
% 67.13/31.19 |
% 67.13/31.19 | Instantiating formula (63) with xm, all_253_1_398, 0 and discharging atoms aNaturalNumber0(xm) = all_253_1_398, aNaturalNumber0(xm) = 0, yields:
% 67.13/31.19 | (1205) all_253_1_398 = 0
% 67.13/31.19 |
% 67.13/31.19 | Equations (1205) can reduce 1204 to:
% 67.13/31.19 | (241) $false
% 67.13/31.19 |
% 67.13/31.19 |-The branch is then unsatisfiable
% 67.13/31.19 |-Branch two:
% 67.13/31.19 | (1205) all_253_1_398 = 0
% 67.13/31.19 | (1208) all_253_0_397 = xm & all_0_9_9 = xm
% 67.13/31.19 |
% 67.13/31.19 | Applying alpha-rule on (1208) yields:
% 67.13/31.20 | (1209) all_253_0_397 = xm
% 67.13/31.20 | (1210) all_0_9_9 = xm
% 67.13/31.20 |
% 67.13/31.20 | Equations (1210) can reduce 541 to:
% 67.13/31.20 | (241) $false
% 67.13/31.20 |
% 67.13/31.20 |-The branch is then unsatisfiable
% 67.13/31.20 |-Branch two:
% 67.13/31.20 | (1212) sdtasdt0(sz00, xm) = all_0_9_9
% 67.13/31.20 | (1213) ? [v0] : ? [v1] : (sdtasdt0(xm, sz00) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v0 = 0) | (v1 = sz00 & all_0_9_9 = sz00)))
% 67.13/31.20 |
% 67.13/31.20 | Instantiating (1213) with all_243_0_402, all_243_1_403 yields:
% 67.13/31.20 | (1214) sdtasdt0(xm, sz00) = all_243_0_402 & aNaturalNumber0(xm) = all_243_1_403 & ( ~ (all_243_1_403 = 0) | (all_243_0_402 = sz00 & all_0_9_9 = sz00))
% 67.13/31.20 |
% 67.13/31.20 | Applying alpha-rule on (1214) yields:
% 67.13/31.20 | (1215) sdtasdt0(xm, sz00) = all_243_0_402
% 67.13/31.20 | (1216) aNaturalNumber0(xm) = all_243_1_403
% 67.13/31.20 | (1217) ~ (all_243_1_403 = 0) | (all_243_0_402 = sz00 & all_0_9_9 = sz00)
% 67.13/31.20 |
% 67.13/31.20 +-Applying beta-rule and splitting (1217), into two cases.
% 67.13/31.20 |-Branch one:
% 67.13/31.20 | (1218) ~ (all_243_1_403 = 0)
% 67.13/31.20 |
% 67.13/31.20 | Instantiating formula (63) with xm, all_243_1_403, 0 and discharging atoms aNaturalNumber0(xm) = all_243_1_403, aNaturalNumber0(xm) = 0, yields:
% 67.13/31.20 | (1219) all_243_1_403 = 0
% 67.13/31.20 |
% 67.13/31.20 | Equations (1219) can reduce 1218 to:
% 67.13/31.20 | (241) $false
% 67.13/31.20 |
% 67.13/31.20 |-The branch is then unsatisfiable
% 67.13/31.20 |-Branch two:
% 67.13/31.20 | (1219) all_243_1_403 = 0
% 67.13/31.20 | (1222) all_243_0_402 = sz00 & all_0_9_9 = sz00
% 67.13/31.20 |
% 67.13/31.20 | Applying alpha-rule on (1222) yields:
% 67.13/31.20 | (1223) all_243_0_402 = sz00
% 67.13/31.20 | (544) all_0_9_9 = sz00
% 67.13/31.20 |
% 67.13/31.20 | Equations (544) can reduce 542 to:
% 67.13/31.20 | (241) $false
% 67.13/31.20 |
% 67.13/31.20 |-The branch is then unsatisfiable
% 67.13/31.20 |-Branch two:
% 67.13/31.20 | (1226) aNaturalNumber0(xr) = all_33_2_52 & aNaturalNumber0(xn) = all_33_1_51 & ( ~ (all_33_1_51 = 0) | ~ (all_33_2_52 = 0))
% 67.13/31.20 |
% 67.13/31.20 | Applying alpha-rule on (1226) yields:
% 67.13/31.20 | (1227) aNaturalNumber0(xr) = all_33_2_52
% 67.13/31.20 | (1228) aNaturalNumber0(xn) = all_33_1_51
% 67.13/31.20 | (1229) ~ (all_33_1_51 = 0) | ~ (all_33_2_52 = 0)
% 67.13/31.20 |
% 67.13/31.20 | Instantiating formula (63) with xr, all_33_2_52, 0 and discharging atoms aNaturalNumber0(xr) = all_33_2_52, aNaturalNumber0(xr) = 0, yields:
% 67.13/31.20 | (1230) all_33_2_52 = 0
% 67.13/31.20 |
% 67.13/31.20 | Instantiating formula (63) with xn, all_33_1_51, 0 and discharging atoms aNaturalNumber0(xn) = all_33_1_51, aNaturalNumber0(xn) = 0, yields:
% 67.13/31.20 | (527) all_33_1_51 = 0
% 67.13/31.20 |
% 67.13/31.20 +-Applying beta-rule and splitting (1229), into two cases.
