TSTP Solution File: NUM501+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM501+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 08:45:11 EDT 2022
% Result : Theorem 23.82s 7.00s
% Output : Proof 67.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM501+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jul 7 16:04:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.62/0.64 ____ _
% 0.62/0.64 ___ / __ \_____(_)___ ________ __________
% 0.62/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.62/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.62/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.62/0.64
% 0.62/0.64 A Theorem Prover for First-Order Logic
% 0.62/0.64 (ePrincess v.1.0)
% 0.62/0.64
% 0.62/0.64 (c) Philipp Rümmer, 2009-2015
% 0.62/0.64 (c) Peter Backeman, 2014-2015
% 0.62/0.64 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.62/0.64 Free software under GNU Lesser General Public License (LGPL).
% 0.62/0.64 Bug reports to peter@backeman.se
% 0.62/0.64
% 0.62/0.64 For more information, visit http://user.uu.se/~petba168/breu/
% 0.62/0.64
% 0.62/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.92/1.07 Prover 0: Preprocessing ...
% 3.81/1.61 Prover 0: Constructing countermodel ...
% 19.44/5.98 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.79/6.11 Prover 1: Preprocessing ...
% 20.77/6.27 Prover 1: Constructing countermodel ...
% 23.82/6.99 Prover 1: proved (1009ms)
% 23.82/7.00 Prover 0: stopped
% 23.82/7.00
% 23.82/7.00 No countermodel exists, formula is valid
% 23.82/7.00 % SZS status Theorem for theBenchmark
% 23.82/7.00
% 23.82/7.00 Generating proof ... found it (size 2791)
% 65.70/28.79
% 65.70/28.79 % SZS output start Proof for theBenchmark
% 65.70/28.79 Assumed formulas after preprocessing and simplification:
% 65.70/28.79 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = 0) & ~ (xk = sz10) & ~ (xk = sz00) & ~ (xp = xm) & ~ (xp = xn) & ~ (sz10 = sz00) & isPrime0(xr) = 0 & isPrime0(xp) = 0 & sdtsldt0(v2, xp) = xk & doDivides0(xr, v2) = v5 & doDivides0(xr, xk) = 0 & doDivides0(xp, v2) = 0 & sdtlseqdt0(xp, xm) = v4 & sdtlseqdt0(xp, xn) = v3 & sdtlseqdt0(xm, xp) = 0 & sdtlseqdt0(xn, xp) = 0 & sdtasdt0(xn, xm) = v2 & sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) = v0 & aNaturalNumber0(xr) = 0 & aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 & ~ (isPrime0(sz10) = 0) & ~ (isPrime0(sz00) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | v6 = sz00 | ~ (sdtlseqdt0(v9, v10) = v11) | ~ (sdtasdt0(v6, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (sdtlseqdt0(v16, v17) = v18 & sdtlseqdt0(v7, v8) = v15 & sdtasdt0(v8, v6) = v17 & sdtasdt0(v7, v6) = v16 & aNaturalNumber0(v8) = v14 & aNaturalNumber0(v7) = v13 & aNaturalNumber0(v6) = v12 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | (v18 = 0 & v11 = 0 & ~ (v17 = v16) & ~ (v10 = v9))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v7 = v6 | ~ (sdtlseqdt0(v9, v10) = v11) | ~ (sdtlseqdt0(v6, v7) = 0) | ~ (sdtpldt0(v7, v8) = v10) | ~ (sdtpldt0(v6, v8) = v9) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((sdtlseqdt0(v13, v14) = v15 & sdtpldt0(v8, v7) = v14 & sdtpldt0(v8, v6) = v13 & aNaturalNumber0(v8) = v12 & ( ~ (v12 = 0) | (v15 = 0 & v11 = 0 & ~ (v14 = v13) & ~ (v10 = v9)))) | (aNaturalNumber0(v7) = v13 & aNaturalNumber0(v6) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v6 = sz00 | ~ (sdtsldt0(v10, v6) = v11) | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v9, v7) = v10) | ? [v12] : ? [v13] : ? [v14] : ((doDivides0(v6, v7) = v14 & aNaturalNumber0(v7) = v13 & aNaturalNumber0(v6) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0))) | (sdtasdt0(v9, v8) = v13 & aNaturalNumber0(v9) = v12 & ( ~ (v12 = 0) | v13 = v11)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v6, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ (sdtpldt0(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (sdtasdt0(v15, v6) = v17 & sdtasdt0(v8, v6) = v19 & sdtasdt0(v7, v6) = v18 & sdtasdt0(v6, v15) = v16 & sdtpldt0(v18, v19) = v20 & sdtpldt0(v7, v8) = v15 & aNaturalNumber0(v8) = v14 & aNaturalNumber0(v7) = v13 & aNaturalNumber0(v6) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | (v20 = v17 & v16 = v11)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (doDivides0(v6, v9) = v10) | ~ (sdtpldt0(v7, v8) = v9) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (doDivides0(v6, v8) = v15 & doDivides0(v6, v7) = v14 & aNaturalNumber0(v8) = v13 & aNaturalNumber0(v7) = v12 & aNaturalNumber0(v6) = v11 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v6, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ (aNaturalNumber0(v6) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v8, v6) = v14 & sdtasdt0(v7, v6) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) | ( ~ (v14 = v13) & ~ (v10 = v9))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v6, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (sdtpldt0(v8, v6) = v15 & sdtpldt0(v7, v6) = v14 & aNaturalNumber0(v8) = v13 & aNaturalNumber0(v7) = v12 & aNaturalNumber0(v6) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ( ~ (v15 = v14) & ~ (v10 = v9))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v9, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (sdtasdt0(v7, v8) = v14 & sdtasdt0(v6, v14) = v15 & aNaturalNumber0(v8) = v13 & aNaturalNumber0(v7) = v12 & aNaturalNumber0(v6) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | v15 = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (sdtpldt0(v7, v8) = v14 & sdtpldt0(v6, v14) = v15 & aNaturalNumber0(v8) = v13 & aNaturalNumber0(v7) = v12 & aNaturalNumber0(v6) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | v15 = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | v6 = sz00 | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v6, v9) = v7) | ? [v10] : ? [v11] : ? [v12] : (( ~ (v10 = 0) & aNaturalNumber0(v9) = v10) | (doDivides0(v6, v7) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (sdtmndt0(v7, v6) = v8) | ~ (sdtpldt0(v6, v9) = v7) | ? [v10] : ? [v11] : ? [v12] : (( ~ (v10 = 0) & aNaturalNumber0(v9) = v10) | (sdtlseqdt0(v6, v7) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | v6 = sz00 | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v6, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (doDivides0(v6, v7) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (sdtmndt0(v7, v6) = v8) | ~ (sdtpldt0(v6, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (sdtlseqdt0(v6, v7) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v6 = sz00 | ~ (sdtlseqdt0(v7, v8) = v9) | ~ (sdtasdt0(v7, v6) = v8) | ? [v10] : ? [v11] : (aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (doDivides0(v6, v8) = v9) | ~ (doDivides0(v6, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (doDivides0(v7, v8) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (sdtlseqdt0(v6, v8) = v9) | ~ (sdtlseqdt0(v6, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (sdtlseqdt0(v7, v8) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (doDivides0(v6, v7) = v8) | ~ (sdtasdt0(v6, v9) = v7) | ? [v10] : ? [v11] : (( ~ (v10 = 0) & aNaturalNumber0(v9) = v10) | (aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (sdtlseqdt0(v6, v7) = v8) | ~ (sdtpldt0(v6, v9) = v7) | ? [v10] : ? [v11] : (( ~ (v10 = 0) & aNaturalNumber0(v9) = v10) | (aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtsldt0(v9, v8) = v7) | ~ (sdtsldt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (doDivides0(v9, v8) = v7) | ~ (doDivides0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (iLess0(v9, v8) = v7) | ~ (iLess0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtmndt0(v9, v8) = v7) | ~ (sdtmndt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtlseqdt0(v9, v8) = v7) | ~ (sdtlseqdt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtasdt0(v9, v8) = v7) | ~ (sdtasdt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v9, v8) = v7) | ~ (sdtpldt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = sz00 | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v6, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v10 = 0 & aNaturalNumber0(v8) = 0) | (doDivides0(v6, v7) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (doDivides0(v8, v9) = 0) | ~ (sdtasdt0(v6, v7) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (isPrime0(v8) = v13 & doDivides0(v8, v7) = v18 & doDivides0(v8, v6) = v17 & iLess0(v15, v1) = v16 & sdtpldt0(v14, v8) = v15 & sdtpldt0(v6, v7) = v14 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v16 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | v18 = 0 | v17 = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (doDivides0(v6, v9) = 0) | ~ (sdtpldt0(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (doDivides0(v6, v8) = v14 & doDivides0(v6, v7) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | v14 = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtmndt0(v7, v6) = v8) | ~ (sdtpldt0(v6, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v10 = 0 & aNaturalNumber0(v8) = 0) | (sdtlseqdt0(v6, v7) = v12 & aNaturalNumber0(v7) = v11 & aNaturalNumber0(v6) = v10 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0))))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = v6 | ~ (iLess0(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (sdtlseqdt0(v6, v7) = v11 & aNaturalNumber0(v7) = v10 & aNaturalNumber0(v6) = v9 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (sdtlseqdt0(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (sdtlseqdt0(v7, v6) = v11 & aNaturalNumber0(v7) = v10 & aNaturalNumber0(v6) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | (v11 = 0 & ~ (v7 = v6))))) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (isPrime0(v8) = v7) | ~ (isPrime0(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (aNaturalNumber0(v8) = v7) | ~ (aNaturalNumber0(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (sdtasdt0(v7, v6) = v11 & aNaturalNumber0(v7) = v10 & aNaturalNumber0(v6) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = v8))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (aNaturalNumber0(v8) = v11 & aNaturalNumber0(v7) = v10 & aNaturalNumber0(v6) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = 0))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (sdtpldt0(v7, v6) = v11 & aNaturalNumber0(v7) = v10 & aNaturalNumber0(v6) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = v8))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (aNaturalNumber0(v8) = v11 & aNaturalNumber0(v7) = v10 & aNaturalNumber0(v6) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = 0))) & ! [v6] : ! [v7] : (v7 = v6 | v7 = sz10 | ~ (isPrime0(v6) = 0) | ~ (doDivides0(v7, v6) = 0) | ? [v8] : (( ~ (v8 = 0) & aNaturalNumber0(v7) = v8) | ( ~ (v8 = 0) & aNaturalNumber0(v6) = v8))) & ! [v6] : ! [v7] : (v7 = v6 | ~ (sdtlseqdt0(v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : (sdtlseqdt0(v7, v6) = v10 & aNaturalNumber0(v7) = v9 & aNaturalNumber0(v6) = v8 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v6] : ! [v7] : (v7 = sz00 | v6 = sz00 | ~ (sdtasdt0(v6, v7) = sz00) | ? [v8] : ? [v9] : (aNaturalNumber0(v7) = v9 & aNaturalNumber0(v6) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v6] : ! [v7] : (v7 = sz00 | ~ (doDivides0(v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : (sdtlseqdt0(v6, v7) = v10 & aNaturalNumber0(v7) = v9 & aNaturalNumber0(v6) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0) | v10 = 0))) & ! [v6] : ! [v7] : (v7 = sz00 | ~ (sdtpldt0(v6, v7) = sz00) | ? [v8] : ? [v9] : (aNaturalNumber0(v7) = v9 & aNaturalNumber0(v6) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v6] : ! [v7] : (v7 = 0 | v6 = sz10 | v6 = sz00 | ~ (isPrime0(v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & ~ (v8 = v6) & ~ (v8 = sz10) & doDivides0(v8, v6) = 0 & aNaturalNumber0(v8) = 0) | ( ~ (v8 = 0) & aNaturalNumber0(v6) = v8))) & ! [v6] : ! [v7] : (v7 = 0 | v6 = sz10 | v6 = sz00 | ~ (sdtlseqdt0(sz10, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & aNaturalNumber0(v6) = v8)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (sdtlseqdt0(v6, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & aNaturalNumber0(v6) = v8)) & ! [v6] : ! [v7] : (v6 = sz00 | ~ (sdtpldt0(v6, v7) = sz00) | ? [v8] : ? [v9] : (aNaturalNumber0(v7) = v9 & aNaturalNumber0(v6) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v6] : ! [v7] : ( ~ (doDivides0(v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v10 = v7 & v9 = 0 & sdtasdt0(v6, v8) = v7 & aNaturalNumber0(v8) = 0) | (aNaturalNumber0(v7) = v9 & aNaturalNumber0(v6) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))) & ! [v6] : ! [v7] : ( ~ (sdtlseqdt0(v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v10 = v7 & v9 = 0 & sdtpldt0(v6, v8) = v7 & aNaturalNumber0(v8) = 0) | (aNaturalNumber0(v7) = v9 & aNaturalNumber0(v6) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))) & ! [v6] : ! [v7] : ( ~ (sdtasdt0(sz10, v6) = v7) | ? [v8] : ? [v9] : (sdtasdt0(v6, sz10) = v9 & aNaturalNumber0(v6) = v8 & ( ~ (v8 = 0) | (v9 = v6 & v7 = v6)))) & ! [v6] : ! [v7] : ( ~ (sdtasdt0(sz00, v6) = v7) | ? [v8] : ? [v9] : (sdtasdt0(v6, sz00) = v9 & aNaturalNumber0(v6) = v8 & ( ~ (v8 = 0) | (v9 = sz00 & v7 = sz00)))) & ! [v6] : ! [v7] : ( ~ (sdtpldt0(sz00, v6) = v7) | ? [v8] : ? [v9] : (sdtpldt0(v6, sz00) = v9 & aNaturalNumber0(v6) = v8 & ( ~ (v8 = 0) | (v9 = v6 & v7 = v6)))) & ! [v6] : (v6 = sz10 | v6 = sz00 | ~ (aNaturalNumber0(v6) = 0) | ? [v7] : (isPrime0(v7) = 0 & doDivides0(v7, v6) = 0 & aNaturalNumber0(v7) = 0)))
% 66.03/28.86 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 66.03/28.86 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0) & ~ (xk = sz10) & ~ (xk = sz00) & ~ (xp = xm) & ~ (xp = xn) & ~ (sz10 = sz00) & isPrime0(xr) = 0 & isPrime0(xp) = 0 & sdtsldt0(all_0_3_3, xp) = xk & doDivides0(xr, all_0_3_3) = all_0_0_0 & doDivides0(xr, xk) = 0 & doDivides0(xp, all_0_3_3) = 0 & sdtlseqdt0(xp, xm) = all_0_1_1 & sdtlseqdt0(xp, xn) = all_0_2_2 & sdtlseqdt0(xm, xp) = 0 & sdtlseqdt0(xn, xp) = 0 & sdtasdt0(xn, xm) = all_0_3_3 & sdtpldt0(all_0_5_5, xp) = all_0_4_4 & sdtpldt0(xn, xm) = all_0_5_5 & aNaturalNumber0(xr) = 0 & aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 & ~ (isPrime0(sz10) = 0) & ~ (isPrime0(sz00) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | v0 = sz00 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (sdtlseqdt0(v10, v11) = v12 & sdtlseqdt0(v1, v2) = v9 & sdtasdt0(v2, v0) = v11 & sdtasdt0(v1, v0) = v10 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v12 = 0 & v5 = 0 & ~ (v11 = v10) & ~ (v4 = v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtlseqdt0(v0, v1) = 0) | ~ (sdtpldt0(v1, v2) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((sdtlseqdt0(v7, v8) = v9 & sdtpldt0(v2, v1) = v8 & sdtpldt0(v2, v0) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0 & ~ (v8 = v7) & ~ (v4 = v3)))) | (aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ((doDivides0(v0, v1) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))) | (sdtasdt0(v3, v2) = v7 & aNaturalNumber0(v3) = v6 & ( ~ (v6 = 0) | v7 = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v9, v0) = v11 & sdtasdt0(v2, v0) = v13 & sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v9) = v10 & sdtpldt0(v12, v13) = v14 & sdtpldt0(v1, v2) = v9 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v14 = v11 & v10 = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (doDivides0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (doDivides0(v0, v2) = v9 & doDivides0(v0, v1) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v8 = v7) & ~ (v4 = v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtpldt0(v2, v0) = v9 & sdtpldt0(v1, v0) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v9 = v8) & ~ (v4 = v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtpldt0(v1, v2) = v8 & sdtpldt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v0 = sz00 | ~ (sdtlseqdt0(v1, v2) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ? [v4] : ? [v5] : (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (doDivides0(v0, v2) = v3) | ~ (doDivides0(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (doDivides0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (sdtlseqdt0(v0, v2) = v3) | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (sdtlseqdt0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (doDivides0(v0, v1) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (doDivides0(v2, v3) = 0) | ~ (sdtasdt0(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (isPrime0(v2) = v7 & doDivides0(v2, v1) = v12 & doDivides0(v2, v0) = v11 & iLess0(v9, all_0_4_4) = v10 & sdtpldt0(v8, v2) = v9 & sdtpldt0(v0, v1) = v8 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v10 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v12 = 0 | v11 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (doDivides0(v0, v3) = 0) | ~ (sdtpldt0(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (doDivides0(v0, v2) = v8 & doDivides0(v0, v1) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (iLess0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtlseqdt0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (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))
% 66.03/28.88 |
% 66.03/28.88 | Applying alpha-rule on (1) yields:
% 66.03/28.88 | (2) sdtasdt0(xn, xm) = all_0_3_3
% 66.03/28.88 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 66.03/28.88 | (4) ~ (isPrime0(sz10) = 0)
% 66.03/28.88 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 66.03/28.88 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (doDivides0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (doDivides0(v0, v2) = v9 & doDivides0(v0, v1) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0))))
% 66.03/28.88 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (doDivides0(v2, v3) = 0) | ~ (sdtasdt0(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (isPrime0(v2) = v7 & doDivides0(v2, v1) = v12 & doDivides0(v2, v0) = v11 & iLess0(v9, all_0_4_4) = v10 & sdtpldt0(v8, v2) = v9 & sdtpldt0(v0, v1) = v8 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v10 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v12 = 0 | v11 = 0)))
% 66.03/28.88 | (8) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0))
% 66.03/28.88 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))))
% 66.03/28.88 | (10) aNaturalNumber0(xr) = 0
% 66.03/28.88 | (11) sdtlseqdt0(xp, xm) = all_0_1_1
% 66.03/28.88 | (12) aNaturalNumber0(xp) = 0
% 66.03/28.88 | (13) ~ (xk = sz00)
% 66.03/28.88 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v8 = v7) & ~ (v4 = v3)))))
% 66.03/28.88 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0))
% 66.03/28.88 | (16) aNaturalNumber0(sz10) = 0
% 66.03/28.88 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0))
% 66.03/28.88 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ((doDivides0(v0, v1) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))) | (sdtasdt0(v3, v2) = v7 & aNaturalNumber0(v3) = v6 & ( ~ (v6 = 0) | v7 = v5))))
% 66.03/28.88 | (19) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00))))
% 66.03/28.88 | (20) sdtlseqdt0(xp, xn) = all_0_2_2
% 66.03/28.88 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (sdtlseqdt0(v0, v2) = v3) | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (sdtlseqdt0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 66.03/28.88 | (22) isPrime0(xr) = 0
% 66.03/28.88 | (23) ~ (all_0_1_1 = 0)
% 66.03/28.88 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtpldt0(v2, v0) = v9 & sdtpldt0(v1, v0) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v9 = v8) & ~ (v4 = v3)))))
% 66.03/28.88 | (25) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 66.03/28.89 | (26) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (sdtlseqdt0(v1, v0) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0))))
% 66.03/28.89 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 66.03/28.89 | (28) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 66.03/28.89 | (29) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ (isPrime0(v0) = 0) | ~ (doDivides0(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 66.03/28.89 | (30) ~ (isPrime0(sz00) = 0)
% 66.03/28.89 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 66.03/28.89 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0))
% 66.03/28.89 | (33) ! [v0] : ! [v1] : ( ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))))
% 66.03/28.89 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))))
% 66.03/28.89 | (35) sdtlseqdt0(xm, xp) = 0
% 66.03/28.89 | (36) aNaturalNumber0(xm) = 0
% 66.03/28.89 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (doDivides0(v0, v1) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 66.03/28.89 | (38) doDivides0(xp, all_0_3_3) = 0
% 66.03/28.89 | (39) ~ (all_0_2_2 = 0)
% 66.03/28.89 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (doDivides0(v0, v3) = 0) | ~ (sdtpldt0(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (doDivides0(v0, v2) = v8 & doDivides0(v0, v1) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v8 = 0)))
% 66.03/28.89 | (41) aNaturalNumber0(sz00) = 0
% 66.03/28.89 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 66.03/28.89 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 66.03/28.89 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | v0 = sz00 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (sdtlseqdt0(v10, v11) = v12 & sdtlseqdt0(v1, v2) = v9 & sdtasdt0(v2, v0) = v11 & sdtasdt0(v1, v0) = v10 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v12 = 0 & v5 = 0 & ~ (v11 = v10) & ~ (v4 = v3)))))
% 66.03/28.89 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4)))
% 66.22/28.89 | (46) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0))
% 66.22/28.89 | (47) sdtsldt0(all_0_3_3, xp) = xk
% 66.22/28.89 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 66.22/28.89 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtpldt0(v1, v2) = v8 & sdtpldt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4)))
% 66.22/28.89 | (50) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 66.22/28.89 | (51) isPrime0(xp) = 0
% 66.22/28.89 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 66.22/28.89 | (53) aNaturalNumber0(xn) = 0
% 66.22/28.89 | (54) doDivides0(xr, xk) = 0
% 66.22/28.89 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 66.22/28.89 | (56) ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (isPrime0(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & ~ (v2 = v0) & ~ (v2 = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 66.22/28.89 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v0 = sz00 | ~ (sdtlseqdt0(v1, v2) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ? [v4] : ? [v5] : (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))
% 66.22/28.89 | (58) sdtpldt0(all_0_5_5, xp) = all_0_4_4
% 66.22/28.89 | (59) ~ (sz10 = sz00)
% 66.22/28.89 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))))
% 66.22/28.90 | (61) doDivides0(xr, all_0_3_3) = all_0_0_0
% 66.22/28.90 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 66.22/28.90 | (63) ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 66.22/28.90 | (64) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 66.22/28.90 | (65) ~ (all_0_0_0 = 0)
% 66.22/28.90 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (doDivides0(v0, v2) = v3) | ~ (doDivides0(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (doDivides0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 66.22/28.90 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0))
% 66.22/28.90 | (68) ~ (xk = sz10)
% 66.22/28.90 | (69) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (iLess0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtlseqdt0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))))
% 66.22/28.90 | (70) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 66.22/28.90 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))))
% 66.22/28.90 | (72) ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 66.22/28.90 | (73) sdtpldt0(xn, xm) = all_0_5_5
% 66.22/28.90 | (74) ~ (xp = xn)
% 66.22/28.90 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v9, v0) = v11 & sdtasdt0(v2, v0) = v13 & sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v9) = v10 & sdtpldt0(v12, v13) = v14 & sdtpldt0(v1, v2) = v9 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v14 = v11 & v10 = v5))))
% 66.22/28.90 | (76) ! [v0] : ! [v1] : ( ~ (doDivides0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))))
% 66.22/28.90 | (77) sdtlseqdt0(xn, xp) = 0
% 66.22/28.90 | (78) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 66.22/28.90 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtlseqdt0(v0, v1) = 0) | ~ (sdtpldt0(v1, v2) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((sdtlseqdt0(v7, v8) = v9 & sdtpldt0(v2, v1) = v8 & sdtpldt0(v2, v0) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0 & ~ (v8 = v7) & ~ (v4 = v3)))) | (aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))))
% 66.22/28.90 | (80) ~ (xp = xm)
% 66.22/28.90 | (81) ! [v0] : ! [v1] : (v1 = sz00 | ~ (doDivides0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (sdtlseqdt0(v0, v1) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0)))
% 66.22/28.90 | (82) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtlseqdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v5 = 0 & ~ (v1 = v0)))))
% 66.22/28.90 |
% 66.22/28.90 | Using (22) and (4) yields:
% 66.22/28.90 | (83) ~ (xr = sz10)
% 66.22/28.90 |
% 66.22/28.90 | Using (51) and (4) yields:
% 66.22/28.90 | (84) ~ (xp = sz10)
% 66.22/28.90 |
% 66.22/28.90 | Using (22) and (30) yields:
% 66.22/28.90 | (85) ~ (xr = sz00)
% 66.22/28.90 |
% 66.22/28.90 | Using (51) and (30) yields:
% 66.22/28.90 | (86) ~ (xp = sz00)
% 66.22/28.90 |
% 66.22/28.90 | Instantiating formula (66) with all_0_0_0, all_0_3_3, xk, xr and discharging atoms doDivides0(xr, all_0_3_3) = all_0_0_0, doDivides0(xr, xk) = 0, yields:
% 66.22/28.90 | (87) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(xk, all_0_3_3) = v3 & aNaturalNumber0(all_0_3_3) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 66.22/28.90 |
% 66.22/28.90 | Instantiating formula (81) with xk, xr and discharging atoms doDivides0(xr, xk) = 0, yields:
% 66.22/28.90 | (88) xk = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xr, xk) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.22/28.90 |
% 66.22/28.90 | Instantiating formula (76) with xk, xr and discharging atoms doDivides0(xr, xk) = 0, yields:
% 66.22/28.90 | (89) ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & v1 = 0 & sdtasdt0(xr, v0) = xk & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 66.22/28.90 |
% 66.22/28.90 | Instantiating formula (81) with all_0_3_3, xp and discharging atoms doDivides0(xp, all_0_3_3) = 0, yields:
% 66.22/28.91 | (90) all_0_3_3 = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.22/28.91 |
% 66.22/28.91 | Instantiating formula (76) with all_0_3_3, xp and discharging atoms doDivides0(xp, all_0_3_3) = 0, yields:
% 66.22/28.91 | (91) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_3_3 & v1 = 0 & sdtasdt0(xp, v0) = all_0_3_3 & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 66.22/28.91 |
% 66.22/28.91 | Instantiating formula (33) with xp, xm and discharging atoms sdtlseqdt0(xm, xp) = 0, yields:
% 66.22/28.91 | (92) ? [v0] : ? [v1] : ? [v2] : ((v2 = xp & v1 = 0 & sdtpldt0(xm, v0) = xp & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 66.22/28.91 |
% 66.22/28.91 | Instantiating formula (33) with xp, xn and discharging atoms sdtlseqdt0(xn, xp) = 0, yields:
% 66.22/28.91 | (93) ? [v0] : ? [v1] : ? [v2] : ((v2 = xp & v1 = 0 & sdtpldt0(xn, v0) = xp & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xp) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 66.22/28.91 |
% 66.22/28.91 | Instantiating formula (7) with all_0_3_3, xp, xm, xn and discharging atoms doDivides0(xp, all_0_3_3) = 0, sdtasdt0(xn, xm) = all_0_3_3, yields:
% 66.22/28.91 | (94) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, xm) = v8 & doDivides0(xp, xn) = v7 & iLess0(v5, all_0_4_4) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xn, xm) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 66.22/28.91 |
% 66.22/28.91 | Instantiating formula (19) with all_0_3_3, xm yields:
% 66.22/28.91 | (95) ~ (sdtasdt0(sz00, xm) = all_0_3_3) | ? [v0] : ? [v1] : (sdtasdt0(xm, sz00) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v0 = 0) | (v1 = sz00 & all_0_3_3 = sz00)))
% 66.22/28.91 |
% 66.22/28.91 | Instantiating formula (27) with all_0_3_3, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_3_3, yields:
% 66.22/28.91 | (96) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_3_3))
% 66.22/28.91 |
% 66.22/28.91 | Instantiating formula (62) with all_0_3_3, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_3_3, yields:
% 66.22/28.91 | (97) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_3_3) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.22/28.91 |
% 66.22/28.91 | Instantiating formula (78) with all_0_4_4, xp, all_0_5_5 and discharging atoms sdtpldt0(all_0_5_5, xp) = all_0_4_4, yields:
% 66.22/28.91 | (98) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, all_0_5_5) = v2 & aNaturalNumber0(all_0_5_5) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_4_4))
% 66.22/28.91 |
% 66.22/28.91 | Instantiating formula (43) with all_0_4_4, xp, all_0_5_5 and discharging atoms sdtpldt0(all_0_5_5, xp) = all_0_4_4, yields:
% 66.22/28.91 | (99) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_4_4) = v2 & aNaturalNumber0(all_0_5_5) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.22/28.91 |
% 66.22/28.91 | Instantiating formula (49) with all_0_4_4, all_0_5_5, xp, xm, xn and discharging atoms sdtpldt0(all_0_5_5, xp) = all_0_4_4, sdtpldt0(xn, xm) = all_0_5_5, yields:
% 66.22/28.91 | (100) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xm, xp) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_4_4))
% 66.22/28.91 |
% 66.22/28.91 | Instantiating formula (78) with all_0_5_5, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_5_5, yields:
% 66.22/28.91 | (101) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_5_5))
% 66.22/28.91 |
% 66.22/28.91 | Instantiating formula (43) with all_0_5_5, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_5_5, yields:
% 66.22/28.91 | (102) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_5_5) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.22/28.91 |
% 66.22/28.91 | Instantiating formula (8) with xr and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 66.22/28.91 | (103) xr = sz10 | xr = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xr) = 0 & aNaturalNumber0(v0) = 0)
% 66.22/28.91 |
% 66.22/28.91 | Instantiating formula (8) with xp and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 66.22/28.91 | (104) xp = sz10 | xp = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 66.22/28.91 |
% 66.22/28.91 | Instantiating formula (8) with xn and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 66.22/28.91 | (105) xn = sz10 | xn = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xn) = 0 & aNaturalNumber0(v0) = 0)
% 66.22/28.91 |
% 66.22/28.91 | Instantiating (102) with all_12_0_6, all_12_1_7, all_12_2_8 yields:
% 66.22/28.91 | (106) aNaturalNumber0(all_0_5_5) = all_12_0_6 & aNaturalNumber0(xm) = all_12_1_7 & aNaturalNumber0(xn) = all_12_2_8 & ( ~ (all_12_1_7 = 0) | ~ (all_12_2_8 = 0) | all_12_0_6 = 0)
% 66.22/28.91 |
% 66.22/28.91 | Applying alpha-rule on (106) yields:
% 66.22/28.91 | (107) aNaturalNumber0(all_0_5_5) = all_12_0_6
% 66.22/28.91 | (108) aNaturalNumber0(xm) = all_12_1_7
% 66.22/28.91 | (109) aNaturalNumber0(xn) = all_12_2_8
% 66.22/28.91 | (110) ~ (all_12_1_7 = 0) | ~ (all_12_2_8 = 0) | all_12_0_6 = 0
% 66.22/28.91 |
% 66.22/28.91 | Instantiating (101) with all_14_0_9, all_14_1_10, all_14_2_11 yields:
% 66.22/28.91 | (111) sdtpldt0(xm, xn) = all_14_0_9 & aNaturalNumber0(xm) = all_14_1_10 & aNaturalNumber0(xn) = all_14_2_11 & ( ~ (all_14_1_10 = 0) | ~ (all_14_2_11 = 0) | all_14_0_9 = all_0_5_5)
% 66.22/28.91 |
% 66.22/28.91 | Applying alpha-rule on (111) yields:
% 66.22/28.91 | (112) sdtpldt0(xm, xn) = all_14_0_9
% 66.22/28.91 | (113) aNaturalNumber0(xm) = all_14_1_10
% 66.22/28.91 | (114) aNaturalNumber0(xn) = all_14_2_11
% 66.22/28.91 | (115) ~ (all_14_1_10 = 0) | ~ (all_14_2_11 = 0) | all_14_0_9 = all_0_5_5
% 66.22/28.91 |
% 66.22/28.91 | Instantiating (98) with all_16_0_12, all_16_1_13, all_16_2_14 yields:
% 66.22/28.91 | (116) sdtpldt0(xp, all_0_5_5) = all_16_0_12 & aNaturalNumber0(all_0_5_5) = all_16_2_14 & aNaturalNumber0(xp) = all_16_1_13 & ( ~ (all_16_1_13 = 0) | ~ (all_16_2_14 = 0) | all_16_0_12 = all_0_4_4)
% 66.22/28.91 |
% 66.22/28.91 | Applying alpha-rule on (116) yields:
% 66.22/28.91 | (117) sdtpldt0(xp, all_0_5_5) = all_16_0_12
% 66.22/28.91 | (118) aNaturalNumber0(all_0_5_5) = all_16_2_14
% 66.22/28.91 | (119) aNaturalNumber0(xp) = all_16_1_13
% 66.22/28.91 | (120) ~ (all_16_1_13 = 0) | ~ (all_16_2_14 = 0) | all_16_0_12 = all_0_4_4
% 66.22/28.91 |
% 66.22/28.91 | Instantiating (93) with all_18_0_15, all_18_1_16, all_18_2_17 yields:
% 66.22/28.91 | (121) (all_18_0_15 = xp & all_18_1_16 = 0 & sdtpldt0(xn, all_18_2_17) = xp & aNaturalNumber0(all_18_2_17) = 0) | (aNaturalNumber0(xp) = all_18_1_16 & aNaturalNumber0(xn) = all_18_2_17 & ( ~ (all_18_1_16 = 0) | ~ (all_18_2_17 = 0)))
% 66.22/28.91 |
% 66.22/28.91 | Instantiating (92) with all_19_0_18, all_19_1_19, all_19_2_20 yields:
% 66.22/28.91 | (122) (all_19_0_18 = xp & all_19_1_19 = 0 & sdtpldt0(xm, all_19_2_20) = xp & aNaturalNumber0(all_19_2_20) = 0) | (aNaturalNumber0(xp) = all_19_1_19 & aNaturalNumber0(xm) = all_19_2_20 & ( ~ (all_19_1_19 = 0) | ~ (all_19_2_20 = 0)))
% 66.22/28.91 |
% 66.22/28.91 | Instantiating (91) with all_20_0_21, all_20_1_22, all_20_2_23 yields:
% 66.22/28.91 | (123) (all_20_0_21 = all_0_3_3 & all_20_1_22 = 0 & sdtasdt0(xp, all_20_2_23) = all_0_3_3 & aNaturalNumber0(all_20_2_23) = 0) | (aNaturalNumber0(all_0_3_3) = all_20_1_22 & aNaturalNumber0(xp) = all_20_2_23 & ( ~ (all_20_1_22 = 0) | ~ (all_20_2_23 = 0)))
% 66.22/28.91 |
% 66.22/28.91 | Instantiating (89) with all_21_0_24, all_21_1_25, all_21_2_26 yields:
% 66.22/28.91 | (124) (all_21_0_24 = xk & all_21_1_25 = 0 & sdtasdt0(xr, all_21_2_26) = xk & aNaturalNumber0(all_21_2_26) = 0) | (aNaturalNumber0(xr) = all_21_2_26 & aNaturalNumber0(xk) = all_21_1_25 & ( ~ (all_21_1_25 = 0) | ~ (all_21_2_26 = 0)))
% 66.22/28.92 |
% 66.22/28.92 | Instantiating (97) with all_22_0_27, all_22_1_28, all_22_2_29 yields:
% 66.22/28.92 | (125) aNaturalNumber0(all_0_3_3) = all_22_0_27 & aNaturalNumber0(xm) = all_22_1_28 & aNaturalNumber0(xn) = all_22_2_29 & ( ~ (all_22_1_28 = 0) | ~ (all_22_2_29 = 0) | all_22_0_27 = 0)
% 66.22/28.92 |
% 66.22/28.92 | Applying alpha-rule on (125) yields:
% 66.22/28.92 | (126) aNaturalNumber0(all_0_3_3) = all_22_0_27
% 66.22/28.92 | (127) aNaturalNumber0(xm) = all_22_1_28
% 66.22/28.92 | (128) aNaturalNumber0(xn) = all_22_2_29
% 66.22/28.92 | (129) ~ (all_22_1_28 = 0) | ~ (all_22_2_29 = 0) | all_22_0_27 = 0
% 66.22/28.92 |
% 66.22/28.92 | Instantiating (100) with all_24_0_30, all_24_1_31, all_24_2_32, all_24_3_33, all_24_4_34 yields:
% 66.22/28.92 | (130) sdtpldt0(xm, xp) = all_24_1_31 & sdtpldt0(xn, all_24_1_31) = all_24_0_30 & aNaturalNumber0(xp) = all_24_2_32 & aNaturalNumber0(xm) = all_24_3_33 & aNaturalNumber0(xn) = all_24_4_34 & ( ~ (all_24_2_32 = 0) | ~ (all_24_3_33 = 0) | ~ (all_24_4_34 = 0) | all_24_0_30 = all_0_4_4)
% 66.22/28.92 |
% 66.22/28.92 | Applying alpha-rule on (130) yields:
% 66.22/28.92 | (131) ~ (all_24_2_32 = 0) | ~ (all_24_3_33 = 0) | ~ (all_24_4_34 = 0) | all_24_0_30 = all_0_4_4
% 66.22/28.92 | (132) aNaturalNumber0(xm) = all_24_3_33
% 66.22/28.92 | (133) sdtpldt0(xn, all_24_1_31) = all_24_0_30
% 66.22/28.92 | (134) aNaturalNumber0(xn) = all_24_4_34
% 66.22/28.92 | (135) sdtpldt0(xm, xp) = all_24_1_31
% 66.22/28.92 | (136) aNaturalNumber0(xp) = all_24_2_32
% 66.22/28.92 |
% 66.22/28.92 | Instantiating (99) with all_26_0_35, all_26_1_36, all_26_2_37 yields:
% 66.22/28.92 | (137) aNaturalNumber0(all_0_4_4) = all_26_0_35 & aNaturalNumber0(all_0_5_5) = all_26_2_37 & aNaturalNumber0(xp) = all_26_1_36 & ( ~ (all_26_1_36 = 0) | ~ (all_26_2_37 = 0) | all_26_0_35 = 0)
% 66.22/28.92 |
% 66.22/28.92 | Applying alpha-rule on (137) yields:
% 66.22/28.92 | (138) aNaturalNumber0(all_0_4_4) = all_26_0_35
% 66.22/28.92 | (139) aNaturalNumber0(all_0_5_5) = all_26_2_37
% 66.22/28.92 | (140) aNaturalNumber0(xp) = all_26_1_36
% 66.22/28.92 | (141) ~ (all_26_1_36 = 0) | ~ (all_26_2_37 = 0) | all_26_0_35 = 0
% 66.22/28.92 |
% 66.22/28.92 | Instantiating (96) with all_28_0_38, all_28_1_39, all_28_2_40 yields:
% 66.22/28.92 | (142) sdtasdt0(xm, xn) = all_28_0_38 & aNaturalNumber0(xm) = all_28_1_39 & aNaturalNumber0(xn) = all_28_2_40 & ( ~ (all_28_1_39 = 0) | ~ (all_28_2_40 = 0) | all_28_0_38 = all_0_3_3)
% 66.22/28.92 |
% 66.22/28.92 | Applying alpha-rule on (142) yields:
% 66.22/28.92 | (143) sdtasdt0(xm, xn) = all_28_0_38
% 66.22/28.92 | (144) aNaturalNumber0(xm) = all_28_1_39
% 66.22/28.92 | (145) aNaturalNumber0(xn) = all_28_2_40
% 66.22/28.92 | (146) ~ (all_28_1_39 = 0) | ~ (all_28_2_40 = 0) | all_28_0_38 = all_0_3_3
% 66.22/28.92 |
% 66.22/28.92 | Instantiating (94) with all_30_0_41, all_30_1_42, all_30_2_43, all_30_3_44, all_30_4_45, all_30_5_46, all_30_6_47, all_30_7_48, all_30_8_49 yields:
% 66.22/28.92 | (147) isPrime0(xp) = all_30_5_46 & doDivides0(xp, xm) = all_30_0_41 & doDivides0(xp, xn) = all_30_1_42 & iLess0(all_30_3_44, all_0_4_4) = all_30_2_43 & sdtpldt0(all_30_4_45, xp) = all_30_3_44 & sdtpldt0(xn, xm) = all_30_4_45 & aNaturalNumber0(xp) = all_30_6_47 & aNaturalNumber0(xm) = all_30_7_48 & aNaturalNumber0(xn) = all_30_8_49 & ( ~ (all_30_2_43 = 0) | ~ (all_30_5_46 = 0) | ~ (all_30_6_47 = 0) | ~ (all_30_7_48 = 0) | ~ (all_30_8_49 = 0) | all_30_0_41 = 0 | all_30_1_42 = 0)
% 66.22/28.92 |
% 66.22/28.92 | Applying alpha-rule on (147) yields:
% 66.22/28.92 | (148) iLess0(all_30_3_44, all_0_4_4) = all_30_2_43
% 66.22/28.92 | (149) doDivides0(xp, xm) = all_30_0_41
% 66.22/28.92 | (150) isPrime0(xp) = all_30_5_46
% 66.22/28.92 | (151) aNaturalNumber0(xp) = all_30_6_47
% 66.22/28.92 | (152) sdtpldt0(all_30_4_45, xp) = all_30_3_44
% 66.22/28.92 | (153) aNaturalNumber0(xn) = all_30_8_49
% 66.22/28.92 | (154) ~ (all_30_2_43 = 0) | ~ (all_30_5_46 = 0) | ~ (all_30_6_47 = 0) | ~ (all_30_7_48 = 0) | ~ (all_30_8_49 = 0) | all_30_0_41 = 0 | all_30_1_42 = 0
% 66.22/28.92 | (155) sdtpldt0(xn, xm) = all_30_4_45
% 66.22/28.92 | (156) aNaturalNumber0(xm) = all_30_7_48
% 66.22/28.92 | (157) doDivides0(xp, xn) = all_30_1_42
% 66.22/28.92 |
% 66.22/28.92 +-Applying beta-rule and splitting (87), into two cases.
% 66.22/28.92 |-Branch one:
% 66.22/28.92 | (158) all_0_0_0 = 0
% 66.22/28.92 |
% 66.22/28.92 | Equations (158) can reduce 65 to:
% 66.22/28.92 | (159) $false
% 66.22/28.92 |
% 66.22/28.92 |-The branch is then unsatisfiable
% 66.22/28.92 |-Branch two:
% 66.22/28.92 | (65) ~ (all_0_0_0 = 0)
% 66.22/28.92 | (161) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(xk, all_0_3_3) = v3 & aNaturalNumber0(all_0_3_3) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 66.22/28.92 |
% 66.22/28.92 | Instantiating (161) with all_36_0_50, all_36_1_51, all_36_2_52, all_36_3_53 yields:
% 66.22/28.92 | (162) doDivides0(xk, all_0_3_3) = all_36_0_50 & aNaturalNumber0(all_0_3_3) = all_36_1_51 & aNaturalNumber0(xr) = all_36_3_53 & aNaturalNumber0(xk) = all_36_2_52 & ( ~ (all_36_0_50 = 0) | ~ (all_36_1_51 = 0) | ~ (all_36_2_52 = 0) | ~ (all_36_3_53 = 0))
% 66.22/28.92 |
% 66.22/28.92 | Applying alpha-rule on (162) yields:
% 66.22/28.92 | (163) aNaturalNumber0(xr) = all_36_3_53
% 66.22/28.92 | (164) doDivides0(xk, all_0_3_3) = all_36_0_50
% 66.22/28.92 | (165) ~ (all_36_0_50 = 0) | ~ (all_36_1_51 = 0) | ~ (all_36_2_52 = 0) | ~ (all_36_3_53 = 0)
% 66.22/28.92 | (166) aNaturalNumber0(xk) = all_36_2_52
% 66.22/28.92 | (167) aNaturalNumber0(all_0_3_3) = all_36_1_51
% 66.22/28.92 |
% 66.22/28.92 +-Applying beta-rule and splitting (88), into two cases.
% 66.22/28.92 |-Branch one:
% 66.22/28.92 | (168) xk = sz00
% 66.22/28.92 |
% 66.22/28.92 | Equations (168) can reduce 13 to:
% 66.22/28.92 | (159) $false
% 66.22/28.92 |
% 66.22/28.92 |-The branch is then unsatisfiable
% 66.22/28.92 |-Branch two:
% 66.22/28.92 | (13) ~ (xk = sz00)
% 66.22/28.92 | (171) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xr, xk) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.22/28.92 |
% 66.22/28.92 | Instantiating (171) with all_41_0_54, all_41_1_55, all_41_2_56 yields:
% 66.22/28.92 | (172) sdtlseqdt0(xr, xk) = all_41_0_54 & aNaturalNumber0(xr) = all_41_2_56 & aNaturalNumber0(xk) = all_41_1_55 & ( ~ (all_41_1_55 = 0) | ~ (all_41_2_56 = 0) | all_41_0_54 = 0)
% 66.22/28.92 |
% 66.22/28.92 | Applying alpha-rule on (172) yields:
% 66.22/28.92 | (173) sdtlseqdt0(xr, xk) = all_41_0_54
% 66.22/28.92 | (174) aNaturalNumber0(xr) = all_41_2_56
% 66.22/28.92 | (175) aNaturalNumber0(xk) = all_41_1_55
% 66.22/28.93 | (176) ~ (all_41_1_55 = 0) | ~ (all_41_2_56 = 0) | all_41_0_54 = 0
% 66.22/28.93 |
% 66.22/28.93 +-Applying beta-rule and splitting (103), into two cases.
% 66.22/28.93 |-Branch one:
% 66.22/28.93 | (177) xr = sz00
% 66.22/28.93 |
% 66.22/28.93 | Equations (177) can reduce 85 to:
% 66.22/28.93 | (159) $false
% 66.22/28.93 |
% 66.22/28.93 |-The branch is then unsatisfiable
% 66.22/28.93 |-Branch two:
% 66.22/28.93 | (85) ~ (xr = sz00)
% 66.22/28.93 | (180) xr = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xr) = 0 & aNaturalNumber0(v0) = 0)
% 66.22/28.93 |
% 66.22/28.93 +-Applying beta-rule and splitting (104), into two cases.
% 66.22/28.93 |-Branch one:
% 66.22/28.93 | (181) xp = sz00
% 66.22/28.93 |
% 66.22/28.93 | Equations (181) can reduce 86 to:
% 66.22/28.93 | (159) $false
% 66.22/28.93 |
% 66.22/28.93 |-The branch is then unsatisfiable
% 66.22/28.93 |-Branch two:
% 66.22/28.93 | (86) ~ (xp = sz00)
% 66.22/28.93 | (184) xp = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 66.22/28.93 |
% 66.22/28.93 +-Applying beta-rule and splitting (180), into two cases.
% 66.22/28.93 |-Branch one:
% 66.22/28.93 | (185) xr = sz10
% 66.22/28.93 |
% 66.22/28.93 | Equations (185) can reduce 83 to:
% 66.22/28.93 | (159) $false
% 66.22/28.93 |
% 66.22/28.93 |-The branch is then unsatisfiable
% 66.22/28.93 |-Branch two:
% 66.22/28.93 | (83) ~ (xr = sz10)
% 66.22/28.93 | (188) ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xr) = 0 & aNaturalNumber0(v0) = 0)
% 66.22/28.93 |
% 66.22/28.93 | Instantiating (188) with all_53_0_57 yields:
% 66.22/28.93 | (189) isPrime0(all_53_0_57) = 0 & doDivides0(all_53_0_57, xr) = 0 & aNaturalNumber0(all_53_0_57) = 0
% 66.22/28.93 |
% 66.22/28.93 | Applying alpha-rule on (189) yields:
% 66.22/28.93 | (190) isPrime0(all_53_0_57) = 0
% 66.22/28.93 | (191) doDivides0(all_53_0_57, xr) = 0
% 66.22/28.93 | (192) aNaturalNumber0(all_53_0_57) = 0
% 66.22/28.93 |
% 66.22/28.93 +-Applying beta-rule and splitting (184), into two cases.
