TSTP Solution File: NUM514+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM514+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 08:45:20 EDT 2022
% Result : Theorem 22.54s 6.82s
% Output : Proof 131.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM514+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jul 6 18:48:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.58 ____ _
% 0.19/0.58 ___ / __ \_____(_)___ ________ __________
% 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic
% 0.19/0.58 (ePrincess v.1.0)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2015
% 0.19/0.58 (c) Peter Backeman, 2014-2015
% 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58 Bug reports to peter@backeman.se
% 0.19/0.58
% 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.64/1.03 Prover 0: Preprocessing ...
% 3.79/1.52 Prover 0: Constructing countermodel ...
% 18.78/5.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 18.96/6.05 Prover 1: Preprocessing ...
% 19.68/6.19 Prover 1: Constructing countermodel ...
% 22.54/6.82 Prover 1: proved (878ms)
% 22.54/6.82 Prover 0: stopped
% 22.54/6.82
% 22.54/6.82 No countermodel exists, formula is valid
% 22.54/6.82 % SZS status Theorem for theBenchmark
% 22.54/6.82
% 22.54/6.82 Generating proof ... found it (size 1373)
% 129.55/89.56
% 129.55/89.56 % SZS output start Proof for theBenchmark
% 129.55/89.56 Assumed formulas after preprocessing and simplification:
% 129.55/89.56 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = 0) & ~ (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(v8, xr) = v9 & sdtsldt0(v2, xp) = xk & sdtsldt0(xk, xr) = v10 & sdtsldt0(xn, xr) = v6 & doDivides0(xr, v2) = 0 & doDivides0(xr, xk) = 0 & doDivides0(xr, xm) = v5 & doDivides0(xr, xn) = 0 & doDivides0(xp, v7) = v11 & 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(v9, xr) = v2 & sdtasdt0(v7, xr) = v2 & sdtasdt0(v6, xm) = v7 & sdtasdt0(xp, v10) = v7 & sdtasdt0(xp, xk) = v8 & 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)))
% 129.80/89.63 | 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:
% 129.80/89.63 | (1) ~ (all_0_0_0 = 0) & ~ (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_3_3, xr) = all_0_2_2 & sdtsldt0(all_0_9_9, xp) = xk & sdtsldt0(xk, xr) = all_0_1_1 & 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_4_4) = all_0_0_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_2_2, xr) = all_0_9_9 & sdtasdt0(all_0_4_4, xr) = all_0_9_9 & sdtasdt0(all_0_5_5, xm) = all_0_4_4 & sdtasdt0(xp, all_0_1_1) = all_0_4_4 & sdtasdt0(xp, xk) = all_0_3_3 & 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))
% 129.80/89.66 |
% 129.80/89.66 | Applying alpha-rule on (1) yields:
% 129.80/89.66 | (2) sdtlseqdt0(xk, xp) = 0
% 129.80/89.66 | (3) doDivides0(xp, all_0_9_9) = 0
% 129.80/89.66 | (4) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ (isPrime0(v0) = 0) | ~ (doDivides0(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 129.80/89.66 | (5) sdtsldt0(xk, xr) = all_0_1_1
% 129.80/89.66 | (6) aNaturalNumber0(sz10) = 0
% 129.80/89.66 | (7) ! [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)))))
% 129.80/89.66 | (8) ! [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))))
% 129.80/89.66 | (9) sdtasdt0(all_0_2_2, xr) = all_0_9_9
% 129.80/89.66 | (10) aNaturalNumber0(xn) = 0
% 129.80/89.66 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0))
% 129.80/89.66 | (12) ! [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)))))
% 129.80/89.66 | (13) aNaturalNumber0(xp) = 0
% 129.80/89.66 | (14) aNaturalNumber0(xm) = 0
% 129.80/89.66 | (15) sdtlseqdt0(xr, xk) = 0
% 129.80/89.66 | (16) ~ (isPrime0(sz00) = 0)
% 129.80/89.66 | (17) ~ (xk = sz00)
% 129.80/89.66 | (18) ! [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))))
% 129.80/89.66 | (19) ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 129.80/89.66 | (20) doDivides0(xr, xm) = all_0_6_6
% 129.80/89.66 | (21) sdtasdt0(all_0_4_4, xr) = all_0_9_9
% 129.80/89.66 | (22) ! [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))))
% 129.80/89.66 | (23) aNaturalNumber0(xr) = 0
% 129.80/89.66 | (24) ! [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))))
% 129.80/89.66 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 129.80/89.66 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0))
% 129.80/89.66 | (27) ! [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)))
% 129.80/89.66 | (28) sdtasdt0(all_0_5_5, xm) = all_0_4_4
% 129.80/89.66 | (29) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 129.80/89.66 | (30) aNaturalNumber0(sz00) = 0
% 129.80/89.66 | (31) ! [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)))))
% 129.80/89.66 | (32) ! [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)))
% 129.80/89.66 | (33) ! [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))))
% 129.80/89.67 | (34) ! [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)))
% 129.80/89.67 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 129.80/89.67 | (36) ! [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)))))
% 129.80/89.67 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 129.80/89.67 | (38) sdtasdt0(xp, all_0_1_1) = all_0_4_4
% 129.80/89.67 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0))
% 129.80/89.67 | (40) ! [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)))))
% 129.80/89.67 | (41) ! [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)))))
% 129.80/89.67 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0))
% 129.80/89.67 | (43) sdtpldt0(xn, xm) = all_0_11_11
% 129.80/89.67 | (44) ~ (all_0_7_7 = 0)
% 129.80/89.67 | (45) sdtsldt0(xn, xr) = all_0_5_5
% 129.80/89.67 | (46) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00))))
% 129.80/89.67 | (47) doDivides0(xr, xn) = 0
% 129.80/89.67 | (48) isPrime0(xr) = 0
% 129.80/89.67 | (49) ! [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)))
% 129.80/89.67 | (50) doDivides0(xr, xk) = 0
% 129.80/89.67 | (51) ! [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)))))
% 129.80/89.67 | (52) ! [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)))))
% 129.80/89.67 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ((doDivides0(v0, v1) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))) | (sdtasdt0(v3, v2) = v7 & aNaturalNumber0(v3) = v6 & ( ~ (v6 = 0) | v7 = v5))))
% 129.80/89.67 | (54) doDivides0(xr, all_0_9_9) = 0
% 129.80/89.67 | (55) ~ (all_0_0_0 = 0)
% 129.80/89.67 | (56) ! [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)))
% 129.80/89.67 | (57) ! [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)))))
% 129.80/89.67 | (58) ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 129.80/89.67 | (59) ~ (all_0_8_8 = 0)
% 129.80/89.67 | (60) sdtlseqdt0(xp, xn) = all_0_8_8
% 129.80/89.67 | (61) ~ (isPrime0(sz10) = 0)
% 129.80/89.67 | (62) ! [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)))))
% 129.80/89.68 | (63) ! [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))))
% 129.80/89.68 | (64) sdtlseqdt0(xp, xm) = all_0_7_7
% 129.80/89.68 | (65) ~ (xk = xp)
% 129.80/89.68 | (66) ! [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)))
% 129.80/89.68 | (67) sdtasdt0(xn, xm) = all_0_9_9
% 129.80/89.68 | (68) isPrime0(xp) = 0
% 129.80/89.68 | (69) ! [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)))
% 129.80/89.68 | (70) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 129.80/89.68 | (71) ! [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))))
% 129.80/89.68 | (72) ! [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)))))
% 129.80/89.68 | (73) ! [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))))
% 129.80/89.68 | (74) ~ (xp = xm)
% 129.80/89.68 | (75) ~ (xk = sz10)
% 129.80/89.68 | (76) sdtlseqdt0(xn, xp) = 0
% 129.80/89.68 | (77) ~ (sz10 = sz00)
% 129.80/89.68 | (78) ~ (xp = xn)
% 129.80/89.68 | (79) sdtpldt0(all_0_11_11, xp) = all_0_10_10
% 129.80/89.68 | (80) sdtasdt0(xp, xk) = all_0_3_3
% 129.80/89.68 | (81) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 129.80/89.68 | (82) ! [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)))))
% 129.80/89.68 | (83) ~ (all_0_5_5 = xn)
% 129.80/89.68 | (84) sdtlseqdt0(xm, xp) = 0
% 129.80/89.68 | (85) ! [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)))
% 129.80/89.68 | (86) ! [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)))))
% 129.80/89.68 | (87) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 129.80/89.68 | (88) sdtsldt0(all_0_3_3, xr) = all_0_2_2
% 129.80/89.68 | (89) ! [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)))
% 129.80/89.69 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0))
% 129.80/89.69 | (91) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 129.80/89.69 | (92) sdtlseqdt0(all_0_5_5, xn) = 0
% 129.80/89.69 | (93) ! [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))))
% 129.80/89.69 | (94) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0))
% 129.80/89.69 | (95) sdtsldt0(all_0_9_9, xp) = xk
% 129.80/89.69 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 129.80/89.69 | (97) doDivides0(xp, all_0_4_4) = all_0_0_0
% 129.80/89.69 | (98) ! [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)))
% 129.80/89.69 |
% 129.80/89.69 | Using (48) and (61) yields:
% 129.80/89.69 | (99) ~ (xr = sz10)
% 129.80/89.69 |
% 129.80/89.69 | Using (68) and (61) yields:
% 129.80/89.69 | (100) ~ (xp = sz10)
% 129.80/89.69 |
% 129.80/89.69 | Using (48) and (16) yields:
% 129.80/89.69 | (101) ~ (xr = sz00)
% 129.80/89.69 |
% 129.80/89.69 | Using (68) and (16) yields:
% 129.80/89.69 | (102) ~ (xp = sz00)
% 129.80/89.69 |
% 129.80/89.69 | Instantiating formula (66) with all_0_9_9, xr and discharging atoms doDivides0(xr, all_0_9_9) = 0, yields:
% 129.80/89.69 | (103) 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))
% 129.80/89.69 |
% 129.80/89.69 | Instantiating formula (36) with all_0_9_9, xr and discharging atoms doDivides0(xr, all_0_9_9) = 0, yields:
% 129.80/89.69 | (104) ? [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))))
% 129.80/89.69 |
% 129.80/89.69 | Instantiating formula (36) with xk, xr and discharging atoms doDivides0(xr, xk) = 0, yields:
% 129.80/89.69 | (105) ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & v1 = 0 & sdtasdt0(xr, v0) = xk & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 129.80/89.69 |
% 129.80/89.69 | Instantiating formula (66) with xn, xr and discharging atoms doDivides0(xr, xn) = 0, yields:
% 129.80/89.69 | (106) xn = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xr, xn) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 129.80/89.69 |
% 129.80/89.69 | Instantiating formula (36) with xn, xr and discharging atoms doDivides0(xr, xn) = 0, yields:
% 129.80/89.69 | (107) ? [v0] : ? [v1] : ? [v2] : ((v2 = xn & v1 = 0 & sdtasdt0(xr, v0) = xn & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 129.80/89.69 |
% 129.80/89.69 | Instantiating formula (24) with all_0_0_0, all_0_4_4, all_0_9_9, xp and discharging atoms doDivides0(xp, all_0_4_4) = all_0_0_0, doDivides0(xp, all_0_9_9) = 0, yields:
% 129.80/89.69 | (108) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_9_9, all_0_4_4) = v3 & aNaturalNumber0(all_0_4_4) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 129.80/89.69 |
% 129.80/89.69 | Instantiating formula (66) with all_0_9_9, xp and discharging atoms doDivides0(xp, all_0_9_9) = 0, yields:
% 129.80/89.69 | (109) 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))
% 129.80/89.69 |
% 129.80/89.69 | Instantiating formula (36) with all_0_9_9, xp and discharging atoms doDivides0(xp, all_0_9_9) = 0, yields:
% 129.80/89.69 | (110) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_9_9 & v1 = 0 & sdtasdt0(xp, v0) = all_0_9_9 & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 129.80/89.69 |
% 129.80/89.69 | Instantiating formula (71) with xn, all_0_5_5 and discharging atoms sdtlseqdt0(all_0_5_5, xn) = 0, yields:
% 129.80/89.69 | (111) 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)))
% 129.80/89.69 |
% 129.80/89.69 | Instantiating formula (51) with xk, xr and discharging atoms sdtlseqdt0(xr, xk) = 0, yields:
% 129.80/89.69 | (112) ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & v1 = 0 & sdtpldt0(xr, v0) = xk & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 129.80/89.69 |
% 129.80/89.69 | Instantiating formula (71) with xp, xk and discharging atoms sdtlseqdt0(xk, xp) = 0, yields:
% 129.80/89.69 | (113) xk = xp | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, xk) = v2 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 129.80/89.70 |
% 129.80/89.70 | Instantiating formula (51) with xp, xk and discharging atoms sdtlseqdt0(xk, xp) = 0, yields:
% 129.80/89.70 | (114) ? [v0] : ? [v1] : ? [v2] : ((v2 = xp & v1 = 0 & sdtpldt0(xk, v0) = xp & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 129.80/89.70 |
% 129.80/89.70 | Instantiating formula (51) with xp, xm and discharging atoms sdtlseqdt0(xm, xp) = 0, yields:
% 129.80/89.70 | (115) ? [v0] : ? [v1] : ? [v2] : ((v2 = xp & v1 = 0 & sdtpldt0(xm, v0) = xp & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 129.80/89.70 |
% 129.80/89.70 | Instantiating formula (56) with all_0_9_9, xr, all_0_2_2 and discharging atoms sdtasdt0(all_0_2_2, xr) = all_0_9_9, yields:
% 129.80/89.70 | (116) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xr, all_0_2_2) = v2 & aNaturalNumber0(all_0_2_2) = v0 & aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_9_9))
% 129.80/89.70 |
% 129.80/89.70 | Instantiating formula (98) with all_0_9_9, xr, all_0_2_2 and discharging atoms sdtasdt0(all_0_2_2, xr) = all_0_9_9, yields:
% 129.80/89.70 | (117) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_2_2) = v0 & aNaturalNumber0(all_0_9_9) = v2 & aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 129.80/89.70 |
% 129.80/89.70 | Instantiating formula (56) with all_0_9_9, xr, all_0_4_4 and discharging atoms sdtasdt0(all_0_4_4, xr) = all_0_9_9, yields:
% 129.80/89.70 | (118) ? [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_9_9))
% 129.80/89.70 |
% 129.80/89.70 | Instantiating formula (98) with all_0_9_9, xr, all_0_4_4 and discharging atoms sdtasdt0(all_0_4_4, xr) = all_0_9_9, yields:
% 129.80/89.70 | (119) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_4_4) = v0 & aNaturalNumber0(all_0_9_9) = v2 & aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 129.80/89.70 |
% 129.80/89.70 | Instantiating formula (69) with all_0_9_9, all_0_4_4, xr, xm, all_0_5_5 and discharging atoms sdtasdt0(all_0_4_4, xr) = all_0_9_9, sdtasdt0(all_0_5_5, xm) = all_0_4_4, yields:
% 129.80/89.70 | (120) ? [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_9_9))
% 129.80/89.70 |
% 129.80/89.70 | Instantiating formula (56) with all_0_4_4, xm, all_0_5_5 and discharging atoms sdtasdt0(all_0_5_5, xm) = all_0_4_4, yields:
% 129.80/89.70 | (121) ? [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))
% 129.80/89.70 |
% 129.80/89.70 | Instantiating formula (98) with all_0_4_4, xm, all_0_5_5 and discharging atoms sdtasdt0(all_0_5_5, xm) = all_0_4_4, yields:
% 129.80/89.70 | (122) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_4_4) = v2 & aNaturalNumber0(all_0_5_5) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 129.80/89.70 |
% 129.80/89.70 | Instantiating formula (69) with all_0_9_9, all_0_4_4, xr, all_0_1_1, xp and discharging atoms sdtasdt0(all_0_4_4, xr) = all_0_9_9, sdtasdt0(xp, all_0_1_1) = all_0_4_4, yields:
% 129.80/89.70 | (123) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_1_1, xr) = v3 & sdtasdt0(xp, v3) = v4 & aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_9_9))
% 129.80/89.70 |
% 129.80/89.70 | Instantiating formula (41) with all_0_1_1, all_0_0_0, all_0_4_4, xp and discharging atoms doDivides0(xp, all_0_4_4) = all_0_0_0, sdtasdt0(xp, all_0_1_1) = all_0_4_4, yields:
% 129.80/89.70 | (124) all_0_0_0 = 0 | ? [v0] : ? [v1] : (( ~ (v0 = 0) & aNaturalNumber0(all_0_1_1) = v0) | (aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 129.80/89.70 |
% 129.80/89.70 | Instantiating formula (56) with all_0_4_4, all_0_1_1, xp and discharging atoms sdtasdt0(xp, all_0_1_1) = all_0_4_4, yields:
% 129.80/89.70 | (125) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_0_1_1, xp) = v2 & aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_4_4))
% 129.80/89.70 |
% 129.80/89.70 | Instantiating formula (98) with all_0_4_4, all_0_1_1, xp and discharging atoms sdtasdt0(xp, all_0_1_1) = all_0_4_4, yields:
% 129.80/89.70 | (126) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(all_0_4_4) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 129.80/89.70 |
% 129.80/89.70 | Instantiating formula (53) with all_0_2_2, all_0_3_3, xp, all_0_1_1, xk, xr and discharging atoms sdtsldt0(all_0_3_3, xr) = all_0_2_2, sdtsldt0(xk, xr) = all_0_1_1, sdtasdt0(xp, xk) = all_0_3_3, yields:
% 129.80/89.70 | (127) xr = sz00 | ? [v0] : ? [v1] : ? [v2] : ((doDivides0(xr, xk) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) | (sdtasdt0(xp, all_0_1_1) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v0 = 0) | v1 = all_0_2_2)))
% 129.80/89.70 |
% 129.80/89.70 | Instantiating formula (18) with all_0_3_3, xk, all_0_9_9, xp and discharging atoms sdtsldt0(all_0_9_9, xp) = xk, sdtasdt0(xp, xk) = all_0_3_3, yields:
% 129.80/89.70 | (128) all_0_3_3 = 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)))
% 129.80/89.70 |
% 129.80/89.70 | Instantiating formula (82) with all_0_3_3, xk, all_0_9_9, xp and discharging atoms sdtsldt0(all_0_9_9, xp) = xk, sdtasdt0(xp, xk) = all_0_3_3, yields:
% 129.80/89.70 | (129) 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))))
% 129.80/89.70 |
% 129.80/89.70 | Instantiating formula (81) with xk, xp yields:
% 129.80/89.70 | (130) xk = sz00 | xp = sz00 | ~ (sdtasdt0(xp, xk) = sz00) | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 129.80/89.71 |
% 129.80/89.71 | Instantiating formula (56) with all_0_3_3, xk, xp and discharging atoms sdtasdt0(xp, xk) = all_0_3_3, yields:
% 129.80/89.71 | (131) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xk, xp) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_3_3))
% 129.80/89.71 |
% 129.80/89.71 | Instantiating formula (98) with all_0_3_3, xk, xp and discharging atoms sdtasdt0(xp, xk) = all_0_3_3, yields:
% 129.80/89.71 | (132) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_3_3) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 129.80/89.71 |
% 129.80/89.71 | Instantiating formula (46) with all_0_9_9, xm yields:
% 129.80/89.71 | (133) ~ (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)))
% 129.80/89.71 |
% 129.80/89.71 | Instantiating formula (56) with all_0_9_9, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_9_9, yields:
% 129.80/89.71 | (134) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_9_9))
% 129.80/89.71 |
% 129.80/89.71 | Instantiating formula (98) with all_0_9_9, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_9_9, yields:
% 129.80/89.71 | (135) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_9_9) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 129.80/89.71 |
% 129.80/89.71 | 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:
% 129.80/89.71 | (136) ? [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))
% 129.80/89.71 |
% 129.80/89.71 | Instantiating formula (89) with all_0_10_10, xp, all_0_11_11 and discharging atoms sdtpldt0(all_0_11_11, xp) = all_0_10_10, yields:
% 129.80/89.71 | (137) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_10_10) = v2 & aNaturalNumber0(all_0_11_11) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 129.80/89.71 |
% 129.80/89.71 | Instantiating formula (85) 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:
% 129.80/89.71 | (138) ? [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))
% 129.80/89.71 |
% 129.80/89.71 | Instantiating formula (27) 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:
% 129.80/89.71 | (139) ? [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))
% 129.80/89.71 |
% 129.80/89.71 | Instantiating formula (34) with all_0_11_11, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_11_11, yields:
% 129.80/89.71 | (140) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_11_11))
% 129.80/89.71 |
% 129.80/89.71 | Instantiating formula (89) with all_0_11_11, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_11_11, yields:
% 129.80/89.71 | (141) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_11_11) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 129.80/89.71 |
% 129.80/89.71 | Instantiating formula (94) with xr and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 129.80/89.71 | (142) xr = sz10 | xr = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xr) = 0 & aNaturalNumber0(v0) = 0)
% 129.80/89.71 |
% 129.80/89.71 | Instantiating formula (94) with xp and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 129.80/89.71 | (143) xp = sz10 | xp = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 129.80/89.71 |
% 129.80/89.71 | Instantiating (141) with all_12_0_12, all_12_1_13, all_12_2_14 yields:
% 129.80/89.71 | (144) 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)
% 129.80/89.71 |
% 129.80/89.71 | Applying alpha-rule on (144) yields:
% 129.80/89.71 | (145) aNaturalNumber0(all_0_11_11) = all_12_0_12
% 129.80/89.71 | (146) aNaturalNumber0(xm) = all_12_1_13
% 129.80/89.71 | (147) aNaturalNumber0(xn) = all_12_2_14
% 129.80/89.71 | (148) ~ (all_12_1_13 = 0) | ~ (all_12_2_14 = 0) | all_12_0_12 = 0
% 129.80/89.71 |
% 129.80/89.71 | Instantiating (140) with all_14_0_15, all_14_1_16, all_14_2_17 yields:
% 129.80/89.71 | (149) sdtpldt0(xm, xn) = all_14_0_15 & aNaturalNumber0(xm) = all_14_1_16 & aNaturalNumber0(xn) = all_14_2_17 & ( ~ (all_14_1_16 = 0) | ~ (all_14_2_17 = 0) | all_14_0_15 = all_0_11_11)
% 129.80/89.71 |
% 129.80/89.71 | Applying alpha-rule on (149) yields:
% 129.80/89.71 | (150) sdtpldt0(xm, xn) = all_14_0_15
% 129.80/89.71 | (151) aNaturalNumber0(xm) = all_14_1_16
% 129.80/89.71 | (152) aNaturalNumber0(xn) = all_14_2_17
% 129.80/89.71 | (153) ~ (all_14_1_16 = 0) | ~ (all_14_2_17 = 0) | all_14_0_15 = all_0_11_11
% 129.80/89.71 |
% 129.80/89.71 | Instantiating (135) with all_16_0_18, all_16_1_19, all_16_2_20 yields:
% 129.80/89.71 | (154) aNaturalNumber0(all_0_9_9) = all_16_0_18 & aNaturalNumber0(xm) = all_16_1_19 & aNaturalNumber0(xn) = all_16_2_20 & ( ~ (all_16_1_19 = 0) | ~ (all_16_2_20 = 0) | all_16_0_18 = 0)
% 129.80/89.71 |
% 129.80/89.71 | Applying alpha-rule on (154) yields:
% 129.80/89.71 | (155) aNaturalNumber0(all_0_9_9) = all_16_0_18
% 129.80/89.71 | (156) aNaturalNumber0(xm) = all_16_1_19
% 129.80/89.71 | (157) aNaturalNumber0(xn) = all_16_2_20
% 129.80/89.71 | (158) ~ (all_16_1_19 = 0) | ~ (all_16_2_20 = 0) | all_16_0_18 = 0
% 129.80/89.71 |
% 129.80/89.71 | Instantiating (134) with all_18_0_21, all_18_1_22, all_18_2_23 yields:
% 129.80/89.71 | (159) sdtasdt0(xm, xn) = all_18_0_21 & aNaturalNumber0(xm) = all_18_1_22 & aNaturalNumber0(xn) = all_18_2_23 & ( ~ (all_18_1_22 = 0) | ~ (all_18_2_23 = 0) | all_18_0_21 = all_0_9_9)
% 129.80/89.72 |
% 129.80/89.72 | Applying alpha-rule on (159) yields:
% 129.80/89.72 | (160) sdtasdt0(xm, xn) = all_18_0_21
% 129.80/89.72 | (161) aNaturalNumber0(xm) = all_18_1_22
% 129.80/89.72 | (162) aNaturalNumber0(xn) = all_18_2_23
% 129.80/89.72 | (163) ~ (all_18_1_22 = 0) | ~ (all_18_2_23 = 0) | all_18_0_21 = all_0_9_9
% 129.80/89.72 |
% 129.80/89.72 | Instantiating (126) with all_20_0_24, all_20_1_25, all_20_2_26 yields:
% 129.80/89.72 | (164) aNaturalNumber0(all_0_1_1) = all_20_1_25 & aNaturalNumber0(all_0_4_4) = all_20_0_24 & aNaturalNumber0(xp) = all_20_2_26 & ( ~ (all_20_1_25 = 0) | ~ (all_20_2_26 = 0) | all_20_0_24 = 0)
% 129.80/89.72 |
% 129.80/89.72 | Applying alpha-rule on (164) yields:
% 129.80/89.72 | (165) aNaturalNumber0(all_0_1_1) = all_20_1_25
% 129.80/89.72 | (166) aNaturalNumber0(all_0_4_4) = all_20_0_24
% 129.80/89.72 | (167) aNaturalNumber0(xp) = all_20_2_26
% 129.80/89.72 | (168) ~ (all_20_1_25 = 0) | ~ (all_20_2_26 = 0) | all_20_0_24 = 0
% 129.80/89.72 |
% 129.80/89.72 | Instantiating (137) with all_22_0_27, all_22_1_28, all_22_2_29 yields:
% 129.80/89.72 | (169) aNaturalNumber0(all_0_10_10) = all_22_0_27 & aNaturalNumber0(all_0_11_11) = all_22_2_29 & aNaturalNumber0(xp) = all_22_1_28 & ( ~ (all_22_1_28 = 0) | ~ (all_22_2_29 = 0) | all_22_0_27 = 0)
% 129.80/89.72 |
% 130.29/89.72 | Applying alpha-rule on (169) yields:
% 130.29/89.72 | (170) aNaturalNumber0(all_0_10_10) = all_22_0_27
% 130.29/89.72 | (171) aNaturalNumber0(all_0_11_11) = all_22_2_29
% 130.29/89.72 | (172) aNaturalNumber0(xp) = all_22_1_28
% 130.29/89.72 | (173) ~ (all_22_1_28 = 0) | ~ (all_22_2_29 = 0) | all_22_0_27 = 0
% 130.29/89.72 |
% 130.29/89.72 | Instantiating (132) with all_24_0_30, all_24_1_31, all_24_2_32 yields:
% 130.29/89.72 | (174) aNaturalNumber0(all_0_3_3) = all_24_0_30 & aNaturalNumber0(xk) = all_24_1_31 & aNaturalNumber0(xp) = all_24_2_32 & ( ~ (all_24_1_31 = 0) | ~ (all_24_2_32 = 0) | all_24_0_30 = 0)
% 130.29/89.72 |
% 130.29/89.72 | Applying alpha-rule on (174) yields:
% 130.29/89.72 | (175) aNaturalNumber0(all_0_3_3) = all_24_0_30
% 130.29/89.72 | (176) aNaturalNumber0(xk) = all_24_1_31
% 130.29/89.72 | (177) aNaturalNumber0(xp) = all_24_2_32
% 130.29/89.72 | (178) ~ (all_24_1_31 = 0) | ~ (all_24_2_32 = 0) | all_24_0_30 = 0
% 130.29/89.72 |
% 130.29/89.72 | Instantiating (131) with all_26_0_33, all_26_1_34, all_26_2_35 yields:
% 130.29/89.72 | (179) sdtasdt0(xk, xp) = all_26_0_33 & aNaturalNumber0(xk) = all_26_1_34 & aNaturalNumber0(xp) = all_26_2_35 & ( ~ (all_26_1_34 = 0) | ~ (all_26_2_35 = 0) | all_26_0_33 = all_0_3_3)
% 130.29/89.72 |
% 130.29/89.72 | Applying alpha-rule on (179) yields:
% 130.29/89.72 | (180) sdtasdt0(xk, xp) = all_26_0_33
% 130.29/89.72 | (181) aNaturalNumber0(xk) = all_26_1_34
% 130.29/89.72 | (182) aNaturalNumber0(xp) = all_26_2_35
% 130.29/89.72 | (183) ~ (all_26_1_34 = 0) | ~ (all_26_2_35 = 0) | all_26_0_33 = all_0_3_3
% 130.29/89.72 |
% 130.29/89.72 | Instantiating (120) with all_28_0_36, all_28_1_37, all_28_2_38, all_28_3_39, all_28_4_40 yields:
% 130.29/89.72 | (184) sdtasdt0(all_0_5_5, all_28_1_37) = all_28_0_36 & sdtasdt0(xm, xr) = all_28_1_37 & aNaturalNumber0(all_0_5_5) = all_28_4_40 & aNaturalNumber0(xr) = all_28_2_38 & aNaturalNumber0(xm) = all_28_3_39 & ( ~ (all_28_2_38 = 0) | ~ (all_28_3_39 = 0) | ~ (all_28_4_40 = 0) | all_28_0_36 = all_0_9_9)
% 130.29/89.72 |
% 130.29/89.72 | Applying alpha-rule on (184) yields:
% 130.29/89.72 | (185) sdtasdt0(all_0_5_5, all_28_1_37) = all_28_0_36
% 130.29/89.72 | (186) ~ (all_28_2_38 = 0) | ~ (all_28_3_39 = 0) | ~ (all_28_4_40 = 0) | all_28_0_36 = all_0_9_9
% 130.29/89.72 | (187) aNaturalNumber0(xr) = all_28_2_38
% 130.29/89.72 | (188) sdtasdt0(xm, xr) = all_28_1_37
% 130.29/89.72 | (189) aNaturalNumber0(all_0_5_5) = all_28_4_40
% 130.29/89.72 | (190) aNaturalNumber0(xm) = all_28_3_39
% 130.29/89.72 |
% 130.29/89.72 | Instantiating (119) with all_30_0_41, all_30_1_42, all_30_2_43 yields:
% 130.29/89.72 | (191) aNaturalNumber0(all_0_4_4) = all_30_2_43 & aNaturalNumber0(all_0_9_9) = all_30_0_41 & aNaturalNumber0(xr) = all_30_1_42 & ( ~ (all_30_1_42 = 0) | ~ (all_30_2_43 = 0) | all_30_0_41 = 0)
% 130.29/89.72 |
% 130.29/89.72 | Applying alpha-rule on (191) yields:
% 130.29/89.72 | (192) aNaturalNumber0(all_0_4_4) = all_30_2_43
% 130.29/89.72 | (193) aNaturalNumber0(all_0_9_9) = all_30_0_41
% 130.29/89.72 | (194) aNaturalNumber0(xr) = all_30_1_42
% 130.29/89.72 | (195) ~ (all_30_1_42 = 0) | ~ (all_30_2_43 = 0) | all_30_0_41 = 0
% 130.29/89.72 |
% 130.29/89.72 | Instantiating (117) with all_32_0_44, all_32_1_45, all_32_2_46 yields:
% 130.29/89.72 | (196) aNaturalNumber0(all_0_2_2) = all_32_2_46 & aNaturalNumber0(all_0_9_9) = all_32_0_44 & aNaturalNumber0(xr) = all_32_1_45 & ( ~ (all_32_1_45 = 0) | ~ (all_32_2_46 = 0) | all_32_0_44 = 0)
% 130.29/89.72 |
% 130.29/89.72 | Applying alpha-rule on (196) yields:
% 130.29/89.72 | (197) aNaturalNumber0(all_0_2_2) = all_32_2_46
% 130.29/89.72 | (198) aNaturalNumber0(all_0_9_9) = all_32_0_44
% 130.29/89.72 | (199) aNaturalNumber0(xr) = all_32_1_45
% 130.29/89.72 | (200) ~ (all_32_1_45 = 0) | ~ (all_32_2_46 = 0) | all_32_0_44 = 0
% 130.29/89.72 |
% 130.29/89.72 | Instantiating (116) with all_34_0_47, all_34_1_48, all_34_2_49 yields:
% 130.29/89.72 | (201) sdtasdt0(xr, all_0_2_2) = all_34_0_47 & aNaturalNumber0(all_0_2_2) = all_34_2_49 & aNaturalNumber0(xr) = all_34_1_48 & ( ~ (all_34_1_48 = 0) | ~ (all_34_2_49 = 0) | all_34_0_47 = all_0_9_9)
% 130.29/89.72 |
% 130.29/89.72 | Applying alpha-rule on (201) yields:
% 130.29/89.72 | (202) sdtasdt0(xr, all_0_2_2) = all_34_0_47
% 130.29/89.72 | (203) aNaturalNumber0(all_0_2_2) = all_34_2_49
% 130.29/89.72 | (204) aNaturalNumber0(xr) = all_34_1_48
% 130.29/89.72 | (205) ~ (all_34_1_48 = 0) | ~ (all_34_2_49 = 0) | all_34_0_47 = all_0_9_9
% 130.29/89.73 |
% 130.29/89.73 | Instantiating (118) with all_36_0_50, all_36_1_51, all_36_2_52 yields:
% 130.29/89.73 | (206) sdtasdt0(xr, all_0_4_4) = all_36_0_50 & aNaturalNumber0(all_0_4_4) = all_36_2_52 & aNaturalNumber0(xr) = all_36_1_51 & ( ~ (all_36_1_51 = 0) | ~ (all_36_2_52 = 0) | all_36_0_50 = all_0_9_9)
% 130.29/89.73 |
% 130.29/89.73 | Applying alpha-rule on (206) yields:
% 130.29/89.73 | (207) sdtasdt0(xr, all_0_4_4) = all_36_0_50
% 130.29/89.73 | (208) aNaturalNumber0(all_0_4_4) = all_36_2_52
% 130.29/89.73 | (209) aNaturalNumber0(xr) = all_36_1_51
% 130.29/89.73 | (210) ~ (all_36_1_51 = 0) | ~ (all_36_2_52 = 0) | all_36_0_50 = all_0_9_9
% 130.29/89.73 |
% 130.29/89.73 | Instantiating (115) with all_39_0_56, all_39_1_57, all_39_2_58 yields:
% 130.29/89.73 | (211) (all_39_0_56 = xp & all_39_1_57 = 0 & sdtpldt0(xm, all_39_2_58) = xp & aNaturalNumber0(all_39_2_58) = 0) | (aNaturalNumber0(xp) = all_39_1_57 & aNaturalNumber0(xm) = all_39_2_58 & ( ~ (all_39_1_57 = 0) | ~ (all_39_2_58 = 0)))
% 130.29/89.73 |
% 130.29/89.73 | Instantiating (136) with all_40_0_59, all_40_1_60, all_40_2_61 yields:
% 130.29/89.73 | (212) sdtpldt0(xp, all_0_11_11) = all_40_0_59 & aNaturalNumber0(all_0_11_11) = all_40_2_61 & aNaturalNumber0(xp) = all_40_1_60 & ( ~ (all_40_1_60 = 0) | ~ (all_40_2_61 = 0) | all_40_0_59 = all_0_10_10)
% 130.29/89.73 |
% 130.29/89.73 | Applying alpha-rule on (212) yields:
% 130.29/89.73 | (213) sdtpldt0(xp, all_0_11_11) = all_40_0_59
% 130.29/89.73 | (214) aNaturalNumber0(all_0_11_11) = all_40_2_61
% 130.29/89.73 | (215) aNaturalNumber0(xp) = all_40_1_60
% 130.29/89.73 | (216) ~ (all_40_1_60 = 0) | ~ (all_40_2_61 = 0) | all_40_0_59 = all_0_10_10
% 130.29/89.73 |
% 130.29/89.73 | Instantiating (125) with all_42_0_62, all_42_1_63, all_42_2_64 yields:
% 130.29/89.73 | (217) sdtasdt0(all_0_1_1, xp) = all_42_0_62 & aNaturalNumber0(all_0_1_1) = all_42_1_63 & aNaturalNumber0(xp) = all_42_2_64 & ( ~ (all_42_1_63 = 0) | ~ (all_42_2_64 = 0) | all_42_0_62 = all_0_4_4)
% 130.29/89.73 |
% 130.29/89.73 | Applying alpha-rule on (217) yields:
% 130.29/89.73 | (218) sdtasdt0(all_0_1_1, xp) = all_42_0_62
% 130.29/89.73 | (219) aNaturalNumber0(all_0_1_1) = all_42_1_63
% 130.29/89.73 | (220) aNaturalNumber0(xp) = all_42_2_64
% 130.29/89.73 | (221) ~ (all_42_1_63 = 0) | ~ (all_42_2_64 = 0) | all_42_0_62 = all_0_4_4
% 130.29/89.73 |
% 130.29/89.73 | Instantiating (123) with all_44_0_65, all_44_1_66, all_44_2_67, all_44_3_68, all_44_4_69 yields:
% 130.29/89.73 | (222) sdtasdt0(all_0_1_1, xr) = all_44_1_66 & sdtasdt0(xp, all_44_1_66) = all_44_0_65 & aNaturalNumber0(all_0_1_1) = all_44_3_68 & aNaturalNumber0(xr) = all_44_2_67 & aNaturalNumber0(xp) = all_44_4_69 & ( ~ (all_44_2_67 = 0) | ~ (all_44_3_68 = 0) | ~ (all_44_4_69 = 0) | all_44_0_65 = all_0_9_9)
% 130.29/89.73 |
% 130.29/89.73 | Applying alpha-rule on (222) yields:
% 130.29/89.73 | (223) sdtasdt0(xp, all_44_1_66) = all_44_0_65
% 130.29/89.73 | (224) sdtasdt0(all_0_1_1, xr) = all_44_1_66
% 130.29/89.73 | (225) aNaturalNumber0(xp) = all_44_4_69
% 130.29/89.73 | (226) aNaturalNumber0(all_0_1_1) = all_44_3_68
% 130.29/89.73 | (227) ~ (all_44_2_67 = 0) | ~ (all_44_3_68 = 0) | ~ (all_44_4_69 = 0) | all_44_0_65 = all_0_9_9
% 130.29/89.73 | (228) aNaturalNumber0(xr) = all_44_2_67
% 130.29/89.73 |
% 130.29/89.73 | Instantiating (122) with all_46_0_70, all_46_1_71, all_46_2_72 yields:
% 130.29/89.73 | (229) aNaturalNumber0(all_0_4_4) = all_46_0_70 & aNaturalNumber0(all_0_5_5) = all_46_2_72 & aNaturalNumber0(xm) = all_46_1_71 & ( ~ (all_46_1_71 = 0) | ~ (all_46_2_72 = 0) | all_46_0_70 = 0)
% 130.29/89.73 |
% 130.29/89.73 | Applying alpha-rule on (229) yields:
% 130.29/89.73 | (230) aNaturalNumber0(all_0_4_4) = all_46_0_70
% 130.29/89.73 | (231) aNaturalNumber0(all_0_5_5) = all_46_2_72
% 130.29/89.73 | (232) aNaturalNumber0(xm) = all_46_1_71
% 130.29/89.73 | (233) ~ (all_46_1_71 = 0) | ~ (all_46_2_72 = 0) | all_46_0_70 = 0
% 130.29/89.73 |
% 130.29/89.73 | Instantiating (112) with all_48_0_73, all_48_1_74, all_48_2_75 yields:
% 130.29/89.73 | (234) (all_48_0_73 = xk & all_48_1_74 = 0 & sdtpldt0(xr, all_48_2_75) = xk & aNaturalNumber0(all_48_2_75) = 0) | (aNaturalNumber0(xr) = all_48_2_75 & aNaturalNumber0(xk) = all_48_1_74 & ( ~ (all_48_1_74 = 0) | ~ (all_48_2_75 = 0)))
% 130.29/89.73 |
% 130.29/89.73 | Instantiating (107) with all_50_0_79, all_50_1_80, all_50_2_81 yields:
% 130.29/89.73 | (235) (all_50_0_79 = xn & all_50_1_80 = 0 & sdtasdt0(xr, all_50_2_81) = xn & aNaturalNumber0(all_50_2_81) = 0) | (aNaturalNumber0(xr) = all_50_2_81 & aNaturalNumber0(xn) = all_50_1_80 & ( ~ (all_50_1_80 = 0) | ~ (all_50_2_81 = 0)))
% 130.29/89.73 |
% 130.29/89.73 | Instantiating (139) with all_51_0_82, all_51_1_83, all_51_2_84, all_51_3_85, all_51_4_86 yields:
% 130.29/89.73 | (236) sdtpldt0(xm, xp) = all_51_1_83 & sdtpldt0(xn, all_51_1_83) = all_51_0_82 & aNaturalNumber0(xp) = all_51_2_84 & aNaturalNumber0(xm) = all_51_3_85 & aNaturalNumber0(xn) = all_51_4_86 & ( ~ (all_51_2_84 = 0) | ~ (all_51_3_85 = 0) | ~ (all_51_4_86 = 0) | all_51_0_82 = all_0_10_10)
% 130.29/89.73 |
% 130.29/89.73 | Applying alpha-rule on (236) yields:
% 130.29/89.73 | (237) aNaturalNumber0(xm) = all_51_3_85
% 130.29/89.73 | (238) aNaturalNumber0(xp) = all_51_2_84
% 130.29/89.73 | (239) sdtpldt0(xn, all_51_1_83) = all_51_0_82
% 130.29/89.73 | (240) aNaturalNumber0(xn) = all_51_4_86
% 130.29/89.73 | (241) ~ (all_51_2_84 = 0) | ~ (all_51_3_85 = 0) | ~ (all_51_4_86 = 0) | all_51_0_82 = all_0_10_10
% 130.29/89.73 | (242) sdtpldt0(xm, xp) = all_51_1_83
% 130.29/89.73 |
% 130.29/89.73 | Instantiating (110) with all_53_0_87, all_53_1_88, all_53_2_89 yields:
% 130.29/89.73 | (243) (all_53_0_87 = all_0_9_9 & all_53_1_88 = 0 & sdtasdt0(xp, all_53_2_89) = all_0_9_9 & aNaturalNumber0(all_53_2_89) = 0) | (aNaturalNumber0(all_0_9_9) = all_53_1_88 & aNaturalNumber0(xp) = all_53_2_89 & ( ~ (all_53_1_88 = 0) | ~ (all_53_2_89 = 0)))
% 130.29/89.73 |
% 130.29/89.73 | Instantiating (138) with all_54_0_90, all_54_1_91, all_54_2_92, all_54_3_93, all_54_4_94, all_54_5_95, all_54_6_96, all_54_7_97, all_54_8_98 yields:
% 130.29/89.73 | (244) isPrime0(xp) = all_54_5_95 & doDivides0(xp, all_54_4_94) = all_54_3_93 & doDivides0(xp, xm) = all_54_0_90 & doDivides0(xp, xn) = all_54_1_91 & iLess0(all_0_10_10, all_0_10_10) = all_54_2_92 & sdtasdt0(xn, xm) = all_54_4_94 & aNaturalNumber0(xp) = all_54_6_96 & aNaturalNumber0(xm) = all_54_7_97 & aNaturalNumber0(xn) = all_54_8_98 & ( ~ (all_54_2_92 = 0) | ~ (all_54_3_93 = 0) | ~ (all_54_5_95 = 0) | ~ (all_54_6_96 = 0) | ~ (all_54_7_97 = 0) | ~ (all_54_8_98 = 0) | all_54_0_90 = 0 | all_54_1_91 = 0)
% 130.29/89.73 |
% 130.29/89.73 | Applying alpha-rule on (244) yields:
% 130.29/89.73 | (245) doDivides0(xp, xn) = all_54_1_91
% 130.29/89.73 | (246) doDivides0(xp, all_54_4_94) = all_54_3_93
% 130.29/89.73 | (247) ~ (all_54_2_92 = 0) | ~ (all_54_3_93 = 0) | ~ (all_54_5_95 = 0) | ~ (all_54_6_96 = 0) | ~ (all_54_7_97 = 0) | ~ (all_54_8_98 = 0) | all_54_0_90 = 0 | all_54_1_91 = 0
% 130.29/89.74 | (248) aNaturalNumber0(xp) = all_54_6_96
% 130.29/89.74 | (249) isPrime0(xp) = all_54_5_95
% 130.29/89.74 | (250) aNaturalNumber0(xn) = all_54_8_98
% 130.29/89.74 | (251) iLess0(all_0_10_10, all_0_10_10) = all_54_2_92
% 130.29/89.74 | (252) doDivides0(xp, xm) = all_54_0_90
% 130.29/89.74 | (253) sdtasdt0(xn, xm) = all_54_4_94
% 130.29/89.74 | (254) aNaturalNumber0(xm) = all_54_7_97
% 130.29/89.74 |
% 130.29/89.74 | Instantiating (105) with all_56_0_99, all_56_1_100, all_56_2_101 yields:
% 130.29/89.74 | (255) (all_56_0_99 = xk & all_56_1_100 = 0 & sdtasdt0(xr, all_56_2_101) = xk & aNaturalNumber0(all_56_2_101) = 0) | (aNaturalNumber0(xr) = all_56_2_101 & aNaturalNumber0(xk) = all_56_1_100 & ( ~ (all_56_1_100 = 0) | ~ (all_56_2_101 = 0)))
% 130.29/89.74 |
% 130.29/89.74 | Instantiating (114) with all_57_0_102, all_57_1_103, all_57_2_104 yields:
% 130.29/89.74 | (256) (all_57_0_102 = xp & all_57_1_103 = 0 & sdtpldt0(xk, all_57_2_104) = xp & aNaturalNumber0(all_57_2_104) = 0) | (aNaturalNumber0(xk) = all_57_2_104 & aNaturalNumber0(xp) = all_57_1_103 & ( ~ (all_57_1_103 = 0) | ~ (all_57_2_104 = 0)))
% 130.29/89.74 |
% 130.29/89.74 | Instantiating (121) with all_58_0_105, all_58_1_106, all_58_2_107 yields:
% 130.29/89.74 | (257) sdtasdt0(xm, all_0_5_5) = all_58_0_105 & aNaturalNumber0(all_0_5_5) = all_58_2_107 & aNaturalNumber0(xm) = all_58_1_106 & ( ~ (all_58_1_106 = 0) | ~ (all_58_2_107 = 0) | all_58_0_105 = all_0_4_4)
% 130.29/89.74 |
% 130.29/89.74 | Applying alpha-rule on (257) yields:
% 130.29/89.74 | (258) sdtasdt0(xm, all_0_5_5) = all_58_0_105
% 130.29/89.74 | (259) aNaturalNumber0(all_0_5_5) = all_58_2_107
% 130.29/89.74 | (260) aNaturalNumber0(xm) = all_58_1_106
% 130.29/89.74 | (261) ~ (all_58_1_106 = 0) | ~ (all_58_2_107 = 0) | all_58_0_105 = all_0_4_4
% 130.29/89.74 |
% 130.29/89.74 | Instantiating (104) with all_60_0_108, all_60_1_109, all_60_2_110 yields:
% 130.29/89.74 | (262) (all_60_0_108 = all_0_9_9 & all_60_1_109 = 0 & sdtasdt0(xr, all_60_2_110) = all_0_9_9 & aNaturalNumber0(all_60_2_110) = 0) | (aNaturalNumber0(all_0_9_9) = all_60_1_109 & aNaturalNumber0(xr) = all_60_2_110 & ( ~ (all_60_1_109 = 0) | ~ (all_60_2_110 = 0)))
% 130.29/89.74 |
% 130.29/89.74 +-Applying beta-rule and splitting (108), into two cases.