% 67.13/31.20 |-Branch one:
% 67.13/31.20 | (1232) ~ (all_33_1_51 = 0)
% 67.13/31.20 |
% 67.13/31.20 | Equations (527) can reduce 1232 to:
% 67.13/31.20 | (241) $false
% 67.13/31.20 |
% 67.13/31.20 |-The branch is then unsatisfiable
% 67.13/31.20 |-Branch two:
% 67.13/31.20 | (527) all_33_1_51 = 0
% 67.13/31.20 | (1235) ~ (all_33_2_52 = 0)
% 67.13/31.20 |
% 67.13/31.20 | Equations (1230) can reduce 1235 to:
% 67.13/31.20 | (241) $false
% 67.13/31.20 |
% 67.13/31.20 |-The branch is then unsatisfiable
% 67.13/31.20 |-Branch two:
% 67.13/31.20 | (1237) aNaturalNumber0(xk) = all_30_2_43 & aNaturalNumber0(xp) = all_30_1_42 & ( ~ (all_30_1_42 = 0) | ~ (all_30_2_43 = 0))
% 67.13/31.20 |
% 67.13/31.20 | Applying alpha-rule on (1237) yields:
% 67.13/31.20 | (1238) aNaturalNumber0(xk) = all_30_2_43
% 67.13/31.20 | (1239) aNaturalNumber0(xp) = all_30_1_42
% 67.13/31.20 | (1240) ~ (all_30_1_42 = 0) | ~ (all_30_2_43 = 0)
% 67.13/31.20 |
% 67.13/31.20 | Instantiating formula (63) with xk, all_30_2_43, 0 and discharging atoms aNaturalNumber0(xk) = all_30_2_43, aNaturalNumber0(xk) = 0, yields:
% 67.13/31.20 | (1241) all_30_2_43 = 0
% 67.13/31.20 |
% 67.13/31.20 | Instantiating formula (63) with xp, all_30_1_42, 0 and discharging atoms aNaturalNumber0(xp) = all_30_1_42, aNaturalNumber0(xp) = 0, yields:
% 67.13/31.20 | (517) all_30_1_42 = 0
% 67.13/31.20 |
% 67.13/31.20 +-Applying beta-rule and splitting (1240), into two cases.