% 66.22/28.93 |-Branch one:
% 66.22/28.93 | (193) xp = sz10
% 66.22/28.93 |
% 66.22/28.93 | Equations (193) can reduce 84 to:
% 66.22/28.93 | (159) $false
% 66.22/28.93 |
% 66.22/28.93 |-The branch is then unsatisfiable
% 66.22/28.93 |-Branch two:
% 66.22/28.93 | (84) ~ (xp = sz10)
% 66.22/28.93 | (196) ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 66.22/28.93 |
% 66.22/28.93 | Instantiating (196) with all_58_0_58 yields:
% 66.22/28.93 | (197) isPrime0(all_58_0_58) = 0 & doDivides0(all_58_0_58, xp) = 0 & aNaturalNumber0(all_58_0_58) = 0
% 66.22/28.93 |
% 66.22/28.93 | Applying alpha-rule on (197) yields:
% 66.22/28.93 | (198) isPrime0(all_58_0_58) = 0
% 66.22/28.93 | (199) doDivides0(all_58_0_58, xp) = 0
% 66.22/28.93 | (200) aNaturalNumber0(all_58_0_58) = 0
% 66.22/28.93 |
% 66.22/28.93 | Using (198) and (4) yields:
% 66.22/28.93 | (201) ~ (all_58_0_58 = sz10)
% 66.22/28.93 |
% 66.22/28.93 | Using (198) and (30) yields:
% 66.22/28.93 | (202) ~ (all_58_0_58 = sz00)
% 66.22/28.93 |
% 66.22/28.93 | Using (190) and (4) yields:
% 66.22/28.93 | (203) ~ (all_53_0_57 = sz10)
% 66.22/28.93 |
% 66.22/28.93 | Using (190) and (30) yields:
% 66.22/28.93 | (204) ~ (all_53_0_57 = sz00)
% 66.22/28.93 |
% 66.22/28.93 | Instantiating formula (15) with xp, all_30_5_46, 0 and discharging atoms isPrime0(xp) = all_30_5_46, isPrime0(xp) = 0, yields:
% 66.22/28.93 | (205) all_30_5_46 = 0
% 66.22/28.93 |
% 66.22/28.93 | Instantiating formula (3) with all_0_5_5, xp, all_30_3_44, all_0_4_4 and discharging atoms sdtpldt0(all_0_5_5, xp) = all_0_4_4, yields:
% 66.22/28.93 | (206) all_30_3_44 = all_0_4_4 | ~ (sdtpldt0(all_0_5_5, xp) = all_30_3_44)
% 66.22/28.93 |
% 66.22/28.93 | Instantiating formula (3) with xn, xm, all_30_4_45, all_0_5_5 and discharging atoms sdtpldt0(xn, xm) = all_30_4_45, sdtpldt0(xn, xm) = all_0_5_5, yields:
% 66.22/28.93 | (207) all_30_4_45 = all_0_5_5
% 66.22/28.93 |
% 66.22/28.93 | Instantiating formula (46) with xr, all_36_1_51, 0 and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 66.22/28.93 | (208) all_36_1_51 = 0 | ~ (aNaturalNumber0(xr) = all_36_1_51)
% 66.22/28.93 |
% 66.22/28.93 | Instantiating formula (46) with xp, all_36_1_51, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 66.22/28.93 | (209) all_36_1_51 = 0 | ~ (aNaturalNumber0(xp) = all_36_1_51)
% 66.22/28.93 |
% 66.22/28.93 | Instantiating formula (46) with xm, all_36_1_51, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 66.22/28.93 | (210) all_36_1_51 = 0 | ~ (aNaturalNumber0(xm) = all_36_1_51)
% 66.22/28.93 |
% 66.22/28.93 | Instantiating formula (46) with xn, all_36_1_51, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 66.22/28.93 | (211) all_36_1_51 = 0 | ~ (aNaturalNumber0(xn) = all_36_1_51)
% 66.22/28.93 |
% 66.22/28.93 | Instantiating formula (46) with sz10, all_36_1_51, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 66.22/28.93 | (212) all_36_1_51 = 0 | ~ (aNaturalNumber0(sz10) = all_36_1_51)
% 66.22/28.93 |
% 66.22/28.93 | Instantiating formula (46) with sz00, all_36_1_51, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 66.22/28.93 | (213) all_36_1_51 = 0 | ~ (aNaturalNumber0(sz00) = all_36_1_51)
% 66.22/28.93 |
% 66.22/28.93 | Instantiating formula (46) with all_0_3_3, all_36_1_51, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_36_1_51, yields:
% 66.22/28.93 | (214) all_36_1_51 = 0 | ~ (aNaturalNumber0(all_0_3_3) = 0)
% 66.22/28.93 |
% 66.22/28.93 | Instantiating formula (46) with xm, all_22_0_27, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 66.22/28.93 | (215) all_22_0_27 = 0 | ~ (aNaturalNumber0(xm) = all_22_0_27)
% 66.22/28.93 |
% 66.22/28.93 | Instantiating formula (46) with xn, all_22_0_27, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 66.22/28.93 | (216) all_22_0_27 = 0 | ~ (aNaturalNumber0(xn) = all_22_0_27)
% 66.22/28.93 |
% 66.22/28.93 | Instantiating formula (46) with sz10, all_22_0_27, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 66.22/28.93 | (217) all_22_0_27 = 0 | ~ (aNaturalNumber0(sz10) = all_22_0_27)
% 66.22/28.93 |
% 66.22/28.93 | Instantiating formula (46) with all_0_3_3, all_22_0_27, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_22_0_27, yields:
% 66.22/28.93 | (218) all_22_0_27 = 0 | ~ (aNaturalNumber0(all_0_3_3) = 0)
% 66.22/28.93 |
% 66.22/28.93 | Instantiating formula (46) with all_0_3_3, all_22_0_27, all_36_1_51 and discharging atoms aNaturalNumber0(all_0_3_3) = all_36_1_51, aNaturalNumber0(all_0_3_3) = all_22_0_27, yields:
% 66.22/28.93 | (219) all_36_1_51 = all_22_0_27
% 66.22/28.93 |
% 66.22/28.93 | Instantiating formula (46) with xr, all_26_0_35, 0 and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 66.22/28.93 | (220) all_26_0_35 = 0 | ~ (aNaturalNumber0(xr) = all_26_0_35)
% 66.22/28.93 |
% 66.22/28.93 | Instantiating formula (46) with xp, all_26_0_35, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 66.22/28.93 | (221) all_26_0_35 = 0 | ~ (aNaturalNumber0(xp) = all_26_0_35)
% 66.22/28.93 |
% 66.22/28.93 | Instantiating formula (46) with xn, all_26_0_35, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 66.22/28.94 | (222) all_26_0_35 = 0 | ~ (aNaturalNumber0(xn) = all_26_0_35)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with all_0_4_4, all_26_0_35, 0 and discharging atoms aNaturalNumber0(all_0_4_4) = all_26_0_35, yields:
% 66.22/28.94 | (223) all_26_0_35 = 0 | ~ (aNaturalNumber0(all_0_4_4) = 0)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with all_0_4_4, all_26_0_35, all_36_1_51 and discharging atoms aNaturalNumber0(all_0_4_4) = all_26_0_35, yields:
% 66.22/28.94 | (224) all_36_1_51 = all_26_0_35 | ~ (aNaturalNumber0(all_0_4_4) = all_36_1_51)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with all_0_4_4, all_26_0_35, all_22_0_27 and discharging atoms aNaturalNumber0(all_0_4_4) = all_26_0_35, yields:
% 66.22/28.94 | (225) all_26_0_35 = all_22_0_27 | ~ (aNaturalNumber0(all_0_4_4) = all_22_0_27)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with xr, all_26_2_37, 0 and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 66.22/28.94 | (226) all_26_2_37 = 0 | ~ (aNaturalNumber0(xr) = all_26_2_37)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with xm, all_26_2_37, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 66.22/28.94 | (227) all_26_2_37 = 0 | ~ (aNaturalNumber0(xm) = all_26_2_37)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with xn, all_26_2_37, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 66.22/28.94 | (228) all_26_2_37 = 0 | ~ (aNaturalNumber0(xn) = all_26_2_37)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with sz00, all_26_2_37, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 66.22/28.94 | (229) all_26_2_37 = 0 | ~ (aNaturalNumber0(sz00) = all_26_2_37)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with all_0_5_5, all_26_2_37, 0 and discharging atoms aNaturalNumber0(all_0_5_5) = all_26_2_37, yields:
% 66.22/28.94 | (230) all_26_2_37 = 0 | ~ (aNaturalNumber0(all_0_5_5) = 0)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with all_0_5_5, all_26_2_37, all_36_1_51 and discharging atoms aNaturalNumber0(all_0_5_5) = all_26_2_37, yields:
% 66.22/28.94 | (231) all_36_1_51 = all_26_2_37 | ~ (aNaturalNumber0(all_0_5_5) = all_36_1_51)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with all_0_5_5, all_26_2_37, all_22_0_27 and discharging atoms aNaturalNumber0(all_0_5_5) = all_26_2_37, yields:
% 66.22/28.94 | (232) all_26_2_37 = all_22_0_27 | ~ (aNaturalNumber0(all_0_5_5) = all_22_0_27)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with all_0_5_5, all_26_2_37, all_26_0_35 and discharging atoms aNaturalNumber0(all_0_5_5) = all_26_2_37, yields:
% 66.22/28.94 | (233) all_26_0_35 = all_26_2_37 | ~ (aNaturalNumber0(all_0_5_5) = all_26_0_35)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with xr, all_16_2_14, 0 and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 66.22/28.94 | (234) all_16_2_14 = 0 | ~ (aNaturalNumber0(xr) = all_16_2_14)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with xp, all_16_2_14, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 66.22/28.94 | (235) all_16_2_14 = 0 | ~ (aNaturalNumber0(xp) = all_16_2_14)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with xm, all_16_2_14, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 66.22/28.94 | (236) all_16_2_14 = 0 | ~ (aNaturalNumber0(xm) = all_16_2_14)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with xn, all_16_2_14, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 66.22/28.94 | (237) all_16_2_14 = 0 | ~ (aNaturalNumber0(xn) = all_16_2_14)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with sz10, all_16_2_14, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 66.22/28.94 | (238) all_16_2_14 = 0 | ~ (aNaturalNumber0(sz10) = all_16_2_14)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with all_0_5_5, all_16_2_14, 0 and discharging atoms aNaturalNumber0(all_0_5_5) = all_16_2_14, yields:
% 66.22/28.94 | (239) all_16_2_14 = 0 | ~ (aNaturalNumber0(all_0_5_5) = 0)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with all_0_5_5, all_16_2_14, all_36_1_51 and discharging atoms aNaturalNumber0(all_0_5_5) = all_16_2_14, yields:
% 66.22/28.94 | (240) all_36_1_51 = all_16_2_14 | ~ (aNaturalNumber0(all_0_5_5) = all_36_1_51)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with all_0_5_5, all_16_2_14, all_26_0_35 and discharging atoms aNaturalNumber0(all_0_5_5) = all_16_2_14, yields:
% 66.22/28.94 | (241) all_26_0_35 = all_16_2_14 | ~ (aNaturalNumber0(all_0_5_5) = all_26_0_35)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with all_0_5_5, all_16_2_14, all_26_2_37 and discharging atoms aNaturalNumber0(all_0_5_5) = all_26_2_37, aNaturalNumber0(all_0_5_5) = all_16_2_14, yields:
% 66.22/28.94 | (242) all_26_2_37 = all_16_2_14
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with xr, all_12_0_6, 0 and discharging atoms aNaturalNumber0(xr) = 0, yields:
% 66.22/28.94 | (243) all_12_0_6 = 0 | ~ (aNaturalNumber0(xr) = all_12_0_6)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with xp, all_12_0_6, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 66.22/28.94 | (244) all_12_0_6 = 0 | ~ (aNaturalNumber0(xp) = all_12_0_6)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with xm, all_12_0_6, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 66.22/28.94 | (245) all_12_0_6 = 0 | ~ (aNaturalNumber0(xm) = all_12_0_6)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with xn, all_12_0_6, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 66.22/28.94 | (246) all_12_0_6 = 0 | ~ (aNaturalNumber0(xn) = all_12_0_6)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with sz10, all_12_0_6, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 66.22/28.94 | (247) all_12_0_6 = 0 | ~ (aNaturalNumber0(sz10) = all_12_0_6)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with sz00, all_12_0_6, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 66.22/28.94 | (248) all_12_0_6 = 0 | ~ (aNaturalNumber0(sz00) = all_12_0_6)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with all_0_5_5, all_12_0_6, all_36_1_51 and discharging atoms aNaturalNumber0(all_0_5_5) = all_12_0_6, yields:
% 66.22/28.94 | (249) all_36_1_51 = all_12_0_6 | ~ (aNaturalNumber0(all_0_5_5) = all_36_1_51)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with all_0_5_5, all_12_0_6, all_22_0_27 and discharging atoms aNaturalNumber0(all_0_5_5) = all_12_0_6, yields:
% 66.22/28.94 | (250) all_22_0_27 = all_12_0_6 | ~ (aNaturalNumber0(all_0_5_5) = all_22_0_27)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with all_0_5_5, all_12_0_6, all_26_0_35 and discharging atoms aNaturalNumber0(all_0_5_5) = all_12_0_6, yields:
% 66.22/28.94 | (251) all_26_0_35 = all_12_0_6 | ~ (aNaturalNumber0(all_0_5_5) = all_26_0_35)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with all_0_5_5, all_12_0_6, all_26_2_37 and discharging atoms aNaturalNumber0(all_0_5_5) = all_26_2_37, aNaturalNumber0(all_0_5_5) = all_12_0_6, yields:
% 66.22/28.94 | (252) all_26_2_37 = all_12_0_6
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with xr, all_41_2_56, 0 and discharging atoms aNaturalNumber0(xr) = all_41_2_56, aNaturalNumber0(xr) = 0, yields:
% 66.22/28.94 | (253) all_41_2_56 = 0
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with xp, all_41_2_56, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 66.22/28.94 | (254) all_41_2_56 = 0 | ~ (aNaturalNumber0(xp) = all_41_2_56)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with xm, all_41_2_56, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 66.22/28.94 | (255) all_41_2_56 = 0 | ~ (aNaturalNumber0(xm) = all_41_2_56)
% 66.22/28.94 |
% 66.22/28.94 | Instantiating formula (46) with xn, all_41_2_56, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 66.22/28.95 | (256) all_41_2_56 = 0 | ~ (aNaturalNumber0(xn) = all_41_2_56)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xr, all_41_2_56, all_36_1_51 and discharging atoms aNaturalNumber0(xr) = all_41_2_56, yields:
% 66.22/28.95 | (257) all_41_2_56 = all_36_1_51 | ~ (aNaturalNumber0(xr) = all_36_1_51)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xr, all_41_2_56, all_22_0_27 and discharging atoms aNaturalNumber0(xr) = all_41_2_56, yields:
% 66.22/28.95 | (258) all_41_2_56 = all_22_0_27 | ~ (aNaturalNumber0(xr) = all_22_0_27)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xr, all_41_2_56, all_26_0_35 and discharging atoms aNaturalNumber0(xr) = all_41_2_56, yields:
% 66.22/28.95 | (259) all_41_2_56 = all_26_0_35 | ~ (aNaturalNumber0(xr) = all_26_0_35)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xr, all_41_2_56, all_26_2_37 and discharging atoms aNaturalNumber0(xr) = all_41_2_56, yields:
% 66.22/28.95 | (260) all_41_2_56 = all_26_2_37 | ~ (aNaturalNumber0(xr) = all_26_2_37)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xr, all_41_2_56, all_12_0_6 and discharging atoms aNaturalNumber0(xr) = all_41_2_56, yields:
% 66.22/28.95 | (261) all_41_2_56 = all_12_0_6 | ~ (aNaturalNumber0(xr) = all_12_0_6)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xp, all_36_3_53, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 66.22/28.95 | (262) all_36_3_53 = 0 | ~ (aNaturalNumber0(xp) = all_36_3_53)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xm, all_36_3_53, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 66.22/28.95 | (263) all_36_3_53 = 0 | ~ (aNaturalNumber0(xm) = all_36_3_53)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xn, all_36_3_53, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 66.22/28.95 | (264) all_36_3_53 = 0 | ~ (aNaturalNumber0(xn) = all_36_3_53)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xr, all_36_3_53, all_36_1_51 and discharging atoms aNaturalNumber0(xr) = all_36_3_53, yields:
% 66.22/28.95 | (265) all_36_1_51 = all_36_3_53 | ~ (aNaturalNumber0(xr) = all_36_1_51)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xr, all_36_3_53, all_22_0_27 and discharging atoms aNaturalNumber0(xr) = all_36_3_53, yields:
% 66.22/28.95 | (266) all_36_3_53 = all_22_0_27 | ~ (aNaturalNumber0(xr) = all_22_0_27)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xr, all_36_3_53, all_26_0_35 and discharging atoms aNaturalNumber0(xr) = all_36_3_53, yields:
% 66.22/28.95 | (267) all_36_3_53 = all_26_0_35 | ~ (aNaturalNumber0(xr) = all_26_0_35)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xr, all_36_3_53, all_26_2_37 and discharging atoms aNaturalNumber0(xr) = all_36_3_53, yields:
% 66.22/28.95 | (268) all_36_3_53 = all_26_2_37 | ~ (aNaturalNumber0(xr) = all_26_2_37)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xr, all_36_3_53, all_16_2_14 and discharging atoms aNaturalNumber0(xr) = all_36_3_53, yields:
% 66.22/28.95 | (269) all_36_3_53 = all_16_2_14 | ~ (aNaturalNumber0(xr) = all_16_2_14)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xr, all_36_3_53, all_12_0_6 and discharging atoms aNaturalNumber0(xr) = all_36_3_53, yields:
% 66.22/28.95 | (270) all_36_3_53 = all_12_0_6 | ~ (aNaturalNumber0(xr) = all_12_0_6)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xr, all_36_3_53, all_41_2_56 and discharging atoms aNaturalNumber0(xr) = all_41_2_56, aNaturalNumber0(xr) = all_36_3_53, yields:
% 66.22/28.95 | (271) all_41_2_56 = all_36_3_53
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xk, all_41_1_55, 0 and discharging atoms aNaturalNumber0(xk) = all_41_1_55, yields:
% 66.22/28.95 | (272) all_41_1_55 = 0 | ~ (aNaturalNumber0(xk) = 0)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xp, all_41_1_55, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 66.22/28.95 | (273) all_41_1_55 = 0 | ~ (aNaturalNumber0(xp) = all_41_1_55)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xm, all_41_1_55, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 66.22/28.95 | (274) all_41_1_55 = 0 | ~ (aNaturalNumber0(xm) = all_41_1_55)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xn, all_41_1_55, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 66.22/28.95 | (275) all_41_1_55 = 0 | ~ (aNaturalNumber0(xn) = all_41_1_55)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xk, all_41_1_55, all_36_1_51 and discharging atoms aNaturalNumber0(xk) = all_41_1_55, yields:
% 66.22/28.95 | (276) all_41_1_55 = all_36_1_51 | ~ (aNaturalNumber0(xk) = all_36_1_51)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xk, all_41_1_55, all_22_0_27 and discharging atoms aNaturalNumber0(xk) = all_41_1_55, yields:
% 66.22/28.95 | (277) all_41_1_55 = all_22_0_27 | ~ (aNaturalNumber0(xk) = all_22_0_27)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xk, all_41_1_55, all_26_0_35 and discharging atoms aNaturalNumber0(xk) = all_41_1_55, yields:
% 66.22/28.95 | (278) all_41_1_55 = all_26_0_35 | ~ (aNaturalNumber0(xk) = all_26_0_35)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xk, all_41_1_55, all_26_2_37 and discharging atoms aNaturalNumber0(xk) = all_41_1_55, yields:
% 66.22/28.95 | (279) all_41_1_55 = all_26_2_37 | ~ (aNaturalNumber0(xk) = all_26_2_37)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xk, all_41_1_55, all_16_2_14 and discharging atoms aNaturalNumber0(xk) = all_41_1_55, yields:
% 66.22/28.95 | (280) all_41_1_55 = all_16_2_14 | ~ (aNaturalNumber0(xk) = all_16_2_14)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xk, all_41_1_55, all_41_2_56 and discharging atoms aNaturalNumber0(xk) = all_41_1_55, yields:
% 66.22/28.95 | (281) all_41_1_55 = all_41_2_56 | ~ (aNaturalNumber0(xk) = all_41_2_56)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xk, all_41_1_55, all_36_3_53 and discharging atoms aNaturalNumber0(xk) = all_41_1_55, yields:
% 66.22/28.95 | (282) all_41_1_55 = all_36_3_53 | ~ (aNaturalNumber0(xk) = all_36_3_53)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xk, all_36_2_52, 0 and discharging atoms aNaturalNumber0(xk) = all_36_2_52, yields:
% 66.22/28.95 | (283) all_36_2_52 = 0 | ~ (aNaturalNumber0(xk) = 0)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xp, all_36_2_52, 0 and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 66.22/28.95 | (284) all_36_2_52 = 0 | ~ (aNaturalNumber0(xp) = all_36_2_52)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xm, all_36_2_52, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 66.22/28.95 | (285) all_36_2_52 = 0 | ~ (aNaturalNumber0(xm) = all_36_2_52)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xn, all_36_2_52, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 66.22/28.95 | (286) all_36_2_52 = 0 | ~ (aNaturalNumber0(xn) = all_36_2_52)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xk, all_36_2_52, all_22_0_27 and discharging atoms aNaturalNumber0(xk) = all_36_2_52, yields:
% 66.22/28.95 | (287) all_36_2_52 = all_22_0_27 | ~ (aNaturalNumber0(xk) = all_22_0_27)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xk, all_36_2_52, all_26_0_35 and discharging atoms aNaturalNumber0(xk) = all_36_2_52, yields:
% 66.22/28.95 | (288) all_36_2_52 = all_26_0_35 | ~ (aNaturalNumber0(xk) = all_26_0_35)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xk, all_36_2_52, all_16_2_14 and discharging atoms aNaturalNumber0(xk) = all_36_2_52, yields:
% 66.22/28.95 | (289) all_36_2_52 = all_16_2_14 | ~ (aNaturalNumber0(xk) = all_16_2_14)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xk, all_36_2_52, all_12_0_6 and discharging atoms aNaturalNumber0(xk) = all_36_2_52, yields:
% 66.22/28.95 | (290) all_36_2_52 = all_12_0_6 | ~ (aNaturalNumber0(xk) = all_12_0_6)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xk, all_36_2_52, all_41_2_56 and discharging atoms aNaturalNumber0(xk) = all_36_2_52, yields:
% 66.22/28.95 | (291) all_41_2_56 = all_36_2_52 | ~ (aNaturalNumber0(xk) = all_41_2_56)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xk, all_36_2_52, all_36_3_53 and discharging atoms aNaturalNumber0(xk) = all_36_2_52, yields:
% 66.22/28.95 | (292) all_36_2_52 = all_36_3_53 | ~ (aNaturalNumber0(xk) = all_36_3_53)
% 66.22/28.95 |
% 66.22/28.95 | Instantiating formula (46) with xk, all_36_2_52, all_41_1_55 and discharging atoms aNaturalNumber0(xk) = all_41_1_55, aNaturalNumber0(xk) = all_36_2_52, yields:
% 66.54/28.95 | (293) all_41_1_55 = all_36_2_52
% 66.54/28.95 |
% 66.54/28.95 | Instantiating formula (46) with xp, all_30_6_47, all_36_1_51 and discharging atoms aNaturalNumber0(xp) = all_30_6_47, yields:
% 66.54/28.95 | (294) all_36_1_51 = all_30_6_47 | ~ (aNaturalNumber0(xp) = all_36_1_51)
% 66.54/28.95 |
% 66.54/28.95 | Instantiating formula (46) with xp, all_30_6_47, all_22_0_27 and discharging atoms aNaturalNumber0(xp) = all_30_6_47, yields:
% 66.54/28.95 | (295) all_30_6_47 = all_22_0_27 | ~ (aNaturalNumber0(xp) = all_22_0_27)
% 66.54/28.95 |
% 66.54/28.95 | Instantiating formula (46) with xp, all_30_6_47, all_26_0_35 and discharging atoms aNaturalNumber0(xp) = all_30_6_47, yields:
% 66.54/28.96 | (296) all_30_6_47 = all_26_0_35 | ~ (aNaturalNumber0(xp) = all_26_0_35)
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_30_6_47, all_26_2_37 and discharging atoms aNaturalNumber0(xp) = all_30_6_47, yields:
% 66.54/28.96 | (297) all_30_6_47 = all_26_2_37 | ~ (aNaturalNumber0(xp) = all_26_2_37)
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_30_6_47, all_16_2_14 and discharging atoms aNaturalNumber0(xp) = all_30_6_47, yields:
% 66.54/28.96 | (298) all_30_6_47 = all_16_2_14 | ~ (aNaturalNumber0(xp) = all_16_2_14)
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_30_6_47, all_12_0_6 and discharging atoms aNaturalNumber0(xp) = all_30_6_47, yields:
% 66.54/28.96 | (299) all_30_6_47 = all_12_0_6 | ~ (aNaturalNumber0(xp) = all_12_0_6)
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_30_6_47, all_41_2_56 and discharging atoms aNaturalNumber0(xp) = all_30_6_47, yields:
% 66.54/28.96 | (300) all_41_2_56 = all_30_6_47 | ~ (aNaturalNumber0(xp) = all_41_2_56)
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_30_6_47, all_36_3_53 and discharging atoms aNaturalNumber0(xp) = all_30_6_47, yields:
% 66.54/28.96 | (301) all_36_3_53 = all_30_6_47 | ~ (aNaturalNumber0(xp) = all_36_3_53)
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_30_6_47, all_41_1_55 and discharging atoms aNaturalNumber0(xp) = all_30_6_47, yields:
% 66.54/28.96 | (302) all_41_1_55 = all_30_6_47 | ~ (aNaturalNumber0(xp) = all_41_1_55)
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_26_1_36, 0 and discharging atoms aNaturalNumber0(xp) = all_26_1_36, aNaturalNumber0(xp) = 0, yields:
% 66.54/28.96 | (303) all_26_1_36 = 0
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_26_1_36, all_36_1_51 and discharging atoms aNaturalNumber0(xp) = all_26_1_36, yields:
% 66.54/28.96 | (304) all_36_1_51 = all_26_1_36 | ~ (aNaturalNumber0(xp) = all_36_1_51)
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_26_1_36, all_22_0_27 and discharging atoms aNaturalNumber0(xp) = all_26_1_36, yields:
% 66.54/28.96 | (305) all_26_1_36 = all_22_0_27 | ~ (aNaturalNumber0(xp) = all_22_0_27)
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_26_1_36, all_26_0_35 and discharging atoms aNaturalNumber0(xp) = all_26_1_36, yields:
% 66.54/28.96 | (306) all_26_0_35 = all_26_1_36 | ~ (aNaturalNumber0(xp) = all_26_0_35)
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_26_1_36, all_26_2_37 and discharging atoms aNaturalNumber0(xp) = all_26_1_36, yields:
% 66.54/28.96 | (307) all_26_1_36 = all_26_2_37 | ~ (aNaturalNumber0(xp) = all_26_2_37)
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_26_1_36, all_16_2_14 and discharging atoms aNaturalNumber0(xp) = all_26_1_36, yields:
% 66.54/28.96 | (308) all_26_1_36 = all_16_2_14 | ~ (aNaturalNumber0(xp) = all_16_2_14)
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_26_1_36, all_12_0_6 and discharging atoms aNaturalNumber0(xp) = all_26_1_36, yields:
% 66.54/28.96 | (309) all_26_1_36 = all_12_0_6 | ~ (aNaturalNumber0(xp) = all_12_0_6)
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_26_1_36, all_41_2_56 and discharging atoms aNaturalNumber0(xp) = all_26_1_36, yields:
% 66.54/28.96 | (310) all_41_2_56 = all_26_1_36 | ~ (aNaturalNumber0(xp) = all_41_2_56)
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_26_1_36, all_36_3_53 and discharging atoms aNaturalNumber0(xp) = all_26_1_36, yields:
% 66.54/28.96 | (311) all_36_3_53 = all_26_1_36 | ~ (aNaturalNumber0(xp) = all_36_3_53)
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_26_1_36, all_36_2_52 and discharging atoms aNaturalNumber0(xp) = all_26_1_36, yields:
% 66.54/28.96 | (312) all_36_2_52 = all_26_1_36 | ~ (aNaturalNumber0(xp) = all_36_2_52)
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_26_1_36, all_30_6_47 and discharging atoms aNaturalNumber0(xp) = all_30_6_47, aNaturalNumber0(xp) = all_26_1_36, yields:
% 66.54/28.96 | (313) all_30_6_47 = all_26_1_36
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_24_2_32, all_36_1_51 and discharging atoms aNaturalNumber0(xp) = all_24_2_32, yields:
% 66.54/28.96 | (314) all_36_1_51 = all_24_2_32 | ~ (aNaturalNumber0(xp) = all_36_1_51)
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_24_2_32, all_22_0_27 and discharging atoms aNaturalNumber0(xp) = all_24_2_32, yields:
% 66.54/28.96 | (315) all_24_2_32 = all_22_0_27 | ~ (aNaturalNumber0(xp) = all_22_0_27)
% 66.54/28.96 |
% 66.54/28.96 | Instantiating formula (46) with xp, all_24_2_32, all_26_0_35 and discharging atoms aNaturalNumber0(xp) = all_24_2_32, yields:
% 66.56/28.96 | (316) all_26_0_35 = all_24_2_32 | ~ (aNaturalNumber0(xp) = all_26_0_35)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xp, all_24_2_32, all_26_2_37 and discharging atoms aNaturalNumber0(xp) = all_24_2_32, yields:
% 66.56/28.96 | (317) all_26_2_37 = all_24_2_32 | ~ (aNaturalNumber0(xp) = all_26_2_37)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xp, all_24_2_32, all_16_2_14 and discharging atoms aNaturalNumber0(xp) = all_24_2_32, yields:
% 66.56/28.96 | (318) all_24_2_32 = all_16_2_14 | ~ (aNaturalNumber0(xp) = all_16_2_14)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xp, all_24_2_32, all_41_2_56 and discharging atoms aNaturalNumber0(xp) = all_24_2_32, yields:
% 66.56/28.96 | (319) all_41_2_56 = all_24_2_32 | ~ (aNaturalNumber0(xp) = all_41_2_56)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xp, all_24_2_32, all_36_3_53 and discharging atoms aNaturalNumber0(xp) = all_24_2_32, yields:
% 66.56/28.96 | (320) all_36_3_53 = all_24_2_32 | ~ (aNaturalNumber0(xp) = all_36_3_53)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xp, all_24_2_32, all_30_6_47 and discharging atoms aNaturalNumber0(xp) = all_30_6_47, aNaturalNumber0(xp) = all_24_2_32, yields:
% 66.56/28.96 | (321) all_30_6_47 = all_24_2_32
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xp, all_16_1_13, all_22_0_27 and discharging atoms aNaturalNumber0(xp) = all_16_1_13, yields:
% 66.56/28.96 | (322) all_22_0_27 = all_16_1_13 | ~ (aNaturalNumber0(xp) = all_22_0_27)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xp, all_16_1_13, all_26_0_35 and discharging atoms aNaturalNumber0(xp) = all_16_1_13, yields:
% 66.56/28.96 | (323) all_26_0_35 = all_16_1_13 | ~ (aNaturalNumber0(xp) = all_26_0_35)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xp, all_16_1_13, all_26_2_37 and discharging atoms aNaturalNumber0(xp) = all_16_1_13, yields:
% 66.56/28.96 | (324) all_26_2_37 = all_16_1_13 | ~ (aNaturalNumber0(xp) = all_26_2_37)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xp, all_16_1_13, all_16_2_14 and discharging atoms aNaturalNumber0(xp) = all_16_1_13, yields:
% 66.56/28.96 | (325) all_16_1_13 = all_16_2_14 | ~ (aNaturalNumber0(xp) = all_16_2_14)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xp, all_16_1_13, all_12_0_6 and discharging atoms aNaturalNumber0(xp) = all_16_1_13, yields:
% 66.56/28.96 | (326) all_16_1_13 = all_12_0_6 | ~ (aNaturalNumber0(xp) = all_12_0_6)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xp, all_16_1_13, all_41_2_56 and discharging atoms aNaturalNumber0(xp) = all_16_1_13, yields:
% 66.56/28.96 | (327) all_41_2_56 = all_16_1_13 | ~ (aNaturalNumber0(xp) = all_41_2_56)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xp, all_16_1_13, all_36_3_53 and discharging atoms aNaturalNumber0(xp) = all_16_1_13, yields:
% 66.56/28.96 | (328) all_36_3_53 = all_16_1_13 | ~ (aNaturalNumber0(xp) = all_36_3_53)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xp, all_16_1_13, all_36_2_52 and discharging atoms aNaturalNumber0(xp) = all_16_1_13, yields:
% 66.56/28.96 | (329) all_36_2_52 = all_16_1_13 | ~ (aNaturalNumber0(xp) = all_36_2_52)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xp, all_16_1_13, all_26_1_36 and discharging atoms aNaturalNumber0(xp) = all_26_1_36, aNaturalNumber0(xp) = all_16_1_13, yields:
% 66.56/28.96 | (330) all_26_1_36 = all_16_1_13
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xm, all_30_7_48, 0 and discharging atoms aNaturalNumber0(xm) = all_30_7_48, aNaturalNumber0(xm) = 0, yields:
% 66.56/28.96 | (331) all_30_7_48 = 0
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xn, all_30_7_48, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 66.56/28.96 | (332) all_30_7_48 = 0 | ~ (aNaturalNumber0(xn) = all_30_7_48)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with sz00, all_30_7_48, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 66.56/28.96 | (333) all_30_7_48 = 0 | ~ (aNaturalNumber0(sz00) = all_30_7_48)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xm, all_30_7_48, all_22_0_27 and discharging atoms aNaturalNumber0(xm) = all_30_7_48, yields:
% 66.56/28.96 | (334) all_30_7_48 = all_22_0_27 | ~ (aNaturalNumber0(xm) = all_22_0_27)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xm, all_30_7_48, all_26_0_35 and discharging atoms aNaturalNumber0(xm) = all_30_7_48, yields:
% 66.56/28.96 | (335) all_30_7_48 = all_26_0_35 | ~ (aNaturalNumber0(xm) = all_26_0_35)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xm, all_30_7_48, all_26_2_37 and discharging atoms aNaturalNumber0(xm) = all_30_7_48, yields:
% 66.56/28.96 | (336) all_30_7_48 = all_26_2_37 | ~ (aNaturalNumber0(xm) = all_26_2_37)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xm, all_30_7_48, all_16_2_14 and discharging atoms aNaturalNumber0(xm) = all_30_7_48, yields:
% 66.56/28.96 | (337) all_30_7_48 = all_16_2_14 | ~ (aNaturalNumber0(xm) = all_16_2_14)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xm, all_30_7_48, all_12_0_6 and discharging atoms aNaturalNumber0(xm) = all_30_7_48, yields:
% 66.56/28.96 | (338) all_30_7_48 = all_12_0_6 | ~ (aNaturalNumber0(xm) = all_12_0_6)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xm, all_30_7_48, all_41_2_56 and discharging atoms aNaturalNumber0(xm) = all_30_7_48, yields:
% 66.56/28.96 | (339) all_41_2_56 = all_30_7_48 | ~ (aNaturalNumber0(xm) = all_41_2_56)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xm, all_30_7_48, all_36_3_53 and discharging atoms aNaturalNumber0(xm) = all_30_7_48, yields:
% 66.56/28.96 | (340) all_36_3_53 = all_30_7_48 | ~ (aNaturalNumber0(xm) = all_36_3_53)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xm, all_30_7_48, all_41_1_55 and discharging atoms aNaturalNumber0(xm) = all_30_7_48, yields:
% 66.56/28.96 | (341) all_41_1_55 = all_30_7_48 | ~ (aNaturalNumber0(xm) = all_41_1_55)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xm, all_30_7_48, all_36_2_52 and discharging atoms aNaturalNumber0(xm) = all_30_7_48, yields:
% 66.56/28.96 | (342) all_36_2_52 = all_30_7_48 | ~ (aNaturalNumber0(xm) = all_36_2_52)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xn, all_28_1_39, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 66.56/28.96 | (343) all_28_1_39 = 0 | ~ (aNaturalNumber0(xn) = all_28_1_39)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with sz10, all_28_1_39, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 66.56/28.96 | (344) all_28_1_39 = 0 | ~ (aNaturalNumber0(sz10) = all_28_1_39)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xm, all_28_1_39, all_36_1_51 and discharging atoms aNaturalNumber0(xm) = all_28_1_39, yields:
% 66.56/28.96 | (345) all_36_1_51 = all_28_1_39 | ~ (aNaturalNumber0(xm) = all_36_1_51)
% 66.56/28.96 |
% 66.56/28.96 | Instantiating formula (46) with xm, all_28_1_39, all_22_0_27 and discharging atoms aNaturalNumber0(xm) = all_28_1_39, yields:
% 66.56/28.96 | (346) all_28_1_39 = all_22_0_27 | ~ (aNaturalNumber0(xm) = all_22_0_27)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_28_1_39, all_41_2_56 and discharging atoms aNaturalNumber0(xm) = all_28_1_39, yields:
% 66.56/28.97 | (347) all_41_2_56 = all_28_1_39 | ~ (aNaturalNumber0(xm) = all_41_2_56)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_28_1_39, all_36_3_53 and discharging atoms aNaturalNumber0(xm) = all_28_1_39, yields:
% 66.56/28.97 | (348) all_36_3_53 = all_28_1_39 | ~ (aNaturalNumber0(xm) = all_36_3_53)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_28_1_39, all_36_2_52 and discharging atoms aNaturalNumber0(xm) = all_28_1_39, yields:
% 66.56/28.97 | (349) all_36_2_52 = all_28_1_39 | ~ (aNaturalNumber0(xm) = all_36_2_52)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_28_1_39, all_30_7_48 and discharging atoms aNaturalNumber0(xm) = all_30_7_48, aNaturalNumber0(xm) = all_28_1_39, yields:
% 66.56/28.97 | (350) all_30_7_48 = all_28_1_39
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xn, all_24_3_33, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 66.56/28.97 | (351) all_24_3_33 = 0 | ~ (aNaturalNumber0(xn) = all_24_3_33)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with sz00, all_24_3_33, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 66.56/28.97 | (352) all_24_3_33 = 0 | ~ (aNaturalNumber0(sz00) = all_24_3_33)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_24_3_33, all_22_0_27 and discharging atoms aNaturalNumber0(xm) = all_24_3_33, yields:
% 66.56/28.97 | (353) all_24_3_33 = all_22_0_27 | ~ (aNaturalNumber0(xm) = all_22_0_27)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_24_3_33, all_26_0_35 and discharging atoms aNaturalNumber0(xm) = all_24_3_33, yields:
% 66.56/28.97 | (354) all_26_0_35 = all_24_3_33 | ~ (aNaturalNumber0(xm) = all_26_0_35)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_24_3_33, all_26_2_37 and discharging atoms aNaturalNumber0(xm) = all_24_3_33, yields:
% 66.56/28.97 | (355) all_26_2_37 = all_24_3_33 | ~ (aNaturalNumber0(xm) = all_26_2_37)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_24_3_33, all_16_2_14 and discharging atoms aNaturalNumber0(xm) = all_24_3_33, yields:
% 66.56/28.97 | (356) all_24_3_33 = all_16_2_14 | ~ (aNaturalNumber0(xm) = all_16_2_14)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_24_3_33, all_12_0_6 and discharging atoms aNaturalNumber0(xm) = all_24_3_33, yields:
% 66.56/28.97 | (357) all_24_3_33 = all_12_0_6 | ~ (aNaturalNumber0(xm) = all_12_0_6)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_24_3_33, all_41_2_56 and discharging atoms aNaturalNumber0(xm) = all_24_3_33, yields:
% 66.56/28.97 | (358) all_41_2_56 = all_24_3_33 | ~ (aNaturalNumber0(xm) = all_41_2_56)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_24_3_33, all_41_1_55 and discharging atoms aNaturalNumber0(xm) = all_24_3_33, yields:
% 66.56/28.97 | (359) all_41_1_55 = all_24_3_33 | ~ (aNaturalNumber0(xm) = all_41_1_55)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_24_3_33, all_36_2_52 and discharging atoms aNaturalNumber0(xm) = all_24_3_33, yields:
% 66.56/28.97 | (360) all_36_2_52 = all_24_3_33 | ~ (aNaturalNumber0(xm) = all_36_2_52)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_24_3_33, all_30_7_48 and discharging atoms aNaturalNumber0(xm) = all_30_7_48, aNaturalNumber0(xm) = all_24_3_33, yields:
% 66.56/28.97 | (361) all_30_7_48 = all_24_3_33
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xn, all_22_1_28, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 66.56/28.97 | (362) all_22_1_28 = 0 | ~ (aNaturalNumber0(xn) = all_22_1_28)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with sz10, all_22_1_28, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 66.56/28.97 | (363) all_22_1_28 = 0 | ~ (aNaturalNumber0(sz10) = all_22_1_28)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with sz00, all_22_1_28, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 66.56/28.97 | (364) all_22_1_28 = 0 | ~ (aNaturalNumber0(sz00) = all_22_1_28)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_22_1_28, all_22_0_27 and discharging atoms aNaturalNumber0(xm) = all_22_1_28, yields:
% 66.56/28.97 | (365) all_22_0_27 = all_22_1_28 | ~ (aNaturalNumber0(xm) = all_22_0_27)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_22_1_28, all_26_0_35 and discharging atoms aNaturalNumber0(xm) = all_22_1_28, yields:
% 66.56/28.97 | (366) all_26_0_35 = all_22_1_28 | ~ (aNaturalNumber0(xm) = all_26_0_35)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_22_1_28, all_26_2_37 and discharging atoms aNaturalNumber0(xm) = all_22_1_28, yields:
% 66.56/28.97 | (367) all_26_2_37 = all_22_1_28 | ~ (aNaturalNumber0(xm) = all_26_2_37)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_22_1_28, all_16_2_14 and discharging atoms aNaturalNumber0(xm) = all_22_1_28, yields:
% 66.56/28.97 | (368) all_22_1_28 = all_16_2_14 | ~ (aNaturalNumber0(xm) = all_16_2_14)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_22_1_28, all_12_0_6 and discharging atoms aNaturalNumber0(xm) = all_22_1_28, yields:
% 66.56/28.97 | (369) all_22_1_28 = all_12_0_6 | ~ (aNaturalNumber0(xm) = all_12_0_6)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_22_1_28, all_36_3_53 and discharging atoms aNaturalNumber0(xm) = all_22_1_28, yields:
% 66.56/28.97 | (370) all_36_3_53 = all_22_1_28 | ~ (aNaturalNumber0(xm) = all_36_3_53)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_22_1_28, all_41_1_55 and discharging atoms aNaturalNumber0(xm) = all_22_1_28, yields:
% 66.56/28.97 | (371) all_41_1_55 = all_22_1_28 | ~ (aNaturalNumber0(xm) = all_41_1_55)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_22_1_28, all_36_2_52 and discharging atoms aNaturalNumber0(xm) = all_22_1_28, yields:
% 66.56/28.97 | (372) all_36_2_52 = all_22_1_28 | ~ (aNaturalNumber0(xm) = all_36_2_52)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_22_1_28, all_28_1_39 and discharging atoms aNaturalNumber0(xm) = all_28_1_39, aNaturalNumber0(xm) = all_22_1_28, yields:
% 66.56/28.97 | (373) all_28_1_39 = all_22_1_28
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xn, all_14_1_10, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 66.56/28.97 | (374) all_14_1_10 = 0 | ~ (aNaturalNumber0(xn) = all_14_1_10)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_14_1_10, all_36_1_51 and discharging atoms aNaturalNumber0(xm) = all_14_1_10, yields:
% 66.56/28.97 | (375) all_36_1_51 = all_14_1_10 | ~ (aNaturalNumber0(xm) = all_36_1_51)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_14_1_10, all_22_0_27 and discharging atoms aNaturalNumber0(xm) = all_14_1_10, yields:
% 66.56/28.97 | (376) all_22_0_27 = all_14_1_10 | ~ (aNaturalNumber0(xm) = all_22_0_27)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_14_1_10, all_26_0_35 and discharging atoms aNaturalNumber0(xm) = all_14_1_10, yields:
% 66.56/28.97 | (377) all_26_0_35 = all_14_1_10 | ~ (aNaturalNumber0(xm) = all_26_0_35)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_14_1_10, all_26_2_37 and discharging atoms aNaturalNumber0(xm) = all_14_1_10, yields:
% 66.56/28.97 | (378) all_26_2_37 = all_14_1_10 | ~ (aNaturalNumber0(xm) = all_26_2_37)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_14_1_10, all_16_2_14 and discharging atoms aNaturalNumber0(xm) = all_14_1_10, yields:
% 66.56/28.97 | (379) all_16_2_14 = all_14_1_10 | ~ (aNaturalNumber0(xm) = all_16_2_14)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_14_1_10, all_12_0_6 and discharging atoms aNaturalNumber0(xm) = all_14_1_10, yields:
% 66.56/28.97 | (380) all_14_1_10 = all_12_0_6 | ~ (aNaturalNumber0(xm) = all_12_0_6)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_14_1_10, all_41_2_56 and discharging atoms aNaturalNumber0(xm) = all_14_1_10, yields:
% 66.56/28.97 | (381) all_41_2_56 = all_14_1_10 | ~ (aNaturalNumber0(xm) = all_41_2_56)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_14_1_10, all_36_3_53 and discharging atoms aNaturalNumber0(xm) = all_14_1_10, yields:
% 66.56/28.97 | (382) all_36_3_53 = all_14_1_10 | ~ (aNaturalNumber0(xm) = all_36_3_53)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_14_1_10, all_36_2_52 and discharging atoms aNaturalNumber0(xm) = all_14_1_10, yields:
% 66.56/28.97 | (383) all_36_2_52 = all_14_1_10 | ~ (aNaturalNumber0(xm) = all_36_2_52)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_14_1_10, all_28_1_39 and discharging atoms aNaturalNumber0(xm) = all_28_1_39, aNaturalNumber0(xm) = all_14_1_10, yields:
% 66.56/28.97 | (384) all_28_1_39 = all_14_1_10
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xn, all_12_1_7, 0 and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 66.56/28.97 | (385) all_12_1_7 = 0 | ~ (aNaturalNumber0(xn) = all_12_1_7)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with sz10, all_12_1_7, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 66.56/28.97 | (386) all_12_1_7 = 0 | ~ (aNaturalNumber0(sz10) = all_12_1_7)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_12_1_7, all_36_1_51 and discharging atoms aNaturalNumber0(xm) = all_12_1_7, yields:
% 66.56/28.97 | (387) all_36_1_51 = all_12_1_7 | ~ (aNaturalNumber0(xm) = all_36_1_51)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_12_1_7, all_22_0_27 and discharging atoms aNaturalNumber0(xm) = all_12_1_7, yields:
% 66.56/28.97 | (388) all_22_0_27 = all_12_1_7 | ~ (aNaturalNumber0(xm) = all_22_0_27)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_12_1_7, all_26_0_35 and discharging atoms aNaturalNumber0(xm) = all_12_1_7, yields:
% 66.56/28.97 | (389) all_26_0_35 = all_12_1_7 | ~ (aNaturalNumber0(xm) = all_26_0_35)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_12_1_7, all_26_2_37 and discharging atoms aNaturalNumber0(xm) = all_12_1_7, yields:
% 66.56/28.97 | (390) all_26_2_37 = all_12_1_7 | ~ (aNaturalNumber0(xm) = all_26_2_37)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_12_1_7, all_12_0_6 and discharging atoms aNaturalNumber0(xm) = all_12_1_7, yields:
% 66.56/28.97 | (391) all_12_0_6 = all_12_1_7 | ~ (aNaturalNumber0(xm) = all_12_0_6)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_12_1_7, all_41_2_56 and discharging atoms aNaturalNumber0(xm) = all_12_1_7, yields:
% 66.56/28.97 | (392) all_41_2_56 = all_12_1_7 | ~ (aNaturalNumber0(xm) = all_41_2_56)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_12_1_7, all_36_2_52 and discharging atoms aNaturalNumber0(xm) = all_12_1_7, yields:
% 66.56/28.97 | (393) all_36_2_52 = all_12_1_7 | ~ (aNaturalNumber0(xm) = all_36_2_52)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xm, all_12_1_7, all_14_1_10 and discharging atoms aNaturalNumber0(xm) = all_14_1_10, aNaturalNumber0(xm) = all_12_1_7, yields:
% 66.56/28.97 | (394) all_14_1_10 = all_12_1_7
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with sz10, all_30_8_49, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 66.56/28.97 | (395) all_30_8_49 = 0 | ~ (aNaturalNumber0(sz10) = all_30_8_49)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xn, all_30_8_49, all_26_0_35 and discharging atoms aNaturalNumber0(xn) = all_30_8_49, yields:
% 66.56/28.97 | (396) all_30_8_49 = all_26_0_35 | ~ (aNaturalNumber0(xn) = all_26_0_35)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xn, all_30_8_49, all_26_2_37 and discharging atoms aNaturalNumber0(xn) = all_30_8_49, yields:
% 66.56/28.97 | (397) all_30_8_49 = all_26_2_37 | ~ (aNaturalNumber0(xn) = all_26_2_37)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xn, all_30_8_49, all_16_2_14 and discharging atoms aNaturalNumber0(xn) = all_30_8_49, yields:
% 66.56/28.97 | (398) all_30_8_49 = all_16_2_14 | ~ (aNaturalNumber0(xn) = all_16_2_14)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xn, all_30_8_49, all_12_0_6 and discharging atoms aNaturalNumber0(xn) = all_30_8_49, yields:
% 66.56/28.97 | (399) all_30_8_49 = all_12_0_6 | ~ (aNaturalNumber0(xn) = all_12_0_6)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xn, all_30_8_49, all_41_2_56 and discharging atoms aNaturalNumber0(xn) = all_30_8_49, yields:
% 66.56/28.97 | (400) all_41_2_56 = all_30_8_49 | ~ (aNaturalNumber0(xn) = all_41_2_56)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xn, all_30_8_49, all_36_3_53 and discharging atoms aNaturalNumber0(xn) = all_30_8_49, yields:
% 66.56/28.97 | (401) all_36_3_53 = all_30_8_49 | ~ (aNaturalNumber0(xn) = all_36_3_53)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xn, all_30_8_49, all_36_2_52 and discharging atoms aNaturalNumber0(xn) = all_30_8_49, yields:
% 66.56/28.97 | (402) all_36_2_52 = all_30_8_49 | ~ (aNaturalNumber0(xn) = all_36_2_52)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xn, all_30_8_49, all_30_7_48 and discharging atoms aNaturalNumber0(xn) = all_30_8_49, yields:
% 66.56/28.97 | (403) all_30_7_48 = all_30_8_49 | ~ (aNaturalNumber0(xn) = all_30_7_48)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xn, all_30_8_49, all_28_1_39 and discharging atoms aNaturalNumber0(xn) = all_30_8_49, yields:
% 66.56/28.97 | (404) all_30_8_49 = all_28_1_39 | ~ (aNaturalNumber0(xn) = all_28_1_39)
% 66.56/28.97 |
% 66.56/28.97 | Instantiating formula (46) with xn, all_30_8_49, all_24_3_33 and discharging atoms aNaturalNumber0(xn) = all_30_8_49, yields:
% 66.56/28.97 | (405) all_30_8_49 = all_24_3_33 | ~ (aNaturalNumber0(xn) = all_24_3_33)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_30_8_49, all_22_1_28 and discharging atoms aNaturalNumber0(xn) = all_30_8_49, yields:
% 66.56/28.98 | (406) all_30_8_49 = all_22_1_28 | ~ (aNaturalNumber0(xn) = all_22_1_28)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_30_8_49, all_14_1_10 and discharging atoms aNaturalNumber0(xn) = all_30_8_49, yields:
% 66.56/28.98 | (407) all_30_8_49 = all_14_1_10 | ~ (aNaturalNumber0(xn) = all_14_1_10)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_30_8_49, all_12_1_7 and discharging atoms aNaturalNumber0(xn) = all_30_8_49, yields:
% 66.56/28.98 | (408) all_30_8_49 = all_12_1_7 | ~ (aNaturalNumber0(xn) = all_12_1_7)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with sz10, all_28_2_40, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 66.56/28.98 | (409) all_28_2_40 = 0 | ~ (aNaturalNumber0(sz10) = all_28_2_40)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with sz00, all_28_2_40, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 66.56/28.98 | (410) all_28_2_40 = 0 | ~ (aNaturalNumber0(sz00) = all_28_2_40)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_28_2_40, all_36_1_51 and discharging atoms aNaturalNumber0(xn) = all_28_2_40, yields:
% 66.56/28.98 | (411) all_36_1_51 = all_28_2_40 | ~ (aNaturalNumber0(xn) = all_36_1_51)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_28_2_40, all_22_0_27 and discharging atoms aNaturalNumber0(xn) = all_28_2_40, yields:
% 66.56/28.98 | (412) all_28_2_40 = all_22_0_27 | ~ (aNaturalNumber0(xn) = all_22_0_27)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_28_2_40, all_26_0_35 and discharging atoms aNaturalNumber0(xn) = all_28_2_40, yields:
% 66.56/28.98 | (413) all_28_2_40 = all_26_0_35 | ~ (aNaturalNumber0(xn) = all_26_0_35)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_28_2_40, all_26_2_37 and discharging atoms aNaturalNumber0(xn) = all_28_2_40, yields:
% 66.56/28.98 | (414) all_28_2_40 = all_26_2_37 | ~ (aNaturalNumber0(xn) = all_26_2_37)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_28_2_40, all_16_2_14 and discharging atoms aNaturalNumber0(xn) = all_28_2_40, yields:
% 66.56/28.98 | (415) all_28_2_40 = all_16_2_14 | ~ (aNaturalNumber0(xn) = all_16_2_14)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_28_2_40, all_12_0_6 and discharging atoms aNaturalNumber0(xn) = all_28_2_40, yields:
% 66.56/28.98 | (416) all_28_2_40 = all_12_0_6 | ~ (aNaturalNumber0(xn) = all_12_0_6)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_28_2_40, all_41_2_56 and discharging atoms aNaturalNumber0(xn) = all_28_2_40, yields:
% 66.56/28.98 | (417) all_41_2_56 = all_28_2_40 | ~ (aNaturalNumber0(xn) = all_41_2_56)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_28_2_40, all_36_3_53 and discharging atoms aNaturalNumber0(xn) = all_28_2_40, yields:
% 66.56/28.98 | (418) all_36_3_53 = all_28_2_40 | ~ (aNaturalNumber0(xn) = all_36_3_53)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_28_2_40, all_41_1_55 and discharging atoms aNaturalNumber0(xn) = all_28_2_40, yields:
% 66.56/28.98 | (419) all_41_1_55 = all_28_2_40 | ~ (aNaturalNumber0(xn) = all_41_1_55)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_28_2_40, all_30_7_48 and discharging atoms aNaturalNumber0(xn) = all_28_2_40, yields:
% 66.56/28.98 | (420) all_30_7_48 = all_28_2_40 | ~ (aNaturalNumber0(xn) = all_30_7_48)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_28_2_40, all_28_1_39 and discharging atoms aNaturalNumber0(xn) = all_28_2_40, yields:
% 66.56/28.98 | (421) all_28_1_39 = all_28_2_40 | ~ (aNaturalNumber0(xn) = all_28_1_39)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_28_2_40, all_22_1_28 and discharging atoms aNaturalNumber0(xn) = all_28_2_40, yields:
% 66.56/28.98 | (422) all_28_2_40 = all_22_1_28 | ~ (aNaturalNumber0(xn) = all_22_1_28)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_28_2_40, all_30_8_49 and discharging atoms aNaturalNumber0(xn) = all_30_8_49, aNaturalNumber0(xn) = all_28_2_40, yields:
% 66.56/28.98 | (423) all_30_8_49 = all_28_2_40
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with sz10, all_24_4_34, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 66.56/28.98 | (424) all_24_4_34 = 0 | ~ (aNaturalNumber0(sz10) = all_24_4_34)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_24_4_34, all_36_1_51 and discharging atoms aNaturalNumber0(xn) = all_24_4_34, yields:
% 66.56/28.98 | (425) all_36_1_51 = all_24_4_34 | ~ (aNaturalNumber0(xn) = all_36_1_51)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_24_4_34, all_22_0_27 and discharging atoms aNaturalNumber0(xn) = all_24_4_34, yields:
% 66.56/28.98 | (426) all_24_4_34 = all_22_0_27 | ~ (aNaturalNumber0(xn) = all_22_0_27)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_24_4_34, all_16_2_14 and discharging atoms aNaturalNumber0(xn) = all_24_4_34, yields:
% 66.56/28.98 | (427) all_24_4_34 = all_16_2_14 | ~ (aNaturalNumber0(xn) = all_16_2_14)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_24_4_34, all_12_0_6 and discharging atoms aNaturalNumber0(xn) = all_24_4_34, yields:
% 66.56/28.98 | (428) all_24_4_34 = all_12_0_6 | ~ (aNaturalNumber0(xn) = all_12_0_6)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_24_4_34, all_41_1_55 and discharging atoms aNaturalNumber0(xn) = all_24_4_34, yields:
% 66.56/28.98 | (429) all_41_1_55 = all_24_4_34 | ~ (aNaturalNumber0(xn) = all_41_1_55)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_24_4_34, all_36_2_52 and discharging atoms aNaturalNumber0(xn) = all_24_4_34, yields:
% 66.56/28.98 | (430) all_36_2_52 = all_24_4_34 | ~ (aNaturalNumber0(xn) = all_36_2_52)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_24_4_34, all_30_7_48 and discharging atoms aNaturalNumber0(xn) = all_24_4_34, yields:
% 66.56/28.98 | (431) all_30_7_48 = all_24_4_34 | ~ (aNaturalNumber0(xn) = all_30_7_48)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_24_4_34, all_28_1_39 and discharging atoms aNaturalNumber0(xn) = all_24_4_34, yields:
% 66.56/28.98 | (432) all_28_1_39 = all_24_4_34 | ~ (aNaturalNumber0(xn) = all_28_1_39)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_24_4_34, all_12_1_7 and discharging atoms aNaturalNumber0(xn) = all_24_4_34, yields:
% 66.56/28.98 | (433) all_24_4_34 = all_12_1_7 | ~ (aNaturalNumber0(xn) = all_12_1_7)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_24_4_34, all_28_2_40 and discharging atoms aNaturalNumber0(xn) = all_28_2_40, aNaturalNumber0(xn) = all_24_4_34, yields:
% 66.56/28.98 | (434) all_28_2_40 = all_24_4_34
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with sz10, all_22_2_29, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 66.56/28.98 | (435) all_22_2_29 = 0 | ~ (aNaturalNumber0(sz10) = all_22_2_29)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with sz00, all_22_2_29, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 66.56/28.98 | (436) all_22_2_29 = 0 | ~ (aNaturalNumber0(sz00) = all_22_2_29)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_22_2_29, all_36_1_51 and discharging atoms aNaturalNumber0(xn) = all_22_2_29, yields:
% 66.56/28.98 | (437) all_36_1_51 = all_22_2_29 | ~ (aNaturalNumber0(xn) = all_36_1_51)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_22_2_29, all_22_0_27 and discharging atoms aNaturalNumber0(xn) = all_22_2_29, yields:
% 66.56/28.98 | (438) all_22_0_27 = all_22_2_29 | ~ (aNaturalNumber0(xn) = all_22_0_27)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_22_2_29, all_26_0_35 and discharging atoms aNaturalNumber0(xn) = all_22_2_29, yields:
% 66.56/28.98 | (439) all_26_0_35 = all_22_2_29 | ~ (aNaturalNumber0(xn) = all_26_0_35)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_22_2_29, all_26_2_37 and discharging atoms aNaturalNumber0(xn) = all_22_2_29, yields:
% 66.56/28.98 | (440) all_26_2_37 = all_22_2_29 | ~ (aNaturalNumber0(xn) = all_26_2_37)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_22_2_29, all_16_2_14 and discharging atoms aNaturalNumber0(xn) = all_22_2_29, yields:
% 66.56/28.98 | (441) all_22_2_29 = all_16_2_14 | ~ (aNaturalNumber0(xn) = all_16_2_14)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_22_2_29, all_12_0_6 and discharging atoms aNaturalNumber0(xn) = all_22_2_29, yields:
% 66.56/28.98 | (442) all_22_2_29 = all_12_0_6 | ~ (aNaturalNumber0(xn) = all_12_0_6)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_22_2_29, all_36_3_53 and discharging atoms aNaturalNumber0(xn) = all_22_2_29, yields:
% 66.56/28.98 | (443) all_36_3_53 = all_22_2_29 | ~ (aNaturalNumber0(xn) = all_36_3_53)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_22_2_29, all_36_2_52 and discharging atoms aNaturalNumber0(xn) = all_22_2_29, yields:
% 66.56/28.98 | (444) all_36_2_52 = all_22_2_29 | ~ (aNaturalNumber0(xn) = all_36_2_52)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_22_2_29, all_30_7_48 and discharging atoms aNaturalNumber0(xn) = all_22_2_29, yields:
% 66.56/28.98 | (445) all_30_7_48 = all_22_2_29 | ~ (aNaturalNumber0(xn) = all_30_7_48)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_22_2_29, all_28_1_39 and discharging atoms aNaturalNumber0(xn) = all_22_2_29, yields:
% 66.56/28.98 | (446) all_28_1_39 = all_22_2_29 | ~ (aNaturalNumber0(xn) = all_28_1_39)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_22_2_29, all_24_3_33 and discharging atoms aNaturalNumber0(xn) = all_22_2_29, yields:
% 66.56/28.98 | (447) all_24_3_33 = all_22_2_29 | ~ (aNaturalNumber0(xn) = all_24_3_33)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_22_2_29, all_22_1_28 and discharging atoms aNaturalNumber0(xn) = all_22_2_29, yields:
% 66.56/28.98 | (448) all_22_1_28 = all_22_2_29 | ~ (aNaturalNumber0(xn) = all_22_1_28)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_22_2_29, all_14_1_10 and discharging atoms aNaturalNumber0(xn) = all_22_2_29, yields:
% 66.56/28.98 | (449) all_22_2_29 = all_14_1_10 | ~ (aNaturalNumber0(xn) = all_14_1_10)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_22_2_29, all_24_4_34 and discharging atoms aNaturalNumber0(xn) = all_24_4_34, aNaturalNumber0(xn) = all_22_2_29, yields:
% 66.56/28.98 | (450) all_24_4_34 = all_22_2_29
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_14_2_11, 0 and discharging atoms aNaturalNumber0(xn) = all_14_2_11, aNaturalNumber0(xn) = 0, yields:
% 66.56/28.98 | (451) all_14_2_11 = 0
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with sz10, all_14_2_11, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 66.56/28.98 | (452) all_14_2_11 = 0 | ~ (aNaturalNumber0(sz10) = all_14_2_11)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with sz00, all_14_2_11, 0 and discharging atoms aNaturalNumber0(sz00) = 0, yields:
% 66.56/28.98 | (453) all_14_2_11 = 0 | ~ (aNaturalNumber0(sz00) = all_14_2_11)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_14_2_11, all_36_1_51 and discharging atoms aNaturalNumber0(xn) = all_14_2_11, yields:
% 66.56/28.98 | (454) all_36_1_51 = all_14_2_11 | ~ (aNaturalNumber0(xn) = all_36_1_51)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_14_2_11, all_22_0_27 and discharging atoms aNaturalNumber0(xn) = all_14_2_11, yields:
% 66.56/28.98 | (455) all_22_0_27 = all_14_2_11 | ~ (aNaturalNumber0(xn) = all_22_0_27)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_14_2_11, all_26_2_37 and discharging atoms aNaturalNumber0(xn) = all_14_2_11, yields:
% 66.56/28.98 | (456) all_26_2_37 = all_14_2_11 | ~ (aNaturalNumber0(xn) = all_26_2_37)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_14_2_11, all_16_2_14 and discharging atoms aNaturalNumber0(xn) = all_14_2_11, yields:
% 66.56/28.98 | (457) all_16_2_14 = all_14_2_11 | ~ (aNaturalNumber0(xn) = all_16_2_14)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_14_2_11, all_41_2_56 and discharging atoms aNaturalNumber0(xn) = all_14_2_11, yields:
% 66.56/28.98 | (458) all_41_2_56 = all_14_2_11 | ~ (aNaturalNumber0(xn) = all_41_2_56)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_14_2_11, all_36_3_53 and discharging atoms aNaturalNumber0(xn) = all_14_2_11, yields:
% 66.56/28.98 | (459) all_36_3_53 = all_14_2_11 | ~ (aNaturalNumber0(xn) = all_36_3_53)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_14_2_11, all_41_1_55 and discharging atoms aNaturalNumber0(xn) = all_14_2_11, yields:
% 66.56/28.98 | (460) all_41_1_55 = all_14_2_11 | ~ (aNaturalNumber0(xn) = all_41_1_55)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_14_2_11, all_28_1_39 and discharging atoms aNaturalNumber0(xn) = all_14_2_11, yields:
% 66.56/28.98 | (461) all_28_1_39 = all_14_2_11 | ~ (aNaturalNumber0(xn) = all_28_1_39)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_14_2_11, all_24_3_33 and discharging atoms aNaturalNumber0(xn) = all_14_2_11, yields:
% 66.56/28.98 | (462) all_24_3_33 = all_14_2_11 | ~ (aNaturalNumber0(xn) = all_24_3_33)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_14_2_11, all_22_1_28 and discharging atoms aNaturalNumber0(xn) = all_14_2_11, yields:
% 66.56/28.98 | (463) all_22_1_28 = all_14_2_11 | ~ (aNaturalNumber0(xn) = all_22_1_28)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_14_2_11, all_14_1_10 and discharging atoms aNaturalNumber0(xn) = all_14_2_11, yields:
% 66.56/28.98 | (464) all_14_1_10 = all_14_2_11 | ~ (aNaturalNumber0(xn) = all_14_1_10)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_14_2_11, all_12_1_7 and discharging atoms aNaturalNumber0(xn) = all_14_2_11, yields:
% 66.56/28.98 | (465) all_14_2_11 = all_12_1_7 | ~ (aNaturalNumber0(xn) = all_12_1_7)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_14_2_11, all_22_2_29 and discharging atoms aNaturalNumber0(xn) = all_22_2_29, aNaturalNumber0(xn) = all_14_2_11, yields:
% 66.56/28.98 | (466) all_22_2_29 = all_14_2_11
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with sz10, all_12_2_8, 0 and discharging atoms aNaturalNumber0(sz10) = 0, yields:
% 66.56/28.98 | (467) all_12_2_8 = 0 | ~ (aNaturalNumber0(sz10) = all_12_2_8)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_12_2_8, all_36_1_51 and discharging atoms aNaturalNumber0(xn) = all_12_2_8, yields:
% 66.56/28.98 | (468) all_36_1_51 = all_12_2_8 | ~ (aNaturalNumber0(xn) = all_36_1_51)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_12_2_8, all_22_0_27 and discharging atoms aNaturalNumber0(xn) = all_12_2_8, yields:
% 66.56/28.98 | (469) all_22_0_27 = all_12_2_8 | ~ (aNaturalNumber0(xn) = all_22_0_27)
% 66.56/28.98 |
% 66.56/28.98 | Instantiating formula (46) with xn, all_12_2_8, all_26_0_35 and discharging atoms aNaturalNumber0(xn) = all_12_2_8, yields:
% 66.56/28.98 | (470) all_26_0_35 = all_12_2_8 | ~ (aNaturalNumber0(xn) = all_26_0_35)
% 66.56/28.99 |
% 66.56/28.99 | Instantiating formula (46) with xn, all_12_2_8, all_26_2_37 and discharging atoms aNaturalNumber0(xn) = all_12_2_8, yields:
% 66.56/28.99 | (471) all_26_2_37 = all_12_2_8 | ~ (aNaturalNumber0(xn) = all_26_2_37)
% 66.56/28.99 |
% 66.56/28.99 | Instantiating formula (46) with xn, all_12_2_8, all_41_2_56 and discharging atoms aNaturalNumber0(xn) = all_12_2_8, yields:
% 66.56/28.99 | (472) all_41_2_56 = all_12_2_8 | ~ (aNaturalNumber0(xn) = all_41_2_56)
% 66.56/28.99 |
% 66.56/28.99 | Instantiating formula (46) with xn, all_12_2_8, all_41_1_55 and discharging atoms aNaturalNumber0(xn) = all_12_2_8, yields:
% 66.56/28.99 | (473) all_41_1_55 = all_12_2_8 | ~ (aNaturalNumber0(xn) = all_41_1_55)
% 66.56/28.99 |
% 66.56/28.99 | Instantiating formula (46) with xn, all_12_2_8, all_36_2_52 and discharging atoms aNaturalNumber0(xn) = all_12_2_8, yields:
% 66.56/28.99 | (474) all_36_2_52 = all_12_2_8 | ~ (aNaturalNumber0(xn) = all_36_2_52)
% 66.56/28.99 |
% 66.56/28.99 | Instantiating formula (46) with xn, all_12_2_8, all_30_7_48 and discharging atoms aNaturalNumber0(xn) = all_12_2_8, yields:
% 66.56/28.99 | (475) all_30_7_48 = all_12_2_8 | ~ (aNaturalNumber0(xn) = all_30_7_48)
% 66.56/28.99 |
% 66.56/28.99 | Instantiating formula (46) with xn, all_12_2_8, all_24_3_33 and discharging atoms aNaturalNumber0(xn) = all_12_2_8, yields:
% 66.56/28.99 | (476) all_24_3_33 = all_12_2_8 | ~ (aNaturalNumber0(xn) = all_24_3_33)
% 66.56/28.99 |
% 66.56/28.99 | Instantiating formula (46) with xn, all_12_2_8, all_22_1_28 and discharging atoms aNaturalNumber0(xn) = all_12_2_8, yields:
% 66.56/28.99 | (477) all_22_1_28 = all_12_2_8 | ~ (aNaturalNumber0(xn) = all_22_1_28)
% 66.56/28.99 |
% 66.56/28.99 | Instantiating formula (46) with xn, all_12_2_8, all_14_1_10 and discharging atoms aNaturalNumber0(xn) = all_12_2_8, yields:
% 66.56/28.99 | (478) all_14_1_10 = all_12_2_8 | ~ (aNaturalNumber0(xn) = all_14_1_10)
% 66.56/28.99 |
% 66.56/28.99 | Instantiating formula (46) with xn, all_12_2_8, all_30_8_49 and discharging atoms aNaturalNumber0(xn) = all_30_8_49, aNaturalNumber0(xn) = all_12_2_8, yields:
% 66.56/28.99 | (479) all_30_8_49 = all_12_2_8
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (253,271) yields a new equation:
% 66.56/28.99 | (480) all_36_3_53 = 0
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (313,321) yields a new equation:
% 66.56/28.99 | (481) all_26_1_36 = all_24_2_32
% 66.56/28.99 |
% 66.56/28.99 | Simplifying 481 yields:
% 66.56/28.99 | (482) all_26_1_36 = all_24_2_32
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (331,361) yields a new equation:
% 66.56/28.99 | (483) all_24_3_33 = 0
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (350,361) yields a new equation:
% 66.56/28.99 | (484) all_28_1_39 = all_24_3_33
% 66.56/28.99 |
% 66.56/28.99 | Simplifying 484 yields:
% 66.56/28.99 | (485) all_28_1_39 = all_24_3_33
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (423,479) yields a new equation:
% 66.56/28.99 | (486) all_28_2_40 = all_12_2_8
% 66.56/28.99 |
% 66.56/28.99 | Simplifying 486 yields:
% 66.56/28.99 | (487) all_28_2_40 = all_12_2_8
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (384,373) yields a new equation:
% 66.56/28.99 | (488) all_22_1_28 = all_14_1_10
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (485,373) yields a new equation:
% 66.56/28.99 | (489) all_24_3_33 = all_22_1_28
% 66.56/28.99 |
% 66.56/28.99 | Simplifying 489 yields:
% 66.56/28.99 | (490) all_24_3_33 = all_22_1_28
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (434,487) yields a new equation:
% 66.56/28.99 | (491) all_24_4_34 = all_12_2_8
% 66.56/28.99 |
% 66.56/28.99 | Simplifying 491 yields:
% 66.56/28.99 | (492) all_24_4_34 = all_12_2_8
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (303,482) yields a new equation:
% 66.56/28.99 | (493) all_24_2_32 = 0
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (330,482) yields a new equation:
% 66.56/28.99 | (494) all_24_2_32 = all_16_1_13
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (252,242) yields a new equation:
% 66.56/28.99 | (495) all_16_2_14 = all_12_0_6
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (494,493) yields a new equation:
% 66.56/28.99 | (496) all_16_1_13 = 0
% 66.56/28.99 |
% 66.56/28.99 | Simplifying 496 yields:
% 66.56/28.99 | (497) all_16_1_13 = 0
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (490,483) yields a new equation:
% 66.56/28.99 | (498) all_22_1_28 = 0
% 66.56/28.99 |
% 66.56/28.99 | Simplifying 498 yields:
% 66.56/28.99 | (499) all_22_1_28 = 0
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (450,492) yields a new equation:
% 66.56/28.99 | (500) all_22_2_29 = all_12_2_8
% 66.56/28.99 |
% 66.56/28.99 | Simplifying 500 yields:
% 66.56/28.99 | (501) all_22_2_29 = all_12_2_8
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (488,499) yields a new equation:
% 66.56/28.99 | (502) all_14_1_10 = 0
% 66.56/28.99 |
% 66.56/28.99 | Simplifying 502 yields:
% 66.56/28.99 | (503) all_14_1_10 = 0
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (466,501) yields a new equation:
% 66.56/28.99 | (504) all_14_2_11 = all_12_2_8
% 66.56/28.99 |
% 66.56/28.99 | Simplifying 504 yields:
% 66.56/28.99 | (505) all_14_2_11 = all_12_2_8
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (394,503) yields a new equation:
% 66.56/28.99 | (506) all_12_1_7 = 0
% 66.56/28.99 |
% 66.56/28.99 | Simplifying 506 yields:
% 66.56/28.99 | (507) all_12_1_7 = 0
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (451,505) yields a new equation:
% 66.56/28.99 | (508) all_12_2_8 = 0
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (508,505) yields a new equation:
% 66.56/28.99 | (451) all_14_2_11 = 0
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (508,501) yields a new equation:
% 66.56/28.99 | (510) all_22_2_29 = 0
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (508,492) yields a new equation:
% 66.56/28.99 | (511) all_24_4_34 = 0
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (495,242) yields a new equation:
% 66.56/28.99 | (252) all_26_2_37 = all_12_0_6
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (493,482) yields a new equation:
% 66.56/28.99 | (303) all_26_1_36 = 0
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (508,487) yields a new equation:
% 66.56/28.99 | (514) all_28_2_40 = 0
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (499,373) yields a new equation:
% 66.56/28.99 | (515) all_28_1_39 = 0
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (508,479) yields a new equation:
% 66.56/28.99 | (516) all_30_8_49 = 0
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (483,361) yields a new equation:
% 66.56/28.99 | (331) all_30_7_48 = 0
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (480,271) yields a new equation:
% 66.56/28.99 | (253) all_41_2_56 = 0
% 66.56/28.99 |
% 66.56/28.99 | From (205) and (150) follows:
% 66.56/28.99 | (51) isPrime0(xp) = 0
% 66.56/28.99 |
% 66.56/28.99 | From (207) and (152) follows:
% 66.56/28.99 | (520) sdtpldt0(all_0_5_5, xp) = all_30_3_44
% 66.56/28.99 |
% 66.56/28.99 | From (207) and (155) follows:
% 66.56/28.99 | (73) sdtpldt0(xn, xm) = all_0_5_5
% 66.56/28.99 |
% 66.56/28.99 | From (219) and (167) follows:
% 66.56/28.99 | (126) aNaturalNumber0(all_0_3_3) = all_22_0_27
% 66.56/28.99 |
% 66.56/28.99 | From (495) and (118) follows:
% 66.56/28.99 | (107) aNaturalNumber0(all_0_5_5) = all_12_0_6
% 66.56/28.99 |
% 66.56/28.99 | From (480) and (163) follows:
% 66.56/28.99 | (10) aNaturalNumber0(xr) = 0
% 66.56/28.99 |
% 66.56/28.99 | From (293) and (175) follows:
% 66.56/28.99 | (166) aNaturalNumber0(xk) = all_36_2_52
% 66.56/28.99 |
% 66.56/28.99 | From (497) and (119) follows:
% 66.56/28.99 | (12) aNaturalNumber0(xp) = 0
% 66.56/28.99 |
% 66.56/28.99 | From (507) and (108) follows:
% 66.56/28.99 | (36) aNaturalNumber0(xm) = 0
% 66.56/28.99 |
% 66.56/28.99 | From (508) and (109) follows:
% 66.56/28.99 | (53) aNaturalNumber0(xn) = 0
% 66.56/28.99 |
% 66.56/28.99 +-Applying beta-rule and splitting (121), into two cases.
% 66.56/28.99 |-Branch one:
% 66.56/28.99 | (529) all_18_0_15 = xp & all_18_1_16 = 0 & sdtpldt0(xn, all_18_2_17) = xp & aNaturalNumber0(all_18_2_17) = 0
% 66.56/28.99 |
% 66.56/28.99 | Applying alpha-rule on (529) yields:
% 66.56/28.99 | (530) all_18_0_15 = xp
% 66.56/28.99 | (531) all_18_1_16 = 0
% 66.56/28.99 | (532) sdtpldt0(xn, all_18_2_17) = xp
% 66.56/28.99 | (533) aNaturalNumber0(all_18_2_17) = 0
% 66.56/28.99 |
% 66.56/28.99 +-Applying beta-rule and splitting (129), into two cases.
% 66.56/28.99 |-Branch one:
% 66.56/28.99 | (534) ~ (all_22_1_28 = 0)
% 66.56/28.99 |
% 66.56/28.99 | Equations (499) can reduce 534 to:
% 66.56/28.99 | (159) $false
% 66.56/28.99 |
% 66.56/28.99 |-The branch is then unsatisfiable
% 66.56/28.99 |-Branch two:
% 66.56/28.99 | (499) all_22_1_28 = 0
% 66.56/28.99 | (537) ~ (all_22_2_29 = 0) | all_22_0_27 = 0
% 66.56/28.99 |
% 66.56/28.99 +-Applying beta-rule and splitting (122), into two cases.
% 66.56/28.99 |-Branch one:
% 66.56/28.99 | (538) all_19_0_18 = xp & all_19_1_19 = 0 & sdtpldt0(xm, all_19_2_20) = xp & aNaturalNumber0(all_19_2_20) = 0
% 66.56/28.99 |
% 66.56/28.99 | Applying alpha-rule on (538) yields:
% 66.56/28.99 | (539) all_19_0_18 = xp
% 66.56/28.99 | (540) all_19_1_19 = 0
% 66.56/28.99 | (541) sdtpldt0(xm, all_19_2_20) = xp
% 66.56/28.99 | (542) aNaturalNumber0(all_19_2_20) = 0
% 66.56/28.99 |
% 66.56/28.99 +-Applying beta-rule and splitting (110), into two cases.
% 66.56/28.99 |-Branch one:
% 66.56/28.99 | (543) ~ (all_12_1_7 = 0)
% 66.56/28.99 |
% 66.56/28.99 | Equations (507) can reduce 543 to:
% 66.56/28.99 | (159) $false
% 66.56/28.99 |
% 66.56/28.99 |-The branch is then unsatisfiable
% 66.56/28.99 |-Branch two:
% 66.56/28.99 | (507) all_12_1_7 = 0
% 66.56/28.99 | (546) ~ (all_12_2_8 = 0) | all_12_0_6 = 0
% 66.56/28.99 |
% 66.56/28.99 +-Applying beta-rule and splitting (115), into two cases.
% 66.56/28.99 |-Branch one:
% 66.56/28.99 | (547) ~ (all_14_1_10 = 0)
% 66.56/28.99 |
% 66.56/28.99 | Equations (503) can reduce 547 to:
% 66.56/28.99 | (159) $false
% 66.56/28.99 |
% 66.56/28.99 |-The branch is then unsatisfiable
% 66.56/28.99 |-Branch two:
% 66.56/28.99 | (503) all_14_1_10 = 0
% 66.56/28.99 | (550) ~ (all_14_2_11 = 0) | all_14_0_9 = all_0_5_5
% 66.56/28.99 |
% 66.56/28.99 +-Applying beta-rule and splitting (537), into two cases.
% 66.56/28.99 |-Branch one:
% 66.56/28.99 | (551) ~ (all_22_2_29 = 0)
% 66.56/28.99 |
% 66.56/28.99 | Equations (510) can reduce 551 to:
% 66.56/28.99 | (159) $false
% 66.56/28.99 |
% 66.56/28.99 |-The branch is then unsatisfiable
% 66.56/28.99 |-Branch two:
% 66.56/28.99 | (510) all_22_2_29 = 0
% 66.56/28.99 | (554) all_22_0_27 = 0
% 66.56/28.99 |
% 66.56/28.99 | Combining equations (554,219) yields a new equation:
% 66.56/28.99 | (555) all_36_1_51 = 0
% 66.56/28.99 |
% 66.56/28.99 | From (554) and (126) follows:
% 66.56/28.99 | (556) aNaturalNumber0(all_0_3_3) = 0
% 66.56/29.00 |
% 66.56/29.00 +-Applying beta-rule and splitting (123), into two cases.
% 66.56/29.00 |-Branch one:
% 66.56/29.00 | (557) all_20_0_21 = all_0_3_3 & all_20_1_22 = 0 & sdtasdt0(xp, all_20_2_23) = all_0_3_3 & aNaturalNumber0(all_20_2_23) = 0
% 66.56/29.00 |
% 66.56/29.00 | Applying alpha-rule on (557) yields:
% 66.56/29.00 | (558) all_20_0_21 = all_0_3_3
% 66.56/29.00 | (559) all_20_1_22 = 0
% 66.56/29.00 | (560) sdtasdt0(xp, all_20_2_23) = all_0_3_3
% 66.56/29.00 | (561) aNaturalNumber0(all_20_2_23) = 0
% 66.56/29.00 |
% 66.56/29.00 +-Applying beta-rule and splitting (550), into two cases.
% 66.56/29.00 |-Branch one:
% 66.56/29.00 | (562) ~ (all_14_2_11 = 0)
% 66.56/29.00 |
% 66.56/29.00 | Equations (451) can reduce 562 to:
% 66.56/29.00 | (159) $false
% 66.56/29.00 |
% 66.56/29.00 |-The branch is then unsatisfiable
% 66.56/29.00 |-Branch two:
% 66.56/29.00 | (451) all_14_2_11 = 0
% 66.56/29.00 | (565) all_14_0_9 = all_0_5_5
% 66.56/29.00 |
% 66.56/29.00 | From (565) and (112) follows:
% 66.56/29.00 | (566) sdtpldt0(xm, xn) = all_0_5_5
% 66.56/29.00 |
% 66.56/29.00 +-Applying beta-rule and splitting (546), into two cases.
% 66.56/29.00 |-Branch one:
% 66.56/29.00 | (567) ~ (all_12_2_8 = 0)
% 66.56/29.00 |
% 66.56/29.00 | Equations (508) can reduce 567 to:
% 66.56/29.00 | (159) $false
% 66.56/29.00 |
% 66.56/29.00 |-The branch is then unsatisfiable
% 66.56/29.00 |-Branch two:
% 66.56/29.00 | (508) all_12_2_8 = 0
% 66.56/29.00 | (570) all_12_0_6 = 0
% 66.56/29.00 |
% 66.56/29.00 | Combining equations (570,495) yields a new equation:
% 66.56/29.00 | (571) all_16_2_14 = 0
% 66.56/29.00 |
% 66.56/29.00 | Combining equations (570,252) yields a new equation:
% 66.56/29.00 | (572) all_26_2_37 = 0
% 66.56/29.00 |
% 66.56/29.00 | From (570) and (107) follows:
% 66.56/29.00 | (573) aNaturalNumber0(all_0_5_5) = 0
% 66.56/29.00 |
% 66.56/29.00 +-Applying beta-rule and splitting (141), into two cases.
% 66.56/29.00 |-Branch one:
% 66.56/29.00 | (574) ~ (all_26_1_36 = 0)
% 66.56/29.00 |
% 66.56/29.00 | Equations (303) can reduce 574 to:
% 66.56/29.00 | (159) $false
% 66.56/29.00 |
% 66.56/29.00 |-The branch is then unsatisfiable
% 66.56/29.00 |-Branch two:
% 66.56/29.00 | (303) all_26_1_36 = 0
% 66.56/29.00 | (577) ~ (all_26_2_37 = 0) | all_26_0_35 = 0
% 66.56/29.00 |
% 66.56/29.00 +-Applying beta-rule and splitting (131), into two cases.
% 66.56/29.00 |-Branch one:
% 66.56/29.00 | (578) ~ (all_24_2_32 = 0)
% 66.56/29.00 |
% 66.56/29.00 | Equations (493) can reduce 578 to:
% 66.56/29.00 | (159) $false
% 66.56/29.00 |
% 66.56/29.00 |-The branch is then unsatisfiable
% 66.56/29.00 |-Branch two:
% 66.56/29.00 | (493) all_24_2_32 = 0
% 66.56/29.00 | (581) ~ (all_24_3_33 = 0) | ~ (all_24_4_34 = 0) | all_24_0_30 = all_0_4_4
% 66.56/29.00 |
% 66.56/29.00 +-Applying beta-rule and splitting (581), into two cases.
% 66.56/29.00 |-Branch one:
% 66.56/29.00 | (582) ~ (all_24_3_33 = 0)
% 66.56/29.00 |
% 66.56/29.00 | Equations (483) can reduce 582 to:
% 66.56/29.00 | (159) $false
% 66.56/29.00 |
% 66.56/29.00 |-The branch is then unsatisfiable
% 66.56/29.00 |-Branch two:
% 66.56/29.00 | (483) all_24_3_33 = 0
% 66.56/29.00 | (585) ~ (all_24_4_34 = 0) | all_24_0_30 = all_0_4_4
% 66.56/29.00 |
% 66.56/29.00 +-Applying beta-rule and splitting (585), into two cases.
% 66.56/29.00 |-Branch one:
% 66.56/29.00 | (586) ~ (all_24_4_34 = 0)
% 66.56/29.00 |
% 66.56/29.00 | Equations (511) can reduce 586 to:
% 66.56/29.00 | (159) $false
% 66.56/29.00 |
% 66.56/29.00 |-The branch is then unsatisfiable
% 66.56/29.00 |-Branch two:
% 66.56/29.00 | (511) all_24_4_34 = 0
% 66.56/29.00 | (589) all_24_0_30 = all_0_4_4
% 66.56/29.00 |
% 66.56/29.00 | From (589) and (133) follows:
% 66.56/29.00 | (590) sdtpldt0(xn, all_24_1_31) = all_0_4_4
% 66.56/29.00 |
% 66.56/29.00 +-Applying beta-rule and splitting (577), into two cases.
% 66.56/29.00 |-Branch one:
% 66.56/29.00 | (591) ~ (all_26_2_37 = 0)
% 66.56/29.00 |
% 66.56/29.00 | Equations (572) can reduce 591 to:
% 66.56/29.00 | (159) $false
% 66.56/29.00 |
% 66.56/29.00 |-The branch is then unsatisfiable
% 66.56/29.00 |-Branch two:
% 66.56/29.00 | (572) all_26_2_37 = 0
% 66.56/29.00 | (594) all_26_0_35 = 0
% 66.56/29.00 |
% 66.56/29.00 | From (594) and (138) follows:
% 66.56/29.00 | (595) aNaturalNumber0(all_0_4_4) = 0
% 66.56/29.00 |
% 66.56/29.00 +-Applying beta-rule and splitting (146), into two cases.
% 66.56/29.00 |-Branch one:
% 66.56/29.00 | (596) ~ (all_28_1_39 = 0)
% 66.56/29.00 |
% 66.56/29.00 | Equations (515) can reduce 596 to:
% 66.56/29.00 | (159) $false
% 66.56/29.00 |
% 66.56/29.00 |-The branch is then unsatisfiable
% 66.56/29.00 |-Branch two:
% 66.56/29.00 | (515) all_28_1_39 = 0
% 66.56/29.00 | (599) ~ (all_28_2_40 = 0) | all_28_0_38 = all_0_3_3
% 66.56/29.00 |
% 66.56/29.00 +-Applying beta-rule and splitting (120), into two cases.
% 66.56/29.00 |-Branch one:
% 66.56/29.00 | (600) ~ (all_16_1_13 = 0)
% 66.56/29.00 |
% 66.56/29.00 | Equations (497) can reduce 600 to:
% 66.56/29.00 | (159) $false
% 66.56/29.00 |
% 66.56/29.00 |-The branch is then unsatisfiable
% 66.56/29.00 |-Branch two:
% 66.56/29.00 | (497) all_16_1_13 = 0
% 66.56/29.00 | (603) ~ (all_16_2_14 = 0) | all_16_0_12 = all_0_4_4
% 66.56/29.00 |
% 66.56/29.00 +-Applying beta-rule and splitting (599), into two cases.
% 66.56/29.00 |-Branch one:
% 66.56/29.00 | (604) ~ (all_28_2_40 = 0)
% 66.56/29.00 |
% 66.56/29.00 | Equations (514) can reduce 604 to:
% 66.56/29.00 | (159) $false
% 66.56/29.00 |
% 66.56/29.00 |-The branch is then unsatisfiable
% 66.56/29.00 |-Branch two:
% 66.56/29.00 | (514) all_28_2_40 = 0
% 66.56/29.00 | (607) all_28_0_38 = all_0_3_3
% 66.56/29.00 |
% 66.56/29.00 | From (607) and (143) follows:
% 66.56/29.00 | (608) sdtasdt0(xm, xn) = all_0_3_3
% 66.56/29.00 |
% 66.56/29.00 +-Applying beta-rule and splitting (603), into two cases.
% 66.56/29.00 |-Branch one:
% 66.56/29.00 | (609) ~ (all_16_2_14 = 0)
% 66.56/29.00 |
% 66.56/29.00 | Equations (571) can reduce 609 to:
% 66.56/29.00 | (159) $false
% 66.56/29.00 |
% 66.56/29.00 |-The branch is then unsatisfiable
% 66.56/29.00 |-Branch two:
% 66.56/29.00 | (571) all_16_2_14 = 0
% 66.56/29.00 | (612) all_16_0_12 = all_0_4_4
% 66.56/29.00 |
% 66.56/29.00 | From (612) and (117) follows:
% 66.56/29.00 | (613) sdtpldt0(xp, all_0_5_5) = all_0_4_4
% 66.56/29.00 |
% 66.56/29.00 +-Applying beta-rule and splitting (206), into two cases.