% 130.29/89.74 |-Branch one:
% 130.29/89.74 | (263) all_0_0_0 = 0
% 130.29/89.74 |
% 130.29/89.74 | Equations (263) can reduce 55 to:
% 130.29/89.74 | (264) $false
% 130.29/89.74 |
% 130.29/89.74 |-The branch is then unsatisfiable
% 130.29/89.74 |-Branch two:
% 130.29/89.74 | (55) ~ (all_0_0_0 = 0)
% 130.29/89.74 | (266) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_9_9, all_0_4_4) = v3 & aNaturalNumber0(all_0_4_4) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 130.29/89.74 |
% 130.29/89.74 | Instantiating (266) with all_65_0_111, all_65_1_112, all_65_2_113, all_65_3_114 yields:
% 130.29/89.74 | (267) doDivides0(all_0_9_9, all_0_4_4) = all_65_0_111 & aNaturalNumber0(all_0_4_4) = all_65_1_112 & aNaturalNumber0(all_0_9_9) = all_65_2_113 & aNaturalNumber0(xp) = all_65_3_114 & ( ~ (all_65_0_111 = 0) | ~ (all_65_1_112 = 0) | ~ (all_65_2_113 = 0) | ~ (all_65_3_114 = 0))
% 130.29/89.74 |
% 130.29/89.74 | Applying alpha-rule on (267) yields:
% 130.29/89.74 | (268) aNaturalNumber0(all_0_9_9) = all_65_2_113
% 130.29/89.74 | (269) aNaturalNumber0(all_0_4_4) = all_65_1_112
% 130.29/89.74 | (270) ~ (all_65_0_111 = 0) | ~ (all_65_1_112 = 0) | ~ (all_65_2_113 = 0) | ~ (all_65_3_114 = 0)
% 130.29/89.74 | (271) doDivides0(all_0_9_9, all_0_4_4) = all_65_0_111
% 130.29/89.74 | (272) aNaturalNumber0(xp) = all_65_3_114
% 130.29/89.74 |
% 130.29/89.74 +-Applying beta-rule and splitting (111), into two cases.
% 130.29/89.74 |-Branch one:
% 130.29/89.74 | (273) all_0_5_5 = xn
% 130.29/89.74 |
% 130.29/89.74 | Equations (273) can reduce 83 to:
% 130.29/89.74 | (264) $false
% 130.29/89.74 |
% 130.29/89.74 |-The branch is then unsatisfiable
% 130.29/89.74 |-Branch two:
% 130.29/89.74 | (83) ~ (all_0_5_5 = xn)
% 130.29/89.74 | (276) ? [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)))
% 130.29/89.74 |
% 130.29/89.74 | Instantiating (276) with all_70_0_115, all_70_1_116, all_70_2_117 yields:
% 130.29/89.74 | (277) sdtlseqdt0(xn, all_0_5_5) = all_70_0_115 & aNaturalNumber0(all_0_5_5) = all_70_2_117 & aNaturalNumber0(xn) = all_70_1_116 & ( ~ (all_70_0_115 = 0) | ~ (all_70_1_116 = 0) | ~ (all_70_2_117 = 0))
% 130.29/89.74 |
% 130.29/89.74 | Applying alpha-rule on (277) yields:
% 130.29/89.74 | (278) sdtlseqdt0(xn, all_0_5_5) = all_70_0_115
% 130.29/89.74 | (279) aNaturalNumber0(all_0_5_5) = all_70_2_117
% 130.29/89.74 | (280) aNaturalNumber0(xn) = all_70_1_116
% 130.29/89.74 | (281) ~ (all_70_0_115 = 0) | ~ (all_70_1_116 = 0) | ~ (all_70_2_117 = 0)
% 130.29/89.74 |
% 130.29/89.74 +-Applying beta-rule and splitting (113), into two cases.
% 130.29/89.74 |-Branch one:
% 130.29/89.74 | (282) xk = xp
% 130.29/89.74 |
% 130.29/89.74 | Equations (282) can reduce 65 to:
% 130.29/89.74 | (264) $false
% 130.29/89.74 |
% 130.29/89.74 |-The branch is then unsatisfiable
% 130.29/89.74 |-Branch two:
% 130.29/89.74 | (65) ~ (xk = xp)
% 130.29/89.74 | (285) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, xk) = v2 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 130.29/89.74 |
% 130.29/89.74 | Instantiating (285) with all_75_0_118, all_75_1_119, all_75_2_120 yields:
% 130.29/89.74 | (286) sdtlseqdt0(xp, xk) = all_75_0_118 & aNaturalNumber0(xk) = all_75_2_120 & aNaturalNumber0(xp) = all_75_1_119 & ( ~ (all_75_0_118 = 0) | ~ (all_75_1_119 = 0) | ~ (all_75_2_120 = 0))
% 130.29/89.74 |
% 130.29/89.74 | Applying alpha-rule on (286) yields:
% 130.29/89.74 | (287) sdtlseqdt0(xp, xk) = all_75_0_118
% 130.29/89.74 | (288) aNaturalNumber0(xk) = all_75_2_120
% 130.29/89.74 | (289) aNaturalNumber0(xp) = all_75_1_119
% 130.29/89.74 | (290) ~ (all_75_0_118 = 0) | ~ (all_75_1_119 = 0) | ~ (all_75_2_120 = 0)
% 130.29/89.74 |
% 130.29/89.74 +-Applying beta-rule and splitting (124), into two cases.
% 130.29/89.74 |-Branch one:
% 130.29/89.74 | (263) all_0_0_0 = 0
% 130.29/89.74 |
% 130.29/89.74 | Equations (263) can reduce 55 to:
% 130.29/89.74 | (264) $false
% 130.29/89.74 |
% 130.29/89.74 |-The branch is then unsatisfiable
% 130.29/89.74 |-Branch two:
% 130.29/89.74 | (55) ~ (all_0_0_0 = 0)
% 130.29/89.74 | (294) ? [v0] : ? [v1] : (( ~ (v0 = 0) & aNaturalNumber0(all_0_1_1) = v0) | (aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 130.29/89.74 |
% 130.29/89.74 | Instantiating (294) with all_80_0_121, all_80_1_122 yields:
% 130.29/89.74 | (295) ( ~ (all_80_1_122 = 0) & aNaturalNumber0(all_0_1_1) = all_80_1_122) | (aNaturalNumber0(all_0_4_4) = all_80_0_121 & aNaturalNumber0(xp) = all_80_1_122 & ( ~ (all_80_0_121 = 0) | ~ (all_80_1_122 = 0)))
% 130.29/89.74 |
% 130.29/89.74 +-Applying beta-rule and splitting (127), into two cases.
% 130.29/89.74 |-Branch one:
% 130.29/89.74 | (296) xr = sz00
% 130.29/89.74 |
% 130.29/89.74 | Equations (296) can reduce 101 to:
% 130.29/89.74 | (264) $false
% 130.29/89.74 |
% 130.29/89.74 |-The branch is then unsatisfiable
% 130.29/89.74 |-Branch two:
% 130.29/89.74 | (101) ~ (xr = sz00)
% 130.29/89.74 | (299) ? [v0] : ? [v1] : ? [v2] : ((doDivides0(xr, xk) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) | (sdtasdt0(xp, all_0_1_1) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v0 = 0) | v1 = all_0_2_2)))
% 130.29/89.75 |
% 130.29/89.75 | Instantiating (299) with all_84_0_123, all_84_1_124, all_84_2_125 yields:
% 130.29/89.75 | (300) (doDivides0(xr, xk) = all_84_0_123 & aNaturalNumber0(xr) = all_84_2_125 & aNaturalNumber0(xk) = all_84_1_124 & ( ~ (all_84_0_123 = 0) | ~ (all_84_1_124 = 0) | ~ (all_84_2_125 = 0))) | (sdtasdt0(xp, all_0_1_1) = all_84_1_124 & aNaturalNumber0(xp) = all_84_2_125 & ( ~ (all_84_2_125 = 0) | all_84_1_124 = all_0_2_2))
% 130.29/89.75 |
% 130.29/89.75 +-Applying beta-rule and splitting (129), into two cases.
% 130.29/89.75 |-Branch one:
% 130.29/89.75 | (301) xp = sz00
% 130.29/89.75 |
% 130.29/89.75 | Equations (301) can reduce 102 to:
% 130.29/89.75 | (264) $false
% 130.29/89.75 |
% 130.29/89.75 |-The branch is then unsatisfiable
% 130.29/89.75 |-Branch two:
% 130.29/89.75 | (102) ~ (xp = sz00)
% 130.29/89.75 | (304) ? [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))))
% 130.29/89.75 |
% 130.29/89.75 | Instantiating (304) with all_88_0_126, all_88_1_127, all_88_2_128 yields:
% 130.29/89.75 | (305) (all_88_2_128 = 0 & aNaturalNumber0(xk) = 0) | (doDivides0(xp, all_0_9_9) = all_88_0_126 & aNaturalNumber0(all_0_9_9) = all_88_1_127 & aNaturalNumber0(xp) = all_88_2_128 & ( ~ (all_88_0_126 = 0) | ~ (all_88_1_127 = 0) | ~ (all_88_2_128 = 0)))
% 130.29/89.75 |
% 130.29/89.75 +-Applying beta-rule and splitting (142), into two cases.
% 130.29/89.75 |-Branch one:
% 130.29/89.75 | (296) xr = sz00
% 130.29/89.75 |
% 130.29/89.75 | Equations (296) can reduce 101 to:
% 130.29/89.75 | (264) $false
% 130.29/89.75 |
% 130.29/89.75 |-The branch is then unsatisfiable
% 130.29/89.75 |-Branch two:
% 130.29/89.75 | (101) ~ (xr = sz00)
% 130.29/89.75 | (309) xr = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xr) = 0 & aNaturalNumber0(v0) = 0)
% 130.29/89.75 |
% 130.29/89.75 +-Applying beta-rule and splitting (143), into two cases.
% 130.29/89.75 |-Branch one:
% 130.29/89.75 | (301) xp = sz00
% 130.29/89.75 |
% 130.29/89.75 | Equations (301) can reduce 102 to:
% 130.29/89.75 | (264) $false
% 130.29/89.75 |
% 130.29/89.75 |-The branch is then unsatisfiable
% 130.29/89.75 |-Branch two:
% 130.29/89.75 | (102) ~ (xp = sz00)
% 130.29/89.75 | (313) xp = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 130.29/89.75 |
% 130.29/89.75 +-Applying beta-rule and splitting (309), into two cases.
% 130.29/89.75 |-Branch one:
% 130.29/89.75 | (314) xr = sz10
% 130.29/89.75 |
% 130.29/89.75 | Equations (314) can reduce 99 to:
% 130.29/89.75 | (264) $false
% 130.29/89.75 |
% 130.29/89.75 |-The branch is then unsatisfiable
% 130.29/89.75 |-Branch two:
% 130.29/89.75 | (99) ~ (xr = sz10)
% 130.29/89.75 | (317) ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xr) = 0 & aNaturalNumber0(v0) = 0)
% 130.29/89.75 |
% 130.29/89.75 | Instantiating (317) with all_99_0_129 yields:
% 130.29/89.75 | (318) isPrime0(all_99_0_129) = 0 & doDivides0(all_99_0_129, xr) = 0 & aNaturalNumber0(all_99_0_129) = 0
% 130.29/89.75 |
% 130.29/89.75 | Applying alpha-rule on (318) yields:
% 130.29/89.75 | (319) isPrime0(all_99_0_129) = 0
% 130.29/89.75 | (320) doDivides0(all_99_0_129, xr) = 0
% 130.29/89.75 | (321) aNaturalNumber0(all_99_0_129) = 0
% 130.29/89.75 |
% 130.29/89.75 +-Applying beta-rule and splitting (313), into two cases.
% 130.29/89.75 |-Branch one:
% 130.29/89.75 | (322) xp = sz10
% 130.29/89.75 |
% 130.29/89.75 | Equations (322) can reduce 100 to:
% 130.29/89.75 | (264) $false
% 130.29/89.75 |
% 130.29/89.75 |-The branch is then unsatisfiable
% 130.29/89.75 |-Branch two:
% 130.29/89.75 | (100) ~ (xp = sz10)
% 130.29/89.75 | (325) ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 130.29/89.75 |
% 130.29/89.75 | Instantiating (325) with all_104_0_130 yields:
% 130.29/89.75 | (326) isPrime0(all_104_0_130) = 0 & doDivides0(all_104_0_130, xp) = 0 & aNaturalNumber0(all_104_0_130) = 0
% 130.29/89.75 |
% 130.29/89.75 | Applying alpha-rule on (326) yields:
% 130.29/89.75 | (327) isPrime0(all_104_0_130) = 0
% 130.29/89.75 | (328) doDivides0(all_104_0_130, xp) = 0
% 130.29/89.75 | (329) aNaturalNumber0(all_104_0_130) = 0
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (42) with xp, all_0_9_9, all_54_3_93, 0 and discharging atoms doDivides0(xp, all_0_9_9) = 0, yields:
% 130.29/89.75 | (330) all_54_3_93 = 0 | ~ (doDivides0(xp, all_0_9_9) = all_54_3_93)
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (37) with xr, all_0_4_4, all_36_0_50, all_34_0_47 and discharging atoms sdtasdt0(xr, all_0_4_4) = all_36_0_50, yields:
% 130.29/89.75 | (331) all_36_0_50 = all_34_0_47 | ~ (sdtasdt0(xr, all_0_4_4) = all_34_0_47)
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (37) with xn, xm, all_54_4_94, all_0_9_9 and discharging atoms sdtasdt0(xn, xm) = all_54_4_94, sdtasdt0(xn, xm) = all_0_9_9, yields:
% 130.29/89.75 | (332) all_54_4_94 = all_0_9_9
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with all_0_1_1, all_42_1_63, 0 and discharging atoms aNaturalNumber0(all_0_1_1) = all_42_1_63, yields:
% 130.29/89.75 | (333) all_42_1_63 = 0 | ~ (aNaturalNumber0(all_0_1_1) = 0)
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with all_0_1_1, all_42_1_63, all_44_3_68 and discharging atoms aNaturalNumber0(all_0_1_1) = all_44_3_68, aNaturalNumber0(all_0_1_1) = all_42_1_63, yields:
% 130.29/89.75 | (334) all_44_3_68 = all_42_1_63
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with all_0_1_1, all_20_1_25, all_44_3_68 and discharging atoms aNaturalNumber0(all_0_1_1) = all_44_3_68, aNaturalNumber0(all_0_1_1) = all_20_1_25, yields:
% 130.29/89.75 | (335) all_44_3_68 = all_20_1_25
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with all_0_2_2, all_32_2_46, all_34_2_49 and discharging atoms aNaturalNumber0(all_0_2_2) = all_34_2_49, aNaturalNumber0(all_0_2_2) = all_32_2_46, yields:
% 130.29/89.75 | (336) all_34_2_49 = all_32_2_46
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with all_0_4_4, all_46_0_70, all_65_1_112 and discharging atoms aNaturalNumber0(all_0_4_4) = all_65_1_112, aNaturalNumber0(all_0_4_4) = all_46_0_70, yields:
% 130.29/89.75 | (337) all_65_1_112 = all_46_0_70
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with all_0_4_4, all_36_2_52, all_46_0_70 and discharging atoms aNaturalNumber0(all_0_4_4) = all_46_0_70, aNaturalNumber0(all_0_4_4) = all_36_2_52, yields:
% 130.29/89.75 | (338) all_46_0_70 = all_36_2_52
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with all_0_4_4, all_20_0_24, all_34_2_49 and discharging atoms aNaturalNumber0(all_0_4_4) = all_20_0_24, yields:
% 130.29/89.75 | (339) all_34_2_49 = all_20_0_24 | ~ (aNaturalNumber0(all_0_4_4) = all_34_2_49)
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with all_0_4_4, all_20_0_24, all_65_1_112 and discharging atoms aNaturalNumber0(all_0_4_4) = all_65_1_112, aNaturalNumber0(all_0_4_4) = all_20_0_24, yields:
% 130.29/89.75 | (340) all_65_1_112 = all_20_0_24
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with all_0_9_9, all_32_0_44, all_65_2_113 and discharging atoms aNaturalNumber0(all_0_9_9) = all_65_2_113, aNaturalNumber0(all_0_9_9) = all_32_0_44, yields:
% 130.29/89.75 | (341) all_65_2_113 = all_32_0_44
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with all_0_9_9, all_30_0_41, all_32_0_44 and discharging atoms aNaturalNumber0(all_0_9_9) = all_32_0_44, aNaturalNumber0(all_0_9_9) = all_30_0_41, yields:
% 130.29/89.75 | (342) all_32_0_44 = all_30_0_41
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with all_0_9_9, all_16_0_18, all_65_2_113 and discharging atoms aNaturalNumber0(all_0_9_9) = all_65_2_113, aNaturalNumber0(all_0_9_9) = all_16_0_18, yields:
% 130.29/89.75 | (343) all_65_2_113 = all_16_0_18
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with all_0_11_11, all_22_2_29, all_40_2_61 and discharging atoms aNaturalNumber0(all_0_11_11) = all_40_2_61, aNaturalNumber0(all_0_11_11) = all_22_2_29, yields:
% 130.29/89.75 | (344) all_40_2_61 = all_22_2_29
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with all_0_11_11, all_12_0_12, all_40_2_61 and discharging atoms aNaturalNumber0(all_0_11_11) = all_40_2_61, aNaturalNumber0(all_0_11_11) = all_12_0_12, yields:
% 130.29/89.75 | (345) all_40_2_61 = all_12_0_12
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with xr, all_36_1_51, 0 and discharging atoms aNaturalNumber0(xr) = all_36_1_51, aNaturalNumber0(xr) = 0, yields:
% 130.29/89.75 | (346) all_36_1_51 = 0
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with xr, all_34_1_48, all_36_1_51 and discharging atoms aNaturalNumber0(xr) = all_36_1_51, aNaturalNumber0(xr) = all_34_1_48, yields:
% 130.29/89.75 | (347) all_36_1_51 = all_34_1_48
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with xr, all_32_1_45, all_44_2_67 and discharging atoms aNaturalNumber0(xr) = all_44_2_67, aNaturalNumber0(xr) = all_32_1_45, yields:
% 130.29/89.75 | (348) all_44_2_67 = all_32_1_45
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with xr, all_32_1_45, all_34_1_48 and discharging atoms aNaturalNumber0(xr) = all_34_1_48, aNaturalNumber0(xr) = all_32_1_45, yields:
% 130.29/89.75 | (349) all_34_1_48 = all_32_1_45
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with xr, all_30_1_42, all_44_2_67 and discharging atoms aNaturalNumber0(xr) = all_44_2_67, aNaturalNumber0(xr) = all_30_1_42, yields:
% 130.29/89.75 | (350) all_44_2_67 = all_30_1_42
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with xr, all_28_2_38, all_32_1_45 and discharging atoms aNaturalNumber0(xr) = all_32_1_45, aNaturalNumber0(xr) = all_28_2_38, yields:
% 130.29/89.75 | (351) all_32_1_45 = all_28_2_38
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with xk, all_26_1_34, all_75_2_120 and discharging atoms aNaturalNumber0(xk) = all_75_2_120, aNaturalNumber0(xk) = all_26_1_34, yields:
% 130.29/89.75 | (352) all_75_2_120 = all_26_1_34
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with xk, all_24_1_31, all_65_2_113 and discharging atoms aNaturalNumber0(xk) = all_24_1_31, yields:
% 130.29/89.75 | (353) all_65_2_113 = all_24_1_31 | ~ (aNaturalNumber0(xk) = all_65_2_113)
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with xk, all_24_1_31, all_75_2_120 and discharging atoms aNaturalNumber0(xk) = all_75_2_120, aNaturalNumber0(xk) = all_24_1_31, yields:
% 130.29/89.75 | (354) all_75_2_120 = all_24_1_31
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with xp, all_75_1_119, 0 and discharging atoms aNaturalNumber0(xp) = all_75_1_119, aNaturalNumber0(xp) = 0, yields:
% 130.29/89.75 | (355) all_75_1_119 = 0
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with xp, all_65_3_114, all_75_1_119 and discharging atoms aNaturalNumber0(xp) = all_75_1_119, aNaturalNumber0(xp) = all_65_3_114, yields:
% 130.29/89.75 | (356) all_75_1_119 = all_65_3_114
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with xp, all_54_6_96, all_65_3_114 and discharging atoms aNaturalNumber0(xp) = all_65_3_114, aNaturalNumber0(xp) = all_54_6_96, yields:
% 130.29/89.75 | (357) all_65_3_114 = all_54_6_96
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with xp, all_44_4_69, all_54_6_96 and discharging atoms aNaturalNumber0(xp) = all_54_6_96, aNaturalNumber0(xp) = all_44_4_69, yields:
% 130.29/89.75 | (358) all_54_6_96 = all_44_4_69
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with xp, all_44_4_69, all_51_2_84 and discharging atoms aNaturalNumber0(xp) = all_51_2_84, aNaturalNumber0(xp) = all_44_4_69, yields:
% 130.29/89.75 | (359) all_51_2_84 = all_44_4_69
% 130.29/89.75 |
% 130.29/89.75 | Instantiating formula (11) with xp, all_40_1_60, all_44_4_69 and discharging atoms aNaturalNumber0(xp) = all_44_4_69, aNaturalNumber0(xp) = all_40_1_60, yields:
% 130.29/89.76 | (360) all_44_4_69 = all_40_1_60
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xp, all_26_2_35, all_44_4_69 and discharging atoms aNaturalNumber0(xp) = all_44_4_69, aNaturalNumber0(xp) = all_26_2_35, yields:
% 130.29/89.76 | (361) all_44_4_69 = all_26_2_35
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xp, all_26_2_35, all_42_2_64 and discharging atoms aNaturalNumber0(xp) = all_42_2_64, aNaturalNumber0(xp) = all_26_2_35, yields:
% 130.29/89.76 | (362) all_42_2_64 = all_26_2_35
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xp, all_24_2_32, all_51_2_84 and discharging atoms aNaturalNumber0(xp) = all_51_2_84, aNaturalNumber0(xp) = all_24_2_32, yields:
% 130.29/89.76 | (363) all_51_2_84 = all_24_2_32
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xp, all_22_1_28, all_42_2_64 and discharging atoms aNaturalNumber0(xp) = all_42_2_64, aNaturalNumber0(xp) = all_22_1_28, yields:
% 130.29/89.76 | (364) all_42_2_64 = all_22_1_28
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xp, all_20_2_26, all_40_1_60 and discharging atoms aNaturalNumber0(xp) = all_40_1_60, aNaturalNumber0(xp) = all_20_2_26, yields:
% 130.29/89.76 | (365) all_40_1_60 = all_20_2_26
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xm, all_54_7_97, 0 and discharging atoms aNaturalNumber0(xm) = all_54_7_97, aNaturalNumber0(xm) = 0, yields:
% 130.29/89.76 | (366) all_54_7_97 = 0
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xm, all_51_3_85, all_58_1_106 and discharging atoms aNaturalNumber0(xm) = all_58_1_106, aNaturalNumber0(xm) = all_51_3_85, yields:
% 130.29/89.76 | (367) all_58_1_106 = all_51_3_85
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xm, all_46_1_71, all_58_1_106 and discharging atoms aNaturalNumber0(xm) = all_58_1_106, aNaturalNumber0(xm) = all_46_1_71, yields:
% 130.29/89.76 | (368) all_58_1_106 = all_46_1_71
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xm, all_28_3_39, all_58_1_106 and discharging atoms aNaturalNumber0(xm) = all_58_1_106, aNaturalNumber0(xm) = all_28_3_39, yields:
% 130.29/89.76 | (369) all_58_1_106 = all_28_3_39
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xm, all_18_1_22, all_51_3_85 and discharging atoms aNaturalNumber0(xm) = all_51_3_85, aNaturalNumber0(xm) = all_18_1_22, yields:
% 130.29/89.76 | (370) all_51_3_85 = all_18_1_22
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xm, all_16_1_19, all_54_7_97 and discharging atoms aNaturalNumber0(xm) = all_54_7_97, aNaturalNumber0(xm) = all_16_1_19, yields:
% 130.29/89.76 | (371) all_54_7_97 = all_16_1_19
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xm, all_16_1_19, all_28_3_39 and discharging atoms aNaturalNumber0(xm) = all_28_3_39, aNaturalNumber0(xm) = all_16_1_19, yields:
% 130.29/89.76 | (372) all_28_3_39 = all_16_1_19
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xm, all_14_1_16, all_28_3_39 and discharging atoms aNaturalNumber0(xm) = all_28_3_39, aNaturalNumber0(xm) = all_14_1_16, yields:
% 130.29/89.76 | (373) all_28_3_39 = all_14_1_16
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) 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:
% 130.29/89.76 | (374) all_16_1_19 = all_12_1_13
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xn, all_54_8_98, all_70_1_116 and discharging atoms aNaturalNumber0(xn) = all_70_1_116, aNaturalNumber0(xn) = all_54_8_98, yields:
% 130.29/89.76 | (375) all_70_1_116 = all_54_8_98
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xn, all_51_4_86, all_54_8_98 and discharging atoms aNaturalNumber0(xn) = all_54_8_98, aNaturalNumber0(xn) = all_51_4_86, yields:
% 130.29/89.76 | (376) all_54_8_98 = all_51_4_86
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xn, all_18_2_23, all_51_4_86 and discharging atoms aNaturalNumber0(xn) = all_51_4_86, aNaturalNumber0(xn) = all_18_2_23, yields:
% 130.29/89.76 | (377) all_51_4_86 = all_18_2_23
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xn, all_16_2_20, all_51_4_86 and discharging atoms aNaturalNumber0(xn) = all_51_4_86, aNaturalNumber0(xn) = all_16_2_20, yields:
% 130.29/89.76 | (378) all_51_4_86 = all_16_2_20
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xn, all_14_2_17, 0 and discharging atoms aNaturalNumber0(xn) = all_14_2_17, aNaturalNumber0(xn) = 0, yields:
% 130.29/89.76 | (379) all_14_2_17 = 0
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xn, all_14_2_17, all_51_4_86 and discharging atoms aNaturalNumber0(xn) = all_51_4_86, aNaturalNumber0(xn) = all_14_2_17, yields:
% 130.29/89.76 | (380) all_51_4_86 = all_14_2_17
% 130.29/89.76 |
% 130.29/89.76 | Instantiating formula (11) with xn, all_12_2_14, all_70_1_116 and discharging atoms aNaturalNumber0(xn) = all_70_1_116, aNaturalNumber0(xn) = all_12_2_14, yields:
% 130.29/89.76 | (381) all_70_1_116 = all_12_2_14
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (356,355) yields a new equation:
% 130.29/89.76 | (382) all_65_3_114 = 0
% 130.29/89.76 |
% 130.29/89.76 | Simplifying 382 yields:
% 130.29/89.76 | (383) all_65_3_114 = 0
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (354,352) yields a new equation:
% 130.29/89.76 | (384) all_26_1_34 = all_24_1_31
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (375,381) yields a new equation:
% 130.29/89.76 | (385) all_54_8_98 = all_12_2_14
% 130.29/89.76 |
% 130.29/89.76 | Simplifying 385 yields:
% 130.29/89.76 | (386) all_54_8_98 = all_12_2_14
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (337,340) yields a new equation:
% 130.29/89.76 | (387) all_46_0_70 = all_20_0_24
% 130.29/89.76 |
% 130.29/89.76 | Simplifying 387 yields:
% 130.29/89.76 | (388) all_46_0_70 = all_20_0_24
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (341,343) yields a new equation:
% 130.29/89.76 | (389) all_32_0_44 = all_16_0_18
% 130.29/89.76 |
% 130.29/89.76 | Simplifying 389 yields:
% 130.29/89.76 | (390) all_32_0_44 = all_16_0_18
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (357,383) yields a new equation:
% 130.29/89.76 | (391) all_54_6_96 = 0
% 130.29/89.76 |
% 130.29/89.76 | Simplifying 391 yields:
% 130.29/89.76 | (392) all_54_6_96 = 0
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (369,368) yields a new equation:
% 130.29/89.76 | (393) all_46_1_71 = all_28_3_39
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (367,368) yields a new equation:
% 130.29/89.76 | (394) all_51_3_85 = all_46_1_71
% 130.29/89.76 |
% 130.29/89.76 | Simplifying 394 yields:
% 130.29/89.76 | (395) all_51_3_85 = all_46_1_71
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (358,392) yields a new equation:
% 130.29/89.76 | (396) all_44_4_69 = 0
% 130.29/89.76 |
% 130.29/89.76 | Simplifying 396 yields:
% 130.29/89.76 | (397) all_44_4_69 = 0
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (371,366) yields a new equation:
% 130.29/89.76 | (398) all_16_1_19 = 0
% 130.29/89.76 |
% 130.29/89.76 | Simplifying 398 yields:
% 130.29/89.76 | (399) all_16_1_19 = 0
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (376,386) yields a new equation:
% 130.29/89.76 | (400) all_51_4_86 = all_12_2_14
% 130.29/89.76 |
% 130.29/89.76 | Simplifying 400 yields:
% 130.29/89.76 | (401) all_51_4_86 = all_12_2_14
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (359,363) yields a new equation:
% 130.29/89.76 | (402) all_44_4_69 = all_24_2_32
% 130.29/89.76 |
% 130.29/89.76 | Simplifying 402 yields:
% 130.29/89.76 | (403) all_44_4_69 = all_24_2_32
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (395,370) yields a new equation:
% 130.29/89.76 | (404) all_46_1_71 = all_18_1_22
% 130.29/89.76 |
% 130.29/89.76 | Simplifying 404 yields:
% 130.29/89.76 | (405) all_46_1_71 = all_18_1_22
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (380,377) yields a new equation:
% 130.29/89.76 | (406) all_18_2_23 = all_14_2_17
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (378,377) yields a new equation:
% 130.29/89.76 | (407) all_18_2_23 = all_16_2_20
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (401,377) yields a new equation:
% 130.29/89.76 | (408) all_18_2_23 = all_12_2_14
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (338,388) yields a new equation:
% 130.29/89.76 | (409) all_36_2_52 = all_20_0_24
% 130.29/89.76 |
% 130.29/89.76 | Simplifying 409 yields:
% 130.29/89.76 | (410) all_36_2_52 = all_20_0_24
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (393,405) yields a new equation:
% 130.29/89.76 | (411) all_28_3_39 = all_18_1_22
% 130.29/89.76 |
% 130.29/89.76 | Simplifying 411 yields:
% 130.29/89.76 | (412) all_28_3_39 = all_18_1_22
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (348,350) yields a new equation:
% 130.29/89.76 | (413) all_32_1_45 = all_30_1_42
% 130.29/89.76 |
% 130.29/89.76 | Simplifying 413 yields:
% 130.29/89.76 | (414) all_32_1_45 = all_30_1_42
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (334,335) yields a new equation:
% 130.29/89.76 | (415) all_42_1_63 = all_20_1_25
% 130.29/89.76 |
% 130.29/89.76 | Simplifying 415 yields:
% 130.29/89.76 | (416) all_42_1_63 = all_20_1_25
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (360,403) yields a new equation:
% 130.29/89.76 | (417) all_40_1_60 = all_24_2_32
% 130.29/89.76 |
% 130.29/89.76 | Simplifying 417 yields:
% 130.29/89.76 | (418) all_40_1_60 = all_24_2_32
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (361,403) yields a new equation:
% 130.29/89.76 | (419) all_26_2_35 = all_24_2_32
% 130.29/89.76 |
% 130.29/89.76 | Simplifying 419 yields:
% 130.29/89.76 | (420) all_26_2_35 = all_24_2_32
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (397,403) yields a new equation:
% 130.29/89.76 | (421) all_24_2_32 = 0
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (362,364) yields a new equation:
% 130.29/89.76 | (422) all_26_2_35 = all_22_1_28
% 130.29/89.76 |
% 130.29/89.76 | Simplifying 422 yields:
% 130.29/89.76 | (423) all_26_2_35 = all_22_1_28
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (418,365) yields a new equation:
% 130.29/89.76 | (424) all_24_2_32 = all_20_2_26
% 130.29/89.76 |
% 130.29/89.76 | Simplifying 424 yields:
% 130.29/89.76 | (425) all_24_2_32 = all_20_2_26
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (345,344) yields a new equation:
% 130.29/89.76 | (426) all_22_2_29 = all_12_0_12
% 130.29/89.76 |
% 130.29/89.76 | Combining equations (347,346) yields a new equation:
% 130.29/89.76 | (427) all_34_1_48 = 0
% 130.29/89.76 |
% 130.29/89.77 | Simplifying 427 yields:
% 130.29/89.77 | (428) all_34_1_48 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (349,428) yields a new equation:
% 130.29/89.77 | (429) all_32_1_45 = 0
% 130.29/89.77 |
% 130.29/89.77 | Simplifying 429 yields:
% 130.29/89.77 | (430) all_32_1_45 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (342,390) yields a new equation:
% 130.29/89.77 | (431) all_30_0_41 = all_16_0_18
% 130.29/89.77 |
% 130.29/89.77 | Simplifying 431 yields:
% 130.29/89.77 | (432) all_30_0_41 = all_16_0_18
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (351,414) yields a new equation:
% 130.29/89.77 | (433) all_30_1_42 = all_28_2_38
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (430,414) yields a new equation:
% 130.29/89.77 | (434) all_30_1_42 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (433,434) yields a new equation:
% 130.29/89.77 | (435) all_28_2_38 = 0
% 130.29/89.77 |
% 130.29/89.77 | Simplifying 435 yields:
% 130.29/89.77 | (436) all_28_2_38 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (373,412) yields a new equation:
% 130.29/89.77 | (437) all_18_1_22 = all_14_1_16
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (372,412) yields a new equation:
% 130.29/89.77 | (438) all_18_1_22 = all_16_1_19
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (420,423) yields a new equation:
% 130.29/89.77 | (439) all_24_2_32 = all_22_1_28
% 130.29/89.77 |
% 130.29/89.77 | Simplifying 439 yields:
% 130.29/89.77 | (440) all_24_2_32 = all_22_1_28
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (425,440) yields a new equation:
% 130.29/89.77 | (441) all_22_1_28 = all_20_2_26
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (421,440) yields a new equation:
% 130.29/89.77 | (442) all_22_1_28 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (441,442) yields a new equation:
% 130.29/89.77 | (443) all_20_2_26 = 0
% 130.29/89.77 |
% 130.29/89.77 | Simplifying 443 yields:
% 130.29/89.77 | (444) all_20_2_26 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (438,437) yields a new equation:
% 130.29/89.77 | (445) all_16_1_19 = all_14_1_16
% 130.29/89.77 |
% 130.29/89.77 | Simplifying 445 yields:
% 130.29/89.77 | (446) all_16_1_19 = all_14_1_16
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (406,407) yields a new equation:
% 130.29/89.77 | (447) all_16_2_20 = all_14_2_17
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (408,407) yields a new equation:
% 130.29/89.77 | (448) all_16_2_20 = all_12_2_14
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (374,446) yields a new equation:
% 130.29/89.77 | (449) all_14_1_16 = all_12_1_13
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (399,446) yields a new equation:
% 130.29/89.77 | (450) all_14_1_16 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (447,448) yields a new equation:
% 130.29/89.77 | (451) all_14_2_17 = all_12_2_14
% 130.29/89.77 |
% 130.29/89.77 | Simplifying 451 yields:
% 130.29/89.77 | (452) all_14_2_17 = all_12_2_14
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (449,450) yields a new equation:
% 130.29/89.77 | (453) all_12_1_13 = 0
% 130.29/89.77 |
% 130.29/89.77 | Simplifying 453 yields:
% 130.29/89.77 | (454) all_12_1_13 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (452,379) yields a new equation:
% 130.29/89.77 | (455) all_12_2_14 = 0
% 130.29/89.77 |
% 130.29/89.77 | Simplifying 455 yields:
% 130.29/89.77 | (456) all_12_2_14 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (456,448) yields a new equation:
% 130.29/89.77 | (457) all_16_2_20 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (450,446) yields a new equation:
% 130.29/89.77 | (399) all_16_1_19 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (457,407) yields a new equation:
% 130.29/89.77 | (459) all_18_2_23 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (450,437) yields a new equation:
% 130.29/89.77 | (460) all_18_1_22 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (442,440) yields a new equation:
% 130.29/89.77 | (421) all_24_2_32 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (442,423) yields a new equation:
% 130.29/89.77 | (462) all_26_2_35 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (426,344) yields a new equation:
% 130.29/89.77 | (345) all_40_2_61 = all_12_0_12
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (444,365) yields a new equation:
% 130.29/89.77 | (464) all_40_1_60 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (442,364) yields a new equation:
% 130.29/89.77 | (465) all_42_2_64 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (421,403) yields a new equation:
% 130.29/89.77 | (397) all_44_4_69 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (434,350) yields a new equation:
% 130.29/89.77 | (467) all_44_2_67 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (459,377) yields a new equation:
% 130.29/89.77 | (468) all_51_4_86 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (460,370) yields a new equation:
% 130.29/89.77 | (469) all_51_3_85 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (421,363) yields a new equation:
% 130.29/89.77 | (470) all_51_2_84 = 0
% 130.29/89.77 |
% 130.29/89.77 | Combining equations (384,352) yields a new equation:
% 130.29/89.77 | (354) all_75_2_120 = all_24_1_31
% 130.29/89.77 |
% 130.29/89.77 | From (332) and (246) follows:
% 130.29/89.77 | (472) doDivides0(xp, all_0_9_9) = all_54_3_93
% 130.29/89.77 |
% 130.29/89.77 | From (332) and (253) follows:
% 130.29/89.77 | (67) sdtasdt0(xn, xm) = all_0_9_9
% 130.29/89.77 |
% 130.29/89.77 | From (416) and (219) follows:
% 130.29/89.77 | (165) aNaturalNumber0(all_0_1_1) = all_20_1_25
% 130.29/89.77 |
% 130.29/89.77 | From (336) and (203) follows:
% 130.29/89.77 | (197) aNaturalNumber0(all_0_2_2) = all_32_2_46
% 130.29/89.77 |
% 130.29/89.77 | From (432) and (193) follows:
% 130.29/89.77 | (155) aNaturalNumber0(all_0_9_9) = all_16_0_18
% 130.29/89.77 |
% 130.29/89.77 | From (436) and (187) follows:
% 130.29/89.77 | (23) aNaturalNumber0(xr) = 0
% 130.29/89.77 |
% 130.29/89.77 | From (384) and (181) follows:
% 130.29/89.77 | (176) aNaturalNumber0(xk) = all_24_1_31
% 130.29/89.77 |
% 130.29/89.77 | From (444) and (167) follows:
% 130.29/89.77 | (13) aNaturalNumber0(xp) = 0
% 130.29/89.77 |
% 130.29/89.77 | From (454) and (146) follows:
% 130.29/89.77 | (14) aNaturalNumber0(xm) = 0
% 130.29/89.77 |
% 130.29/89.77 | From (456) and (147) follows:
% 130.29/89.77 | (10) aNaturalNumber0(xn) = 0
% 130.29/89.77 |
% 130.29/89.77 +-Applying beta-rule and splitting (241), into two cases.
% 130.29/89.77 |-Branch one:
% 130.29/89.77 | (482) ~ (all_51_2_84 = 0)
% 130.29/89.77 |
% 130.29/89.77 | Equations (470) can reduce 482 to:
% 130.29/89.77 | (264) $false
% 130.29/89.77 |
% 130.29/89.77 |-The branch is then unsatisfiable
% 130.29/89.77 |-Branch two:
% 130.29/89.77 | (470) all_51_2_84 = 0
% 130.29/89.77 | (485) ~ (all_51_3_85 = 0) | ~ (all_51_4_86 = 0) | all_51_0_82 = all_0_10_10
% 130.29/89.77 |
% 130.29/89.77 +-Applying beta-rule and splitting (235), into two cases.
% 130.29/89.77 |-Branch one:
% 130.29/89.77 | (486) all_50_0_79 = xn & all_50_1_80 = 0 & sdtasdt0(xr, all_50_2_81) = xn & aNaturalNumber0(all_50_2_81) = 0
% 130.29/89.77 |
% 130.29/89.77 | Applying alpha-rule on (486) yields:
% 130.29/89.77 | (487) all_50_0_79 = xn
% 130.29/89.77 | (488) all_50_1_80 = 0
% 130.29/89.77 | (489) sdtasdt0(xr, all_50_2_81) = xn
% 130.29/89.77 | (490) aNaturalNumber0(all_50_2_81) = 0
% 130.29/89.77 |
% 130.29/89.77 +-Applying beta-rule and splitting (163), into two cases.
% 130.29/89.77 |-Branch one:
% 130.29/89.77 | (491) ~ (all_18_1_22 = 0)
% 130.29/89.77 |
% 130.29/89.77 | Equations (460) can reduce 491 to:
% 130.29/89.77 | (264) $false
% 130.29/89.77 |
% 130.29/89.77 |-The branch is then unsatisfiable
% 130.29/89.77 |-Branch two:
% 130.29/89.77 | (460) all_18_1_22 = 0
% 130.29/89.77 | (494) ~ (all_18_2_23 = 0) | all_18_0_21 = all_0_9_9
% 130.29/89.77 |
% 130.29/89.77 +-Applying beta-rule and splitting (494), into two cases.
% 130.29/89.77 |-Branch one:
% 130.29/89.77 | (495) ~ (all_18_2_23 = 0)
% 130.29/89.77 |
% 130.29/89.77 | Equations (459) can reduce 495 to:
% 130.29/89.77 | (264) $false
% 130.29/89.77 |
% 130.29/89.77 |-The branch is then unsatisfiable
% 130.29/89.77 |-Branch two:
% 130.29/89.77 | (459) all_18_2_23 = 0
% 130.29/89.77 | (498) all_18_0_21 = all_0_9_9
% 130.29/89.77 |
% 130.29/89.77 | From (498) and (160) follows:
% 130.29/89.77 | (499) sdtasdt0(xm, xn) = all_0_9_9
% 130.29/89.77 |
% 130.29/89.77 +-Applying beta-rule and splitting (158), into two cases.