% 67.13/31.20 |-Branch one:
% 67.13/31.20 | (1243) ~ (all_30_1_42 = 0)
% 67.13/31.20 |
% 67.13/31.20 | Equations (517) can reduce 1243 to:
% 67.13/31.20 | (241) $false
% 67.13/31.20 |
% 67.13/31.20 |-The branch is then unsatisfiable
% 67.13/31.20 |-Branch two:
% 67.13/31.20 | (517) all_30_1_42 = 0
% 67.13/31.20 | (1246) ~ (all_30_2_43 = 0)
% 67.13/31.20 |
% 67.13/31.20 | Equations (1241) can reduce 1246 to:
% 67.13/31.20 | (241) $false
% 67.13/31.20 |
% 67.13/31.20 |-The branch is then unsatisfiable
% 67.13/31.20 |-Branch two:
% 67.13/31.20 | (1248) ~ (all_0_2_2 = all_0_9_9)
% 67.13/31.20 | (1249) ? [v0] : ? [v1] : ? [v2] : (doDivides0(xp, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 67.13/31.20 |
% 67.13/31.20 | Instantiating (1249) with all_207_0_416, all_207_1_417, all_207_2_418 yields:
% 67.13/31.20 | (1250) doDivides0(xp, all_0_9_9) = all_207_0_416 & aNaturalNumber0(all_0_9_9) = all_207_1_417 & aNaturalNumber0(xp) = all_207_2_418 & ( ~ (all_207_0_416 = 0) | ~ (all_207_1_417 = 0) | ~ (all_207_2_418 = 0))
% 67.13/31.20 |
% 67.13/31.20 | Applying alpha-rule on (1250) yields:
% 67.13/31.20 | (1251) doDivides0(xp, all_0_9_9) = all_207_0_416
% 67.13/31.20 | (1252) aNaturalNumber0(all_0_9_9) = all_207_1_417
% 67.13/31.20 | (1253) aNaturalNumber0(xp) = all_207_2_418
% 67.13/31.20 | (1254) ~ (all_207_0_416 = 0) | ~ (all_207_1_417 = 0) | ~ (all_207_2_418 = 0)
% 67.13/31.20 |
% 67.13/31.20 | Instantiating formula (19) with xp, all_0_9_9, all_207_0_416, 0 and discharging atoms doDivides0(xp, all_0_9_9) = all_207_0_416, doDivides0(xp, all_0_9_9) = 0, yields:
% 67.13/31.20 | (1255) all_207_0_416 = 0
% 67.13/31.20 |
% 67.13/31.20 | Instantiating formula (63) with all_0_9_9, all_207_1_417, 0 and discharging atoms aNaturalNumber0(all_0_9_9) = all_207_1_417, aNaturalNumber0(all_0_9_9) = 0, yields:
% 67.13/31.20 | (1256) all_207_1_417 = 0
% 67.13/31.20 |
% 67.13/31.20 | Instantiating formula (63) with xp, all_207_2_418, 0 and discharging atoms aNaturalNumber0(xp) = all_207_2_418, aNaturalNumber0(xp) = 0, yields:
% 67.13/31.20 | (1257) all_207_2_418 = 0
% 67.13/31.20 |
% 67.13/31.20 +-Applying beta-rule and splitting (1254), into two cases.
% 67.13/31.20 |-Branch one:
% 67.13/31.20 | (1258) ~ (all_207_0_416 = 0)
% 67.13/31.20 |
% 67.13/31.20 | Equations (1255) can reduce 1258 to:
% 67.13/31.20 | (241) $false
% 67.13/31.20 |
% 67.13/31.20 |-The branch is then unsatisfiable
% 67.13/31.20 |-Branch two:
% 67.13/31.20 | (1255) all_207_0_416 = 0
% 67.13/31.20 | (1261) ~ (all_207_1_417 = 0) | ~ (all_207_2_418 = 0)
% 67.13/31.20 |
% 67.13/31.20 +-Applying beta-rule and splitting (1261), into two cases.
% 67.13/31.20 |-Branch one:
% 67.13/31.20 | (1262) ~ (all_207_1_417 = 0)
% 67.13/31.20 |
% 67.13/31.20 | Equations (1256) can reduce 1262 to:
% 67.13/31.20 | (241) $false
% 67.13/31.20 |
% 67.13/31.20 |-The branch is then unsatisfiable
% 67.13/31.20 |-Branch two:
% 67.13/31.20 | (1256) all_207_1_417 = 0
% 67.13/31.20 | (1265) ~ (all_207_2_418 = 0)
% 67.13/31.20 |
% 67.13/31.20 | Equations (1257) can reduce 1265 to:
% 67.13/31.20 | (241) $false
% 67.13/31.20 |
% 67.13/31.20 |-The branch is then unsatisfiable
% 67.13/31.20 |-Branch two:
% 67.13/31.20 | (1267) sdtasdt0(xp, xk) = xm
% 67.13/31.20 | (1268) all_0_7_7 = 0 | xk = sz00 | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 67.13/31.20 |
% 67.13/31.20 +-Applying beta-rule and splitting (1268), into two cases.