% 66.56/29.00 |-Branch one:
% 66.56/29.00 | (614) ~ (sdtpldt0(all_0_5_5, xp) = all_30_3_44)
% 66.56/29.00 |
% 66.56/29.00 | Using (520) and (614) yields:
% 66.56/29.00 | (615) $false
% 66.56/29.00 |
% 66.56/29.00 |-The branch is then unsatisfiable
% 66.56/29.00 |-Branch two:
% 66.56/29.00 | (520) sdtpldt0(all_0_5_5, xp) = all_30_3_44
% 66.56/29.00 | (617) all_30_3_44 = all_0_4_4
% 66.56/29.00 |
% 66.56/29.00 | From (617) and (520) follows:
% 66.56/29.00 | (58) sdtpldt0(all_0_5_5, xp) = all_0_4_4
% 66.56/29.00 |
% 66.56/29.00 | Instantiating formula (29) with all_58_0_58, xp and discharging atoms isPrime0(xp) = 0, doDivides0(all_58_0_58, xp) = 0, yields:
% 66.56/29.00 | (619) all_58_0_58 = xp | all_58_0_58 = sz10 | ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_58_0_58) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0))
% 66.56/29.00 |
% 66.56/29.00 | Instantiating formula (81) with xp, all_58_0_58 and discharging atoms doDivides0(all_58_0_58, xp) = 0, yields:
% 66.56/29.00 | (620) xp = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_58_0_58, xp) = v2 & aNaturalNumber0(all_58_0_58) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.56/29.00 |
% 66.56/29.00 | Instantiating formula (76) with xp, all_58_0_58 and discharging atoms doDivides0(all_58_0_58, xp) = 0, yields:
% 66.56/29.00 | (621) ? [v0] : ? [v1] : ? [v2] : ((v2 = xp & v1 = 0 & sdtasdt0(all_58_0_58, v0) = xp & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_58_0_58) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 66.77/29.00 |
% 66.77/29.00 | Instantiating formula (29) with all_53_0_57, xr and discharging atoms isPrime0(xr) = 0, doDivides0(all_53_0_57, xr) = 0, yields:
% 66.77/29.00 | (622) all_53_0_57 = xr | all_53_0_57 = sz10 | ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_53_0_57) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xr) = v0))
% 66.77/29.00 |
% 66.77/29.00 | Instantiating formula (81) with xr, all_53_0_57 and discharging atoms doDivides0(all_53_0_57, xr) = 0, yields:
% 66.77/29.00 | (623) xr = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_53_0_57, xr) = v2 & aNaturalNumber0(all_53_0_57) = v0 & aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.77/29.00 |
% 66.77/29.00 | Instantiating formula (66) with all_30_0_41, xm, all_0_3_3, xp and discharging atoms doDivides0(xp, all_0_3_3) = 0, doDivides0(xp, xm) = all_30_0_41, yields:
% 66.77/29.00 | (624) all_30_0_41 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_3_3, xm) = v3 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 66.77/29.00 |
% 66.77/29.00 | Instantiating formula (81) with xm, xp yields:
% 66.77/29.00 | (625) xm = sz00 | ~ (doDivides0(xp, xm) = 0) | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, xm) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.77/29.00 |
% 66.77/29.00 | Instantiating formula (66) with all_30_1_42, xn, all_0_3_3, xp and discharging atoms doDivides0(xp, all_0_3_3) = 0, doDivides0(xp, xn) = all_30_1_42, yields:
% 66.77/29.00 | (626) all_30_1_42 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_3_3, xn) = v3 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 66.77/29.00 |
% 66.77/29.00 | Instantiating formula (81) with xn, xp yields:
% 66.77/29.00 | (627) xn = sz00 | ~ (doDivides0(xp, xn) = 0) | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, xn) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.77/29.00 |
% 66.77/29.00 | Instantiating formula (9) with all_0_3_3, xk, all_0_3_3, xp and discharging atoms sdtsldt0(all_0_3_3, xp) = xk, yields:
% 66.77/29.00 | (628) xp = sz00 | ~ (sdtasdt0(xp, xk) = all_0_3_3) | ? [v0] : ? [v1] : ? [v2] : ((v0 = 0 & aNaturalNumber0(xk) = 0) | (doDivides0(xp, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 66.77/29.00 |
% 66.77/29.00 | Instantiating formula (34) with all_20_2_23, xk, all_0_3_3, xp and discharging atoms sdtsldt0(all_0_3_3, xp) = xk, sdtasdt0(xp, all_20_2_23) = all_0_3_3, yields:
% 66.77/29.00 | (629) all_20_2_23 = xk | xp = sz00 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_20_2_23) = v0) | (doDivides0(xp, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 66.77/29.00 |
% 66.77/29.00 | Instantiating formula (7) with all_0_3_3, xp, all_20_2_23, xp and discharging atoms doDivides0(xp, all_0_3_3) = 0, sdtasdt0(xp, all_20_2_23) = all_0_3_3, yields:
% 66.77/29.00 | (630) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, all_20_2_23) = v8 & doDivides0(xp, xp) = v7 & iLess0(v5, all_0_4_4) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xp, all_20_2_23) = v4 & aNaturalNumber0(all_20_2_23) = v1 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 66.77/29.00 |
% 66.77/29.00 | Instantiating formula (50) with all_20_2_23, xp yields:
% 66.77/29.00 | (631) all_20_2_23 = sz00 | xp = sz00 | ~ (sdtasdt0(xp, all_20_2_23) = sz00) | ? [v0] : ? [v1] : (aNaturalNumber0(all_20_2_23) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (27) with all_0_3_3, all_20_2_23, xp and discharging atoms sdtasdt0(xp, all_20_2_23) = all_0_3_3, yields:
% 66.77/29.01 | (632) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_20_2_23, xp) = v2 & aNaturalNumber0(all_20_2_23) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_3_3))
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (7) with all_0_3_3, xp, xn, xm and discharging atoms doDivides0(xp, all_0_3_3) = 0, sdtasdt0(xm, xn) = all_0_3_3, yields:
% 66.77/29.01 | (633) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, xm) = v7 & doDivides0(xp, xn) = v8 & iLess0(v5, all_0_4_4) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xm, xn) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (19) with all_0_3_3, xn yields:
% 66.77/29.01 | (634) ~ (sdtasdt0(sz00, xn) = all_0_3_3) | ? [v0] : ? [v1] : (sdtasdt0(xn, sz00) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v0 = 0) | (v1 = sz00 & all_0_3_3 = sz00)))
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (40) with xp, all_19_2_20, xm, all_58_0_58 and discharging atoms doDivides0(all_58_0_58, xp) = 0, sdtpldt0(xm, all_19_2_20) = xp, yields:
% 66.77/29.01 | (635) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(all_58_0_58, all_19_2_20) = v4 & doDivides0(all_58_0_58, xm) = v3 & aNaturalNumber0(all_58_0_58) = v0 & aNaturalNumber0(all_19_2_20) = v2 & aNaturalNumber0(xm) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (49) with all_0_4_4, xp, all_0_5_5, all_19_2_20, xm and discharging atoms sdtpldt0(xp, all_0_5_5) = all_0_4_4, sdtpldt0(xm, all_19_2_20) = xp, yields:
% 66.77/29.01 | (636) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_19_2_20, all_0_5_5) = v3 & sdtpldt0(xm, v3) = v4 & aNaturalNumber0(all_19_2_20) = v1 & aNaturalNumber0(all_0_5_5) = v2 & aNaturalNumber0(xm) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_4_4))
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (78) with xp, all_19_2_20, xm and discharging atoms sdtpldt0(xm, all_19_2_20) = xp, yields:
% 66.77/29.01 | (637) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_19_2_20, xm) = v2 & aNaturalNumber0(all_19_2_20) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xp))
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (78) with all_24_1_31, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_24_1_31, yields:
% 66.77/29.01 | (638) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, xm) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_24_1_31))
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (43) with all_24_1_31, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_24_1_31, yields:
% 66.77/29.01 | (639) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_24_1_31) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (49) with all_0_4_4, all_0_5_5, xp, xn, xm and discharging atoms sdtpldt0(all_0_5_5, xp) = all_0_4_4, sdtpldt0(xm, xn) = all_0_5_5, yields:
% 66.77/29.01 | (640) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xm, v3) = v4 & sdtpldt0(xn, xp) = v3 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_4_4))
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (24) with all_0_5_5, all_24_1_31, xn, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_24_1_31, sdtpldt0(xm, xn) = all_0_5_5, yields:
% 66.77/29.01 | (641) xp = xn | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xp, xm) = v3 & sdtpldt0(xn, xm) = v4 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v4 = v3) & ~ (all_24_1_31 = all_0_5_5))))
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (24) with all_24_1_31, all_0_5_5, xp, xn, xm and discharging atoms sdtpldt0(xm, xp) = all_24_1_31, sdtpldt0(xm, xn) = all_0_5_5, yields:
% 66.77/29.01 | (642) xp = xn | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xp, xm) = v4 & sdtpldt0(xn, xm) = v3 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v4 = v3) & ~ (all_24_1_31 = all_0_5_5))))
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (78) with all_0_4_4, all_24_1_31, xn and discharging atoms sdtpldt0(xn, all_24_1_31) = all_0_4_4, yields:
% 66.77/29.01 | (643) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_24_1_31, xn) = v2 & aNaturalNumber0(all_24_1_31) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_4_4))
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (43) with all_0_4_4, all_24_1_31, xn and discharging atoms sdtpldt0(xn, all_24_1_31) = all_0_4_4, yields:
% 66.77/29.01 | (644) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_24_1_31) = v1 & aNaturalNumber0(all_0_4_4) = v2 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (40) with xp, all_18_2_17, xn, all_58_0_58 and discharging atoms doDivides0(all_58_0_58, xp) = 0, sdtpldt0(xn, all_18_2_17) = xp, yields:
% 66.77/29.01 | (645) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(all_58_0_58, all_18_2_17) = v4 & doDivides0(all_58_0_58, xn) = v3 & aNaturalNumber0(all_58_0_58) = v0 & aNaturalNumber0(all_18_2_17) = v2 & aNaturalNumber0(xn) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (49) with all_0_4_4, xp, all_0_5_5, all_18_2_17, xn and discharging atoms sdtpldt0(xp, all_0_5_5) = all_0_4_4, sdtpldt0(xn, all_18_2_17) = xp, yields:
% 66.77/29.01 | (646) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_18_2_17, all_0_5_5) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(all_18_2_17) = v1 & aNaturalNumber0(all_0_5_5) = v2 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_4_4))
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (78) with xp, all_18_2_17, xn and discharging atoms sdtpldt0(xn, all_18_2_17) = xp, yields:
% 66.77/29.01 | (647) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_18_2_17, xn) = v2 & aNaturalNumber0(all_18_2_17) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xp))
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (8) with all_58_0_58 and discharging atoms aNaturalNumber0(all_58_0_58) = 0, yields:
% 66.77/29.01 | (648) all_58_0_58 = sz10 | all_58_0_58 = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_58_0_58) = 0 & aNaturalNumber0(v0) = 0)
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (8) with all_53_0_57 and discharging atoms aNaturalNumber0(all_53_0_57) = 0, yields:
% 66.77/29.01 | (649) all_53_0_57 = sz10 | all_53_0_57 = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_53_0_57) = 0 & aNaturalNumber0(v0) = 0)
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (8) with all_20_2_23 and discharging atoms aNaturalNumber0(all_20_2_23) = 0, yields:
% 66.77/29.01 | (650) all_20_2_23 = sz10 | all_20_2_23 = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_20_2_23) = 0 & aNaturalNumber0(v0) = 0)
% 66.77/29.01 |
% 66.77/29.01 | Instantiating formula (8) with xk yields:
% 66.77/29.01 | (651) xk = sz10 | xk = sz00 | ~ (aNaturalNumber0(xk) = 0) | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xk) = 0 & aNaturalNumber0(v0) = 0)
% 66.77/29.01 |
% 66.77/29.01 | Instantiating (647) with all_157_0_59, all_157_1_60, all_157_2_61 yields:
% 66.77/29.01 | (652) sdtpldt0(all_18_2_17, xn) = all_157_0_59 & aNaturalNumber0(all_18_2_17) = all_157_1_60 & aNaturalNumber0(xn) = all_157_2_61 & ( ~ (all_157_1_60 = 0) | ~ (all_157_2_61 = 0) | all_157_0_59 = xp)
% 66.77/29.01 |
% 66.77/29.01 | Applying alpha-rule on (652) yields:
% 66.77/29.01 | (653) sdtpldt0(all_18_2_17, xn) = all_157_0_59
% 66.77/29.01 | (654) aNaturalNumber0(all_18_2_17) = all_157_1_60
% 66.77/29.01 | (655) aNaturalNumber0(xn) = all_157_2_61
% 66.77/29.01 | (656) ~ (all_157_1_60 = 0) | ~ (all_157_2_61 = 0) | all_157_0_59 = xp
% 66.77/29.01 |
% 66.77/29.01 | Instantiating (645) with all_159_0_62, all_159_1_63, all_159_2_64, all_159_3_65, all_159_4_66 yields:
% 66.77/29.01 | (657) doDivides0(all_58_0_58, all_18_2_17) = all_159_0_62 & doDivides0(all_58_0_58, xn) = all_159_1_63 & aNaturalNumber0(all_58_0_58) = all_159_4_66 & aNaturalNumber0(all_18_2_17) = all_159_2_64 & aNaturalNumber0(xn) = all_159_3_65 & ( ~ (all_159_1_63 = 0) | ~ (all_159_2_64 = 0) | ~ (all_159_3_65 = 0) | ~ (all_159_4_66 = 0) | all_159_0_62 = 0)
% 66.77/29.01 |
% 66.77/29.01 | Applying alpha-rule on (657) yields:
% 66.77/29.01 | (658) aNaturalNumber0(xn) = all_159_3_65
% 66.77/29.01 | (659) doDivides0(all_58_0_58, all_18_2_17) = all_159_0_62
% 66.77/29.01 | (660) ~ (all_159_1_63 = 0) | ~ (all_159_2_64 = 0) | ~ (all_159_3_65 = 0) | ~ (all_159_4_66 = 0) | all_159_0_62 = 0
% 66.77/29.01 | (661) aNaturalNumber0(all_18_2_17) = all_159_2_64
% 66.77/29.01 | (662) doDivides0(all_58_0_58, xn) = all_159_1_63
% 66.77/29.01 | (663) aNaturalNumber0(all_58_0_58) = all_159_4_66
% 66.77/29.01 |
% 66.77/29.01 | Instantiating (640) with all_161_0_67, all_161_1_68, all_161_2_69, all_161_3_70, all_161_4_71 yields:
% 66.77/29.01 | (664) sdtpldt0(xm, all_161_1_68) = all_161_0_67 & sdtpldt0(xn, xp) = all_161_1_68 & aNaturalNumber0(xp) = all_161_2_69 & aNaturalNumber0(xm) = all_161_4_71 & aNaturalNumber0(xn) = all_161_3_70 & ( ~ (all_161_2_69 = 0) | ~ (all_161_3_70 = 0) | ~ (all_161_4_71 = 0) | all_161_0_67 = all_0_4_4)
% 66.77/29.01 |
% 66.77/29.01 | Applying alpha-rule on (664) yields:
% 66.77/29.01 | (665) sdtpldt0(xm, all_161_1_68) = all_161_0_67
% 66.77/29.01 | (666) aNaturalNumber0(xn) = all_161_3_70
% 66.77/29.01 | (667) aNaturalNumber0(xp) = all_161_2_69
% 66.77/29.01 | (668) aNaturalNumber0(xm) = all_161_4_71
% 66.77/29.01 | (669) sdtpldt0(xn, xp) = all_161_1_68
% 66.77/29.01 | (670) ~ (all_161_2_69 = 0) | ~ (all_161_3_70 = 0) | ~ (all_161_4_71 = 0) | all_161_0_67 = all_0_4_4
% 66.77/29.01 |
% 66.77/29.01 | Instantiating (639) with all_163_0_72, all_163_1_73, all_163_2_74 yields:
% 66.77/29.01 | (671) aNaturalNumber0(all_24_1_31) = all_163_0_72 & aNaturalNumber0(xp) = all_163_1_73 & aNaturalNumber0(xm) = all_163_2_74 & ( ~ (all_163_1_73 = 0) | ~ (all_163_2_74 = 0) | all_163_0_72 = 0)
% 66.77/29.01 |
% 66.77/29.01 | Applying alpha-rule on (671) yields:
% 66.77/29.01 | (672) aNaturalNumber0(all_24_1_31) = all_163_0_72
% 66.77/29.01 | (673) aNaturalNumber0(xp) = all_163_1_73
% 66.77/29.01 | (674) aNaturalNumber0(xm) = all_163_2_74
% 66.77/29.02 | (675) ~ (all_163_1_73 = 0) | ~ (all_163_2_74 = 0) | all_163_0_72 = 0
% 66.77/29.02 |
% 66.77/29.02 | Instantiating (644) with all_165_0_75, all_165_1_76, all_165_2_77 yields:
% 66.77/29.02 | (676) aNaturalNumber0(all_24_1_31) = all_165_1_76 & aNaturalNumber0(all_0_4_4) = all_165_0_75 & aNaturalNumber0(xn) = all_165_2_77 & ( ~ (all_165_1_76 = 0) | ~ (all_165_2_77 = 0) | all_165_0_75 = 0)
% 66.77/29.02 |
% 66.77/29.02 | Applying alpha-rule on (676) yields:
% 66.77/29.02 | (677) aNaturalNumber0(all_24_1_31) = all_165_1_76
% 66.77/29.02 | (678) aNaturalNumber0(all_0_4_4) = all_165_0_75
% 66.77/29.02 | (679) aNaturalNumber0(xn) = all_165_2_77
% 66.77/29.02 | (680) ~ (all_165_1_76 = 0) | ~ (all_165_2_77 = 0) | all_165_0_75 = 0
% 66.77/29.02 |
% 66.77/29.02 | Instantiating (643) with all_167_0_78, all_167_1_79, all_167_2_80 yields:
% 66.77/29.02 | (681) sdtpldt0(all_24_1_31, xn) = all_167_0_78 & aNaturalNumber0(all_24_1_31) = all_167_1_79 & aNaturalNumber0(xn) = all_167_2_80 & ( ~ (all_167_1_79 = 0) | ~ (all_167_2_80 = 0) | all_167_0_78 = all_0_4_4)
% 66.77/29.02 |
% 66.77/29.02 | Applying alpha-rule on (681) yields:
% 66.77/29.02 | (682) sdtpldt0(all_24_1_31, xn) = all_167_0_78
% 66.77/29.02 | (683) aNaturalNumber0(all_24_1_31) = all_167_1_79
% 66.77/29.02 | (684) aNaturalNumber0(xn) = all_167_2_80
% 66.77/29.02 | (685) ~ (all_167_1_79 = 0) | ~ (all_167_2_80 = 0) | all_167_0_78 = all_0_4_4
% 66.77/29.02 |
% 66.77/29.02 | Instantiating (646) with all_169_0_81, all_169_1_82, all_169_2_83, all_169_3_84, all_169_4_85 yields:
% 66.77/29.02 | (686) sdtpldt0(all_18_2_17, all_0_5_5) = all_169_1_82 & sdtpldt0(xn, all_169_1_82) = all_169_0_81 & aNaturalNumber0(all_18_2_17) = all_169_3_84 & aNaturalNumber0(all_0_5_5) = all_169_2_83 & aNaturalNumber0(xn) = all_169_4_85 & ( ~ (all_169_2_83 = 0) | ~ (all_169_3_84 = 0) | ~ (all_169_4_85 = 0) | all_169_0_81 = all_0_4_4)
% 66.77/29.02 |
% 66.77/29.02 | Applying alpha-rule on (686) yields:
% 66.77/29.02 | (687) sdtpldt0(all_18_2_17, all_0_5_5) = all_169_1_82
% 66.77/29.02 | (688) aNaturalNumber0(xn) = all_169_4_85
% 66.77/29.02 | (689) aNaturalNumber0(all_18_2_17) = all_169_3_84
% 66.77/29.02 | (690) sdtpldt0(xn, all_169_1_82) = all_169_0_81
% 66.77/29.02 | (691) aNaturalNumber0(all_0_5_5) = all_169_2_83
% 66.77/29.02 | (692) ~ (all_169_2_83 = 0) | ~ (all_169_3_84 = 0) | ~ (all_169_4_85 = 0) | all_169_0_81 = all_0_4_4
% 66.77/29.02 |
% 66.77/29.02 | Instantiating (638) with all_171_0_86, all_171_1_87, all_171_2_88 yields:
% 66.77/29.02 | (693) sdtpldt0(xp, xm) = all_171_0_86 & aNaturalNumber0(xp) = all_171_1_87 & aNaturalNumber0(xm) = all_171_2_88 & ( ~ (all_171_1_87 = 0) | ~ (all_171_2_88 = 0) | all_171_0_86 = all_24_1_31)
% 66.77/29.02 |
% 66.77/29.02 | Applying alpha-rule on (693) yields:
% 66.77/29.02 | (694) sdtpldt0(xp, xm) = all_171_0_86
% 66.77/29.02 | (695) aNaturalNumber0(xp) = all_171_1_87
% 66.77/29.02 | (696) aNaturalNumber0(xm) = all_171_2_88
% 66.77/29.02 | (697) ~ (all_171_1_87 = 0) | ~ (all_171_2_88 = 0) | all_171_0_86 = all_24_1_31
% 66.77/29.02 |
% 66.77/29.02 | Instantiating (637) with all_173_0_89, all_173_1_90, all_173_2_91 yields:
% 66.77/29.02 | (698) sdtpldt0(all_19_2_20, xm) = all_173_0_89 & aNaturalNumber0(all_19_2_20) = all_173_1_90 & aNaturalNumber0(xm) = all_173_2_91 & ( ~ (all_173_1_90 = 0) | ~ (all_173_2_91 = 0) | all_173_0_89 = xp)
% 66.77/29.02 |
% 66.77/29.02 | Applying alpha-rule on (698) yields:
% 66.77/29.02 | (699) sdtpldt0(all_19_2_20, xm) = all_173_0_89
% 66.77/29.02 | (700) aNaturalNumber0(all_19_2_20) = all_173_1_90
% 66.77/29.02 | (701) aNaturalNumber0(xm) = all_173_2_91
% 66.77/29.02 | (702) ~ (all_173_1_90 = 0) | ~ (all_173_2_91 = 0) | all_173_0_89 = xp
% 66.77/29.02 |
% 66.77/29.02 | Instantiating (636) with all_175_0_92, all_175_1_93, all_175_2_94, all_175_3_95, all_175_4_96 yields:
% 66.77/29.02 | (703) sdtpldt0(all_19_2_20, all_0_5_5) = all_175_1_93 & sdtpldt0(xm, all_175_1_93) = all_175_0_92 & aNaturalNumber0(all_19_2_20) = all_175_3_95 & aNaturalNumber0(all_0_5_5) = all_175_2_94 & aNaturalNumber0(xm) = all_175_4_96 & ( ~ (all_175_2_94 = 0) | ~ (all_175_3_95 = 0) | ~ (all_175_4_96 = 0) | all_175_0_92 = all_0_4_4)
% 66.77/29.02 |
% 66.77/29.02 | Applying alpha-rule on (703) yields:
% 66.77/29.02 | (704) aNaturalNumber0(all_19_2_20) = all_175_3_95
% 66.77/29.02 | (705) aNaturalNumber0(all_0_5_5) = all_175_2_94
% 66.77/29.02 | (706) aNaturalNumber0(xm) = all_175_4_96
% 66.77/29.02 | (707) sdtpldt0(all_19_2_20, all_0_5_5) = all_175_1_93
% 66.77/29.02 | (708) sdtpldt0(xm, all_175_1_93) = all_175_0_92
% 66.77/29.02 | (709) ~ (all_175_2_94 = 0) | ~ (all_175_3_95 = 0) | ~ (all_175_4_96 = 0) | all_175_0_92 = all_0_4_4
% 66.77/29.02 |
% 66.77/29.02 | Instantiating (632) with all_177_0_97, all_177_1_98, all_177_2_99 yields:
% 66.77/29.02 | (710) sdtasdt0(all_20_2_23, xp) = all_177_0_97 & aNaturalNumber0(all_20_2_23) = all_177_1_98 & aNaturalNumber0(xp) = all_177_2_99 & ( ~ (all_177_1_98 = 0) | ~ (all_177_2_99 = 0) | all_177_0_97 = all_0_3_3)
% 66.77/29.02 |
% 66.77/29.02 | Applying alpha-rule on (710) yields:
% 66.77/29.02 | (711) sdtasdt0(all_20_2_23, xp) = all_177_0_97
% 66.77/29.02 | (712) aNaturalNumber0(all_20_2_23) = all_177_1_98
% 66.77/29.02 | (713) aNaturalNumber0(xp) = all_177_2_99
% 66.77/29.02 | (714) ~ (all_177_1_98 = 0) | ~ (all_177_2_99 = 0) | all_177_0_97 = all_0_3_3
% 66.77/29.02 |
% 66.77/29.02 | Instantiating (630) with all_179_0_100, all_179_1_101, all_179_2_102, all_179_3_103, all_179_4_104, all_179_5_105, all_179_6_106, all_179_7_107, all_179_8_108 yields:
% 66.77/29.02 | (715) isPrime0(xp) = all_179_5_105 & doDivides0(xp, all_20_2_23) = all_179_0_100 & doDivides0(xp, xp) = all_179_1_101 & iLess0(all_179_3_103, all_0_4_4) = all_179_2_102 & sdtpldt0(all_179_4_104, xp) = all_179_3_103 & sdtpldt0(xp, all_20_2_23) = all_179_4_104 & aNaturalNumber0(all_20_2_23) = all_179_7_107 & aNaturalNumber0(xp) = all_179_6_106 & aNaturalNumber0(xp) = all_179_8_108 & ( ~ (all_179_2_102 = 0) | ~ (all_179_5_105 = 0) | ~ (all_179_6_106 = 0) | ~ (all_179_7_107 = 0) | ~ (all_179_8_108 = 0) | all_179_0_100 = 0 | all_179_1_101 = 0)
% 66.77/29.02 |
% 66.77/29.02 | Applying alpha-rule on (715) yields:
% 66.77/29.02 | (716) ~ (all_179_2_102 = 0) | ~ (all_179_5_105 = 0) | ~ (all_179_6_106 = 0) | ~ (all_179_7_107 = 0) | ~ (all_179_8_108 = 0) | all_179_0_100 = 0 | all_179_1_101 = 0
% 66.77/29.02 | (717) doDivides0(xp, all_20_2_23) = all_179_0_100
% 66.77/29.02 | (718) iLess0(all_179_3_103, all_0_4_4) = all_179_2_102
% 66.77/29.02 | (719) aNaturalNumber0(xp) = all_179_8_108
% 66.77/29.02 | (720) aNaturalNumber0(xp) = all_179_6_106
% 66.77/29.02 | (721) isPrime0(xp) = all_179_5_105
% 66.77/29.02 | (722) doDivides0(xp, xp) = all_179_1_101
% 66.77/29.02 | (723) aNaturalNumber0(all_20_2_23) = all_179_7_107
% 66.77/29.02 | (724) sdtpldt0(xp, all_20_2_23) = all_179_4_104
% 66.77/29.02 | (725) sdtpldt0(all_179_4_104, xp) = all_179_3_103
% 66.77/29.02 |
% 66.77/29.02 | Instantiating (635) with all_182_0_112, all_182_1_113, all_182_2_114, all_182_3_115, all_182_4_116 yields:
% 66.77/29.02 | (726) doDivides0(all_58_0_58, all_19_2_20) = all_182_0_112 & doDivides0(all_58_0_58, xm) = all_182_1_113 & aNaturalNumber0(all_58_0_58) = all_182_4_116 & aNaturalNumber0(all_19_2_20) = all_182_2_114 & aNaturalNumber0(xm) = all_182_3_115 & ( ~ (all_182_1_113 = 0) | ~ (all_182_2_114 = 0) | ~ (all_182_3_115 = 0) | ~ (all_182_4_116 = 0) | all_182_0_112 = 0)
% 66.77/29.02 |
% 66.77/29.02 | Applying alpha-rule on (726) yields:
% 66.77/29.02 | (727) aNaturalNumber0(all_19_2_20) = all_182_2_114
% 66.77/29.02 | (728) aNaturalNumber0(all_58_0_58) = all_182_4_116
% 66.77/29.02 | (729) aNaturalNumber0(xm) = all_182_3_115
% 66.77/29.02 | (730) doDivides0(all_58_0_58, xm) = all_182_1_113
% 66.77/29.02 | (731) ~ (all_182_1_113 = 0) | ~ (all_182_2_114 = 0) | ~ (all_182_3_115 = 0) | ~ (all_182_4_116 = 0) | all_182_0_112 = 0
% 66.77/29.02 | (732) doDivides0(all_58_0_58, all_19_2_20) = all_182_0_112
% 66.77/29.02 |
% 66.77/29.02 | Instantiating (633) with all_184_0_117, all_184_1_118, all_184_2_119, all_184_3_120, all_184_4_121, all_184_5_122, all_184_6_123, all_184_7_124, all_184_8_125 yields:
% 66.77/29.02 | (733) isPrime0(xp) = all_184_5_122 & doDivides0(xp, xm) = all_184_1_118 & doDivides0(xp, xn) = all_184_0_117 & iLess0(all_184_3_120, all_0_4_4) = all_184_2_119 & sdtpldt0(all_184_4_121, xp) = all_184_3_120 & sdtpldt0(xm, xn) = all_184_4_121 & aNaturalNumber0(xp) = all_184_6_123 & aNaturalNumber0(xm) = all_184_8_125 & aNaturalNumber0(xn) = all_184_7_124 & ( ~ (all_184_2_119 = 0) | ~ (all_184_5_122 = 0) | ~ (all_184_6_123 = 0) | ~ (all_184_7_124 = 0) | ~ (all_184_8_125 = 0) | all_184_0_117 = 0 | all_184_1_118 = 0)
% 66.77/29.02 |
% 66.77/29.02 | Applying alpha-rule on (733) yields:
% 66.77/29.02 | (734) doDivides0(xp, xn) = all_184_0_117
% 66.77/29.02 | (735) aNaturalNumber0(xm) = all_184_8_125
% 66.77/29.02 | (736) sdtpldt0(all_184_4_121, xp) = all_184_3_120
% 66.77/29.02 | (737) aNaturalNumber0(xp) = all_184_6_123
% 66.77/29.02 | (738) ~ (all_184_2_119 = 0) | ~ (all_184_5_122 = 0) | ~ (all_184_6_123 = 0) | ~ (all_184_7_124 = 0) | ~ (all_184_8_125 = 0) | all_184_0_117 = 0 | all_184_1_118 = 0
% 66.77/29.02 | (739) isPrime0(xp) = all_184_5_122
% 66.77/29.02 | (740) doDivides0(xp, xm) = all_184_1_118
% 66.77/29.02 | (741) aNaturalNumber0(xn) = all_184_7_124
% 66.77/29.02 | (742) iLess0(all_184_3_120, all_0_4_4) = all_184_2_119
% 66.77/29.02 | (743) sdtpldt0(xm, xn) = all_184_4_121
% 66.77/29.02 |
% 66.77/29.02 | Instantiating (621) with all_186_0_126, all_186_1_127, all_186_2_128 yields:
% 66.77/29.02 | (744) (all_186_0_126 = xp & all_186_1_127 = 0 & sdtasdt0(all_58_0_58, all_186_2_128) = xp & aNaturalNumber0(all_186_2_128) = 0) | (aNaturalNumber0(all_58_0_58) = all_186_2_128 & aNaturalNumber0(xp) = all_186_1_127 & ( ~ (all_186_1_127 = 0) | ~ (all_186_2_128 = 0)))
% 66.77/29.02 |
% 66.77/29.02 +-Applying beta-rule and splitting (623), into two cases.
% 66.77/29.02 |-Branch one:
% 66.77/29.02 | (177) xr = sz00
% 66.77/29.02 |
% 66.77/29.02 | Equations (177) can reduce 85 to:
% 66.77/29.02 | (159) $false
% 66.77/29.02 |
% 66.77/29.02 |-The branch is then unsatisfiable
% 66.77/29.02 |-Branch two:
% 66.77/29.02 | (85) ~ (xr = sz00)
% 66.77/29.02 | (748) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_53_0_57, xr) = v2 & aNaturalNumber0(all_53_0_57) = v0 & aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.77/29.02 |
% 66.77/29.02 | Instantiating (748) with all_191_0_129, all_191_1_130, all_191_2_131 yields:
% 66.77/29.02 | (749) sdtlseqdt0(all_53_0_57, xr) = all_191_0_129 & aNaturalNumber0(all_53_0_57) = all_191_2_131 & aNaturalNumber0(xr) = all_191_1_130 & ( ~ (all_191_1_130 = 0) | ~ (all_191_2_131 = 0) | all_191_0_129 = 0)
% 66.77/29.02 |
% 66.77/29.02 | Applying alpha-rule on (749) yields:
% 66.77/29.02 | (750) sdtlseqdt0(all_53_0_57, xr) = all_191_0_129
% 66.77/29.02 | (751) aNaturalNumber0(all_53_0_57) = all_191_2_131
% 66.77/29.02 | (752) aNaturalNumber0(xr) = all_191_1_130
% 66.77/29.02 | (753) ~ (all_191_1_130 = 0) | ~ (all_191_2_131 = 0) | all_191_0_129 = 0
% 66.77/29.02 |
% 66.77/29.02 +-Applying beta-rule and splitting (648), into two cases.
% 66.77/29.02 |-Branch one:
% 66.77/29.02 | (754) all_58_0_58 = sz00
% 66.77/29.03 |
% 66.77/29.03 | Equations (754) can reduce 202 to:
% 66.77/29.03 | (159) $false
% 66.77/29.03 |
% 66.77/29.03 |-The branch is then unsatisfiable
% 66.77/29.03 |-Branch two:
% 66.77/29.03 | (202) ~ (all_58_0_58 = sz00)
% 66.77/29.03 | (757) all_58_0_58 = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_58_0_58) = 0 & aNaturalNumber0(v0) = 0)
% 66.77/29.03 |
% 66.77/29.03 +-Applying beta-rule and splitting (649), into two cases.
% 66.77/29.03 |-Branch one:
% 66.77/29.03 | (758) all_53_0_57 = sz00
% 66.77/29.03 |
% 66.77/29.03 | Equations (758) can reduce 204 to:
% 66.77/29.03 | (159) $false
% 66.77/29.03 |
% 66.77/29.03 |-The branch is then unsatisfiable
% 66.77/29.03 |-Branch two:
% 66.77/29.03 | (204) ~ (all_53_0_57 = sz00)
% 66.77/29.03 | (761) all_53_0_57 = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_53_0_57) = 0 & aNaturalNumber0(v0) = 0)
% 66.77/29.03 |
% 66.77/29.03 +-Applying beta-rule and splitting (620), into two cases.
% 66.77/29.03 |-Branch one:
% 66.77/29.03 | (181) xp = sz00
% 66.77/29.03 |
% 66.77/29.03 | Equations (181) can reduce 86 to:
% 66.77/29.03 | (159) $false
% 66.77/29.03 |
% 66.77/29.03 |-The branch is then unsatisfiable
% 66.77/29.03 |-Branch two:
% 66.77/29.03 | (86) ~ (xp = sz00)
% 66.77/29.03 | (765) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_58_0_58, xp) = v2 & aNaturalNumber0(all_58_0_58) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.77/29.03 |
% 66.77/29.03 | Instantiating (765) with all_203_0_132, all_203_1_133, all_203_2_134 yields:
% 66.77/29.03 | (766) sdtlseqdt0(all_58_0_58, xp) = all_203_0_132 & aNaturalNumber0(all_58_0_58) = all_203_2_134 & aNaturalNumber0(xp) = all_203_1_133 & ( ~ (all_203_1_133 = 0) | ~ (all_203_2_134 = 0) | all_203_0_132 = 0)
% 66.77/29.03 |
% 66.77/29.03 | Applying alpha-rule on (766) yields:
% 66.77/29.03 | (767) sdtlseqdt0(all_58_0_58, xp) = all_203_0_132
% 66.77/29.03 | (768) aNaturalNumber0(all_58_0_58) = all_203_2_134
% 66.77/29.03 | (769) aNaturalNumber0(xp) = all_203_1_133
% 66.77/29.03 | (770) ~ (all_203_1_133 = 0) | ~ (all_203_2_134 = 0) | all_203_0_132 = 0
% 66.77/29.03 |
% 66.77/29.03 +-Applying beta-rule and splitting (757), into two cases.
% 66.77/29.03 |-Branch one:
% 66.77/29.03 | (771) all_58_0_58 = sz10
% 66.77/29.03 |
% 66.77/29.03 | Equations (771) can reduce 201 to:
% 66.77/29.03 | (159) $false
% 66.77/29.03 |
% 66.77/29.03 |-The branch is then unsatisfiable
% 66.77/29.03 |-Branch two:
% 66.77/29.03 | (201) ~ (all_58_0_58 = sz10)
% 66.77/29.03 | (774) ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_58_0_58) = 0 & aNaturalNumber0(v0) = 0)
% 66.77/29.03 |
% 66.77/29.03 | Instantiating (774) with all_208_0_135 yields:
% 66.77/29.03 | (775) isPrime0(all_208_0_135) = 0 & doDivides0(all_208_0_135, all_58_0_58) = 0 & aNaturalNumber0(all_208_0_135) = 0
% 66.77/29.03 |
% 66.77/29.03 | Applying alpha-rule on (775) yields:
% 66.77/29.03 | (776) isPrime0(all_208_0_135) = 0
% 66.77/29.03 | (777) doDivides0(all_208_0_135, all_58_0_58) = 0
% 66.77/29.03 | (778) aNaturalNumber0(all_208_0_135) = 0
% 66.77/29.03 |
% 66.77/29.03 +-Applying beta-rule and splitting (761), into two cases.
% 66.77/29.03 |-Branch one:
% 66.77/29.03 | (779) all_53_0_57 = sz10
% 66.77/29.03 |
% 66.77/29.03 | Equations (779) can reduce 203 to:
% 66.77/29.03 | (159) $false
% 66.77/29.03 |
% 66.77/29.03 |-The branch is then unsatisfiable
% 66.77/29.03 |-Branch two:
% 66.77/29.03 | (203) ~ (all_53_0_57 = sz10)
% 66.77/29.03 | (782) ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_53_0_57) = 0 & aNaturalNumber0(v0) = 0)
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (32) with xp, xn, all_159_1_63, all_30_1_42 and discharging atoms doDivides0(xp, xn) = all_30_1_42, yields:
% 66.77/29.03 | (783) all_159_1_63 = all_30_1_42 | ~ (doDivides0(xp, xn) = all_159_1_63)
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (32) with xp, xp, all_179_1_101, 0 and discharging atoms doDivides0(xp, xp) = all_179_1_101, yields:
% 66.77/29.03 | (784) all_179_1_101 = 0 | ~ (doDivides0(xp, xp) = 0)
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (32) with xp, xm, all_184_1_118, all_30_0_41 and discharging atoms doDivides0(xp, xm) = all_184_1_118, doDivides0(xp, xm) = all_30_0_41, yields:
% 66.77/29.03 | (785) all_184_1_118 = all_30_0_41
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (32) with xp, xm, all_184_1_118, all_182_1_113 and discharging atoms doDivides0(xp, xm) = all_184_1_118, yields:
% 66.77/29.03 | (786) all_184_1_118 = all_182_1_113 | ~ (doDivides0(xp, xm) = all_182_1_113)
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with all_58_0_58, all_182_4_116, 0 and discharging atoms aNaturalNumber0(all_58_0_58) = all_182_4_116, aNaturalNumber0(all_58_0_58) = 0, yields:
% 66.77/29.03 | (787) all_182_4_116 = 0
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with all_58_0_58, all_182_4_116, all_203_2_134 and discharging atoms aNaturalNumber0(all_58_0_58) = all_203_2_134, aNaturalNumber0(all_58_0_58) = all_182_4_116, yields:
% 66.77/29.03 | (788) all_203_2_134 = all_182_4_116
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with all_58_0_58, all_159_4_66, all_203_2_134 and discharging atoms aNaturalNumber0(all_58_0_58) = all_203_2_134, aNaturalNumber0(all_58_0_58) = all_159_4_66, yields:
% 66.77/29.03 | (789) all_203_2_134 = all_159_4_66
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with all_53_0_57, all_191_2_131, 0 and discharging atoms aNaturalNumber0(all_53_0_57) = all_191_2_131, aNaturalNumber0(all_53_0_57) = 0, yields:
% 66.77/29.03 | (790) all_191_2_131 = 0
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with all_24_1_31, all_163_0_72, all_167_1_79 and discharging atoms aNaturalNumber0(all_24_1_31) = all_167_1_79, aNaturalNumber0(all_24_1_31) = all_163_0_72, yields:
% 66.77/29.03 | (791) all_167_1_79 = all_163_0_72
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with all_20_2_23, all_179_7_107, 0 and discharging atoms aNaturalNumber0(all_20_2_23) = all_179_7_107, aNaturalNumber0(all_20_2_23) = 0, yields:
% 66.77/29.03 | (792) all_179_7_107 = 0
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with all_20_2_23, all_177_1_98, all_179_7_107 and discharging atoms aNaturalNumber0(all_20_2_23) = all_179_7_107, aNaturalNumber0(all_20_2_23) = all_177_1_98, yields:
% 66.77/29.03 | (793) all_179_7_107 = all_177_1_98
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with all_19_2_20, all_182_2_114, 0 and discharging atoms aNaturalNumber0(all_19_2_20) = all_182_2_114, aNaturalNumber0(all_19_2_20) = 0, yields:
% 66.77/29.03 | (794) all_182_2_114 = 0
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xk, all_182_2_114, all_36_2_52 and discharging atoms aNaturalNumber0(xk) = all_36_2_52, yields:
% 66.77/29.03 | (795) all_182_2_114 = all_36_2_52 | ~ (aNaturalNumber0(xk) = all_182_2_114)
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with all_19_2_20, all_175_3_95, all_182_2_114 and discharging atoms aNaturalNumber0(all_19_2_20) = all_182_2_114, aNaturalNumber0(all_19_2_20) = all_175_3_95, yields:
% 66.77/29.03 | (796) all_182_2_114 = all_175_3_95
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with all_19_2_20, all_173_1_90, all_175_3_95 and discharging atoms aNaturalNumber0(all_19_2_20) = all_175_3_95, aNaturalNumber0(all_19_2_20) = all_173_1_90, yields:
% 66.77/29.03 | (797) all_175_3_95 = all_173_1_90
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with all_18_2_17, all_169_3_84, 0 and discharging atoms aNaturalNumber0(all_18_2_17) = all_169_3_84, aNaturalNumber0(all_18_2_17) = 0, yields:
% 66.77/29.03 | (798) all_169_3_84 = 0
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with all_18_2_17, all_159_2_64, all_169_3_84 and discharging atoms aNaturalNumber0(all_18_2_17) = all_169_3_84, aNaturalNumber0(all_18_2_17) = all_159_2_64, yields:
% 66.77/29.03 | (799) all_169_3_84 = all_159_2_64
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with all_18_2_17, all_157_1_60, all_159_2_64 and discharging atoms aNaturalNumber0(all_18_2_17) = all_159_2_64, aNaturalNumber0(all_18_2_17) = all_157_1_60, yields:
% 66.77/29.03 | (800) all_159_2_64 = all_157_1_60
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with all_0_4_4, all_165_0_75, 0 and discharging atoms aNaturalNumber0(all_0_4_4) = all_165_0_75, aNaturalNumber0(all_0_4_4) = 0, yields:
% 66.77/29.03 | (801) all_165_0_75 = 0
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with all_0_5_5, all_175_2_94, 0 and discharging atoms aNaturalNumber0(all_0_5_5) = all_175_2_94, aNaturalNumber0(all_0_5_5) = 0, yields:
% 66.77/29.03 | (802) all_175_2_94 = 0
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with all_0_5_5, all_169_2_83, all_175_2_94 and discharging atoms aNaturalNumber0(all_0_5_5) = all_175_2_94, aNaturalNumber0(all_0_5_5) = all_169_2_83, yields:
% 66.77/29.03 | (803) all_175_2_94 = all_169_2_83
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xr, all_191_1_130, 0 and discharging atoms aNaturalNumber0(xr) = all_191_1_130, aNaturalNumber0(xr) = 0, yields:
% 66.77/29.03 | (804) all_191_1_130 = 0
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xp, all_184_6_123, all_203_1_133 and discharging atoms aNaturalNumber0(xp) = all_203_1_133, aNaturalNumber0(xp) = all_184_6_123, yields:
% 66.77/29.03 | (805) all_203_1_133 = all_184_6_123
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xp, all_179_8_108, all_179_6_106 and discharging atoms aNaturalNumber0(xp) = all_179_6_106, aNaturalNumber0(xp) = all_179_8_108, yields:
% 66.77/29.03 | (806) all_179_6_106 = all_179_8_108
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xp, all_177_2_99, all_179_8_108 and discharging atoms aNaturalNumber0(xp) = all_179_8_108, aNaturalNumber0(xp) = all_177_2_99, yields:
% 66.77/29.03 | (807) all_179_8_108 = all_177_2_99
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xp, all_171_1_87, 0 and discharging atoms aNaturalNumber0(xp) = all_171_1_87, aNaturalNumber0(xp) = 0, yields:
% 66.77/29.03 | (808) all_171_1_87 = 0
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xp, all_171_1_87, all_203_1_133 and discharging atoms aNaturalNumber0(xp) = all_203_1_133, aNaturalNumber0(xp) = all_171_1_87, yields:
% 66.77/29.03 | (809) all_203_1_133 = all_171_1_87
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xp, all_171_1_87, all_177_2_99 and discharging atoms aNaturalNumber0(xp) = all_177_2_99, aNaturalNumber0(xp) = all_171_1_87, yields:
% 66.77/29.03 | (810) all_177_2_99 = all_171_1_87
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xp, all_163_1_73, all_203_1_133 and discharging atoms aNaturalNumber0(xp) = all_203_1_133, aNaturalNumber0(xp) = all_163_1_73, yields:
% 66.77/29.03 | (811) all_203_1_133 = all_163_1_73
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xp, all_161_2_69, all_179_6_106 and discharging atoms aNaturalNumber0(xp) = all_179_6_106, aNaturalNumber0(xp) = all_161_2_69, yields:
% 66.77/29.03 | (812) all_179_6_106 = all_161_2_69
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xm, all_182_3_115, all_184_8_125 and discharging atoms aNaturalNumber0(xm) = all_184_8_125, aNaturalNumber0(xm) = all_182_3_115, yields:
% 66.77/29.03 | (813) all_184_8_125 = all_182_3_115
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xm, all_175_4_96, all_182_3_115 and discharging atoms aNaturalNumber0(xm) = all_182_3_115, aNaturalNumber0(xm) = all_175_4_96, yields:
% 66.77/29.03 | (814) all_182_3_115 = all_175_4_96
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xm, all_173_2_91, 0 and discharging atoms aNaturalNumber0(xm) = all_173_2_91, aNaturalNumber0(xm) = 0, yields:
% 66.77/29.03 | (815) all_173_2_91 = 0
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xm, all_173_2_91, all_182_3_115 and discharging atoms aNaturalNumber0(xm) = all_182_3_115, aNaturalNumber0(xm) = all_173_2_91, yields:
% 66.77/29.03 | (816) all_182_3_115 = all_173_2_91
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xm, all_171_2_88, all_184_8_125 and discharging atoms aNaturalNumber0(xm) = all_184_8_125, aNaturalNumber0(xm) = all_171_2_88, yields:
% 66.77/29.03 | (817) all_184_8_125 = all_171_2_88
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xm, all_163_2_74, all_182_3_115 and discharging atoms aNaturalNumber0(xm) = all_182_3_115, aNaturalNumber0(xm) = all_163_2_74, yields:
% 66.77/29.03 | (818) all_182_3_115 = all_163_2_74
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xm, all_161_4_71, all_175_4_96 and discharging atoms aNaturalNumber0(xm) = all_175_4_96, aNaturalNumber0(xm) = all_161_4_71, yields:
% 66.77/29.03 | (819) all_175_4_96 = all_161_4_71
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xn, all_169_4_85, all_184_7_124 and discharging atoms aNaturalNumber0(xn) = all_184_7_124, aNaturalNumber0(xn) = all_169_4_85, yields:
% 66.77/29.03 | (820) all_184_7_124 = all_169_4_85
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xn, all_167_2_80, all_184_7_124 and discharging atoms aNaturalNumber0(xn) = all_184_7_124, aNaturalNumber0(xn) = all_167_2_80, yields:
% 66.77/29.03 | (821) all_184_7_124 = all_167_2_80
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xn, all_165_2_77, 0 and discharging atoms aNaturalNumber0(xn) = all_165_2_77, aNaturalNumber0(xn) = 0, yields:
% 66.77/29.03 | (822) all_165_2_77 = 0
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xn, all_161_3_70, all_169_4_85 and discharging atoms aNaturalNumber0(xn) = all_169_4_85, aNaturalNumber0(xn) = all_161_3_70, yields:
% 66.77/29.03 | (823) all_169_4_85 = all_161_3_70
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xn, all_161_3_70, all_165_2_77 and discharging atoms aNaturalNumber0(xn) = all_165_2_77, aNaturalNumber0(xn) = all_161_3_70, yields:
% 66.77/29.03 | (824) all_165_2_77 = all_161_3_70
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xn, all_159_3_65, all_169_4_85 and discharging atoms aNaturalNumber0(xn) = all_169_4_85, aNaturalNumber0(xn) = all_159_3_65, yields:
% 66.77/29.03 | (825) all_169_4_85 = all_159_3_65
% 66.77/29.03 |
% 66.77/29.03 | Instantiating formula (46) with xn, all_157_2_61, all_161_3_70 and discharging atoms aNaturalNumber0(xn) = all_161_3_70, aNaturalNumber0(xn) = all_157_2_61, yields:
% 66.77/29.03 | (826) all_161_3_70 = all_157_2_61
% 66.77/29.03 |
% 66.77/29.03 | Combining equations (811,805) yields a new equation:
% 66.77/29.03 | (827) all_184_6_123 = all_163_1_73
% 66.77/29.03 |
% 66.77/29.03 | Combining equations (809,805) yields a new equation:
% 66.77/29.04 | (828) all_184_6_123 = all_171_1_87
% 66.77/29.04 |
% 66.77/29.04 | Combining equations (788,789) yields a new equation:
% 66.77/29.04 | (829) all_182_4_116 = all_159_4_66
% 66.77/29.04 |
% 66.77/29.04 | Simplifying 829 yields:
% 66.77/29.04 | (830) all_182_4_116 = all_159_4_66
% 66.77/29.04 |
% 66.77/29.04 | Combining equations (828,827) yields a new equation:
% 66.77/29.04 | (831) all_171_1_87 = all_163_1_73
% 66.77/29.04 |
% 66.77/29.04 | Simplifying 831 yields:
% 66.77/29.04 | (832) all_171_1_87 = all_163_1_73
% 66.77/29.04 |
% 66.77/29.04 | Combining equations (820,821) yields a new equation:
% 66.77/29.04 | (833) all_169_4_85 = all_167_2_80
% 66.77/29.04 |
% 66.77/29.04 | Simplifying 833 yields:
% 66.77/29.04 | (834) all_169_4_85 = all_167_2_80
% 66.77/29.04 |
% 66.77/29.04 | Combining equations (813,817) yields a new equation:
% 66.77/29.04 | (835) all_182_3_115 = all_171_2_88
% 66.77/29.04 |
% 66.77/29.04 | Simplifying 835 yields:
% 66.77/29.04 | (836) all_182_3_115 = all_171_2_88
% 66.77/29.04 |
% 66.77/29.04 | Combining equations (796,794) yields a new equation:
% 66.77/29.04 | (837) all_175_3_95 = 0
% 66.77/29.04 |
% 66.77/29.04 | Simplifying 837 yields:
% 66.77/29.04 | (838) all_175_3_95 = 0
% 66.77/29.04 |
% 66.77/29.04 | Combining equations (818,836) yields a new equation:
% 66.77/29.04 | (839) all_171_2_88 = all_163_2_74
% 66.77/29.04 |
% 66.77/29.04 | Combining equations (816,836) yields a new equation:
% 66.77/29.04 | (840) all_173_2_91 = all_171_2_88
% 66.77/29.04 |
% 66.77/29.04 | Simplifying 840 yields:
% 66.77/29.04 | (841) all_173_2_91 = all_171_2_88
% 66.77/29.04 |
% 66.77/29.04 | Combining equations (814,836) yields a new equation:
% 66.77/29.04 | (842) all_175_4_96 = all_171_2_88
% 66.77/29.04 |
% 66.77/29.04 | Simplifying 842 yields:
% 66.77/29.04 | (843) all_175_4_96 = all_171_2_88
% 66.77/29.04 |
% 66.77/29.04 | Combining equations (787,830) yields a new equation:
% 66.77/29.04 | (844) all_159_4_66 = 0
% 66.77/29.04 |
% 66.77/29.04 | Combining equations (806,812) yields a new equation:
% 66.77/29.04 | (845) all_179_8_108 = all_161_2_69
% 66.77/29.04 |
% 66.77/29.04 | Simplifying 845 yields:
% 66.77/29.04 | (846) all_179_8_108 = all_161_2_69
% 66.77/29.04 |
% 66.77/29.04 | Combining equations (793,792) yields a new equation:
% 66.77/29.04 | (847) all_177_1_98 = 0
% 66.77/29.04 |
% 66.77/29.04 | Simplifying 847 yields:
% 66.77/29.04 | (848) all_177_1_98 = 0
% 66.77/29.04 |
% 66.77/29.04 | Combining equations (807,846) yields a new equation:
% 66.77/29.04 | (849) all_177_2_99 = all_161_2_69
% 66.77/29.04 |
% 66.77/29.04 | Simplifying 849 yields:
% 66.77/29.04 | (850) all_177_2_99 = all_161_2_69
% 66.77/29.04 |
% 66.77/29.04 | Combining equations (810,850) yields a new equation:
% 66.77/29.04 | (851) all_171_1_87 = all_161_2_69
% 66.77/29.04 |
% 66.77/29.04 | Simplifying 851 yields:
% 66.77/29.04 | (852) all_171_1_87 = all_161_2_69
% 66.77/29.04 |
% 66.77/29.04 | Combining equations (802,803) yields a new equation:
% 66.77/29.04 | (853) all_169_2_83 = 0
% 66.77/29.04 |
% 66.77/29.04 | Combining equations (797,838) yields a new equation:
% 66.77/29.04 | (854) all_173_1_90 = 0
% 66.77/29.04 |
% 66.77/29.04 | Simplifying 854 yields:
% 66.77/29.04 | (855) all_173_1_90 = 0
% 66.77/29.04 |
% 66.77/29.04 | Combining equations (843,819) yields a new equation:
% 66.93/29.04 | (856) all_171_2_88 = all_161_4_71
% 66.93/29.04 |
% 66.93/29.04 | Simplifying 856 yields:
% 66.93/29.04 | (857) all_171_2_88 = all_161_4_71
% 66.93/29.04 |
% 66.93/29.04 | Combining equations (841,815) yields a new equation:
% 66.93/29.04 | (858) all_171_2_88 = 0
% 66.93/29.04 |
% 66.93/29.04 | Simplifying 858 yields:
% 66.93/29.04 | (859) all_171_2_88 = 0
% 66.93/29.04 |
% 66.93/29.04 | Combining equations (852,832) yields a new equation:
% 66.93/29.04 | (860) all_163_1_73 = all_161_2_69
% 66.93/29.04 |
% 66.93/29.04 | Combining equations (808,832) yields a new equation:
% 66.93/29.04 | (861) all_163_1_73 = 0
% 66.93/29.04 |
% 66.93/29.04 | Combining equations (859,839) yields a new equation:
% 66.93/29.04 | (862) all_163_2_74 = 0
% 66.93/29.04 |
% 66.93/29.04 | Combining equations (857,839) yields a new equation:
% 66.93/29.04 | (863) all_163_2_74 = all_161_4_71
% 66.93/29.04 |
% 66.93/29.04 | Combining equations (799,798) yields a new equation:
% 66.93/29.04 | (864) all_159_2_64 = 0
% 66.93/29.04 |
% 66.93/29.04 | Simplifying 864 yields:
% 66.93/29.04 | (865) all_159_2_64 = 0
% 66.93/29.04 |
% 66.93/29.04 | Combining equations (825,834) yields a new equation:
% 66.93/29.04 | (866) all_167_2_80 = all_159_3_65
% 66.93/29.04 |
% 66.93/29.04 | Combining equations (823,834) yields a new equation:
% 66.93/29.04 | (867) all_167_2_80 = all_161_3_70
% 66.93/29.04 |
% 66.93/29.04 | Combining equations (867,866) yields a new equation:
% 66.93/29.04 | (868) all_161_3_70 = all_159_3_65
% 66.93/29.04 |
% 66.93/29.04 | Simplifying 868 yields:
% 66.93/29.04 | (869) all_161_3_70 = all_159_3_65
% 66.93/29.04 |
% 66.93/29.04 | Combining equations (824,822) yields a new equation:
% 66.93/29.04 | (870) all_161_3_70 = 0
% 66.93/29.04 |
% 66.93/29.04 | Simplifying 870 yields:
% 66.93/29.04 | (871) all_161_3_70 = 0
% 66.93/29.04 |
% 66.93/29.04 | Combining equations (861,860) yields a new equation:
% 66.93/29.04 | (872) all_161_2_69 = 0
% 66.93/29.04 |
% 66.93/29.04 | Combining equations (863,862) yields a new equation:
% 66.93/29.04 | (873) all_161_4_71 = 0
% 66.93/29.04 |
% 66.93/29.04 | Simplifying 873 yields:
% 66.93/29.04 | (874) all_161_4_71 = 0
% 66.93/29.04 |
% 66.93/29.04 | Combining equations (826,869) yields a new equation:
% 66.93/29.04 | (875) all_159_3_65 = all_157_2_61
% 66.93/29.04 |
% 66.93/29.04 | Combining equations (871,869) yields a new equation:
% 66.93/29.04 | (876) all_159_3_65 = 0
% 66.93/29.04 |
% 66.93/29.04 | Combining equations (800,865) yields a new equation:
% 66.93/29.04 | (877) all_157_1_60 = 0
% 66.93/29.04 |
% 66.93/29.04 | Simplifying 877 yields:
% 66.93/29.04 | (878) all_157_1_60 = 0
% 66.93/29.04 |
% 66.93/29.04 | Combining equations (875,876) yields a new equation:
% 66.93/29.04 | (879) all_157_2_61 = 0
% 66.93/29.04 |
% 66.93/29.04 | Simplifying 879 yields:
% 66.93/29.04 | (880) all_157_2_61 = 0
% 66.93/29.04 |
% 66.93/29.04 | Combining equations (872,860) yields a new equation:
% 66.93/29.04 | (861) all_163_1_73 = 0
% 66.93/29.04 |
% 66.93/29.04 | Combining equations (876,866) yields a new equation:
% 66.93/29.04 | (882) all_167_2_80 = 0
% 66.93/29.04 |
% 66.93/29.04 | Combining equations (872,850) yields a new equation:
% 66.93/29.04 | (883) all_177_2_99 = 0
% 66.93/29.04 |
% 66.93/29.04 | From (844) and (663) follows:
% 66.93/29.04 | (200) aNaturalNumber0(all_58_0_58) = 0
% 66.93/29.04 |
% 66.93/29.04 | From (790) and (751) follows:
% 66.93/29.04 | (192) aNaturalNumber0(all_53_0_57) = 0
% 66.93/29.04 |
% 66.93/29.04 | From (848) and (712) follows:
% 66.93/29.04 | (561) aNaturalNumber0(all_20_2_23) = 0
% 66.93/29.04 |
% 66.93/29.04 | From (801) and (678) follows:
% 66.93/29.04 | (595) aNaturalNumber0(all_0_4_4) = 0
% 66.93/29.04 |
% 66.93/29.04 | From (853) and (691) follows:
% 66.93/29.04 | (573) aNaturalNumber0(all_0_5_5) = 0
% 66.93/29.04 |
% 66.93/29.04 | From (804) and (752) follows:
% 66.93/29.04 | (10) aNaturalNumber0(xr) = 0
% 66.93/29.04 |
% 66.93/29.04 | From (872) and (667) follows:
% 66.93/29.04 | (12) aNaturalNumber0(xp) = 0
% 66.93/29.04 |
% 66.93/29.04 | From (874) and (668) follows:
% 66.93/29.04 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.04 |
% 66.93/29.04 | From (880) and (655) follows:
% 66.93/29.05 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.05 |
% 66.93/29.05 +-Applying beta-rule and splitting (714), into two cases.