% 130.29/89.77 |-Branch one:
% 130.29/89.77 | (500) ~ (all_16_1_19 = 0)
% 130.29/89.77 |
% 130.29/89.77 | Equations (399) can reduce 500 to:
% 130.29/89.77 | (264) $false
% 130.29/89.77 |
% 130.29/89.77 |-The branch is then unsatisfiable
% 130.29/89.77 |-Branch two:
% 130.29/89.77 | (399) all_16_1_19 = 0
% 130.29/89.78 | (503) ~ (all_16_2_20 = 0) | all_16_0_18 = 0
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (148), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (504) ~ (all_12_1_13 = 0)
% 130.29/89.78 |
% 130.29/89.78 | Equations (454) can reduce 504 to:
% 130.29/89.78 | (264) $false
% 130.29/89.78 |
% 130.29/89.78 |-The branch is then unsatisfiable
% 130.29/89.78 |-Branch two:
% 130.29/89.78 | (454) all_12_1_13 = 0
% 130.29/89.78 | (507) ~ (all_12_2_14 = 0) | all_12_0_12 = 0
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (503), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (508) ~ (all_16_2_20 = 0)
% 130.29/89.78 |
% 130.29/89.78 | Equations (457) can reduce 508 to:
% 130.29/89.78 | (264) $false
% 130.29/89.78 |
% 130.29/89.78 |-The branch is then unsatisfiable
% 130.29/89.78 |-Branch two:
% 130.29/89.78 | (457) all_16_2_20 = 0
% 130.29/89.78 | (511) all_16_0_18 = 0
% 130.29/89.78 |
% 130.29/89.78 | Combining equations (511,343) yields a new equation:
% 130.29/89.78 | (512) all_65_2_113 = 0
% 130.29/89.78 |
% 130.29/89.78 | From (511) and (155) follows:
% 130.29/89.78 | (513) aNaturalNumber0(all_0_9_9) = 0
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (211), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (514) all_39_0_56 = xp & all_39_1_57 = 0 & sdtpldt0(xm, all_39_2_58) = xp & aNaturalNumber0(all_39_2_58) = 0
% 130.29/89.78 |
% 130.29/89.78 | Applying alpha-rule on (514) yields:
% 130.29/89.78 | (515) all_39_0_56 = xp
% 130.29/89.78 | (516) all_39_1_57 = 0
% 130.29/89.78 | (517) sdtpldt0(xm, all_39_2_58) = xp
% 130.29/89.78 | (518) aNaturalNumber0(all_39_2_58) = 0
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (485), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (519) ~ (all_51_3_85 = 0)
% 130.29/89.78 |
% 130.29/89.78 | Equations (469) can reduce 519 to:
% 130.29/89.78 | (264) $false
% 130.29/89.78 |
% 130.29/89.78 |-The branch is then unsatisfiable
% 130.29/89.78 |-Branch two:
% 130.29/89.78 | (469) all_51_3_85 = 0
% 130.29/89.78 | (522) ~ (all_51_4_86 = 0) | all_51_0_82 = all_0_10_10
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (522), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (523) ~ (all_51_4_86 = 0)
% 130.29/89.78 |
% 130.29/89.78 | Equations (468) can reduce 523 to:
% 130.29/89.78 | (264) $false
% 130.29/89.78 |
% 130.29/89.78 |-The branch is then unsatisfiable
% 130.29/89.78 |-Branch two:
% 130.29/89.78 | (468) all_51_4_86 = 0
% 130.29/89.78 | (526) all_51_0_82 = all_0_10_10
% 130.29/89.78 |
% 130.29/89.78 | From (526) and (239) follows:
% 130.29/89.78 | (527) sdtpldt0(xn, all_51_1_83) = all_0_10_10
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (153), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (528) ~ (all_14_1_16 = 0)
% 130.29/89.78 |
% 130.29/89.78 | Equations (450) can reduce 528 to:
% 130.29/89.78 | (264) $false
% 130.29/89.78 |
% 130.29/89.78 |-The branch is then unsatisfiable
% 130.29/89.78 |-Branch two:
% 130.29/89.78 | (450) all_14_1_16 = 0
% 130.29/89.78 | (531) ~ (all_14_2_17 = 0) | all_14_0_15 = all_0_11_11
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (243), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (532) all_53_0_87 = all_0_9_9 & all_53_1_88 = 0 & sdtasdt0(xp, all_53_2_89) = all_0_9_9 & aNaturalNumber0(all_53_2_89) = 0
% 130.29/89.78 |
% 130.29/89.78 | Applying alpha-rule on (532) yields:
% 130.29/89.78 | (533) all_53_0_87 = all_0_9_9
% 130.29/89.78 | (534) all_53_1_88 = 0
% 130.29/89.78 | (535) sdtasdt0(xp, all_53_2_89) = all_0_9_9
% 130.29/89.78 | (536) aNaturalNumber0(all_53_2_89) = 0
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (262), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (537) all_60_0_108 = all_0_9_9 & all_60_1_109 = 0 & sdtasdt0(xr, all_60_2_110) = all_0_9_9 & aNaturalNumber0(all_60_2_110) = 0
% 130.29/89.78 |
% 130.29/89.78 | Applying alpha-rule on (537) yields:
% 130.29/89.78 | (538) all_60_0_108 = all_0_9_9
% 130.29/89.78 | (539) all_60_1_109 = 0
% 130.29/89.78 | (540) sdtasdt0(xr, all_60_2_110) = all_0_9_9
% 130.29/89.78 | (541) aNaturalNumber0(all_60_2_110) = 0
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (330), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (542) ~ (doDivides0(xp, all_0_9_9) = all_54_3_93)
% 130.29/89.78 |
% 130.29/89.78 | Using (472) and (542) yields:
% 130.29/89.78 | (543) $false
% 130.29/89.78 |
% 130.29/89.78 |-The branch is then unsatisfiable
% 130.29/89.78 |-Branch two:
% 130.29/89.78 | (472) doDivides0(xp, all_0_9_9) = all_54_3_93
% 130.29/89.78 | (545) all_54_3_93 = 0
% 130.29/89.78 |
% 130.29/89.78 | From (545) and (472) follows:
% 130.29/89.78 | (3) doDivides0(xp, all_0_9_9) = 0
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (305), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (547) all_88_2_128 = 0 & aNaturalNumber0(xk) = 0
% 130.29/89.78 |
% 130.29/89.78 | Applying alpha-rule on (547) yields:
% 130.29/89.78 | (548) all_88_2_128 = 0
% 130.29/89.78 | (549) aNaturalNumber0(xk) = 0
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (353), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (550) ~ (aNaturalNumber0(xk) = all_65_2_113)
% 130.29/89.78 |
% 130.29/89.78 | From (512) and (550) follows:
% 130.29/89.78 | (551) ~ (aNaturalNumber0(xk) = 0)
% 130.29/89.78 |
% 130.29/89.78 | Using (549) and (551) yields:
% 130.29/89.78 | (543) $false
% 130.29/89.78 |
% 130.29/89.78 |-The branch is then unsatisfiable
% 130.29/89.78 |-Branch two:
% 130.29/89.78 | (553) aNaturalNumber0(xk) = all_65_2_113
% 130.29/89.78 | (554) all_65_2_113 = all_24_1_31
% 130.29/89.78 |
% 130.29/89.78 | Combining equations (512,554) yields a new equation:
% 130.29/89.78 | (555) all_24_1_31 = 0
% 130.29/89.78 |
% 130.29/89.78 | Combining equations (555,384) yields a new equation:
% 130.29/89.78 | (556) all_26_1_34 = 0
% 130.29/89.78 |
% 130.29/89.78 | Combining equations (555,354) yields a new equation:
% 130.29/89.78 | (557) all_75_2_120 = 0
% 130.29/89.78 |
% 130.29/89.78 | From (555) and (176) follows:
% 130.29/89.78 | (549) aNaturalNumber0(xk) = 0
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (128), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (301) xp = sz00
% 130.29/89.78 |
% 130.29/89.78 | Equations (301) can reduce 102 to:
% 130.29/89.78 | (264) $false
% 130.29/89.78 |
% 130.29/89.78 |-The branch is then unsatisfiable
% 130.29/89.78 |-Branch two:
% 130.29/89.78 | (102) ~ (xp = sz00)
% 130.29/89.78 | (562) all_0_3_3 = 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)))
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (562), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (563) all_0_3_3 = all_0_9_9
% 130.29/89.78 |
% 130.29/89.78 | From (563) and (88) follows:
% 130.29/89.78 | (564) sdtsldt0(all_0_9_9, xr) = all_0_2_2
% 130.29/89.78 |
% 130.29/89.78 | From (563) and (80) follows:
% 130.29/89.78 | (565) sdtasdt0(xp, xk) = all_0_9_9
% 130.29/89.78 |
% 130.29/89.78 | From (563) and (175) follows:
% 130.29/89.78 | (566) aNaturalNumber0(all_0_9_9) = all_24_0_30
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (290), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (567) ~ (all_75_0_118 = 0)
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (178), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (568) ~ (all_24_1_31 = 0)
% 130.29/89.78 |
% 130.29/89.78 | Equations (555) can reduce 568 to:
% 130.29/89.78 | (264) $false
% 130.29/89.78 |
% 130.29/89.78 |-The branch is then unsatisfiable
% 130.29/89.78 |-Branch two:
% 130.29/89.78 | (555) all_24_1_31 = 0
% 130.29/89.78 | (571) ~ (all_24_2_32 = 0) | all_24_0_30 = 0
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (571), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (572) ~ (all_24_2_32 = 0)
% 130.29/89.78 |
% 130.29/89.78 | Equations (421) can reduce 572 to:
% 130.29/89.78 | (264) $false
% 130.29/89.78 |
% 130.29/89.78 |-The branch is then unsatisfiable
% 130.29/89.78 |-Branch two:
% 130.29/89.78 | (421) all_24_2_32 = 0
% 130.29/89.78 | (575) all_24_0_30 = 0
% 130.29/89.78 |
% 130.29/89.78 | From (575) and (566) follows:
% 130.29/89.78 | (513) aNaturalNumber0(all_0_9_9) = 0
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (130), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (577) ~ (sdtasdt0(xp, xk) = sz00)
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (531), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (578) ~ (all_14_2_17 = 0)
% 130.29/89.78 |
% 130.29/89.78 | Equations (379) can reduce 578 to:
% 130.29/89.78 | (264) $false
% 130.29/89.78 |
% 130.29/89.78 |-The branch is then unsatisfiable
% 130.29/89.78 |-Branch two:
% 130.29/89.78 | (379) all_14_2_17 = 0
% 130.29/89.78 | (581) all_14_0_15 = all_0_11_11
% 130.29/89.78 |
% 130.29/89.78 | From (581) and (150) follows:
% 130.29/89.78 | (582) sdtpldt0(xm, xn) = all_0_11_11
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (234), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (583) all_48_0_73 = xk & all_48_1_74 = 0 & sdtpldt0(xr, all_48_2_75) = xk & aNaturalNumber0(all_48_2_75) = 0
% 130.29/89.78 |
% 130.29/89.78 | Applying alpha-rule on (583) yields:
% 130.29/89.78 | (584) all_48_0_73 = xk
% 130.29/89.78 | (585) all_48_1_74 = 0
% 130.29/89.78 | (586) sdtpldt0(xr, all_48_2_75) = xk
% 130.29/89.78 | (587) aNaturalNumber0(all_48_2_75) = 0
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (300), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (588) doDivides0(xr, xk) = all_84_0_123 & aNaturalNumber0(xr) = all_84_2_125 & aNaturalNumber0(xk) = all_84_1_124 & ( ~ (all_84_0_123 = 0) | ~ (all_84_1_124 = 0) | ~ (all_84_2_125 = 0))
% 130.29/89.78 |
% 130.29/89.78 | Applying alpha-rule on (588) yields:
% 130.29/89.78 | (589) doDivides0(xr, xk) = all_84_0_123
% 130.29/89.78 | (590) aNaturalNumber0(xr) = all_84_2_125
% 130.29/89.78 | (591) aNaturalNumber0(xk) = all_84_1_124
% 130.29/89.78 | (592) ~ (all_84_0_123 = 0) | ~ (all_84_1_124 = 0) | ~ (all_84_2_125 = 0)
% 130.29/89.78 |
% 130.29/89.78 | Instantiating formula (42) with xr, xk, all_84_0_123, 0 and discharging atoms doDivides0(xr, xk) = all_84_0_123, doDivides0(xr, xk) = 0, yields:
% 130.29/89.78 | (593) all_84_0_123 = 0
% 130.29/89.78 |
% 130.29/89.78 | Instantiating formula (11) with xr, all_84_2_125, 0 and discharging atoms aNaturalNumber0(xr) = all_84_2_125, aNaturalNumber0(xr) = 0, yields:
% 130.29/89.78 | (594) all_84_2_125 = 0
% 130.29/89.78 |
% 130.29/89.78 | Instantiating formula (11) with xk, all_84_1_124, 0 and discharging atoms aNaturalNumber0(xk) = all_84_1_124, aNaturalNumber0(xk) = 0, yields:
% 130.29/89.78 | (595) all_84_1_124 = 0
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (592), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (596) ~ (all_84_0_123 = 0)
% 130.29/89.78 |
% 130.29/89.78 | Equations (593) can reduce 596 to:
% 130.29/89.78 | (264) $false
% 130.29/89.78 |
% 130.29/89.78 |-The branch is then unsatisfiable
% 130.29/89.78 |-Branch two:
% 130.29/89.78 | (593) all_84_0_123 = 0
% 130.29/89.78 | (599) ~ (all_84_1_124 = 0) | ~ (all_84_2_125 = 0)
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (599), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (600) ~ (all_84_1_124 = 0)
% 130.29/89.78 |
% 130.29/89.78 | Equations (595) can reduce 600 to:
% 130.29/89.78 | (264) $false
% 130.29/89.78 |
% 130.29/89.78 |-The branch is then unsatisfiable
% 130.29/89.78 |-Branch two:
% 130.29/89.78 | (595) all_84_1_124 = 0
% 130.29/89.78 | (603) ~ (all_84_2_125 = 0)
% 130.29/89.78 |
% 130.29/89.78 | Equations (594) can reduce 603 to:
% 130.29/89.78 | (264) $false
% 130.29/89.78 |
% 130.29/89.78 |-The branch is then unsatisfiable
% 130.29/89.78 |-Branch two:
% 130.29/89.78 | (605) sdtasdt0(xp, all_0_1_1) = all_84_1_124 & aNaturalNumber0(xp) = all_84_2_125 & ( ~ (all_84_2_125 = 0) | all_84_1_124 = all_0_2_2)
% 130.29/89.78 |
% 130.29/89.78 | Applying alpha-rule on (605) yields:
% 130.29/89.78 | (606) sdtasdt0(xp, all_0_1_1) = all_84_1_124
% 130.29/89.78 | (607) aNaturalNumber0(xp) = all_84_2_125
% 130.29/89.78 | (608) ~ (all_84_2_125 = 0) | all_84_1_124 = all_0_2_2
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (183), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (609) ~ (all_26_1_34 = 0)
% 130.29/89.78 |
% 130.29/89.78 | Equations (556) can reduce 609 to:
% 130.29/89.78 | (264) $false
% 130.29/89.78 |
% 130.29/89.78 |-The branch is then unsatisfiable
% 130.29/89.78 |-Branch two:
% 130.29/89.78 | (556) all_26_1_34 = 0
% 130.29/89.78 | (612) ~ (all_26_2_35 = 0) | all_26_0_33 = all_0_3_3
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (507), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (613) ~ (all_12_2_14 = 0)
% 130.29/89.78 |
% 130.29/89.78 | Equations (456) can reduce 613 to:
% 130.29/89.78 | (264) $false
% 130.29/89.78 |
% 130.29/89.78 |-The branch is then unsatisfiable
% 130.29/89.78 |-Branch two:
% 130.29/89.78 | (456) all_12_2_14 = 0
% 130.29/89.78 | (616) all_12_0_12 = 0
% 130.29/89.78 |
% 130.29/89.78 | Combining equations (616,345) yields a new equation:
% 130.29/89.78 | (617) all_40_2_61 = 0
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (255), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (618) all_56_0_99 = xk & all_56_1_100 = 0 & sdtasdt0(xr, all_56_2_101) = xk & aNaturalNumber0(all_56_2_101) = 0
% 130.29/89.78 |
% 130.29/89.78 | Applying alpha-rule on (618) yields:
% 130.29/89.78 | (619) all_56_0_99 = xk
% 130.29/89.78 | (620) all_56_1_100 = 0
% 130.29/89.78 | (621) sdtasdt0(xr, all_56_2_101) = xk
% 130.29/89.78 | (622) aNaturalNumber0(all_56_2_101) = 0
% 130.29/89.78 |
% 130.29/89.78 +-Applying beta-rule and splitting (216), into two cases.
% 130.29/89.78 |-Branch one:
% 130.29/89.78 | (623) ~ (all_40_1_60 = 0)
% 130.29/89.79 |
% 130.29/89.79 | Equations (464) can reduce 623 to:
% 130.29/89.79 | (264) $false
% 130.29/89.79 |
% 130.29/89.79 |-The branch is then unsatisfiable
% 130.29/89.79 |-Branch two:
% 130.29/89.79 | (464) all_40_1_60 = 0
% 130.29/89.79 | (626) ~ (all_40_2_61 = 0) | all_40_0_59 = all_0_10_10
% 130.29/89.79 |
% 130.29/89.79 +-Applying beta-rule and splitting (626), into two cases.
% 130.29/89.79 |-Branch one:
% 130.29/89.79 | (627) ~ (all_40_2_61 = 0)
% 130.29/89.79 |
% 130.29/89.79 | Equations (617) can reduce 627 to:
% 130.29/89.79 | (264) $false
% 130.29/89.79 |
% 130.29/89.79 |-The branch is then unsatisfiable
% 130.29/89.79 |-Branch two:
% 130.29/89.79 | (617) all_40_2_61 = 0
% 130.29/89.79 | (630) all_40_0_59 = all_0_10_10
% 130.29/89.79 |
% 130.29/89.79 | From (630) and (213) follows:
% 130.29/89.79 | (631) sdtpldt0(xp, all_0_11_11) = all_0_10_10
% 130.29/89.79 |
% 130.29/89.79 +-Applying beta-rule and splitting (612), into two cases.
% 130.29/89.79 |-Branch one:
% 130.29/89.79 | (632) ~ (all_26_2_35 = 0)
% 130.29/89.79 |
% 130.29/89.79 | Equations (462) can reduce 632 to:
% 130.29/89.79 | (264) $false
% 130.29/89.79 |
% 130.29/89.79 |-The branch is then unsatisfiable
% 130.29/89.79 |-Branch two:
% 130.29/89.79 | (462) all_26_2_35 = 0
% 130.29/89.79 | (635) all_26_0_33 = all_0_3_3
% 130.29/89.79 |
% 130.29/89.79 | Combining equations (563,635) yields a new equation:
% 130.29/89.79 | (636) all_26_0_33 = all_0_9_9
% 130.29/89.79 |
% 130.29/89.79 | From (636) and (180) follows:
% 130.29/89.79 | (637) sdtasdt0(xk, xp) = all_0_9_9
% 130.29/89.79 |
% 130.29/89.79 | Instantiating formula (37) with xp, all_0_1_1, all_84_1_124, all_0_4_4 and discharging atoms sdtasdt0(xp, all_0_1_1) = all_84_1_124, sdtasdt0(xp, all_0_1_1) = all_0_4_4, yields:
% 130.29/89.79 | (638) all_84_1_124 = all_0_4_4
% 130.29/89.79 |
% 130.29/89.79 | Instantiating formula (11) with xp, all_84_2_125, 0 and discharging atoms aNaturalNumber0(xp) = all_84_2_125, aNaturalNumber0(xp) = 0, yields:
% 130.29/89.79 | (594) all_84_2_125 = 0
% 130.29/89.79 |
% 130.29/89.79 | Using (565) and (577) yields:
% 130.29/89.79 | (640) ~ (all_0_9_9 = sz00)
% 130.29/89.79 |
% 130.29/89.79 | From (594) and (607) follows:
% 130.29/89.79 | (13) aNaturalNumber0(xp) = 0
% 130.29/89.79 |
% 130.29/89.79 +-Applying beta-rule and splitting (109), into two cases.
% 130.29/89.79 |-Branch one:
% 130.29/89.79 | (642) all_0_9_9 = sz00
% 130.29/89.79 |
% 130.29/89.79 | Equations (642) can reduce 640 to:
% 130.29/89.79 | (264) $false
% 130.29/89.79 |
% 130.29/89.79 |-The branch is then unsatisfiable
% 130.29/89.79 |-Branch two:
% 130.29/89.79 | (640) ~ (all_0_9_9 = sz00)
% 130.29/89.79 | (645) ? [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))
% 130.29/89.79 |
% 130.29/89.79 | Instantiating (645) with all_262_0_134, all_262_1_135, all_262_2_136 yields:
% 130.29/89.79 | (646) sdtlseqdt0(xp, all_0_9_9) = all_262_0_134 & aNaturalNumber0(all_0_9_9) = all_262_1_135 & aNaturalNumber0(xp) = all_262_2_136 & ( ~ (all_262_1_135 = 0) | ~ (all_262_2_136 = 0) | all_262_0_134 = 0)
% 130.29/89.79 |
% 130.29/89.79 | Applying alpha-rule on (646) yields:
% 130.29/89.79 | (647) sdtlseqdt0(xp, all_0_9_9) = all_262_0_134
% 130.29/89.79 | (648) aNaturalNumber0(all_0_9_9) = all_262_1_135
% 130.29/89.79 | (649) aNaturalNumber0(xp) = all_262_2_136
% 130.29/89.79 | (650) ~ (all_262_1_135 = 0) | ~ (all_262_2_136 = 0) | all_262_0_134 = 0
% 130.29/89.79 |
% 130.29/89.79 +-Applying beta-rule and splitting (133), into two cases.
% 130.29/89.79 |-Branch one:
% 130.29/89.79 | (651) ~ (sdtasdt0(sz00, xm) = all_0_9_9)
% 130.29/89.79 |
% 130.29/89.79 +-Applying beta-rule and splitting (608), into two cases.
% 130.29/89.79 |-Branch one:
% 130.29/89.79 | (603) ~ (all_84_2_125 = 0)
% 130.29/89.79 |
% 130.29/89.79 | Equations (594) can reduce 603 to:
% 130.29/89.79 | (264) $false
% 130.29/89.79 |
% 130.29/89.79 |-The branch is then unsatisfiable
% 130.29/89.79 |-Branch two:
% 130.29/89.79 | (594) all_84_2_125 = 0
% 130.29/89.79 | (655) all_84_1_124 = all_0_2_2
% 130.29/89.79 |
% 130.29/89.79 | Combining equations (655,638) yields a new equation:
% 130.29/89.79 | (656) all_0_2_2 = all_0_4_4
% 130.29/89.79 |
% 130.29/89.79 | Simplifying 656 yields:
% 130.29/89.79 | (657) all_0_2_2 = all_0_4_4
% 130.29/89.79 |
% 130.29/89.79 | From (657) and (564) follows:
% 130.29/89.79 | (658) sdtsldt0(all_0_9_9, xr) = all_0_4_4
% 130.29/89.79 |
% 130.29/89.79 | From (657) and (9) follows:
% 130.29/89.79 | (21) sdtasdt0(all_0_4_4, xr) = all_0_9_9
% 130.29/89.79 |
% 130.29/89.79 | From (657) and (202) follows:
% 130.29/89.79 | (660) sdtasdt0(xr, all_0_4_4) = all_34_0_47
% 130.29/89.79 |
% 130.29/89.79 | From (657) and (197) follows:
% 130.29/89.79 | (661) aNaturalNumber0(all_0_4_4) = all_32_2_46
% 130.29/89.79 |
% 130.29/89.79 +-Applying beta-rule and splitting (103), into two cases.
% 130.29/89.79 |-Branch one:
% 130.29/89.79 | (642) all_0_9_9 = sz00
% 130.29/89.79 |
% 130.29/89.79 | Equations (642) can reduce 640 to:
% 130.29/89.79 | (264) $false
% 130.29/89.79 |
% 130.29/89.79 |-The branch is then unsatisfiable
% 130.29/89.79 |-Branch two:
% 130.29/89.79 | (640) ~ (all_0_9_9 = sz00)
% 130.29/89.79 | (665) ? [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))
% 130.29/89.79 |
% 130.29/89.79 | Instantiating (665) with all_279_0_137, all_279_1_138, all_279_2_139 yields:
% 130.29/89.79 | (666) sdtlseqdt0(xr, all_0_9_9) = all_279_0_137 & aNaturalNumber0(all_0_9_9) = all_279_1_138 & aNaturalNumber0(xr) = all_279_2_139 & ( ~ (all_279_1_138 = 0) | ~ (all_279_2_139 = 0) | all_279_0_137 = 0)
% 130.29/89.79 |
% 130.29/89.79 | Applying alpha-rule on (666) yields:
% 130.29/89.79 | (667) sdtlseqdt0(xr, all_0_9_9) = all_279_0_137
% 130.29/89.79 | (668) aNaturalNumber0(all_0_9_9) = all_279_1_138
% 130.29/89.79 | (669) aNaturalNumber0(xr) = all_279_2_139
% 130.29/89.79 | (670) ~ (all_279_1_138 = 0) | ~ (all_279_2_139 = 0) | all_279_0_137 = 0
% 130.29/89.79 |
% 130.29/89.79 +-Applying beta-rule and splitting (331), into two cases.
% 130.29/89.79 |-Branch one:
% 130.29/89.79 | (671) ~ (sdtasdt0(xr, all_0_4_4) = all_34_0_47)
% 130.29/89.79 |
% 130.29/89.79 | Using (660) and (671) yields:
% 130.29/89.79 | (543) $false
% 130.29/89.79 |
% 130.29/89.79 |-The branch is then unsatisfiable
% 130.29/89.79 |-Branch two:
% 130.29/89.79 | (660) sdtasdt0(xr, all_0_4_4) = all_34_0_47
% 130.29/89.79 | (674) all_36_0_50 = all_34_0_47
% 130.29/89.79 |
% 130.29/89.79 | From (674) and (207) follows:
% 130.29/89.79 | (660) sdtasdt0(xr, all_0_4_4) = all_34_0_47
% 130.29/89.79 |
% 130.29/89.79 +-Applying beta-rule and splitting (339), into two cases.
% 130.29/89.79 |-Branch one:
% 130.29/89.79 | (676) ~ (aNaturalNumber0(all_0_4_4) = all_34_2_49)
% 130.29/89.79 |
% 130.29/89.79 | From (336) and (676) follows:
% 130.29/89.79 | (677) ~ (aNaturalNumber0(all_0_4_4) = all_32_2_46)
% 130.29/89.79 |
% 130.29/89.79 | Using (661) and (677) yields:
% 130.29/89.79 | (543) $false
% 130.29/89.79 |
% 130.29/89.79 |-The branch is then unsatisfiable
% 130.29/89.79 |-Branch two:
% 130.29/89.79 | (679) aNaturalNumber0(all_0_4_4) = all_34_2_49
% 130.29/89.79 | (680) all_34_2_49 = all_20_0_24
% 130.29/89.79 |
% 130.29/89.79 | Combining equations (336,680) yields a new equation:
% 130.29/89.79 | (681) all_32_2_46 = all_20_0_24
% 130.29/89.79 |
% 130.29/89.79 | Simplifying 681 yields:
% 130.29/89.79 | (682) all_32_2_46 = all_20_0_24
% 130.29/89.79 |
% 130.29/89.79 | From (682) and (661) follows:
% 130.29/89.79 | (166) aNaturalNumber0(all_0_4_4) = all_20_0_24
% 130.29/89.79 |
% 130.29/89.79 | Instantiating formula (11) with all_0_9_9, all_279_1_138, 0 and discharging atoms aNaturalNumber0(all_0_9_9) = all_279_1_138, aNaturalNumber0(all_0_9_9) = 0, yields:
% 130.29/89.79 | (684) all_279_1_138 = 0
% 130.29/89.79 |
% 130.29/89.79 | Instantiating formula (11) with all_0_9_9, all_262_1_135, all_279_1_138 and discharging atoms aNaturalNumber0(all_0_9_9) = all_279_1_138, aNaturalNumber0(all_0_9_9) = all_262_1_135, yields:
% 130.29/89.79 | (685) all_279_1_138 = all_262_1_135
% 130.29/89.79 |
% 130.29/89.79 | Instantiating formula (11) with xr, all_279_2_139, 0 and discharging atoms aNaturalNumber0(xr) = all_279_2_139, aNaturalNumber0(xr) = 0, yields:
% 130.29/89.79 | (686) all_279_2_139 = 0
% 130.29/89.79 |
% 130.29/89.79 | Instantiating formula (11) with xp, all_262_2_136, 0 and discharging atoms aNaturalNumber0(xp) = all_262_2_136, aNaturalNumber0(xp) = 0, yields:
% 130.29/89.79 | (687) all_262_2_136 = 0
% 130.29/89.79 |
% 130.29/89.79 | Using (67) and (651) yields:
% 130.29/89.79 | (688) ~ (xn = sz00)
% 130.29/89.79 |
% 130.29/89.79 | Combining equations (684,685) yields a new equation:
% 130.29/89.79 | (689) all_262_1_135 = 0
% 130.29/89.79 |
% 130.29/89.79 | From (689) and (648) follows:
% 130.29/89.79 | (513) aNaturalNumber0(all_0_9_9) = 0
% 130.29/89.79 |
% 130.29/89.79 | From (686) and (669) follows:
% 130.29/89.79 | (23) aNaturalNumber0(xr) = 0
% 130.29/89.79 |
% 130.29/89.79 | From (687) and (649) follows:
% 130.29/89.79 | (13) aNaturalNumber0(xp) = 0
% 130.29/89.79 |
% 130.29/89.79 +-Applying beta-rule and splitting (106), into two cases.
% 130.29/89.79 |-Branch one:
% 130.29/89.79 | (693) xn = sz00
% 130.29/89.79 |
% 130.29/89.79 | Equations (693) can reduce 688 to:
% 130.29/89.79 | (264) $false
% 130.29/89.79 |
% 130.29/89.79 |-The branch is then unsatisfiable
% 130.29/89.79 |-Branch two:
% 130.29/89.79 | (688) ~ (xn = sz00)
% 130.29/89.79 | (696) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xr, xn) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 130.29/89.79 |
% 130.29/89.79 | Instantiating (696) with all_305_0_140, all_305_1_141, all_305_2_142 yields:
% 130.29/89.79 | (697) sdtlseqdt0(xr, xn) = all_305_0_140 & aNaturalNumber0(xr) = all_305_2_142 & aNaturalNumber0(xn) = all_305_1_141 & ( ~ (all_305_1_141 = 0) | ~ (all_305_2_142 = 0) | all_305_0_140 = 0)
% 130.29/89.79 |
% 130.29/89.79 | Applying alpha-rule on (697) yields:
% 130.29/89.79 | (698) sdtlseqdt0(xr, xn) = all_305_0_140
% 130.29/89.79 | (699) aNaturalNumber0(xr) = all_305_2_142
% 130.29/89.79 | (700) aNaturalNumber0(xn) = all_305_1_141
% 130.29/89.79 | (701) ~ (all_305_1_141 = 0) | ~ (all_305_2_142 = 0) | all_305_0_140 = 0
% 130.29/89.79 |
% 130.29/89.79 +-Applying beta-rule and splitting (650), into two cases.
% 130.29/89.79 |-Branch one:
% 130.29/89.79 | (702) ~ (all_262_1_135 = 0)
% 130.29/89.79 |
% 130.29/89.79 | Equations (689) can reduce 702 to:
% 130.29/89.79 | (264) $false
% 130.29/89.79 |
% 130.29/89.79 |-The branch is then unsatisfiable
% 130.29/89.79 |-Branch two:
% 130.29/89.79 | (689) all_262_1_135 = 0
% 130.29/89.79 | (705) ~ (all_262_2_136 = 0) | all_262_0_134 = 0
% 130.29/89.79 |
% 130.29/89.79 +-Applying beta-rule and splitting (705), into two cases.
% 130.29/89.79 |-Branch one:
% 130.29/89.79 | (706) ~ (all_262_2_136 = 0)
% 130.29/89.79 |
% 130.29/89.79 | Equations (687) can reduce 706 to:
% 130.29/89.79 | (264) $false
% 130.29/89.79 |
% 130.29/89.79 |-The branch is then unsatisfiable
% 130.29/89.79 |-Branch two:
% 130.29/89.79 | (687) all_262_2_136 = 0
% 130.29/89.79 | (709) all_262_0_134 = 0
% 130.29/89.79 |
% 130.29/89.79 | From (709) and (647) follows:
% 130.29/89.79 | (710) sdtlseqdt0(xp, all_0_9_9) = 0
% 130.29/89.79 |
% 130.29/89.79 +-Applying beta-rule and splitting (256), into two cases.
% 130.29/89.79 |-Branch one:
% 130.29/89.79 | (711) all_57_0_102 = xp & all_57_1_103 = 0 & sdtpldt0(xk, all_57_2_104) = xp & aNaturalNumber0(all_57_2_104) = 0
% 130.29/89.79 |
% 130.29/89.79 | Applying alpha-rule on (711) yields:
% 130.29/89.79 | (712) all_57_0_102 = xp
% 130.29/89.79 | (713) all_57_1_103 = 0
% 130.29/89.79 | (714) sdtpldt0(xk, all_57_2_104) = xp
% 130.29/89.79 | (715) aNaturalNumber0(all_57_2_104) = 0
% 130.29/89.79 |
% 130.29/89.79 | Instantiating formula (11) with xr, all_305_2_142, 0 and discharging atoms aNaturalNumber0(xr) = all_305_2_142, aNaturalNumber0(xr) = 0, yields:
% 130.29/89.79 | (716) all_305_2_142 = 0
% 130.29/89.79 |
% 130.29/89.79 | From (716) and (699) follows:
% 130.29/89.79 | (23) aNaturalNumber0(xr) = 0
% 130.29/89.79 |
% 130.29/89.79 | Instantiating formula (66) with xp, all_104_0_130 and discharging atoms doDivides0(all_104_0_130, xp) = 0, yields:
% 130.29/89.79 | (718) xp = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_104_0_130, xp) = v2 & aNaturalNumber0(all_104_0_130) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 130.29/89.79 |
% 130.29/89.79 | Instantiating formula (66) with xr, all_99_0_129 and discharging atoms doDivides0(all_99_0_129, xr) = 0, yields:
% 130.29/89.79 | (719) xr = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_99_0_129, xr) = v2 & aNaturalNumber0(all_99_0_129) = v0 & aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 130.29/89.79 |
% 130.29/89.79 | Instantiating formula (73) 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:
% 130.29/89.79 | (720) 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)))
% 130.29/89.79 |
% 130.29/89.79 | Instantiating formula (73) 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:
% 130.29/89.79 | (721) 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)))
% 130.29/89.79 |
% 130.29/89.79 | Instantiating formula (73) with all_75_0_118, xk, all_0_9_9, xp and discharging atoms sdtlseqdt0(xp, all_0_9_9) = 0, sdtlseqdt0(xp, xk) = all_75_0_118, yields:
% 130.29/89.79 | (722) all_75_0_118 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtlseqdt0(all_0_9_9, xk) = v3 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xk) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (56) with all_44_1_66, xr, all_0_1_1 and discharging atoms sdtasdt0(all_0_1_1, xr) = all_44_1_66, yields:
% 130.29/89.80 | (723) ? [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_44_1_66))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (98) with all_44_1_66, xr, all_0_1_1 and discharging atoms sdtasdt0(all_0_1_1, xr) = all_44_1_66, yields:
% 130.29/89.80 | (724) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_44_1_66) = v2 & aNaturalNumber0(all_0_1_1) = v0 & aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (69) with all_0_9_9, all_0_4_4, xr, xp, all_0_1_1 and discharging atoms sdtasdt0(all_0_4_4, xr) = all_0_9_9, yields:
% 130.29/89.80 | (725) ~ (sdtasdt0(all_0_1_1, xp) = all_0_4_4) | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_1_1, v3) = v4 & sdtasdt0(xp, xr) = v3 & aNaturalNumber0(all_0_1_1) = v0 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_9_9))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (56) with all_42_0_62, xp, all_0_1_1 and discharging atoms sdtasdt0(all_0_1_1, xp) = all_42_0_62, yields:
% 130.29/89.80 | (726) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xp, all_0_1_1) = v2 & aNaturalNumber0(all_0_1_1) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_42_0_62))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (98) with all_42_0_62, xp, all_0_1_1 and discharging atoms sdtasdt0(all_0_1_1, xp) = all_42_0_62, yields:
% 130.29/89.80 | (727) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_42_0_62) = v2 & aNaturalNumber0(all_0_1_1) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (56) with all_0_9_9, all_60_2_110, xr and discharging atoms sdtasdt0(xr, all_60_2_110) = all_0_9_9, yields:
% 130.29/89.80 | (728) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_60_2_110, xr) = v2 & aNaturalNumber0(all_60_2_110) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_9_9))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (7) with all_56_2_101, all_0_1_1, xk, xr and discharging atoms sdtsldt0(xk, xr) = all_0_1_1, sdtasdt0(xr, all_56_2_101) = xk, yields:
% 130.29/89.80 | (729) all_56_2_101 = all_0_1_1 | xr = sz00 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_56_2_101) = v0) | (doDivides0(xr, xk) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (56) with xk, all_56_2_101, xr and discharging atoms sdtasdt0(xr, all_56_2_101) = xk, yields:
% 130.29/89.80 | (730) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_56_2_101, xr) = v2 & aNaturalNumber0(all_56_2_101) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xk))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (69) with all_0_9_9, xn, xm, all_50_2_81, xr and discharging atoms sdtasdt0(xr, all_50_2_81) = xn, sdtasdt0(xn, xm) = all_0_9_9, yields:
% 130.29/89.80 | (731) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_50_2_81, xm) = v3 & sdtasdt0(xr, v3) = v4 & aNaturalNumber0(all_50_2_81) = v1 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_9_9))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (56) with xn, all_50_2_81, xr and discharging atoms sdtasdt0(xr, all_50_2_81) = xn, yields:
% 130.29/89.80 | (732) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_50_2_81, xr) = v2 & aNaturalNumber0(all_50_2_81) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xn))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (18) with all_34_0_47, all_0_4_4, all_0_9_9, xr and discharging atoms sdtsldt0(all_0_9_9, xr) = all_0_4_4, sdtasdt0(xr, all_0_4_4) = all_34_0_47, yields:
% 130.29/89.80 | (733) all_34_0_47 = all_0_9_9 | xr = sz00 | ? [v0] : ? [v1] : ? [v2] : (doDivides0(xr, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (82) with all_34_0_47, all_0_4_4, all_0_9_9, xr and discharging atoms sdtsldt0(all_0_9_9, xr) = all_0_4_4, sdtasdt0(xr, all_0_4_4) = all_34_0_47, yields:
% 130.29/89.80 | (734) xr = sz00 | ? [v0] : ? [v1] : ? [v2] : ((v0 = 0 & aNaturalNumber0(all_0_4_4) = 0) | (doDivides0(xr, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (56) with all_34_0_47, all_0_4_4, xr and discharging atoms sdtasdt0(xr, all_0_4_4) = all_34_0_47, yields:
% 130.29/89.80 | (735) ? [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_34_0_47))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (98) with all_34_0_47, all_0_4_4, xr and discharging atoms sdtasdt0(xr, all_0_4_4) = all_34_0_47, yields:
% 130.29/89.80 | (736) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_34_0_47) = v2 & aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (69) with all_0_9_9, xk, xp, xr, all_0_1_1 and discharging atoms sdtasdt0(xk, xp) = all_0_9_9, yields:
% 130.29/89.80 | (737) ~ (sdtasdt0(all_0_1_1, xr) = xk) | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_1_1, v3) = v4 & sdtasdt0(xr, xp) = v3 & aNaturalNumber0(all_0_1_1) = v0 & aNaturalNumber0(xr) = v1 & aNaturalNumber0(xp) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_9_9))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (69) with all_0_9_9, xk, xp, all_56_2_101, xr and discharging atoms sdtasdt0(xr, all_56_2_101) = xk, sdtasdt0(xk, xp) = all_0_9_9, yields:
% 130.29/89.80 | (738) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_56_2_101, xp) = v3 & sdtasdt0(xr, v3) = v4 & aNaturalNumber0(all_56_2_101) = v1 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xp) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_9_9))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (7) with all_53_2_89, xk, all_0_9_9, xp and discharging atoms sdtsldt0(all_0_9_9, xp) = xk, sdtasdt0(xp, all_53_2_89) = all_0_9_9, yields:
% 130.29/89.80 | (739) all_53_2_89 = xk | xp = sz00 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_53_2_89) = v0) | (doDivides0(xp, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (56) with all_0_9_9, all_53_2_89, xp and discharging atoms sdtasdt0(xp, all_53_2_89) = all_0_9_9, yields:
% 130.29/89.80 | (740) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_53_2_89, xp) = v2 & aNaturalNumber0(all_53_2_89) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_9_9))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (7) with all_44_1_66, xk, all_0_9_9, xp and discharging atoms sdtsldt0(all_0_9_9, xp) = xk, yields:
% 130.29/89.80 | (741) all_44_1_66 = xk | xp = sz00 | ~ (sdtasdt0(xp, all_44_1_66) = all_0_9_9) | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_44_1_66) = v0) | (doDivides0(xp, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (72) with all_44_0_65, all_0_9_9, all_44_1_66, all_53_2_89, xp and discharging atoms sdtasdt0(xp, all_53_2_89) = all_0_9_9, sdtasdt0(xp, all_44_1_66) = all_44_0_65, aNaturalNumber0(xp) = 0, yields:
% 130.29/89.80 | (742) all_53_2_89 = all_44_1_66 | xp = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_53_2_89, xp) = v2 & sdtasdt0(all_44_1_66, xp) = v3 & aNaturalNumber0(all_53_2_89) = v0 & aNaturalNumber0(all_44_1_66) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = v2) & ~ (all_44_0_65 = all_0_9_9))))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (72) with all_0_9_9, all_44_0_65, all_53_2_89, all_44_1_66, xp and discharging atoms sdtasdt0(xp, all_53_2_89) = all_0_9_9, sdtasdt0(xp, all_44_1_66) = all_44_0_65, aNaturalNumber0(xp) = 0, yields:
% 130.29/89.80 | (743) all_53_2_89 = all_44_1_66 | xp = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_53_2_89, xp) = v3 & sdtasdt0(all_44_1_66, xp) = v2 & aNaturalNumber0(all_53_2_89) = v1 & aNaturalNumber0(all_44_1_66) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = v2) & ~ (all_44_0_65 = all_0_9_9))))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (56) with all_44_0_65, all_44_1_66, xp and discharging atoms sdtasdt0(xp, all_44_1_66) = all_44_0_65, yields:
% 130.29/89.80 | (744) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_44_1_66, xp) = v2 & aNaturalNumber0(all_44_1_66) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_44_0_65))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (98) with all_44_0_65, all_44_1_66, xp and discharging atoms sdtasdt0(xp, all_44_1_66) = all_44_0_65, yields:
% 130.29/89.80 | (745) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_44_0_65) = v2 & aNaturalNumber0(all_44_1_66) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (72) with all_0_9_9, all_0_9_9, xk, all_53_2_89, xp and discharging atoms sdtasdt0(xp, all_53_2_89) = all_0_9_9, sdtasdt0(xp, xk) = all_0_9_9, aNaturalNumber0(xp) = 0, yields:
% 130.29/89.80 | (746) all_53_2_89 = xk | xp = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_53_2_89, xp) = v2 & sdtasdt0(xk, xp) = v3 & aNaturalNumber0(all_53_2_89) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (72) with all_0_9_9, all_0_9_9, all_53_2_89, xk, xp and discharging atoms sdtasdt0(xp, all_53_2_89) = all_0_9_9, sdtasdt0(xp, xk) = all_0_9_9, aNaturalNumber0(xp) = 0, yields:
% 130.29/89.80 | (747) all_53_2_89 = xk | xp = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_53_2_89, xp) = v3 & sdtasdt0(xk, xp) = v2 & aNaturalNumber0(all_53_2_89) = v1 & aNaturalNumber0(xk) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (56) with all_58_0_105, all_0_5_5, xm and discharging atoms sdtasdt0(xm, all_0_5_5) = all_58_0_105, yields:
% 130.29/89.80 | (748) ? [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_58_0_105))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (98) with all_58_0_105, all_0_5_5, xm and discharging atoms sdtasdt0(xm, all_0_5_5) = all_58_0_105, yields:
% 130.29/89.80 | (749) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_58_0_105) = v2 & aNaturalNumber0(all_0_5_5) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (56) with all_28_1_37, xr, xm and discharging atoms sdtasdt0(xm, xr) = all_28_1_37, yields:
% 130.29/89.80 | (750) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xr, xm) = v2 & aNaturalNumber0(xr) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_28_1_37))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (98) with all_28_1_37, xr, xm and discharging atoms sdtasdt0(xm, xr) = all_28_1_37, yields:
% 130.29/89.80 | (751) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_28_1_37) = v2 & aNaturalNumber0(xr) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 130.29/89.80 |
% 130.29/89.80 | Instantiating formula (53) with all_0_4_4, all_0_9_9, xm, all_0_5_5, xn, xr and discharging atoms sdtsldt0(all_0_9_9, xr) = all_0_4_4, sdtsldt0(xn, xr) = all_0_5_5, sdtasdt0(xm, xn) = all_0_9_9, yields:
% 130.29/89.80 | (752) 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_4_4)))
% 130.29/89.81 |
% 130.29/89.81 | Instantiating formula (49) with xk, all_48_2_75, xr, xr and discharging atoms doDivides0(xr, xk) = 0, sdtpldt0(xr, all_48_2_75) = xk, yields:
% 130.29/89.81 | (753) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(xr, all_48_2_75) = v4 & doDivides0(xr, xr) = v3 & aNaturalNumber0(all_48_2_75) = v2 & aNaturalNumber0(xr) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 130.29/89.81 |
% 130.29/89.81 | Instantiating formula (34) with xk, all_48_2_75, xr and discharging atoms sdtpldt0(xr, all_48_2_75) = xk, yields:
% 130.29/89.81 | (754) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_48_2_75, xr) = v2 & aNaturalNumber0(all_48_2_75) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xk))
% 130.29/89.81 |
% 130.29/89.81 | Instantiating formula (49) with xp, all_57_2_104, xk, all_104_0_130 and discharging atoms doDivides0(all_104_0_130, xp) = 0, sdtpldt0(xk, all_57_2_104) = xp, yields:
% 130.29/89.81 | (755) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(all_104_0_130, all_57_2_104) = v4 & doDivides0(all_104_0_130, xk) = v3 & aNaturalNumber0(all_104_0_130) = v0 & aNaturalNumber0(all_57_2_104) = v2 & aNaturalNumber0(xk) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 130.29/89.81 |
% 130.29/89.81 | Instantiating formula (85) with xp, xk, all_57_2_104, all_48_2_75, xr and discharging atoms sdtpldt0(xr, all_48_2_75) = xk, sdtpldt0(xk, all_57_2_104) = xp, yields:
% 130.29/89.81 | (756) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(all_57_2_104) = v3 & doDivides0(all_57_2_104, v4) = v5 & doDivides0(all_57_2_104, all_48_2_75) = v8 & doDivides0(all_57_2_104, xr) = v7 & iLess0(xp, all_0_10_10) = v6 & sdtasdt0(xr, all_48_2_75) = v4 & aNaturalNumber0(all_57_2_104) = v2 & aNaturalNumber0(all_48_2_75) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 130.29/89.81 |
% 130.29/89.81 | Instantiating formula (27) with xp, xk, all_57_2_104, all_48_2_75, xr and discharging atoms sdtpldt0(xr, all_48_2_75) = xk, sdtpldt0(xk, all_57_2_104) = xp, yields:
% 130.29/89.81 | (757) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_48_2_75, all_57_2_104) = v3 & sdtpldt0(xr, v3) = v4 & aNaturalNumber0(all_57_2_104) = v2 & aNaturalNumber0(all_48_2_75) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = xp))
% 130.29/89.81 |
% 130.29/89.81 | Instantiating formula (34) with xp, all_57_2_104, xk and discharging atoms sdtpldt0(xk, all_57_2_104) = xp, yields:
% 130.29/89.81 | (758) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_57_2_104, xk) = v2 & aNaturalNumber0(all_57_2_104) = v1 & aNaturalNumber0(xk) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xp))
% 130.29/89.81 |
% 130.29/89.81 | Instantiating formula (85) with all_0_10_10, xp, all_0_11_11, all_57_2_104, xk and discharging atoms sdtpldt0(xk, all_57_2_104) = xp, sdtpldt0(xp, all_0_11_11) = all_0_10_10, yields:
% 130.29/89.81 | (759) ? [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_57_2_104) = v8 & doDivides0(all_0_11_11, xk) = v7 & iLess0(all_0_10_10, all_0_10_10) = v6 & sdtasdt0(xk, all_57_2_104) = v4 & aNaturalNumber0(all_57_2_104) = v1 & aNaturalNumber0(all_0_11_11) = v2 & aNaturalNumber0(xk) = v0 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 130.29/89.81 |
% 130.29/89.81 | Instantiating formula (27) with all_0_10_10, xp, all_0_11_11, all_57_2_104, xk and discharging atoms sdtpldt0(xk, all_57_2_104) = xp, sdtpldt0(xp, all_0_11_11) = all_0_10_10, yields:
% 130.29/89.81 | (760) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_57_2_104, all_0_11_11) = v3 & sdtpldt0(xk, v3) = v4 & aNaturalNumber0(all_57_2_104) = v1 & aNaturalNumber0(all_0_11_11) = v2 & aNaturalNumber0(xk) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_10_10))
% 130.29/89.81 |
% 130.29/89.81 | Instantiating formula (49) with xp, all_39_2_58, xm, all_104_0_130 and discharging atoms doDivides0(all_104_0_130, xp) = 0, sdtpldt0(xm, all_39_2_58) = xp, yields:
% 130.29/89.81 | (761) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(all_104_0_130, all_39_2_58) = v4 & doDivides0(all_104_0_130, xm) = v3 & aNaturalNumber0(all_104_0_130) = v0 & aNaturalNumber0(all_39_2_58) = v2 & aNaturalNumber0(xm) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 130.29/89.81 |
% 130.29/89.81 | Instantiating formula (85) with all_0_10_10, xp, all_0_11_11, all_39_2_58, xm and discharging atoms sdtpldt0(xp, all_0_11_11) = all_0_10_10, sdtpldt0(xm, all_39_2_58) = xp, yields:
% 130.29/89.81 | (762) ? [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_39_2_58) = v8 & doDivides0(all_0_11_11, xm) = v7 & iLess0(all_0_10_10, all_0_10_10) = v6 & sdtasdt0(xm, all_39_2_58) = v4 & aNaturalNumber0(all_39_2_58) = 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))
% 130.29/89.81 |
% 130.29/89.81 | Instantiating formula (27) with all_0_10_10, xp, all_0_11_11, all_39_2_58, xm and discharging atoms sdtpldt0(xp, all_0_11_11) = all_0_10_10, sdtpldt0(xm, all_39_2_58) = xp, yields:
% 130.29/89.81 | (763) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_39_2_58, all_0_11_11) = v3 & sdtpldt0(xm, v3) = v4 & aNaturalNumber0(all_39_2_58) = v1 & aNaturalNumber0(all_0_11_11) = v2 & aNaturalNumber0(xm) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_10_10))
% 130.29/89.81 |
% 130.29/89.81 | Instantiating formula (34) with xp, all_39_2_58, xm and discharging atoms sdtpldt0(xm, all_39_2_58) = xp, yields:
% 130.29/89.81 | (764) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_39_2_58, xm) = v2 & aNaturalNumber0(all_39_2_58) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xp))
% 130.29/89.81 |
% 130.29/89.81 | Instantiating formula (34) with all_51_1_83, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_51_1_83, yields:
% 130.29/89.81 | (765) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, xm) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_51_1_83))
% 130.29/89.81 |
% 130.29/89.81 | Instantiating formula (89) with all_51_1_83, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_51_1_83, yields:
% 130.29/89.81 | (766) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_51_1_83) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 130.29/89.81 |
% 130.29/89.81 | Instantiating formula (85) 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:
% 130.29/89.81 | (767) ? [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))
% 130.29/89.81 |
% 130.29/89.81 | Instantiating formula (27) 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:
% 130.29/89.81 | (768) ? [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))
% 130.29/89.81 |
% 130.29/89.81 | Instantiating formula (34) with all_0_10_10, all_51_1_83, xn and discharging atoms sdtpldt0(xn, all_51_1_83) = all_0_10_10, yields:
% 130.29/89.81 | (769) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_51_1_83, xn) = v2 & aNaturalNumber0(all_51_1_83) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_10_10))
% 130.29/89.81 |
% 130.29/89.81 | Instantiating formula (89) with all_0_10_10, all_51_1_83, xn and discharging atoms sdtpldt0(xn, all_51_1_83) = all_0_10_10, yields:
% 130.29/89.81 | (770) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_51_1_83) = v1 & aNaturalNumber0(all_0_10_10) = v2 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 130.29/89.81 |
% 130.29/89.81 | Instantiating (768) with all_378_0_152, all_378_1_153, all_378_2_154, all_378_3_155, all_378_4_156 yields:
% 130.29/89.81 | (771) sdtpldt0(xm, all_378_1_153) = all_378_0_152 & sdtpldt0(xn, xp) = all_378_1_153 & aNaturalNumber0(xp) = all_378_2_154 & aNaturalNumber0(xm) = all_378_4_156 & aNaturalNumber0(xn) = all_378_3_155 & ( ~ (all_378_2_154 = 0) | ~ (all_378_3_155 = 0) | ~ (all_378_4_156 = 0) | all_378_0_152 = all_0_10_10)
% 130.29/89.81 |
% 130.29/89.81 | Applying alpha-rule on (771) yields:
% 130.29/89.81 | (772) aNaturalNumber0(xp) = all_378_2_154
% 130.29/89.81 | (773) ~ (all_378_2_154 = 0) | ~ (all_378_3_155 = 0) | ~ (all_378_4_156 = 0) | all_378_0_152 = all_0_10_10
% 130.29/89.81 | (774) aNaturalNumber0(xm) = all_378_4_156
% 130.29/89.81 | (775) aNaturalNumber0(xn) = all_378_3_155
% 130.29/89.81 | (776) sdtpldt0(xm, all_378_1_153) = all_378_0_152
% 130.29/89.81 | (777) sdtpldt0(xn, xp) = all_378_1_153
% 130.29/89.81 |
% 130.29/89.81 | Instantiating (764) with all_380_0_157, all_380_1_158, all_380_2_159 yields:
% 130.29/89.81 | (778) sdtpldt0(all_39_2_58, xm) = all_380_0_157 & aNaturalNumber0(all_39_2_58) = all_380_1_158 & aNaturalNumber0(xm) = all_380_2_159 & ( ~ (all_380_1_158 = 0) | ~ (all_380_2_159 = 0) | all_380_0_157 = xp)
% 130.29/89.81 |
% 130.29/89.81 | Applying alpha-rule on (778) yields:
% 130.29/89.81 | (779) sdtpldt0(all_39_2_58, xm) = all_380_0_157
% 130.29/89.81 | (780) aNaturalNumber0(all_39_2_58) = all_380_1_158
% 130.29/89.81 | (781) aNaturalNumber0(xm) = all_380_2_159
% 130.29/89.81 | (782) ~ (all_380_1_158 = 0) | ~ (all_380_2_159 = 0) | all_380_0_157 = xp
% 130.29/89.81 |
% 130.29/89.81 | Instantiating (763) with all_382_0_160, all_382_1_161, all_382_2_162, all_382_3_163, all_382_4_164 yields:
% 130.29/89.81 | (783) sdtpldt0(all_39_2_58, all_0_11_11) = all_382_1_161 & sdtpldt0(xm, all_382_1_161) = all_382_0_160 & aNaturalNumber0(all_39_2_58) = all_382_3_163 & aNaturalNumber0(all_0_11_11) = all_382_2_162 & aNaturalNumber0(xm) = all_382_4_164 & ( ~ (all_382_2_162 = 0) | ~ (all_382_3_163 = 0) | ~ (all_382_4_164 = 0) | all_382_0_160 = all_0_10_10)
% 130.29/89.81 |
% 130.29/89.81 | Applying alpha-rule on (783) yields:
% 130.29/89.81 | (784) aNaturalNumber0(xm) = all_382_4_164
% 130.29/89.81 | (785) sdtpldt0(xm, all_382_1_161) = all_382_0_160
% 130.29/89.81 | (786) sdtpldt0(all_39_2_58, all_0_11_11) = all_382_1_161
% 130.29/89.81 | (787) aNaturalNumber0(all_0_11_11) = all_382_2_162
% 130.29/89.81 | (788) aNaturalNumber0(all_39_2_58) = all_382_3_163
% 130.29/89.81 | (789) ~ (all_382_2_162 = 0) | ~ (all_382_3_163 = 0) | ~ (all_382_4_164 = 0) | all_382_0_160 = all_0_10_10
% 130.29/89.81 |
% 130.29/89.81 | Instantiating (762) with all_384_0_165, all_384_1_166, all_384_2_167, all_384_3_168, all_384_4_169, all_384_5_170, all_384_6_171, all_384_7_172, all_384_8_173 yields:
% 130.29/89.81 | (790) isPrime0(all_0_11_11) = all_384_5_170 & doDivides0(all_0_11_11, all_384_4_169) = all_384_3_168 & doDivides0(all_0_11_11, all_39_2_58) = all_384_0_165 & doDivides0(all_0_11_11, xm) = all_384_1_166 & iLess0(all_0_10_10, all_0_10_10) = all_384_2_167 & sdtasdt0(xm, all_39_2_58) = all_384_4_169 & aNaturalNumber0(all_39_2_58) = all_384_7_172 & aNaturalNumber0(all_0_11_11) = all_384_6_171 & aNaturalNumber0(xm) = all_384_8_173 & ( ~ (all_384_2_167 = 0) | ~ (all_384_3_168 = 0) | ~ (all_384_5_170 = 0) | ~ (all_384_6_171 = 0) | ~ (all_384_7_172 = 0) | ~ (all_384_8_173 = 0) | all_384_0_165 = 0 | all_384_1_166 = 0)
% 130.29/89.81 |
% 130.29/89.81 | Applying alpha-rule on (790) yields:
% 130.29/89.81 | (791) iLess0(all_0_10_10, all_0_10_10) = all_384_2_167
% 130.29/89.81 | (792) isPrime0(all_0_11_11) = all_384_5_170
% 130.29/89.81 | (793) sdtasdt0(xm, all_39_2_58) = all_384_4_169
% 130.29/89.82 | (794) aNaturalNumber0(xm) = all_384_8_173
% 130.29/89.82 | (795) doDivides0(all_0_11_11, all_39_2_58) = all_384_0_165
% 130.29/89.82 | (796) doDivides0(all_0_11_11, xm) = all_384_1_166
% 130.29/89.82 | (797) doDivides0(all_0_11_11, all_384_4_169) = all_384_3_168
% 130.29/89.82 | (798) aNaturalNumber0(all_0_11_11) = all_384_6_171
% 130.29/89.82 | (799) aNaturalNumber0(all_39_2_58) = all_384_7_172
% 130.29/89.82 | (800) ~ (all_384_2_167 = 0) | ~ (all_384_3_168 = 0) | ~ (all_384_5_170 = 0) | ~ (all_384_6_171 = 0) | ~ (all_384_7_172 = 0) | ~ (all_384_8_173 = 0) | all_384_0_165 = 0 | all_384_1_166 = 0
% 130.29/89.82 |
% 130.29/89.82 | Instantiating (758) with all_386_0_174, all_386_1_175, all_386_2_176 yields:
% 130.29/89.82 | (801) sdtpldt0(all_57_2_104, xk) = all_386_0_174 & aNaturalNumber0(all_57_2_104) = all_386_1_175 & aNaturalNumber0(xk) = all_386_2_176 & ( ~ (all_386_1_175 = 0) | ~ (all_386_2_176 = 0) | all_386_0_174 = xp)
% 130.29/89.82 |
% 130.29/89.82 | Applying alpha-rule on (801) yields:
% 130.29/89.82 | (802) sdtpldt0(all_57_2_104, xk) = all_386_0_174
% 130.29/89.82 | (803) aNaturalNumber0(all_57_2_104) = all_386_1_175
% 130.29/89.82 | (804) aNaturalNumber0(xk) = all_386_2_176
% 130.29/89.82 | (805) ~ (all_386_1_175 = 0) | ~ (all_386_2_176 = 0) | all_386_0_174 = xp
% 130.29/89.82 |
% 130.29/89.82 | Instantiating (755) with all_388_0_177, all_388_1_178, all_388_2_179, all_388_3_180, all_388_4_181 yields:
% 130.29/89.82 | (806) doDivides0(all_104_0_130, all_57_2_104) = all_388_0_177 & doDivides0(all_104_0_130, xk) = all_388_1_178 & aNaturalNumber0(all_104_0_130) = all_388_4_181 & aNaturalNumber0(all_57_2_104) = all_388_2_179 & aNaturalNumber0(xk) = all_388_3_180 & ( ~ (all_388_1_178 = 0) | ~ (all_388_2_179 = 0) | ~ (all_388_3_180 = 0) | ~ (all_388_4_181 = 0) | all_388_0_177 = 0)
% 130.29/89.82 |
% 130.29/89.82 | Applying alpha-rule on (806) yields:
% 130.29/89.82 | (807) doDivides0(all_104_0_130, xk) = all_388_1_178
% 130.29/89.82 | (808) aNaturalNumber0(all_104_0_130) = all_388_4_181
% 130.29/89.82 | (809) aNaturalNumber0(all_57_2_104) = all_388_2_179
% 130.77/89.82 | (810) ~ (all_388_1_178 = 0) | ~ (all_388_2_179 = 0) | ~ (all_388_3_180 = 0) | ~ (all_388_4_181 = 0) | all_388_0_177 = 0
% 130.77/89.82 | (811) doDivides0(all_104_0_130, all_57_2_104) = all_388_0_177
% 130.77/89.82 | (812) aNaturalNumber0(xk) = all_388_3_180
% 130.77/89.82 |
% 130.77/89.82 | Instantiating (757) with all_390_0_182, all_390_1_183, all_390_2_184, all_390_3_185, all_390_4_186 yields:
% 130.77/89.82 | (813) sdtpldt0(all_48_2_75, all_57_2_104) = all_390_1_183 & sdtpldt0(xr, all_390_1_183) = all_390_0_182 & aNaturalNumber0(all_57_2_104) = all_390_2_184 & aNaturalNumber0(all_48_2_75) = all_390_3_185 & aNaturalNumber0(xr) = all_390_4_186 & ( ~ (all_390_2_184 = 0) | ~ (all_390_3_185 = 0) | ~ (all_390_4_186 = 0) | all_390_0_182 = xp)
% 130.77/89.82 |
% 130.77/89.82 | Applying alpha-rule on (813) yields:
% 130.77/89.82 | (814) ~ (all_390_2_184 = 0) | ~ (all_390_3_185 = 0) | ~ (all_390_4_186 = 0) | all_390_0_182 = xp
% 130.77/89.82 | (815) aNaturalNumber0(all_48_2_75) = all_390_3_185
% 130.77/89.82 | (816) sdtpldt0(all_48_2_75, all_57_2_104) = all_390_1_183
% 130.77/89.82 | (817) sdtpldt0(xr, all_390_1_183) = all_390_0_182
% 130.77/89.82 | (818) aNaturalNumber0(xr) = all_390_4_186
% 130.77/89.82 | (819) aNaturalNumber0(all_57_2_104) = all_390_2_184
% 130.77/89.82 |
% 130.77/89.82 | Instantiating (756) with all_392_0_187, all_392_1_188, all_392_2_189, all_392_3_190, all_392_4_191, all_392_5_192, all_392_6_193, all_392_7_194, all_392_8_195 yields:
% 130.77/89.82 | (820) isPrime0(all_57_2_104) = all_392_5_192 & doDivides0(all_57_2_104, all_392_4_191) = all_392_3_190 & doDivides0(all_57_2_104, all_48_2_75) = all_392_0_187 & doDivides0(all_57_2_104, xr) = all_392_1_188 & iLess0(xp, all_0_10_10) = all_392_2_189 & sdtasdt0(xr, all_48_2_75) = all_392_4_191 & aNaturalNumber0(all_57_2_104) = all_392_6_193 & aNaturalNumber0(all_48_2_75) = all_392_7_194 & aNaturalNumber0(xr) = all_392_8_195 & ( ~ (all_392_2_189 = 0) | ~ (all_392_3_190 = 0) | ~ (all_392_5_192 = 0) | ~ (all_392_6_193 = 0) | ~ (all_392_7_194 = 0) | ~ (all_392_8_195 = 0) | all_392_0_187 = 0 | all_392_1_188 = 0)
% 130.77/89.82 |
% 130.77/89.82 | Applying alpha-rule on (820) yields:
% 130.77/89.82 | (821) doDivides0(all_57_2_104, xr) = all_392_1_188
% 130.77/89.82 | (822) aNaturalNumber0(xr) = all_392_8_195
% 130.77/89.82 | (823) doDivides0(all_57_2_104, all_392_4_191) = all_392_3_190
% 130.77/89.82 | (824) isPrime0(all_57_2_104) = all_392_5_192
% 130.77/89.82 | (825) iLess0(xp, all_0_10_10) = all_392_2_189
% 130.77/89.82 | (826) sdtasdt0(xr, all_48_2_75) = all_392_4_191
% 130.77/89.82 | (827) doDivides0(all_57_2_104, all_48_2_75) = all_392_0_187
% 130.77/89.82 | (828) ~ (all_392_2_189 = 0) | ~ (all_392_3_190 = 0) | ~ (all_392_5_192 = 0) | ~ (all_392_6_193 = 0) | ~ (all_392_7_194 = 0) | ~ (all_392_8_195 = 0) | all_392_0_187 = 0 | all_392_1_188 = 0
% 130.77/89.82 | (829) aNaturalNumber0(all_57_2_104) = all_392_6_193
% 130.77/89.82 | (830) aNaturalNumber0(all_48_2_75) = all_392_7_194
% 130.77/89.82 |
% 130.77/89.82 | Instantiating (754) with all_394_0_196, all_394_1_197, all_394_2_198 yields:
% 130.77/89.82 | (831) sdtpldt0(all_48_2_75, xr) = all_394_0_196 & aNaturalNumber0(all_48_2_75) = all_394_1_197 & aNaturalNumber0(xr) = all_394_2_198 & ( ~ (all_394_1_197 = 0) | ~ (all_394_2_198 = 0) | all_394_0_196 = xk)
% 130.77/89.82 |
% 130.77/89.82 | Applying alpha-rule on (831) yields:
% 130.77/89.82 | (832) sdtpldt0(all_48_2_75, xr) = all_394_0_196
% 130.77/89.82 | (833) aNaturalNumber0(all_48_2_75) = all_394_1_197
% 130.77/89.82 | (834) aNaturalNumber0(xr) = all_394_2_198
% 130.77/89.82 | (835) ~ (all_394_1_197 = 0) | ~ (all_394_2_198 = 0) | all_394_0_196 = xk
% 130.77/89.82 |
% 130.77/89.82 | Instantiating (753) with all_396_0_199, all_396_1_200, all_396_2_201, all_396_3_202, all_396_4_203 yields:
% 130.77/89.82 | (836) doDivides0(xr, all_48_2_75) = all_396_0_199 & doDivides0(xr, xr) = all_396_1_200 & aNaturalNumber0(all_48_2_75) = all_396_2_201 & aNaturalNumber0(xr) = all_396_3_202 & aNaturalNumber0(xr) = all_396_4_203 & ( ~ (all_396_1_200 = 0) | ~ (all_396_2_201 = 0) | ~ (all_396_3_202 = 0) | ~ (all_396_4_203 = 0) | all_396_0_199 = 0)
% 130.77/89.82 |
% 130.77/89.82 | Applying alpha-rule on (836) yields:
% 130.77/89.82 | (837) aNaturalNumber0(xr) = all_396_3_202
% 130.77/89.82 | (838) aNaturalNumber0(all_48_2_75) = all_396_2_201
% 130.77/89.82 | (839) doDivides0(xr, all_48_2_75) = all_396_0_199
% 130.77/89.82 | (840) ~ (all_396_1_200 = 0) | ~ (all_396_2_201 = 0) | ~ (all_396_3_202 = 0) | ~ (all_396_4_203 = 0) | all_396_0_199 = 0
% 130.77/89.82 | (841) doDivides0(xr, xr) = all_396_1_200
% 130.77/89.82 | (842) aNaturalNumber0(xr) = all_396_4_203
% 130.77/89.82 |
% 130.77/89.82 | Instantiating (761) with all_398_0_204, all_398_1_205, all_398_2_206, all_398_3_207, all_398_4_208 yields:
% 130.77/89.82 | (843) doDivides0(all_104_0_130, all_39_2_58) = all_398_0_204 & doDivides0(all_104_0_130, xm) = all_398_1_205 & aNaturalNumber0(all_104_0_130) = all_398_4_208 & aNaturalNumber0(all_39_2_58) = all_398_2_206 & aNaturalNumber0(xm) = all_398_3_207 & ( ~ (all_398_1_205 = 0) | ~ (all_398_2_206 = 0) | ~ (all_398_3_207 = 0) | ~ (all_398_4_208 = 0) | all_398_0_204 = 0)
% 130.77/89.82 |
% 130.77/89.82 | Applying alpha-rule on (843) yields:
% 130.77/89.82 | (844) doDivides0(all_104_0_130, xm) = all_398_1_205
% 130.77/89.82 | (845) aNaturalNumber0(all_39_2_58) = all_398_2_206
% 130.77/89.82 | (846) ~ (all_398_1_205 = 0) | ~ (all_398_2_206 = 0) | ~ (all_398_3_207 = 0) | ~ (all_398_4_208 = 0) | all_398_0_204 = 0
% 130.77/89.82 | (847) doDivides0(all_104_0_130, all_39_2_58) = all_398_0_204
% 130.77/89.82 | (848) aNaturalNumber0(all_104_0_130) = all_398_4_208
% 130.77/89.82 | (849) aNaturalNumber0(xm) = all_398_3_207
% 130.77/89.82 |
% 130.77/89.82 | Instantiating (767) with all_400_0_209, all_400_1_210, all_400_2_211, all_400_3_212, all_400_4_213, all_400_5_214, all_400_6_215, all_400_7_216, all_400_8_217 yields:
% 130.77/89.82 | (850) isPrime0(xp) = all_400_5_214 & doDivides0(xp, all_400_4_213) = all_400_3_212 & doDivides0(xp, xm) = all_400_1_210 & doDivides0(xp, xn) = all_400_0_209 & iLess0(all_0_10_10, all_0_10_10) = all_400_2_211 & sdtasdt0(xm, xn) = all_400_4_213 & aNaturalNumber0(xp) = all_400_6_215 & aNaturalNumber0(xm) = all_400_8_217 & aNaturalNumber0(xn) = all_400_7_216 & ( ~ (all_400_2_211 = 0) | ~ (all_400_3_212 = 0) | ~ (all_400_5_214 = 0) | ~ (all_400_6_215 = 0) | ~ (all_400_7_216 = 0) | ~ (all_400_8_217 = 0) | all_400_0_209 = 0 | all_400_1_210 = 0)
% 130.77/89.82 |
% 130.77/89.82 | Applying alpha-rule on (850) yields:
% 130.77/89.82 | (851) aNaturalNumber0(xn) = all_400_7_216
% 130.77/89.82 | (852) iLess0(all_0_10_10, all_0_10_10) = all_400_2_211
% 130.77/89.82 | (853) ~ (all_400_2_211 = 0) | ~ (all_400_3_212 = 0) | ~ (all_400_5_214 = 0) | ~ (all_400_6_215 = 0) | ~ (all_400_7_216 = 0) | ~ (all_400_8_217 = 0) | all_400_0_209 = 0 | all_400_1_210 = 0
% 130.77/89.82 | (854) aNaturalNumber0(xm) = all_400_8_217
% 130.77/89.82 | (855) doDivides0(xp, all_400_4_213) = all_400_3_212
% 130.77/89.82 | (856) aNaturalNumber0(xp) = all_400_6_215
% 130.77/89.82 | (857) isPrime0(xp) = all_400_5_214
% 130.77/89.82 | (858) doDivides0(xp, xn) = all_400_0_209
% 130.77/89.82 | (859) sdtasdt0(xm, xn) = all_400_4_213
% 130.77/89.82 | (860) doDivides0(xp, xm) = all_400_1_210
% 130.77/89.82 |
% 130.77/89.82 | Instantiating (766) with all_402_0_218, all_402_1_219, all_402_2_220 yields:
% 130.77/89.82 | (861) aNaturalNumber0(all_51_1_83) = all_402_0_218 & aNaturalNumber0(xp) = all_402_1_219 & aNaturalNumber0(xm) = all_402_2_220 & ( ~ (all_402_1_219 = 0) | ~ (all_402_2_220 = 0) | all_402_0_218 = 0)
% 130.77/89.82 |
% 130.77/89.82 | Applying alpha-rule on (861) yields:
% 130.77/89.82 | (862) aNaturalNumber0(all_51_1_83) = all_402_0_218
% 130.77/89.82 | (863) aNaturalNumber0(xp) = all_402_1_219
% 130.77/89.82 | (864) aNaturalNumber0(xm) = all_402_2_220
% 130.77/89.82 | (865) ~ (all_402_1_219 = 0) | ~ (all_402_2_220 = 0) | all_402_0_218 = 0
% 130.77/89.82 |
% 130.77/89.82 | Instantiating (770) with all_404_0_221, all_404_1_222, all_404_2_223 yields:
% 130.77/89.82 | (866) aNaturalNumber0(all_51_1_83) = all_404_1_222 & aNaturalNumber0(all_0_10_10) = all_404_0_221 & aNaturalNumber0(xn) = all_404_2_223 & ( ~ (all_404_1_222 = 0) | ~ (all_404_2_223 = 0) | all_404_0_221 = 0)
% 130.77/89.82 |
% 130.77/89.82 | Applying alpha-rule on (866) yields:
% 130.77/89.82 | (867) aNaturalNumber0(all_51_1_83) = all_404_1_222
% 130.77/89.82 | (868) aNaturalNumber0(all_0_10_10) = all_404_0_221
% 130.77/89.82 | (869) aNaturalNumber0(xn) = all_404_2_223
% 130.77/89.82 | (870) ~ (all_404_1_222 = 0) | ~ (all_404_2_223 = 0) | all_404_0_221 = 0
% 130.77/89.82 |
% 130.77/89.82 | Instantiating (769) with all_406_0_224, all_406_1_225, all_406_2_226 yields:
% 130.77/89.82 | (871) sdtpldt0(all_51_1_83, xn) = all_406_0_224 & aNaturalNumber0(all_51_1_83) = all_406_1_225 & aNaturalNumber0(xn) = all_406_2_226 & ( ~ (all_406_1_225 = 0) | ~ (all_406_2_226 = 0) | all_406_0_224 = all_0_10_10)
% 130.77/89.82 |
% 130.77/89.82 | Applying alpha-rule on (871) yields:
% 130.77/89.82 | (872) sdtpldt0(all_51_1_83, xn) = all_406_0_224
% 130.77/89.82 | (873) aNaturalNumber0(all_51_1_83) = all_406_1_225
% 130.77/89.82 | (874) aNaturalNumber0(xn) = all_406_2_226
% 130.77/89.82 | (875) ~ (all_406_1_225 = 0) | ~ (all_406_2_226 = 0) | all_406_0_224 = all_0_10_10
% 130.77/89.82 |
% 130.77/89.82 | Instantiating (765) with all_408_0_227, all_408_1_228, all_408_2_229 yields:
% 130.77/89.82 | (876) sdtpldt0(xp, xm) = all_408_0_227 & aNaturalNumber0(xp) = all_408_1_228 & aNaturalNumber0(xm) = all_408_2_229 & ( ~ (all_408_1_228 = 0) | ~ (all_408_2_229 = 0) | all_408_0_227 = all_51_1_83)
% 130.77/89.82 |
% 130.77/89.82 | Applying alpha-rule on (876) yields:
% 130.77/89.82 | (877) sdtpldt0(xp, xm) = all_408_0_227
% 130.77/89.82 | (878) aNaturalNumber0(xp) = all_408_1_228
% 130.77/89.83 | (879) aNaturalNumber0(xm) = all_408_2_229
% 130.77/89.83 | (880) ~ (all_408_1_228 = 0) | ~ (all_408_2_229 = 0) | all_408_0_227 = all_51_1_83
% 130.77/89.83 |
% 130.77/89.83 | Instantiating (760) with all_410_0_230, all_410_1_231, all_410_2_232, all_410_3_233, all_410_4_234 yields:
% 130.77/89.83 | (881) sdtpldt0(all_57_2_104, all_0_11_11) = all_410_1_231 & sdtpldt0(xk, all_410_1_231) = all_410_0_230 & aNaturalNumber0(all_57_2_104) = all_410_3_233 & aNaturalNumber0(all_0_11_11) = all_410_2_232 & aNaturalNumber0(xk) = all_410_4_234 & ( ~ (all_410_2_232 = 0) | ~ (all_410_3_233 = 0) | ~ (all_410_4_234 = 0) | all_410_0_230 = all_0_10_10)
% 130.77/89.83 |
% 130.77/89.83 | Applying alpha-rule on (881) yields:
% 130.77/89.83 | (882) sdtpldt0(all_57_2_104, all_0_11_11) = all_410_1_231
% 130.77/89.83 | (883) ~ (all_410_2_232 = 0) | ~ (all_410_3_233 = 0) | ~ (all_410_4_234 = 0) | all_410_0_230 = all_0_10_10
% 130.77/89.83 | (884) aNaturalNumber0(all_0_11_11) = all_410_2_232
% 130.77/89.83 | (885) aNaturalNumber0(all_57_2_104) = all_410_3_233
% 130.77/89.83 | (886) sdtpldt0(xk, all_410_1_231) = all_410_0_230
% 130.77/89.83 | (887) aNaturalNumber0(xk) = all_410_4_234
% 130.77/89.83 |
% 130.77/89.83 | Instantiating (759) with all_412_0_235, all_412_1_236, all_412_2_237, all_412_3_238, all_412_4_239, all_412_5_240, all_412_6_241, all_412_7_242, all_412_8_243 yields:
% 130.77/89.83 | (888) isPrime0(all_0_11_11) = all_412_5_240 & doDivides0(all_0_11_11, all_412_4_239) = all_412_3_238 & doDivides0(all_0_11_11, all_57_2_104) = all_412_0_235 & doDivides0(all_0_11_11, xk) = all_412_1_236 & iLess0(all_0_10_10, all_0_10_10) = all_412_2_237 & sdtasdt0(xk, all_57_2_104) = all_412_4_239 & aNaturalNumber0(all_57_2_104) = all_412_7_242 & aNaturalNumber0(all_0_11_11) = all_412_6_241 & aNaturalNumber0(xk) = all_412_8_243 & ( ~ (all_412_2_237 = 0) | ~ (all_412_3_238 = 0) | ~ (all_412_5_240 = 0) | ~ (all_412_6_241 = 0) | ~ (all_412_7_242 = 0) | ~ (all_412_8_243 = 0) | all_412_0_235 = 0 | all_412_1_236 = 0)
% 130.77/89.83 |
% 130.77/89.83 | Applying alpha-rule on (888) yields:
% 130.77/89.83 | (889) aNaturalNumber0(all_57_2_104) = all_412_7_242
% 130.77/89.83 | (890) doDivides0(all_0_11_11, all_57_2_104) = all_412_0_235
% 130.77/89.83 | (891) ~ (all_412_2_237 = 0) | ~ (all_412_3_238 = 0) | ~ (all_412_5_240 = 0) | ~ (all_412_6_241 = 0) | ~ (all_412_7_242 = 0) | ~ (all_412_8_243 = 0) | all_412_0_235 = 0 | all_412_1_236 = 0
% 130.77/89.83 | (892) iLess0(all_0_10_10, all_0_10_10) = all_412_2_237
% 130.77/89.83 | (893) aNaturalNumber0(all_0_11_11) = all_412_6_241
% 130.77/89.83 | (894) sdtasdt0(xk, all_57_2_104) = all_412_4_239
% 130.77/89.83 | (895) doDivides0(all_0_11_11, xk) = all_412_1_236
% 130.77/89.83 | (896) isPrime0(all_0_11_11) = all_412_5_240
% 130.77/89.83 | (897) aNaturalNumber0(xk) = all_412_8_243
% 130.77/89.83 | (898) doDivides0(all_0_11_11, all_412_4_239) = all_412_3_238
% 130.77/89.83 |
% 130.77/89.83 | Instantiating (751) with all_416_0_249, all_416_1_250, all_416_2_251 yields:
% 130.77/89.83 | (899) aNaturalNumber0(all_28_1_37) = all_416_0_249 & aNaturalNumber0(xr) = all_416_1_250 & aNaturalNumber0(xm) = all_416_2_251 & ( ~ (all_416_1_250 = 0) | ~ (all_416_2_251 = 0) | all_416_0_249 = 0)
% 130.77/89.83 |
% 130.77/89.83 | Applying alpha-rule on (899) yields:
% 130.77/89.83 | (900) aNaturalNumber0(all_28_1_37) = all_416_0_249
% 130.77/89.83 | (901) aNaturalNumber0(xr) = all_416_1_250
% 130.77/89.83 | (902) aNaturalNumber0(xm) = all_416_2_251
% 130.77/89.83 | (903) ~ (all_416_1_250 = 0) | ~ (all_416_2_251 = 0) | all_416_0_249 = 0
% 130.77/89.83 |
% 130.77/89.83 | Instantiating (745) with all_418_0_252, all_418_1_253, all_418_2_254 yields:
% 130.77/89.83 | (904) aNaturalNumber0(all_44_0_65) = all_418_0_252 & aNaturalNumber0(all_44_1_66) = all_418_1_253 & aNaturalNumber0(xp) = all_418_2_254 & ( ~ (all_418_1_253 = 0) | ~ (all_418_2_254 = 0) | all_418_0_252 = 0)
% 130.77/89.83 |
% 130.77/89.83 | Applying alpha-rule on (904) yields:
% 130.77/89.83 | (905) aNaturalNumber0(all_44_0_65) = all_418_0_252
% 130.77/89.83 | (906) aNaturalNumber0(all_44_1_66) = all_418_1_253
% 130.77/89.83 | (907) aNaturalNumber0(xp) = all_418_2_254
% 130.77/89.83 | (908) ~ (all_418_1_253 = 0) | ~ (all_418_2_254 = 0) | all_418_0_252 = 0
% 130.77/89.83 |
% 130.77/89.83 | Instantiating (740) with all_420_0_255, all_420_1_256, all_420_2_257 yields:
% 130.77/89.83 | (909) sdtasdt0(all_53_2_89, xp) = all_420_0_255 & aNaturalNumber0(all_53_2_89) = all_420_1_256 & aNaturalNumber0(xp) = all_420_2_257 & ( ~ (all_420_1_256 = 0) | ~ (all_420_2_257 = 0) | all_420_0_255 = all_0_9_9)
% 130.77/89.83 |
% 130.77/89.83 | Applying alpha-rule on (909) yields:
% 130.77/89.83 | (910) sdtasdt0(all_53_2_89, xp) = all_420_0_255
% 130.77/89.83 | (911) aNaturalNumber0(all_53_2_89) = all_420_1_256
% 130.77/89.83 | (912) aNaturalNumber0(xp) = all_420_2_257
% 130.77/89.83 | (913) ~ (all_420_1_256 = 0) | ~ (all_420_2_257 = 0) | all_420_0_255 = all_0_9_9
% 130.77/89.83 |
% 130.77/89.83 | Instantiating (744) with all_422_0_258, all_422_1_259, all_422_2_260 yields:
% 130.77/89.83 | (914) sdtasdt0(all_44_1_66, xp) = all_422_0_258 & aNaturalNumber0(all_44_1_66) = all_422_1_259 & aNaturalNumber0(xp) = all_422_2_260 & ( ~ (all_422_1_259 = 0) | ~ (all_422_2_260 = 0) | all_422_0_258 = all_44_0_65)
% 130.77/89.83 |
% 130.77/89.83 | Applying alpha-rule on (914) yields:
% 130.77/89.83 | (915) sdtasdt0(all_44_1_66, xp) = all_422_0_258
% 130.77/89.83 | (916) aNaturalNumber0(all_44_1_66) = all_422_1_259
% 130.77/89.83 | (917) aNaturalNumber0(xp) = all_422_2_260
% 130.77/89.83 | (918) ~ (all_422_1_259 = 0) | ~ (all_422_2_260 = 0) | all_422_0_258 = all_44_0_65
% 130.77/89.83 |
% 130.77/89.83 | Instantiating (738) with all_424_0_261, all_424_1_262, all_424_2_263, all_424_3_264, all_424_4_265 yields:
% 130.77/89.83 | (919) sdtasdt0(all_56_2_101, xp) = all_424_1_262 & sdtasdt0(xr, all_424_1_262) = all_424_0_261 & aNaturalNumber0(all_56_2_101) = all_424_3_264 & aNaturalNumber0(xr) = all_424_4_265 & aNaturalNumber0(xp) = all_424_2_263 & ( ~ (all_424_2_263 = 0) | ~ (all_424_3_264 = 0) | ~ (all_424_4_265 = 0) | all_424_0_261 = all_0_9_9)
% 130.77/89.83 |
% 130.77/89.83 | Applying alpha-rule on (919) yields:
% 130.77/89.83 | (920) aNaturalNumber0(all_56_2_101) = all_424_3_264
% 130.77/89.83 | (921) ~ (all_424_2_263 = 0) | ~ (all_424_3_264 = 0) | ~ (all_424_4_265 = 0) | all_424_0_261 = all_0_9_9
% 130.77/89.83 | (922) sdtasdt0(all_56_2_101, xp) = all_424_1_262
% 130.77/89.83 | (923) aNaturalNumber0(xr) = all_424_4_265
% 130.77/89.83 | (924) aNaturalNumber0(xp) = all_424_2_263
% 130.77/89.83 | (925) sdtasdt0(xr, all_424_1_262) = all_424_0_261
% 130.77/89.83 |
% 130.77/89.83 | Instantiating (750) with all_426_0_266, all_426_1_267, all_426_2_268 yields:
% 130.77/89.83 | (926) sdtasdt0(xr, xm) = all_426_0_266 & aNaturalNumber0(xr) = all_426_1_267 & aNaturalNumber0(xm) = all_426_2_268 & ( ~ (all_426_1_267 = 0) | ~ (all_426_2_268 = 0) | all_426_0_266 = all_28_1_37)
% 130.77/89.83 |
% 130.77/89.83 | Applying alpha-rule on (926) yields:
% 130.77/89.83 | (927) sdtasdt0(xr, xm) = all_426_0_266
% 130.77/89.83 | (928) aNaturalNumber0(xr) = all_426_1_267
% 130.77/89.83 | (929) aNaturalNumber0(xm) = all_426_2_268
% 130.77/89.83 | (930) ~ (all_426_1_267 = 0) | ~ (all_426_2_268 = 0) | all_426_0_266 = all_28_1_37
% 130.77/89.83 |
% 130.77/89.83 | Instantiating (732) with all_428_0_269, all_428_1_270, all_428_2_271 yields:
% 130.77/89.83 | (931) sdtasdt0(all_50_2_81, xr) = all_428_0_269 & aNaturalNumber0(all_50_2_81) = all_428_1_270 & aNaturalNumber0(xr) = all_428_2_271 & ( ~ (all_428_1_270 = 0) | ~ (all_428_2_271 = 0) | all_428_0_269 = xn)
% 130.77/89.83 |
% 130.77/89.83 | Applying alpha-rule on (931) yields:
% 130.77/89.83 | (932) sdtasdt0(all_50_2_81, xr) = all_428_0_269
% 130.77/89.83 | (933) aNaturalNumber0(all_50_2_81) = all_428_1_270
% 130.77/89.83 | (934) aNaturalNumber0(xr) = all_428_2_271
% 130.77/89.83 | (935) ~ (all_428_1_270 = 0) | ~ (all_428_2_271 = 0) | all_428_0_269 = xn
% 130.77/89.83 |
% 130.77/89.83 | Instantiating (730) with all_430_0_272, all_430_1_273, all_430_2_274 yields:
% 130.77/89.83 | (936) sdtasdt0(all_56_2_101, xr) = all_430_0_272 & aNaturalNumber0(all_56_2_101) = all_430_1_273 & aNaturalNumber0(xr) = all_430_2_274 & ( ~ (all_430_1_273 = 0) | ~ (all_430_2_274 = 0) | all_430_0_272 = xk)
% 130.77/89.83 |
% 130.77/89.83 | Applying alpha-rule on (936) yields:
% 130.77/89.83 | (937) sdtasdt0(all_56_2_101, xr) = all_430_0_272
% 130.77/89.83 | (938) aNaturalNumber0(all_56_2_101) = all_430_1_273
% 130.77/89.83 | (939) aNaturalNumber0(xr) = all_430_2_274
% 130.77/89.83 | (940) ~ (all_430_1_273 = 0) | ~ (all_430_2_274 = 0) | all_430_0_272 = xk
% 130.77/89.83 |
% 130.77/89.83 | Instantiating (731) with all_432_0_275, all_432_1_276, all_432_2_277, all_432_3_278, all_432_4_279 yields:
% 130.77/89.83 | (941) sdtasdt0(all_50_2_81, xm) = all_432_1_276 & sdtasdt0(xr, all_432_1_276) = all_432_0_275 & aNaturalNumber0(all_50_2_81) = all_432_3_278 & aNaturalNumber0(xr) = all_432_4_279 & aNaturalNumber0(xm) = all_432_2_277 & ( ~ (all_432_2_277 = 0) | ~ (all_432_3_278 = 0) | ~ (all_432_4_279 = 0) | all_432_0_275 = all_0_9_9)
% 130.77/89.83 |
% 130.77/89.83 | Applying alpha-rule on (941) yields:
% 130.77/89.83 | (942) sdtasdt0(all_50_2_81, xm) = all_432_1_276
% 130.77/89.83 | (943) aNaturalNumber0(xr) = all_432_4_279
% 130.77/89.83 | (944) ~ (all_432_2_277 = 0) | ~ (all_432_3_278 = 0) | ~ (all_432_4_279 = 0) | all_432_0_275 = all_0_9_9
% 130.77/89.83 | (945) sdtasdt0(xr, all_432_1_276) = all_432_0_275
% 130.77/89.83 | (946) aNaturalNumber0(all_50_2_81) = all_432_3_278
% 130.77/89.83 | (947) aNaturalNumber0(xm) = all_432_2_277
% 130.77/89.83 |
% 130.77/89.83 | Instantiating (749) with all_438_0_286, all_438_1_287, all_438_2_288 yields:
% 130.77/89.83 | (948) aNaturalNumber0(all_58_0_105) = all_438_0_286 & aNaturalNumber0(all_0_5_5) = all_438_1_287 & aNaturalNumber0(xm) = all_438_2_288 & ( ~ (all_438_1_287 = 0) | ~ (all_438_2_288 = 0) | all_438_0_286 = 0)
% 130.77/89.83 |
% 130.77/89.83 | Applying alpha-rule on (948) yields:
% 130.77/89.83 | (949) aNaturalNumber0(all_58_0_105) = all_438_0_286
% 130.77/89.83 | (950) aNaturalNumber0(all_0_5_5) = all_438_1_287
% 130.77/89.83 | (951) aNaturalNumber0(xm) = all_438_2_288
% 130.77/89.83 | (952) ~ (all_438_1_287 = 0) | ~ (all_438_2_288 = 0) | all_438_0_286 = 0
% 130.77/89.83 |
% 130.77/89.83 | Instantiating (748) with all_440_0_289, all_440_1_290, all_440_2_291 yields:
% 130.77/89.83 | (953) sdtasdt0(all_0_5_5, xm) = all_440_0_289 & aNaturalNumber0(all_0_5_5) = all_440_1_290 & aNaturalNumber0(xm) = all_440_2_291 & ( ~ (all_440_1_290 = 0) | ~ (all_440_2_291 = 0) | all_440_0_289 = all_58_0_105)
% 130.77/89.83 |
% 130.77/89.83 | Applying alpha-rule on (953) yields:
% 130.77/89.83 | (954) sdtasdt0(all_0_5_5, xm) = all_440_0_289
% 130.77/89.83 | (955) aNaturalNumber0(all_0_5_5) = all_440_1_290
% 130.77/89.83 | (956) aNaturalNumber0(xm) = all_440_2_291
% 130.77/89.83 | (957) ~ (all_440_1_290 = 0) | ~ (all_440_2_291 = 0) | all_440_0_289 = all_58_0_105
% 130.77/89.83 |
% 130.77/89.83 | Instantiating (736) with all_444_0_301, all_444_1_302, all_444_2_303 yields:
% 130.77/89.83 | (958) aNaturalNumber0(all_34_0_47) = all_444_0_301 & aNaturalNumber0(all_0_4_4) = all_444_1_302 & aNaturalNumber0(xr) = all_444_2_303 & ( ~ (all_444_1_302 = 0) | ~ (all_444_2_303 = 0) | all_444_0_301 = 0)
% 130.77/89.83 |
% 130.77/89.83 | Applying alpha-rule on (958) yields:
% 130.77/89.83 | (959) aNaturalNumber0(all_34_0_47) = all_444_0_301
% 130.77/89.83 | (960) aNaturalNumber0(all_0_4_4) = all_444_1_302
% 130.77/89.83 | (961) aNaturalNumber0(xr) = all_444_2_303
% 130.77/89.83 | (962) ~ (all_444_1_302 = 0) | ~ (all_444_2_303 = 0) | all_444_0_301 = 0
% 130.77/89.83 |
% 130.77/89.83 | Instantiating (735) with all_446_0_304, all_446_1_305, all_446_2_306 yields:
% 130.77/89.83 | (963) sdtasdt0(all_0_4_4, xr) = all_446_0_304 & aNaturalNumber0(all_0_4_4) = all_446_1_305 & aNaturalNumber0(xr) = all_446_2_306 & ( ~ (all_446_1_305 = 0) | ~ (all_446_2_306 = 0) | all_446_0_304 = all_34_0_47)
% 130.77/89.83 |
% 130.77/89.83 | Applying alpha-rule on (963) yields:
% 130.77/89.83 | (964) sdtasdt0(all_0_4_4, xr) = all_446_0_304
% 130.77/89.83 | (965) aNaturalNumber0(all_0_4_4) = all_446_1_305
% 130.77/89.83 | (966) aNaturalNumber0(xr) = all_446_2_306
% 130.77/89.83 | (967) ~ (all_446_1_305 = 0) | ~ (all_446_2_306 = 0) | all_446_0_304 = all_34_0_47
% 130.77/89.83 |
% 130.77/89.83 | Instantiating (728) with all_448_0_307, all_448_1_308, all_448_2_309 yields:
% 130.77/89.83 | (968) sdtasdt0(all_60_2_110, xr) = all_448_0_307 & aNaturalNumber0(all_60_2_110) = all_448_1_308 & aNaturalNumber0(xr) = all_448_2_309 & ( ~ (all_448_1_308 = 0) | ~ (all_448_2_309 = 0) | all_448_0_307 = all_0_9_9)
% 130.77/89.83 |
% 130.77/89.83 | Applying alpha-rule on (968) yields:
% 130.77/89.84 | (969) sdtasdt0(all_60_2_110, xr) = all_448_0_307
% 130.77/89.84 | (970) aNaturalNumber0(all_60_2_110) = all_448_1_308
% 130.77/89.84 | (971) aNaturalNumber0(xr) = all_448_2_309
% 130.77/89.84 | (972) ~ (all_448_1_308 = 0) | ~ (all_448_2_309 = 0) | all_448_0_307 = all_0_9_9
% 130.77/89.84 |
% 130.77/89.84 | Instantiating (724) with all_450_0_310, all_450_1_311, all_450_2_312 yields:
% 130.77/89.84 | (973) aNaturalNumber0(all_44_1_66) = all_450_0_310 & aNaturalNumber0(all_0_1_1) = all_450_2_312 & aNaturalNumber0(xr) = all_450_1_311 & ( ~ (all_450_1_311 = 0) | ~ (all_450_2_312 = 0) | all_450_0_310 = 0)
% 130.77/89.84 |
% 130.77/89.84 | Applying alpha-rule on (973) yields:
% 130.77/89.84 | (974) aNaturalNumber0(all_44_1_66) = all_450_0_310
% 130.77/89.84 | (975) aNaturalNumber0(all_0_1_1) = all_450_2_312
% 130.77/89.84 | (976) aNaturalNumber0(xr) = all_450_1_311
% 130.77/89.84 | (977) ~ (all_450_1_311 = 0) | ~ (all_450_2_312 = 0) | all_450_0_310 = 0
% 130.77/89.84 |
% 130.77/89.84 | Instantiating (723) with all_452_0_313, all_452_1_314, all_452_2_315 yields:
% 130.77/89.84 | (978) sdtasdt0(xr, all_0_1_1) = all_452_0_313 & aNaturalNumber0(all_0_1_1) = all_452_2_315 & aNaturalNumber0(xr) = all_452_1_314 & ( ~ (all_452_1_314 = 0) | ~ (all_452_2_315 = 0) | all_452_0_313 = all_44_1_66)
% 130.77/89.84 |
% 130.77/89.84 | Applying alpha-rule on (978) yields:
% 130.77/89.84 | (979) sdtasdt0(xr, all_0_1_1) = all_452_0_313
% 130.77/89.84 | (980) aNaturalNumber0(all_0_1_1) = all_452_2_315
% 130.77/89.84 | (981) aNaturalNumber0(xr) = all_452_1_314
% 130.77/89.84 | (982) ~ (all_452_1_314 = 0) | ~ (all_452_2_315 = 0) | all_452_0_313 = all_44_1_66
% 130.77/89.84 |
% 130.77/89.84 | Instantiating (727) with all_455_0_319, all_455_1_320, all_455_2_321 yields:
% 130.77/89.84 | (983) aNaturalNumber0(all_42_0_62) = all_455_0_319 & aNaturalNumber0(all_0_1_1) = all_455_2_321 & aNaturalNumber0(xp) = all_455_1_320 & ( ~ (all_455_1_320 = 0) | ~ (all_455_2_321 = 0) | all_455_0_319 = 0)
% 130.77/89.84 |
% 130.77/89.84 | Applying alpha-rule on (983) yields:
% 130.77/89.84 | (984) aNaturalNumber0(all_42_0_62) = all_455_0_319
% 130.77/89.84 | (985) aNaturalNumber0(all_0_1_1) = all_455_2_321
% 130.77/89.84 | (986) aNaturalNumber0(xp) = all_455_1_320
% 130.77/89.84 | (987) ~ (all_455_1_320 = 0) | ~ (all_455_2_321 = 0) | all_455_0_319 = 0
% 130.77/89.84 |
% 130.77/89.84 | Instantiating (726) with all_457_0_322, all_457_1_323, all_457_2_324 yields:
% 130.77/89.84 | (988) sdtasdt0(xp, all_0_1_1) = all_457_0_322 & aNaturalNumber0(all_0_1_1) = all_457_2_324 & aNaturalNumber0(xp) = all_457_1_323 & ( ~ (all_457_1_323 = 0) | ~ (all_457_2_324 = 0) | all_457_0_322 = all_42_0_62)
% 130.77/89.84 |
% 130.77/89.84 | Applying alpha-rule on (988) yields:
% 130.77/89.84 | (989) sdtasdt0(xp, all_0_1_1) = all_457_0_322
% 130.77/89.84 | (990) aNaturalNumber0(all_0_1_1) = all_457_2_324
% 130.77/89.84 | (991) aNaturalNumber0(xp) = all_457_1_323
% 130.77/89.84 | (992) ~ (all_457_1_323 = 0) | ~ (all_457_2_324 = 0) | all_457_0_322 = all_42_0_62
% 130.77/89.84 |
% 130.77/89.84 +-Applying beta-rule and splitting (722), into two cases.