% 67.13/31.20 |-Branch one:
% 67.13/31.20 | (1269) xk = sz00
% 67.13/31.20 |
% 67.13/31.20 | Equations (1269) can reduce 31 to:
% 67.13/31.20 | (241) $false
% 67.13/31.20 |
% 67.13/31.20 |-The branch is then unsatisfiable
% 67.13/31.20 |-Branch two:
% 67.13/31.20 | (31) ~ (xk = sz00)
% 67.13/31.20 | (1272) all_0_7_7 = 0 | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 67.13/31.20 |
% 67.13/31.20 +-Applying beta-rule and splitting (1272), into two cases.
% 67.13/31.20 |-Branch one:
% 67.13/31.20 | (862) all_0_7_7 = 0
% 67.13/31.20 |
% 67.13/31.20 | Equations (862) can reduce 81 to:
% 67.13/31.20 | (241) $false
% 67.13/31.20 |
% 67.13/31.20 |-The branch is then unsatisfiable
% 67.13/31.20 |-Branch two:
% 67.13/31.20 | (81) ~ (all_0_7_7 = 0)
% 67.13/31.20 | (1276) ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 67.13/31.20 |
% 67.13/31.20 | Instantiating (1276) with all_231_0_419, all_231_1_420 yields:
% 67.13/31.20 | (1277) aNaturalNumber0(xk) = all_231_1_420 & aNaturalNumber0(xp) = all_231_0_419 & ( ~ (all_231_0_419 = 0) | ~ (all_231_1_420 = 0))
% 67.13/31.20 |
% 67.13/31.20 | Applying alpha-rule on (1277) yields:
% 67.13/31.20 | (1278) aNaturalNumber0(xk) = all_231_1_420
% 67.13/31.20 | (1279) aNaturalNumber0(xp) = all_231_0_419
% 67.13/31.20 | (1280) ~ (all_231_0_419 = 0) | ~ (all_231_1_420 = 0)
% 67.13/31.20 |
% 67.13/31.20 | Instantiating formula (63) with xk, all_231_1_420, 0 and discharging atoms aNaturalNumber0(xk) = all_231_1_420, aNaturalNumber0(xk) = 0, yields:
% 67.13/31.20 | (1281) all_231_1_420 = 0
% 67.13/31.20 |
% 67.13/31.20 | Instantiating formula (63) with xp, all_231_0_419, 0 and discharging atoms aNaturalNumber0(xp) = all_231_0_419, aNaturalNumber0(xp) = 0, yields:
% 67.13/31.20 | (1282) all_231_0_419 = 0
% 67.13/31.20 |
% 67.13/31.20 +-Applying beta-rule and splitting (1280), into two cases.
% 67.13/31.20 |-Branch one:
% 67.13/31.20 | (1283) ~ (all_231_0_419 = 0)
% 67.13/31.20 |
% 67.13/31.20 | Equations (1282) can reduce 1283 to:
% 67.13/31.20 | (241) $false
% 67.13/31.20 |
% 67.13/31.20 |-The branch is then unsatisfiable
% 67.13/31.20 |-Branch two:
% 67.13/31.20 | (1282) all_231_0_419 = 0
% 67.13/31.20 | (1286) ~ (all_231_1_420 = 0)
% 67.13/31.20 |
% 67.13/31.20 | Equations (1281) can reduce 1286 to:
% 67.13/31.20 | (241) $false
% 67.13/31.20 |
% 67.13/31.20 |-The branch is then unsatisfiable
% 67.13/31.20 |-Branch two:
% 67.13/31.20 | (1288) sdtasdt0(xp, xk) = sz00
% 67.13/31.20 | (1289) xk = sz00 | xp = sz00 | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 67.13/31.20 |
% 67.13/31.20 +-Applying beta-rule and splitting (1289), into two cases.