% 66.93/29.05 |-Branch one:
% 66.93/29.05 | (893) ~ (all_177_1_98 = 0)
% 66.93/29.05 |
% 66.93/29.05 | Equations (848) can reduce 893 to:
% 66.93/29.05 | (159) $false
% 66.93/29.05 |
% 66.93/29.05 |-The branch is then unsatisfiable
% 66.93/29.05 |-Branch two:
% 66.93/29.05 | (848) all_177_1_98 = 0
% 66.93/29.05 | (896) ~ (all_177_2_99 = 0) | all_177_0_97 = all_0_3_3
% 66.93/29.05 |
% 66.93/29.05 +-Applying beta-rule and splitting (642), into two cases.
% 66.93/29.05 |-Branch one:
% 66.93/29.05 | (897) xp = xn
% 66.93/29.05 |
% 66.93/29.05 | Equations (897) can reduce 74 to:
% 66.93/29.05 | (159) $false
% 66.93/29.05 |
% 66.93/29.05 |-The branch is then unsatisfiable
% 66.93/29.05 |-Branch two:
% 66.93/29.05 | (74) ~ (xp = xn)
% 66.93/29.05 | (900) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xp, xm) = v4 & sdtpldt0(xn, xm) = v3 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v4 = v3) & ~ (all_24_1_31 = all_0_5_5))))
% 66.93/29.05 |
% 66.93/29.05 | Instantiating (900) with all_227_0_137, all_227_1_138, all_227_2_139, all_227_3_140, all_227_4_141 yields:
% 66.93/29.05 | (901) sdtpldt0(xp, xm) = all_227_0_137 & sdtpldt0(xn, xm) = all_227_1_138 & aNaturalNumber0(xp) = all_227_2_139 & aNaturalNumber0(xm) = all_227_4_141 & aNaturalNumber0(xn) = all_227_3_140 & ( ~ (all_227_2_139 = 0) | ~ (all_227_3_140 = 0) | ~ (all_227_4_141 = 0) | ( ~ (all_227_0_137 = all_227_1_138) & ~ (all_24_1_31 = all_0_5_5)))
% 66.93/29.05 |
% 66.93/29.05 | Applying alpha-rule on (901) yields:
% 66.93/29.05 | (902) aNaturalNumber0(xn) = all_227_3_140
% 66.93/29.05 | (903) ~ (all_227_2_139 = 0) | ~ (all_227_3_140 = 0) | ~ (all_227_4_141 = 0) | ( ~ (all_227_0_137 = all_227_1_138) & ~ (all_24_1_31 = all_0_5_5))
% 66.93/29.05 | (904) sdtpldt0(xn, xm) = all_227_1_138
% 66.93/29.05 | (905) sdtpldt0(xp, xm) = all_227_0_137
% 66.93/29.05 | (906) aNaturalNumber0(xp) = all_227_2_139
% 66.93/29.05 | (907) aNaturalNumber0(xm) = all_227_4_141
% 66.93/29.05 |
% 66.93/29.05 +-Applying beta-rule and splitting (622), into two cases.
% 66.93/29.05 |-Branch one:
% 66.93/29.05 | (908) all_53_0_57 = xr
% 66.93/29.05 |
% 66.93/29.05 | From (908) and (192) follows:
% 66.93/29.05 | (10) aNaturalNumber0(xr) = 0
% 66.93/29.05 |
% 66.93/29.05 +-Applying beta-rule and splitting (702), into two cases.
% 66.93/29.05 |-Branch one:
% 66.93/29.05 | (910) ~ (all_173_1_90 = 0)
% 66.93/29.05 |
% 66.93/29.05 | Equations (855) can reduce 910 to:
% 66.93/29.05 | (159) $false
% 66.93/29.05 |
% 66.93/29.05 |-The branch is then unsatisfiable
% 66.93/29.05 |-Branch two:
% 66.93/29.05 | (855) all_173_1_90 = 0
% 66.93/29.05 | (913) ~ (all_173_2_91 = 0) | all_173_0_89 = xp
% 66.93/29.05 |
% 66.93/29.05 +-Applying beta-rule and splitting (656), into two cases.
% 66.93/29.05 |-Branch one:
% 66.93/29.05 | (914) ~ (all_157_1_60 = 0)
% 66.93/29.05 |
% 66.93/29.05 | Equations (878) can reduce 914 to:
% 66.93/29.05 | (159) $false
% 66.93/29.05 |
% 66.93/29.05 |-The branch is then unsatisfiable
% 66.93/29.05 |-Branch two:
% 66.93/29.05 | (878) all_157_1_60 = 0
% 66.93/29.05 | (917) ~ (all_157_2_61 = 0) | all_157_0_59 = xp
% 66.93/29.05 |
% 66.93/29.05 +-Applying beta-rule and splitting (913), into two cases.
% 66.93/29.05 |-Branch one:
% 66.93/29.05 | (918) ~ (all_173_2_91 = 0)
% 66.93/29.05 |
% 66.93/29.05 | Equations (815) can reduce 918 to:
% 66.93/29.05 | (159) $false
% 66.93/29.05 |
% 66.93/29.05 |-The branch is then unsatisfiable
% 66.93/29.05 |-Branch two:
% 66.93/29.05 | (815) all_173_2_91 = 0
% 66.93/29.05 | (921) all_173_0_89 = xp
% 66.93/29.05 |
% 66.93/29.05 | From (921) and (699) follows:
% 66.93/29.05 | (922) sdtpldt0(all_19_2_20, xm) = xp
% 66.93/29.05 |
% 66.93/29.05 +-Applying beta-rule and splitting (917), into two cases.
% 66.93/29.05 |-Branch one:
% 66.93/29.05 | (923) ~ (all_157_2_61 = 0)
% 66.93/29.05 |
% 66.93/29.05 | Equations (880) can reduce 923 to:
% 66.93/29.05 | (159) $false
% 66.93/29.05 |
% 66.93/29.05 |-The branch is then unsatisfiable
% 66.93/29.05 |-Branch two:
% 66.93/29.05 | (880) all_157_2_61 = 0
% 66.93/29.05 | (926) all_157_0_59 = xp
% 66.93/29.05 |
% 66.93/29.05 | From (926) and (653) follows:
% 66.93/29.05 | (927) sdtpldt0(all_18_2_17, xn) = xp
% 66.93/29.05 |
% 66.93/29.05 +-Applying beta-rule and splitting (896), into two cases.
% 66.93/29.05 |-Branch one:
% 66.93/29.05 | (928) ~ (all_177_2_99 = 0)
% 66.93/29.05 |
% 66.93/29.05 | Equations (883) can reduce 928 to:
% 66.93/29.05 | (159) $false
% 66.93/29.05 |
% 66.93/29.05 |-The branch is then unsatisfiable
% 66.93/29.05 |-Branch two:
% 66.93/29.05 | (883) all_177_2_99 = 0
% 66.93/29.05 | (931) all_177_0_97 = all_0_3_3
% 66.93/29.05 |
% 66.93/29.05 | From (931) and (711) follows:
% 66.93/29.05 | (932) sdtasdt0(all_20_2_23, xp) = all_0_3_3
% 66.93/29.05 |
% 66.93/29.05 +-Applying beta-rule and splitting (675), into two cases.
% 66.93/29.05 |-Branch one:
% 66.93/29.05 | (933) ~ (all_163_1_73 = 0)
% 66.93/29.05 |
% 66.93/29.05 | Equations (861) can reduce 933 to:
% 66.93/29.05 | (159) $false
% 66.93/29.05 |
% 66.93/29.05 |-The branch is then unsatisfiable
% 66.93/29.05 |-Branch two:
% 66.93/29.05 | (861) all_163_1_73 = 0
% 66.93/29.05 | (936) ~ (all_163_2_74 = 0) | all_163_0_72 = 0
% 66.93/29.05 |
% 66.93/29.05 +-Applying beta-rule and splitting (936), into two cases.
% 66.93/29.05 |-Branch one:
% 66.93/29.05 | (937) ~ (all_163_2_74 = 0)
% 66.93/29.05 |
% 66.93/29.05 | Equations (862) can reduce 937 to:
% 66.93/29.05 | (159) $false
% 66.93/29.05 |
% 66.93/29.05 |-The branch is then unsatisfiable
% 66.93/29.05 |-Branch two:
% 66.93/29.05 | (862) all_163_2_74 = 0
% 66.93/29.05 | (940) all_163_0_72 = 0
% 66.93/29.05 |
% 66.93/29.05 | Combining equations (940,791) yields a new equation:
% 66.93/29.05 | (941) all_167_1_79 = 0
% 66.93/29.05 |
% 66.93/29.05 +-Applying beta-rule and splitting (685), into two cases.
% 66.93/29.05 |-Branch one:
% 66.93/29.05 | (942) ~ (all_167_1_79 = 0)
% 66.93/29.05 |
% 66.93/29.05 | Equations (941) can reduce 942 to:
% 66.93/29.05 | (159) $false
% 66.93/29.05 |
% 66.93/29.05 |-The branch is then unsatisfiable
% 66.93/29.05 |-Branch two:
% 66.93/29.05 | (941) all_167_1_79 = 0
% 66.93/29.05 | (945) ~ (all_167_2_80 = 0) | all_167_0_78 = all_0_4_4
% 66.93/29.05 |
% 66.93/29.05 +-Applying beta-rule and splitting (945), into two cases.
% 66.93/29.05 |-Branch one:
% 66.93/29.05 | (946) ~ (all_167_2_80 = 0)
% 66.93/29.05 |
% 66.93/29.05 | Equations (882) can reduce 946 to:
% 66.93/29.05 | (159) $false
% 66.93/29.05 |
% 66.93/29.05 |-The branch is then unsatisfiable
% 66.93/29.05 |-Branch two:
% 66.93/29.05 | (882) all_167_2_80 = 0
% 66.93/29.05 | (949) all_167_0_78 = all_0_4_4
% 66.93/29.05 |
% 66.93/29.05 | From (949) and (682) follows:
% 66.93/29.05 | (950) sdtpldt0(all_24_1_31, xn) = all_0_4_4
% 66.93/29.05 |
% 66.93/29.05 | Instantiating formula (3) with xn, xm, all_227_1_138, all_0_5_5 and discharging atoms sdtpldt0(xn, xm) = all_227_1_138, sdtpldt0(xn, xm) = all_0_5_5, yields:
% 66.93/29.05 | (951) all_227_1_138 = all_0_5_5
% 66.93/29.05 |
% 66.93/29.05 | Instantiating formula (46) with xp, all_227_2_139, 0 and discharging atoms aNaturalNumber0(xp) = all_227_2_139, aNaturalNumber0(xp) = 0, yields:
% 66.93/29.05 | (952) all_227_2_139 = 0
% 66.93/29.05 |
% 66.93/29.05 | Instantiating formula (46) with xm, all_227_4_141, 0 and discharging atoms aNaturalNumber0(xm) = all_227_4_141, aNaturalNumber0(xm) = 0, yields:
% 66.93/29.05 | (953) all_227_4_141 = 0
% 66.93/29.05 |
% 66.93/29.05 | Instantiating formula (46) with xn, all_227_3_140, 0 and discharging atoms aNaturalNumber0(xn) = all_227_3_140, aNaturalNumber0(xn) = 0, yields:
% 66.93/29.05 | (954) all_227_3_140 = 0
% 66.93/29.05 |
% 66.93/29.05 | From (951) and (904) follows:
% 66.93/29.05 | (73) sdtpldt0(xn, xm) = all_0_5_5
% 66.93/29.05 |
% 66.93/29.05 | From (952) and (906) follows:
% 66.93/29.05 | (12) aNaturalNumber0(xp) = 0
% 66.93/29.05 |
% 66.93/29.05 | From (953) and (907) follows:
% 66.93/29.05 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.05 |
% 66.93/29.05 | From (954) and (902) follows:
% 66.93/29.05 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.05 |
% 66.93/29.05 +-Applying beta-rule and splitting (744), into two cases.
% 66.93/29.05 |-Branch one:
% 66.93/29.05 | (959) all_186_0_126 = xp & all_186_1_127 = 0 & sdtasdt0(all_58_0_58, all_186_2_128) = xp & aNaturalNumber0(all_186_2_128) = 0
% 66.93/29.05 |
% 66.93/29.05 | Applying alpha-rule on (959) yields:
% 66.93/29.05 | (960) all_186_0_126 = xp
% 66.93/29.05 | (961) all_186_1_127 = 0
% 66.93/29.05 | (962) sdtasdt0(all_58_0_58, all_186_2_128) = xp
% 66.93/29.05 | (963) aNaturalNumber0(all_186_2_128) = 0
% 66.93/29.05 |
% 66.93/29.05 +-Applying beta-rule and splitting (629), into two cases.
% 66.93/29.05 |-Branch one:
% 66.93/29.05 | (181) xp = sz00
% 66.93/29.05 |
% 66.93/29.05 | Equations (181) can reduce 86 to:
% 66.93/29.05 | (159) $false
% 66.93/29.05 |
% 66.93/29.05 |-The branch is then unsatisfiable
% 66.93/29.05 |-Branch two:
% 66.93/29.05 | (86) ~ (xp = sz00)
% 66.93/29.05 | (967) all_20_2_23 = xk | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_20_2_23) = v0) | (doDivides0(xp, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 66.93/29.05 |
% 66.93/29.05 +-Applying beta-rule and splitting (967), into two cases.
% 66.93/29.05 |-Branch one:
% 66.93/29.05 | (968) all_20_2_23 = xk
% 66.93/29.06 |
% 66.93/29.06 | From (968) and (932) follows:
% 66.93/29.06 | (969) sdtasdt0(xk, xp) = all_0_3_3
% 66.93/29.06 |
% 66.93/29.06 | From (968) and (560) follows:
% 66.93/29.06 | (970) sdtasdt0(xp, xk) = all_0_3_3
% 66.93/29.06 |
% 66.93/29.06 | From (968) and (724) follows:
% 66.93/29.06 | (971) sdtpldt0(xp, xk) = all_179_4_104
% 66.93/29.06 |
% 66.93/29.06 | From (968) and (561) follows:
% 66.93/29.06 | (972) aNaturalNumber0(xk) = 0
% 66.93/29.06 |
% 66.93/29.06 +-Applying beta-rule and splitting (795), into two cases.
% 66.93/29.06 |-Branch one:
% 66.93/29.06 | (973) ~ (aNaturalNumber0(xk) = all_182_2_114)
% 66.93/29.06 |
% 66.93/29.06 | From (794) and (973) follows:
% 66.93/29.06 | (974) ~ (aNaturalNumber0(xk) = 0)
% 66.93/29.06 |
% 66.93/29.06 | Using (972) and (974) yields:
% 66.93/29.06 | (615) $false
% 66.93/29.06 |
% 66.93/29.06 |-The branch is then unsatisfiable
% 66.93/29.06 |-Branch two:
% 66.93/29.06 | (976) aNaturalNumber0(xk) = all_182_2_114
% 66.93/29.06 | (977) all_182_2_114 = all_36_2_52
% 66.93/29.06 |
% 66.93/29.06 | Combining equations (977,794) yields a new equation:
% 66.93/29.06 | (978) all_36_2_52 = 0
% 66.93/29.06 |
% 66.93/29.06 | Simplifying 978 yields:
% 66.93/29.06 | (979) all_36_2_52 = 0
% 66.93/29.06 |
% 66.93/29.06 | Combining equations (979,293) yields a new equation:
% 66.93/29.06 | (980) all_41_1_55 = 0
% 66.93/29.06 |
% 66.93/29.06 | From (979) and (166) follows:
% 66.93/29.06 | (972) aNaturalNumber0(xk) = 0
% 66.93/29.06 |
% 66.93/29.06 +-Applying beta-rule and splitting (650), into two cases.
% 66.93/29.06 |-Branch one:
% 66.93/29.06 | (982) all_20_2_23 = sz00
% 66.93/29.06 |
% 66.93/29.06 | Combining equations (982,968) yields a new equation:
% 66.93/29.06 | (168) xk = sz00
% 66.93/29.06 |
% 66.93/29.06 | Equations (168) can reduce 13 to:
% 66.93/29.06 | (159) $false
% 66.93/29.06 |
% 66.93/29.06 |-The branch is then unsatisfiable
% 66.93/29.06 |-Branch two:
% 66.93/29.06 | (985) ~ (all_20_2_23 = sz00)
% 66.93/29.06 | (986) all_20_2_23 = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_20_2_23) = 0 & aNaturalNumber0(v0) = 0)
% 66.93/29.06 |
% 66.93/29.06 | Equations (968) can reduce 985 to:
% 66.93/29.06 | (13) ~ (xk = sz00)
% 66.93/29.06 |
% 66.93/29.06 +-Applying beta-rule and splitting (124), into two cases.
% 66.93/29.06 |-Branch one:
% 66.93/29.06 | (988) all_21_0_24 = xk & all_21_1_25 = 0 & sdtasdt0(xr, all_21_2_26) = xk & aNaturalNumber0(all_21_2_26) = 0
% 66.93/29.06 |
% 66.93/29.06 | Applying alpha-rule on (988) yields:
% 66.93/29.06 | (989) all_21_0_24 = xk
% 66.93/29.06 | (990) all_21_1_25 = 0
% 66.93/29.06 | (991) sdtasdt0(xr, all_21_2_26) = xk
% 66.93/29.06 | (992) aNaturalNumber0(all_21_2_26) = 0
% 66.93/29.06 |
% 66.93/29.06 +-Applying beta-rule and splitting (651), into two cases.
% 66.93/29.06 |-Branch one:
% 66.93/29.06 | (974) ~ (aNaturalNumber0(xk) = 0)
% 66.93/29.06 |
% 66.93/29.06 | Using (972) and (974) yields:
% 66.93/29.06 | (615) $false
% 66.93/29.06 |
% 66.93/29.06 |-The branch is then unsatisfiable
% 66.93/29.06 |-Branch two:
% 66.93/29.06 | (972) aNaturalNumber0(xk) = 0
% 66.93/29.06 | (996) xk = sz10 | xk = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xk) = 0 & aNaturalNumber0(v0) = 0)
% 66.93/29.06 |
% 66.93/29.06 +-Applying beta-rule and splitting (986), into two cases.
% 66.93/29.06 |-Branch one:
% 66.93/29.06 | (997) all_20_2_23 = sz10
% 66.93/29.06 |
% 66.93/29.06 | Combining equations (968,997) yields a new equation:
% 66.93/29.06 | (998) xk = sz10
% 66.93/29.06 |
% 66.93/29.06 | Simplifying 998 yields:
% 66.93/29.06 | (999) xk = sz10
% 66.93/29.06 |
% 66.93/29.06 | Equations (999) can reduce 68 to:
% 66.93/29.06 | (159) $false
% 66.93/29.06 |
% 66.93/29.06 |-The branch is then unsatisfiable
% 66.93/29.06 |-Branch two:
% 66.93/29.06 | (1001) ~ (all_20_2_23 = sz10)
% 66.93/29.06 | (1002) ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_20_2_23) = 0 & aNaturalNumber0(v0) = 0)
% 66.93/29.06 |
% 66.93/29.06 | Instantiating (1002) with all_386_0_142 yields:
% 66.93/29.06 | (1003) isPrime0(all_386_0_142) = 0 & doDivides0(all_386_0_142, all_20_2_23) = 0 & aNaturalNumber0(all_386_0_142) = 0
% 66.93/29.06 |
% 66.93/29.06 | Applying alpha-rule on (1003) yields:
% 66.93/29.06 | (1004) isPrime0(all_386_0_142) = 0
% 66.93/29.06 | (1005) doDivides0(all_386_0_142, all_20_2_23) = 0
% 66.93/29.06 | (1006) aNaturalNumber0(all_386_0_142) = 0
% 66.93/29.06 |
% 66.93/29.06 | Equations (968) can reduce 1001 to:
% 66.93/29.06 | (68) ~ (xk = sz10)
% 66.93/29.06 |
% 66.93/29.06 | From (968) and (1005) follows:
% 66.93/29.06 | (1008) doDivides0(all_386_0_142, xk) = 0
% 66.93/29.06 |
% 66.93/29.06 +-Applying beta-rule and splitting (619), into two cases.
% 66.93/29.06 |-Branch one:
% 66.93/29.06 | (1009) all_58_0_58 = xp
% 66.93/29.06 |
% 66.93/29.06 | Equations (1009) can reduce 202 to:
% 66.93/29.06 | (86) ~ (xp = sz00)
% 66.93/29.06 |
% 66.93/29.06 | From (1009) and (777) follows:
% 66.93/29.06 | (1011) doDivides0(all_208_0_135, xp) = 0
% 66.93/29.06 |
% 66.93/29.06 | From (1009) and (199) follows:
% 66.93/29.06 | (1012) doDivides0(xp, xp) = 0
% 66.93/29.06 |
% 66.93/29.06 | From (1009) and (730) follows:
% 66.93/29.06 | (1013) doDivides0(xp, xm) = all_182_1_113
% 66.93/29.06 |
% 66.93/29.06 | From (1009) and (662) follows:
% 66.93/29.06 | (1014) doDivides0(xp, xn) = all_159_1_63
% 66.93/29.06 |
% 66.93/29.06 | From (1009) and (962) follows:
% 66.93/29.06 | (1015) sdtasdt0(xp, all_186_2_128) = xp
% 66.93/29.06 |
% 66.93/29.06 | From (1009) and (200) follows:
% 66.93/29.06 | (12) aNaturalNumber0(xp) = 0
% 66.93/29.06 |
% 66.93/29.06 +-Applying beta-rule and splitting (786), into two cases.
% 66.93/29.06 |-Branch one:
% 66.93/29.06 | (1017) ~ (doDivides0(xp, xm) = all_182_1_113)
% 66.93/29.06 |
% 66.93/29.06 | Using (1013) and (1017) yields:
% 66.93/29.06 | (615) $false
% 66.93/29.06 |
% 66.93/29.06 |-The branch is then unsatisfiable
% 66.93/29.06 |-Branch two:
% 66.93/29.06 | (1013) doDivides0(xp, xm) = all_182_1_113
% 66.93/29.06 | (1020) all_184_1_118 = all_182_1_113
% 66.93/29.06 |
% 66.93/29.06 | Combining equations (785,1020) yields a new equation:
% 66.93/29.06 | (1021) all_182_1_113 = all_30_0_41
% 66.93/29.06 |
% 66.93/29.06 | From (1021) and (1013) follows:
% 66.93/29.06 | (149) doDivides0(xp, xm) = all_30_0_41
% 66.93/29.06 |
% 66.93/29.06 +-Applying beta-rule and splitting (641), into two cases.
% 66.93/29.06 |-Branch one:
% 66.93/29.06 | (897) xp = xn
% 66.93/29.06 |
% 66.93/29.06 | Equations (897) can reduce 74 to:
% 66.93/29.06 | (159) $false
% 66.93/29.06 |
% 66.93/29.06 |-The branch is then unsatisfiable
% 66.93/29.06 |-Branch two:
% 66.93/29.06 | (74) ~ (xp = xn)
% 66.93/29.06 | (1026) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xp, xm) = v3 & sdtpldt0(xn, xm) = v4 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v4 = v3) & ~ (all_24_1_31 = all_0_5_5))))
% 66.93/29.06 |
% 66.93/29.06 | Instantiating (1026) with all_404_0_143, all_404_1_144, all_404_2_145, all_404_3_146, all_404_4_147 yields:
% 66.93/29.06 | (1027) sdtpldt0(xp, xm) = all_404_1_144 & sdtpldt0(xn, xm) = all_404_0_143 & aNaturalNumber0(xp) = all_404_3_146 & aNaturalNumber0(xm) = all_404_4_147 & aNaturalNumber0(xn) = all_404_2_145 & ( ~ (all_404_2_145 = 0) | ~ (all_404_3_146 = 0) | ~ (all_404_4_147 = 0) | ( ~ (all_404_0_143 = all_404_1_144) & ~ (all_24_1_31 = all_0_5_5)))
% 66.93/29.06 |
% 66.93/29.06 | Applying alpha-rule on (1027) yields:
% 66.93/29.06 | (1028) sdtpldt0(xn, xm) = all_404_0_143
% 66.93/29.06 | (1029) aNaturalNumber0(xp) = all_404_3_146
% 66.93/29.06 | (1030) aNaturalNumber0(xm) = all_404_4_147
% 66.93/29.07 | (1031) aNaturalNumber0(xn) = all_404_2_145
% 66.93/29.07 | (1032) sdtpldt0(xp, xm) = all_404_1_144
% 66.93/29.07 | (1033) ~ (all_404_2_145 = 0) | ~ (all_404_3_146 = 0) | ~ (all_404_4_147 = 0) | ( ~ (all_404_0_143 = all_404_1_144) & ~ (all_24_1_31 = all_0_5_5))
% 66.93/29.07 |
% 66.93/29.07 +-Applying beta-rule and splitting (783), into two cases.
% 66.93/29.07 |-Branch one:
% 66.93/29.07 | (1034) ~ (doDivides0(xp, xn) = all_159_1_63)
% 66.93/29.07 |
% 66.93/29.07 | Using (1014) and (1034) yields:
% 66.93/29.07 | (615) $false
% 66.93/29.07 |
% 66.93/29.07 |-The branch is then unsatisfiable
% 66.93/29.07 |-Branch two:
% 66.93/29.07 | (1014) doDivides0(xp, xn) = all_159_1_63
% 66.93/29.07 | (1037) all_159_1_63 = all_30_1_42
% 66.93/29.07 |
% 66.93/29.07 | From (1037) and (1014) follows:
% 66.93/29.07 | (157) doDivides0(xp, xn) = all_30_1_42
% 66.93/29.07 |
% 66.93/29.07 +-Applying beta-rule and splitting (176), into two cases.
% 66.93/29.07 |-Branch one:
% 66.93/29.07 | (1039) ~ (all_41_1_55 = 0)
% 66.93/29.07 |
% 66.93/29.07 | Equations (980) can reduce 1039 to:
% 66.93/29.07 | (159) $false
% 66.93/29.07 |
% 66.93/29.07 |-The branch is then unsatisfiable
% 66.93/29.07 |-Branch two:
% 66.93/29.07 | (980) all_41_1_55 = 0
% 66.93/29.07 | (1042) ~ (all_41_2_56 = 0) | all_41_0_54 = 0
% 66.93/29.07 |
% 66.93/29.07 +-Applying beta-rule and splitting (996), into two cases.
% 66.93/29.07 |-Branch one:
% 66.93/29.07 | (168) xk = sz00
% 66.93/29.07 |
% 66.93/29.07 | Equations (168) can reduce 13 to:
% 66.93/29.07 | (159) $false
% 66.93/29.07 |
% 66.93/29.07 |-The branch is then unsatisfiable
% 66.93/29.07 |-Branch two:
% 66.93/29.07 | (13) ~ (xk = sz00)
% 66.93/29.07 | (1046) xk = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xk) = 0 & aNaturalNumber0(v0) = 0)
% 66.93/29.07 |
% 66.93/29.07 +-Applying beta-rule and splitting (1042), into two cases.
% 66.93/29.07 |-Branch one:
% 66.93/29.07 | (1047) ~ (all_41_2_56 = 0)
% 66.93/29.07 |
% 66.93/29.07 | Equations (253) can reduce 1047 to:
% 66.93/29.07 | (159) $false
% 66.93/29.07 |
% 66.93/29.07 |-The branch is then unsatisfiable
% 66.93/29.07 |-Branch two:
% 66.93/29.07 | (253) all_41_2_56 = 0
% 66.93/29.07 | (1050) all_41_0_54 = 0
% 66.93/29.07 |
% 66.93/29.07 +-Applying beta-rule and splitting (165), into two cases.
% 66.93/29.07 |-Branch one:
% 66.93/29.07 | (1051) ~ (all_36_0_50 = 0)
% 66.93/29.07 |
% 66.93/29.07 +-Applying beta-rule and splitting (1046), into two cases.
% 66.93/29.07 |-Branch one:
% 66.93/29.07 | (999) xk = sz10
% 66.93/29.07 |
% 66.93/29.07 | Equations (999) can reduce 68 to:
% 66.93/29.07 | (159) $false
% 66.93/29.07 |
% 66.93/29.07 |-The branch is then unsatisfiable
% 66.93/29.07 |-Branch two:
% 66.93/29.07 | (68) ~ (xk = sz10)
% 66.93/29.07 | (1055) ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xk) = 0 & aNaturalNumber0(v0) = 0)
% 66.93/29.07 |
% 66.93/29.07 | Instantiating (1055) with all_432_0_148 yields:
% 66.93/29.07 | (1056) isPrime0(all_432_0_148) = 0 & doDivides0(all_432_0_148, xk) = 0 & aNaturalNumber0(all_432_0_148) = 0
% 66.93/29.07 |
% 66.93/29.07 | Applying alpha-rule on (1056) yields:
% 66.93/29.07 | (1057) isPrime0(all_432_0_148) = 0
% 66.93/29.07 | (1058) doDivides0(all_432_0_148, xk) = 0
% 66.93/29.07 | (1059) aNaturalNumber0(all_432_0_148) = 0
% 66.93/29.07 |
% 66.93/29.07 +-Applying beta-rule and splitting (628), into two cases.
% 66.93/29.07 |-Branch one:
% 66.93/29.07 | (1060) ~ (sdtasdt0(xp, xk) = all_0_3_3)
% 66.93/29.07 |
% 66.93/29.07 | Using (970) and (1060) yields:
% 66.93/29.07 | (615) $false
% 66.93/29.07 |
% 66.93/29.07 |-The branch is then unsatisfiable
% 66.93/29.07 |-Branch two:
% 66.93/29.07 | (970) sdtasdt0(xp, xk) = all_0_3_3
% 66.93/29.07 | (1063) xp = sz00 | ? [v0] : ? [v1] : ? [v2] : ((v0 = 0 & aNaturalNumber0(xk) = 0) | (doDivides0(xp, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 66.93/29.07 |
% 66.93/29.07 +-Applying beta-rule and splitting (784), into two cases.
% 66.93/29.07 |-Branch one:
% 66.93/29.07 | (1064) ~ (doDivides0(xp, xp) = 0)
% 66.93/29.07 |
% 66.93/29.07 | Using (1012) and (1064) yields:
% 66.93/29.07 | (615) $false
% 66.93/29.07 |
% 66.93/29.07 |-The branch is then unsatisfiable
% 66.93/29.07 |-Branch two:
% 66.93/29.07 | (1012) doDivides0(xp, xp) = 0
% 66.93/29.07 | (1067) all_179_1_101 = 0
% 66.93/29.07 |
% 66.93/29.07 | From (1067) and (722) follows:
% 66.93/29.07 | (1012) doDivides0(xp, xp) = 0
% 66.93/29.07 |
% 66.93/29.07 +-Applying beta-rule and splitting (1063), into two cases.
% 66.93/29.07 |-Branch one:
% 66.93/29.07 | (181) xp = sz00
% 66.93/29.07 |
% 66.93/29.07 | Equations (181) can reduce 86 to:
% 66.93/29.07 | (159) $false
% 66.93/29.07 |
% 66.93/29.07 |-The branch is then unsatisfiable
% 66.93/29.07 |-Branch two:
% 66.93/29.07 | (86) ~ (xp = sz00)
% 66.93/29.07 | (1072) ? [v0] : ? [v1] : ? [v2] : ((v0 = 0 & aNaturalNumber0(xk) = 0) | (doDivides0(xp, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 66.93/29.07 |
% 66.93/29.07 | Instantiating (1072) with all_456_0_152, all_456_1_153, all_456_2_154 yields:
% 66.93/29.07 | (1073) (all_456_2_154 = 0 & aNaturalNumber0(xk) = 0) | (doDivides0(xp, all_0_3_3) = all_456_0_152 & aNaturalNumber0(all_0_3_3) = all_456_1_153 & aNaturalNumber0(xp) = all_456_2_154 & ( ~ (all_456_0_152 = 0) | ~ (all_456_1_153 = 0) | ~ (all_456_2_154 = 0)))
% 66.93/29.07 |
% 66.93/29.07 | Instantiating formula (3) with xn, xm, all_404_0_143, all_0_5_5 and discharging atoms sdtpldt0(xn, xm) = all_404_0_143, sdtpldt0(xn, xm) = all_0_5_5, yields:
% 66.93/29.07 | (1074) all_404_0_143 = all_0_5_5
% 66.93/29.07 |
% 66.93/29.07 | Instantiating formula (46) with xp, all_404_3_146, 0 and discharging atoms aNaturalNumber0(xp) = all_404_3_146, aNaturalNumber0(xp) = 0, yields:
% 66.93/29.07 | (1075) all_404_3_146 = 0
% 66.93/29.07 |
% 66.93/29.07 | Instantiating formula (46) with xm, all_404_4_147, 0 and discharging atoms aNaturalNumber0(xm) = all_404_4_147, aNaturalNumber0(xm) = 0, yields:
% 66.93/29.07 | (1076) all_404_4_147 = 0
% 66.93/29.07 |
% 66.93/29.07 | Instantiating formula (46) with xn, all_404_2_145, 0 and discharging atoms aNaturalNumber0(xn) = all_404_2_145, aNaturalNumber0(xn) = 0, yields:
% 66.93/29.07 | (1077) all_404_2_145 = 0
% 66.93/29.07 |
% 66.93/29.07 | From (1074) and (1028) follows:
% 66.93/29.07 | (73) sdtpldt0(xn, xm) = all_0_5_5
% 66.93/29.07 |
% 66.93/29.07 | From (1075) and (1029) follows:
% 66.93/29.07 | (12) aNaturalNumber0(xp) = 0
% 66.93/29.07 |
% 66.93/29.07 | From (1076) and (1030) follows:
% 66.93/29.07 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.07 |
% 66.93/29.07 | From (1077) and (1031) follows:
% 66.93/29.07 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.07 |
% 66.93/29.07 +-Applying beta-rule and splitting (631), into two cases.
% 66.93/29.07 |-Branch one:
% 66.93/29.07 | (1082) ~ (sdtasdt0(xp, all_20_2_23) = sz00)
% 66.93/29.07 |
% 66.93/29.07 | From (968) and (1082) follows:
% 66.93/29.07 | (1083) ~ (sdtasdt0(xp, xk) = sz00)
% 66.93/29.07 |
% 66.93/29.07 +-Applying beta-rule and splitting (1073), into two cases.
% 66.93/29.07 |-Branch one:
% 66.93/29.07 | (1084) all_456_2_154 = 0 & aNaturalNumber0(xk) = 0
% 66.93/29.07 |
% 66.93/29.07 | Applying alpha-rule on (1084) yields:
% 66.93/29.07 | (1085) all_456_2_154 = 0
% 66.93/29.07 | (972) aNaturalNumber0(xk) = 0
% 66.93/29.07 |
% 66.93/29.07 | Using (970) and (1083) yields:
% 66.93/29.07 | (1087) ~ (all_0_3_3 = sz00)
% 66.93/29.07 |
% 66.93/29.07 +-Applying beta-rule and splitting (95), into two cases.
% 66.93/29.07 |-Branch one:
% 66.93/29.07 | (1088) ~ (sdtasdt0(sz00, xm) = all_0_3_3)
% 66.93/29.07 |
% 66.93/29.07 +-Applying beta-rule and splitting (90), into two cases.
% 66.93/29.07 |-Branch one:
% 66.93/29.07 | (1089) all_0_3_3 = sz00
% 66.93/29.07 |
% 66.93/29.07 | Equations (1089) can reduce 1087 to:
% 66.93/29.07 | (159) $false
% 66.93/29.07 |
% 66.93/29.07 |-The branch is then unsatisfiable
% 66.93/29.07 |-Branch two:
% 66.93/29.07 | (1087) ~ (all_0_3_3 = sz00)
% 66.93/29.07 | (1092) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 66.93/29.07 |
% 66.93/29.07 | Instantiating (1092) with all_517_0_155, all_517_1_156, all_517_2_157 yields:
% 66.93/29.07 | (1093) sdtlseqdt0(xp, all_0_3_3) = all_517_0_155 & aNaturalNumber0(all_0_3_3) = all_517_1_156 & aNaturalNumber0(xp) = all_517_2_157 & ( ~ (all_517_1_156 = 0) | ~ (all_517_2_157 = 0) | all_517_0_155 = 0)
% 66.93/29.07 |
% 66.93/29.07 | Applying alpha-rule on (1093) yields:
% 66.93/29.07 | (1094) sdtlseqdt0(xp, all_0_3_3) = all_517_0_155
% 66.93/29.07 | (1095) aNaturalNumber0(all_0_3_3) = all_517_1_156
% 66.93/29.07 | (1096) aNaturalNumber0(xp) = all_517_2_157
% 66.93/29.07 | (1097) ~ (all_517_1_156 = 0) | ~ (all_517_2_157 = 0) | all_517_0_155 = 0
% 66.93/29.07 |
% 66.93/29.07 +-Applying beta-rule and splitting (634), into two cases.
% 66.93/29.07 |-Branch one:
% 66.93/29.07 | (1098) ~ (sdtasdt0(sz00, xn) = all_0_3_3)
% 66.93/29.07 |
% 66.93/29.07 | Instantiating formula (46) with all_0_3_3, all_517_1_156, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_517_1_156, aNaturalNumber0(all_0_3_3) = 0, yields:
% 66.93/29.08 | (1099) all_517_1_156 = 0
% 66.93/29.08 |
% 66.93/29.08 | Instantiating formula (46) with xp, all_517_2_157, 0 and discharging atoms aNaturalNumber0(xp) = all_517_2_157, aNaturalNumber0(xp) = 0, yields:
% 66.93/29.08 | (1100) all_517_2_157 = 0
% 66.93/29.08 |
% 66.93/29.08 | Using (2) and (1088) yields:
% 66.93/29.08 | (1101) ~ (xn = sz00)
% 66.93/29.08 |
% 66.93/29.08 | Using (608) and (1098) yields:
% 66.93/29.08 | (1102) ~ (xm = sz00)
% 66.93/29.08 |
% 66.93/29.08 | From (1099) and (1095) follows:
% 66.93/29.08 | (556) aNaturalNumber0(all_0_3_3) = 0
% 66.93/29.08 |
% 66.93/29.08 | From (1100) and (1096) follows:
% 66.93/29.08 | (12) aNaturalNumber0(xp) = 0
% 66.93/29.08 |
% 66.93/29.08 +-Applying beta-rule and splitting (627), into two cases.
% 66.93/29.08 |-Branch one:
% 66.93/29.08 | (1105) ~ (doDivides0(xp, xn) = 0)
% 66.93/29.08 |
% 66.93/29.08 +-Applying beta-rule and splitting (625), into two cases.
% 66.93/29.08 |-Branch one:
% 66.93/29.08 | (1106) ~ (doDivides0(xp, xm) = 0)
% 66.93/29.08 |
% 66.93/29.08 | Using (149) and (1106) yields:
% 66.93/29.08 | (1107) ~ (all_30_0_41 = 0)
% 66.93/29.08 |
% 66.93/29.08 | Using (157) and (1105) yields:
% 66.93/29.08 | (1108) ~ (all_30_1_42 = 0)
% 66.93/29.08 |
% 66.93/29.08 +-Applying beta-rule and splitting (626), into two cases.
% 66.93/29.08 |-Branch one:
% 66.93/29.08 | (1109) all_30_1_42 = 0
% 66.93/29.08 |
% 66.93/29.08 | Equations (1109) can reduce 1108 to:
% 66.93/29.08 | (159) $false
% 66.93/29.08 |
% 66.93/29.08 |-The branch is then unsatisfiable
% 66.93/29.08 |-Branch two:
% 66.93/29.08 | (1108) ~ (all_30_1_42 = 0)
% 66.93/29.08 | (1112) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_3_3, xn) = v3 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 66.93/29.08 |
% 66.93/29.08 | Instantiating (1112) with all_583_0_160, all_583_1_161, all_583_2_162, all_583_3_163 yields:
% 66.93/29.08 | (1113) doDivides0(all_0_3_3, xn) = all_583_0_160 & aNaturalNumber0(all_0_3_3) = all_583_2_162 & aNaturalNumber0(xp) = all_583_3_163 & aNaturalNumber0(xn) = all_583_1_161 & ( ~ (all_583_0_160 = 0) | ~ (all_583_1_161 = 0) | ~ (all_583_2_162 = 0) | ~ (all_583_3_163 = 0))
% 66.93/29.08 |
% 66.93/29.08 | Applying alpha-rule on (1113) yields:
% 66.93/29.08 | (1114) aNaturalNumber0(xp) = all_583_3_163
% 66.93/29.08 | (1115) aNaturalNumber0(all_0_3_3) = all_583_2_162
% 66.93/29.08 | (1116) doDivides0(all_0_3_3, xn) = all_583_0_160
% 66.93/29.08 | (1117) ~ (all_583_0_160 = 0) | ~ (all_583_1_161 = 0) | ~ (all_583_2_162 = 0) | ~ (all_583_3_163 = 0)
% 66.93/29.08 | (1118) aNaturalNumber0(xn) = all_583_1_161
% 66.93/29.08 |
% 66.93/29.08 +-Applying beta-rule and splitting (624), into two cases.