% 130.77/89.84 |-Branch one:
% 130.77/89.84 | (993) all_75_0_118 = 0
% 130.77/89.84 |
% 130.77/89.84 | Equations (993) can reduce 567 to:
% 130.77/89.84 | (264) $false
% 130.77/89.84 |
% 130.77/89.84 |-The branch is then unsatisfiable
% 130.77/89.84 |-Branch two:
% 130.77/89.84 | (567) ~ (all_75_0_118 = 0)
% 130.77/89.84 | (996) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtlseqdt0(all_0_9_9, xk) = v3 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xk) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 130.77/89.84 |
% 130.77/89.84 | Instantiating (996) with all_468_0_340, all_468_1_341, all_468_2_342, all_468_3_343 yields:
% 130.77/89.84 | (997) sdtlseqdt0(all_0_9_9, xk) = all_468_0_340 & aNaturalNumber0(all_0_9_9) = all_468_2_342 & aNaturalNumber0(xk) = all_468_1_341 & aNaturalNumber0(xp) = all_468_3_343 & ( ~ (all_468_0_340 = 0) | ~ (all_468_1_341 = 0) | ~ (all_468_2_342 = 0) | ~ (all_468_3_343 = 0))
% 130.77/89.84 |
% 130.77/89.84 | Applying alpha-rule on (997) yields:
% 130.77/89.84 | (998) sdtlseqdt0(all_0_9_9, xk) = all_468_0_340
% 130.77/89.84 | (999) ~ (all_468_0_340 = 0) | ~ (all_468_1_341 = 0) | ~ (all_468_2_342 = 0) | ~ (all_468_3_343 = 0)
% 130.77/89.84 | (1000) aNaturalNumber0(xp) = all_468_3_343
% 130.77/89.84 | (1001) aNaturalNumber0(xk) = all_468_1_341
% 130.77/89.84 | (1002) aNaturalNumber0(all_0_9_9) = all_468_2_342
% 130.77/89.84 |
% 130.77/89.84 +-Applying beta-rule and splitting (718), into two cases.
% 130.77/89.84 |-Branch one:
% 130.77/89.84 | (301) xp = sz00
% 130.77/89.84 |
% 130.77/89.84 | Equations (301) can reduce 102 to:
% 130.77/89.84 | (264) $false
% 130.77/89.84 |
% 130.77/89.84 |-The branch is then unsatisfiable
% 130.77/89.84 |-Branch two:
% 130.77/89.84 | (102) ~ (xp = sz00)
% 130.77/89.84 | (1006) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_104_0_130, xp) = v2 & aNaturalNumber0(all_104_0_130) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 130.77/89.84 |
% 130.77/89.84 | Instantiating (1006) with all_473_0_344, all_473_1_345, all_473_2_346 yields:
% 130.77/89.84 | (1007) sdtlseqdt0(all_104_0_130, xp) = all_473_0_344 & aNaturalNumber0(all_104_0_130) = all_473_2_346 & aNaturalNumber0(xp) = all_473_1_345 & ( ~ (all_473_1_345 = 0) | ~ (all_473_2_346 = 0) | all_473_0_344 = 0)
% 130.77/89.84 |
% 130.77/89.84 | Applying alpha-rule on (1007) yields:
% 130.77/89.84 | (1008) sdtlseqdt0(all_104_0_130, xp) = all_473_0_344
% 130.77/89.84 | (1009) aNaturalNumber0(all_104_0_130) = all_473_2_346
% 130.77/89.84 | (1010) aNaturalNumber0(xp) = all_473_1_345
% 130.77/89.84 | (1011) ~ (all_473_1_345 = 0) | ~ (all_473_2_346 = 0) | all_473_0_344 = 0
% 130.77/89.84 |
% 130.77/89.84 +-Applying beta-rule and splitting (719), into two cases.
% 130.77/89.84 |-Branch one:
% 130.77/89.84 | (296) xr = sz00
% 130.77/89.84 |
% 130.77/89.84 | Equations (296) can reduce 101 to:
% 130.77/89.84 | (264) $false
% 130.77/89.84 |
% 130.77/89.84 |-The branch is then unsatisfiable
% 130.77/89.84 |-Branch two:
% 130.77/89.84 | (101) ~ (xr = sz00)
% 130.77/89.84 | (1015) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_99_0_129, xr) = v2 & aNaturalNumber0(all_99_0_129) = v0 & aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 130.77/89.84 |
% 130.77/89.84 | Instantiating (1015) with all_478_0_347, all_478_1_348, all_478_2_349 yields:
% 130.77/89.84 | (1016) sdtlseqdt0(all_99_0_129, xr) = all_478_0_347 & aNaturalNumber0(all_99_0_129) = all_478_2_349 & aNaturalNumber0(xr) = all_478_1_348 & ( ~ (all_478_1_348 = 0) | ~ (all_478_2_349 = 0) | all_478_0_347 = 0)
% 130.77/89.84 |
% 130.77/89.84 | Applying alpha-rule on (1016) yields:
% 130.77/89.84 | (1017) sdtlseqdt0(all_99_0_129, xr) = all_478_0_347
% 130.77/89.84 | (1018) aNaturalNumber0(all_99_0_129) = all_478_2_349
% 130.77/89.84 | (1019) aNaturalNumber0(xr) = all_478_1_348
% 130.77/89.84 | (1020) ~ (all_478_1_348 = 0) | ~ (all_478_2_349 = 0) | all_478_0_347 = 0
% 130.77/89.84 |
% 130.77/89.84 +-Applying beta-rule and splitting (734), into two cases.
% 130.77/89.84 |-Branch one:
% 130.77/89.84 | (296) xr = sz00
% 130.77/89.84 |
% 130.77/89.84 | Equations (296) can reduce 101 to:
% 130.77/89.84 | (264) $false
% 130.77/89.84 |
% 130.77/89.84 |-The branch is then unsatisfiable
% 130.77/89.84 |-Branch two:
% 130.77/89.84 | (101) ~ (xr = sz00)
% 130.77/89.84 | (1024) ? [v0] : ? [v1] : ? [v2] : ((v0 = 0 & aNaturalNumber0(all_0_4_4) = 0) | (doDivides0(xr, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 130.77/89.84 |
% 130.77/89.84 +-Applying beta-rule and splitting (721), into two cases.
% 130.77/89.84 |-Branch one:
% 130.77/89.84 | (1025) all_0_8_8 = 0
% 130.77/89.84 |
% 130.77/89.84 | Equations (1025) can reduce 59 to:
% 130.77/89.84 | (264) $false
% 130.77/89.84 |
% 130.77/89.84 |-The branch is then unsatisfiable
% 130.77/89.84 |-Branch two:
% 130.77/89.84 | (59) ~ (all_0_8_8 = 0)
% 130.77/89.84 | (1028) ? [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)))
% 130.77/89.84 |
% 130.77/89.84 | Instantiating (1028) with all_487_0_353, all_487_1_354, all_487_2_355, all_487_3_356 yields:
% 130.77/89.84 | (1029) sdtlseqdt0(all_0_9_9, xn) = all_487_0_353 & aNaturalNumber0(all_0_9_9) = all_487_2_355 & aNaturalNumber0(xp) = all_487_3_356 & aNaturalNumber0(xn) = all_487_1_354 & ( ~ (all_487_0_353 = 0) | ~ (all_487_1_354 = 0) | ~ (all_487_2_355 = 0) | ~ (all_487_3_356 = 0))
% 130.77/89.84 |
% 130.77/89.84 | Applying alpha-rule on (1029) yields:
% 130.77/89.84 | (1030) aNaturalNumber0(all_0_9_9) = all_487_2_355
% 130.77/89.84 | (1031) ~ (all_487_0_353 = 0) | ~ (all_487_1_354 = 0) | ~ (all_487_2_355 = 0) | ~ (all_487_3_356 = 0)
% 130.77/89.84 | (1032) aNaturalNumber0(xp) = all_487_3_356
% 130.77/89.84 | (1033) aNaturalNumber0(xn) = all_487_1_354
% 130.77/89.84 | (1034) sdtlseqdt0(all_0_9_9, xn) = all_487_0_353
% 130.77/89.84 |
% 130.77/89.84 +-Applying beta-rule and splitting (720), into two cases.
% 130.77/89.84 |-Branch one:
% 130.77/89.84 | (1035) all_0_7_7 = 0
% 130.77/89.84 |
% 130.77/89.84 | Equations (1035) can reduce 44 to:
% 130.77/89.84 | (264) $false
% 130.77/89.84 |
% 130.77/89.84 |-The branch is then unsatisfiable
% 130.77/89.84 |-Branch two:
% 130.77/89.84 | (44) ~ (all_0_7_7 = 0)
% 130.77/89.84 | (1038) ? [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)))
% 130.77/89.84 |
% 130.77/89.84 | Instantiating (1038) with all_492_0_357, all_492_1_358, all_492_2_359, all_492_3_360 yields:
% 130.77/89.84 | (1039) sdtlseqdt0(all_0_9_9, xm) = all_492_0_357 & aNaturalNumber0(all_0_9_9) = all_492_2_359 & aNaturalNumber0(xp) = all_492_3_360 & aNaturalNumber0(xm) = all_492_1_358 & ( ~ (all_492_0_357 = 0) | ~ (all_492_1_358 = 0) | ~ (all_492_2_359 = 0) | ~ (all_492_3_360 = 0))
% 130.77/89.84 |
% 130.77/89.84 | Applying alpha-rule on (1039) yields:
% 130.77/89.84 | (1040) ~ (all_492_0_357 = 0) | ~ (all_492_1_358 = 0) | ~ (all_492_2_359 = 0) | ~ (all_492_3_360 = 0)
% 130.77/89.84 | (1041) aNaturalNumber0(all_0_9_9) = all_492_2_359
% 130.77/89.84 | (1042) aNaturalNumber0(xm) = all_492_1_358
% 130.77/89.84 | (1043) aNaturalNumber0(xp) = all_492_3_360
% 130.77/89.84 | (1044) sdtlseqdt0(all_0_9_9, xm) = all_492_0_357
% 130.77/89.84 |
% 130.77/89.84 +-Applying beta-rule and splitting (752), into two cases.
% 130.77/89.84 |-Branch one:
% 130.77/89.84 | (296) xr = sz00
% 130.77/89.84 |
% 130.77/89.84 | Equations (296) can reduce 101 to:
% 130.77/89.84 | (264) $false
% 130.77/89.84 |
% 130.77/89.84 |-The branch is then unsatisfiable
% 130.77/89.84 |-Branch two:
% 130.77/89.84 | (101) ~ (xr = sz00)
% 130.77/89.84 | (1048) ? [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_4_4)))
% 130.77/89.84 |
% 130.77/89.84 | Instantiating formula (37) with all_0_1_1, xr, all_430_0_272, all_44_1_66 and discharging atoms sdtasdt0(all_0_1_1, xr) = all_44_1_66, yields:
% 130.77/89.84 | (1049) all_430_0_272 = all_44_1_66 | ~ (sdtasdt0(all_0_1_1, xr) = all_430_0_272)
% 130.77/89.84 |
% 130.77/89.84 | Instantiating formula (37) with all_0_4_4, xr, all_446_0_304, all_0_9_9 and discharging atoms sdtasdt0(all_0_4_4, xr) = all_446_0_304, sdtasdt0(all_0_4_4, xr) = all_0_9_9, yields:
% 130.77/89.84 | (1050) all_446_0_304 = all_0_9_9
% 130.77/89.84 |
% 130.77/89.84 | Instantiating formula (37) with xr, all_0_1_1, all_452_0_313, xk and discharging atoms sdtasdt0(xr, all_0_1_1) = all_452_0_313, yields:
% 130.77/89.84 | (1051) all_452_0_313 = xk | ~ (sdtasdt0(xr, all_0_1_1) = xk)
% 130.77/89.84 |
% 130.77/89.84 | Instantiating formula (11) with all_104_0_130, all_398_4_208, 0 and discharging atoms aNaturalNumber0(all_104_0_130) = all_398_4_208, aNaturalNumber0(all_104_0_130) = 0, yields:
% 130.77/89.84 | (1052) all_398_4_208 = 0
% 130.77/89.84 |
% 130.77/89.84 | Instantiating formula (11) with all_57_2_104, all_412_7_242, 0 and discharging atoms aNaturalNumber0(all_57_2_104) = all_412_7_242, aNaturalNumber0(all_57_2_104) = 0, yields:
% 130.77/89.85 | (1053) all_412_7_242 = 0
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_57_2_104, all_410_3_233, all_412_7_242 and discharging atoms aNaturalNumber0(all_57_2_104) = all_412_7_242, aNaturalNumber0(all_57_2_104) = all_410_3_233, yields:
% 130.77/89.85 | (1054) all_412_7_242 = all_410_3_233
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_57_2_104, all_392_6_193, all_412_7_242 and discharging atoms aNaturalNumber0(all_57_2_104) = all_412_7_242, aNaturalNumber0(all_57_2_104) = all_392_6_193, yields:
% 130.77/89.85 | (1055) all_412_7_242 = all_392_6_193
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_57_2_104, all_390_2_184, all_412_7_242 and discharging atoms aNaturalNumber0(all_57_2_104) = all_412_7_242, aNaturalNumber0(all_57_2_104) = all_390_2_184, yields:
% 130.77/89.85 | (1056) all_412_7_242 = all_390_2_184
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_57_2_104, all_388_2_179, all_410_3_233 and discharging atoms aNaturalNumber0(all_57_2_104) = all_410_3_233, aNaturalNumber0(all_57_2_104) = all_388_2_179, yields:
% 130.77/89.85 | (1057) all_410_3_233 = all_388_2_179
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_57_2_104, all_386_1_175, all_410_3_233 and discharging atoms aNaturalNumber0(all_57_2_104) = all_410_3_233, aNaturalNumber0(all_57_2_104) = all_386_1_175, yields:
% 130.77/89.85 | (1058) all_410_3_233 = all_386_1_175
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_56_2_101, all_430_1_273, 0 and discharging atoms aNaturalNumber0(all_56_2_101) = all_430_1_273, aNaturalNumber0(all_56_2_101) = 0, yields:
% 130.77/89.85 | (1059) all_430_1_273 = 0
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_56_2_101, all_424_3_264, all_430_1_273 and discharging atoms aNaturalNumber0(all_56_2_101) = all_430_1_273, aNaturalNumber0(all_56_2_101) = all_424_3_264, yields:
% 130.77/89.85 | (1060) all_430_1_273 = all_424_3_264
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_53_2_89, all_420_1_256, 0 and discharging atoms aNaturalNumber0(all_53_2_89) = all_420_1_256, aNaturalNumber0(all_53_2_89) = 0, yields:
% 130.77/89.85 | (1061) all_420_1_256 = 0
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_51_1_83, all_404_1_222, all_406_1_225 and discharging atoms aNaturalNumber0(all_51_1_83) = all_406_1_225, aNaturalNumber0(all_51_1_83) = all_404_1_222, yields:
% 130.77/89.85 | (1062) all_406_1_225 = all_404_1_222
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_51_1_83, all_402_0_218, all_406_1_225 and discharging atoms aNaturalNumber0(all_51_1_83) = all_406_1_225, aNaturalNumber0(all_51_1_83) = all_402_0_218, yields:
% 130.77/89.85 | (1063) all_406_1_225 = all_402_0_218
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_44_1_66, all_450_0_310, all_398_4_208 and discharging atoms aNaturalNumber0(all_44_1_66) = all_450_0_310, yields:
% 130.77/89.85 | (1064) all_450_0_310 = all_398_4_208 | ~ (aNaturalNumber0(all_44_1_66) = all_398_4_208)
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_44_1_66, all_422_1_259, all_450_0_310 and discharging atoms aNaturalNumber0(all_44_1_66) = all_450_0_310, aNaturalNumber0(all_44_1_66) = all_422_1_259, yields:
% 130.77/89.85 | (1065) all_450_0_310 = all_422_1_259
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_44_1_66, all_418_1_253, all_450_0_310 and discharging atoms aNaturalNumber0(all_44_1_66) = all_450_0_310, aNaturalNumber0(all_44_1_66) = all_418_1_253, yields:
% 130.77/89.85 | (1066) all_450_0_310 = all_418_1_253
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_42_0_62, all_455_0_319, 0 and discharging atoms aNaturalNumber0(all_42_0_62) = all_455_0_319, yields:
% 130.77/89.85 | (1067) all_455_0_319 = 0 | ~ (aNaturalNumber0(all_42_0_62) = 0)
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_0_1_1, all_455_0_319, all_20_1_25 and discharging atoms aNaturalNumber0(all_0_1_1) = all_20_1_25, yields:
% 130.77/89.85 | (1068) all_455_0_319 = all_20_1_25 | ~ (aNaturalNumber0(all_0_1_1) = all_455_0_319)
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_0_1_1, all_444_0_301, all_20_1_25 and discharging atoms aNaturalNumber0(all_0_1_1) = all_20_1_25, yields:
% 130.77/89.85 | (1069) all_444_0_301 = all_20_1_25 | ~ (aNaturalNumber0(all_0_1_1) = all_444_0_301)
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_34_0_47, all_444_0_301, all_410_3_233 and discharging atoms aNaturalNumber0(all_34_0_47) = all_444_0_301, yields:
% 130.77/89.85 | (1070) all_444_0_301 = all_410_3_233 | ~ (aNaturalNumber0(all_34_0_47) = all_410_3_233)
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_0_1_1, all_457_2_324, all_406_1_225 and discharging atoms aNaturalNumber0(all_0_1_1) = all_457_2_324, yields:
% 130.77/89.85 | (1071) all_457_2_324 = all_406_1_225 | ~ (aNaturalNumber0(all_0_1_1) = all_406_1_225)
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_0_1_1, all_455_2_321, all_457_2_324 and discharging atoms aNaturalNumber0(all_0_1_1) = all_457_2_324, aNaturalNumber0(all_0_1_1) = all_455_2_321, yields:
% 130.77/89.85 | (1072) all_457_2_324 = all_455_2_321
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_0_1_1, all_452_2_315, all_20_1_25 and discharging atoms aNaturalNumber0(all_0_1_1) = all_452_2_315, aNaturalNumber0(all_0_1_1) = all_20_1_25, yields:
% 130.77/89.85 | (1073) all_452_2_315 = all_20_1_25
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_0_1_1, all_452_2_315, all_418_1_253 and discharging atoms aNaturalNumber0(all_0_1_1) = all_452_2_315, yields:
% 130.77/89.85 | (1074) all_452_2_315 = all_418_1_253 | ~ (aNaturalNumber0(all_0_1_1) = all_418_1_253)
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_0_1_1, all_452_2_315, all_455_0_319 and discharging atoms aNaturalNumber0(all_0_1_1) = all_452_2_315, yields:
% 130.77/89.85 | (1075) all_455_0_319 = all_452_2_315 | ~ (aNaturalNumber0(all_0_1_1) = all_455_0_319)
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_0_1_1, all_452_2_315, all_455_2_321 and discharging atoms aNaturalNumber0(all_0_1_1) = all_455_2_321, aNaturalNumber0(all_0_1_1) = all_452_2_315, yields:
% 130.77/89.85 | (1076) all_455_2_321 = all_452_2_315
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_0_1_1, all_450_2_312, all_416_0_249 and discharging atoms aNaturalNumber0(all_0_1_1) = all_450_2_312, yields:
% 130.77/89.85 | (1077) all_450_2_312 = all_416_0_249 | ~ (aNaturalNumber0(all_0_1_1) = all_416_0_249)
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_0_1_1, all_450_2_312, all_457_2_324 and discharging atoms aNaturalNumber0(all_0_1_1) = all_457_2_324, aNaturalNumber0(all_0_1_1) = all_450_2_312, yields:
% 130.77/89.85 | (1078) all_457_2_324 = all_450_2_312
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_0_4_4, all_446_1_305, all_20_0_24 and discharging atoms aNaturalNumber0(all_0_4_4) = all_446_1_305, aNaturalNumber0(all_0_4_4) = all_20_0_24, yields:
% 130.77/89.85 | (1079) all_446_1_305 = all_20_0_24
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_0_4_4, all_446_1_305, all_455_0_319 and discharging atoms aNaturalNumber0(all_0_4_4) = all_446_1_305, yields:
% 130.77/89.85 | (1080) all_455_0_319 = all_446_1_305 | ~ (aNaturalNumber0(all_0_4_4) = all_455_0_319)
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_0_4_4, all_444_1_302, all_446_1_305 and discharging atoms aNaturalNumber0(all_0_4_4) = all_446_1_305, aNaturalNumber0(all_0_4_4) = all_444_1_302, yields:
% 130.77/89.85 | (1081) all_446_1_305 = all_444_1_302
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_0_9_9, all_492_2_359, 0 and discharging atoms aNaturalNumber0(all_0_9_9) = all_492_2_359, aNaturalNumber0(all_0_9_9) = 0, yields:
% 130.77/89.85 | (1082) all_492_2_359 = 0
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_0_9_9, all_492_2_359, all_418_0_252 and discharging atoms aNaturalNumber0(all_0_9_9) = all_492_2_359, yields:
% 130.77/89.85 | (1083) all_492_2_359 = all_418_0_252 | ~ (aNaturalNumber0(all_0_9_9) = all_418_0_252)
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with all_0_9_9, all_492_2_359, all_444_0_301 and discharging atoms aNaturalNumber0(all_0_9_9) = all_492_2_359, yields:
% 130.77/89.85 | (1084) all_492_2_359 = all_444_0_301 | ~ (aNaturalNumber0(all_0_9_9) = all_444_0_301)
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xr, all_444_2_303, all_452_1_314 and discharging atoms aNaturalNumber0(xr) = all_452_1_314, aNaturalNumber0(xr) = all_444_2_303, yields:
% 130.77/89.85 | (1085) all_452_1_314 = all_444_2_303
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xr, all_444_2_303, all_448_2_309 and discharging atoms aNaturalNumber0(xr) = all_448_2_309, aNaturalNumber0(xr) = all_444_2_303, yields:
% 130.77/89.85 | (1086) all_448_2_309 = all_444_2_303
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xr, all_444_2_303, all_446_2_306 and discharging atoms aNaturalNumber0(xr) = all_446_2_306, aNaturalNumber0(xr) = all_444_2_303, yields:
% 130.77/89.85 | (1087) all_446_2_306 = all_444_2_303
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xr, all_432_4_279, all_450_1_311 and discharging atoms aNaturalNumber0(xr) = all_450_1_311, aNaturalNumber0(xr) = all_432_4_279, yields:
% 130.77/89.85 | (1088) all_450_1_311 = all_432_4_279
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xr, all_430_2_274, all_432_4_279 and discharging atoms aNaturalNumber0(xr) = all_432_4_279, aNaturalNumber0(xr) = all_430_2_274, yields:
% 130.77/89.85 | (1089) all_432_4_279 = all_430_2_274
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xr, all_428_2_271, all_430_2_274 and discharging atoms aNaturalNumber0(xr) = all_430_2_274, aNaturalNumber0(xr) = all_428_2_271, yields:
% 130.77/89.85 | (1090) all_430_2_274 = all_428_2_271
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xr, all_426_1_267, all_446_2_306 and discharging atoms aNaturalNumber0(xr) = all_446_2_306, aNaturalNumber0(xr) = all_426_1_267, yields:
% 130.77/89.85 | (1091) all_446_2_306 = all_426_1_267
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xr, all_424_4_265, all_452_1_314 and discharging atoms aNaturalNumber0(xr) = all_452_1_314, aNaturalNumber0(xr) = all_424_4_265, yields:
% 130.77/89.85 | (1092) all_452_1_314 = all_424_4_265
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xr, all_416_1_250, all_452_1_314 and discharging atoms aNaturalNumber0(xr) = all_452_1_314, aNaturalNumber0(xr) = all_416_1_250, yields:
% 130.77/89.85 | (1093) all_452_1_314 = all_416_1_250
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xr, all_416_1_250, all_428_2_271 and discharging atoms aNaturalNumber0(xr) = all_428_2_271, aNaturalNumber0(xr) = all_416_1_250, yields:
% 130.77/89.85 | (1094) all_428_2_271 = all_416_1_250
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xr, all_396_3_202, 0 and discharging atoms aNaturalNumber0(xr) = all_396_3_202, aNaturalNumber0(xr) = 0, yields:
% 130.77/89.85 | (1095) all_396_3_202 = 0
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xr, all_396_3_202, all_478_1_348 and discharging atoms aNaturalNumber0(xr) = all_478_1_348, aNaturalNumber0(xr) = all_396_3_202, yields:
% 130.77/89.85 | (1096) all_478_1_348 = all_396_3_202
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xr, all_396_3_202, all_428_2_271 and discharging atoms aNaturalNumber0(xr) = all_428_2_271, aNaturalNumber0(xr) = all_396_3_202, yields:
% 130.77/89.85 | (1097) all_428_2_271 = all_396_3_202
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xr, all_396_4_203, all_478_1_348 and discharging atoms aNaturalNumber0(xr) = all_478_1_348, aNaturalNumber0(xr) = all_396_4_203, yields:
% 130.77/89.85 | (1098) all_478_1_348 = all_396_4_203
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xr, all_394_2_198, all_450_1_311 and discharging atoms aNaturalNumber0(xr) = all_450_1_311, aNaturalNumber0(xr) = all_394_2_198, yields:
% 130.77/89.85 | (1099) all_450_1_311 = all_394_2_198
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xr, all_392_8_195, all_448_2_309 and discharging atoms aNaturalNumber0(xr) = all_448_2_309, aNaturalNumber0(xr) = all_392_8_195, yields:
% 130.77/89.85 | (1100) all_448_2_309 = all_392_8_195
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xr, all_390_4_186, all_428_2_271 and discharging atoms aNaturalNumber0(xr) = all_428_2_271, aNaturalNumber0(xr) = all_390_4_186, yields:
% 130.77/89.85 | (1101) all_428_2_271 = all_390_4_186
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xk, all_468_1_341, 0 and discharging atoms aNaturalNumber0(xk) = all_468_1_341, aNaturalNumber0(xk) = 0, yields:
% 130.77/89.85 | (1102) all_468_1_341 = 0
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xk, all_412_8_243, all_468_1_341 and discharging atoms aNaturalNumber0(xk) = all_468_1_341, aNaturalNumber0(xk) = all_412_8_243, yields:
% 130.77/89.85 | (1103) all_468_1_341 = all_412_8_243
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xk, all_410_4_234, all_412_8_243 and discharging atoms aNaturalNumber0(xk) = all_412_8_243, aNaturalNumber0(xk) = all_410_4_234, yields:
% 130.77/89.85 | (1104) all_412_8_243 = all_410_4_234
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xk, all_388_3_180, all_450_0_310 and discharging atoms aNaturalNumber0(xk) = all_388_3_180, yields:
% 130.77/89.85 | (1105) all_450_0_310 = all_388_3_180 | ~ (aNaturalNumber0(xk) = all_450_0_310)
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xk, all_388_3_180, all_410_4_234 and discharging atoms aNaturalNumber0(xk) = all_410_4_234, aNaturalNumber0(xk) = all_388_3_180, yields:
% 130.77/89.85 | (1106) all_410_4_234 = all_388_3_180
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xk, all_386_2_176, all_388_3_180 and discharging atoms aNaturalNumber0(xk) = all_388_3_180, aNaturalNumber0(xk) = all_386_2_176, yields:
% 130.77/89.85 | (1107) all_388_3_180 = all_386_2_176
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xp, all_473_1_345, all_487_3_356 and discharging atoms aNaturalNumber0(xp) = all_487_3_356, aNaturalNumber0(xp) = all_473_1_345, yields:
% 130.77/89.85 | (1108) all_487_3_356 = all_473_1_345
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xp, all_468_3_343, all_473_1_345 and discharging atoms aNaturalNumber0(xp) = all_473_1_345, aNaturalNumber0(xp) = all_468_3_343, yields:
% 130.77/89.85 | (1109) all_473_1_345 = all_468_3_343
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xp, all_457_1_323, all_468_3_343 and discharging atoms aNaturalNumber0(xp) = all_468_3_343, aNaturalNumber0(xp) = all_457_1_323, yields:
% 130.77/89.85 | (1110) all_468_3_343 = all_457_1_323
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xp, all_455_1_320, all_492_3_360 and discharging atoms aNaturalNumber0(xp) = all_492_3_360, aNaturalNumber0(xp) = all_455_1_320, yields:
% 130.77/89.85 | (1111) all_492_3_360 = all_455_1_320
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xp, all_455_1_320, all_457_1_323 and discharging atoms aNaturalNumber0(xp) = all_457_1_323, aNaturalNumber0(xp) = all_455_1_320, yields:
% 130.77/89.85 | (1112) all_457_1_323 = all_455_1_320
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xp, all_422_2_260, all_455_1_320 and discharging atoms aNaturalNumber0(xp) = all_455_1_320, aNaturalNumber0(xp) = all_422_2_260, yields:
% 130.77/89.85 | (1113) all_455_1_320 = all_422_2_260
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xp, all_420_2_257, all_424_2_263 and discharging atoms aNaturalNumber0(xp) = all_424_2_263, aNaturalNumber0(xp) = all_420_2_257, yields:
% 130.77/89.85 | (1114) all_424_2_263 = all_420_2_257
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xp, all_418_2_254, all_487_3_356 and discharging atoms aNaturalNumber0(xp) = all_487_3_356, aNaturalNumber0(xp) = all_418_2_254, yields:
% 130.77/89.85 | (1115) all_487_3_356 = all_418_2_254
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xp, all_408_1_228, all_422_2_260 and discharging atoms aNaturalNumber0(xp) = all_422_2_260, aNaturalNumber0(xp) = all_408_1_228, yields:
% 130.77/89.85 | (1116) all_422_2_260 = all_408_1_228
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xp, all_402_1_219, 0 and discharging atoms aNaturalNumber0(xp) = all_402_1_219, aNaturalNumber0(xp) = 0, yields:
% 130.77/89.85 | (1117) all_402_1_219 = 0
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xp, all_402_1_219, all_422_2_260 and discharging atoms aNaturalNumber0(xp) = all_422_2_260, aNaturalNumber0(xp) = all_402_1_219, yields:
% 130.77/89.85 | (1118) all_422_2_260 = all_402_1_219
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xp, all_402_1_219, all_420_2_257 and discharging atoms aNaturalNumber0(xp) = all_420_2_257, aNaturalNumber0(xp) = all_402_1_219, yields:
% 130.77/89.85 | (1119) all_420_2_257 = all_402_1_219
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xp, all_400_6_215, all_492_3_360 and discharging atoms aNaturalNumber0(xp) = all_492_3_360, aNaturalNumber0(xp) = all_400_6_215, yields:
% 130.77/89.85 | (1120) all_492_3_360 = all_400_6_215
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xp, all_378_2_154, all_424_2_263 and discharging atoms aNaturalNumber0(xp) = all_424_2_263, aNaturalNumber0(xp) = all_378_2_154, yields:
% 130.77/89.85 | (1121) all_424_2_263 = all_378_2_154
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xm, all_440_2_291, all_492_1_358 and discharging atoms aNaturalNumber0(xm) = all_492_1_358, aNaturalNumber0(xm) = all_440_2_291, yields:
% 130.77/89.85 | (1122) all_492_1_358 = all_440_2_291
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xm, all_438_2_288, all_492_1_358 and discharging atoms aNaturalNumber0(xm) = all_492_1_358, aNaturalNumber0(xm) = all_438_2_288, yields:
% 130.77/89.85 | (1123) all_492_1_358 = all_438_2_288
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xm, all_432_2_277, all_440_2_291 and discharging atoms aNaturalNumber0(xm) = all_440_2_291, aNaturalNumber0(xm) = all_432_2_277, yields:
% 130.77/89.85 | (1124) all_440_2_291 = all_432_2_277
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xm, all_408_2_229, all_440_2_291 and discharging atoms aNaturalNumber0(xm) = all_440_2_291, aNaturalNumber0(xm) = all_408_2_229, yields:
% 130.77/89.85 | (1125) all_440_2_291 = all_408_2_229
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xm, all_408_2_229, all_416_2_251 and discharging atoms aNaturalNumber0(xm) = all_416_2_251, aNaturalNumber0(xm) = all_408_2_229, yields:
% 130.77/89.85 | (1126) all_416_2_251 = all_408_2_229
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xm, all_402_2_220, all_440_2_291 and discharging atoms aNaturalNumber0(xm) = all_440_2_291, aNaturalNumber0(xm) = all_402_2_220, yields:
% 130.77/89.85 | (1127) all_440_2_291 = all_402_2_220
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xm, all_400_8_217, all_416_2_251 and discharging atoms aNaturalNumber0(xm) = all_416_2_251, aNaturalNumber0(xm) = all_400_8_217, yields:
% 130.77/89.85 | (1128) all_416_2_251 = all_400_8_217
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xm, all_398_3_207, all_426_2_268 and discharging atoms aNaturalNumber0(xm) = all_426_2_268, aNaturalNumber0(xm) = all_398_3_207, yields:
% 130.77/89.85 | (1129) all_426_2_268 = all_398_3_207
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xm, all_398_3_207, all_416_2_251 and discharging atoms aNaturalNumber0(xm) = all_416_2_251, aNaturalNumber0(xm) = all_398_3_207, yields:
% 130.77/89.85 | (1130) all_416_2_251 = all_398_3_207
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xm, all_384_8_173, 0 and discharging atoms aNaturalNumber0(xm) = all_384_8_173, aNaturalNumber0(xm) = 0, yields:
% 130.77/89.85 | (1131) all_384_8_173 = 0
% 130.77/89.85 |
% 130.77/89.85 | Instantiating formula (11) with xm, all_384_8_173, all_426_2_268 and discharging atoms aNaturalNumber0(xm) = all_426_2_268, aNaturalNumber0(xm) = all_384_8_173, yields:
% 130.77/89.86 | (1132) all_426_2_268 = all_384_8_173
% 130.77/89.86 |
% 130.77/89.86 | Instantiating formula (11) with xm, all_382_4_164, all_426_2_268 and discharging atoms aNaturalNumber0(xm) = all_426_2_268, aNaturalNumber0(xm) = all_382_4_164, yields:
% 130.77/89.86 | (1133) all_426_2_268 = all_382_4_164
% 130.77/89.86 |
% 130.77/89.86 | Instantiating formula (11) with xm, all_380_2_159, all_408_2_229 and discharging atoms aNaturalNumber0(xm) = all_408_2_229, aNaturalNumber0(xm) = all_380_2_159, yields:
% 130.77/89.86 | (1134) all_408_2_229 = all_380_2_159
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1122,1123) yields a new equation:
% 130.77/89.86 | (1135) all_440_2_291 = all_438_2_288
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1135 yields:
% 130.77/89.86 | (1136) all_440_2_291 = all_438_2_288
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1111,1120) yields a new equation:
% 130.77/89.86 | (1137) all_455_1_320 = all_400_6_215
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1137 yields:
% 130.77/89.86 | (1138) all_455_1_320 = all_400_6_215
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1108,1115) yields a new equation:
% 130.77/89.86 | (1139) all_473_1_345 = all_418_2_254
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1139 yields:
% 130.77/89.86 | (1140) all_473_1_345 = all_418_2_254
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1096,1098) yields a new equation:
% 130.77/89.86 | (1141) all_396_3_202 = all_396_4_203
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1141 yields:
% 130.77/89.86 | (1142) all_396_3_202 = all_396_4_203
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1109,1140) yields a new equation:
% 130.77/89.86 | (1143) all_468_3_343 = all_418_2_254
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1143 yields:
% 130.77/89.86 | (1144) all_468_3_343 = all_418_2_254
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1103,1102) yields a new equation:
% 130.77/89.86 | (1145) all_412_8_243 = 0
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1145 yields:
% 130.77/89.86 | (1146) all_412_8_243 = 0
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1110,1144) yields a new equation:
% 130.77/89.86 | (1147) all_457_1_323 = all_418_2_254
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1147 yields:
% 130.77/89.86 | (1148) all_457_1_323 = all_418_2_254
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1112,1148) yields a new equation:
% 130.77/89.86 | (1149) all_455_1_320 = all_418_2_254
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1149 yields:
% 130.77/89.86 | (1150) all_455_1_320 = all_418_2_254
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1072,1078) yields a new equation:
% 130.77/89.86 | (1151) all_455_2_321 = all_450_2_312
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1151 yields:
% 130.77/89.86 | (1152) all_455_2_321 = all_450_2_312
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1138,1150) yields a new equation:
% 130.77/89.86 | (1153) all_418_2_254 = all_400_6_215
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1113,1150) yields a new equation:
% 130.77/89.86 | (1154) all_422_2_260 = all_418_2_254
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1154 yields:
% 130.77/89.86 | (1155) all_422_2_260 = all_418_2_254
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1076,1152) yields a new equation:
% 130.77/89.86 | (1156) all_452_2_315 = all_450_2_312
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1156 yields:
% 130.77/89.86 | (1157) all_452_2_315 = all_450_2_312
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1085,1092) yields a new equation:
% 130.77/89.86 | (1158) all_444_2_303 = all_424_4_265
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1158 yields:
% 130.77/89.86 | (1159) all_444_2_303 = all_424_4_265
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1093,1092) yields a new equation:
% 130.77/89.86 | (1160) all_424_4_265 = all_416_1_250
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1157,1073) yields a new equation:
% 130.77/89.86 | (1161) all_450_2_312 = all_20_1_25
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1161 yields:
% 130.77/89.86 | (1162) all_450_2_312 = all_20_1_25
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1065,1066) yields a new equation:
% 130.77/89.86 | (1163) all_422_1_259 = all_418_1_253
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1163 yields:
% 130.77/89.86 | (1164) all_422_1_259 = all_418_1_253
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1088,1099) yields a new equation:
% 130.77/89.86 | (1165) all_432_4_279 = all_394_2_198
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1165 yields:
% 130.77/89.86 | (1166) all_432_4_279 = all_394_2_198
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1086,1100) yields a new equation:
% 130.77/89.86 | (1167) all_444_2_303 = all_392_8_195
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1167 yields:
% 130.77/89.86 | (1168) all_444_2_303 = all_392_8_195
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1081,1079) yields a new equation:
% 130.77/89.86 | (1169) all_444_1_302 = all_20_0_24
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1169 yields:
% 130.77/89.86 | (1170) all_444_1_302 = all_20_0_24
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1087,1091) yields a new equation:
% 130.77/89.86 | (1171) all_444_2_303 = all_426_1_267
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1171 yields:
% 130.77/89.86 | (1172) all_444_2_303 = all_426_1_267
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1168,1172) yields a new equation:
% 130.77/89.86 | (1173) all_426_1_267 = all_392_8_195
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1159,1172) yields a new equation:
% 130.77/89.86 | (1174) all_426_1_267 = all_424_4_265
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1124,1136) yields a new equation:
% 130.77/89.86 | (1175) all_438_2_288 = all_432_2_277
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1125,1136) yields a new equation:
% 130.77/89.86 | (1176) all_438_2_288 = all_408_2_229
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1127,1136) yields a new equation:
% 130.77/89.86 | (1177) all_438_2_288 = all_402_2_220
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1176,1175) yields a new equation:
% 130.77/89.86 | (1178) all_432_2_277 = all_408_2_229
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1177,1175) yields a new equation:
% 130.77/89.86 | (1179) all_432_2_277 = all_402_2_220
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1178,1179) yields a new equation:
% 130.77/89.86 | (1180) all_408_2_229 = all_402_2_220
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1180 yields:
% 130.77/89.86 | (1181) all_408_2_229 = all_402_2_220
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1089,1166) yields a new equation:
% 130.77/89.86 | (1182) all_430_2_274 = all_394_2_198
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1182 yields:
% 130.77/89.86 | (1183) all_430_2_274 = all_394_2_198
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1060,1059) yields a new equation:
% 130.77/89.86 | (1184) all_424_3_264 = 0
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1184 yields:
% 130.77/89.86 | (1185) all_424_3_264 = 0
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1090,1183) yields a new equation:
% 130.77/89.86 | (1186) all_428_2_271 = all_394_2_198
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1186 yields:
% 130.77/89.86 | (1187) all_428_2_271 = all_394_2_198
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1101,1187) yields a new equation:
% 130.77/89.86 | (1188) all_394_2_198 = all_390_4_186
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1094,1187) yields a new equation:
% 130.77/89.86 | (1189) all_416_1_250 = all_394_2_198
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1189 yields:
% 130.77/89.86 | (1190) all_416_1_250 = all_394_2_198
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1097,1187) yields a new equation:
% 130.77/89.86 | (1191) all_396_3_202 = all_394_2_198
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1191 yields:
% 130.77/89.86 | (1192) all_396_3_202 = all_394_2_198
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1174,1173) yields a new equation:
% 130.77/89.86 | (1193) all_424_4_265 = all_392_8_195
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1193 yields:
% 130.77/89.86 | (1194) all_424_4_265 = all_392_8_195
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1129,1133) yields a new equation:
% 130.77/89.86 | (1195) all_398_3_207 = all_382_4_164
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1195 yields:
% 130.77/89.86 | (1196) all_398_3_207 = all_382_4_164
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1132,1133) yields a new equation:
% 130.77/89.86 | (1197) all_384_8_173 = all_382_4_164
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1197 yields:
% 130.77/89.86 | (1198) all_384_8_173 = all_382_4_164
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1114,1121) yields a new equation:
% 130.77/89.86 | (1199) all_420_2_257 = all_378_2_154
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1199 yields:
% 130.77/89.86 | (1200) all_420_2_257 = all_378_2_154
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1160,1194) yields a new equation:
% 130.77/89.86 | (1201) all_416_1_250 = all_392_8_195
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1201 yields:
% 130.77/89.86 | (1202) all_416_1_250 = all_392_8_195
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1118,1116) yields a new equation:
% 130.77/89.86 | (1203) all_408_1_228 = all_402_1_219
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1155,1116) yields a new equation:
% 130.77/89.86 | (1204) all_418_2_254 = all_408_1_228
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1204 yields:
% 130.77/89.86 | (1205) all_418_2_254 = all_408_1_228
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1119,1200) yields a new equation:
% 130.77/89.86 | (1206) all_402_1_219 = all_378_2_154
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1206 yields:
% 130.77/89.86 | (1207) all_402_1_219 = all_378_2_154
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1205,1153) yields a new equation:
% 130.77/89.86 | (1208) all_408_1_228 = all_400_6_215
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1208 yields:
% 130.77/89.86 | (1209) all_408_1_228 = all_400_6_215
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1190,1202) yields a new equation:
% 130.77/89.86 | (1210) all_394_2_198 = all_392_8_195
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1210 yields:
% 130.77/89.86 | (1211) all_394_2_198 = all_392_8_195
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1130,1128) yields a new equation:
% 130.77/89.86 | (1212) all_400_8_217 = all_398_3_207
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1126,1128) yields a new equation:
% 130.77/89.86 | (1213) all_408_2_229 = all_400_8_217
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1213 yields:
% 130.77/89.86 | (1214) all_408_2_229 = all_400_8_217
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1056,1055) yields a new equation:
% 130.77/89.86 | (1215) all_392_6_193 = all_390_2_184
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1053,1055) yields a new equation:
% 130.77/89.86 | (1216) all_392_6_193 = 0
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1054,1055) yields a new equation:
% 130.77/89.86 | (1217) all_410_3_233 = all_392_6_193
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1217 yields:
% 130.77/89.86 | (1218) all_410_3_233 = all_392_6_193
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1104,1146) yields a new equation:
% 130.77/89.86 | (1219) all_410_4_234 = 0
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1219 yields:
% 130.77/89.86 | (1220) all_410_4_234 = 0
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1058,1057) yields a new equation:
% 130.77/89.86 | (1221) all_388_2_179 = all_386_1_175
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1218,1057) yields a new equation:
% 130.77/89.86 | (1222) all_392_6_193 = all_388_2_179
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1222 yields:
% 130.77/89.86 | (1223) all_392_6_193 = all_388_2_179
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1106,1220) yields a new equation:
% 130.77/89.86 | (1224) all_388_3_180 = 0
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1224 yields:
% 130.77/89.86 | (1225) all_388_3_180 = 0
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1203,1209) yields a new equation:
% 130.77/89.86 | (1226) all_402_1_219 = all_400_6_215
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1226 yields:
% 130.77/89.86 | (1227) all_402_1_219 = all_400_6_215
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1214,1181) yields a new equation:
% 130.77/89.86 | (1228) all_402_2_220 = all_400_8_217
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1134,1181) yields a new equation:
% 130.77/89.86 | (1229) all_402_2_220 = all_380_2_159
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1063,1062) yields a new equation:
% 130.77/89.86 | (1230) all_404_1_222 = all_402_0_218
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1207,1227) yields a new equation:
% 130.77/89.86 | (1231) all_400_6_215 = all_378_2_154
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1117,1227) yields a new equation:
% 130.77/89.86 | (1232) all_400_6_215 = 0
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1228,1229) yields a new equation:
% 130.77/89.86 | (1233) all_400_8_217 = all_380_2_159
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1233 yields:
% 130.77/89.86 | (1234) all_400_8_217 = all_380_2_159
% 130.77/89.86 |
% 130.77/89.86 | Combining equations (1231,1232) yields a new equation:
% 130.77/89.86 | (1235) all_378_2_154 = 0
% 130.77/89.86 |
% 130.77/89.86 | Simplifying 1235 yields:
% 130.77/89.86 | (1236) all_378_2_154 = 0
% 130.77/89.86 |
% 130.77/89.87 | Combining equations (1212,1234) yields a new equation:
% 130.77/89.87 | (1237) all_398_3_207 = all_380_2_159
% 130.77/89.87 |
% 130.77/89.87 | Simplifying 1237 yields:
% 130.77/89.87 | (1238) all_398_3_207 = all_380_2_159
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1196,1238) yields a new equation:
% 130.77/89.87 | (1239) all_382_4_164 = all_380_2_159
% 130.77/89.87 |
% 130.77/89.87 | Simplifying 1239 yields:
% 130.77/89.87 | (1240) all_382_4_164 = all_380_2_159
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1095,1142) yields a new equation:
% 130.77/89.87 | (1241) all_396_4_203 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1192,1142) yields a new equation:
% 130.77/89.87 | (1242) all_396_4_203 = all_394_2_198
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1242,1241) yields a new equation:
% 130.77/89.87 | (1243) all_394_2_198 = 0
% 130.77/89.87 |
% 130.77/89.87 | Simplifying 1243 yields:
% 130.77/89.87 | (1244) all_394_2_198 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1244,1211) yields a new equation:
% 130.77/89.87 | (1245) all_392_8_195 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1188,1211) yields a new equation:
% 130.77/89.87 | (1246) all_392_8_195 = all_390_4_186
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1216,1215) yields a new equation:
% 130.77/89.87 | (1247) all_390_2_184 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1223,1215) yields a new equation:
% 130.77/89.87 | (1248) all_390_2_184 = all_388_2_179
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1246,1245) yields a new equation:
% 130.77/89.87 | (1249) all_390_4_186 = 0
% 130.77/89.87 |
% 130.77/89.87 | Simplifying 1249 yields:
% 130.77/89.87 | (1250) all_390_4_186 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1248,1247) yields a new equation:
% 130.77/89.87 | (1251) all_388_2_179 = 0
% 130.77/89.87 |
% 130.77/89.87 | Simplifying 1251 yields:
% 130.77/89.87 | (1252) all_388_2_179 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1252,1221) yields a new equation:
% 130.77/89.87 | (1253) all_386_1_175 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1107,1225) yields a new equation:
% 130.77/89.87 | (1254) all_386_2_176 = 0
% 130.77/89.87 |
% 130.77/89.87 | Simplifying 1254 yields:
% 130.77/89.87 | (1255) all_386_2_176 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1198,1131) yields a new equation:
% 130.77/89.87 | (1256) all_382_4_164 = 0
% 130.77/89.87 |
% 130.77/89.87 | Simplifying 1256 yields:
% 130.77/89.87 | (1257) all_382_4_164 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1257,1240) yields a new equation:
% 130.77/89.87 | (1258) all_380_2_159 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1253,1221) yields a new equation:
% 130.77/89.87 | (1252) all_388_2_179 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1245,1211) yields a new equation:
% 130.77/89.87 | (1244) all_394_2_198 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1258,1234) yields a new equation:
% 130.77/89.87 | (1261) all_400_8_217 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1258,1229) yields a new equation:
% 130.77/89.87 | (1262) all_402_2_220 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1232,1227) yields a new equation:
% 130.77/89.87 | (1117) all_402_1_219 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1230,1062) yields a new equation:
% 130.77/89.87 | (1063) all_406_1_225 = all_402_0_218
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1252,1057) yields a new equation:
% 130.77/89.87 | (1265) all_410_3_233 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1261,1128) yields a new equation:
% 130.77/89.87 | (1266) all_416_2_251 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1245,1202) yields a new equation:
% 130.77/89.87 | (1267) all_416_1_250 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1245,1194) yields a new equation:
% 130.77/89.87 | (1268) all_424_4_265 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1245,1173) yields a new equation:
% 130.77/89.87 | (1269) all_426_1_267 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1244,1183) yields a new equation:
% 130.77/89.87 | (1270) all_430_2_274 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1269,1091) yields a new equation:
% 130.77/89.87 | (1271) all_446_2_306 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1268,1092) yields a new equation:
% 130.77/89.87 | (1272) all_452_1_314 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1162,1078) yields a new equation:
% 130.77/89.87 | (1273) all_457_2_324 = all_20_1_25
% 130.77/89.87 |
% 130.77/89.87 | From (1185) and (920) follows:
% 130.77/89.87 | (622) aNaturalNumber0(all_56_2_101) = 0
% 130.77/89.87 |
% 130.77/89.87 | From (1061) and (911) follows:
% 130.77/89.87 | (536) aNaturalNumber0(all_53_2_89) = 0
% 130.77/89.87 |
% 130.77/89.87 | From (1164) and (916) follows:
% 130.77/89.87 | (906) aNaturalNumber0(all_44_1_66) = all_418_1_253
% 130.77/89.87 |
% 130.77/89.87 | From (1162) and (975) follows:
% 130.77/89.87 | (165) aNaturalNumber0(all_0_1_1) = all_20_1_25
% 130.77/89.87 |
% 130.77/89.87 | From (1170) and (960) follows:
% 130.77/89.87 | (166) aNaturalNumber0(all_0_4_4) = all_20_0_24
% 130.77/89.87 |
% 130.77/89.87 | From (1250) and (818) follows:
% 130.77/89.87 | (23) aNaturalNumber0(xr) = 0
% 130.77/89.87 |
% 130.77/89.87 | From (1255) and (804) follows:
% 130.77/89.87 | (549) aNaturalNumber0(xk) = 0
% 130.77/89.87 |
% 130.77/89.87 | From (1236) and (772) follows:
% 130.77/89.87 | (13) aNaturalNumber0(xp) = 0
% 130.77/89.87 |
% 130.77/89.87 +-Applying beta-rule and splitting (739), into two cases.