% 67.13/31.20 |-Branch one:
% 67.13/31.20 | (1269) xk = sz00
% 67.13/31.20 |
% 67.13/31.20 | Equations (1269) can reduce 31 to:
% 67.13/31.20 | (241) $false
% 67.13/31.20 |
% 67.13/31.20 |-The branch is then unsatisfiable
% 67.13/31.20 |-Branch two:
% 67.13/31.20 | (31) ~ (xk = sz00)
% 67.13/31.20 | (1293) xp = sz00 | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 67.13/31.20 |
% 67.13/31.20 +-Applying beta-rule and splitting (1293), into two cases.
% 67.13/31.20 |-Branch one:
% 67.13/31.20 | (258) xp = sz00
% 67.13/31.20 |
% 67.13/31.20 | Equations (258) can reduce 99 to:
% 67.13/31.20 | (241) $false
% 67.13/31.20 |
% 67.13/31.20 |-The branch is then unsatisfiable
% 67.13/31.20 |-Branch two:
% 67.13/31.21 | (99) ~ (xp = sz00)
% 67.13/31.21 | (1297) ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 67.13/31.21 |
% 67.13/31.21 | Instantiating (1297) with all_207_0_427, all_207_1_428 yields:
% 67.13/31.21 | (1298) aNaturalNumber0(xk) = all_207_0_427 & aNaturalNumber0(xp) = all_207_1_428 & ( ~ (all_207_0_427 = 0) | ~ (all_207_1_428 = 0))
% 67.13/31.21 |
% 67.13/31.21 | Applying alpha-rule on (1298) yields:
% 67.13/31.21 | (1299) aNaturalNumber0(xk) = all_207_0_427
% 67.13/31.21 | (1300) aNaturalNumber0(xp) = all_207_1_428
% 67.13/31.21 | (1301) ~ (all_207_0_427 = 0) | ~ (all_207_1_428 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Instantiating formula (63) with xk, all_207_0_427, 0 and discharging atoms aNaturalNumber0(xk) = all_207_0_427, aNaturalNumber0(xk) = 0, yields:
% 67.13/31.21 | (1302) all_207_0_427 = 0
% 67.13/31.21 |
% 67.13/31.21 | Instantiating formula (63) with xp, all_207_1_428, 0 and discharging atoms aNaturalNumber0(xp) = all_207_1_428, aNaturalNumber0(xp) = 0, yields:
% 67.13/31.21 | (1303) all_207_1_428 = 0
% 67.13/31.21 |
% 67.13/31.21 +-Applying beta-rule and splitting (1301), into two cases.
% 67.13/31.21 |-Branch one:
% 67.13/31.21 | (1304) ~ (all_207_0_427 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Equations (1302) can reduce 1304 to:
% 67.13/31.21 | (241) $false
% 67.13/31.21 |
% 67.13/31.21 |-The branch is then unsatisfiable
% 67.13/31.21 |-Branch two:
% 67.13/31.21 | (1302) all_207_0_427 = 0
% 67.13/31.21 | (1307) ~ (all_207_1_428 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Equations (1303) can reduce 1307 to:
% 67.13/31.21 | (241) $false
% 67.13/31.21 |
% 67.13/31.21 |-The branch is then unsatisfiable
% 67.13/31.21 |-Branch two:
% 67.13/31.21 | (1309) aNaturalNumber0(xr) = all_31_2_46 & aNaturalNumber0(xk) = all_31_1_45 & ( ~ (all_31_1_45 = 0) | ~ (all_31_2_46 = 0))
% 67.13/31.21 |
% 67.13/31.21 | Applying alpha-rule on (1309) yields:
% 67.13/31.21 | (1310) aNaturalNumber0(xr) = all_31_2_46
% 67.13/31.21 | (1311) aNaturalNumber0(xk) = all_31_1_45
% 67.13/31.21 | (1312) ~ (all_31_1_45 = 0) | ~ (all_31_2_46 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Instantiating formula (63) with xr, all_31_2_46, 0 and discharging atoms aNaturalNumber0(xr) = all_31_2_46, aNaturalNumber0(xr) = 0, yields:
% 67.13/31.21 | (1313) all_31_2_46 = 0
% 67.13/31.21 |
% 67.13/31.21 | Instantiating formula (63) with xk, all_31_1_45, 0 and discharging atoms aNaturalNumber0(xk) = all_31_1_45, aNaturalNumber0(xk) = 0, yields:
% 67.13/31.21 | (500) all_31_1_45 = 0
% 67.13/31.21 |
% 67.13/31.21 +-Applying beta-rule and splitting (1312), into two cases.