% 66.93/29.08 |-Branch one:
% 66.93/29.08 | (1119) all_30_0_41 = 0
% 66.93/29.08 |
% 66.93/29.08 | Equations (1119) can reduce 1107 to:
% 66.93/29.08 | (159) $false
% 66.93/29.08 |
% 66.93/29.08 |-The branch is then unsatisfiable
% 66.93/29.08 |-Branch two:
% 66.93/29.08 | (1107) ~ (all_30_0_41 = 0)
% 66.93/29.08 | (1122) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_3_3, xm) = v3 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 66.93/29.08 |
% 66.93/29.08 | Instantiating (1122) with all_589_0_164, all_589_1_165, all_589_2_166, all_589_3_167 yields:
% 66.93/29.08 | (1123) doDivides0(all_0_3_3, xm) = all_589_0_164 & aNaturalNumber0(all_0_3_3) = all_589_2_166 & aNaturalNumber0(xp) = all_589_3_167 & aNaturalNumber0(xm) = all_589_1_165 & ( ~ (all_589_0_164 = 0) | ~ (all_589_1_165 = 0) | ~ (all_589_2_166 = 0) | ~ (all_589_3_167 = 0))
% 66.93/29.08 |
% 66.93/29.08 | Applying alpha-rule on (1123) yields:
% 66.93/29.08 | (1124) ~ (all_589_0_164 = 0) | ~ (all_589_1_165 = 0) | ~ (all_589_2_166 = 0) | ~ (all_589_3_167 = 0)
% 66.93/29.08 | (1125) doDivides0(all_0_3_3, xm) = all_589_0_164
% 66.93/29.08 | (1126) aNaturalNumber0(xp) = all_589_3_167
% 66.93/29.08 | (1127) aNaturalNumber0(all_0_3_3) = all_589_2_166
% 66.93/29.08 | (1128) aNaturalNumber0(xm) = all_589_1_165
% 66.93/29.08 |
% 66.93/29.08 | Instantiating formula (46) with all_0_3_3, all_589_2_166, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_589_2_166, aNaturalNumber0(all_0_3_3) = 0, yields:
% 66.93/29.08 | (1129) all_589_2_166 = 0
% 66.93/29.08 |
% 66.93/29.08 | Instantiating formula (46) with all_0_3_3, all_583_2_162, all_589_2_166 and discharging atoms aNaturalNumber0(all_0_3_3) = all_589_2_166, aNaturalNumber0(all_0_3_3) = all_583_2_162, yields:
% 66.93/29.08 | (1130) all_589_2_166 = all_583_2_162
% 66.93/29.08 |
% 66.93/29.08 | Instantiating formula (46) with xp, all_589_3_167, 0 and discharging atoms aNaturalNumber0(xp) = all_589_3_167, aNaturalNumber0(xp) = 0, yields:
% 66.93/29.08 | (1131) all_589_3_167 = 0
% 66.93/29.08 |
% 66.93/29.08 | Instantiating formula (46) with xp, all_583_3_163, all_589_3_167 and discharging atoms aNaturalNumber0(xp) = all_589_3_167, aNaturalNumber0(xp) = all_583_3_163, yields:
% 66.93/29.08 | (1132) all_589_3_167 = all_583_3_163
% 66.93/29.08 |
% 66.93/29.08 | Instantiating formula (46) with xm, all_589_1_165, 0 and discharging atoms aNaturalNumber0(xm) = all_589_1_165, aNaturalNumber0(xm) = 0, yields:
% 66.93/29.08 | (1133) all_589_1_165 = 0
% 66.93/29.08 |
% 66.93/29.08 | Instantiating formula (46) with xn, all_583_1_161, 0 and discharging atoms aNaturalNumber0(xn) = all_583_1_161, aNaturalNumber0(xn) = 0, yields:
% 66.93/29.08 | (1134) all_583_1_161 = 0
% 66.93/29.08 |
% 66.93/29.08 | Combining equations (1130,1129) yields a new equation:
% 66.93/29.08 | (1135) all_583_2_162 = 0
% 66.93/29.08 |
% 66.93/29.08 | Simplifying 1135 yields:
% 66.93/29.08 | (1136) all_583_2_162 = 0
% 66.93/29.08 |
% 66.93/29.08 | Combining equations (1132,1131) yields a new equation:
% 66.93/29.08 | (1137) all_583_3_163 = 0
% 66.93/29.08 |
% 66.93/29.08 | Simplifying 1137 yields:
% 66.93/29.08 | (1138) all_583_3_163 = 0
% 66.93/29.08 |
% 66.93/29.08 | From (1136) and (1115) follows:
% 66.93/29.08 | (556) aNaturalNumber0(all_0_3_3) = 0
% 66.93/29.08 |
% 66.93/29.08 | From (1138) and (1114) follows:
% 66.93/29.08 | (12) aNaturalNumber0(xp) = 0
% 66.93/29.08 |
% 66.93/29.08 | From (1133) and (1128) follows:
% 66.93/29.08 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.08 |
% 66.93/29.08 | From (1134) and (1118) follows:
% 66.93/29.08 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.08 |
% 66.93/29.08 +-Applying beta-rule and splitting (421), into two cases.
% 66.93/29.08 |-Branch one:
% 66.93/29.08 | (1143) ~ (aNaturalNumber0(xn) = all_28_1_39)
% 66.93/29.08 |
% 66.93/29.08 | From (515) and (1143) follows:
% 66.93/29.08 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.08 |
% 66.93/29.08 | Using (53) and (1144) yields:
% 66.93/29.08 | (615) $false
% 66.93/29.08 |
% 66.93/29.08 |-The branch is then unsatisfiable
% 66.93/29.08 |-Branch two:
% 66.93/29.08 | (1146) aNaturalNumber0(xn) = all_28_1_39
% 66.93/29.08 | (1147) all_28_1_39 = all_28_2_40
% 66.93/29.08 |
% 66.93/29.08 | Combining equations (515,1147) yields a new equation:
% 66.93/29.08 | (514) all_28_2_40 = 0
% 66.93/29.08 |
% 66.93/29.08 | Combining equations (514,1147) yields a new equation:
% 66.93/29.08 | (515) all_28_1_39 = 0
% 66.93/29.08 |
% 66.93/29.08 | From (515) and (1146) follows:
% 66.93/29.08 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.08 |
% 66.93/29.08 +-Applying beta-rule and splitting (469), into two cases.
% 66.93/29.08 |-Branch one:
% 66.93/29.08 | (1151) ~ (aNaturalNumber0(xn) = all_22_0_27)
% 66.93/29.08 |
% 66.93/29.08 | From (554) and (1151) follows:
% 66.93/29.08 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.08 |
% 66.93/29.08 | Using (53) and (1144) yields:
% 66.93/29.08 | (615) $false
% 66.93/29.08 |
% 66.93/29.08 |-The branch is then unsatisfiable
% 66.93/29.08 |-Branch two:
% 66.93/29.08 | (1154) aNaturalNumber0(xn) = all_22_0_27
% 66.93/29.08 | (1155) all_22_0_27 = all_12_2_8
% 66.93/29.08 |
% 66.93/29.08 | Combining equations (554,1155) yields a new equation:
% 66.93/29.08 | (508) all_12_2_8 = 0
% 66.93/29.08 |
% 66.93/29.08 | Combining equations (508,1155) yields a new equation:
% 66.93/29.08 | (554) all_22_0_27 = 0
% 66.93/29.08 |
% 66.93/29.08 | From (554) and (1154) follows:
% 66.93/29.08 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.08 |
% 66.93/29.08 +-Applying beta-rule and splitting (408), into two cases.
% 66.93/29.08 |-Branch one:
% 66.93/29.08 | (1159) ~ (aNaturalNumber0(xn) = all_12_1_7)
% 66.93/29.08 |
% 66.93/29.08 | From (507) and (1159) follows:
% 66.93/29.08 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.08 |
% 66.93/29.08 | Using (53) and (1144) yields:
% 66.93/29.08 | (615) $false
% 66.93/29.08 |
% 66.93/29.08 |-The branch is then unsatisfiable
% 66.93/29.08 |-Branch two:
% 66.93/29.08 | (1162) aNaturalNumber0(xn) = all_12_1_7
% 66.93/29.08 | (1163) all_30_8_49 = all_12_1_7
% 66.93/29.08 |
% 66.93/29.08 | Combining equations (516,1163) yields a new equation:
% 66.93/29.08 | (507) all_12_1_7 = 0
% 66.93/29.08 |
% 66.93/29.08 | From (507) and (1162) follows:
% 66.93/29.08 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.08 |
% 66.93/29.08 +-Applying beta-rule and splitting (475), into two cases.
% 66.93/29.08 |-Branch one:
% 66.93/29.08 | (1166) ~ (aNaturalNumber0(xn) = all_30_7_48)
% 66.93/29.08 |
% 66.93/29.08 | From (331) and (1166) follows:
% 66.93/29.08 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.08 |
% 66.93/29.08 | Using (53) and (1144) yields:
% 66.93/29.08 | (615) $false
% 66.93/29.08 |
% 66.93/29.08 |-The branch is then unsatisfiable
% 66.93/29.08 |-Branch two:
% 66.93/29.08 | (1169) aNaturalNumber0(xn) = all_30_7_48
% 66.93/29.08 | (1170) all_30_7_48 = all_12_2_8
% 66.93/29.08 |
% 66.93/29.08 | Combining equations (331,1170) yields a new equation:
% 66.93/29.08 | (508) all_12_2_8 = 0
% 66.93/29.08 |
% 66.93/29.08 | Combining equations (508,1170) yields a new equation:
% 66.93/29.08 | (331) all_30_7_48 = 0
% 66.93/29.08 |
% 66.93/29.08 | From (331) and (1169) follows:
% 66.93/29.08 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.08 |
% 66.93/29.08 +-Applying beta-rule and splitting (400), into two cases.
% 66.93/29.08 |-Branch one:
% 66.93/29.08 | (1174) ~ (aNaturalNumber0(xn) = all_41_2_56)
% 66.93/29.08 |
% 66.93/29.08 | From (253) and (1174) follows:
% 66.93/29.08 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.08 |
% 66.93/29.08 | Using (53) and (1144) yields:
% 66.93/29.08 | (615) $false
% 66.93/29.08 |
% 66.93/29.08 |-The branch is then unsatisfiable
% 66.93/29.08 |-Branch two:
% 66.93/29.08 | (1177) aNaturalNumber0(xn) = all_41_2_56
% 66.93/29.08 | (1178) all_41_2_56 = all_30_8_49
% 66.93/29.08 |
% 66.93/29.08 | Combining equations (253,1178) yields a new equation:
% 66.93/29.08 | (516) all_30_8_49 = 0
% 66.93/29.08 |
% 66.93/29.08 | Combining equations (516,1178) yields a new equation:
% 66.93/29.08 | (253) all_41_2_56 = 0
% 66.93/29.08 |
% 66.93/29.08 | From (253) and (1177) follows:
% 66.93/29.08 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.08 |
% 66.93/29.08 +-Applying beta-rule and splitting (463), into two cases.
% 66.93/29.08 |-Branch one:
% 66.93/29.08 | (1182) ~ (aNaturalNumber0(xn) = all_22_1_28)
% 66.93/29.08 |
% 66.93/29.08 | From (499) and (1182) follows:
% 66.93/29.08 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.08 |
% 66.93/29.08 | Using (53) and (1144) yields:
% 66.93/29.08 | (615) $false
% 66.93/29.08 |
% 66.93/29.08 |-The branch is then unsatisfiable
% 66.93/29.08 |-Branch two:
% 66.93/29.08 | (1185) aNaturalNumber0(xn) = all_22_1_28
% 66.93/29.08 | (1186) all_22_1_28 = all_14_2_11
% 66.93/29.08 |
% 66.93/29.08 | Combining equations (499,1186) yields a new equation:
% 66.93/29.08 | (451) all_14_2_11 = 0
% 66.93/29.08 |
% 66.93/29.08 | Combining equations (451,1186) yields a new equation:
% 66.93/29.08 | (499) all_22_1_28 = 0
% 66.93/29.08 |
% 66.93/29.08 | From (499) and (1185) follows:
% 66.93/29.08 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.08 |
% 66.93/29.08 +-Applying beta-rule and splitting (334), into two cases.
% 66.93/29.08 |-Branch one:
% 66.93/29.08 | (1190) ~ (aNaturalNumber0(xm) = all_22_0_27)
% 66.93/29.08 |
% 66.93/29.08 | From (554) and (1190) follows:
% 66.93/29.08 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 66.93/29.08 |
% 66.93/29.08 | Using (36) and (1191) yields:
% 66.93/29.08 | (615) $false
% 66.93/29.08 |
% 66.93/29.08 |-The branch is then unsatisfiable
% 66.93/29.08 |-Branch two:
% 66.93/29.08 | (1193) aNaturalNumber0(xm) = all_22_0_27
% 66.93/29.08 | (1194) all_30_7_48 = all_22_0_27
% 66.93/29.08 |
% 66.93/29.08 | Combining equations (331,1194) yields a new equation:
% 66.93/29.08 | (554) all_22_0_27 = 0
% 66.93/29.08 |
% 66.93/29.08 | From (554) and (1193) follows:
% 66.93/29.08 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.08 |
% 66.93/29.08 +-Applying beta-rule and splitting (327), into two cases.
% 66.93/29.08 |-Branch one:
% 66.93/29.08 | (1197) ~ (aNaturalNumber0(xp) = all_41_2_56)
% 66.93/29.08 |
% 66.93/29.08 | From (253) and (1197) follows:
% 66.93/29.08 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 66.93/29.08 |
% 66.93/29.08 | Using (12) and (1198) yields:
% 66.93/29.08 | (615) $false
% 66.93/29.08 |
% 66.93/29.08 |-The branch is then unsatisfiable
% 66.93/29.08 |-Branch two:
% 66.93/29.08 | (1200) aNaturalNumber0(xp) = all_41_2_56
% 66.93/29.08 | (1201) all_41_2_56 = all_16_1_13
% 66.93/29.08 |
% 66.93/29.08 | Combining equations (253,1201) yields a new equation:
% 66.93/29.08 | (497) all_16_1_13 = 0
% 66.93/29.08 |
% 66.93/29.08 | Combining equations (497,1201) yields a new equation:
% 66.93/29.08 | (253) all_41_2_56 = 0
% 66.93/29.08 |
% 66.93/29.08 | From (253) and (1200) follows:
% 66.93/29.08 | (12) aNaturalNumber0(xp) = 0
% 66.93/29.08 |
% 66.93/29.08 +-Applying beta-rule and splitting (324), into two cases.
% 66.93/29.08 |-Branch one:
% 66.93/29.08 | (1205) ~ (aNaturalNumber0(xp) = all_26_2_37)
% 66.93/29.08 |
% 66.93/29.08 | From (572) and (1205) follows:
% 66.93/29.08 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 66.93/29.08 |
% 66.93/29.08 | Using (12) and (1198) yields:
% 66.93/29.08 | (615) $false
% 66.93/29.08 |
% 66.93/29.08 |-The branch is then unsatisfiable
% 66.93/29.08 |-Branch two:
% 66.93/29.08 | (1208) aNaturalNumber0(xp) = all_26_2_37
% 66.93/29.09 | (1209) all_26_2_37 = all_16_1_13
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (572,1209) yields a new equation:
% 66.93/29.09 | (497) all_16_1_13 = 0
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (497,1209) yields a new equation:
% 66.93/29.09 | (572) all_26_2_37 = 0
% 66.93/29.09 |
% 66.93/29.09 | From (572) and (1208) follows:
% 66.93/29.09 | (12) aNaturalNumber0(xp) = 0
% 66.93/29.09 |
% 66.93/29.09 +-Applying beta-rule and splitting (316), into two cases.
% 66.93/29.09 |-Branch one:
% 66.93/29.09 | (1213) ~ (aNaturalNumber0(xp) = all_26_0_35)
% 66.93/29.09 |
% 66.93/29.09 | From (594) and (1213) follows:
% 66.93/29.09 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 66.93/29.09 |
% 66.93/29.09 | Using (12) and (1198) yields:
% 66.93/29.09 | (615) $false
% 66.93/29.09 |
% 66.93/29.09 |-The branch is then unsatisfiable
% 66.93/29.09 |-Branch two:
% 66.93/29.09 | (1216) aNaturalNumber0(xp) = all_26_0_35
% 66.93/29.09 | (1217) all_26_0_35 = all_24_2_32
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (594,1217) yields a new equation:
% 66.93/29.09 | (493) all_24_2_32 = 0
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (493,1217) yields a new equation:
% 66.93/29.09 | (594) all_26_0_35 = 0
% 66.93/29.09 |
% 66.93/29.09 | From (594) and (1216) follows:
% 66.93/29.09 | (12) aNaturalNumber0(xp) = 0
% 66.93/29.09 |
% 66.93/29.09 +-Applying beta-rule and splitting (404), into two cases.
% 66.93/29.09 |-Branch one:
% 66.93/29.09 | (1143) ~ (aNaturalNumber0(xn) = all_28_1_39)
% 66.93/29.09 |
% 66.93/29.09 | From (515) and (1143) follows:
% 66.93/29.09 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.09 |
% 66.93/29.09 | Using (53) and (1144) yields:
% 66.93/29.09 | (615) $false
% 66.93/29.09 |
% 66.93/29.09 |-The branch is then unsatisfiable
% 66.93/29.09 |-Branch two:
% 66.93/29.09 | (1146) aNaturalNumber0(xn) = all_28_1_39
% 66.93/29.09 | (1225) all_30_8_49 = all_28_1_39
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (516,1225) yields a new equation:
% 66.93/29.09 | (515) all_28_1_39 = 0
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (515,1225) yields a new equation:
% 66.93/29.09 | (516) all_30_8_49 = 0
% 66.93/29.09 |
% 66.93/29.09 | From (515) and (1146) follows:
% 66.93/29.09 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.09 |
% 66.93/29.09 +-Applying beta-rule and splitting (430), into two cases.
% 66.93/29.09 |-Branch one:
% 66.93/29.09 | (1229) ~ (aNaturalNumber0(xn) = all_36_2_52)
% 66.93/29.09 |
% 66.93/29.09 | From (979) and (1229) follows:
% 66.93/29.09 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.09 |
% 66.93/29.09 | Using (53) and (1144) yields:
% 66.93/29.09 | (615) $false
% 66.93/29.09 |
% 66.93/29.09 |-The branch is then unsatisfiable
% 66.93/29.09 |-Branch two:
% 66.93/29.09 | (1232) aNaturalNumber0(xn) = all_36_2_52
% 66.93/29.09 | (1233) all_36_2_52 = all_24_4_34
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (979,1233) yields a new equation:
% 66.93/29.09 | (511) all_24_4_34 = 0
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (511,1233) yields a new equation:
% 66.93/29.09 | (979) all_36_2_52 = 0
% 66.93/29.09 |
% 66.93/29.09 | From (979) and (1232) follows:
% 66.93/29.09 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.09 |
% 66.93/29.09 +-Applying beta-rule and splitting (302), into two cases.
% 66.93/29.09 |-Branch one:
% 66.93/29.09 | (1237) ~ (aNaturalNumber0(xp) = all_41_1_55)
% 66.93/29.09 |
% 66.93/29.09 | From (980) and (1237) follows:
% 66.93/29.09 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 66.93/29.09 |
% 66.93/29.09 | Using (12) and (1198) yields:
% 66.93/29.09 | (615) $false
% 66.93/29.09 |
% 66.93/29.09 |-The branch is then unsatisfiable
% 66.93/29.09 |-Branch two:
% 66.93/29.09 | (1240) aNaturalNumber0(xp) = all_41_1_55
% 66.93/29.09 | (1241) all_41_1_55 = all_30_6_47
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (980,1241) yields a new equation:
% 66.93/29.09 | (1242) all_30_6_47 = 0
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (1242,1241) yields a new equation:
% 66.93/29.09 | (980) all_41_1_55 = 0
% 66.93/29.09 |
% 66.93/29.09 | From (980) and (1240) follows:
% 66.93/29.09 | (12) aNaturalNumber0(xp) = 0
% 66.93/29.09 |
% 66.93/29.09 +-Applying beta-rule and splitting (228), into two cases.
% 66.93/29.09 |-Branch one:
% 66.93/29.09 | (1245) ~ (aNaturalNumber0(xn) = all_26_2_37)
% 66.93/29.09 |
% 66.93/29.09 | From (572) and (1245) follows:
% 66.93/29.09 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.09 |
% 66.93/29.09 | Using (53) and (1144) yields:
% 66.93/29.09 | (615) $false
% 66.93/29.09 |
% 66.93/29.09 |-The branch is then unsatisfiable
% 66.93/29.09 |-Branch two:
% 66.93/29.09 | (1248) aNaturalNumber0(xn) = all_26_2_37
% 66.93/29.09 | (572) all_26_2_37 = 0
% 66.93/29.09 |
% 66.93/29.09 | From (572) and (1248) follows:
% 66.93/29.09 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.09 |
% 66.93/29.09 +-Applying beta-rule and splitting (386), into two cases.
% 66.93/29.09 |-Branch one:
% 66.93/29.09 | (1251) ~ (aNaturalNumber0(sz10) = all_12_1_7)
% 66.93/29.09 |
% 66.93/29.09 | From (507) and (1251) follows:
% 66.93/29.09 | (1252) ~ (aNaturalNumber0(sz10) = 0)
% 66.93/29.09 |
% 66.93/29.09 | Using (16) and (1252) yields:
% 66.93/29.09 | (615) $false
% 66.93/29.09 |
% 66.93/29.09 |-The branch is then unsatisfiable
% 66.93/29.09 |-Branch two:
% 66.93/29.09 | (1254) aNaturalNumber0(sz10) = all_12_1_7
% 66.93/29.09 | (507) all_12_1_7 = 0
% 66.93/29.09 |
% 66.93/29.09 | From (507) and (1254) follows:
% 66.93/29.09 | (16) aNaturalNumber0(sz10) = 0
% 66.93/29.09 |
% 66.93/29.09 +-Applying beta-rule and splitting (232), into two cases.
% 66.93/29.09 |-Branch one:
% 66.93/29.09 | (1257) ~ (aNaturalNumber0(all_0_5_5) = all_22_0_27)
% 66.93/29.09 |
% 66.93/29.09 | From (554) and (1257) follows:
% 66.93/29.09 | (1258) ~ (aNaturalNumber0(all_0_5_5) = 0)
% 66.93/29.09 |
% 66.93/29.09 | Using (573) and (1258) yields:
% 66.93/29.09 | (615) $false
% 66.93/29.09 |
% 66.93/29.09 |-The branch is then unsatisfiable
% 66.93/29.09 |-Branch two:
% 66.93/29.09 | (1260) aNaturalNumber0(all_0_5_5) = all_22_0_27
% 66.93/29.09 | (1261) all_26_2_37 = all_22_0_27
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (572,1261) yields a new equation:
% 66.93/29.09 | (554) all_22_0_27 = 0
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (554,1261) yields a new equation:
% 66.93/29.09 | (572) all_26_2_37 = 0
% 66.93/29.09 |
% 66.93/29.09 | From (554) and (1260) follows:
% 66.93/29.09 | (573) aNaturalNumber0(all_0_5_5) = 0
% 66.93/29.09 |
% 66.93/29.09 +-Applying beta-rule and splitting (277), into two cases.
% 66.93/29.09 |-Branch one:
% 66.93/29.09 | (1265) ~ (aNaturalNumber0(xk) = all_22_0_27)
% 66.93/29.09 |
% 66.93/29.09 | From (554) and (1265) follows:
% 66.93/29.09 | (974) ~ (aNaturalNumber0(xk) = 0)
% 66.93/29.09 |
% 66.93/29.09 | Using (972) and (974) yields:
% 66.93/29.09 | (615) $false
% 66.93/29.09 |
% 66.93/29.09 |-The branch is then unsatisfiable
% 66.93/29.09 |-Branch two:
% 66.93/29.09 | (1268) aNaturalNumber0(xk) = all_22_0_27
% 66.93/29.09 | (1269) all_41_1_55 = all_22_0_27
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (980,1269) yields a new equation:
% 66.93/29.09 | (554) all_22_0_27 = 0
% 66.93/29.09 |
% 66.93/29.09 | From (554) and (1268) follows:
% 66.93/29.09 | (972) aNaturalNumber0(xk) = 0
% 66.93/29.09 |
% 66.93/29.09 +-Applying beta-rule and splitting (301), into two cases.
% 66.93/29.09 |-Branch one:
% 66.93/29.09 | (1272) ~ (aNaturalNumber0(xp) = all_36_3_53)
% 66.93/29.09 |
% 66.93/29.09 | From (480) and (1272) follows:
% 66.93/29.09 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 66.93/29.09 |
% 66.93/29.09 | Using (12) and (1198) yields:
% 66.93/29.09 | (615) $false
% 66.93/29.09 |
% 66.93/29.09 |-The branch is then unsatisfiable
% 66.93/29.09 |-Branch two:
% 66.93/29.09 | (1275) aNaturalNumber0(xp) = all_36_3_53
% 66.93/29.09 | (1276) all_36_3_53 = all_30_6_47
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (480,1276) yields a new equation:
% 66.93/29.09 | (1242) all_30_6_47 = 0
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (1242,1276) yields a new equation:
% 66.93/29.09 | (480) all_36_3_53 = 0
% 66.93/29.09 |
% 66.93/29.09 | From (480) and (1275) follows:
% 66.93/29.09 | (12) aNaturalNumber0(xp) = 0
% 66.93/29.09 |
% 66.93/29.09 +-Applying beta-rule and splitting (284), into two cases.
% 66.93/29.09 |-Branch one:
% 66.93/29.09 | (1280) ~ (aNaturalNumber0(xp) = all_36_2_52)
% 66.93/29.09 |
% 66.93/29.09 | From (979) and (1280) follows:
% 66.93/29.09 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 66.93/29.09 |
% 66.93/29.09 | Using (12) and (1198) yields:
% 66.93/29.09 | (615) $false
% 66.93/29.09 |
% 66.93/29.09 |-The branch is then unsatisfiable
% 66.93/29.09 |-Branch two:
% 66.93/29.09 | (1283) aNaturalNumber0(xp) = all_36_2_52
% 66.93/29.09 | (979) all_36_2_52 = 0
% 66.93/29.09 |
% 66.93/29.09 | From (979) and (1283) follows:
% 66.93/29.09 | (12) aNaturalNumber0(xp) = 0
% 66.93/29.09 |
% 66.93/29.09 +-Applying beta-rule and splitting (260), into two cases.
% 66.93/29.09 |-Branch one:
% 66.93/29.09 | (1286) ~ (aNaturalNumber0(xr) = all_26_2_37)
% 66.93/29.09 |
% 66.93/29.09 | From (572) and (1286) follows:
% 66.93/29.09 | (1287) ~ (aNaturalNumber0(xr) = 0)
% 66.93/29.09 |
% 66.93/29.09 | Using (10) and (1287) yields:
% 66.93/29.09 | (615) $false
% 66.93/29.09 |
% 66.93/29.09 |-The branch is then unsatisfiable
% 66.93/29.09 |-Branch two:
% 66.93/29.09 | (1289) aNaturalNumber0(xr) = all_26_2_37
% 66.93/29.09 | (1290) all_41_2_56 = all_26_2_37
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (253,1290) yields a new equation:
% 66.93/29.09 | (572) all_26_2_37 = 0
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (572,1290) yields a new equation:
% 66.93/29.09 | (253) all_41_2_56 = 0
% 66.93/29.09 |
% 66.93/29.09 | From (572) and (1289) follows:
% 66.93/29.09 | (10) aNaturalNumber0(xr) = 0
% 66.93/29.09 |
% 66.93/29.09 +-Applying beta-rule and splitting (449), into two cases.
% 66.93/29.09 |-Branch one:
% 66.93/29.09 | (1294) ~ (aNaturalNumber0(xn) = all_14_1_10)
% 66.93/29.09 |
% 66.93/29.09 | From (503) and (1294) follows:
% 66.93/29.09 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.09 |
% 66.93/29.09 | Using (53) and (1144) yields:
% 66.93/29.09 | (615) $false
% 66.93/29.09 |
% 66.93/29.09 |-The branch is then unsatisfiable
% 66.93/29.09 |-Branch two:
% 66.93/29.09 | (1297) aNaturalNumber0(xn) = all_14_1_10
% 66.93/29.09 | (1298) all_22_2_29 = all_14_1_10
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (1298,510) yields a new equation:
% 66.93/29.09 | (502) all_14_1_10 = 0
% 66.93/29.09 |
% 66.93/29.09 | Simplifying 502 yields:
% 66.93/29.09 | (503) all_14_1_10 = 0
% 66.93/29.09 |
% 66.93/29.09 | From (503) and (1297) follows:
% 66.93/29.09 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.09 |
% 66.93/29.09 +-Applying beta-rule and splitting (239), into two cases.
% 66.93/29.09 |-Branch one:
% 66.93/29.09 | (1258) ~ (aNaturalNumber0(all_0_5_5) = 0)
% 66.93/29.09 |
% 66.93/29.09 | Using (573) and (1258) yields:
% 66.93/29.09 | (615) $false
% 66.93/29.09 |
% 66.93/29.09 |-The branch is then unsatisfiable
% 66.93/29.09 |-Branch two:
% 66.93/29.09 | (573) aNaturalNumber0(all_0_5_5) = 0
% 66.93/29.09 | (571) all_16_2_14 = 0
% 66.93/29.09 |
% 66.93/29.09 +-Applying beta-rule and splitting (369), into two cases.
% 66.93/29.09 |-Branch one:
% 66.93/29.09 | (1306) ~ (aNaturalNumber0(xm) = all_12_0_6)
% 66.93/29.09 |
% 66.93/29.09 | From (570) and (1306) follows:
% 66.93/29.09 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 66.93/29.09 |
% 66.93/29.09 | Using (36) and (1191) yields:
% 66.93/29.09 | (615) $false
% 66.93/29.09 |
% 66.93/29.09 |-The branch is then unsatisfiable
% 66.93/29.09 |-Branch two:
% 66.93/29.09 | (1309) aNaturalNumber0(xm) = all_12_0_6
% 66.93/29.09 | (1310) all_22_1_28 = all_12_0_6
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (499,1310) yields a new equation:
% 66.93/29.09 | (570) all_12_0_6 = 0
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (570,1310) yields a new equation:
% 66.93/29.09 | (499) all_22_1_28 = 0
% 66.93/29.09 |
% 66.93/29.09 | From (570) and (1309) follows:
% 66.93/29.09 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.09 |
% 66.93/29.09 +-Applying beta-rule and splitting (358), into two cases.
% 66.93/29.09 |-Branch one:
% 66.93/29.09 | (1314) ~ (aNaturalNumber0(xm) = all_41_2_56)
% 66.93/29.09 |
% 66.93/29.09 | From (253) and (1314) follows:
% 66.93/29.09 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 66.93/29.09 |
% 66.93/29.09 | Using (36) and (1191) yields:
% 66.93/29.09 | (615) $false
% 66.93/29.09 |
% 66.93/29.09 |-The branch is then unsatisfiable
% 66.93/29.09 |-Branch two:
% 66.93/29.09 | (1317) aNaturalNumber0(xm) = all_41_2_56
% 66.93/29.09 | (1318) all_41_2_56 = all_24_3_33
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (253,1318) yields a new equation:
% 66.93/29.09 | (483) all_24_3_33 = 0
% 66.93/29.09 |
% 66.93/29.09 | Combining equations (483,1318) yields a new equation:
% 66.93/29.09 | (253) all_41_2_56 = 0
% 66.93/29.09 |
% 66.93/29.09 | From (253) and (1317) follows:
% 66.93/29.10 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.10 |
% 66.93/29.10 +-Applying beta-rule and splitting (249), into two cases.
% 66.93/29.10 |-Branch one:
% 66.93/29.10 | (1322) ~ (aNaturalNumber0(all_0_5_5) = all_36_1_51)
% 66.93/29.10 |
% 66.93/29.10 | From (555) and (1322) follows:
% 66.93/29.10 | (1258) ~ (aNaturalNumber0(all_0_5_5) = 0)
% 66.93/29.10 |
% 66.93/29.10 | Using (573) and (1258) yields:
% 66.93/29.10 | (615) $false
% 66.93/29.10 |
% 66.93/29.10 |-The branch is then unsatisfiable
% 66.93/29.10 |-Branch two:
% 66.93/29.10 | (1325) aNaturalNumber0(all_0_5_5) = all_36_1_51
% 66.93/29.10 | (1326) all_36_1_51 = all_12_0_6
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (555,1326) yields a new equation:
% 66.93/29.10 | (570) all_12_0_6 = 0
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (570,1326) yields a new equation:
% 66.93/29.10 | (555) all_36_1_51 = 0
% 66.93/29.10 |
% 66.93/29.10 | From (555) and (1325) follows:
% 66.93/29.10 | (573) aNaturalNumber0(all_0_5_5) = 0
% 66.93/29.10 |
% 66.93/29.10 +-Applying beta-rule and splitting (340), into two cases.
% 66.93/29.10 |-Branch one:
% 66.93/29.10 | (1330) ~ (aNaturalNumber0(xm) = all_36_3_53)
% 66.93/29.10 |
% 66.93/29.10 | From (480) and (1330) follows:
% 66.93/29.10 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 66.93/29.10 |
% 66.93/29.10 | Using (36) and (1191) yields:
% 66.93/29.10 | (615) $false
% 66.93/29.10 |
% 66.93/29.10 |-The branch is then unsatisfiable
% 66.93/29.10 |-Branch two:
% 66.93/29.10 | (1333) aNaturalNumber0(xm) = all_36_3_53
% 66.93/29.10 | (1334) all_36_3_53 = all_30_7_48
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (480,1334) yields a new equation:
% 66.93/29.10 | (331) all_30_7_48 = 0
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (331,1334) yields a new equation:
% 66.93/29.10 | (480) all_36_3_53 = 0
% 66.93/29.10 |
% 66.93/29.10 | From (480) and (1333) follows:
% 66.93/29.10 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.10 |
% 66.93/29.10 +-Applying beta-rule and splitting (393), into two cases.
% 66.93/29.10 |-Branch one:
% 66.93/29.10 | (1338) ~ (aNaturalNumber0(xm) = all_36_2_52)
% 66.93/29.10 |
% 66.93/29.10 | From (979) and (1338) follows:
% 66.93/29.10 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 66.93/29.10 |
% 66.93/29.10 | Using (36) and (1191) yields:
% 66.93/29.10 | (615) $false
% 66.93/29.10 |
% 66.93/29.10 |-The branch is then unsatisfiable
% 66.93/29.10 |-Branch two:
% 66.93/29.10 | (1341) aNaturalNumber0(xm) = all_36_2_52
% 66.93/29.10 | (1342) all_36_2_52 = all_12_1_7
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (979,1342) yields a new equation:
% 66.93/29.10 | (507) all_12_1_7 = 0
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (507,1342) yields a new equation:
% 66.93/29.10 | (979) all_36_2_52 = 0
% 66.93/29.10 |
% 66.93/29.10 | From (979) and (1341) follows:
% 66.93/29.10 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.10 |
% 66.93/29.10 +-Applying beta-rule and splitting (338), into two cases.
% 66.93/29.10 |-Branch one:
% 66.93/29.10 | (1306) ~ (aNaturalNumber0(xm) = all_12_0_6)
% 66.93/29.10 |
% 66.93/29.10 | From (570) and (1306) follows:
% 66.93/29.10 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 66.93/29.10 |
% 66.93/29.10 | Using (36) and (1191) yields:
% 66.93/29.10 | (615) $false
% 66.93/29.10 |
% 66.93/29.10 |-The branch is then unsatisfiable
% 66.93/29.10 |-Branch two:
% 66.93/29.10 | (1309) aNaturalNumber0(xm) = all_12_0_6
% 66.93/29.10 | (1350) all_30_7_48 = all_12_0_6
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (331,1350) yields a new equation:
% 66.93/29.10 | (570) all_12_0_6 = 0
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (570,1350) yields a new equation:
% 66.93/29.10 | (331) all_30_7_48 = 0
% 66.93/29.10 |
% 66.93/29.10 | From (570) and (1309) follows:
% 66.93/29.10 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.10 |
% 66.93/29.10 +-Applying beta-rule and splitting (396), into two cases.
% 66.93/29.10 |-Branch one:
% 66.93/29.10 | (1354) ~ (aNaturalNumber0(xn) = all_26_0_35)
% 66.93/29.10 |
% 66.93/29.10 | From (594) and (1354) follows:
% 66.93/29.10 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.10 |
% 66.93/29.10 | Using (53) and (1144) yields:
% 66.93/29.10 | (615) $false
% 66.93/29.10 |
% 66.93/29.10 |-The branch is then unsatisfiable
% 66.93/29.10 |-Branch two:
% 66.93/29.10 | (1357) aNaturalNumber0(xn) = all_26_0_35
% 66.93/29.10 | (1358) all_30_8_49 = all_26_0_35
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (516,1358) yields a new equation:
% 66.93/29.10 | (594) all_26_0_35 = 0
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (594,1358) yields a new equation:
% 66.93/29.10 | (516) all_30_8_49 = 0
% 66.93/29.10 |
% 66.93/29.10 | From (594) and (1357) follows:
% 66.93/29.10 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.10 |
% 66.93/29.10 +-Applying beta-rule and splitting (357), into two cases.
% 66.93/29.10 |-Branch one:
% 66.93/29.10 | (1306) ~ (aNaturalNumber0(xm) = all_12_0_6)
% 66.93/29.10 |
% 66.93/29.10 | From (570) and (1306) follows:
% 66.93/29.10 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 66.93/29.10 |
% 66.93/29.10 | Using (36) and (1191) yields:
% 66.93/29.10 | (615) $false
% 66.93/29.10 |
% 66.93/29.10 |-The branch is then unsatisfiable
% 66.93/29.10 |-Branch two:
% 66.93/29.10 | (1309) aNaturalNumber0(xm) = all_12_0_6
% 66.93/29.10 | (1366) all_24_3_33 = all_12_0_6
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (483,1366) yields a new equation:
% 66.93/29.10 | (570) all_12_0_6 = 0
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (570,1366) yields a new equation:
% 66.93/29.10 | (483) all_24_3_33 = 0
% 66.93/29.10 |
% 66.93/29.10 | From (570) and (1309) follows:
% 66.93/29.10 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.10 |
% 66.93/29.10 +-Applying beta-rule and splitting (454), into two cases.
% 66.93/29.10 |-Branch one:
% 66.93/29.10 | (1370) ~ (aNaturalNumber0(xn) = all_36_1_51)
% 66.93/29.10 |
% 66.93/29.10 | From (555) and (1370) follows:
% 66.93/29.10 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.10 |
% 66.93/29.10 | Using (53) and (1144) yields:
% 66.93/29.10 | (615) $false
% 66.93/29.10 |
% 66.93/29.10 |-The branch is then unsatisfiable
% 66.93/29.10 |-Branch two:
% 66.93/29.10 | (1373) aNaturalNumber0(xn) = all_36_1_51
% 66.93/29.10 | (1374) all_36_1_51 = all_14_2_11
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (555,1374) yields a new equation:
% 66.93/29.10 | (451) all_14_2_11 = 0
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (451,1374) yields a new equation:
% 66.93/29.10 | (555) all_36_1_51 = 0
% 66.93/29.10 |
% 66.93/29.10 | From (555) and (1373) follows:
% 66.93/29.10 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.10 |
% 66.93/29.10 +-Applying beta-rule and splitting (347), into two cases.
% 66.93/29.10 |-Branch one:
% 66.93/29.10 | (1314) ~ (aNaturalNumber0(xm) = all_41_2_56)
% 66.93/29.10 |
% 66.93/29.10 | From (253) and (1314) follows:
% 66.93/29.10 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 66.93/29.10 |
% 66.93/29.10 | Using (36) and (1191) yields:
% 66.93/29.10 | (615) $false
% 66.93/29.10 |
% 66.93/29.10 |-The branch is then unsatisfiable
% 66.93/29.10 |-Branch two:
% 66.93/29.10 | (1317) aNaturalNumber0(xm) = all_41_2_56
% 66.93/29.10 | (1382) all_41_2_56 = all_28_1_39
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (253,1382) yields a new equation:
% 66.93/29.10 | (515) all_28_1_39 = 0
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (515,1382) yields a new equation:
% 66.93/29.10 | (253) all_41_2_56 = 0
% 66.93/29.10 |
% 66.93/29.10 | From (253) and (1317) follows:
% 66.93/29.10 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.10 |
% 66.93/29.10 +-Applying beta-rule and splitting (390), into two cases.
% 66.93/29.10 |-Branch one:
% 66.93/29.10 | (1386) ~ (aNaturalNumber0(xm) = all_26_2_37)
% 66.93/29.10 |
% 66.93/29.10 | From (572) and (1386) follows:
% 66.93/29.10 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 66.93/29.10 |
% 66.93/29.10 | Using (36) and (1191) yields:
% 66.93/29.10 | (615) $false
% 66.93/29.10 |
% 66.93/29.10 |-The branch is then unsatisfiable
% 66.93/29.10 |-Branch two:
% 66.93/29.10 | (1389) aNaturalNumber0(xm) = all_26_2_37
% 66.93/29.10 | (1390) all_26_2_37 = all_12_1_7
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (572,1390) yields a new equation:
% 66.93/29.10 | (507) all_12_1_7 = 0
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (507,1390) yields a new equation:
% 66.93/29.10 | (572) all_26_2_37 = 0
% 66.93/29.10 |
% 66.93/29.10 | From (572) and (1389) follows:
% 66.93/29.10 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.10 |
% 66.93/29.10 +-Applying beta-rule and splitting (376), into two cases.
% 66.93/29.10 |-Branch one:
% 66.93/29.10 | (1190) ~ (aNaturalNumber0(xm) = all_22_0_27)
% 66.93/29.10 |
% 66.93/29.10 | From (554) and (1190) follows:
% 66.93/29.10 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 66.93/29.10 |
% 66.93/29.10 | Using (36) and (1191) yields:
% 66.93/29.10 | (615) $false
% 66.93/29.10 |
% 66.93/29.10 |-The branch is then unsatisfiable
% 66.93/29.10 |-Branch two:
% 66.93/29.10 | (1193) aNaturalNumber0(xm) = all_22_0_27
% 66.93/29.10 | (1398) all_22_0_27 = all_14_1_10
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (554,1398) yields a new equation:
% 66.93/29.10 | (503) all_14_1_10 = 0
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (503,1398) yields a new equation:
% 66.93/29.10 | (554) all_22_0_27 = 0
% 66.93/29.10 |
% 66.93/29.10 | From (554) and (1193) follows:
% 66.93/29.10 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.10 |
% 66.93/29.10 +-Applying beta-rule and splitting (231), into two cases.
% 66.93/29.10 |-Branch one:
% 66.93/29.10 | (1322) ~ (aNaturalNumber0(all_0_5_5) = all_36_1_51)
% 66.93/29.10 |
% 66.93/29.10 | From (555) and (1322) follows:
% 66.93/29.10 | (1258) ~ (aNaturalNumber0(all_0_5_5) = 0)
% 66.93/29.10 |
% 66.93/29.10 | Using (573) and (1258) yields:
% 66.93/29.10 | (615) $false
% 66.93/29.10 |
% 66.93/29.10 |-The branch is then unsatisfiable
% 66.93/29.10 |-Branch two:
% 66.93/29.10 | (1325) aNaturalNumber0(all_0_5_5) = all_36_1_51
% 66.93/29.10 | (1406) all_36_1_51 = all_26_2_37
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (555,1406) yields a new equation:
% 66.93/29.10 | (572) all_26_2_37 = 0
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (572,1406) yields a new equation:
% 66.93/29.10 | (555) all_36_1_51 = 0
% 66.93/29.10 |
% 66.93/29.10 | From (555) and (1325) follows:
% 66.93/29.10 | (573) aNaturalNumber0(all_0_5_5) = 0
% 66.93/29.10 |
% 66.93/29.10 +-Applying beta-rule and splitting (306), into two cases.
% 66.93/29.10 |-Branch one:
% 66.93/29.10 | (1213) ~ (aNaturalNumber0(xp) = all_26_0_35)
% 66.93/29.10 |
% 66.93/29.10 | From (594) and (1213) follows:
% 66.93/29.10 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 66.93/29.10 |
% 66.93/29.10 | Using (12) and (1198) yields:
% 66.93/29.10 | (615) $false
% 66.93/29.10 |
% 66.93/29.10 |-The branch is then unsatisfiable
% 66.93/29.10 |-Branch two:
% 66.93/29.10 | (1216) aNaturalNumber0(xp) = all_26_0_35
% 66.93/29.10 | (1414) all_26_0_35 = all_26_1_36
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (594,1414) yields a new equation:
% 66.93/29.10 | (303) all_26_1_36 = 0
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (303,1414) yields a new equation:
% 66.93/29.10 | (594) all_26_0_35 = 0
% 66.93/29.10 |
% 66.93/29.10 | From (594) and (1216) follows:
% 66.93/29.10 | (12) aNaturalNumber0(xp) = 0
% 66.93/29.10 |
% 66.93/29.10 +-Applying beta-rule and splitting (304), into two cases.
% 66.93/29.10 |-Branch one:
% 66.93/29.10 | (1418) ~ (aNaturalNumber0(xp) = all_36_1_51)
% 66.93/29.10 |
% 66.93/29.10 | From (555) and (1418) follows:
% 66.93/29.10 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 66.93/29.10 |
% 66.93/29.10 | Using (12) and (1198) yields:
% 66.93/29.10 | (615) $false
% 66.93/29.10 |
% 66.93/29.10 |-The branch is then unsatisfiable
% 66.93/29.10 |-Branch two:
% 66.93/29.10 | (1421) aNaturalNumber0(xp) = all_36_1_51
% 66.93/29.10 | (1422) all_36_1_51 = all_26_1_36
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (555,1422) yields a new equation:
% 66.93/29.10 | (303) all_26_1_36 = 0
% 66.93/29.10 |
% 66.93/29.10 | Combining equations (303,1422) yields a new equation:
% 66.93/29.10 | (555) all_36_1_51 = 0
% 66.93/29.10 |
% 66.93/29.10 | From (555) and (1421) follows:
% 66.93/29.10 | (12) aNaturalNumber0(xp) = 0
% 66.93/29.10 |
% 66.93/29.10 +-Applying beta-rule and splitting (240), into two cases.
% 66.93/29.10 |-Branch one:
% 66.93/29.10 | (1322) ~ (aNaturalNumber0(all_0_5_5) = all_36_1_51)
% 66.93/29.11 |
% 66.93/29.11 | From (555) and (1322) follows:
% 66.93/29.11 | (1258) ~ (aNaturalNumber0(all_0_5_5) = 0)
% 66.93/29.11 |
% 66.93/29.11 | Using (573) and (1258) yields:
% 66.93/29.11 | (615) $false
% 66.93/29.11 |
% 66.93/29.11 |-The branch is then unsatisfiable
% 66.93/29.11 |-Branch two:
% 66.93/29.11 | (1325) aNaturalNumber0(all_0_5_5) = all_36_1_51
% 66.93/29.11 | (1430) all_36_1_51 = all_16_2_14
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (555,1430) yields a new equation:
% 66.93/29.11 | (571) all_16_2_14 = 0
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (571,1430) yields a new equation:
% 66.93/29.11 | (555) all_36_1_51 = 0
% 66.93/29.11 |
% 66.93/29.11 | From (555) and (1325) follows:
% 66.93/29.11 | (573) aNaturalNumber0(all_0_5_5) = 0
% 66.93/29.11 |
% 66.93/29.11 +-Applying beta-rule and splitting (456), into two cases.
% 66.93/29.11 |-Branch one:
% 66.93/29.11 | (1245) ~ (aNaturalNumber0(xn) = all_26_2_37)
% 66.93/29.11 |
% 66.93/29.11 | From (572) and (1245) follows:
% 66.93/29.11 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.11 |
% 66.93/29.11 | Using (53) and (1144) yields:
% 66.93/29.11 | (615) $false
% 66.93/29.11 |
% 66.93/29.11 |-The branch is then unsatisfiable
% 66.93/29.11 |-Branch two:
% 66.93/29.11 | (1248) aNaturalNumber0(xn) = all_26_2_37
% 66.93/29.11 | (1438) all_26_2_37 = all_14_2_11
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (572,1438) yields a new equation:
% 66.93/29.11 | (451) all_14_2_11 = 0
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (451,1438) yields a new equation:
% 66.93/29.11 | (572) all_26_2_37 = 0
% 66.93/29.11 |
% 66.93/29.11 | From (572) and (1248) follows:
% 66.93/29.11 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.11 |
% 66.93/29.11 +-Applying beta-rule and splitting (259), into two cases.