% 130.77/89.87 |-Branch one:
% 130.77/89.87 | (301) xp = sz00
% 130.77/89.87 |
% 130.77/89.87 | Equations (301) can reduce 102 to:
% 130.77/89.87 | (264) $false
% 130.77/89.87 |
% 130.77/89.87 |-The branch is then unsatisfiable
% 130.77/89.87 |-Branch two:
% 130.77/89.87 | (102) ~ (xp = sz00)
% 130.77/89.87 | (1285) all_53_2_89 = xk | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_53_2_89) = v0) | (doDivides0(xp, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 130.77/89.87 |
% 130.77/89.87 +-Applying beta-rule and splitting (1285), into two cases.
% 130.77/89.87 |-Branch one:
% 130.77/89.87 | (1286) all_53_2_89 = xk
% 130.77/89.87 |
% 130.77/89.87 | From (1286) and (536) follows:
% 130.77/89.87 | (549) aNaturalNumber0(xk) = 0
% 130.77/89.87 |
% 130.77/89.87 +-Applying beta-rule and splitting (729), into two cases.
% 130.77/89.87 |-Branch one:
% 130.77/89.87 | (296) xr = sz00
% 130.77/89.87 |
% 130.77/89.87 | Equations (296) can reduce 101 to:
% 130.77/89.87 | (264) $false
% 130.77/89.87 |
% 130.77/89.87 |-The branch is then unsatisfiable
% 130.77/89.87 |-Branch two:
% 130.77/89.87 | (101) ~ (xr = sz00)
% 130.77/89.87 | (1291) all_56_2_101 = all_0_1_1 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_56_2_101) = v0) | (doDivides0(xr, xk) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 130.77/89.87 |
% 130.77/89.87 +-Applying beta-rule and splitting (1291), into two cases.
% 130.77/89.87 |-Branch one:
% 130.77/89.87 | (1292) all_56_2_101 = all_0_1_1
% 130.77/89.87 |
% 130.77/89.87 | From (1292) and (937) follows:
% 130.77/89.87 | (1293) sdtasdt0(all_0_1_1, xr) = all_430_0_272
% 130.77/89.87 |
% 130.77/89.87 | From (1292) and (621) follows:
% 130.77/89.87 | (1294) sdtasdt0(xr, all_0_1_1) = xk
% 130.77/89.87 |
% 130.77/89.87 | From (1292) and (622) follows:
% 130.77/89.87 | (1295) aNaturalNumber0(all_0_1_1) = 0
% 130.77/89.87 |
% 130.77/89.87 +-Applying beta-rule and splitting (333), into two cases.
% 130.77/89.87 |-Branch one:
% 130.77/89.87 | (1296) ~ (aNaturalNumber0(all_0_1_1) = 0)
% 130.77/89.87 |
% 130.77/89.87 | Using (1295) and (1296) yields:
% 130.77/89.87 | (543) $false
% 130.77/89.87 |
% 130.77/89.87 |-The branch is then unsatisfiable
% 130.77/89.87 |-Branch two:
% 130.77/89.87 | (1295) aNaturalNumber0(all_0_1_1) = 0
% 130.77/89.87 | (1299) all_42_1_63 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (416,1299) yields a new equation:
% 130.77/89.87 | (1300) all_20_1_25 = 0
% 130.77/89.87 |
% 130.77/89.87 | Simplifying 1300 yields:
% 130.77/89.87 | (1301) all_20_1_25 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1301,335) yields a new equation:
% 130.77/89.87 | (1302) all_44_3_68 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1301,1162) yields a new equation:
% 130.77/89.87 | (1303) all_450_2_312 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1301,1073) yields a new equation:
% 130.77/89.87 | (1304) all_452_2_315 = 0
% 130.77/89.87 |
% 130.77/89.87 | Combining equations (1301,1273) yields a new equation:
% 130.77/89.87 | (1305) all_457_2_324 = 0
% 130.77/89.87 |
% 130.77/89.87 | From (1301) and (165) follows:
% 130.77/89.87 | (1295) aNaturalNumber0(all_0_1_1) = 0
% 130.77/89.87 |
% 130.77/89.87 +-Applying beta-rule and splitting (295), into two cases.
% 130.77/89.87 |-Branch one:
% 130.77/89.87 | (1307) ~ (all_80_1_122 = 0) & aNaturalNumber0(all_0_1_1) = all_80_1_122
% 130.77/89.87 |
% 130.77/89.87 | Applying alpha-rule on (1307) yields:
% 130.77/89.87 | (1308) ~ (all_80_1_122 = 0)
% 130.77/89.87 | (1309) aNaturalNumber0(all_0_1_1) = all_80_1_122
% 130.77/89.87 |
% 130.77/89.87 +-Applying beta-rule and splitting (1077), into two cases.
% 130.77/89.87 |-Branch one:
% 130.77/89.87 | (1310) ~ (aNaturalNumber0(all_0_1_1) = all_416_0_249)
% 130.77/89.87 |
% 130.77/89.87 +-Applying beta-rule and splitting (1069), into two cases.
% 130.77/89.87 |-Branch one:
% 130.77/89.87 | (1311) ~ (aNaturalNumber0(all_0_1_1) = all_444_0_301)
% 130.77/89.87 |
% 130.77/89.87 +-Applying beta-rule and splitting (227), into two cases.
% 130.77/89.87 |-Branch one:
% 130.77/89.87 | (1312) ~ (all_44_2_67 = 0)
% 130.77/89.87 |
% 130.77/89.87 | Equations (467) can reduce 1312 to:
% 130.77/89.87 | (264) $false
% 130.77/89.87 |
% 130.77/89.87 |-The branch is then unsatisfiable
% 130.77/89.87 |-Branch two:
% 130.77/89.87 | (467) all_44_2_67 = 0
% 130.77/89.87 | (1315) ~ (all_44_3_68 = 0) | ~ (all_44_4_69 = 0) | all_44_0_65 = all_0_9_9
% 130.77/89.87 |
% 130.77/89.87 +-Applying beta-rule and splitting (1315), into two cases.
% 130.77/89.87 |-Branch one:
% 130.77/89.87 | (1316) ~ (all_44_3_68 = 0)
% 130.77/89.87 |
% 130.77/89.87 | Equations (1302) can reduce 1316 to:
% 130.77/89.87 | (264) $false
% 130.77/89.87 |
% 130.77/89.87 |-The branch is then unsatisfiable
% 130.77/89.87 |-Branch two:
% 130.77/89.87 | (1302) all_44_3_68 = 0
% 130.77/89.87 | (1319) ~ (all_44_4_69 = 0) | all_44_0_65 = all_0_9_9
% 130.77/89.87 |
% 130.77/89.87 +-Applying beta-rule and splitting (1319), into two cases.
% 130.77/89.87 |-Branch one:
% 130.77/89.87 | (1320) ~ (all_44_4_69 = 0)
% 130.77/89.87 |
% 130.77/89.87 | Equations (397) can reduce 1320 to:
% 130.77/89.87 | (264) $false
% 130.77/89.87 |
% 130.77/89.87 |-The branch is then unsatisfiable
% 130.77/89.87 |-Branch two:
% 130.77/89.87 | (397) all_44_4_69 = 0
% 130.77/89.87 | (1323) all_44_0_65 = all_0_9_9
% 130.77/89.87 |
% 130.77/89.87 | From (1323) and (905) follows:
% 130.77/89.87 | (1324) aNaturalNumber0(all_0_9_9) = all_418_0_252
% 130.77/89.87 |
% 130.77/89.87 +-Applying beta-rule and splitting (1083), into two cases.
% 130.77/89.87 |-Branch one:
% 130.77/89.87 | (1325) ~ (aNaturalNumber0(all_0_9_9) = all_418_0_252)
% 130.77/89.87 |
% 130.77/89.87 | Using (1324) and (1325) yields:
% 130.77/89.87 | (543) $false
% 130.77/89.87 |
% 130.77/89.87 |-The branch is then unsatisfiable
% 130.77/89.87 |-Branch two:
% 130.77/89.87 | (1324) aNaturalNumber0(all_0_9_9) = all_418_0_252
% 130.77/89.88 | (1328) all_492_2_359 = all_418_0_252
% 130.77/89.88 |
% 130.77/89.88 | Combining equations (1328,1082) yields a new equation:
% 130.77/89.88 | (1329) all_418_0_252 = 0
% 130.77/89.88 |
% 130.77/89.88 | Simplifying 1329 yields:
% 130.77/89.88 | (1330) all_418_0_252 = 0
% 130.77/89.88 |
% 130.77/89.88 | From (1330) and (1324) follows:
% 130.77/89.88 | (513) aNaturalNumber0(all_0_9_9) = 0
% 130.77/89.88 |
% 130.77/89.88 +-Applying beta-rule and splitting (1075), into two cases.
% 130.77/89.88 |-Branch one:
% 130.77/89.88 | (1332) ~ (aNaturalNumber0(all_0_1_1) = all_455_0_319)
% 130.77/89.88 |
% 130.77/89.88 +-Applying beta-rule and splitting (221), into two cases.
% 130.77/89.88 |-Branch one:
% 130.77/89.88 | (1333) ~ (all_42_1_63 = 0)
% 130.77/89.88 |
% 130.77/89.88 | Equations (1299) can reduce 1333 to:
% 130.77/89.88 | (264) $false
% 130.77/89.88 |
% 130.77/89.88 |-The branch is then unsatisfiable
% 130.77/89.88 |-Branch two:
% 130.77/89.88 | (1299) all_42_1_63 = 0
% 130.77/89.88 | (1336) ~ (all_42_2_64 = 0) | all_42_0_62 = all_0_4_4
% 130.77/89.88 |
% 130.77/89.88 +-Applying beta-rule and splitting (1336), into two cases.
% 130.77/89.88 |-Branch one:
% 130.77/89.88 | (1337) ~ (all_42_2_64 = 0)
% 130.77/89.88 |
% 130.77/89.88 | Equations (465) can reduce 1337 to:
% 130.77/89.88 | (264) $false
% 130.77/89.88 |
% 130.77/89.88 |-The branch is then unsatisfiable
% 130.77/89.88 |-Branch two:
% 130.77/89.88 | (465) all_42_2_64 = 0
% 130.77/89.88 | (1340) all_42_0_62 = all_0_4_4
% 130.77/89.88 |
% 130.77/89.88 | From (1340) and (984) follows:
% 130.77/89.88 | (1341) aNaturalNumber0(all_0_4_4) = all_455_0_319
% 130.77/89.88 |
% 130.77/89.88 +-Applying beta-rule and splitting (1080), into two cases.
% 130.77/89.88 |-Branch one:
% 130.77/89.88 | (1342) ~ (aNaturalNumber0(all_0_4_4) = all_455_0_319)
% 130.77/89.88 |
% 130.77/89.88 | Using (1341) and (1342) yields:
% 130.77/89.88 | (543) $false
% 130.77/89.88 |
% 130.77/89.88 |-The branch is then unsatisfiable
% 130.77/89.88 |-Branch two:
% 130.77/89.88 | (1341) aNaturalNumber0(all_0_4_4) = all_455_0_319
% 130.77/89.88 | (1345) all_455_0_319 = all_446_1_305
% 130.77/89.88 |
% 130.77/89.88 | Combining equations (1079,1345) yields a new equation:
% 130.77/89.88 | (1346) all_455_0_319 = all_20_0_24
% 130.77/89.88 |
% 130.77/89.88 | From (1346) and (1332) follows:
% 130.77/89.88 | (1347) ~ (aNaturalNumber0(all_0_1_1) = all_20_0_24)
% 130.77/89.88 |
% 130.77/89.88 +-Applying beta-rule and splitting (168), into two cases.
% 130.77/89.88 |-Branch one:
% 130.77/89.88 | (1348) ~ (all_20_1_25 = 0)
% 130.77/89.88 |
% 130.77/89.88 | Equations (1301) can reduce 1348 to:
% 130.77/89.88 | (264) $false
% 130.77/89.88 |
% 130.77/89.88 |-The branch is then unsatisfiable
% 130.77/89.88 |-Branch two:
% 130.77/89.88 | (1301) all_20_1_25 = 0
% 130.77/89.88 | (1351) ~ (all_20_2_26 = 0) | all_20_0_24 = 0
% 130.77/89.88 |
% 130.77/89.88 +-Applying beta-rule and splitting (1351), into two cases.
% 130.77/89.88 |-Branch one:
% 130.77/89.88 | (1352) ~ (all_20_2_26 = 0)
% 130.77/89.88 |
% 130.77/89.88 | Equations (444) can reduce 1352 to:
% 130.77/89.88 | (264) $false
% 130.77/89.88 |
% 130.77/89.88 |-The branch is then unsatisfiable
% 130.77/89.88 |-Branch two:
% 130.77/89.88 | (444) all_20_2_26 = 0
% 130.77/89.88 | (1355) all_20_0_24 = 0
% 130.77/89.88 |
% 130.77/89.88 | From (1355) and (1347) follows:
% 130.77/89.88 | (1296) ~ (aNaturalNumber0(all_0_1_1) = 0)
% 130.77/89.88 |
% 130.77/89.88 | Using (1295) and (1296) yields:
% 130.77/89.88 | (543) $false
% 130.77/89.88 |
% 130.77/89.88 |-The branch is then unsatisfiable
% 130.77/89.88 |-Branch two:
% 130.77/89.88 | (1358) aNaturalNumber0(all_0_1_1) = all_455_0_319
% 130.77/89.88 | (1359) all_455_0_319 = all_452_2_315
% 130.77/89.88 |
% 130.77/89.88 | Combining equations (1304,1359) yields a new equation:
% 130.77/89.88 | (1360) all_455_0_319 = 0
% 130.77/89.88 |
% 130.77/89.88 | From (1360) and (1358) follows:
% 130.77/89.88 | (1295) aNaturalNumber0(all_0_1_1) = 0
% 130.77/89.88 |
% 130.77/89.88 +-Applying beta-rule and splitting (168), into two cases.
% 130.77/89.88 |-Branch one:
% 130.77/89.88 | (1348) ~ (all_20_1_25 = 0)
% 130.77/89.88 |
% 130.77/89.88 | Equations (1301) can reduce 1348 to:
% 130.77/89.88 | (264) $false
% 130.77/89.88 |
% 130.77/89.88 |-The branch is then unsatisfiable
% 130.77/89.88 |-Branch two:
% 130.77/89.88 | (1301) all_20_1_25 = 0
% 130.77/89.88 | (1351) ~ (all_20_2_26 = 0) | all_20_0_24 = 0
% 130.77/89.88 |
% 130.77/89.88 +-Applying beta-rule and splitting (1351), into two cases.
% 130.77/89.88 |-Branch one:
% 130.77/89.88 | (1352) ~ (all_20_2_26 = 0)
% 130.77/89.88 |
% 130.77/89.88 | Equations (444) can reduce 1352 to:
% 130.77/89.88 | (264) $false
% 130.77/89.88 |
% 130.77/89.88 |-The branch is then unsatisfiable
% 130.77/89.88 |-Branch two:
% 130.77/89.88 | (444) all_20_2_26 = 0
% 130.77/89.88 | (1355) all_20_0_24 = 0
% 130.77/89.88 |
% 130.77/89.88 | Combining equations (1355,410) yields a new equation:
% 130.77/89.88 | (1370) all_36_2_52 = 0
% 130.77/89.88 |
% 130.77/89.88 +-Applying beta-rule and splitting (210), into two cases.
% 130.77/89.88 |-Branch one:
% 130.77/89.88 | (1371) ~ (all_36_1_51 = 0)
% 130.77/89.88 |
% 130.77/89.88 | Equations (346) can reduce 1371 to:
% 130.77/89.88 | (264) $false
% 130.77/89.88 |
% 130.77/89.88 |-The branch is then unsatisfiable
% 130.77/89.88 |-Branch two:
% 130.77/89.88 | (346) all_36_1_51 = 0
% 130.77/89.88 | (1374) ~ (all_36_2_52 = 0) | all_36_0_50 = all_0_9_9
% 130.77/89.88 |
% 130.77/89.88 +-Applying beta-rule and splitting (1374), into two cases.
% 130.77/89.88 |-Branch one:
% 130.77/89.88 | (1375) ~ (all_36_2_52 = 0)
% 130.77/89.88 |
% 130.77/89.88 | Equations (1370) can reduce 1375 to:
% 130.77/89.88 | (264) $false
% 130.77/89.88 |
% 130.77/89.88 |-The branch is then unsatisfiable
% 130.77/89.88 |-Branch two:
% 130.77/89.88 | (1370) all_36_2_52 = 0
% 130.77/89.88 | (1378) all_36_0_50 = all_0_9_9
% 130.77/89.88 |
% 130.77/89.88 | Combining equations (674,1378) yields a new equation:
% 130.77/89.88 | (1379) all_34_0_47 = all_0_9_9
% 130.77/89.88 |
% 130.77/89.88 | Simplifying 1379 yields:
% 130.77/89.88 | (1380) all_34_0_47 = all_0_9_9
% 130.77/89.88 |
% 130.77/89.88 +-Applying beta-rule and splitting (1070), into two cases.
% 130.77/89.88 |-Branch one:
% 130.77/89.88 | (1381) ~ (aNaturalNumber0(all_34_0_47) = all_410_3_233)
% 130.77/89.88 |
% 130.77/89.88 | From (1380)(1265) and (1381) follows:
% 130.77/89.88 | (1382) ~ (aNaturalNumber0(all_0_9_9) = 0)
% 130.77/89.88 |
% 130.77/89.88 | Using (513) and (1382) yields:
% 130.77/89.88 | (543) $false
% 130.77/89.88 |
% 130.77/89.88 |-The branch is then unsatisfiable
% 130.77/89.88 |-Branch two:
% 130.77/89.88 | (1384) aNaturalNumber0(all_34_0_47) = all_410_3_233
% 130.77/89.88 | (1385) all_444_0_301 = all_410_3_233
% 130.77/89.88 |
% 130.77/89.88 | Combining equations (1265,1385) yields a new equation:
% 130.77/89.88 | (1386) all_444_0_301 = 0
% 130.77/89.88 |
% 130.77/89.88 | From (1386) and (1311) follows:
% 130.77/89.88 | (1296) ~ (aNaturalNumber0(all_0_1_1) = 0)
% 130.77/89.88 |
% 130.77/89.88 | Using (1295) and (1296) yields:
% 130.77/89.88 | (543) $false
% 130.77/89.88 |
% 130.77/89.88 |-The branch is then unsatisfiable
% 130.77/89.88 |-Branch two:
% 130.77/89.88 | (1389) aNaturalNumber0(all_0_1_1) = all_444_0_301
% 130.77/89.88 | (1390) all_444_0_301 = all_20_1_25
% 130.77/89.88 |
% 130.77/89.88 | Combining equations (1301,1390) yields a new equation:
% 130.77/89.88 | (1386) all_444_0_301 = 0
% 130.77/89.88 |
% 130.77/89.88 | From (1386) and (1389) follows:
% 130.77/89.88 | (1295) aNaturalNumber0(all_0_1_1) = 0
% 130.77/89.88 |
% 130.77/89.88 +-Applying beta-rule and splitting (903), into two cases.
% 130.77/89.88 |-Branch one:
% 130.77/89.88 | (1393) ~ (all_416_1_250 = 0)
% 130.77/89.88 |
% 130.77/89.88 | Equations (1267) can reduce 1393 to:
% 130.77/89.88 | (264) $false
% 130.77/89.88 |
% 130.77/89.88 |-The branch is then unsatisfiable
% 130.77/89.88 |-Branch two:
% 130.77/89.88 | (1267) all_416_1_250 = 0
% 130.77/89.88 | (1396) ~ (all_416_2_251 = 0) | all_416_0_249 = 0
% 130.77/89.88 |
% 130.77/89.88 +-Applying beta-rule and splitting (1396), into two cases.
% 130.77/89.88 |-Branch one:
% 130.77/89.88 | (1397) ~ (all_416_2_251 = 0)
% 130.77/89.88 |
% 130.77/89.88 | Equations (1266) can reduce 1397 to:
% 130.77/89.88 | (264) $false
% 130.77/89.88 |
% 130.77/89.88 |-The branch is then unsatisfiable
% 130.77/89.88 |-Branch two:
% 130.77/89.88 | (1266) all_416_2_251 = 0
% 130.77/89.88 | (1400) all_416_0_249 = 0
% 130.77/89.88 |
% 130.77/89.88 | From (1400) and (1310) follows:
% 130.77/89.88 | (1296) ~ (aNaturalNumber0(all_0_1_1) = 0)
% 130.77/89.88 |
% 130.77/89.88 | Using (1295) and (1296) yields:
% 130.77/89.88 | (543) $false
% 130.77/89.88 |
% 130.77/89.88 |-The branch is then unsatisfiable
% 130.77/89.88 |-Branch two:
% 130.77/89.88 | (1403) aNaturalNumber0(all_0_1_1) = all_416_0_249
% 130.77/89.88 | (1404) all_450_2_312 = all_416_0_249
% 130.77/89.88 |
% 130.77/89.88 | Combining equations (1303,1404) yields a new equation:
% 130.77/89.88 | (1400) all_416_0_249 = 0
% 130.77/89.88 |
% 130.77/89.88 | From (1400) and (1403) follows:
% 130.77/89.88 | (1295) aNaturalNumber0(all_0_1_1) = 0
% 130.77/89.88 |
% 130.77/89.88 +-Applying beta-rule and splitting (1069), into two cases.
% 130.77/89.88 |-Branch one:
% 130.77/89.88 | (1311) ~ (aNaturalNumber0(all_0_1_1) = all_444_0_301)
% 130.77/89.88 |
% 130.77/89.88 +-Applying beta-rule and splitting (733), into two cases.
% 130.77/89.88 |-Branch one:
% 130.77/89.88 | (296) xr = sz00
% 130.77/89.88 |
% 130.77/89.88 | Equations (296) can reduce 101 to:
% 130.77/89.88 | (264) $false
% 130.77/89.88 |
% 130.77/89.88 |-The branch is then unsatisfiable
% 130.77/89.88 |-Branch two:
% 130.77/89.88 | (101) ~ (xr = sz00)
% 130.77/89.88 | (1411) all_34_0_47 = all_0_9_9 | ? [v0] : ? [v1] : ? [v2] : (doDivides0(xr, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 130.77/89.88 |
% 130.77/89.88 +-Applying beta-rule and splitting (1411), into two cases.
% 130.77/89.88 |-Branch one:
% 130.77/89.88 | (1380) all_34_0_47 = all_0_9_9
% 130.77/89.88 |
% 130.77/89.88 | From (1380) and (959) follows:
% 130.77/89.88 | (1413) aNaturalNumber0(all_0_9_9) = all_444_0_301
% 130.77/89.88 |
% 130.77/89.88 +-Applying beta-rule and splitting (1084), into two cases.
% 130.77/89.88 |-Branch one:
% 130.77/89.88 | (1414) ~ (aNaturalNumber0(all_0_9_9) = all_444_0_301)
% 130.77/89.88 |
% 130.77/89.88 | Using (1413) and (1414) yields:
% 130.77/89.88 | (543) $false
% 130.77/89.88 |
% 130.77/89.88 |-The branch is then unsatisfiable
% 130.77/89.88 |-Branch two:
% 130.77/89.89 | (1413) aNaturalNumber0(all_0_9_9) = all_444_0_301
% 130.77/89.89 | (1417) all_492_2_359 = all_444_0_301
% 130.77/89.89 |
% 130.77/89.89 | Combining equations (1417,1082) yields a new equation:
% 130.77/89.89 | (1418) all_444_0_301 = 0
% 130.77/89.89 |
% 130.77/89.89 | Simplifying 1418 yields:
% 130.77/89.89 | (1386) all_444_0_301 = 0
% 130.77/89.89 |
% 130.77/89.89 | From (1386) and (1311) follows:
% 130.77/89.89 | (1296) ~ (aNaturalNumber0(all_0_1_1) = 0)
% 130.77/89.89 |
% 130.77/89.89 | Using (1295) and (1296) yields:
% 130.77/89.89 | (543) $false
% 130.77/89.89 |
% 130.77/89.89 |-The branch is then unsatisfiable
% 130.77/89.89 |-Branch two:
% 130.77/89.89 | (1422) ~ (all_34_0_47 = all_0_9_9)
% 130.77/89.89 | (1423) ? [v0] : ? [v1] : ? [v2] : (doDivides0(xr, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 130.77/89.89 |
% 130.77/89.89 +-Applying beta-rule and splitting (967), into two cases.
% 130.77/89.89 |-Branch one:
% 130.77/89.89 | (1424) ~ (all_446_1_305 = 0)
% 130.77/89.89 |
% 130.77/89.89 | Equations (1079) can reduce 1424 to:
% 130.77/89.89 | (1425) ~ (all_20_0_24 = 0)
% 130.77/89.89 |
% 130.77/89.89 +-Applying beta-rule and splitting (168), into two cases.
% 130.77/89.89 |-Branch one:
% 130.77/89.89 | (1348) ~ (all_20_1_25 = 0)
% 130.77/89.89 |
% 130.77/89.89 | Equations (1301) can reduce 1348 to:
% 130.77/89.89 | (264) $false
% 130.77/89.89 |
% 130.77/89.89 |-The branch is then unsatisfiable
% 130.77/89.89 |-Branch two:
% 130.77/89.89 | (1301) all_20_1_25 = 0
% 130.77/89.89 | (1351) ~ (all_20_2_26 = 0) | all_20_0_24 = 0
% 130.77/89.89 |
% 130.77/89.89 +-Applying beta-rule and splitting (1351), into two cases.
% 130.77/89.89 |-Branch one:
% 130.77/89.89 | (1352) ~ (all_20_2_26 = 0)
% 130.77/89.89 |
% 130.77/89.89 | Equations (444) can reduce 1352 to:
% 130.77/89.89 | (264) $false
% 130.77/89.89 |
% 130.77/89.89 |-The branch is then unsatisfiable
% 130.77/89.89 |-Branch two:
% 130.77/89.89 | (444) all_20_2_26 = 0
% 130.77/89.89 | (1355) all_20_0_24 = 0
% 130.77/89.89 |
% 130.77/89.89 | Equations (1355) can reduce 1425 to:
% 130.77/89.89 | (264) $false
% 130.77/89.89 |
% 130.77/89.89 |-The branch is then unsatisfiable
% 130.77/89.89 |-Branch two:
% 130.77/89.89 | (1435) all_446_1_305 = 0
% 130.77/89.89 | (1436) ~ (all_446_2_306 = 0) | all_446_0_304 = all_34_0_47
% 130.77/89.89 |
% 130.77/89.89 +-Applying beta-rule and splitting (1436), into two cases.
% 130.77/89.89 |-Branch one:
% 130.77/89.89 | (1437) ~ (all_446_2_306 = 0)
% 130.77/89.89 |
% 130.77/89.89 | Equations (1271) can reduce 1437 to:
% 130.77/89.89 | (264) $false
% 130.77/89.89 |
% 130.77/89.89 |-The branch is then unsatisfiable
% 130.77/89.89 |-Branch two:
% 130.77/89.89 | (1271) all_446_2_306 = 0
% 130.77/89.89 | (1440) all_446_0_304 = all_34_0_47
% 130.77/89.89 |
% 130.77/89.89 | Combining equations (1050,1440) yields a new equation:
% 130.77/89.89 | (1380) all_34_0_47 = all_0_9_9
% 130.77/89.89 |
% 130.77/89.89 | Equations (1380) can reduce 1422 to:
% 130.77/89.89 | (264) $false
% 130.77/89.89 |
% 130.77/89.89 |-The branch is then unsatisfiable
% 130.77/89.89 |-Branch two:
% 130.77/89.89 | (1389) aNaturalNumber0(all_0_1_1) = all_444_0_301
% 130.77/89.89 | (1390) all_444_0_301 = all_20_1_25
% 130.77/89.89 |
% 130.77/89.89 | Combining equations (1301,1390) yields a new equation:
% 130.77/89.89 | (1386) all_444_0_301 = 0
% 130.77/89.89 |
% 130.77/89.89 | From (1386) and (1389) follows:
% 130.77/89.89 | (1295) aNaturalNumber0(all_0_1_1) = 0
% 130.77/89.89 |
% 130.77/89.89 +-Applying beta-rule and splitting (221), into two cases.
% 130.77/89.89 |-Branch one:
% 130.77/89.89 | (1333) ~ (all_42_1_63 = 0)
% 130.77/89.89 |
% 130.77/89.89 | Equations (1299) can reduce 1333 to:
% 130.77/89.89 | (264) $false
% 130.77/89.89 |
% 130.77/89.89 |-The branch is then unsatisfiable
% 130.77/89.89 |-Branch two:
% 130.77/89.89 | (1299) all_42_1_63 = 0
% 130.77/89.89 | (1336) ~ (all_42_2_64 = 0) | all_42_0_62 = all_0_4_4
% 130.77/89.89 |
% 130.77/89.89 +-Applying beta-rule and splitting (1336), into two cases.
% 130.77/89.89 |-Branch one:
% 130.77/89.89 | (1337) ~ (all_42_2_64 = 0)
% 130.77/89.89 |
% 130.77/89.89 | Equations (465) can reduce 1337 to:
% 130.77/89.89 | (264) $false
% 130.77/89.89 |
% 130.77/89.89 |-The branch is then unsatisfiable
% 130.77/89.89 |-Branch two:
% 130.77/89.89 | (465) all_42_2_64 = 0
% 130.77/89.89 | (1340) all_42_0_62 = all_0_4_4
% 130.77/89.89 |
% 130.77/89.89 | From (1340) and (218) follows:
% 130.77/89.89 | (1455) sdtasdt0(all_0_1_1, xp) = all_0_4_4
% 130.77/89.89 |
% 130.77/89.89 +-Applying beta-rule and splitting (227), into two cases.
% 130.77/89.89 |-Branch one:
% 130.77/89.89 | (1312) ~ (all_44_2_67 = 0)
% 130.77/89.89 |
% 130.77/89.89 | Equations (467) can reduce 1312 to:
% 130.77/89.89 | (264) $false
% 130.77/89.89 |
% 130.77/89.89 |-The branch is then unsatisfiable
% 130.77/89.89 |-Branch two:
% 130.77/89.89 | (467) all_44_2_67 = 0
% 130.77/89.89 | (1315) ~ (all_44_3_68 = 0) | ~ (all_44_4_69 = 0) | all_44_0_65 = all_0_9_9
% 130.77/89.89 |
% 130.77/89.89 +-Applying beta-rule and splitting (1315), into two cases.
% 130.77/89.89 |-Branch one:
% 130.77/89.89 | (1316) ~ (all_44_3_68 = 0)
% 130.77/89.89 |
% 130.77/89.89 | Equations (1302) can reduce 1316 to:
% 130.77/89.89 | (264) $false
% 130.77/89.89 |
% 130.77/89.89 |-The branch is then unsatisfiable
% 130.77/89.89 |-Branch two:
% 130.77/89.89 | (1302) all_44_3_68 = 0
% 130.77/89.89 | (1319) ~ (all_44_4_69 = 0) | all_44_0_65 = all_0_9_9
% 130.77/89.89 |
% 130.77/89.89 +-Applying beta-rule and splitting (1319), into two cases.
% 130.77/89.89 |-Branch one:
% 130.77/89.89 | (1320) ~ (all_44_4_69 = 0)
% 130.77/89.89 |
% 130.77/89.89 | Equations (397) can reduce 1320 to:
% 130.77/89.89 | (264) $false
% 130.77/89.89 |
% 130.77/89.89 |-The branch is then unsatisfiable
% 130.77/89.89 |-Branch two:
% 130.77/89.89 | (397) all_44_4_69 = 0
% 130.77/89.89 | (1323) all_44_0_65 = all_0_9_9
% 130.77/89.89 |
% 130.77/89.89 | From (1323) and (223) follows:
% 130.77/89.89 | (1468) sdtasdt0(xp, all_44_1_66) = all_0_9_9
% 130.77/89.89 |
% 130.77/89.89 +-Applying beta-rule and splitting (1068), into two cases.
% 130.77/89.89 |-Branch one:
% 130.77/89.89 | (1332) ~ (aNaturalNumber0(all_0_1_1) = all_455_0_319)
% 130.77/89.89 |
% 130.77/89.89 +-Applying beta-rule and splitting (1071), into two cases.
% 130.77/89.89 |-Branch one:
% 130.77/89.89 | (1470) ~ (aNaturalNumber0(all_0_1_1) = all_406_1_225)
% 130.77/89.89 |
% 130.77/89.89 | From (1063) and (1470) follows:
% 130.77/89.89 | (1471) ~ (aNaturalNumber0(all_0_1_1) = all_402_0_218)
% 130.77/89.89 |
% 130.77/89.89 +-Applying beta-rule and splitting (865), into two cases.
% 130.77/89.89 |-Branch one:
% 130.77/89.89 | (1472) ~ (all_402_1_219 = 0)
% 130.77/89.89 |
% 130.77/89.89 | Equations (1117) can reduce 1472 to:
% 130.77/89.89 | (264) $false
% 130.77/89.89 |
% 130.77/89.89 |-The branch is then unsatisfiable
% 130.77/89.89 |-Branch two:
% 130.77/89.89 | (1117) all_402_1_219 = 0
% 130.77/89.89 | (1475) ~ (all_402_2_220 = 0) | all_402_0_218 = 0
% 130.77/89.89 |
% 130.77/89.89 +-Applying beta-rule and splitting (1475), into two cases.
% 130.77/89.89 |-Branch one:
% 130.77/89.89 | (1476) ~ (all_402_2_220 = 0)
% 130.77/89.89 |
% 130.77/89.89 | Equations (1262) can reduce 1476 to:
% 130.77/89.89 | (264) $false
% 130.77/89.89 |
% 130.77/89.89 |-The branch is then unsatisfiable
% 130.77/89.89 |-Branch two:
% 130.77/89.89 | (1262) all_402_2_220 = 0
% 130.77/89.89 | (1479) all_402_0_218 = 0
% 130.77/89.89 |
% 130.77/89.89 | From (1479) and (1471) follows:
% 130.77/89.89 | (1296) ~ (aNaturalNumber0(all_0_1_1) = 0)
% 130.77/89.89 |
% 130.77/89.89 | Using (1295) and (1296) yields:
% 130.77/89.89 | (543) $false
% 130.77/89.89 |
% 130.77/89.89 |-The branch is then unsatisfiable
% 130.77/89.89 |-Branch two:
% 130.77/89.89 | (1482) aNaturalNumber0(all_0_1_1) = all_406_1_225
% 130.77/89.89 | (1483) all_457_2_324 = all_406_1_225
% 130.77/89.89 |
% 130.77/89.89 | Combining equations (1483,1305) yields a new equation:
% 130.77/89.89 | (1484) all_406_1_225 = 0
% 130.77/89.89 |
% 130.77/89.89 | Simplifying 1484 yields:
% 130.77/89.89 | (1485) all_406_1_225 = 0
% 130.77/89.89 |
% 130.77/89.89 | Combining equations (1485,1063) yields a new equation:
% 130.77/89.89 | (1479) all_402_0_218 = 0
% 130.77/89.89 |
% 130.77/89.89 | Combining equations (1479,1063) yields a new equation:
% 130.77/89.89 | (1485) all_406_1_225 = 0
% 130.77/89.89 |
% 130.77/89.89 | From (1485) and (1482) follows:
% 130.77/89.89 | (1295) aNaturalNumber0(all_0_1_1) = 0
% 130.77/89.89 |
% 130.77/89.89 +-Applying beta-rule and splitting (168), into two cases.
% 130.77/89.89 |-Branch one:
% 130.77/89.89 | (1348) ~ (all_20_1_25 = 0)
% 130.77/89.89 |
% 130.77/89.89 | Equations (1301) can reduce 1348 to:
% 130.77/89.89 | (264) $false
% 130.77/89.89 |
% 130.77/89.89 |-The branch is then unsatisfiable
% 130.77/89.89 |-Branch two:
% 130.77/89.89 | (1301) all_20_1_25 = 0
% 130.77/89.89 | (1351) ~ (all_20_2_26 = 0) | all_20_0_24 = 0
% 130.77/89.89 |
% 130.77/89.89 +-Applying beta-rule and splitting (1351), into two cases.
% 130.77/89.89 |-Branch one:
% 130.77/89.89 | (1352) ~ (all_20_2_26 = 0)
% 130.77/89.89 |
% 130.77/89.89 | Equations (444) can reduce 1352 to:
% 130.77/89.89 | (264) $false
% 130.77/89.89 |
% 130.77/89.89 |-The branch is then unsatisfiable
% 130.77/89.89 |-Branch two:
% 130.77/89.89 | (444) all_20_2_26 = 0
% 130.77/89.89 | (1355) all_20_0_24 = 0
% 130.77/89.89 |
% 130.77/89.89 | From (1355) and (166) follows:
% 130.77/89.89 | (1497) aNaturalNumber0(all_0_4_4) = 0
% 130.77/89.89 |
% 130.77/89.89 +-Applying beta-rule and splitting (1067), into two cases.