% 67.13/31.21 |-Branch one:
% 67.13/31.21 | (1315) ~ (all_31_1_45 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Equations (500) can reduce 1315 to:
% 67.13/31.21 | (241) $false
% 67.13/31.21 |
% 67.13/31.21 |-The branch is then unsatisfiable
% 67.13/31.21 |-Branch two:
% 67.13/31.21 | (500) all_31_1_45 = 0
% 67.13/31.21 | (1318) ~ (all_31_2_46 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Equations (1313) can reduce 1318 to:
% 67.13/31.21 | (241) $false
% 67.13/31.21 |
% 67.13/31.21 |-The branch is then unsatisfiable
% 67.13/31.21 |-Branch two:
% 67.13/31.21 | (1320) aNaturalNumber0(xr) = all_37_2_61 & aNaturalNumber0(xk) = all_37_1_60 & ( ~ (all_37_1_60 = 0) | ~ (all_37_2_61 = 0))
% 67.13/31.21 |
% 67.13/31.21 | Applying alpha-rule on (1320) yields:
% 67.13/31.21 | (1321) aNaturalNumber0(xr) = all_37_2_61
% 67.13/31.21 | (1322) aNaturalNumber0(xk) = all_37_1_60
% 67.13/31.21 | (1323) ~ (all_37_1_60 = 0) | ~ (all_37_2_61 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Instantiating formula (63) with xr, all_37_2_61, 0 and discharging atoms aNaturalNumber0(xr) = all_37_2_61, aNaturalNumber0(xr) = 0, yields:
% 67.13/31.21 | (1324) all_37_2_61 = 0
% 67.13/31.21 |
% 67.13/31.21 | Instantiating formula (63) with xk, all_37_1_60, 0 and discharging atoms aNaturalNumber0(xk) = all_37_1_60, aNaturalNumber0(xk) = 0, yields:
% 67.13/31.21 | (495) all_37_1_60 = 0
% 67.13/31.21 |
% 67.13/31.21 +-Applying beta-rule and splitting (1323), into two cases.
% 67.13/31.21 |-Branch one:
% 67.13/31.21 | (1326) ~ (all_37_1_60 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Equations (495) can reduce 1326 to:
% 67.13/31.21 | (241) $false
% 67.13/31.21 |
% 67.13/31.21 |-The branch is then unsatisfiable
% 67.13/31.21 |-Branch two:
% 67.13/31.21 | (495) all_37_1_60 = 0
% 67.13/31.21 | (1329) ~ (all_37_2_61 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Equations (1324) can reduce 1329 to:
% 67.13/31.21 | (241) $false
% 67.13/31.21 |
% 67.13/31.21 |-The branch is then unsatisfiable
% 67.13/31.21 |-Branch two:
% 67.13/31.21 | (1331) doDivides0(xp, all_0_9_9) = all_69_0_106 & aNaturalNumber0(all_0_9_9) = all_69_1_107 & aNaturalNumber0(xp) = all_69_2_108 & ( ~ (all_69_0_106 = 0) | ~ (all_69_1_107 = 0) | ~ (all_69_2_108 = 0))
% 67.13/31.21 |
% 67.13/31.21 | Applying alpha-rule on (1331) yields:
% 67.13/31.21 | (1332) doDivides0(xp, all_0_9_9) = all_69_0_106
% 67.13/31.21 | (1333) aNaturalNumber0(all_0_9_9) = all_69_1_107
% 67.13/31.21 | (1334) aNaturalNumber0(xp) = all_69_2_108
% 67.13/31.21 | (1335) ~ (all_69_0_106 = 0) | ~ (all_69_1_107 = 0) | ~ (all_69_2_108 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Instantiating formula (19) with xp, all_0_9_9, all_69_0_106, 0 and discharging atoms doDivides0(xp, all_0_9_9) = all_69_0_106, doDivides0(xp, all_0_9_9) = 0, yields:
% 67.13/31.21 | (1336) all_69_0_106 = 0
% 67.13/31.21 |
% 67.13/31.21 | Instantiating formula (63) with all_0_9_9, all_69_1_107, 0 and discharging atoms aNaturalNumber0(all_0_9_9) = all_69_1_107, aNaturalNumber0(all_0_9_9) = 0, yields:
% 67.13/31.21 | (1337) all_69_1_107 = 0
% 67.13/31.21 |
% 67.13/31.21 | Instantiating formula (63) with xp, all_69_2_108, 0 and discharging atoms aNaturalNumber0(xp) = all_69_2_108, aNaturalNumber0(xp) = 0, yields:
% 67.13/31.21 | (482) all_69_2_108 = 0
% 67.13/31.21 |
% 67.13/31.21 +-Applying beta-rule and splitting (1335), into two cases.