% 66.93/29.11 |-Branch one:
% 66.93/29.11 | (1442) ~ (aNaturalNumber0(xr) = all_26_0_35)
% 66.93/29.11 |
% 66.93/29.11 | From (594) and (1442) follows:
% 66.93/29.11 | (1287) ~ (aNaturalNumber0(xr) = 0)
% 66.93/29.11 |
% 66.93/29.11 | Using (10) and (1287) yields:
% 66.93/29.11 | (615) $false
% 66.93/29.11 |
% 66.93/29.11 |-The branch is then unsatisfiable
% 66.93/29.11 |-Branch two:
% 66.93/29.11 | (1445) aNaturalNumber0(xr) = all_26_0_35
% 66.93/29.11 | (1446) all_41_2_56 = all_26_0_35
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (253,1446) yields a new equation:
% 66.93/29.11 | (594) all_26_0_35 = 0
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (594,1446) yields a new equation:
% 66.93/29.11 | (253) all_41_2_56 = 0
% 66.93/29.11 |
% 66.93/29.11 | From (594) and (1445) follows:
% 66.93/29.11 | (10) aNaturalNumber0(xr) = 0
% 66.93/29.11 |
% 66.93/29.11 +-Applying beta-rule and splitting (222), into two cases.
% 66.93/29.11 |-Branch one:
% 66.93/29.11 | (1354) ~ (aNaturalNumber0(xn) = all_26_0_35)
% 66.93/29.11 |
% 66.93/29.11 | From (594) and (1354) follows:
% 66.93/29.11 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.11 |
% 66.93/29.11 | Using (53) and (1144) yields:
% 66.93/29.11 | (615) $false
% 66.93/29.11 |
% 66.93/29.11 |-The branch is then unsatisfiable
% 66.93/29.11 |-Branch two:
% 66.93/29.11 | (1357) aNaturalNumber0(xn) = all_26_0_35
% 66.93/29.11 | (594) all_26_0_35 = 0
% 66.93/29.11 |
% 66.93/29.11 | From (594) and (1357) follows:
% 66.93/29.11 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.11 |
% 66.93/29.11 +-Applying beta-rule and splitting (411), into two cases.
% 66.93/29.11 |-Branch one:
% 66.93/29.11 | (1370) ~ (aNaturalNumber0(xn) = all_36_1_51)
% 66.93/29.11 |
% 66.93/29.11 | From (555) and (1370) follows:
% 66.93/29.11 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.11 |
% 66.93/29.11 | Using (53) and (1144) yields:
% 66.93/29.11 | (615) $false
% 66.93/29.11 |
% 66.93/29.11 |-The branch is then unsatisfiable
% 66.93/29.11 |-Branch two:
% 66.93/29.11 | (1373) aNaturalNumber0(xn) = all_36_1_51
% 66.93/29.11 | (1460) all_36_1_51 = all_28_2_40
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (555,1460) yields a new equation:
% 66.93/29.11 | (514) all_28_2_40 = 0
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (514,1460) yields a new equation:
% 66.93/29.11 | (555) all_36_1_51 = 0
% 66.93/29.11 |
% 66.93/29.11 | From (555) and (1373) follows:
% 66.93/29.11 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.11 |
% 66.93/29.11 +-Applying beta-rule and splitting (298), into two cases.
% 66.93/29.11 |-Branch one:
% 66.93/29.11 | (1464) ~ (aNaturalNumber0(xp) = all_16_2_14)
% 66.93/29.11 |
% 66.93/29.11 | From (571) and (1464) follows:
% 66.93/29.11 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 66.93/29.11 |
% 66.93/29.11 | Using (12) and (1198) yields:
% 66.93/29.11 | (615) $false
% 66.93/29.11 |
% 66.93/29.11 |-The branch is then unsatisfiable
% 66.93/29.11 |-Branch two:
% 66.93/29.11 | (1467) aNaturalNumber0(xp) = all_16_2_14
% 66.93/29.11 | (1468) all_30_6_47 = all_16_2_14
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (1242,1468) yields a new equation:
% 66.93/29.11 | (571) all_16_2_14 = 0
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (571,1468) yields a new equation:
% 66.93/29.11 | (1242) all_30_6_47 = 0
% 66.93/29.11 |
% 66.93/29.11 | From (571) and (1467) follows:
% 66.93/29.11 | (12) aNaturalNumber0(xp) = 0
% 66.93/29.11 |
% 66.93/29.11 +-Applying beta-rule and splitting (470), into two cases.
% 66.93/29.11 |-Branch one:
% 66.93/29.11 | (1354) ~ (aNaturalNumber0(xn) = all_26_0_35)
% 66.93/29.11 |
% 66.93/29.11 | From (594) and (1354) follows:
% 66.93/29.11 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.11 |
% 66.93/29.11 | Using (53) and (1144) yields:
% 66.93/29.11 | (615) $false
% 66.93/29.11 |
% 66.93/29.11 |-The branch is then unsatisfiable
% 66.93/29.11 |-Branch two:
% 66.93/29.11 | (1357) aNaturalNumber0(xn) = all_26_0_35
% 66.93/29.11 | (1476) all_26_0_35 = all_12_2_8
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (594,1476) yields a new equation:
% 66.93/29.11 | (508) all_12_2_8 = 0
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (508,1476) yields a new equation:
% 66.93/29.11 | (594) all_26_0_35 = 0
% 66.93/29.11 |
% 66.93/29.11 | From (594) and (1357) follows:
% 66.93/29.11 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.11 |
% 66.93/29.11 +-Applying beta-rule and splitting (457), into two cases.
% 66.93/29.11 |-Branch one:
% 66.93/29.11 | (1480) ~ (aNaturalNumber0(xn) = all_16_2_14)
% 66.93/29.11 |
% 66.93/29.11 | From (571) and (1480) follows:
% 66.93/29.11 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.11 |
% 66.93/29.11 | Using (53) and (1144) yields:
% 66.93/29.11 | (615) $false
% 66.93/29.11 |
% 66.93/29.11 |-The branch is then unsatisfiable
% 66.93/29.11 |-Branch two:
% 66.93/29.11 | (1483) aNaturalNumber0(xn) = all_16_2_14
% 66.93/29.11 | (1484) all_16_2_14 = all_14_2_11
% 66.93/29.11 |
% 66.93/29.11 | From (571) and (1483) follows:
% 66.93/29.11 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.11 |
% 66.93/29.11 +-Applying beta-rule and splitting (461), into two cases.
% 66.93/29.11 |-Branch one:
% 66.93/29.11 | (1143) ~ (aNaturalNumber0(xn) = all_28_1_39)
% 66.93/29.11 |
% 66.93/29.11 | From (515) and (1143) follows:
% 66.93/29.11 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.11 |
% 66.93/29.11 | Using (53) and (1144) yields:
% 66.93/29.11 | (615) $false
% 66.93/29.11 |
% 66.93/29.11 |-The branch is then unsatisfiable
% 66.93/29.11 |-Branch two:
% 66.93/29.11 | (1146) aNaturalNumber0(xn) = all_28_1_39
% 66.93/29.11 | (1490) all_28_1_39 = all_14_2_11
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (515,1490) yields a new equation:
% 66.93/29.11 | (451) all_14_2_11 = 0
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (451,1490) yields a new equation:
% 66.93/29.11 | (515) all_28_1_39 = 0
% 66.93/29.11 |
% 66.93/29.11 | From (515) and (1146) follows:
% 66.93/29.11 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.11 |
% 66.93/29.11 +-Applying beta-rule and splitting (448), into two cases.
% 66.93/29.11 |-Branch one:
% 66.93/29.11 | (1182) ~ (aNaturalNumber0(xn) = all_22_1_28)
% 66.93/29.11 |
% 66.93/29.11 | From (499) and (1182) follows:
% 66.93/29.11 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.11 |
% 66.93/29.11 | Using (53) and (1144) yields:
% 66.93/29.11 | (615) $false
% 66.93/29.11 |
% 66.93/29.11 |-The branch is then unsatisfiable
% 66.93/29.11 |-Branch two:
% 66.93/29.11 | (1185) aNaturalNumber0(xn) = all_22_1_28
% 66.93/29.11 | (1498) all_22_1_28 = all_22_2_29
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (499,1498) yields a new equation:
% 66.93/29.11 | (510) all_22_2_29 = 0
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (510,1498) yields a new equation:
% 66.93/29.11 | (499) all_22_1_28 = 0
% 66.93/29.11 |
% 66.93/29.11 | From (499) and (1185) follows:
% 66.93/29.11 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.11 |
% 66.93/29.11 +-Applying beta-rule and splitting (248), into two cases.
% 66.93/29.11 |-Branch one:
% 66.93/29.11 | (1502) ~ (aNaturalNumber0(sz00) = all_12_0_6)
% 66.93/29.11 |
% 66.93/29.11 | From (570) and (1502) follows:
% 66.93/29.11 | (1503) ~ (aNaturalNumber0(sz00) = 0)
% 66.93/29.11 |
% 66.93/29.11 | Using (41) and (1503) yields:
% 66.93/29.11 | (615) $false
% 66.93/29.11 |
% 66.93/29.11 |-The branch is then unsatisfiable
% 66.93/29.11 |-Branch two:
% 66.93/29.11 | (1505) aNaturalNumber0(sz00) = all_12_0_6
% 66.93/29.11 | (570) all_12_0_6 = 0
% 66.93/29.11 |
% 66.93/29.11 | From (570) and (1505) follows:
% 66.93/29.11 | (41) aNaturalNumber0(sz00) = 0
% 66.93/29.11 |
% 66.93/29.11 +-Applying beta-rule and splitting (261), into two cases.
% 66.93/29.11 |-Branch one:
% 66.93/29.11 | (1508) ~ (aNaturalNumber0(xr) = all_12_0_6)
% 66.93/29.11 |
% 66.93/29.11 | From (570) and (1508) follows:
% 66.93/29.11 | (1287) ~ (aNaturalNumber0(xr) = 0)
% 66.93/29.11 |
% 66.93/29.11 | Using (10) and (1287) yields:
% 66.93/29.11 | (615) $false
% 66.93/29.11 |
% 66.93/29.11 |-The branch is then unsatisfiable
% 66.93/29.11 |-Branch two:
% 66.93/29.11 | (1511) aNaturalNumber0(xr) = all_12_0_6
% 66.93/29.11 | (1512) all_41_2_56 = all_12_0_6
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (253,1512) yields a new equation:
% 66.93/29.11 | (570) all_12_0_6 = 0
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (570,1512) yields a new equation:
% 66.93/29.11 | (253) all_41_2_56 = 0
% 66.93/29.11 |
% 66.93/29.11 | From (570) and (1511) follows:
% 66.93/29.11 | (10) aNaturalNumber0(xr) = 0
% 66.93/29.11 |
% 66.93/29.11 +-Applying beta-rule and splitting (345), into two cases.
% 66.93/29.11 |-Branch one:
% 66.93/29.11 | (1516) ~ (aNaturalNumber0(xm) = all_36_1_51)
% 66.93/29.11 |
% 66.93/29.11 | From (555) and (1516) follows:
% 66.93/29.11 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 66.93/29.11 |
% 66.93/29.11 | Using (36) and (1191) yields:
% 66.93/29.11 | (615) $false
% 66.93/29.11 |
% 66.93/29.11 |-The branch is then unsatisfiable
% 66.93/29.11 |-Branch two:
% 66.93/29.11 | (1519) aNaturalNumber0(xm) = all_36_1_51
% 66.93/29.11 | (1520) all_36_1_51 = all_28_1_39
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (555,1520) yields a new equation:
% 66.93/29.11 | (515) all_28_1_39 = 0
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (515,1520) yields a new equation:
% 66.93/29.11 | (555) all_36_1_51 = 0
% 66.93/29.11 |
% 66.93/29.11 | From (555) and (1519) follows:
% 66.93/29.11 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.11 |
% 66.93/29.11 +-Applying beta-rule and splitting (265), into two cases.
% 66.93/29.11 |-Branch one:
% 66.93/29.11 | (1524) ~ (aNaturalNumber0(xr) = all_36_1_51)
% 66.93/29.11 |
% 66.93/29.11 | From (555) and (1524) follows:
% 66.93/29.11 | (1287) ~ (aNaturalNumber0(xr) = 0)
% 66.93/29.11 |
% 66.93/29.11 | Using (10) and (1287) yields:
% 66.93/29.11 | (615) $false
% 66.93/29.11 |
% 66.93/29.11 |-The branch is then unsatisfiable
% 66.93/29.11 |-Branch two:
% 66.93/29.11 | (1527) aNaturalNumber0(xr) = all_36_1_51
% 66.93/29.11 | (1528) all_36_1_51 = all_36_3_53
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (555,1528) yields a new equation:
% 66.93/29.11 | (480) all_36_3_53 = 0
% 66.93/29.11 |
% 66.93/29.11 | Combining equations (480,1528) yields a new equation:
% 66.93/29.11 | (555) all_36_1_51 = 0
% 66.93/29.11 |
% 66.93/29.11 | From (555) and (1527) follows:
% 66.93/29.11 | (10) aNaturalNumber0(xr) = 0
% 66.93/29.11 |
% 66.93/29.11 +-Applying beta-rule and splitting (266), into two cases.
% 66.93/29.11 |-Branch one:
% 66.93/29.11 | (1532) ~ (aNaturalNumber0(xr) = all_22_0_27)
% 66.93/29.11 |
% 66.93/29.11 | From (554) and (1532) follows:
% 66.93/29.11 | (1287) ~ (aNaturalNumber0(xr) = 0)
% 66.93/29.12 |
% 66.93/29.12 | Using (10) and (1287) yields:
% 66.93/29.12 | (615) $false
% 66.93/29.12 |
% 66.93/29.12 |-The branch is then unsatisfiable
% 66.93/29.12 |-Branch two:
% 66.93/29.12 | (1535) aNaturalNumber0(xr) = all_22_0_27
% 66.93/29.12 | (1536) all_36_3_53 = all_22_0_27
% 66.93/29.12 |
% 66.93/29.12 | Combining equations (480,1536) yields a new equation:
% 66.93/29.12 | (554) all_22_0_27 = 0
% 66.93/29.12 |
% 66.93/29.12 | Combining equations (554,1536) yields a new equation:
% 66.93/29.12 | (480) all_36_3_53 = 0
% 66.93/29.12 |
% 66.93/29.12 | From (554) and (1535) follows:
% 66.93/29.12 | (10) aNaturalNumber0(xr) = 0
% 66.93/29.12 |
% 66.93/29.12 +-Applying beta-rule and splitting (297), into two cases.
% 66.93/29.12 |-Branch one:
% 66.93/29.12 | (1205) ~ (aNaturalNumber0(xp) = all_26_2_37)
% 66.93/29.12 |
% 66.93/29.12 | From (572) and (1205) follows:
% 66.93/29.12 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 66.93/29.12 |
% 66.93/29.12 | Using (12) and (1198) yields:
% 66.93/29.12 | (615) $false
% 66.93/29.12 |
% 66.93/29.12 |-The branch is then unsatisfiable
% 66.93/29.12 |-Branch two:
% 66.93/29.12 | (1208) aNaturalNumber0(xp) = all_26_2_37
% 66.93/29.12 | (1544) all_30_6_47 = all_26_2_37
% 66.93/29.12 |
% 66.93/29.12 | Combining equations (1242,1544) yields a new equation:
% 66.93/29.12 | (572) all_26_2_37 = 0
% 66.93/29.12 |
% 66.93/29.12 | Combining equations (572,1544) yields a new equation:
% 66.93/29.12 | (1242) all_30_6_47 = 0
% 66.93/29.12 |
% 66.93/29.12 | From (572) and (1208) follows:
% 66.93/29.12 | (12) aNaturalNumber0(xp) = 0
% 66.93/29.12 |
% 66.93/29.12 +-Applying beta-rule and splitting (363), into two cases.
% 66.93/29.12 |-Branch one:
% 66.93/29.12 | (1548) ~ (aNaturalNumber0(sz10) = all_22_1_28)
% 66.93/29.12 |
% 66.93/29.12 | From (499) and (1548) follows:
% 66.93/29.12 | (1252) ~ (aNaturalNumber0(sz10) = 0)
% 66.93/29.12 |
% 66.93/29.12 | Using (16) and (1252) yields:
% 66.93/29.12 | (615) $false
% 66.93/29.12 |
% 66.93/29.12 |-The branch is then unsatisfiable
% 66.93/29.12 |-Branch two:
% 66.93/29.12 | (1551) aNaturalNumber0(sz10) = all_22_1_28
% 66.93/29.12 | (499) all_22_1_28 = 0
% 66.93/29.12 |
% 66.93/29.12 | From (499) and (1551) follows:
% 66.93/29.12 | (16) aNaturalNumber0(sz10) = 0
% 66.93/29.12 |
% 66.93/29.12 +-Applying beta-rule and splitting (305), into two cases.
% 66.93/29.12 |-Branch one:
% 66.93/29.12 | (1554) ~ (aNaturalNumber0(xp) = all_22_0_27)
% 66.93/29.12 |
% 66.93/29.12 | From (554) and (1554) follows:
% 66.93/29.12 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 66.93/29.12 |
% 66.93/29.12 | Using (12) and (1198) yields:
% 66.93/29.12 | (615) $false
% 66.93/29.12 |
% 66.93/29.12 |-The branch is then unsatisfiable
% 66.93/29.12 |-Branch two:
% 66.93/29.12 | (1557) aNaturalNumber0(xp) = all_22_0_27
% 66.93/29.12 | (1558) all_26_1_36 = all_22_0_27
% 66.93/29.12 |
% 66.93/29.12 | Combining equations (303,1558) yields a new equation:
% 66.93/29.12 | (554) all_22_0_27 = 0
% 66.93/29.12 |
% 66.93/29.12 | Combining equations (554,1558) yields a new equation:
% 66.93/29.12 | (303) all_26_1_36 = 0
% 66.93/29.12 |
% 66.93/29.12 | From (554) and (1557) follows:
% 66.93/29.12 | (12) aNaturalNumber0(xp) = 0
% 66.93/29.12 |
% 66.93/29.12 +-Applying beta-rule and splitting (236), into two cases.
% 66.93/29.12 |-Branch one:
% 66.93/29.12 | (1562) ~ (aNaturalNumber0(xm) = all_16_2_14)
% 66.93/29.12 |
% 66.93/29.12 | From (571) and (1562) follows:
% 66.93/29.12 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 66.93/29.12 |
% 66.93/29.12 | Using (36) and (1191) yields:
% 66.93/29.12 | (615) $false
% 66.93/29.12 |
% 66.93/29.12 |-The branch is then unsatisfiable
% 66.93/29.12 |-Branch two:
% 66.93/29.12 | (1565) aNaturalNumber0(xm) = all_16_2_14
% 66.93/29.12 | (571) all_16_2_14 = 0
% 66.93/29.12 |
% 66.93/29.12 | From (571) and (1565) follows:
% 66.93/29.12 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.12 |
% 66.93/29.12 +-Applying beta-rule and splitting (405), into two cases.
% 66.93/29.12 |-Branch one:
% 66.93/29.12 | (1568) ~ (aNaturalNumber0(xn) = all_24_3_33)
% 66.93/29.12 |
% 66.93/29.12 | From (483) and (1568) follows:
% 66.93/29.12 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.12 |
% 66.93/29.12 | Using (53) and (1144) yields:
% 66.93/29.12 | (615) $false
% 66.93/29.12 |
% 66.93/29.12 |-The branch is then unsatisfiable
% 66.93/29.12 |-Branch two:
% 66.93/29.12 | (1571) aNaturalNumber0(xn) = all_24_3_33
% 66.93/29.12 | (1572) all_30_8_49 = all_24_3_33
% 66.93/29.12 |
% 66.93/29.12 | Combining equations (516,1572) yields a new equation:
% 66.93/29.12 | (483) all_24_3_33 = 0
% 66.93/29.12 |
% 66.93/29.12 | Combining equations (483,1572) yields a new equation:
% 66.93/29.12 | (516) all_30_8_49 = 0
% 66.93/29.12 |
% 66.93/29.12 | From (483) and (1571) follows:
% 66.93/29.12 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.12 |
% 66.93/29.12 +-Applying beta-rule and splitting (398), into two cases.
% 66.93/29.12 |-Branch one:
% 66.93/29.12 | (1480) ~ (aNaturalNumber0(xn) = all_16_2_14)
% 66.93/29.12 |
% 66.93/29.12 | From (571) and (1480) follows:
% 66.93/29.12 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.12 |
% 66.93/29.12 | Using (53) and (1144) yields:
% 66.93/29.12 | (615) $false
% 66.93/29.12 |
% 66.93/29.12 |-The branch is then unsatisfiable
% 66.93/29.12 |-Branch two:
% 66.93/29.12 | (1483) aNaturalNumber0(xn) = all_16_2_14
% 66.93/29.12 | (1580) all_30_8_49 = all_16_2_14
% 66.93/29.12 |
% 66.93/29.12 | Combining equations (516,1580) yields a new equation:
% 66.93/29.12 | (571) all_16_2_14 = 0
% 66.93/29.12 |
% 66.93/29.12 | Combining equations (571,1580) yields a new equation:
% 66.93/29.12 | (516) all_30_8_49 = 0
% 66.93/29.12 |
% 66.93/29.12 | From (571) and (1483) follows:
% 66.93/29.12 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.12 |
% 66.93/29.12 +-Applying beta-rule and splitting (250), into two cases.
% 66.93/29.12 |-Branch one:
% 66.93/29.12 | (1257) ~ (aNaturalNumber0(all_0_5_5) = all_22_0_27)
% 66.93/29.12 |
% 66.93/29.12 | From (554) and (1257) follows:
% 66.93/29.12 | (1258) ~ (aNaturalNumber0(all_0_5_5) = 0)
% 66.93/29.12 |
% 66.93/29.12 | Using (573) and (1258) yields:
% 66.93/29.12 | (615) $false
% 66.93/29.12 |
% 66.93/29.12 |-The branch is then unsatisfiable
% 66.93/29.12 |-Branch two:
% 66.93/29.12 | (1260) aNaturalNumber0(all_0_5_5) = all_22_0_27
% 66.93/29.12 | (1588) all_22_0_27 = all_12_0_6
% 66.93/29.12 |
% 66.93/29.12 | Combining equations (554,1588) yields a new equation:
% 66.93/29.12 | (570) all_12_0_6 = 0
% 66.93/29.12 |
% 66.93/29.12 | Combining equations (570,1588) yields a new equation:
% 66.93/29.12 | (554) all_22_0_27 = 0
% 66.93/29.12 |
% 66.93/29.12 | From (554) and (1260) follows:
% 66.93/29.12 | (573) aNaturalNumber0(all_0_5_5) = 0
% 66.93/29.12 |
% 66.93/29.12 +-Applying beta-rule and splitting (397), into two cases.
% 66.93/29.12 |-Branch one:
% 66.93/29.12 | (1245) ~ (aNaturalNumber0(xn) = all_26_2_37)
% 66.93/29.12 |
% 66.93/29.12 | From (572) and (1245) follows:
% 66.93/29.12 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.12 |
% 66.93/29.12 | Using (53) and (1144) yields:
% 66.93/29.12 | (615) $false
% 66.93/29.12 |
% 66.93/29.12 |-The branch is then unsatisfiable
% 66.93/29.12 |-Branch two:
% 66.93/29.12 | (1248) aNaturalNumber0(xn) = all_26_2_37
% 66.93/29.12 | (1596) all_30_8_49 = all_26_2_37
% 66.93/29.12 |
% 66.93/29.12 | Combining equations (516,1596) yields a new equation:
% 66.93/29.12 | (572) all_26_2_37 = 0
% 66.93/29.12 |
% 66.93/29.12 | From (572) and (1248) follows:
% 66.93/29.12 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.12 |
% 66.93/29.12 +-Applying beta-rule and splitting (272), into two cases.
% 66.93/29.12 |-Branch one:
% 66.93/29.12 | (974) ~ (aNaturalNumber0(xk) = 0)
% 66.93/29.12 |
% 66.93/29.12 | Using (972) and (974) yields:
% 66.93/29.12 | (615) $false
% 66.93/29.12 |
% 66.93/29.12 |-The branch is then unsatisfiable
% 66.93/29.12 |-Branch two:
% 66.93/29.12 | (972) aNaturalNumber0(xk) = 0
% 66.93/29.12 | (980) all_41_1_55 = 0
% 66.93/29.12 |
% 66.93/29.12 +-Applying beta-rule and splitting (233), into two cases.
% 66.93/29.12 |-Branch one:
% 66.93/29.12 | (1603) ~ (aNaturalNumber0(all_0_5_5) = all_26_0_35)
% 66.93/29.12 |
% 66.93/29.12 | From (594) and (1603) follows:
% 66.93/29.12 | (1258) ~ (aNaturalNumber0(all_0_5_5) = 0)
% 66.93/29.12 |
% 66.93/29.12 | Using (573) and (1258) yields:
% 66.93/29.12 | (615) $false
% 66.93/29.12 |
% 66.93/29.12 |-The branch is then unsatisfiable
% 66.93/29.12 |-Branch two:
% 66.93/29.12 | (1606) aNaturalNumber0(all_0_5_5) = all_26_0_35
% 66.93/29.12 | (1607) all_26_0_35 = all_26_2_37
% 66.93/29.12 |
% 66.93/29.12 | Combining equations (594,1607) yields a new equation:
% 66.93/29.12 | (572) all_26_2_37 = 0
% 66.93/29.12 |
% 66.93/29.12 | Combining equations (572,1607) yields a new equation:
% 66.93/29.12 | (594) all_26_0_35 = 0
% 66.93/29.12 |
% 66.93/29.12 | From (594) and (1606) follows:
% 66.93/29.12 | (573) aNaturalNumber0(all_0_5_5) = 0
% 66.93/29.12 |
% 66.93/29.12 +-Applying beta-rule and splitting (375), into two cases.
% 66.93/29.12 |-Branch one:
% 66.93/29.12 | (1516) ~ (aNaturalNumber0(xm) = all_36_1_51)
% 66.93/29.12 |
% 66.93/29.12 | From (555) and (1516) follows:
% 66.93/29.12 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 66.93/29.12 |
% 66.93/29.12 | Using (36) and (1191) yields:
% 66.93/29.12 | (615) $false
% 66.93/29.12 |
% 66.93/29.12 |-The branch is then unsatisfiable
% 66.93/29.12 |-Branch two:
% 66.93/29.12 | (1519) aNaturalNumber0(xm) = all_36_1_51
% 66.93/29.12 | (1615) all_36_1_51 = all_14_1_10
% 66.93/29.12 |
% 66.93/29.12 | Combining equations (555,1615) yields a new equation:
% 66.93/29.12 | (503) all_14_1_10 = 0
% 66.93/29.12 |
% 66.93/29.12 | Combining equations (503,1615) yields a new equation:
% 66.93/29.12 | (555) all_36_1_51 = 0
% 66.93/29.12 |
% 66.93/29.12 | From (555) and (1519) follows:
% 66.93/29.12 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.12 |
% 66.93/29.12 +-Applying beta-rule and splitting (436), into two cases.
% 66.93/29.12 |-Branch one:
% 66.93/29.12 | (1619) ~ (aNaturalNumber0(sz00) = all_22_2_29)
% 66.93/29.12 |
% 66.93/29.12 | From (510) and (1619) follows:
% 66.93/29.12 | (1503) ~ (aNaturalNumber0(sz00) = 0)
% 66.93/29.12 |
% 66.93/29.12 | Using (41) and (1503) yields:
% 66.93/29.12 | (615) $false
% 66.93/29.12 |
% 66.93/29.12 |-The branch is then unsatisfiable
% 66.93/29.12 |-Branch two:
% 66.93/29.12 | (1622) aNaturalNumber0(sz00) = all_22_2_29
% 66.93/29.12 | (510) all_22_2_29 = 0
% 66.93/29.12 |
% 66.93/29.12 | From (510) and (1622) follows:
% 66.93/29.12 | (41) aNaturalNumber0(sz00) = 0
% 66.93/29.12 |
% 66.93/29.12 +-Applying beta-rule and splitting (444), into two cases.
% 66.93/29.12 |-Branch one:
% 66.93/29.12 | (1229) ~ (aNaturalNumber0(xn) = all_36_2_52)
% 66.93/29.12 |
% 66.93/29.12 | From (979) and (1229) follows:
% 66.93/29.12 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.12 |
% 66.93/29.12 | Using (53) and (1144) yields:
% 66.93/29.12 | (615) $false
% 66.93/29.12 |
% 66.93/29.12 |-The branch is then unsatisfiable
% 66.93/29.12 |-Branch two:
% 66.93/29.12 | (1232) aNaturalNumber0(xn) = all_36_2_52
% 66.93/29.12 | (1629) all_36_2_52 = all_22_2_29
% 66.93/29.12 |
% 66.93/29.12 | Combining equations (979,1629) yields a new equation:
% 66.93/29.12 | (510) all_22_2_29 = 0
% 66.93/29.12 |
% 66.93/29.12 | Combining equations (510,1629) yields a new equation:
% 66.93/29.12 | (979) all_36_2_52 = 0
% 66.93/29.12 |
% 66.93/29.12 | From (979) and (1232) follows:
% 66.93/29.12 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.12 |
% 66.93/29.12 +-Applying beta-rule and splitting (415), into two cases.
% 66.93/29.12 |-Branch one:
% 66.93/29.12 | (1480) ~ (aNaturalNumber0(xn) = all_16_2_14)
% 66.93/29.12 |
% 66.93/29.12 | From (571) and (1480) follows:
% 66.93/29.12 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.12 |
% 66.93/29.12 | Using (53) and (1144) yields:
% 66.93/29.12 | (615) $false
% 66.93/29.12 |
% 66.93/29.12 |-The branch is then unsatisfiable
% 66.93/29.12 |-Branch two:
% 66.93/29.12 | (1483) aNaturalNumber0(xn) = all_16_2_14
% 66.93/29.12 | (1637) all_28_2_40 = all_16_2_14
% 66.93/29.13 |
% 66.93/29.13 | Combining equations (514,1637) yields a new equation:
% 66.93/29.13 | (571) all_16_2_14 = 0
% 66.93/29.13 |
% 66.93/29.13 | From (571) and (1483) follows:
% 66.93/29.13 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.13 |
% 66.93/29.13 +-Applying beta-rule and splitting (332), into two cases.
% 66.93/29.13 |-Branch one:
% 66.93/29.13 | (1166) ~ (aNaturalNumber0(xn) = all_30_7_48)
% 66.93/29.13 |
% 66.93/29.13 | From (331) and (1166) follows:
% 66.93/29.13 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.13 |
% 66.93/29.13 | Using (53) and (1144) yields:
% 66.93/29.13 | (615) $false
% 66.93/29.13 |
% 66.93/29.13 |-The branch is then unsatisfiable
% 66.93/29.13 |-Branch two:
% 66.93/29.13 | (1169) aNaturalNumber0(xn) = all_30_7_48
% 66.93/29.13 | (331) all_30_7_48 = 0
% 66.93/29.13 |
% 66.93/29.13 | From (331) and (1169) follows:
% 66.93/29.13 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.13 |
% 66.93/29.13 +-Applying beta-rule and splitting (246), into two cases.
% 66.93/29.13 |-Branch one:
% 66.93/29.13 | (1646) ~ (aNaturalNumber0(xn) = all_12_0_6)
% 66.93/29.13 |
% 66.93/29.13 | From (570) and (1646) follows:
% 66.93/29.13 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.13 |
% 66.93/29.13 | Using (53) and (1144) yields:
% 66.93/29.13 | (615) $false
% 66.93/29.13 |
% 66.93/29.13 |-The branch is then unsatisfiable
% 66.93/29.13 |-Branch two:
% 66.93/29.13 | (1649) aNaturalNumber0(xn) = all_12_0_6
% 66.93/29.13 | (570) all_12_0_6 = 0
% 66.93/29.13 |
% 66.93/29.13 | From (570) and (1649) follows:
% 66.93/29.13 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.13 |
% 66.93/29.13 +-Applying beta-rule and splitting (349), into two cases.
% 66.93/29.13 |-Branch one:
% 66.93/29.13 | (1338) ~ (aNaturalNumber0(xm) = all_36_2_52)
% 66.93/29.13 |
% 66.93/29.13 | From (979) and (1338) follows:
% 66.93/29.13 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 66.93/29.13 |
% 66.93/29.13 | Using (36) and (1191) yields:
% 66.93/29.13 | (615) $false
% 66.93/29.13 |
% 66.93/29.13 |-The branch is then unsatisfiable
% 66.93/29.13 |-Branch two:
% 66.93/29.13 | (1341) aNaturalNumber0(xm) = all_36_2_52
% 66.93/29.13 | (1656) all_36_2_52 = all_28_1_39
% 66.93/29.13 |
% 66.93/29.13 | Combining equations (979,1656) yields a new equation:
% 66.93/29.13 | (515) all_28_1_39 = 0
% 66.93/29.13 |
% 66.93/29.13 | Combining equations (515,1656) yields a new equation:
% 66.93/29.13 | (979) all_36_2_52 = 0
% 66.93/29.13 |
% 66.93/29.13 | From (979) and (1341) follows:
% 66.93/29.13 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.13 |
% 66.93/29.13 +-Applying beta-rule and splitting (307), into two cases.
% 66.93/29.13 |-Branch one:
% 66.93/29.13 | (1205) ~ (aNaturalNumber0(xp) = all_26_2_37)
% 66.93/29.13 |
% 66.93/29.13 | From (572) and (1205) follows:
% 66.93/29.13 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 66.93/29.13 |
% 66.93/29.13 | Using (12) and (1198) yields:
% 66.93/29.13 | (615) $false
% 66.93/29.13 |
% 66.93/29.13 |-The branch is then unsatisfiable
% 66.93/29.13 |-Branch two:
% 66.93/29.13 | (1208) aNaturalNumber0(xp) = all_26_2_37
% 66.93/29.13 | (1664) all_26_1_36 = all_26_2_37
% 66.93/29.13 |
% 66.93/29.13 | Combining equations (303,1664) yields a new equation:
% 66.93/29.13 | (572) all_26_2_37 = 0
% 66.93/29.13 |
% 66.93/29.13 | From (572) and (1208) follows:
% 66.93/29.13 | (12) aNaturalNumber0(xp) = 0
% 66.93/29.13 |
% 66.93/29.13 +-Applying beta-rule and splitting (227), into two cases.
% 66.93/29.13 |-Branch one:
% 66.93/29.13 | (1386) ~ (aNaturalNumber0(xm) = all_26_2_37)
% 66.93/29.13 |
% 66.93/29.13 | From (572) and (1386) follows:
% 66.93/29.13 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 66.93/29.13 |
% 66.93/29.13 | Using (36) and (1191) yields:
% 66.93/29.13 | (615) $false
% 66.93/29.13 |
% 66.93/29.13 |-The branch is then unsatisfiable
% 66.93/29.13 |-Branch two:
% 66.93/29.13 | (1389) aNaturalNumber0(xm) = all_26_2_37
% 66.93/29.13 | (572) all_26_2_37 = 0
% 66.93/29.13 |
% 66.93/29.13 | From (572) and (1389) follows:
% 66.93/29.13 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.13 |
% 66.93/29.13 +-Applying beta-rule and splitting (460), into two cases.
% 66.93/29.13 |-Branch one:
% 66.93/29.13 | (1673) ~ (aNaturalNumber0(xn) = all_41_1_55)
% 66.93/29.13 |
% 66.93/29.13 | From (980) and (1673) follows:
% 66.93/29.13 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.13 |
% 66.93/29.13 | Using (53) and (1144) yields:
% 66.93/29.13 | (615) $false
% 66.93/29.13 |
% 66.93/29.13 |-The branch is then unsatisfiable
% 66.93/29.13 |-Branch two:
% 66.93/29.13 | (1676) aNaturalNumber0(xn) = all_41_1_55
% 66.93/29.13 | (1677) all_41_1_55 = all_14_2_11
% 66.93/29.13 |
% 66.93/29.13 | Combining equations (980,1677) yields a new equation:
% 66.93/29.13 | (451) all_14_2_11 = 0
% 66.93/29.13 |
% 66.93/29.13 | Combining equations (451,1677) yields a new equation:
% 66.93/29.13 | (980) all_41_1_55 = 0
% 66.93/29.13 |
% 66.93/29.13 | From (980) and (1676) follows:
% 66.93/29.13 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.13 |
% 66.93/29.13 +-Applying beta-rule and splitting (243), into two cases.
% 66.93/29.13 |-Branch one:
% 66.93/29.13 | (1508) ~ (aNaturalNumber0(xr) = all_12_0_6)
% 66.93/29.13 |
% 66.93/29.13 | From (570) and (1508) follows:
% 66.93/29.13 | (1287) ~ (aNaturalNumber0(xr) = 0)
% 66.93/29.13 |
% 66.93/29.13 | Using (10) and (1287) yields:
% 66.93/29.13 | (615) $false
% 66.93/29.13 |
% 66.93/29.13 |-The branch is then unsatisfiable
% 66.93/29.13 |-Branch two:
% 66.93/29.13 | (1511) aNaturalNumber0(xr) = all_12_0_6
% 66.93/29.13 | (570) all_12_0_6 = 0
% 66.93/29.13 |
% 66.93/29.13 | From (570) and (1511) follows:
% 66.93/29.13 | (10) aNaturalNumber0(xr) = 0
% 66.93/29.13 |
% 66.93/29.13 +-Applying beta-rule and splitting (312), into two cases.
% 66.93/29.13 |-Branch one:
% 66.93/29.13 | (1280) ~ (aNaturalNumber0(xp) = all_36_2_52)
% 66.93/29.13 |
% 66.93/29.13 | From (979) and (1280) follows:
% 66.93/29.13 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 66.93/29.13 |
% 66.93/29.13 | Using (12) and (1198) yields:
% 66.93/29.13 | (615) $false
% 66.93/29.13 |
% 66.93/29.13 |-The branch is then unsatisfiable
% 66.93/29.13 |-Branch two:
% 66.93/29.13 | (1283) aNaturalNumber0(xp) = all_36_2_52
% 66.93/29.13 | (1691) all_36_2_52 = all_26_1_36
% 66.93/29.13 |
% 66.93/29.13 | Combining equations (979,1691) yields a new equation:
% 66.93/29.13 | (303) all_26_1_36 = 0
% 66.93/29.13 |
% 66.93/29.13 | Combining equations (303,1691) yields a new equation:
% 66.93/29.13 | (979) all_36_2_52 = 0
% 66.93/29.13 |
% 66.93/29.13 | From (979) and (1283) follows:
% 66.93/29.13 | (12) aNaturalNumber0(xp) = 0
% 66.93/29.13 |
% 66.93/29.13 +-Applying beta-rule and splitting (424), into two cases.
% 66.93/29.13 |-Branch one:
% 66.93/29.13 | (1695) ~ (aNaturalNumber0(sz10) = all_24_4_34)
% 66.93/29.13 |
% 66.93/29.13 | From (511) and (1695) follows:
% 66.93/29.13 | (1252) ~ (aNaturalNumber0(sz10) = 0)
% 66.93/29.13 |
% 66.93/29.13 | Using (16) and (1252) yields:
% 66.93/29.13 | (615) $false
% 66.93/29.13 |
% 66.93/29.13 |-The branch is then unsatisfiable
% 66.93/29.13 |-Branch two:
% 66.93/29.13 | (1698) aNaturalNumber0(sz10) = all_24_4_34
% 66.93/29.13 | (511) all_24_4_34 = 0
% 66.93/29.13 |
% 66.93/29.13 | From (511) and (1698) follows:
% 66.93/29.13 | (16) aNaturalNumber0(sz10) = 0
% 66.93/29.13 |
% 66.93/29.13 +-Applying beta-rule and splitting (402), into two cases.
% 66.93/29.13 |-Branch one:
% 66.93/29.13 | (1229) ~ (aNaturalNumber0(xn) = all_36_2_52)
% 66.93/29.13 |
% 66.93/29.13 | From (979) and (1229) follows:
% 66.93/29.13 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 66.93/29.13 |
% 66.93/29.13 | Using (53) and (1144) yields:
% 66.93/29.13 | (615) $false
% 66.93/29.13 |
% 66.93/29.13 |-The branch is then unsatisfiable
% 66.93/29.13 |-Branch two:
% 66.93/29.13 | (1232) aNaturalNumber0(xn) = all_36_2_52
% 66.93/29.13 | (1705) all_36_2_52 = all_30_8_49
% 66.93/29.13 |
% 66.93/29.13 | Combining equations (979,1705) yields a new equation:
% 66.93/29.13 | (516) all_30_8_49 = 0
% 66.93/29.13 |
% 66.93/29.13 | Combining equations (516,1705) yields a new equation:
% 66.93/29.13 | (979) all_36_2_52 = 0
% 66.93/29.13 |
% 66.93/29.13 | From (979) and (1232) follows:
% 66.93/29.13 | (53) aNaturalNumber0(xn) = 0
% 66.93/29.13 |
% 66.93/29.13 +-Applying beta-rule and splitting (283), into two cases.
% 66.93/29.13 |-Branch one:
% 66.93/29.13 | (974) ~ (aNaturalNumber0(xk) = 0)
% 66.93/29.13 |
% 66.93/29.13 | Using (972) and (974) yields:
% 66.93/29.13 | (615) $false
% 66.93/29.13 |
% 66.93/29.13 |-The branch is then unsatisfiable
% 66.93/29.13 |-Branch two:
% 66.93/29.13 | (972) aNaturalNumber0(xk) = 0
% 66.93/29.13 | (979) all_36_2_52 = 0
% 66.93/29.13 |
% 66.93/29.13 +-Applying beta-rule and splitting (368), into two cases.
% 66.93/29.13 |-Branch one:
% 66.93/29.13 | (1562) ~ (aNaturalNumber0(xm) = all_16_2_14)
% 66.93/29.13 |
% 66.93/29.13 | From (571) and (1562) follows:
% 66.93/29.13 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 66.93/29.13 |
% 66.93/29.13 | Using (36) and (1191) yields:
% 66.93/29.13 | (615) $false
% 66.93/29.13 |
% 66.93/29.13 |-The branch is then unsatisfiable
% 66.93/29.13 |-Branch two:
% 66.93/29.13 | (1565) aNaturalNumber0(xm) = all_16_2_14
% 66.93/29.13 | (1717) all_22_1_28 = all_16_2_14
% 66.93/29.13 |
% 66.93/29.13 | Combining equations (499,1717) yields a new equation:
% 66.93/29.13 | (571) all_16_2_14 = 0
% 66.93/29.13 |
% 66.93/29.13 | From (571) and (1565) follows:
% 66.93/29.13 | (36) aNaturalNumber0(xm) = 0
% 66.93/29.13 |
% 66.93/29.13 +-Applying beta-rule and splitting (269), into two cases.
% 66.93/29.13 |-Branch one:
% 66.93/29.13 | (1720) ~ (aNaturalNumber0(xr) = all_16_2_14)
% 66.93/29.13 |
% 66.93/29.13 | From (571) and (1720) follows:
% 66.93/29.13 | (1287) ~ (aNaturalNumber0(xr) = 0)
% 66.93/29.13 |
% 66.93/29.13 | Using (10) and (1287) yields:
% 66.93/29.13 | (615) $false
% 66.93/29.13 |
% 66.93/29.13 |-The branch is then unsatisfiable
% 66.93/29.13 |-Branch two:
% 66.93/29.13 | (1723) aNaturalNumber0(xr) = all_16_2_14
% 66.93/29.13 | (1724) all_36_3_53 = all_16_2_14
% 66.93/29.13 |
% 66.93/29.13 | Combining equations (480,1724) yields a new equation:
% 66.93/29.13 | (571) all_16_2_14 = 0
% 66.93/29.13 |
% 66.93/29.13 | Combining equations (571,1724) yields a new equation:
% 66.93/29.13 | (480) all_36_3_53 = 0
% 66.93/29.13 |
% 66.93/29.13 | From (571) and (1723) follows:
% 66.93/29.13 | (10) aNaturalNumber0(xr) = 0
% 66.93/29.13 |
% 66.93/29.13 +-Applying beta-rule and splitting (401), into two cases.
% 66.93/29.13 |-Branch one:
% 66.93/29.13 | (1728) ~ (aNaturalNumber0(xn) = all_36_3_53)
% 66.93/29.13 |
% 66.93/29.13 | From (480) and (1728) follows:
% 66.93/29.13 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.13 |
% 67.33/29.13 | Using (53) and (1144) yields:
% 67.33/29.13 | (615) $false
% 67.33/29.13 |
% 67.33/29.13 |-The branch is then unsatisfiable
% 67.33/29.13 |-Branch two:
% 67.33/29.13 | (1731) aNaturalNumber0(xn) = all_36_3_53
% 67.33/29.13 | (1732) all_36_3_53 = all_30_8_49
% 67.33/29.13 |
% 67.33/29.13 | Combining equations (480,1732) yields a new equation:
% 67.33/29.13 | (516) all_30_8_49 = 0
% 67.33/29.13 |
% 67.33/29.13 | Combining equations (516,1732) yields a new equation:
% 67.33/29.13 | (480) all_36_3_53 = 0
% 67.33/29.13 |
% 67.33/29.13 | From (480) and (1731) follows:
% 67.33/29.13 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.13 |
% 67.33/29.13 +-Applying beta-rule and splitting (287), into two cases.
% 67.33/29.13 |-Branch one:
% 67.33/29.13 | (1265) ~ (aNaturalNumber0(xk) = all_22_0_27)
% 67.33/29.13 |
% 67.33/29.13 | From (554) and (1265) follows:
% 67.33/29.13 | (974) ~ (aNaturalNumber0(xk) = 0)
% 67.33/29.14 |
% 67.33/29.14 | Using (972) and (974) yields:
% 67.33/29.14 | (615) $false
% 67.33/29.14 |
% 67.33/29.14 |-The branch is then unsatisfiable
% 67.33/29.14 |-Branch two:
% 67.33/29.14 | (1268) aNaturalNumber0(xk) = all_22_0_27
% 67.33/29.14 | (1740) all_36_2_52 = all_22_0_27
% 67.33/29.14 |
% 67.33/29.14 | Combining equations (979,1740) yields a new equation:
% 67.33/29.14 | (554) all_22_0_27 = 0
% 67.33/29.14 |
% 67.33/29.14 | Combining equations (554,1740) yields a new equation:
% 67.33/29.14 | (979) all_36_2_52 = 0
% 67.33/29.14 |
% 67.33/29.14 | From (554) and (1268) follows:
% 67.33/29.14 | (972) aNaturalNumber0(xk) = 0
% 67.33/29.14 |
% 67.33/29.14 +-Applying beta-rule and splitting (471), into two cases.
% 67.33/29.14 |-Branch one:
% 67.33/29.14 | (1245) ~ (aNaturalNumber0(xn) = all_26_2_37)
% 67.33/29.14 |
% 67.33/29.14 | From (572) and (1245) follows:
% 67.33/29.14 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.14 |
% 67.33/29.14 | Using (53) and (1144) yields:
% 67.33/29.14 | (615) $false
% 67.33/29.14 |
% 67.33/29.14 |-The branch is then unsatisfiable
% 67.33/29.14 |-Branch two:
% 67.33/29.14 | (1248) aNaturalNumber0(xn) = all_26_2_37
% 67.33/29.14 | (1748) all_26_2_37 = all_12_2_8
% 67.33/29.14 |
% 67.33/29.14 | Combining equations (572,1748) yields a new equation:
% 67.33/29.14 | (508) all_12_2_8 = 0
% 67.33/29.14 |
% 67.33/29.14 | Combining equations (508,1748) yields a new equation:
% 67.33/29.14 | (572) all_26_2_37 = 0
% 67.33/29.14 |
% 67.33/29.14 | From (572) and (1248) follows:
% 67.33/29.14 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.14 |
% 67.33/29.14 +-Applying beta-rule and splitting (275), into two cases.