% 130.77/89.89 |-Branch one:
% 130.77/89.89 | (1498) ~ (aNaturalNumber0(all_42_0_62) = 0)
% 130.77/89.89 |
% 130.77/89.89 | From (1340) and (1498) follows:
% 130.77/89.89 | (1499) ~ (aNaturalNumber0(all_0_4_4) = 0)
% 130.77/89.89 |
% 130.77/89.89 | Using (1497) and (1499) yields:
% 130.77/89.89 | (543) $false
% 130.77/89.89 |
% 130.77/89.89 |-The branch is then unsatisfiable
% 130.77/89.89 |-Branch two:
% 130.77/89.89 | (1501) aNaturalNumber0(all_42_0_62) = 0
% 130.77/89.89 | (1360) all_455_0_319 = 0
% 130.77/89.89 |
% 130.77/89.89 | From (1360) and (1332) follows:
% 130.77/89.89 | (1296) ~ (aNaturalNumber0(all_0_1_1) = 0)
% 130.77/89.89 |
% 130.77/89.89 | Using (1295) and (1296) yields:
% 130.77/89.89 | (543) $false
% 130.77/89.89 |
% 130.77/89.89 |-The branch is then unsatisfiable
% 130.77/89.89 |-Branch two:
% 130.77/89.89 | (1358) aNaturalNumber0(all_0_1_1) = all_455_0_319
% 130.77/89.89 | (1506) all_455_0_319 = all_20_1_25
% 130.77/89.89 |
% 130.77/89.89 | Combining equations (1301,1506) yields a new equation:
% 130.77/89.89 | (1360) all_455_0_319 = 0
% 130.77/89.89 |
% 130.77/89.89 | From (1360) and (1358) follows:
% 130.77/89.89 | (1295) aNaturalNumber0(all_0_1_1) = 0
% 130.77/89.89 |
% 130.77/89.89 +-Applying beta-rule and splitting (1074), into two cases.
% 130.77/89.89 |-Branch one:
% 130.77/89.89 | (1509) ~ (aNaturalNumber0(all_0_1_1) = all_418_1_253)
% 130.77/89.90 |
% 130.77/89.90 +-Applying beta-rule and splitting (982), into two cases.
% 130.77/89.90 |-Branch one:
% 130.77/89.90 | (1510) ~ (all_452_1_314 = 0)
% 130.77/89.90 |
% 130.77/89.90 | Equations (1272) can reduce 1510 to:
% 130.77/89.90 | (264) $false
% 130.77/89.90 |
% 130.77/89.90 |-The branch is then unsatisfiable
% 130.77/89.90 |-Branch two:
% 130.77/89.90 | (1272) all_452_1_314 = 0
% 130.77/89.90 | (1513) ~ (all_452_2_315 = 0) | all_452_0_313 = all_44_1_66
% 130.77/89.90 |
% 130.77/89.90 +-Applying beta-rule and splitting (1513), into two cases.
% 130.77/89.90 |-Branch one:
% 130.77/89.90 | (1514) ~ (all_452_2_315 = 0)
% 130.77/89.90 |
% 130.77/89.90 | Equations (1304) can reduce 1514 to:
% 130.77/89.90 | (264) $false
% 130.77/89.90 |
% 130.77/89.90 |-The branch is then unsatisfiable
% 130.77/89.90 |-Branch two:
% 130.77/89.90 | (1304) all_452_2_315 = 0
% 130.77/89.90 | (1517) all_452_0_313 = all_44_1_66
% 130.77/89.90 |
% 130.77/89.90 +-Applying beta-rule and splitting (1051), into two cases.
% 130.77/89.90 |-Branch one:
% 130.77/89.90 | (1518) ~ (sdtasdt0(xr, all_0_1_1) = xk)
% 130.77/89.90 |
% 130.77/89.90 | Using (1294) and (1518) yields:
% 130.77/89.90 | (543) $false
% 130.77/89.90 |
% 130.77/89.90 |-The branch is then unsatisfiable
% 130.77/89.90 |-Branch two:
% 130.77/89.90 | (1294) sdtasdt0(xr, all_0_1_1) = xk
% 130.77/89.90 | (1521) all_452_0_313 = xk
% 130.77/89.90 |
% 130.77/89.90 | Combining equations (1521,1517) yields a new equation:
% 130.77/89.90 | (1522) all_44_1_66 = xk
% 130.77/89.90 |
% 130.77/89.90 +-Applying beta-rule and splitting (1064), into two cases.
% 130.77/89.90 |-Branch one:
% 130.77/89.90 | (1523) ~ (aNaturalNumber0(all_44_1_66) = all_398_4_208)
% 130.77/89.90 |
% 130.77/89.90 | From (1522)(1052) and (1523) follows:
% 130.77/89.90 | (551) ~ (aNaturalNumber0(xk) = 0)
% 131.10/89.90 |
% 131.10/89.90 | Using (549) and (551) yields:
% 131.10/89.90 | (543) $false
% 131.10/89.90 |
% 131.10/89.90 |-The branch is then unsatisfiable
% 131.10/89.90 |-Branch two:
% 131.10/89.90 | (1526) aNaturalNumber0(all_44_1_66) = all_398_4_208
% 131.10/89.90 | (1527) all_450_0_310 = all_398_4_208
% 131.10/89.90 |
% 131.10/89.90 | Combining equations (1527,1066) yields a new equation:
% 131.10/89.90 | (1528) all_418_1_253 = all_398_4_208
% 131.10/89.90 |
% 131.10/89.90 | Combining equations (1052,1528) yields a new equation:
% 131.10/89.90 | (1529) all_418_1_253 = 0
% 131.10/89.90 |
% 131.10/89.90 | From (1529) and (1509) follows:
% 131.10/89.90 | (1296) ~ (aNaturalNumber0(all_0_1_1) = 0)
% 131.10/89.90 |
% 131.10/89.90 | Using (1295) and (1296) yields:
% 131.10/89.90 | (543) $false
% 131.10/89.90 |
% 131.10/89.90 |-The branch is then unsatisfiable
% 131.10/89.90 |-Branch two:
% 131.10/89.90 | (1532) aNaturalNumber0(all_0_1_1) = all_418_1_253
% 131.10/89.90 | (1533) all_452_2_315 = all_418_1_253
% 131.10/89.90 |
% 131.10/89.90 | Combining equations (1304,1533) yields a new equation:
% 131.10/89.90 | (1529) all_418_1_253 = 0
% 131.10/89.90 |
% 131.10/89.90 | From (1529) and (1532) follows:
% 131.10/89.90 | (1295) aNaturalNumber0(all_0_1_1) = 0
% 131.10/89.90 |
% 131.10/89.90 +-Applying beta-rule and splitting (743), into two cases.
% 131.10/89.90 |-Branch one:
% 131.10/89.90 | (301) xp = sz00
% 131.10/89.90 |
% 131.10/89.90 | Equations (301) can reduce 102 to:
% 131.10/89.90 | (264) $false
% 131.10/89.90 |
% 131.10/89.90 |-The branch is then unsatisfiable
% 131.10/89.90 |-Branch two:
% 131.10/89.90 | (102) ~ (xp = sz00)
% 131.10/89.90 | (1539) all_53_2_89 = all_44_1_66 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_53_2_89, xp) = v3 & sdtasdt0(all_44_1_66, xp) = v2 & aNaturalNumber0(all_53_2_89) = v1 & aNaturalNumber0(all_44_1_66) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = v2) & ~ (all_44_0_65 = all_0_9_9))))
% 131.10/89.90 |
% 131.10/89.90 +-Applying beta-rule and splitting (742), into two cases.
% 131.10/89.90 |-Branch one:
% 131.10/89.90 | (301) xp = sz00
% 131.10/89.90 |
% 131.10/89.90 | Equations (301) can reduce 102 to:
% 131.10/89.90 | (264) $false
% 131.10/89.90 |
% 131.10/89.90 |-The branch is then unsatisfiable
% 131.10/89.90 |-Branch two:
% 131.10/89.90 | (102) ~ (xp = sz00)
% 131.10/89.90 | (1543) all_53_2_89 = all_44_1_66 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_53_2_89, xp) = v2 & sdtasdt0(all_44_1_66, xp) = v3 & aNaturalNumber0(all_53_2_89) = v0 & aNaturalNumber0(all_44_1_66) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = v2) & ~ (all_44_0_65 = all_0_9_9))))
% 131.10/89.90 |
% 131.10/89.90 +-Applying beta-rule and splitting (1543), into two cases.
% 131.10/89.90 |-Branch one:
% 131.10/89.90 | (1544) all_53_2_89 = all_44_1_66
% 131.10/89.90 |
% 131.10/89.90 | Combining equations (1286,1544) yields a new equation:
% 131.10/89.90 | (1522) all_44_1_66 = xk
% 131.10/89.90 |
% 131.10/89.90 | From (1522) and (224) follows:
% 131.10/89.90 | (1546) sdtasdt0(all_0_1_1, xr) = xk
% 131.10/89.90 |
% 131.10/89.90 +-Applying beta-rule and splitting (1071), into two cases.
% 131.10/89.90 |-Branch one:
% 131.10/89.90 | (1470) ~ (aNaturalNumber0(all_0_1_1) = all_406_1_225)
% 131.10/89.90 |
% 131.10/89.90 | From (1063) and (1470) follows:
% 131.10/89.90 | (1471) ~ (aNaturalNumber0(all_0_1_1) = all_402_0_218)
% 131.10/89.90 |
% 131.10/89.90 +-Applying beta-rule and splitting (865), into two cases.
% 131.10/89.90 |-Branch one:
% 131.10/89.90 | (1472) ~ (all_402_1_219 = 0)
% 131.10/89.90 |
% 131.10/89.90 | Equations (1117) can reduce 1472 to:
% 131.10/89.90 | (264) $false
% 131.10/89.90 |
% 131.10/89.90 |-The branch is then unsatisfiable
% 131.10/89.90 |-Branch two:
% 131.10/89.90 | (1117) all_402_1_219 = 0
% 131.10/89.90 | (1475) ~ (all_402_2_220 = 0) | all_402_0_218 = 0
% 131.10/89.90 |
% 131.10/89.90 +-Applying beta-rule and splitting (1475), into two cases.
% 131.10/89.90 |-Branch one:
% 131.10/89.90 | (1476) ~ (all_402_2_220 = 0)
% 131.10/89.90 |
% 131.10/89.90 | Equations (1262) can reduce 1476 to:
% 131.10/89.90 | (264) $false
% 131.10/89.90 |
% 131.10/89.90 |-The branch is then unsatisfiable
% 131.10/89.90 |-Branch two:
% 131.10/89.90 | (1262) all_402_2_220 = 0
% 131.10/89.90 | (1479) all_402_0_218 = 0
% 131.10/89.90 |
% 131.10/89.90 | From (1479) and (1471) follows:
% 131.10/89.90 | (1296) ~ (aNaturalNumber0(all_0_1_1) = 0)
% 131.10/89.90 |
% 131.10/89.90 | Using (1295) and (1296) yields:
% 131.10/89.90 | (543) $false
% 131.10/89.90 |
% 131.10/89.90 |-The branch is then unsatisfiable
% 131.10/89.90 |-Branch two:
% 131.10/89.90 | (1482) aNaturalNumber0(all_0_1_1) = all_406_1_225
% 131.10/89.90 | (1483) all_457_2_324 = all_406_1_225
% 131.10/89.90 |
% 131.10/89.90 | Combining equations (1483,1305) yields a new equation:
% 131.10/89.90 | (1484) all_406_1_225 = 0
% 131.10/89.90 |
% 131.10/89.90 | Simplifying 1484 yields:
% 131.10/89.90 | (1485) all_406_1_225 = 0
% 131.10/89.90 |
% 131.10/89.90 | Combining equations (1485,1063) yields a new equation:
% 131.10/89.90 | (1479) all_402_0_218 = 0
% 131.10/89.90 |
% 131.10/89.90 | Combining equations (1479,1063) yields a new equation:
% 131.10/89.90 | (1485) all_406_1_225 = 0
% 131.10/89.90 |
% 131.10/89.90 | From (1485) and (1482) follows:
% 131.10/89.90 | (1295) aNaturalNumber0(all_0_1_1) = 0
% 131.10/89.90 |
% 131.10/89.90 +-Applying beta-rule and splitting (737), into two cases.
% 131.10/89.90 |-Branch one:
% 131.10/89.90 | (1566) ~ (sdtasdt0(all_0_1_1, xr) = xk)
% 131.10/89.90 |
% 131.10/89.90 | Using (1546) and (1566) yields:
% 131.10/89.90 | (543) $false
% 131.10/89.90 |
% 131.10/89.90 |-The branch is then unsatisfiable
% 131.10/89.90 |-Branch two:
% 131.10/89.90 | (1546) sdtasdt0(all_0_1_1, xr) = xk
% 131.10/89.90 | (1569) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_1_1, v3) = v4 & sdtasdt0(xr, xp) = v3 & aNaturalNumber0(all_0_1_1) = v0 & aNaturalNumber0(xr) = v1 & aNaturalNumber0(xp) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_9_9))
% 131.10/89.90 |
% 131.10/89.90 | Instantiating (1569) with all_872_0_512, all_872_1_513, all_872_2_514, all_872_3_515, all_872_4_516 yields:
% 131.10/89.90 | (1570) sdtasdt0(all_0_1_1, all_872_1_513) = all_872_0_512 & sdtasdt0(xr, xp) = all_872_1_513 & aNaturalNumber0(all_0_1_1) = all_872_4_516 & aNaturalNumber0(xr) = all_872_3_515 & aNaturalNumber0(xp) = all_872_2_514 & ( ~ (all_872_2_514 = 0) | ~ (all_872_3_515 = 0) | ~ (all_872_4_516 = 0) | all_872_0_512 = all_0_9_9)
% 131.10/89.90 |
% 131.10/89.90 | Applying alpha-rule on (1570) yields:
% 131.10/89.90 | (1571) sdtasdt0(xr, xp) = all_872_1_513
% 131.10/89.90 | (1572) aNaturalNumber0(all_0_1_1) = all_872_4_516
% 131.10/89.90 | (1573) aNaturalNumber0(xp) = all_872_2_514
% 131.10/89.90 | (1574) aNaturalNumber0(xr) = all_872_3_515
% 131.10/89.90 | (1575) ~ (all_872_2_514 = 0) | ~ (all_872_3_515 = 0) | ~ (all_872_4_516 = 0) | all_872_0_512 = all_0_9_9
% 131.10/89.90 | (1576) sdtasdt0(all_0_1_1, all_872_1_513) = all_872_0_512
% 131.10/89.90 |
% 131.10/89.90 +-Applying beta-rule and splitting (725), into two cases.
% 131.10/89.90 |-Branch one:
% 131.10/89.90 | (1577) ~ (sdtasdt0(all_0_1_1, xp) = all_0_4_4)
% 131.10/89.90 |
% 131.10/89.90 | Using (1455) and (1577) yields:
% 131.10/89.90 | (543) $false
% 131.10/89.90 |
% 131.10/89.90 |-The branch is then unsatisfiable
% 131.10/89.90 |-Branch two:
% 131.10/89.90 | (1455) sdtasdt0(all_0_1_1, xp) = all_0_4_4
% 131.10/89.90 | (1580) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_1_1, v3) = v4 & sdtasdt0(xp, xr) = v3 & aNaturalNumber0(all_0_1_1) = v0 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_9_9))
% 131.10/89.90 |
% 131.10/89.90 | Instantiating (1580) with all_881_0_517, all_881_1_518, all_881_2_519, all_881_3_520, all_881_4_521 yields:
% 131.10/89.90 | (1581) sdtasdt0(all_0_1_1, all_881_1_518) = all_881_0_517 & sdtasdt0(xp, xr) = all_881_1_518 & aNaturalNumber0(all_0_1_1) = all_881_4_521 & aNaturalNumber0(xr) = all_881_2_519 & aNaturalNumber0(xp) = all_881_3_520 & ( ~ (all_881_2_519 = 0) | ~ (all_881_3_520 = 0) | ~ (all_881_4_521 = 0) | all_881_0_517 = all_0_9_9)
% 131.10/89.90 |
% 131.10/89.90 | Applying alpha-rule on (1581) yields:
% 131.10/89.90 | (1582) sdtasdt0(xp, xr) = all_881_1_518
% 131.10/89.90 | (1583) aNaturalNumber0(all_0_1_1) = all_881_4_521
% 131.10/89.90 | (1584) sdtasdt0(all_0_1_1, all_881_1_518) = all_881_0_517
% 131.10/89.90 | (1585) aNaturalNumber0(xp) = all_881_3_520
% 131.10/89.91 | (1586) aNaturalNumber0(xr) = all_881_2_519
% 131.10/89.91 | (1587) ~ (all_881_2_519 = 0) | ~ (all_881_3_520 = 0) | ~ (all_881_4_521 = 0) | all_881_0_517 = all_0_9_9
% 131.10/89.91 |
% 131.10/89.91 | Instantiating formula (11) with all_0_1_1, all_881_4_521, 0 and discharging atoms aNaturalNumber0(all_0_1_1) = all_881_4_521, aNaturalNumber0(all_0_1_1) = 0, yields:
% 131.10/89.91 | (1588) all_881_4_521 = 0
% 131.10/89.91 |
% 131.10/89.91 | Instantiating formula (11) with all_0_1_1, all_872_4_516, all_881_4_521 and discharging atoms aNaturalNumber0(all_0_1_1) = all_881_4_521, aNaturalNumber0(all_0_1_1) = all_872_4_516, yields:
% 131.10/89.91 | (1589) all_881_4_521 = all_872_4_516
% 131.10/89.91 |
% 131.10/89.91 | Instantiating formula (11) with all_0_1_1, all_80_1_122, all_881_4_521 and discharging atoms aNaturalNumber0(all_0_1_1) = all_881_4_521, aNaturalNumber0(all_0_1_1) = all_80_1_122, yields:
% 131.10/89.91 | (1590) all_881_4_521 = all_80_1_122
% 131.10/89.91 |
% 131.10/89.91 | Combining equations (1588,1589) yields a new equation:
% 131.10/89.91 | (1591) all_872_4_516 = 0
% 131.10/89.91 |
% 131.10/89.91 | Combining equations (1590,1589) yields a new equation:
% 131.10/89.91 | (1592) all_872_4_516 = all_80_1_122
% 131.10/89.91 |
% 131.10/89.91 | Combining equations (1592,1591) yields a new equation:
% 131.10/89.91 | (1593) all_80_1_122 = 0
% 131.10/89.91 |
% 131.10/89.91 | Simplifying 1593 yields:
% 131.10/89.91 | (1594) all_80_1_122 = 0
% 131.10/89.91 |
% 131.10/89.91 | Equations (1594) can reduce 1308 to:
% 131.10/89.91 | (264) $false
% 131.10/89.91 |
% 131.10/89.91 |-The branch is then unsatisfiable
% 131.10/89.91 |-Branch two:
% 131.10/89.91 | (1596) ~ (all_53_2_89 = all_44_1_66)
% 131.10/89.91 | (1597) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_53_2_89, xp) = v2 & sdtasdt0(all_44_1_66, xp) = v3 & aNaturalNumber0(all_53_2_89) = v0 & aNaturalNumber0(all_44_1_66) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = v2) & ~ (all_44_0_65 = all_0_9_9))))
% 131.10/89.91 |
% 131.10/89.91 | Equations (1286) can reduce 1596 to:
% 131.10/89.91 | (1598) ~ (all_44_1_66 = xk)
% 131.10/89.91 |
% 131.10/89.91 | Simplifying 1598 yields:
% 131.10/89.91 | (1599) ~ (all_44_1_66 = xk)
% 131.10/89.91 |
% 131.10/89.91 +-Applying beta-rule and splitting (741), into two cases.
% 131.10/89.91 |-Branch one:
% 131.10/89.91 | (1600) ~ (sdtasdt0(xp, all_44_1_66) = all_0_9_9)
% 131.10/89.91 |
% 131.10/89.91 | Using (1468) and (1600) yields:
% 131.10/89.91 | (543) $false
% 131.10/89.91 |
% 131.10/89.91 |-The branch is then unsatisfiable
% 131.10/89.91 |-Branch two:
% 131.10/89.91 | (1468) sdtasdt0(xp, all_44_1_66) = all_0_9_9
% 131.10/89.91 | (1603) all_44_1_66 = xk | xp = sz00 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_44_1_66) = v0) | (doDivides0(xp, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 131.10/89.91 |
% 131.10/89.91 +-Applying beta-rule and splitting (1603), into two cases.
% 131.10/89.91 |-Branch one:
% 131.10/89.91 | (301) xp = sz00
% 131.10/89.91 |
% 131.10/89.91 | Equations (301) can reduce 102 to:
% 131.10/89.91 | (264) $false
% 131.10/89.91 |
% 131.10/89.91 |-The branch is then unsatisfiable
% 131.10/89.91 |-Branch two:
% 131.10/89.91 | (102) ~ (xp = sz00)
% 131.10/89.91 | (1607) all_44_1_66 = xk | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_44_1_66) = v0) | (doDivides0(xp, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 131.10/89.91 |
% 131.10/89.91 +-Applying beta-rule and splitting (1607), into two cases.
% 131.10/89.91 |-Branch one:
% 131.10/89.91 | (1522) all_44_1_66 = xk
% 131.10/89.91 |
% 131.10/89.91 | Equations (1522) can reduce 1599 to:
% 131.10/89.91 | (264) $false
% 131.10/89.91 |
% 131.10/89.91 |-The branch is then unsatisfiable
% 131.10/89.91 |-Branch two:
% 131.10/89.91 | (1599) ~ (all_44_1_66 = xk)
% 131.10/89.91 | (1611) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_44_1_66) = v0) | (doDivides0(xp, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 131.10/89.91 |
% 131.10/89.91 +-Applying beta-rule and splitting (940), into two cases.
% 131.10/89.91 |-Branch one:
% 131.10/89.91 | (1612) ~ (all_430_1_273 = 0)
% 131.10/89.91 |
% 131.10/89.91 | Equations (1059) can reduce 1612 to:
% 131.10/89.91 | (264) $false
% 131.10/89.91 |
% 131.10/89.91 |-The branch is then unsatisfiable
% 131.10/89.91 |-Branch two:
% 131.10/89.91 | (1059) all_430_1_273 = 0
% 131.10/89.91 | (1615) ~ (all_430_2_274 = 0) | all_430_0_272 = xk
% 131.10/89.91 |
% 131.10/89.91 +-Applying beta-rule and splitting (1615), into two cases.
% 131.10/89.91 |-Branch one:
% 131.10/89.91 | (1616) ~ (all_430_2_274 = 0)
% 131.10/89.91 |
% 131.10/89.91 | Equations (1270) can reduce 1616 to:
% 131.10/89.91 | (264) $false
% 131.10/89.91 |
% 131.10/89.91 |-The branch is then unsatisfiable
% 131.10/89.91 |-Branch two:
% 131.10/89.91 | (1270) all_430_2_274 = 0
% 131.10/89.91 | (1619) all_430_0_272 = xk
% 131.10/89.91 |
% 131.10/89.91 | From (1619) and (1293) follows:
% 131.10/89.91 | (1546) sdtasdt0(all_0_1_1, xr) = xk
% 131.10/89.91 |
% 131.10/89.91 +-Applying beta-rule and splitting (1049), into two cases.
% 131.10/89.91 |-Branch one:
% 131.10/89.91 | (1621) ~ (sdtasdt0(all_0_1_1, xr) = all_430_0_272)
% 131.10/89.91 |
% 131.10/89.91 | From (1619) and (1621) follows:
% 131.10/89.91 | (1566) ~ (sdtasdt0(all_0_1_1, xr) = xk)
% 131.10/89.91 |
% 131.10/89.91 | Using (1546) and (1566) yields:
% 131.10/89.91 | (543) $false
% 131.10/89.91 |
% 131.10/89.91 |-The branch is then unsatisfiable
% 131.10/89.91 |-Branch two:
% 131.10/89.91 | (1293) sdtasdt0(all_0_1_1, xr) = all_430_0_272
% 131.10/89.91 | (1625) all_430_0_272 = all_44_1_66
% 131.10/89.91 |
% 131.10/89.91 | Combining equations (1625,1619) yields a new equation:
% 131.10/89.91 | (1626) all_44_1_66 = xk
% 131.10/89.91 |
% 131.10/89.91 | Simplifying 1626 yields:
% 131.10/89.91 | (1522) all_44_1_66 = xk
% 131.10/89.91 |
% 131.10/89.91 | Equations (1522) can reduce 1599 to:
% 131.10/89.91 | (264) $false
% 131.10/89.91 |
% 131.10/89.91 |-The branch is then unsatisfiable
% 131.10/89.91 |-Branch two:
% 131.10/89.91 | (1629) aNaturalNumber0(all_0_4_4) = all_80_0_121 & aNaturalNumber0(xp) = all_80_1_122 & ( ~ (all_80_0_121 = 0) | ~ (all_80_1_122 = 0))
% 131.10/89.91 |
% 131.10/89.91 | Applying alpha-rule on (1629) yields:
% 131.10/89.91 | (1630) aNaturalNumber0(all_0_4_4) = all_80_0_121
% 131.10/89.91 | (1631) aNaturalNumber0(xp) = all_80_1_122
% 131.10/89.91 | (1632) ~ (all_80_0_121 = 0) | ~ (all_80_1_122 = 0)
% 131.10/89.91 |
% 131.10/89.91 +-Applying beta-rule and splitting (221), into two cases.
% 131.10/89.91 |-Branch one:
% 131.10/89.91 | (1333) ~ (all_42_1_63 = 0)
% 131.10/89.91 |
% 131.10/89.91 | Equations (1299) can reduce 1333 to:
% 131.10/89.91 | (264) $false
% 131.10/89.91 |
% 131.10/89.91 |-The branch is then unsatisfiable
% 131.10/89.91 |-Branch two:
% 131.10/89.91 | (1299) all_42_1_63 = 0
% 131.10/89.91 | (1336) ~ (all_42_2_64 = 0) | all_42_0_62 = all_0_4_4
% 131.10/89.91 |
% 131.10/89.91 +-Applying beta-rule and splitting (1336), into two cases.
% 131.10/89.91 |-Branch one:
% 131.10/89.91 | (1337) ~ (all_42_2_64 = 0)
% 131.10/89.91 |
% 131.10/89.91 | Equations (465) can reduce 1337 to:
% 131.10/89.91 | (264) $false
% 131.10/89.91 |
% 131.10/89.91 |-The branch is then unsatisfiable
% 131.10/89.91 |-Branch two:
% 131.10/89.91 | (465) all_42_2_64 = 0
% 131.10/89.91 | (1340) all_42_0_62 = all_0_4_4
% 131.10/89.91 |
% 131.10/89.91 | From (1340) and (218) follows:
% 131.10/89.91 | (1455) sdtasdt0(all_0_1_1, xp) = all_0_4_4
% 131.10/89.91 |
% 131.10/89.91 | From (1340) and (984) follows:
% 131.10/89.91 | (1341) aNaturalNumber0(all_0_4_4) = all_455_0_319
% 131.10/89.91 |
% 131.10/89.91 +-Applying beta-rule and splitting (1080), into two cases.
% 131.10/89.91 |-Branch one:
% 131.10/89.91 | (1342) ~ (aNaturalNumber0(all_0_4_4) = all_455_0_319)
% 131.10/89.91 |
% 131.10/89.91 | Using (1341) and (1342) yields:
% 131.10/89.91 | (543) $false
% 131.10/89.91 |
% 131.10/89.91 |-The branch is then unsatisfiable
% 131.10/89.91 |-Branch two:
% 131.10/89.91 | (1341) aNaturalNumber0(all_0_4_4) = all_455_0_319
% 131.10/89.91 | (1345) all_455_0_319 = all_446_1_305
% 131.10/89.91 |
% 131.10/89.91 | Combining equations (1079,1345) yields a new equation:
% 131.10/89.91 | (1346) all_455_0_319 = all_20_0_24
% 131.10/89.91 |
% 131.10/89.91 | From (1346) and (1341) follows:
% 131.10/89.91 | (166) aNaturalNumber0(all_0_4_4) = all_20_0_24
% 131.10/89.91 |
% 131.10/89.91 +-Applying beta-rule and splitting (168), into two cases.
% 131.10/89.91 |-Branch one:
% 131.10/89.91 | (1348) ~ (all_20_1_25 = 0)
% 131.10/89.91 |
% 131.10/89.91 | Equations (1301) can reduce 1348 to:
% 131.10/89.91 | (264) $false
% 131.10/89.91 |
% 131.10/89.91 |-The branch is then unsatisfiable
% 131.10/89.91 |-Branch two:
% 131.10/89.91 | (1301) all_20_1_25 = 0
% 131.10/89.91 | (1351) ~ (all_20_2_26 = 0) | all_20_0_24 = 0
% 131.10/89.91 |
% 131.10/89.91 +-Applying beta-rule and splitting (1351), into two cases.
% 131.10/89.91 |-Branch one:
% 131.10/89.91 | (1352) ~ (all_20_2_26 = 0)
% 131.10/89.91 |
% 131.10/89.91 | Equations (444) can reduce 1352 to:
% 131.10/89.91 | (264) $false
% 131.10/89.91 |
% 131.10/89.91 |-The branch is then unsatisfiable
% 131.10/89.91 |-Branch two:
% 131.10/89.91 | (444) all_20_2_26 = 0
% 131.10/89.91 | (1355) all_20_0_24 = 0
% 131.10/89.91 |
% 131.10/89.91 | From (1355) and (166) follows:
% 131.10/89.91 | (1497) aNaturalNumber0(all_0_4_4) = 0
% 131.10/89.91 |
% 131.10/89.91 +-Applying beta-rule and splitting (725), into two cases.
% 131.10/89.91 |-Branch one:
% 131.10/89.91 | (1577) ~ (sdtasdt0(all_0_1_1, xp) = all_0_4_4)
% 131.10/89.91 |
% 131.10/89.91 | Using (1455) and (1577) yields:
% 131.10/89.91 | (543) $false
% 131.10/89.91 |
% 131.10/89.91 |-The branch is then unsatisfiable
% 131.10/89.91 |-Branch two:
% 131.10/89.91 | (1455) sdtasdt0(all_0_1_1, xp) = all_0_4_4
% 131.10/89.91 | (1580) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_1_1, v3) = v4 & sdtasdt0(xp, xr) = v3 & aNaturalNumber0(all_0_1_1) = v0 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_9_9))
% 131.10/89.91 |
% 131.10/89.92 | Instantiating (1580) with all_721_0_680, all_721_1_681, all_721_2_682, all_721_3_683, all_721_4_684 yields:
% 131.10/89.92 | (1662) sdtasdt0(all_0_1_1, all_721_1_681) = all_721_0_680 & sdtasdt0(xp, xr) = all_721_1_681 & aNaturalNumber0(all_0_1_1) = all_721_4_684 & aNaturalNumber0(xr) = all_721_2_682 & aNaturalNumber0(xp) = all_721_3_683 & ( ~ (all_721_2_682 = 0) | ~ (all_721_3_683 = 0) | ~ (all_721_4_684 = 0) | all_721_0_680 = all_0_9_9)
% 131.10/89.92 |
% 131.10/89.92 | Applying alpha-rule on (1662) yields:
% 131.10/89.92 | (1663) aNaturalNumber0(xp) = all_721_3_683
% 131.10/89.92 | (1664) aNaturalNumber0(all_0_1_1) = all_721_4_684
% 131.10/89.92 | (1665) sdtasdt0(xp, xr) = all_721_1_681
% 131.10/89.92 | (1666) aNaturalNumber0(xr) = all_721_2_682
% 131.10/89.92 | (1667) sdtasdt0(all_0_1_1, all_721_1_681) = all_721_0_680
% 131.10/89.92 | (1668) ~ (all_721_2_682 = 0) | ~ (all_721_3_683 = 0) | ~ (all_721_4_684 = 0) | all_721_0_680 = all_0_9_9
% 131.10/89.92 |
% 131.10/89.92 +-Applying beta-rule and splitting (940), into two cases.
% 131.10/89.92 |-Branch one:
% 131.10/89.92 | (1612) ~ (all_430_1_273 = 0)
% 131.10/89.92 |
% 131.10/89.92 | Equations (1059) can reduce 1612 to:
% 131.10/89.92 | (264) $false
% 131.10/89.92 |
% 131.10/89.92 |-The branch is then unsatisfiable
% 131.10/89.92 |-Branch two:
% 131.10/89.92 | (1059) all_430_1_273 = 0
% 131.10/89.92 | (1615) ~ (all_430_2_274 = 0) | all_430_0_272 = xk
% 131.10/89.92 |
% 131.10/89.92 +-Applying beta-rule and splitting (1615), into two cases.
% 131.10/89.92 |-Branch one:
% 131.10/89.92 | (1616) ~ (all_430_2_274 = 0)
% 131.10/89.92 |
% 131.10/89.92 | Equations (1270) can reduce 1616 to:
% 131.10/89.92 | (264) $false
% 131.10/89.92 |
% 131.10/89.92 |-The branch is then unsatisfiable
% 131.10/89.92 |-Branch two:
% 131.10/89.92 | (1270) all_430_2_274 = 0
% 131.10/89.92 | (1619) all_430_0_272 = xk
% 131.10/89.92 |
% 131.10/89.92 | From (1619) and (1293) follows:
% 131.10/89.92 | (1546) sdtasdt0(all_0_1_1, xr) = xk
% 131.10/89.92 |
% 131.10/89.92 +-Applying beta-rule and splitting (737), into two cases.
% 131.10/89.92 |-Branch one:
% 131.10/89.92 | (1566) ~ (sdtasdt0(all_0_1_1, xr) = xk)
% 131.10/89.92 |
% 131.10/89.92 | Using (1546) and (1566) yields:
% 131.10/89.92 | (543) $false
% 131.10/89.92 |
% 131.10/89.92 |-The branch is then unsatisfiable
% 131.10/89.92 |-Branch two:
% 131.10/89.92 | (1546) sdtasdt0(all_0_1_1, xr) = xk
% 131.10/89.92 | (1569) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_1_1, v3) = v4 & sdtasdt0(xr, xp) = v3 & aNaturalNumber0(all_0_1_1) = v0 & aNaturalNumber0(xr) = v1 & aNaturalNumber0(xp) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_9_9))
% 131.10/89.92 |
% 131.10/89.92 | Instantiating (1569) with all_901_0_685, all_901_1_686, all_901_2_687, all_901_3_688, all_901_4_689 yields:
% 131.10/89.92 | (1682) sdtasdt0(all_0_1_1, all_901_1_686) = all_901_0_685 & sdtasdt0(xr, xp) = all_901_1_686 & aNaturalNumber0(all_0_1_1) = all_901_4_689 & aNaturalNumber0(xr) = all_901_3_688 & aNaturalNumber0(xp) = all_901_2_687 & ( ~ (all_901_2_687 = 0) | ~ (all_901_3_688 = 0) | ~ (all_901_4_689 = 0) | all_901_0_685 = all_0_9_9)
% 131.10/89.92 |
% 131.10/89.92 | Applying alpha-rule on (1682) yields:
% 131.10/89.92 | (1683) sdtasdt0(xr, xp) = all_901_1_686
% 131.10/89.92 | (1684) ~ (all_901_2_687 = 0) | ~ (all_901_3_688 = 0) | ~ (all_901_4_689 = 0) | all_901_0_685 = all_0_9_9
% 131.10/89.92 | (1685) aNaturalNumber0(xp) = all_901_2_687
% 131.10/89.92 | (1686) sdtasdt0(all_0_1_1, all_901_1_686) = all_901_0_685
% 131.10/89.92 | (1687) aNaturalNumber0(all_0_1_1) = all_901_4_689
% 131.10/89.92 | (1688) aNaturalNumber0(xr) = all_901_3_688
% 131.10/89.92 |
% 131.10/89.92 | Instantiating formula (11) with all_0_4_4, all_80_0_121, 0 and discharging atoms aNaturalNumber0(all_0_4_4) = all_80_0_121, aNaturalNumber0(all_0_4_4) = 0, yields:
% 131.10/89.92 | (1689) all_80_0_121 = 0
% 131.10/89.92 |
% 131.10/89.92 | Instantiating formula (11) with xp, all_721_3_683, 0 and discharging atoms aNaturalNumber0(xp) = all_721_3_683, aNaturalNumber0(xp) = 0, yields:
% 131.10/89.92 | (1690) all_721_3_683 = 0
% 131.10/89.92 |
% 131.10/89.92 | Instantiating formula (11) with xp, all_721_3_683, all_901_2_687 and discharging atoms aNaturalNumber0(xp) = all_901_2_687, aNaturalNumber0(xp) = all_721_3_683, yields:
% 131.10/89.92 | (1691) all_901_2_687 = all_721_3_683
% 131.10/89.92 |
% 131.10/89.92 | Instantiating formula (11) with xp, all_80_1_122, all_901_2_687 and discharging atoms aNaturalNumber0(xp) = all_901_2_687, aNaturalNumber0(xp) = all_80_1_122, yields:
% 131.10/89.92 | (1692) all_901_2_687 = all_80_1_122
% 131.10/89.92 |
% 131.10/89.92 | Combining equations (1691,1692) yields a new equation:
% 131.10/89.92 | (1693) all_721_3_683 = all_80_1_122
% 131.10/89.92 |
% 131.10/89.92 | Simplifying 1693 yields:
% 131.10/89.92 | (1694) all_721_3_683 = all_80_1_122
% 131.10/89.92 |
% 131.10/89.92 | Combining equations (1690,1694) yields a new equation:
% 131.10/89.92 | (1594) all_80_1_122 = 0
% 131.10/89.92 |
% 131.10/89.92 +-Applying beta-rule and splitting (1632), into two cases.
% 131.10/89.92 |-Branch one:
% 131.10/89.92 | (1696) ~ (all_80_0_121 = 0)
% 131.10/89.92 |
% 131.10/89.92 | Equations (1689) can reduce 1696 to:
% 131.10/89.92 | (264) $false
% 131.10/89.92 |
% 131.10/89.92 |-The branch is then unsatisfiable
% 131.10/89.92 |-Branch two:
% 131.10/89.92 | (1689) all_80_0_121 = 0
% 131.10/89.92 | (1308) ~ (all_80_1_122 = 0)
% 131.10/89.92 |
% 131.10/89.92 | Equations (1594) can reduce 1308 to:
% 131.10/89.92 | (264) $false
% 131.10/89.92 |
% 131.10/89.92 |-The branch is then unsatisfiable
% 131.10/89.92 |-Branch two:
% 131.10/89.92 | (1701) ~ (all_56_2_101 = all_0_1_1)
% 131.10/89.92 | (1702) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_56_2_101) = v0) | (doDivides0(xr, xk) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 131.10/89.92 |
% 131.10/89.92 | Instantiating (1702) with all_596_0_701, all_596_1_702, all_596_2_703 yields:
% 131.10/89.92 | (1703) ( ~ (all_596_2_703 = 0) & aNaturalNumber0(all_56_2_101) = all_596_2_703) | (doDivides0(xr, xk) = all_596_0_701 & aNaturalNumber0(xr) = all_596_2_703 & aNaturalNumber0(xk) = all_596_1_702 & ( ~ (all_596_0_701 = 0) | ~ (all_596_1_702 = 0) | ~ (all_596_2_703 = 0)))
% 131.10/89.92 |
% 131.10/89.92 +-Applying beta-rule and splitting (1703), into two cases.
% 131.10/89.92 |-Branch one:
% 131.10/89.92 | (1704) ~ (all_596_2_703 = 0) & aNaturalNumber0(all_56_2_101) = all_596_2_703
% 131.10/89.92 |
% 131.10/89.92 | Applying alpha-rule on (1704) yields:
% 131.10/89.92 | (1705) ~ (all_596_2_703 = 0)
% 131.10/89.92 | (1706) aNaturalNumber0(all_56_2_101) = all_596_2_703
% 131.10/89.92 |
% 131.10/89.92 | Instantiating formula (11) with all_56_2_101, all_596_2_703, 0 and discharging atoms aNaturalNumber0(all_56_2_101) = all_596_2_703, aNaturalNumber0(all_56_2_101) = 0, yields:
% 131.10/89.92 | (1707) all_596_2_703 = 0
% 131.10/89.92 |
% 131.10/89.92 | Equations (1707) can reduce 1705 to:
% 131.10/89.92 | (264) $false
% 131.10/89.92 |
% 131.10/89.92 |-The branch is then unsatisfiable
% 131.10/89.92 |-Branch two:
% 131.10/89.92 | (1709) doDivides0(xr, xk) = all_596_0_701 & aNaturalNumber0(xr) = all_596_2_703 & aNaturalNumber0(xk) = all_596_1_702 & ( ~ (all_596_0_701 = 0) | ~ (all_596_1_702 = 0) | ~ (all_596_2_703 = 0))
% 131.10/89.92 |
% 131.10/89.92 | Applying alpha-rule on (1709) yields:
% 131.10/89.92 | (1710) doDivides0(xr, xk) = all_596_0_701
% 131.10/89.92 | (1711) aNaturalNumber0(xr) = all_596_2_703
% 131.10/89.92 | (1712) aNaturalNumber0(xk) = all_596_1_702
% 131.10/89.92 | (1713) ~ (all_596_0_701 = 0) | ~ (all_596_1_702 = 0) | ~ (all_596_2_703 = 0)
% 131.10/89.92 |
% 131.10/89.92 | Instantiating formula (42) with xr, xk, all_596_0_701, 0 and discharging atoms doDivides0(xr, xk) = all_596_0_701, doDivides0(xr, xk) = 0, yields:
% 131.10/89.92 | (1714) all_596_0_701 = 0
% 131.10/89.92 |
% 131.10/89.92 | Instantiating formula (11) with xr, all_596_2_703, 0 and discharging atoms aNaturalNumber0(xr) = all_596_2_703, aNaturalNumber0(xr) = 0, yields:
% 131.10/89.92 | (1707) all_596_2_703 = 0
% 131.10/89.92 |
% 131.10/89.92 | Instantiating formula (11) with xk, all_596_1_702, 0 and discharging atoms aNaturalNumber0(xk) = all_596_1_702, aNaturalNumber0(xk) = 0, yields:
% 131.10/89.92 | (1716) all_596_1_702 = 0
% 131.10/89.92 |
% 131.10/89.92 +-Applying beta-rule and splitting (1713), into two cases.
% 131.10/89.92 |-Branch one:
% 131.10/89.92 | (1717) ~ (all_596_0_701 = 0)
% 131.10/89.92 |
% 131.10/89.92 | Equations (1714) can reduce 1717 to:
% 131.10/89.92 | (264) $false
% 131.10/89.92 |
% 131.10/89.92 |-The branch is then unsatisfiable
% 131.10/89.92 |-Branch two:
% 131.10/89.92 | (1714) all_596_0_701 = 0
% 131.10/89.92 | (1720) ~ (all_596_1_702 = 0) | ~ (all_596_2_703 = 0)
% 131.10/89.92 |
% 131.10/89.92 +-Applying beta-rule and splitting (1720), into two cases.
% 131.10/89.92 |-Branch one:
% 131.10/89.92 | (1721) ~ (all_596_1_702 = 0)
% 131.10/89.92 |
% 131.10/89.92 | Equations (1716) can reduce 1721 to:
% 131.10/89.92 | (264) $false
% 131.10/89.92 |
% 131.10/89.92 |-The branch is then unsatisfiable
% 131.10/89.92 |-Branch two:
% 131.10/89.92 | (1716) all_596_1_702 = 0
% 131.10/89.92 | (1705) ~ (all_596_2_703 = 0)
% 131.10/89.92 |
% 131.10/89.92 | Equations (1707) can reduce 1705 to:
% 131.10/89.92 | (264) $false
% 131.10/89.92 |
% 131.10/89.92 |-The branch is then unsatisfiable
% 131.10/89.92 |-Branch two:
% 131.10/89.92 | (1726) ~ (all_53_2_89 = xk)
% 131.10/89.92 | (1727) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_53_2_89) = v0) | (doDivides0(xp, all_0_9_9) = v2 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 131.10/89.92 |
% 131.10/89.92 +-Applying beta-rule and splitting (746), into two cases.
% 131.10/89.92 |-Branch one:
% 131.10/89.92 | (301) xp = sz00
% 131.10/89.92 |
% 131.10/89.92 | Equations (301) can reduce 102 to:
% 131.10/89.92 | (264) $false
% 131.10/89.92 |
% 131.10/89.92 |-The branch is then unsatisfiable
% 131.10/89.92 |-Branch two:
% 131.10/89.92 | (102) ~ (xp = sz00)
% 131.10/89.92 | (1731) all_53_2_89 = xk | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_53_2_89, xp) = v2 & sdtasdt0(xk, xp) = v3 & aNaturalNumber0(all_53_2_89) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 131.10/89.92 |
% 131.10/89.92 +-Applying beta-rule and splitting (729), into two cases.
% 131.10/89.92 |-Branch one:
% 131.10/89.92 | (296) xr = sz00
% 131.10/89.92 |
% 131.10/89.92 | Equations (296) can reduce 101 to:
% 131.10/89.92 | (264) $false
% 131.10/89.92 |
% 131.10/89.92 |-The branch is then unsatisfiable
% 131.10/89.92 |-Branch two:
% 131.10/89.92 | (101) ~ (xr = sz00)
% 131.10/89.93 | (1291) all_56_2_101 = all_0_1_1 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_56_2_101) = v0) | (doDivides0(xr, xk) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 131.10/89.93 |
% 131.10/89.93 +-Applying beta-rule and splitting (1291), into two cases.
% 131.10/89.93 |-Branch one:
% 131.10/89.93 | (1292) all_56_2_101 = all_0_1_1
% 131.10/89.93 |
% 131.10/89.93 | From (1292) and (937) follows:
% 131.10/89.93 | (1293) sdtasdt0(all_0_1_1, xr) = all_430_0_272
% 131.10/89.93 |
% 131.10/89.93 +-Applying beta-rule and splitting (747), into two cases.