% 67.13/31.21 |-Branch one:
% 67.13/31.21 | (1339) ~ (all_69_0_106 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Equations (1336) can reduce 1339 to:
% 67.13/31.21 | (241) $false
% 67.13/31.21 |
% 67.13/31.21 |-The branch is then unsatisfiable
% 67.13/31.21 |-Branch two:
% 67.13/31.21 | (1336) all_69_0_106 = 0
% 67.13/31.21 | (1342) ~ (all_69_1_107 = 0) | ~ (all_69_2_108 = 0)
% 67.13/31.21 |
% 67.13/31.21 +-Applying beta-rule and splitting (1342), into two cases.
% 67.13/31.21 |-Branch one:
% 67.13/31.21 | (1343) ~ (all_69_1_107 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Equations (1337) can reduce 1343 to:
% 67.13/31.21 | (241) $false
% 67.13/31.21 |
% 67.13/31.21 |-The branch is then unsatisfiable
% 67.13/31.21 |-Branch two:
% 67.13/31.21 | (1337) all_69_1_107 = 0
% 67.13/31.21 | (1346) ~ (all_69_2_108 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Equations (482) can reduce 1346 to:
% 67.13/31.21 | (241) $false
% 67.13/31.21 |
% 67.13/31.21 |-The branch is then unsatisfiable
% 67.13/31.21 |-Branch two:
% 67.13/31.21 | (1348) aNaturalNumber0(all_0_9_9) = all_38_1_63 & aNaturalNumber0(xr) = all_38_2_64 & ( ~ (all_38_1_63 = 0) | ~ (all_38_2_64 = 0))
% 67.13/31.21 |
% 67.13/31.21 | Applying alpha-rule on (1348) yields:
% 67.13/31.21 | (1349) aNaturalNumber0(all_0_9_9) = all_38_1_63
% 67.13/31.21 | (1350) aNaturalNumber0(xr) = all_38_2_64
% 67.13/31.21 | (1351) ~ (all_38_1_63 = 0) | ~ (all_38_2_64 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Instantiating formula (63) with all_0_9_9, all_38_1_63, 0 and discharging atoms aNaturalNumber0(all_0_9_9) = all_38_1_63, aNaturalNumber0(all_0_9_9) = 0, yields:
% 67.13/31.21 | (474) all_38_1_63 = 0
% 67.13/31.21 |
% 67.13/31.21 | Instantiating formula (63) with xr, all_38_2_64, 0 and discharging atoms aNaturalNumber0(xr) = all_38_2_64, aNaturalNumber0(xr) = 0, yields:
% 67.13/31.21 | (1353) all_38_2_64 = 0
% 67.13/31.21 |
% 67.13/31.21 +-Applying beta-rule and splitting (1351), into two cases.
% 67.13/31.21 |-Branch one:
% 67.13/31.21 | (1354) ~ (all_38_1_63 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Equations (474) can reduce 1354 to:
% 67.13/31.21 | (241) $false
% 67.13/31.21 |
% 67.13/31.21 |-The branch is then unsatisfiable
% 67.13/31.21 |-Branch two:
% 67.13/31.21 | (474) all_38_1_63 = 0
% 67.13/31.21 | (1357) ~ (all_38_2_64 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Equations (1353) can reduce 1357 to:
% 67.13/31.21 | (241) $false
% 67.13/31.21 |
% 67.13/31.21 |-The branch is then unsatisfiable
% 67.13/31.21 |-Branch two:
% 67.13/31.21 | (1359) aNaturalNumber0(xp) = all_45_1_77 & aNaturalNumber0(xn) = all_45_2_78 & ( ~ (all_45_1_77 = 0) | ~ (all_45_2_78 = 0))
% 67.13/31.21 |
% 67.13/31.21 | Applying alpha-rule on (1359) yields:
% 67.13/31.21 | (1360) aNaturalNumber0(xp) = all_45_1_77
% 67.13/31.21 | (1361) aNaturalNumber0(xn) = all_45_2_78
% 67.13/31.21 | (1362) ~ (all_45_1_77 = 0) | ~ (all_45_2_78 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Instantiating formula (63) with xp, all_45_1_77, 0 and discharging atoms aNaturalNumber0(xp) = all_45_1_77, aNaturalNumber0(xp) = 0, yields:
% 67.13/31.21 | (420) all_45_1_77 = 0
% 67.13/31.21 |
% 67.13/31.21 | Instantiating formula (63) with xn, all_45_2_78, 0 and discharging atoms aNaturalNumber0(xn) = all_45_2_78, aNaturalNumber0(xn) = 0, yields:
% 67.13/31.21 | (1364) all_45_2_78 = 0
% 67.13/31.21 |
% 67.13/31.21 +-Applying beta-rule and splitting (1362), into two cases.
% 67.13/31.21 |-Branch one:
% 67.13/31.21 | (1365) ~ (all_45_1_77 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Equations (420) can reduce 1365 to:
% 67.13/31.21 | (241) $false
% 67.13/31.21 |
% 67.13/31.21 |-The branch is then unsatisfiable
% 67.13/31.21 |-Branch two:
% 67.13/31.21 | (420) all_45_1_77 = 0
% 67.13/31.21 | (1368) ~ (all_45_2_78 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Equations (1364) can reduce 1368 to:
% 67.13/31.21 | (241) $false
% 67.13/31.21 |
% 67.13/31.21 |-The branch is then unsatisfiable
% 67.13/31.21 |-Branch two:
% 67.13/31.21 | (1370) aNaturalNumber0(xp) = all_46_1_80 & aNaturalNumber0(xm) = all_46_2_81 & ( ~ (all_46_1_80 = 0) | ~ (all_46_2_81 = 0))
% 67.13/31.21 |
% 67.13/31.21 | Applying alpha-rule on (1370) yields:
% 67.13/31.21 | (1371) aNaturalNumber0(xp) = all_46_1_80
% 67.13/31.21 | (1372) aNaturalNumber0(xm) = all_46_2_81
% 67.13/31.21 | (1373) ~ (all_46_1_80 = 0) | ~ (all_46_2_81 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Instantiating formula (63) with xp, all_46_1_80, 0 and discharging atoms aNaturalNumber0(xp) = all_46_1_80, aNaturalNumber0(xp) = 0, yields:
% 67.13/31.21 | (415) all_46_1_80 = 0
% 67.13/31.21 |
% 67.13/31.21 | Instantiating formula (63) with xm, all_46_2_81, 0 and discharging atoms aNaturalNumber0(xm) = all_46_2_81, aNaturalNumber0(xm) = 0, yields:
% 67.13/31.21 | (1375) all_46_2_81 = 0
% 67.13/31.21 |
% 67.13/31.21 +-Applying beta-rule and splitting (1373), into two cases.
% 67.13/31.21 |-Branch one:
% 67.13/31.21 | (1376) ~ (all_46_1_80 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Equations (415) can reduce 1376 to:
% 67.13/31.21 | (241) $false
% 67.13/31.21 |
% 67.13/31.21 |-The branch is then unsatisfiable
% 67.13/31.21 |-Branch two:
% 67.13/31.21 | (415) all_46_1_80 = 0
% 67.13/31.21 | (1379) ~ (all_46_2_81 = 0)
% 67.13/31.21 |
% 67.13/31.21 | Equations (1375) can reduce 1379 to:
% 67.13/31.21 | (241) $false
% 67.13/31.21 |
% 67.13/31.21 |-The branch is then unsatisfiable
% 67.13/31.21 % SZS output end Proof for theBenchmark
% 67.13/31.21
% 67.13/31.22 30620ms
%------------------------------------------------------------------------------