% 131.10/89.93 |-Branch one:
% 131.10/89.93 | (301) xp = sz00
% 131.10/89.93 |
% 131.10/89.93 | Equations (301) can reduce 102 to:
% 131.10/89.93 | (264) $false
% 131.10/89.93 |
% 131.10/89.93 |-The branch is then unsatisfiable
% 131.10/89.93 |-Branch two:
% 131.10/89.93 | (102) ~ (xp = sz00)
% 131.10/89.93 | (1741) all_53_2_89 = xk | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_53_2_89, xp) = v3 & sdtasdt0(xk, xp) = v2 & aNaturalNumber0(all_53_2_89) = v1 & aNaturalNumber0(xk) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 131.10/89.93 |
% 131.10/89.93 +-Applying beta-rule and splitting (1741), into two cases.
% 131.10/89.93 |-Branch one:
% 131.10/89.93 | (1286) all_53_2_89 = xk
% 131.10/89.93 |
% 131.10/89.93 | Equations (1286) can reduce 1726 to:
% 131.10/89.93 | (264) $false
% 131.10/89.93 |
% 131.10/89.93 |-The branch is then unsatisfiable
% 131.10/89.93 |-Branch two:
% 131.10/89.93 | (1726) ~ (all_53_2_89 = xk)
% 131.10/89.93 | (1745) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_53_2_89, xp) = v3 & sdtasdt0(xk, xp) = v2 & aNaturalNumber0(all_53_2_89) = v1 & aNaturalNumber0(xk) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 131.10/89.93 |
% 131.10/89.93 | Instantiating (1745) with all_717_0_814, all_717_1_815, all_717_2_816, all_717_3_817 yields:
% 131.10/89.93 | (1746) sdtasdt0(all_53_2_89, xp) = all_717_0_814 & sdtasdt0(xk, xp) = all_717_1_815 & aNaturalNumber0(all_53_2_89) = all_717_2_816 & aNaturalNumber0(xk) = all_717_3_817 & ( ~ (all_717_2_816 = 0) | ~ (all_717_3_817 = 0))
% 131.10/89.93 |
% 131.10/89.93 | Applying alpha-rule on (1746) yields:
% 131.10/89.93 | (1747) ~ (all_717_2_816 = 0) | ~ (all_717_3_817 = 0)
% 131.10/89.93 | (1748) aNaturalNumber0(all_53_2_89) = all_717_2_816
% 131.10/89.93 | (1749) sdtasdt0(all_53_2_89, xp) = all_717_0_814
% 131.10/89.93 | (1750) sdtasdt0(xk, xp) = all_717_1_815
% 131.10/89.93 | (1751) aNaturalNumber0(xk) = all_717_3_817
% 131.10/89.93 |
% 131.10/89.93 +-Applying beta-rule and splitting (1049), into two cases.
% 131.10/89.93 |-Branch one:
% 131.10/89.93 | (1621) ~ (sdtasdt0(all_0_1_1, xr) = all_430_0_272)
% 131.10/89.93 |
% 131.10/89.93 | Using (1293) and (1621) yields:
% 131.10/89.93 | (543) $false
% 131.10/89.93 |
% 131.10/89.93 |-The branch is then unsatisfiable
% 131.10/89.93 |-Branch two:
% 131.10/89.93 | (1293) sdtasdt0(all_0_1_1, xr) = all_430_0_272
% 131.10/89.93 | (1625) all_430_0_272 = all_44_1_66
% 131.10/89.93 |
% 131.10/89.93 +-Applying beta-rule and splitting (940), into two cases.
% 131.10/89.93 |-Branch one:
% 131.10/89.93 | (1612) ~ (all_430_1_273 = 0)
% 131.10/89.93 |
% 131.10/89.93 | Equations (1059) can reduce 1612 to:
% 131.10/89.93 | (264) $false
% 131.10/89.93 |
% 131.10/89.93 |-The branch is then unsatisfiable
% 131.10/89.93 |-Branch two:
% 131.10/89.93 | (1059) all_430_1_273 = 0
% 131.10/89.93 | (1615) ~ (all_430_2_274 = 0) | all_430_0_272 = xk
% 131.10/89.93 |
% 131.10/89.93 +-Applying beta-rule and splitting (1615), into two cases.
% 131.10/89.93 |-Branch one:
% 131.10/89.93 | (1616) ~ (all_430_2_274 = 0)
% 131.10/89.93 |
% 131.10/89.93 | Equations (1270) can reduce 1616 to:
% 131.10/89.93 | (264) $false
% 131.10/89.93 |
% 131.10/89.93 |-The branch is then unsatisfiable
% 131.10/89.93 |-Branch two:
% 131.10/89.93 | (1270) all_430_2_274 = 0
% 131.10/89.93 | (1619) all_430_0_272 = xk
% 131.10/89.93 |
% 131.10/89.93 | Combining equations (1625,1619) yields a new equation:
% 131.10/89.93 | (1626) all_44_1_66 = xk
% 131.10/89.93 |
% 131.10/89.93 | Simplifying 1626 yields:
% 131.10/89.93 | (1522) all_44_1_66 = xk
% 131.10/89.93 |
% 131.10/89.93 | From (1522) and (906) follows:
% 131.10/89.93 | (1766) aNaturalNumber0(xk) = all_418_1_253
% 131.10/89.93 |
% 131.10/89.93 +-Applying beta-rule and splitting (1105), into two cases.
% 131.10/89.93 |-Branch one:
% 131.10/89.93 | (1767) ~ (aNaturalNumber0(xk) = all_450_0_310)
% 131.10/89.93 |
% 131.10/89.93 | From (1066) and (1767) follows:
% 131.10/89.93 | (1768) ~ (aNaturalNumber0(xk) = all_418_1_253)
% 131.10/89.93 |
% 131.10/89.93 | Using (1766) and (1768) yields:
% 131.10/89.93 | (543) $false
% 131.10/89.93 |
% 131.10/89.93 |-The branch is then unsatisfiable
% 131.10/89.93 |-Branch two:
% 131.10/89.93 | (1770) aNaturalNumber0(xk) = all_450_0_310
% 131.10/89.93 | (1771) all_450_0_310 = all_388_3_180
% 131.10/89.93 |
% 131.10/89.93 | Combining equations (1771,1066) yields a new equation:
% 131.10/89.93 | (1772) all_418_1_253 = all_388_3_180
% 131.10/89.93 |
% 131.10/89.93 | Combining equations (1225,1772) yields a new equation:
% 131.10/89.93 | (1529) all_418_1_253 = 0
% 131.10/89.93 |
% 131.10/89.93 | From (1529) and (1766) follows:
% 131.10/89.93 | (549) aNaturalNumber0(xk) = 0
% 131.10/89.93 |
% 131.10/89.93 | Instantiating formula (11) with all_53_2_89, all_717_2_816, 0 and discharging atoms aNaturalNumber0(all_53_2_89) = all_717_2_816, aNaturalNumber0(all_53_2_89) = 0, yields:
% 131.10/89.93 | (1775) all_717_2_816 = 0
% 131.10/89.93 |
% 131.10/89.93 | Instantiating formula (11) with xk, all_717_3_817, 0 and discharging atoms aNaturalNumber0(xk) = all_717_3_817, aNaturalNumber0(xk) = 0, yields:
% 131.10/89.93 | (1776) all_717_3_817 = 0
% 131.10/89.93 |
% 131.10/89.93 +-Applying beta-rule and splitting (1747), into two cases.
% 131.10/89.93 |-Branch one:
% 131.10/89.93 | (1777) ~ (all_717_2_816 = 0)
% 131.10/89.93 |
% 131.10/89.93 | Equations (1775) can reduce 1777 to:
% 131.10/89.93 | (264) $false
% 131.10/89.93 |
% 131.10/89.93 |-The branch is then unsatisfiable
% 131.10/89.93 |-Branch two:
% 131.10/89.93 | (1775) all_717_2_816 = 0
% 131.10/89.93 | (1780) ~ (all_717_3_817 = 0)
% 131.10/89.93 |
% 131.10/89.93 | Equations (1776) can reduce 1780 to:
% 131.10/89.93 | (264) $false
% 131.10/89.93 |
% 131.10/89.93 |-The branch is then unsatisfiable
% 131.10/89.93 |-Branch two:
% 131.10/89.93 | (1701) ~ (all_56_2_101 = all_0_1_1)
% 131.10/89.93 | (1702) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_56_2_101) = v0) | (doDivides0(xr, xk) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 131.10/89.93 |
% 131.10/89.93 | Instantiating (1702) with all_597_0_832, all_597_1_833, all_597_2_834 yields:
% 131.10/89.93 | (1784) ( ~ (all_597_2_834 = 0) & aNaturalNumber0(all_56_2_101) = all_597_2_834) | (doDivides0(xr, xk) = all_597_0_832 & aNaturalNumber0(xr) = all_597_2_834 & aNaturalNumber0(xk) = all_597_1_833 & ( ~ (all_597_0_832 = 0) | ~ (all_597_1_833 = 0) | ~ (all_597_2_834 = 0)))
% 131.10/89.93 |
% 131.10/89.93 +-Applying beta-rule and splitting (1784), into two cases.
% 131.10/89.93 |-Branch one:
% 131.10/89.93 | (1785) ~ (all_597_2_834 = 0) & aNaturalNumber0(all_56_2_101) = all_597_2_834
% 131.10/89.93 |
% 131.10/89.93 | Applying alpha-rule on (1785) yields:
% 131.10/89.93 | (1786) ~ (all_597_2_834 = 0)
% 131.10/89.93 | (1787) aNaturalNumber0(all_56_2_101) = all_597_2_834
% 131.10/89.93 |
% 131.10/89.93 | Instantiating formula (11) with all_56_2_101, all_597_2_834, 0 and discharging atoms aNaturalNumber0(all_56_2_101) = all_597_2_834, aNaturalNumber0(all_56_2_101) = 0, yields:
% 131.10/89.93 | (1788) all_597_2_834 = 0
% 131.10/89.93 |
% 131.10/89.93 | Equations (1788) can reduce 1786 to:
% 131.10/89.93 | (264) $false
% 131.10/89.93 |
% 131.10/89.93 |-The branch is then unsatisfiable
% 131.10/89.93 |-Branch two:
% 131.10/89.93 | (1790) doDivides0(xr, xk) = all_597_0_832 & aNaturalNumber0(xr) = all_597_2_834 & aNaturalNumber0(xk) = all_597_1_833 & ( ~ (all_597_0_832 = 0) | ~ (all_597_1_833 = 0) | ~ (all_597_2_834 = 0))
% 131.10/89.93 |
% 131.10/89.93 | Applying alpha-rule on (1790) yields:
% 131.10/89.93 | (1791) doDivides0(xr, xk) = all_597_0_832
% 131.10/89.93 | (1792) aNaturalNumber0(xr) = all_597_2_834
% 131.10/89.93 | (1793) aNaturalNumber0(xk) = all_597_1_833
% 131.10/89.93 | (1794) ~ (all_597_0_832 = 0) | ~ (all_597_1_833 = 0) | ~ (all_597_2_834 = 0)
% 131.10/89.93 |
% 131.10/89.93 +-Applying beta-rule and splitting (747), into two cases.
% 131.10/89.93 |-Branch one:
% 131.10/89.93 | (301) xp = sz00
% 131.10/89.93 |
% 131.10/89.93 | Equations (301) can reduce 102 to:
% 131.10/89.93 | (264) $false
% 131.10/89.93 |
% 131.10/89.93 |-The branch is then unsatisfiable
% 131.10/89.93 |-Branch two:
% 131.10/89.93 | (102) ~ (xp = sz00)
% 131.10/89.93 | (1741) all_53_2_89 = xk | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_53_2_89, xp) = v3 & sdtasdt0(xk, xp) = v2 & aNaturalNumber0(all_53_2_89) = v1 & aNaturalNumber0(xk) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 131.10/89.93 |
% 131.10/89.93 +-Applying beta-rule and splitting (1741), into two cases.
% 131.10/89.93 |-Branch one:
% 131.10/89.93 | (1286) all_53_2_89 = xk
% 131.10/89.93 |
% 131.10/89.93 | Equations (1286) can reduce 1726 to:
% 131.10/89.93 | (264) $false
% 131.10/89.93 |
% 131.10/89.93 |-The branch is then unsatisfiable
% 131.10/89.93 |-Branch two:
% 131.10/89.93 | (1726) ~ (all_53_2_89 = xk)
% 131.10/89.93 | (1745) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_53_2_89, xp) = v3 & sdtasdt0(xk, xp) = v2 & aNaturalNumber0(all_53_2_89) = v1 & aNaturalNumber0(xk) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 131.10/89.93 |
% 131.10/89.93 | Instantiating (1745) with all_674_0_843, all_674_1_844, all_674_2_845, all_674_3_846 yields:
% 131.10/89.93 | (1803) sdtasdt0(all_53_2_89, xp) = all_674_0_843 & sdtasdt0(xk, xp) = all_674_1_844 & aNaturalNumber0(all_53_2_89) = all_674_2_845 & aNaturalNumber0(xk) = all_674_3_846 & ( ~ (all_674_2_845 = 0) | ~ (all_674_3_846 = 0))
% 131.10/89.93 |
% 131.10/89.93 | Applying alpha-rule on (1803) yields:
% 131.10/89.93 | (1804) sdtasdt0(xk, xp) = all_674_1_844
% 131.10/89.93 | (1805) sdtasdt0(all_53_2_89, xp) = all_674_0_843
% 131.10/89.94 | (1806) ~ (all_674_2_845 = 0) | ~ (all_674_3_846 = 0)
% 131.10/89.94 | (1807) aNaturalNumber0(all_53_2_89) = all_674_2_845
% 131.10/89.94 | (1808) aNaturalNumber0(xk) = all_674_3_846
% 131.10/89.94 |
% 131.10/89.94 | Instantiating formula (42) with xr, xk, all_597_0_832, 0 and discharging atoms doDivides0(xr, xk) = all_597_0_832, doDivides0(xr, xk) = 0, yields:
% 131.10/89.94 | (1809) all_597_0_832 = 0
% 131.10/89.94 |
% 131.10/89.94 | Instantiating formula (11) with xr, all_597_2_834, 0 and discharging atoms aNaturalNumber0(xr) = all_597_2_834, aNaturalNumber0(xr) = 0, yields:
% 131.10/89.94 | (1788) all_597_2_834 = 0
% 131.10/89.94 |
% 131.10/89.94 | Instantiating formula (11) with xk, all_674_3_846, 0 and discharging atoms aNaturalNumber0(xk) = all_674_3_846, aNaturalNumber0(xk) = 0, yields:
% 131.10/89.94 | (1811) all_674_3_846 = 0
% 131.10/89.94 |
% 131.10/89.94 | Instantiating formula (11) with xk, all_597_1_833, all_674_3_846 and discharging atoms aNaturalNumber0(xk) = all_674_3_846, aNaturalNumber0(xk) = all_597_1_833, yields:
% 131.10/89.94 | (1812) all_674_3_846 = all_597_1_833
% 131.10/89.94 |
% 131.10/89.94 | Combining equations (1812,1811) yields a new equation:
% 131.10/89.94 | (1813) all_597_1_833 = 0
% 131.10/89.94 |
% 131.10/89.94 | Simplifying 1813 yields:
% 131.10/89.94 | (1814) all_597_1_833 = 0
% 131.10/89.94 |
% 131.10/89.94 +-Applying beta-rule and splitting (1794), into two cases.
% 131.10/89.94 |-Branch one:
% 131.10/89.94 | (1815) ~ (all_597_0_832 = 0)
% 131.10/89.94 |
% 131.10/89.94 | Equations (1809) can reduce 1815 to:
% 131.10/89.94 | (264) $false
% 131.10/89.94 |
% 131.10/89.94 |-The branch is then unsatisfiable
% 131.10/89.94 |-Branch two:
% 131.10/89.94 | (1809) all_597_0_832 = 0
% 131.10/89.94 | (1818) ~ (all_597_1_833 = 0) | ~ (all_597_2_834 = 0)
% 131.10/89.94 |
% 131.10/89.94 +-Applying beta-rule and splitting (1818), into two cases.
% 131.10/89.94 |-Branch one:
% 131.10/89.94 | (1819) ~ (all_597_1_833 = 0)
% 131.10/89.94 |
% 131.10/89.94 | Equations (1814) can reduce 1819 to:
% 131.10/89.94 | (264) $false
% 131.10/89.94 |
% 131.10/89.94 |-The branch is then unsatisfiable
% 131.10/89.94 |-Branch two:
% 131.10/89.94 | (1814) all_597_1_833 = 0
% 131.10/89.94 | (1786) ~ (all_597_2_834 = 0)
% 131.10/89.94 |
% 131.10/89.94 | Equations (1788) can reduce 1786 to:
% 131.10/89.94 | (264) $false
% 131.10/89.94 |
% 131.10/89.94 |-The branch is then unsatisfiable
% 131.10/89.94 |-Branch two:
% 131.10/89.94 | (1824) aNaturalNumber0(xk) = all_57_2_104 & aNaturalNumber0(xp) = all_57_1_103 & ( ~ (all_57_1_103 = 0) | ~ (all_57_2_104 = 0))
% 131.10/89.94 |
% 131.10/89.94 | Applying alpha-rule on (1824) yields:
% 131.10/89.94 | (1825) aNaturalNumber0(xk) = all_57_2_104
% 131.10/89.94 | (1826) aNaturalNumber0(xp) = all_57_1_103
% 131.10/89.94 | (1827) ~ (all_57_1_103 = 0) | ~ (all_57_2_104 = 0)
% 131.10/89.94 |
% 131.10/89.94 | Instantiating formula (11) with xk, all_57_2_104, 0 and discharging atoms aNaturalNumber0(xk) = all_57_2_104, aNaturalNumber0(xk) = 0, yields:
% 131.10/89.94 | (1828) all_57_2_104 = 0
% 131.10/89.94 |
% 131.10/89.94 | Instantiating formula (11) with xp, all_57_1_103, 0 and discharging atoms aNaturalNumber0(xp) = all_57_1_103, aNaturalNumber0(xp) = 0, yields:
% 131.10/89.94 | (713) all_57_1_103 = 0
% 131.10/89.94 |
% 131.10/89.94 +-Applying beta-rule and splitting (1827), into two cases.
% 131.10/89.94 |-Branch one:
% 131.10/89.94 | (1830) ~ (all_57_1_103 = 0)
% 131.10/89.94 |
% 131.10/89.94 | Equations (713) can reduce 1830 to:
% 131.10/89.94 | (264) $false
% 131.10/89.94 |
% 131.10/89.94 |-The branch is then unsatisfiable
% 131.10/89.94 |-Branch two:
% 131.10/89.94 | (713) all_57_1_103 = 0
% 131.10/89.94 | (1833) ~ (all_57_2_104 = 0)
% 131.10/89.94 |
% 131.10/89.94 | Equations (1828) can reduce 1833 to:
% 131.10/89.94 | (264) $false
% 131.10/89.94 |
% 131.10/89.94 |-The branch is then unsatisfiable
% 131.10/89.94 |-Branch two:
% 131.10/89.94 | (1835) sdtasdt0(sz00, xm) = all_0_9_9
% 131.10/89.94 | (1836) ? [v0] : ? [v1] : (sdtasdt0(xm, sz00) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v0 = 0) | (v1 = sz00 & all_0_9_9 = sz00)))
% 131.10/89.94 |
% 131.10/89.94 | Instantiating (1836) with all_268_0_847, all_268_1_848 yields:
% 131.10/89.94 | (1837) sdtasdt0(xm, sz00) = all_268_0_847 & aNaturalNumber0(xm) = all_268_1_848 & ( ~ (all_268_1_848 = 0) | (all_268_0_847 = sz00 & all_0_9_9 = sz00))
% 131.10/89.94 |
% 131.10/89.94 | Applying alpha-rule on (1837) yields:
% 131.10/89.94 | (1838) sdtasdt0(xm, sz00) = all_268_0_847
% 131.10/89.94 | (1839) aNaturalNumber0(xm) = all_268_1_848
% 131.10/89.94 | (1840) ~ (all_268_1_848 = 0) | (all_268_0_847 = sz00 & all_0_9_9 = sz00)
% 131.10/89.94 |
% 131.10/89.94 +-Applying beta-rule and splitting (1840), into two cases.
% 131.10/89.94 |-Branch one:
% 131.10/89.94 | (1841) ~ (all_268_1_848 = 0)
% 131.10/89.94 |
% 131.10/89.94 | Instantiating formula (11) with xm, all_268_1_848, 0 and discharging atoms aNaturalNumber0(xm) = all_268_1_848, aNaturalNumber0(xm) = 0, yields:
% 131.10/89.94 | (1842) all_268_1_848 = 0
% 131.10/89.94 |
% 131.10/89.94 | Equations (1842) can reduce 1841 to:
% 131.10/89.94 | (264) $false
% 131.10/89.94 |
% 131.10/89.94 |-The branch is then unsatisfiable
% 131.10/89.94 |-Branch two:
% 131.10/89.94 | (1842) all_268_1_848 = 0
% 131.10/89.94 | (1845) all_268_0_847 = sz00 & all_0_9_9 = sz00
% 131.10/89.94 |
% 131.10/89.94 | Applying alpha-rule on (1845) yields:
% 131.10/89.94 | (1846) all_268_0_847 = sz00
% 131.10/89.94 | (642) all_0_9_9 = sz00
% 131.10/89.94 |
% 131.10/89.94 | Equations (642) can reduce 640 to:
% 131.10/89.94 | (264) $false
% 131.10/89.94 |
% 131.10/89.94 |-The branch is then unsatisfiable
% 131.10/89.94 |-Branch two:
% 131.10/89.94 | (1849) aNaturalNumber0(xr) = all_56_2_101 & aNaturalNumber0(xk) = all_56_1_100 & ( ~ (all_56_1_100 = 0) | ~ (all_56_2_101 = 0))
% 131.10/89.94 |
% 131.10/89.94 | Applying alpha-rule on (1849) yields:
% 131.10/89.94 | (1850) aNaturalNumber0(xr) = all_56_2_101
% 131.10/89.94 | (1851) aNaturalNumber0(xk) = all_56_1_100
% 131.10/89.94 | (1852) ~ (all_56_1_100 = 0) | ~ (all_56_2_101 = 0)
% 131.10/89.94 |
% 131.10/89.94 | Instantiating formula (11) with xr, all_56_2_101, 0 and discharging atoms aNaturalNumber0(xr) = all_56_2_101, aNaturalNumber0(xr) = 0, yields:
% 131.10/89.94 | (1853) all_56_2_101 = 0
% 131.10/89.94 |
% 131.10/89.94 | Instantiating formula (11) with xk, all_56_1_100, 0 and discharging atoms aNaturalNumber0(xk) = all_56_1_100, aNaturalNumber0(xk) = 0, yields:
% 131.10/89.94 | (620) all_56_1_100 = 0
% 131.10/89.94 |
% 131.10/89.94 +-Applying beta-rule and splitting (1852), into two cases.
% 131.10/89.94 |-Branch one:
% 131.10/89.94 | (1855) ~ (all_56_1_100 = 0)
% 131.10/89.94 |
% 131.10/89.94 | Equations (620) can reduce 1855 to:
% 131.10/89.94 | (264) $false
% 131.10/89.94 |
% 131.10/89.94 |-The branch is then unsatisfiable
% 131.10/89.94 |-Branch two:
% 131.10/89.94 | (620) all_56_1_100 = 0
% 131.10/89.94 | (1858) ~ (all_56_2_101 = 0)
% 131.10/89.94 |
% 131.10/89.94 | Equations (1853) can reduce 1858 to:
% 131.10/89.94 | (264) $false
% 131.10/89.94 |
% 131.10/89.94 |-The branch is then unsatisfiable
% 131.10/89.94 |-Branch two:
% 131.10/89.94 | (1860) aNaturalNumber0(xr) = all_48_2_75 & aNaturalNumber0(xk) = all_48_1_74 & ( ~ (all_48_1_74 = 0) | ~ (all_48_2_75 = 0))
% 131.10/89.94 |
% 131.10/89.94 | Applying alpha-rule on (1860) yields:
% 131.10/89.94 | (1861) aNaturalNumber0(xr) = all_48_2_75
% 131.10/89.94 | (1862) aNaturalNumber0(xk) = all_48_1_74
% 131.10/89.94 | (1863) ~ (all_48_1_74 = 0) | ~ (all_48_2_75 = 0)
% 131.10/89.94 |
% 131.10/89.94 | Instantiating formula (11) with xr, all_48_2_75, 0 and discharging atoms aNaturalNumber0(xr) = all_48_2_75, aNaturalNumber0(xr) = 0, yields:
% 131.10/89.94 | (1864) all_48_2_75 = 0
% 131.10/89.94 |
% 131.10/89.94 | Instantiating formula (11) with xk, all_48_1_74, 0 and discharging atoms aNaturalNumber0(xk) = all_48_1_74, aNaturalNumber0(xk) = 0, yields:
% 131.10/89.94 | (585) all_48_1_74 = 0
% 131.10/89.94 |
% 131.10/89.94 +-Applying beta-rule and splitting (1863), into two cases.
% 131.10/89.94 |-Branch one:
% 131.10/89.94 | (1866) ~ (all_48_1_74 = 0)
% 131.10/89.94 |
% 131.10/89.94 | Equations (585) can reduce 1866 to:
% 131.10/89.94 | (264) $false
% 131.10/89.94 |
% 131.10/89.94 |-The branch is then unsatisfiable
% 131.10/89.94 |-Branch two:
% 131.10/89.94 | (585) all_48_1_74 = 0
% 131.10/89.94 | (1869) ~ (all_48_2_75 = 0)
% 131.10/89.94 |
% 131.10/89.94 | Equations (1864) can reduce 1869 to:
% 131.10/89.94 | (264) $false
% 131.10/89.94 |
% 131.10/89.94 |-The branch is then unsatisfiable
% 131.10/89.94 |-Branch two:
% 131.10/89.94 | (1871) sdtasdt0(xp, xk) = sz00
% 131.10/89.94 | (1872) xk = sz00 | xp = sz00 | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 131.10/89.94 |
% 131.10/89.94 +-Applying beta-rule and splitting (1872), into two cases.
% 131.10/89.94 |-Branch one:
% 131.10/89.94 | (1873) xk = sz00
% 131.10/89.94 |
% 131.10/89.94 | Equations (1873) can reduce 17 to:
% 131.10/89.94 | (264) $false
% 131.10/89.94 |
% 131.10/89.94 |-The branch is then unsatisfiable
% 131.10/89.94 |-Branch two:
% 131.10/89.94 | (17) ~ (xk = sz00)
% 131.10/89.94 | (1876) xp = sz00 | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 131.10/89.94 |
% 131.10/89.94 +-Applying beta-rule and splitting (1876), into two cases.
% 131.10/89.94 |-Branch one:
% 131.10/89.94 | (301) xp = sz00
% 131.10/89.94 |
% 131.10/89.94 | Equations (301) can reduce 102 to:
% 131.10/89.94 | (264) $false
% 131.10/89.94 |
% 131.10/89.94 |-The branch is then unsatisfiable
% 131.10/89.94 |-Branch two:
% 131.10/89.94 | (102) ~ (xp = sz00)
% 131.10/89.95 | (1880) ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 131.10/89.95 |
% 131.10/89.95 | Instantiating (1880) with all_218_0_852, all_218_1_853 yields:
% 131.10/89.95 | (1881) aNaturalNumber0(xk) = all_218_0_852 & aNaturalNumber0(xp) = all_218_1_853 & ( ~ (all_218_0_852 = 0) | ~ (all_218_1_853 = 0))
% 131.10/89.95 |
% 131.10/89.95 | Applying alpha-rule on (1881) yields:
% 131.10/89.95 | (1882) aNaturalNumber0(xk) = all_218_0_852
% 131.10/89.95 | (1883) aNaturalNumber0(xp) = all_218_1_853
% 131.10/89.95 | (1884) ~ (all_218_0_852 = 0) | ~ (all_218_1_853 = 0)
% 131.10/89.95 |
% 131.10/89.95 | Instantiating formula (11) with xk, all_218_0_852, 0 and discharging atoms aNaturalNumber0(xk) = all_218_0_852, aNaturalNumber0(xk) = 0, yields:
% 131.10/89.95 | (1885) all_218_0_852 = 0
% 131.10/89.95 |
% 131.10/89.95 | Instantiating formula (11) with xp, all_218_1_853, 0 and discharging atoms aNaturalNumber0(xp) = all_218_1_853, aNaturalNumber0(xp) = 0, yields:
% 131.10/89.95 | (1886) all_218_1_853 = 0
% 131.10/89.95 |
% 131.10/89.95 +-Applying beta-rule and splitting (1884), into two cases.
% 131.10/89.95 |-Branch one:
% 131.10/89.95 | (1887) ~ (all_218_0_852 = 0)
% 131.10/89.95 |
% 131.10/89.95 | Equations (1885) can reduce 1887 to:
% 131.10/89.95 | (264) $false
% 131.10/89.95 |
% 131.10/89.95 |-The branch is then unsatisfiable
% 131.10/89.95 |-Branch two:
% 131.10/89.95 | (1885) all_218_0_852 = 0
% 131.10/89.95 | (1890) ~ (all_218_1_853 = 0)
% 131.10/89.95 |
% 131.10/89.95 | Equations (1886) can reduce 1890 to:
% 131.10/89.95 | (264) $false
% 131.10/89.95 |
% 131.10/89.95 |-The branch is then unsatisfiable
% 131.10/89.95 |-Branch two:
% 131.10/89.95 | (993) all_75_0_118 = 0
% 131.10/89.95 | (1893) ~ (all_75_1_119 = 0) | ~ (all_75_2_120 = 0)
% 131.10/89.95 |
% 131.10/89.95 +-Applying beta-rule and splitting (1893), into two cases.
% 131.10/89.95 |-Branch one:
% 131.10/89.95 | (1894) ~ (all_75_1_119 = 0)
% 131.10/89.95 |
% 131.10/89.95 | Equations (355) can reduce 1894 to:
% 131.10/89.95 | (264) $false
% 131.10/89.95 |
% 131.10/89.95 |-The branch is then unsatisfiable
% 131.10/89.95 |-Branch two:
% 131.10/89.95 | (355) all_75_1_119 = 0
% 131.10/89.95 | (1897) ~ (all_75_2_120 = 0)
% 131.10/89.95 |
% 131.10/89.95 | Equations (557) can reduce 1897 to:
% 131.10/89.95 | (264) $false
% 131.10/89.95 |
% 131.10/89.95 |-The branch is then unsatisfiable
% 131.10/89.95 |-Branch two:
% 131.10/89.95 | (1899) ~ (all_0_3_3 = all_0_9_9)
% 131.10/89.95 | (1900) ? [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)))
% 131.10/89.95 |
% 131.10/89.95 | Instantiating (1900) with all_190_0_860, all_190_1_861, all_190_2_862 yields:
% 131.10/89.95 | (1901) doDivides0(xp, all_0_9_9) = all_190_0_860 & aNaturalNumber0(all_0_9_9) = all_190_1_861 & aNaturalNumber0(xp) = all_190_2_862 & ( ~ (all_190_0_860 = 0) | ~ (all_190_1_861 = 0) | ~ (all_190_2_862 = 0))
% 131.10/89.95 |
% 131.10/89.95 | Applying alpha-rule on (1901) yields:
% 131.10/89.95 | (1902) doDivides0(xp, all_0_9_9) = all_190_0_860
% 131.10/89.95 | (1903) aNaturalNumber0(all_0_9_9) = all_190_1_861
% 131.10/89.95 | (1904) aNaturalNumber0(xp) = all_190_2_862
% 131.10/89.95 | (1905) ~ (all_190_0_860 = 0) | ~ (all_190_1_861 = 0) | ~ (all_190_2_862 = 0)
% 131.10/89.95 |
% 131.10/89.95 | Instantiating formula (42) with xp, all_0_9_9, all_190_0_860, 0 and discharging atoms doDivides0(xp, all_0_9_9) = all_190_0_860, doDivides0(xp, all_0_9_9) = 0, yields:
% 131.10/89.95 | (1906) all_190_0_860 = 0
% 131.10/89.95 |
% 131.10/89.95 | Instantiating formula (11) with all_0_9_9, all_190_1_861, 0 and discharging atoms aNaturalNumber0(all_0_9_9) = all_190_1_861, aNaturalNumber0(all_0_9_9) = 0, yields:
% 131.10/89.95 | (1907) all_190_1_861 = 0
% 131.10/89.95 |
% 131.10/89.95 | Instantiating formula (11) with xp, all_190_2_862, 0 and discharging atoms aNaturalNumber0(xp) = all_190_2_862, aNaturalNumber0(xp) = 0, yields:
% 131.10/89.95 | (1908) all_190_2_862 = 0
% 131.10/89.95 |
% 131.10/89.95 +-Applying beta-rule and splitting (1905), into two cases.
% 131.10/89.95 |-Branch one:
% 131.10/89.95 | (1909) ~ (all_190_0_860 = 0)
% 131.10/89.95 |
% 131.10/89.95 | Equations (1906) can reduce 1909 to:
% 131.10/89.95 | (264) $false
% 131.10/89.95 |
% 131.10/89.95 |-The branch is then unsatisfiable
% 131.10/89.95 |-Branch two:
% 131.10/89.95 | (1906) all_190_0_860 = 0
% 131.10/89.95 | (1912) ~ (all_190_1_861 = 0) | ~ (all_190_2_862 = 0)
% 131.10/89.95 |
% 131.10/89.95 +-Applying beta-rule and splitting (1912), into two cases.
% 131.10/89.95 |-Branch one:
% 131.10/89.95 | (1913) ~ (all_190_1_861 = 0)
% 131.10/89.95 |
% 131.10/89.95 | Equations (1907) can reduce 1913 to:
% 131.10/89.95 | (264) $false
% 131.10/89.95 |
% 131.10/89.95 |-The branch is then unsatisfiable
% 131.10/89.95 |-Branch two:
% 131.10/89.95 | (1907) all_190_1_861 = 0
% 131.10/89.95 | (1916) ~ (all_190_2_862 = 0)
% 131.10/89.95 |
% 131.10/89.95 | Equations (1908) can reduce 1916 to:
% 131.10/89.95 | (264) $false
% 131.10/89.95 |
% 131.10/89.95 |-The branch is then unsatisfiable
% 131.10/89.95 |-Branch two:
% 131.10/89.95 | (1918) doDivides0(xp, all_0_9_9) = all_88_0_126 & aNaturalNumber0(all_0_9_9) = all_88_1_127 & aNaturalNumber0(xp) = all_88_2_128 & ( ~ (all_88_0_126 = 0) | ~ (all_88_1_127 = 0) | ~ (all_88_2_128 = 0))
% 131.10/89.95 |
% 131.10/89.95 | Applying alpha-rule on (1918) yields:
% 131.10/89.95 | (1919) doDivides0(xp, all_0_9_9) = all_88_0_126
% 131.10/89.95 | (1920) aNaturalNumber0(all_0_9_9) = all_88_1_127
% 131.10/89.95 | (1921) aNaturalNumber0(xp) = all_88_2_128
% 131.10/89.95 | (1922) ~ (all_88_0_126 = 0) | ~ (all_88_1_127 = 0) | ~ (all_88_2_128 = 0)
% 131.10/89.95 |
% 131.10/89.95 | Instantiating formula (42) with xp, all_0_9_9, all_88_0_126, 0 and discharging atoms doDivides0(xp, all_0_9_9) = all_88_0_126, doDivides0(xp, all_0_9_9) = 0, yields:
% 131.10/89.95 | (1923) all_88_0_126 = 0
% 131.10/89.95 |
% 131.10/89.95 | Instantiating formula (11) with all_0_9_9, all_88_1_127, 0 and discharging atoms aNaturalNumber0(all_0_9_9) = all_88_1_127, aNaturalNumber0(all_0_9_9) = 0, yields:
% 131.10/89.95 | (1924) all_88_1_127 = 0
% 131.10/89.95 |
% 131.10/89.95 | Instantiating formula (11) with xp, all_88_2_128, 0 and discharging atoms aNaturalNumber0(xp) = all_88_2_128, aNaturalNumber0(xp) = 0, yields:
% 131.10/89.95 | (548) all_88_2_128 = 0
% 131.10/89.95 |
% 131.10/89.95 +-Applying beta-rule and splitting (1922), into two cases.
% 131.10/89.95 |-Branch one:
% 131.10/89.95 | (1926) ~ (all_88_0_126 = 0)
% 131.10/89.95 |
% 131.10/89.95 | Equations (1923) can reduce 1926 to:
% 131.10/89.95 | (264) $false
% 131.10/89.95 |
% 131.10/89.95 |-The branch is then unsatisfiable
% 131.10/89.95 |-Branch two:
% 131.10/89.95 | (1923) all_88_0_126 = 0
% 131.10/89.95 | (1929) ~ (all_88_1_127 = 0) | ~ (all_88_2_128 = 0)
% 131.10/89.95 |
% 131.10/89.95 +-Applying beta-rule and splitting (1929), into two cases.
% 131.10/89.95 |-Branch one:
% 131.10/89.95 | (1930) ~ (all_88_1_127 = 0)
% 131.10/89.95 |
% 131.10/89.95 | Equations (1924) can reduce 1930 to:
% 131.10/89.95 | (264) $false
% 131.10/89.95 |
% 131.10/89.95 |-The branch is then unsatisfiable
% 131.10/89.95 |-Branch two:
% 131.10/89.95 | (1924) all_88_1_127 = 0
% 131.10/89.95 | (1933) ~ (all_88_2_128 = 0)
% 131.10/89.95 |
% 131.10/89.95 | Equations (548) can reduce 1933 to:
% 131.10/89.95 | (264) $false
% 131.10/89.95 |
% 131.10/89.95 |-The branch is then unsatisfiable
% 131.10/89.95 |-Branch two:
% 131.10/89.95 | (1935) aNaturalNumber0(all_0_9_9) = all_60_1_109 & aNaturalNumber0(xr) = all_60_2_110 & ( ~ (all_60_1_109 = 0) | ~ (all_60_2_110 = 0))
% 131.10/89.95 |
% 131.10/89.95 | Applying alpha-rule on (1935) yields:
% 131.10/89.95 | (1936) aNaturalNumber0(all_0_9_9) = all_60_1_109
% 131.10/89.95 | (1937) aNaturalNumber0(xr) = all_60_2_110
% 131.10/89.95 | (1938) ~ (all_60_1_109 = 0) | ~ (all_60_2_110 = 0)
% 131.10/89.95 |
% 131.10/89.95 | Instantiating formula (11) with all_0_9_9, all_60_1_109, 0 and discharging atoms aNaturalNumber0(all_0_9_9) = all_60_1_109, aNaturalNumber0(all_0_9_9) = 0, yields:
% 131.10/89.95 | (539) all_60_1_109 = 0
% 131.10/89.95 |
% 131.10/89.95 | Instantiating formula (11) with xr, all_60_2_110, 0 and discharging atoms aNaturalNumber0(xr) = all_60_2_110, aNaturalNumber0(xr) = 0, yields:
% 131.10/89.95 | (1940) all_60_2_110 = 0
% 131.10/89.95 |
% 131.10/89.95 +-Applying beta-rule and splitting (1938), into two cases.
% 131.10/89.95 |-Branch one:
% 131.10/89.95 | (1941) ~ (all_60_1_109 = 0)
% 131.10/89.95 |
% 131.10/89.95 | Equations (539) can reduce 1941 to:
% 131.10/89.95 | (264) $false
% 131.10/89.95 |
% 131.10/89.95 |-The branch is then unsatisfiable
% 131.10/89.95 |-Branch two:
% 131.10/89.95 | (539) all_60_1_109 = 0
% 131.10/89.95 | (1944) ~ (all_60_2_110 = 0)
% 131.10/89.95 |
% 131.10/89.95 | Equations (1940) can reduce 1944 to:
% 131.10/89.95 | (264) $false
% 131.10/89.95 |
% 131.10/89.95 |-The branch is then unsatisfiable
% 131.10/89.95 |-Branch two:
% 131.10/89.95 | (1946) aNaturalNumber0(all_0_9_9) = all_53_1_88 & aNaturalNumber0(xp) = all_53_2_89 & ( ~ (all_53_1_88 = 0) | ~ (all_53_2_89 = 0))
% 131.10/89.95 |
% 131.10/89.95 | Applying alpha-rule on (1946) yields:
% 131.10/89.95 | (1947) aNaturalNumber0(all_0_9_9) = all_53_1_88
% 131.10/89.95 | (1948) aNaturalNumber0(xp) = all_53_2_89
% 131.10/89.95 | (1949) ~ (all_53_1_88 = 0) | ~ (all_53_2_89 = 0)
% 131.10/89.95 |
% 131.10/89.95 | Instantiating formula (11) with all_0_9_9, all_53_1_88, 0 and discharging atoms aNaturalNumber0(all_0_9_9) = all_53_1_88, aNaturalNumber0(all_0_9_9) = 0, yields:
% 131.10/89.95 | (534) all_53_1_88 = 0
% 131.10/89.95 |
% 131.10/89.95 | Instantiating formula (11) with xp, all_53_2_89, 0 and discharging atoms aNaturalNumber0(xp) = all_53_2_89, aNaturalNumber0(xp) = 0, yields:
% 131.10/89.95 | (1951) all_53_2_89 = 0
% 131.10/89.95 |
% 131.10/89.95 +-Applying beta-rule and splitting (1949), into two cases.
% 131.10/89.95 |-Branch one:
% 131.10/89.95 | (1952) ~ (all_53_1_88 = 0)
% 131.10/89.95 |
% 131.10/89.95 | Equations (534) can reduce 1952 to:
% 131.10/89.95 | (264) $false
% 131.10/89.95 |
% 131.10/89.95 |-The branch is then unsatisfiable
% 131.10/89.95 |-Branch two:
% 131.10/89.95 | (534) all_53_1_88 = 0
% 131.10/89.95 | (1955) ~ (all_53_2_89 = 0)
% 131.10/89.95 |
% 131.10/89.95 | Equations (1951) can reduce 1955 to:
% 131.10/89.95 | (264) $false
% 131.10/89.96 |
% 131.10/89.96 |-The branch is then unsatisfiable
% 131.10/89.96 |-Branch two:
% 131.10/89.96 | (1957) aNaturalNumber0(xp) = all_39_1_57 & aNaturalNumber0(xm) = all_39_2_58 & ( ~ (all_39_1_57 = 0) | ~ (all_39_2_58 = 0))
% 131.10/89.96 |
% 131.10/89.96 | Applying alpha-rule on (1957) yields:
% 131.10/89.96 | (1958) aNaturalNumber0(xp) = all_39_1_57
% 131.10/89.96 | (1959) aNaturalNumber0(xm) = all_39_2_58
% 131.10/89.96 | (1960) ~ (all_39_1_57 = 0) | ~ (all_39_2_58 = 0)
% 131.10/89.96 |
% 131.10/89.96 | Instantiating formula (11) with xp, all_39_1_57, 0 and discharging atoms aNaturalNumber0(xp) = all_39_1_57, aNaturalNumber0(xp) = 0, yields:
% 131.10/89.96 | (516) all_39_1_57 = 0
% 131.10/89.96 |
% 131.10/89.96 | Instantiating formula (11) with xm, all_39_2_58, 0 and discharging atoms aNaturalNumber0(xm) = all_39_2_58, aNaturalNumber0(xm) = 0, yields:
% 131.10/89.96 | (1962) all_39_2_58 = 0
% 131.10/89.96 |
% 131.10/89.96 +-Applying beta-rule and splitting (1960), into two cases.
% 131.10/89.96 |-Branch one:
% 131.10/89.96 | (1963) ~ (all_39_1_57 = 0)
% 131.10/89.96 |
% 131.10/89.96 | Equations (516) can reduce 1963 to:
% 131.10/89.96 | (264) $false
% 131.10/89.96 |
% 131.10/89.96 |-The branch is then unsatisfiable
% 131.10/89.96 |-Branch two:
% 131.10/89.96 | (516) all_39_1_57 = 0
% 131.10/89.96 | (1966) ~ (all_39_2_58 = 0)
% 131.10/89.96 |
% 131.10/89.96 | Equations (1962) can reduce 1966 to:
% 131.10/89.96 | (264) $false
% 131.10/89.96 |
% 131.10/89.96 |-The branch is then unsatisfiable
% 131.10/89.96 |-Branch two:
% 131.10/89.96 | (1968) aNaturalNumber0(xr) = all_50_2_81 & aNaturalNumber0(xn) = all_50_1_80 & ( ~ (all_50_1_80 = 0) | ~ (all_50_2_81 = 0))
% 131.10/89.96 |
% 131.10/89.96 | Applying alpha-rule on (1968) yields:
% 131.10/89.96 | (1969) aNaturalNumber0(xr) = all_50_2_81
% 131.10/89.96 | (1970) aNaturalNumber0(xn) = all_50_1_80
% 131.10/89.96 | (1971) ~ (all_50_1_80 = 0) | ~ (all_50_2_81 = 0)
% 131.10/89.96 |
% 131.10/89.96 | Instantiating formula (11) with xr, all_50_2_81, 0 and discharging atoms aNaturalNumber0(xr) = all_50_2_81, aNaturalNumber0(xr) = 0, yields:
% 131.10/89.96 | (1972) all_50_2_81 = 0
% 131.10/89.96 |
% 131.10/89.96 | Instantiating formula (11) with xn, all_50_1_80, 0 and discharging atoms aNaturalNumber0(xn) = all_50_1_80, aNaturalNumber0(xn) = 0, yields:
% 131.10/89.96 | (488) all_50_1_80 = 0
% 131.10/89.96 |
% 131.10/89.96 +-Applying beta-rule and splitting (1971), into two cases.
% 131.10/89.96 |-Branch one:
% 131.10/89.96 | (1974) ~ (all_50_1_80 = 0)
% 131.10/89.96 |
% 131.10/89.96 | Equations (488) can reduce 1974 to:
% 131.10/89.96 | (264) $false
% 131.10/89.96 |
% 131.10/89.96 |-The branch is then unsatisfiable
% 131.10/89.96 |-Branch two:
% 131.10/89.96 | (488) all_50_1_80 = 0
% 131.10/89.96 | (1977) ~ (all_50_2_81 = 0)
% 131.10/89.96 |
% 131.10/89.96 | Equations (1972) can reduce 1977 to:
% 131.10/89.96 | (264) $false
% 131.10/89.96 |
% 131.10/89.96 |-The branch is then unsatisfiable
% 131.10/89.96 % SZS output end Proof for theBenchmark
% 131.10/89.96
% 131.10/89.96 89366ms
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