% 67.33/29.14 |-Branch one:
% 67.33/29.14 | (1673) ~ (aNaturalNumber0(xn) = all_41_1_55)
% 67.33/29.14 |
% 67.33/29.14 | From (980) and (1673) follows:
% 67.33/29.14 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.14 |
% 67.33/29.14 | Using (53) and (1144) yields:
% 67.33/29.14 | (615) $false
% 67.33/29.14 |
% 67.33/29.14 |-The branch is then unsatisfiable
% 67.33/29.14 |-Branch two:
% 67.33/29.14 | (1676) aNaturalNumber0(xn) = all_41_1_55
% 67.33/29.14 | (980) all_41_1_55 = 0
% 67.33/29.14 |
% 67.33/29.14 | From (980) and (1676) follows:
% 67.33/29.14 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.14 |
% 67.33/29.14 +-Applying beta-rule and splitting (467), into two cases.
% 67.33/29.14 |-Branch one:
% 67.33/29.14 | (1758) ~ (aNaturalNumber0(sz10) = all_12_2_8)
% 67.33/29.14 |
% 67.33/29.14 | From (508) and (1758) follows:
% 67.33/29.14 | (1252) ~ (aNaturalNumber0(sz10) = 0)
% 67.33/29.14 |
% 67.33/29.14 | Using (16) and (1252) yields:
% 67.33/29.14 | (615) $false
% 67.33/29.14 |
% 67.33/29.14 |-The branch is then unsatisfiable
% 67.33/29.14 |-Branch two:
% 67.33/29.14 | (1761) aNaturalNumber0(sz10) = all_12_2_8
% 67.33/29.14 | (508) all_12_2_8 = 0
% 67.33/29.14 |
% 67.33/29.14 | From (508) and (1761) follows:
% 67.33/29.14 | (16) aNaturalNumber0(sz10) = 0
% 67.33/29.14 |
% 67.33/29.14 +-Applying beta-rule and splitting (273), into two cases.
% 67.33/29.14 |-Branch one:
% 67.33/29.14 | (1237) ~ (aNaturalNumber0(xp) = all_41_1_55)
% 67.33/29.14 |
% 67.33/29.14 | From (980) and (1237) follows:
% 67.33/29.14 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.33/29.14 |
% 67.33/29.14 | Using (12) and (1198) yields:
% 67.33/29.14 | (615) $false
% 67.33/29.14 |
% 67.33/29.14 |-The branch is then unsatisfiable
% 67.33/29.14 |-Branch two:
% 67.33/29.14 | (1240) aNaturalNumber0(xp) = all_41_1_55
% 67.33/29.14 | (980) all_41_1_55 = 0
% 67.33/29.14 |
% 67.33/29.14 | From (980) and (1240) follows:
% 67.33/29.14 | (12) aNaturalNumber0(xp) = 0
% 67.33/29.14 |
% 67.33/29.14 +-Applying beta-rule and splitting (267), into two cases.
% 67.33/29.14 |-Branch one:
% 67.33/29.14 | (1442) ~ (aNaturalNumber0(xr) = all_26_0_35)
% 67.33/29.14 |
% 67.33/29.14 | From (594) and (1442) follows:
% 67.33/29.14 | (1287) ~ (aNaturalNumber0(xr) = 0)
% 67.33/29.14 |
% 67.33/29.14 | Using (10) and (1287) yields:
% 67.33/29.14 | (615) $false
% 67.33/29.14 |
% 67.33/29.14 |-The branch is then unsatisfiable
% 67.33/29.14 |-Branch two:
% 67.33/29.14 | (1445) aNaturalNumber0(xr) = all_26_0_35
% 67.33/29.14 | (1774) all_36_3_53 = all_26_0_35
% 67.33/29.14 |
% 67.33/29.14 | Combining equations (480,1774) yields a new equation:
% 67.33/29.14 | (594) all_26_0_35 = 0
% 67.33/29.14 |
% 67.33/29.14 | Combining equations (594,1774) yields a new equation:
% 67.33/29.14 | (480) all_36_3_53 = 0
% 67.33/29.14 |
% 67.33/29.14 | From (594) and (1445) follows:
% 67.33/29.14 | (10) aNaturalNumber0(xr) = 0
% 67.33/29.14 |
% 67.33/29.14 +-Applying beta-rule and splitting (367), into two cases.
% 67.33/29.14 |-Branch one:
% 67.33/29.14 | (1386) ~ (aNaturalNumber0(xm) = all_26_2_37)
% 67.33/29.14 |
% 67.33/29.14 | From (572) and (1386) follows:
% 67.33/29.14 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.33/29.14 |
% 67.33/29.14 | Using (36) and (1191) yields:
% 67.33/29.14 | (615) $false
% 67.33/29.14 |
% 67.33/29.14 |-The branch is then unsatisfiable
% 67.33/29.14 |-Branch two:
% 67.33/29.14 | (1389) aNaturalNumber0(xm) = all_26_2_37
% 67.33/29.14 | (1782) all_26_2_37 = all_22_1_28
% 67.33/29.14 |
% 67.33/29.14 | Combining equations (572,1782) yields a new equation:
% 67.33/29.14 | (499) all_22_1_28 = 0
% 67.33/29.14 |
% 67.33/29.14 | Combining equations (499,1782) yields a new equation:
% 67.33/29.14 | (572) all_26_2_37 = 0
% 67.33/29.14 |
% 67.33/29.14 | From (572) and (1389) follows:
% 67.33/29.14 | (36) aNaturalNumber0(xm) = 0
% 67.33/29.14 |
% 67.33/29.14 +-Applying beta-rule and splitting (364), into two cases.
% 67.33/29.14 |-Branch one:
% 67.33/29.14 | (1786) ~ (aNaturalNumber0(sz00) = all_22_1_28)
% 67.33/29.14 |
% 67.33/29.14 | From (499) and (1786) follows:
% 67.33/29.14 | (1503) ~ (aNaturalNumber0(sz00) = 0)
% 67.33/29.14 |
% 67.33/29.14 | Using (41) and (1503) yields:
% 67.33/29.14 | (615) $false
% 67.33/29.14 |
% 67.33/29.14 |-The branch is then unsatisfiable
% 67.33/29.14 |-Branch two:
% 67.33/29.14 | (1789) aNaturalNumber0(sz00) = all_22_1_28
% 67.33/29.14 | (499) all_22_1_28 = 0
% 67.33/29.14 |
% 67.33/29.14 | From (499) and (1789) follows:
% 67.33/29.14 | (41) aNaturalNumber0(sz00) = 0
% 67.33/29.14 |
% 67.33/29.14 +-Applying beta-rule and splitting (420), into two cases.
% 67.33/29.14 |-Branch one:
% 67.33/29.14 | (1166) ~ (aNaturalNumber0(xn) = all_30_7_48)
% 67.33/29.14 |
% 67.33/29.14 | From (331) and (1166) follows:
% 67.33/29.14 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.14 |
% 67.33/29.14 | Using (53) and (1144) yields:
% 67.33/29.14 | (615) $false
% 67.33/29.14 |
% 67.33/29.14 |-The branch is then unsatisfiable
% 67.33/29.14 |-Branch two:
% 67.33/29.14 | (1169) aNaturalNumber0(xn) = all_30_7_48
% 67.33/29.14 | (1796) all_30_7_48 = all_28_2_40
% 67.33/29.14 |
% 67.33/29.14 | Combining equations (331,1796) yields a new equation:
% 67.33/29.14 | (514) all_28_2_40 = 0
% 67.33/29.14 |
% 67.33/29.14 | Combining equations (514,1796) yields a new equation:
% 67.33/29.14 | (331) all_30_7_48 = 0
% 67.33/29.14 |
% 67.33/29.14 | From (331) and (1169) follows:
% 67.33/29.14 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.14 |
% 67.33/29.14 +-Applying beta-rule and splitting (412), into two cases.
% 67.33/29.14 |-Branch one:
% 67.33/29.14 | (1151) ~ (aNaturalNumber0(xn) = all_22_0_27)
% 67.33/29.14 |
% 67.33/29.14 | From (554) and (1151) follows:
% 67.33/29.14 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.14 |
% 67.33/29.14 | Using (53) and (1144) yields:
% 67.33/29.14 | (615) $false
% 67.33/29.14 |
% 67.33/29.14 |-The branch is then unsatisfiable
% 67.33/29.14 |-Branch two:
% 67.33/29.14 | (1154) aNaturalNumber0(xn) = all_22_0_27
% 67.33/29.14 | (1804) all_28_2_40 = all_22_0_27
% 67.33/29.14 |
% 67.33/29.14 | Combining equations (514,1804) yields a new equation:
% 67.33/29.14 | (554) all_22_0_27 = 0
% 67.33/29.14 |
% 67.33/29.14 | From (554) and (1154) follows:
% 67.33/29.14 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.14 |
% 67.33/29.14 +-Applying beta-rule and splitting (417), into two cases.
% 67.33/29.14 |-Branch one:
% 67.33/29.14 | (1174) ~ (aNaturalNumber0(xn) = all_41_2_56)
% 67.33/29.14 |
% 67.33/29.14 | From (253) and (1174) follows:
% 67.33/29.14 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.14 |
% 67.33/29.14 | Using (53) and (1144) yields:
% 67.33/29.14 | (615) $false
% 67.33/29.14 |
% 67.33/29.14 |-The branch is then unsatisfiable
% 67.33/29.14 |-Branch two:
% 67.33/29.14 | (1177) aNaturalNumber0(xn) = all_41_2_56
% 67.33/29.14 | (1811) all_41_2_56 = all_28_2_40
% 67.33/29.14 |
% 67.33/29.14 | Combining equations (253,1811) yields a new equation:
% 67.33/29.14 | (514) all_28_2_40 = 0
% 67.33/29.14 |
% 67.33/29.14 | Combining equations (514,1811) yields a new equation:
% 67.33/29.14 | (253) all_41_2_56 = 0
% 67.33/29.14 |
% 67.33/29.14 | From (253) and (1177) follows:
% 67.33/29.14 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.14 |
% 67.33/29.14 +-Applying beta-rule and splitting (339), into two cases.
% 67.33/29.14 |-Branch one:
% 67.33/29.14 | (1314) ~ (aNaturalNumber0(xm) = all_41_2_56)
% 67.33/29.14 |
% 67.33/29.14 | From (253) and (1314) follows:
% 67.33/29.14 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.33/29.14 |
% 67.33/29.14 | Using (36) and (1191) yields:
% 67.33/29.14 | (615) $false
% 67.33/29.14 |
% 67.33/29.14 |-The branch is then unsatisfiable
% 67.33/29.14 |-Branch two:
% 67.33/29.14 | (1317) aNaturalNumber0(xm) = all_41_2_56
% 67.33/29.14 | (1819) all_41_2_56 = all_30_7_48
% 67.33/29.14 |
% 67.33/29.14 | Combining equations (253,1819) yields a new equation:
% 67.33/29.14 | (331) all_30_7_48 = 0
% 67.33/29.14 |
% 67.33/29.14 | Combining equations (331,1819) yields a new equation:
% 67.33/29.14 | (253) all_41_2_56 = 0
% 67.33/29.14 |
% 67.33/29.14 | From (253) and (1317) follows:
% 67.33/29.14 | (36) aNaturalNumber0(xm) = 0
% 67.33/29.14 |
% 67.33/29.14 +-Applying beta-rule and splitting (342), into two cases.
% 67.33/29.14 |-Branch one:
% 67.33/29.14 | (1338) ~ (aNaturalNumber0(xm) = all_36_2_52)
% 67.33/29.14 |
% 67.33/29.14 | From (979) and (1338) follows:
% 67.33/29.14 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.33/29.14 |
% 67.33/29.14 | Using (36) and (1191) yields:
% 67.33/29.14 | (615) $false
% 67.33/29.14 |
% 67.33/29.14 |-The branch is then unsatisfiable
% 67.33/29.14 |-Branch two:
% 67.33/29.14 | (1341) aNaturalNumber0(xm) = all_36_2_52
% 67.33/29.14 | (1827) all_36_2_52 = all_30_7_48
% 67.33/29.14 |
% 67.33/29.14 | Combining equations (979,1827) yields a new equation:
% 67.33/29.14 | (331) all_30_7_48 = 0
% 67.33/29.14 |
% 67.33/29.14 | Combining equations (331,1827) yields a new equation:
% 67.33/29.14 | (979) all_36_2_52 = 0
% 67.33/29.14 |
% 67.33/29.14 | From (979) and (1341) follows:
% 67.33/29.14 | (36) aNaturalNumber0(xm) = 0
% 67.33/29.14 |
% 67.33/29.14 +-Applying beta-rule and splitting (238), into two cases.
% 67.33/29.14 |-Branch one:
% 67.33/29.14 | (1831) ~ (aNaturalNumber0(sz10) = all_16_2_14)
% 67.33/29.14 |
% 67.33/29.14 | From (571) and (1831) follows:
% 67.33/29.14 | (1252) ~ (aNaturalNumber0(sz10) = 0)
% 67.33/29.14 |
% 67.33/29.14 | Using (16) and (1252) yields:
% 67.33/29.14 | (615) $false
% 67.33/29.14 |
% 67.33/29.14 |-The branch is then unsatisfiable
% 67.33/29.14 |-Branch two:
% 67.33/29.14 | (1834) aNaturalNumber0(sz10) = all_16_2_14
% 67.33/29.14 | (571) all_16_2_14 = 0
% 67.33/29.14 |
% 67.33/29.14 | From (571) and (1834) follows:
% 67.33/29.14 | (16) aNaturalNumber0(sz10) = 0
% 67.33/29.14 |
% 67.33/29.14 +-Applying beta-rule and splitting (437), into two cases.
% 67.33/29.14 |-Branch one:
% 67.33/29.14 | (1370) ~ (aNaturalNumber0(xn) = all_36_1_51)
% 67.33/29.14 |
% 67.33/29.14 | From (555) and (1370) follows:
% 67.33/29.14 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.14 |
% 67.33/29.14 | Using (53) and (1144) yields:
% 67.33/29.14 | (615) $false
% 67.33/29.14 |
% 67.33/29.14 |-The branch is then unsatisfiable
% 67.33/29.14 |-Branch two:
% 67.33/29.14 | (1373) aNaturalNumber0(xn) = all_36_1_51
% 67.33/29.14 | (1841) all_36_1_51 = all_22_2_29
% 67.33/29.14 |
% 67.33/29.15 | Combining equations (555,1841) yields a new equation:
% 67.33/29.15 | (510) all_22_2_29 = 0
% 67.33/29.15 |
% 67.33/29.15 | Combining equations (510,1841) yields a new equation:
% 67.33/29.15 | (555) all_36_1_51 = 0
% 67.33/29.15 |
% 67.33/29.15 | From (555) and (1373) follows:
% 67.33/29.15 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.15 |
% 67.33/29.15 +-Applying beta-rule and splitting (435), into two cases.
% 67.33/29.15 |-Branch one:
% 67.33/29.15 | (1845) ~ (aNaturalNumber0(sz10) = all_22_2_29)
% 67.33/29.15 |
% 67.33/29.15 | From (510) and (1845) follows:
% 67.33/29.15 | (1252) ~ (aNaturalNumber0(sz10) = 0)
% 67.33/29.15 |
% 67.33/29.15 | Using (16) and (1252) yields:
% 67.33/29.15 | (615) $false
% 67.33/29.15 |
% 67.33/29.15 |-The branch is then unsatisfiable
% 67.33/29.15 |-Branch two:
% 67.33/29.15 | (1848) aNaturalNumber0(sz10) = all_22_2_29
% 67.33/29.15 | (510) all_22_2_29 = 0
% 67.33/29.15 |
% 67.33/29.15 | From (510) and (1848) follows:
% 67.33/29.15 | (16) aNaturalNumber0(sz10) = 0
% 67.33/29.15 |
% 67.33/29.15 +-Applying beta-rule and splitting (371), into two cases.
% 67.33/29.15 |-Branch one:
% 67.33/29.15 | (1851) ~ (aNaturalNumber0(xm) = all_41_1_55)
% 67.33/29.15 |
% 67.33/29.15 | From (980) and (1851) follows:
% 67.33/29.15 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.33/29.15 |
% 67.33/29.15 | Using (36) and (1191) yields:
% 67.33/29.15 | (615) $false
% 67.33/29.15 |
% 67.33/29.15 |-The branch is then unsatisfiable
% 67.33/29.15 |-Branch two:
% 67.33/29.15 | (1854) aNaturalNumber0(xm) = all_41_1_55
% 67.33/29.15 | (1855) all_41_1_55 = all_22_1_28
% 67.33/29.15 |
% 67.33/29.15 | Combining equations (980,1855) yields a new equation:
% 67.33/29.15 | (499) all_22_1_28 = 0
% 67.33/29.15 |
% 67.33/29.15 | Combining equations (499,1855) yields a new equation:
% 67.33/29.15 | (980) all_41_1_55 = 0
% 67.33/29.15 |
% 67.33/29.15 | From (980) and (1854) follows:
% 67.33/29.15 | (36) aNaturalNumber0(xm) = 0
% 67.33/29.15 |
% 67.33/29.15 +-Applying beta-rule and splitting (235), into two cases.
% 67.33/29.15 |-Branch one:
% 67.33/29.15 | (1464) ~ (aNaturalNumber0(xp) = all_16_2_14)
% 67.33/29.15 |
% 67.33/29.15 | From (571) and (1464) follows:
% 67.33/29.15 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.33/29.15 |
% 67.33/29.15 | Using (12) and (1198) yields:
% 67.33/29.15 | (615) $false
% 67.33/29.15 |
% 67.33/29.15 |-The branch is then unsatisfiable
% 67.33/29.15 |-Branch two:
% 67.33/29.15 | (1467) aNaturalNumber0(xp) = all_16_2_14
% 67.33/29.15 | (571) all_16_2_14 = 0
% 67.33/29.15 |
% 67.33/29.15 | From (571) and (1467) follows:
% 67.33/29.15 | (12) aNaturalNumber0(xp) = 0
% 67.33/29.15 |
% 67.33/29.15 +-Applying beta-rule and splitting (211), into two cases.
% 67.33/29.15 |-Branch one:
% 67.33/29.15 | (1370) ~ (aNaturalNumber0(xn) = all_36_1_51)
% 67.33/29.15 |
% 67.33/29.15 | From (555) and (1370) follows:
% 67.33/29.15 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.15 |
% 67.33/29.15 | Using (53) and (1144) yields:
% 67.33/29.15 | (615) $false
% 67.33/29.15 |
% 67.33/29.15 |-The branch is then unsatisfiable
% 67.33/29.15 |-Branch two:
% 67.33/29.15 | (1373) aNaturalNumber0(xn) = all_36_1_51
% 67.33/29.15 | (555) all_36_1_51 = 0
% 67.33/29.15 |
% 67.33/29.15 | From (555) and (1373) follows:
% 67.33/29.15 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.15 |
% 67.33/29.15 +-Applying beta-rule and splitting (335), into two cases.
% 67.33/29.15 |-Branch one:
% 67.33/29.15 | (1871) ~ (aNaturalNumber0(xm) = all_26_0_35)
% 67.33/29.15 |
% 67.33/29.15 | From (594) and (1871) follows:
% 67.33/29.15 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.33/29.15 |
% 67.33/29.15 | Using (36) and (1191) yields:
% 67.33/29.15 | (615) $false
% 67.33/29.15 |
% 67.33/29.15 |-The branch is then unsatisfiable
% 67.33/29.15 |-Branch two:
% 67.33/29.15 | (1874) aNaturalNumber0(xm) = all_26_0_35
% 67.33/29.15 | (1875) all_30_7_48 = all_26_0_35
% 67.33/29.15 |
% 67.33/29.15 | Combining equations (331,1875) yields a new equation:
% 67.33/29.15 | (594) all_26_0_35 = 0
% 67.33/29.15 |
% 67.33/29.15 | Combining equations (594,1875) yields a new equation:
% 67.33/29.15 | (331) all_30_7_48 = 0
% 67.33/29.15 |
% 67.33/29.15 | From (594) and (1874) follows:
% 67.33/29.15 | (36) aNaturalNumber0(xm) = 0
% 67.33/29.15 |
% 67.33/29.15 +-Applying beta-rule and splitting (419), into two cases.
% 67.33/29.15 |-Branch one:
% 67.33/29.15 | (1673) ~ (aNaturalNumber0(xn) = all_41_1_55)
% 67.33/29.15 |
% 67.33/29.15 | From (980) and (1673) follows:
% 67.33/29.15 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.15 |
% 67.33/29.15 | Using (53) and (1144) yields:
% 67.33/29.15 | (615) $false
% 67.33/29.15 |
% 67.33/29.15 |-The branch is then unsatisfiable
% 67.33/29.15 |-Branch two:
% 67.33/29.15 | (1676) aNaturalNumber0(xn) = all_41_1_55
% 67.33/29.15 | (1883) all_41_1_55 = all_28_2_40
% 67.33/29.15 |
% 67.33/29.15 | Combining equations (980,1883) yields a new equation:
% 67.33/29.15 | (514) all_28_2_40 = 0
% 67.33/29.15 |
% 67.33/29.15 | Combining equations (514,1883) yields a new equation:
% 67.33/29.15 | (980) all_41_1_55 = 0
% 67.33/29.15 |
% 67.33/29.15 | From (980) and (1676) follows:
% 67.33/29.15 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.15 |
% 67.33/29.15 +-Applying beta-rule and splitting (352), into two cases.
% 67.33/29.15 |-Branch one:
% 67.33/29.15 | (1887) ~ (aNaturalNumber0(sz00) = all_24_3_33)
% 67.33/29.15 |
% 67.33/29.15 | From (483) and (1887) follows:
% 67.33/29.15 | (1503) ~ (aNaturalNumber0(sz00) = 0)
% 67.33/29.15 |
% 67.33/29.15 | Using (41) and (1503) yields:
% 67.33/29.15 | (615) $false
% 67.33/29.15 |
% 67.33/29.15 |-The branch is then unsatisfiable
% 67.33/29.15 |-Branch two:
% 67.33/29.15 | (1890) aNaturalNumber0(sz00) = all_24_3_33
% 67.33/29.15 | (483) all_24_3_33 = 0
% 67.33/29.15 |
% 67.33/29.15 | From (483) and (1890) follows:
% 67.33/29.15 | (41) aNaturalNumber0(sz00) = 0
% 67.33/29.15 |
% 67.33/29.15 +-Applying beta-rule and splitting (374), into two cases.
% 67.33/29.15 |-Branch one:
% 67.33/29.15 | (1294) ~ (aNaturalNumber0(xn) = all_14_1_10)
% 67.33/29.15 |
% 67.33/29.15 | From (503) and (1294) follows:
% 67.33/29.15 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.15 |
% 67.33/29.15 | Using (53) and (1144) yields:
% 67.33/29.15 | (615) $false
% 67.33/29.15 |
% 67.33/29.15 |-The branch is then unsatisfiable
% 67.33/29.15 |-Branch two:
% 67.33/29.15 | (1297) aNaturalNumber0(xn) = all_14_1_10
% 67.33/29.15 | (503) all_14_1_10 = 0
% 67.33/29.15 |
% 67.33/29.15 | From (503) and (1297) follows:
% 67.33/29.15 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.15 |
% 67.33/29.15 +-Applying beta-rule and splitting (418), into two cases.
% 67.33/29.15 |-Branch one:
% 67.33/29.15 | (1728) ~ (aNaturalNumber0(xn) = all_36_3_53)
% 67.33/29.15 |
% 67.33/29.15 | From (480) and (1728) follows:
% 67.33/29.15 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.15 |
% 67.33/29.15 | Using (53) and (1144) yields:
% 67.33/29.15 | (615) $false
% 67.33/29.15 |
% 67.33/29.15 |-The branch is then unsatisfiable
% 67.33/29.15 |-Branch two:
% 67.33/29.15 | (1731) aNaturalNumber0(xn) = all_36_3_53
% 67.33/29.15 | (1903) all_36_3_53 = all_28_2_40
% 67.33/29.15 |
% 67.33/29.15 | Combining equations (480,1903) yields a new equation:
% 67.33/29.15 | (514) all_28_2_40 = 0
% 67.33/29.15 |
% 67.33/29.15 | Combining equations (514,1903) yields a new equation:
% 67.33/29.15 | (480) all_36_3_53 = 0
% 67.33/29.15 |
% 67.33/29.15 | From (480) and (1731) follows:
% 67.33/29.15 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.15 |
% 67.33/29.15 +-Applying beta-rule and splitting (383), into two cases.
% 67.33/29.15 |-Branch one:
% 67.33/29.15 | (1338) ~ (aNaturalNumber0(xm) = all_36_2_52)
% 67.33/29.15 |
% 67.33/29.15 | From (979) and (1338) follows:
% 67.33/29.15 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.33/29.15 |
% 67.33/29.15 | Using (36) and (1191) yields:
% 67.33/29.15 | (615) $false
% 67.33/29.15 |
% 67.33/29.15 |-The branch is then unsatisfiable
% 67.33/29.15 |-Branch two:
% 67.33/29.15 | (1341) aNaturalNumber0(xm) = all_36_2_52
% 67.33/29.15 | (1911) all_36_2_52 = all_14_1_10
% 67.33/29.15 |
% 67.33/29.15 | Combining equations (979,1911) yields a new equation:
% 67.33/29.15 | (503) all_14_1_10 = 0
% 67.33/29.15 |
% 67.33/29.15 | Combining equations (503,1911) yields a new equation:
% 67.33/29.15 | (979) all_36_2_52 = 0
% 67.33/29.15 |
% 67.33/29.15 | From (979) and (1341) follows:
% 67.33/29.15 | (36) aNaturalNumber0(xm) = 0
% 67.33/29.15 |
% 67.33/29.15 +-Applying beta-rule and splitting (356), into two cases.
% 67.33/29.15 |-Branch one:
% 67.33/29.15 | (1562) ~ (aNaturalNumber0(xm) = all_16_2_14)
% 67.33/29.15 |
% 67.33/29.15 | From (571) and (1562) follows:
% 67.33/29.15 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.33/29.15 |
% 67.33/29.15 | Using (36) and (1191) yields:
% 67.33/29.15 | (615) $false
% 67.33/29.15 |
% 67.33/29.15 |-The branch is then unsatisfiable
% 67.33/29.15 |-Branch two:
% 67.33/29.15 | (1565) aNaturalNumber0(xm) = all_16_2_14
% 67.33/29.15 | (1919) all_24_3_33 = all_16_2_14
% 67.33/29.15 |
% 67.33/29.15 | Combining equations (483,1919) yields a new equation:
% 67.33/29.15 | (571) all_16_2_14 = 0
% 67.33/29.15 |
% 67.33/29.15 | Combining equations (571,1919) yields a new equation:
% 67.33/29.15 | (483) all_24_3_33 = 0
% 67.33/29.15 |
% 67.33/29.15 | From (571) and (1565) follows:
% 67.33/29.15 | (36) aNaturalNumber0(xm) = 0
% 67.33/29.15 |
% 67.33/29.15 +-Applying beta-rule and splitting (476), into two cases.
% 67.33/29.15 |-Branch one:
% 67.33/29.15 | (1568) ~ (aNaturalNumber0(xn) = all_24_3_33)
% 67.33/29.15 |
% 67.33/29.15 | From (483) and (1568) follows:
% 67.33/29.15 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.15 |
% 67.33/29.15 | Using (53) and (1144) yields:
% 67.33/29.15 | (615) $false
% 67.33/29.15 |
% 67.33/29.15 |-The branch is then unsatisfiable
% 67.33/29.15 |-Branch two:
% 67.33/29.15 | (1571) aNaturalNumber0(xn) = all_24_3_33
% 67.33/29.15 | (1927) all_24_3_33 = all_12_2_8
% 67.33/29.15 |
% 67.33/29.15 | Combining equations (483,1927) yields a new equation:
% 67.33/29.15 | (508) all_12_2_8 = 0
% 67.33/29.15 |
% 67.33/29.15 | Combining equations (508,1927) yields a new equation:
% 67.33/29.15 | (483) all_24_3_33 = 0
% 67.33/29.15 |
% 67.33/29.15 | From (483) and (1571) follows:
% 67.33/29.15 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.15 |
% 67.33/29.15 +-Applying beta-rule and splitting (245), into two cases.
% 67.33/29.15 |-Branch one:
% 67.33/29.15 | (1306) ~ (aNaturalNumber0(xm) = all_12_0_6)
% 67.33/29.15 |
% 67.33/29.15 | From (570) and (1306) follows:
% 67.33/29.15 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.33/29.15 |
% 67.33/29.15 | Using (36) and (1191) yields:
% 67.33/29.15 | (615) $false
% 67.33/29.15 |
% 67.33/29.15 |-The branch is then unsatisfiable
% 67.33/29.15 |-Branch two:
% 67.33/29.15 | (1309) aNaturalNumber0(xm) = all_12_0_6
% 67.33/29.15 | (570) all_12_0_6 = 0
% 67.33/29.15 |
% 67.33/29.15 | From (570) and (1309) follows:
% 67.33/29.15 | (36) aNaturalNumber0(xm) = 0
% 67.33/29.15 |
% 67.33/29.15 +-Applying beta-rule and splitting (214), into two cases.
% 67.33/29.15 |-Branch one:
% 67.33/29.15 | (1937) ~ (aNaturalNumber0(all_0_3_3) = 0)
% 67.33/29.15 |
% 67.33/29.15 | Using (556) and (1937) yields:
% 67.33/29.15 | (615) $false
% 67.33/29.15 |
% 67.33/29.15 |-The branch is then unsatisfiable
% 67.33/29.15 |-Branch two:
% 67.33/29.15 | (556) aNaturalNumber0(all_0_3_3) = 0
% 67.33/29.15 | (555) all_36_1_51 = 0
% 67.33/29.15 |
% 67.33/29.15 +-Applying beta-rule and splitting (433), into two cases.
% 67.33/29.15 |-Branch one:
% 67.33/29.15 | (1159) ~ (aNaturalNumber0(xn) = all_12_1_7)
% 67.33/29.15 |
% 67.33/29.15 | From (507) and (1159) follows:
% 67.33/29.15 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.15 |
% 67.33/29.15 | Using (53) and (1144) yields:
% 67.33/29.15 | (615) $false
% 67.33/29.15 |
% 67.33/29.15 |-The branch is then unsatisfiable
% 67.33/29.15 |-Branch two:
% 67.33/29.15 | (1162) aNaturalNumber0(xn) = all_12_1_7
% 67.33/29.16 | (1945) all_24_4_34 = all_12_1_7
% 67.33/29.16 |
% 67.33/29.16 | Combining equations (511,1945) yields a new equation:
% 67.33/29.16 | (507) all_12_1_7 = 0
% 67.33/29.16 |
% 67.33/29.16 | From (507) and (1162) follows:
% 67.33/29.16 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.16 |
% 67.33/29.16 +-Applying beta-rule and splitting (226), into two cases.
% 67.33/29.16 |-Branch one:
% 67.33/29.16 | (1286) ~ (aNaturalNumber0(xr) = all_26_2_37)
% 67.33/29.16 |
% 67.33/29.16 | From (572) and (1286) follows:
% 67.33/29.16 | (1287) ~ (aNaturalNumber0(xr) = 0)
% 67.33/29.16 |
% 67.33/29.16 | Using (10) and (1287) yields:
% 67.33/29.16 | (615) $false
% 67.33/29.16 |
% 67.33/29.16 |-The branch is then unsatisfiable
% 67.33/29.16 |-Branch two:
% 67.33/29.16 | (1289) aNaturalNumber0(xr) = all_26_2_37
% 67.33/29.16 | (572) all_26_2_37 = 0
% 67.33/29.16 |
% 67.33/29.16 | From (572) and (1289) follows:
% 67.33/29.16 | (10) aNaturalNumber0(xr) = 0
% 67.33/29.16 |
% 67.33/29.16 +-Applying beta-rule and splitting (217), into two cases.
% 67.33/29.16 |-Branch one:
% 67.33/29.16 | (1954) ~ (aNaturalNumber0(sz10) = all_22_0_27)
% 67.33/29.16 |
% 67.33/29.16 | From (554) and (1954) follows:
% 67.33/29.16 | (1252) ~ (aNaturalNumber0(sz10) = 0)
% 67.33/29.16 |
% 67.33/29.16 | Using (16) and (1252) yields:
% 67.33/29.16 | (615) $false
% 67.33/29.16 |
% 67.33/29.16 |-The branch is then unsatisfiable
% 67.33/29.16 |-Branch two:
% 67.33/29.16 | (1957) aNaturalNumber0(sz10) = all_22_0_27
% 67.33/29.16 | (554) all_22_0_27 = 0
% 67.33/29.16 |
% 67.33/29.16 | From (554) and (1957) follows:
% 67.33/29.16 | (16) aNaturalNumber0(sz10) = 0
% 67.33/29.16 |
% 67.33/29.16 +-Applying beta-rule and splitting (320), into two cases.
% 67.33/29.16 |-Branch one:
% 67.33/29.16 | (1272) ~ (aNaturalNumber0(xp) = all_36_3_53)
% 67.33/29.16 |
% 67.33/29.16 | From (480) and (1272) follows:
% 67.33/29.16 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.33/29.16 |
% 67.33/29.16 | Using (12) and (1198) yields:
% 67.33/29.16 | (615) $false
% 67.33/29.16 |
% 67.33/29.16 |-The branch is then unsatisfiable
% 67.33/29.16 |-Branch two:
% 67.33/29.16 | (1275) aNaturalNumber0(xp) = all_36_3_53
% 67.33/29.16 | (1964) all_36_3_53 = all_24_2_32
% 67.33/29.16 |
% 67.33/29.16 | Combining equations (480,1964) yields a new equation:
% 67.33/29.16 | (493) all_24_2_32 = 0
% 67.33/29.16 |
% 67.33/29.16 | Combining equations (493,1964) yields a new equation:
% 67.33/29.16 | (480) all_36_3_53 = 0
% 67.33/29.16 |
% 67.33/29.16 | From (480) and (1275) follows:
% 67.33/29.16 | (12) aNaturalNumber0(xp) = 0
% 67.33/29.16 |
% 67.33/29.16 +-Applying beta-rule and splitting (455), into two cases.
% 67.33/29.16 |-Branch one:
% 67.33/29.16 | (1151) ~ (aNaturalNumber0(xn) = all_22_0_27)
% 67.33/29.16 |
% 67.33/29.16 | From (554) and (1151) follows:
% 67.33/29.16 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.16 |
% 67.33/29.16 | Using (53) and (1144) yields:
% 67.33/29.16 | (615) $false
% 67.33/29.16 |
% 67.33/29.16 |-The branch is then unsatisfiable
% 67.33/29.16 |-Branch two:
% 67.33/29.16 | (1154) aNaturalNumber0(xn) = all_22_0_27
% 67.33/29.16 | (1972) all_22_0_27 = all_14_2_11
% 67.33/29.16 |
% 67.33/29.16 | Combining equations (554,1972) yields a new equation:
% 67.33/29.16 | (451) all_14_2_11 = 0
% 67.33/29.16 |
% 67.33/29.16 | Combining equations (451,1972) yields a new equation:
% 67.33/29.16 | (554) all_22_0_27 = 0
% 67.33/29.16 |
% 67.33/29.16 | From (554) and (1154) follows:
% 67.33/29.16 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.16 |
% 67.33/29.16 +-Applying beta-rule and splitting (333), into two cases.
% 67.33/29.16 |-Branch one:
% 67.33/29.16 | (1976) ~ (aNaturalNumber0(sz00) = all_30_7_48)
% 67.33/29.16 |
% 67.33/29.16 | From (331) and (1976) follows:
% 67.33/29.16 | (1503) ~ (aNaturalNumber0(sz00) = 0)
% 67.33/29.16 |
% 67.33/29.16 | Using (41) and (1503) yields:
% 67.33/29.16 | (615) $false
% 67.33/29.16 |
% 67.33/29.16 |-The branch is then unsatisfiable
% 67.33/29.16 |-Branch two:
% 67.33/29.16 | (1979) aNaturalNumber0(sz00) = all_30_7_48
% 67.33/29.16 | (331) all_30_7_48 = 0
% 67.33/29.16 |
% 67.33/29.16 | From (331) and (1979) follows:
% 67.33/29.16 | (41) aNaturalNumber0(sz00) = 0
% 67.33/29.16 |
% 67.33/29.16 +-Applying beta-rule and splitting (362), into two cases.
% 67.33/29.16 |-Branch one:
% 67.33/29.16 | (1182) ~ (aNaturalNumber0(xn) = all_22_1_28)
% 67.33/29.16 |
% 67.33/29.16 | From (499) and (1182) follows:
% 67.33/29.16 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.16 |
% 67.33/29.16 | Using (53) and (1144) yields:
% 67.33/29.16 | (615) $false
% 67.33/29.16 |
% 67.33/29.16 |-The branch is then unsatisfiable
% 67.33/29.16 |-Branch two:
% 67.33/29.16 | (1185) aNaturalNumber0(xn) = all_22_1_28
% 67.33/29.16 | (499) all_22_1_28 = 0
% 67.33/29.16 |
% 67.33/29.16 | From (499) and (1185) follows:
% 67.33/29.16 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.16 |
% 67.33/29.16 +-Applying beta-rule and splitting (329), into two cases.
% 67.33/29.16 |-Branch one:
% 67.33/29.16 | (1280) ~ (aNaturalNumber0(xp) = all_36_2_52)
% 67.33/29.16 |
% 67.33/29.16 | From (979) and (1280) follows:
% 67.33/29.16 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.33/29.16 |
% 67.33/29.16 | Using (12) and (1198) yields:
% 67.33/29.16 | (615) $false
% 67.33/29.16 |
% 67.33/29.16 |-The branch is then unsatisfiable
% 67.33/29.16 |-Branch two:
% 67.33/29.16 | (1283) aNaturalNumber0(xp) = all_36_2_52
% 67.33/29.16 | (1992) all_36_2_52 = all_16_1_13
% 67.33/29.16 |
% 67.33/29.16 | Combining equations (979,1992) yields a new equation:
% 67.33/29.16 | (497) all_16_1_13 = 0
% 67.33/29.16 |
% 67.33/29.16 | Combining equations (497,1992) yields a new equation:
% 67.33/29.16 | (979) all_36_2_52 = 0
% 67.33/29.16 |
% 67.33/29.16 | From (979) and (1283) follows:
% 67.33/29.16 | (12) aNaturalNumber0(xp) = 0
% 67.33/29.16 |
% 67.33/29.16 +-Applying beta-rule and splitting (431), into two cases.
% 67.33/29.16 |-Branch one:
% 67.33/29.16 | (1166) ~ (aNaturalNumber0(xn) = all_30_7_48)
% 67.33/29.16 |
% 67.33/29.16 | From (331) and (1166) follows:
% 67.33/29.16 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.16 |
% 67.33/29.16 | Using (53) and (1144) yields:
% 67.33/29.16 | (615) $false
% 67.33/29.16 |
% 67.33/29.16 |-The branch is then unsatisfiable
% 67.33/29.16 |-Branch two:
% 67.33/29.16 | (1169) aNaturalNumber0(xn) = all_30_7_48
% 67.33/29.16 | (2000) all_30_7_48 = all_24_4_34
% 67.33/29.16 |
% 67.33/29.16 | Combining equations (331,2000) yields a new equation:
% 67.33/29.16 | (511) all_24_4_34 = 0
% 67.33/29.16 |
% 67.33/29.16 | Combining equations (511,2000) yields a new equation:
% 67.33/29.16 | (331) all_30_7_48 = 0
% 67.33/29.16 |
% 67.33/29.16 | From (331) and (1169) follows:
% 67.33/29.16 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.16 |
% 67.33/29.16 +-Applying beta-rule and splitting (406), into two cases.
% 67.33/29.16 |-Branch one:
% 67.33/29.16 | (1182) ~ (aNaturalNumber0(xn) = all_22_1_28)
% 67.33/29.16 |
% 67.33/29.16 | From (499) and (1182) follows:
% 67.33/29.16 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.16 |
% 67.33/29.16 | Using (53) and (1144) yields:
% 67.33/29.16 | (615) $false
% 67.33/29.16 |
% 67.33/29.16 |-The branch is then unsatisfiable
% 67.33/29.16 |-Branch two:
% 67.33/29.16 | (1185) aNaturalNumber0(xn) = all_22_1_28
% 67.33/29.16 | (2008) all_30_8_49 = all_22_1_28
% 67.33/29.16 |
% 67.33/29.16 | Combining equations (516,2008) yields a new equation:
% 67.33/29.16 | (499) all_22_1_28 = 0
% 67.33/29.16 |
% 67.33/29.16 | Combining equations (499,2008) yields a new equation:
% 67.33/29.16 | (516) all_30_8_49 = 0
% 67.33/29.16 |
% 67.33/29.16 | From (499) and (1185) follows:
% 67.33/29.16 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.16 |
% 67.33/29.16 +-Applying beta-rule and splitting (291), into two cases.
% 67.33/29.16 |-Branch one:
% 67.33/29.16 | (2012) ~ (aNaturalNumber0(xk) = all_41_2_56)
% 67.33/29.16 |
% 67.33/29.16 | From (253) and (2012) follows:
% 67.33/29.16 | (974) ~ (aNaturalNumber0(xk) = 0)
% 67.33/29.16 |
% 67.33/29.16 | Using (972) and (974) yields:
% 67.33/29.16 | (615) $false
% 67.33/29.16 |
% 67.33/29.16 |-The branch is then unsatisfiable
% 67.33/29.16 |-Branch two:
% 67.33/29.16 | (2015) aNaturalNumber0(xk) = all_41_2_56
% 67.33/29.16 | (2016) all_41_2_56 = all_36_2_52
% 67.33/29.16 |
% 67.33/29.16 | Combining equations (253,2016) yields a new equation:
% 67.33/29.16 | (979) all_36_2_52 = 0
% 67.33/29.16 |
% 67.33/29.16 | Combining equations (979,2016) yields a new equation:
% 67.33/29.16 | (253) all_41_2_56 = 0
% 67.33/29.16 |
% 67.33/29.16 | From (253) and (2015) follows:
% 67.33/29.16 | (972) aNaturalNumber0(xk) = 0
% 67.33/29.16 |
% 67.33/29.16 +-Applying beta-rule and splitting (473), into two cases.
% 67.33/29.16 |-Branch one:
% 67.33/29.16 | (1673) ~ (aNaturalNumber0(xn) = all_41_1_55)
% 67.33/29.16 |
% 67.33/29.16 | From (980) and (1673) follows:
% 67.33/29.16 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.16 |
% 67.33/29.16 | Using (53) and (1144) yields:
% 67.33/29.16 | (615) $false
% 67.33/29.16 |
% 67.33/29.16 |-The branch is then unsatisfiable
% 67.33/29.16 |-Branch two:
% 67.33/29.16 | (1676) aNaturalNumber0(xn) = all_41_1_55
% 67.33/29.16 | (2024) all_41_1_55 = all_12_2_8
% 67.33/29.16 |
% 67.33/29.16 | Combining equations (980,2024) yields a new equation:
% 67.33/29.16 | (508) all_12_2_8 = 0
% 67.33/29.16 |
% 67.33/29.16 | Combining equations (508,2024) yields a new equation:
% 67.33/29.16 | (980) all_41_1_55 = 0
% 67.33/29.16 |
% 67.33/29.16 | From (980) and (1676) follows:
% 67.33/29.16 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.16 |
% 67.33/29.16 +-Applying beta-rule and splitting (241), into two cases.
% 67.33/29.16 |-Branch one:
% 67.33/29.16 | (1603) ~ (aNaturalNumber0(all_0_5_5) = all_26_0_35)
% 67.33/29.16 |
% 67.33/29.16 | From (594) and (1603) follows:
% 67.33/29.16 | (1258) ~ (aNaturalNumber0(all_0_5_5) = 0)
% 67.33/29.16 |
% 67.33/29.16 | Using (573) and (1258) yields:
% 67.33/29.16 | (615) $false
% 67.33/29.16 |
% 67.33/29.16 |-The branch is then unsatisfiable
% 67.33/29.16 |-Branch two:
% 67.33/29.16 | (1606) aNaturalNumber0(all_0_5_5) = all_26_0_35
% 67.33/29.16 | (2032) all_26_0_35 = all_16_2_14
% 67.33/29.16 |
% 67.33/29.16 | Combining equations (594,2032) yields a new equation:
% 67.33/29.16 | (571) all_16_2_14 = 0
% 67.33/29.16 |
% 67.33/29.16 | Combining equations (571,2032) yields a new equation:
% 67.33/29.16 | (594) all_26_0_35 = 0
% 67.33/29.16 |
% 67.33/29.16 | From (594) and (1606) follows:
% 67.33/29.16 | (573) aNaturalNumber0(all_0_5_5) = 0
% 67.33/29.16 |
% 67.33/29.16 +-Applying beta-rule and splitting (237), into two cases.
% 67.33/29.16 |-Branch one:
% 67.33/29.16 | (1480) ~ (aNaturalNumber0(xn) = all_16_2_14)
% 67.33/29.16 |
% 67.33/29.16 | From (571) and (1480) follows:
% 67.33/29.16 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.16 |
% 67.33/29.16 | Using (53) and (1144) yields:
% 67.33/29.16 | (615) $false
% 67.33/29.16 |
% 67.33/29.16 |-The branch is then unsatisfiable
% 67.33/29.16 |-Branch two:
% 67.33/29.16 | (1483) aNaturalNumber0(xn) = all_16_2_14
% 67.33/29.16 | (571) all_16_2_14 = 0
% 67.33/29.16 |
% 67.33/29.16 | From (571) and (1483) follows:
% 67.33/29.16 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.16 |
% 67.33/29.16 +-Applying beta-rule and splitting (286), into two cases.
% 67.33/29.16 |-Branch one:
% 67.33/29.16 | (1229) ~ (aNaturalNumber0(xn) = all_36_2_52)
% 67.33/29.16 |
% 67.33/29.16 | From (979) and (1229) follows:
% 67.33/29.16 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.16 |
% 67.33/29.16 | Using (53) and (1144) yields:
% 67.33/29.16 | (615) $false
% 67.33/29.16 |
% 67.33/29.16 |-The branch is then unsatisfiable
% 67.33/29.16 |-Branch two:
% 67.33/29.16 | (1232) aNaturalNumber0(xn) = all_36_2_52
% 67.33/29.16 | (979) all_36_2_52 = 0
% 67.33/29.16 |
% 67.33/29.16 | From (979) and (1232) follows:
% 67.33/29.16 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.16 |
% 67.33/29.16 +-Applying beta-rule and splitting (274), into two cases.
% 67.33/29.16 |-Branch one:
% 67.33/29.16 | (1851) ~ (aNaturalNumber0(xm) = all_41_1_55)
% 67.33/29.16 |
% 67.33/29.16 | From (980) and (1851) follows:
% 67.33/29.17 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.33/29.17 |
% 67.33/29.17 | Using (36) and (1191) yields:
% 67.33/29.17 | (615) $false
% 67.33/29.17 |
% 67.33/29.17 |-The branch is then unsatisfiable
% 67.33/29.17 |-Branch two:
% 67.33/29.17 | (1854) aNaturalNumber0(xm) = all_41_1_55
% 67.33/29.17 | (980) all_41_1_55 = 0
% 67.33/29.17 |
% 67.33/29.17 | From (980) and (1854) follows:
% 67.33/29.17 | (36) aNaturalNumber0(xm) = 0
% 67.33/29.17 |
% 67.33/29.17 +-Applying beta-rule and splitting (309), into two cases.
% 67.33/29.17 |-Branch one:
% 67.33/29.17 | (2054) ~ (aNaturalNumber0(xp) = all_12_0_6)
% 67.33/29.17 |
% 67.33/29.17 | From (570) and (2054) follows:
% 67.33/29.17 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.33/29.17 |
% 67.33/29.17 | Using (12) and (1198) yields:
% 67.33/29.17 | (615) $false
% 67.33/29.17 |
% 67.33/29.17 |-The branch is then unsatisfiable
% 67.33/29.17 |-Branch two:
% 67.33/29.17 | (2057) aNaturalNumber0(xp) = all_12_0_6
% 67.33/29.17 | (2058) all_26_1_36 = all_12_0_6
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (303,2058) yields a new equation:
% 67.33/29.17 | (570) all_12_0_6 = 0
% 67.33/29.17 |
% 67.33/29.17 | From (570) and (2057) follows:
% 67.33/29.17 | (12) aNaturalNumber0(xp) = 0
% 67.33/29.17 |
% 67.33/29.17 +-Applying beta-rule and splitting (477), into two cases.
% 67.33/29.17 |-Branch one:
% 67.33/29.17 | (1182) ~ (aNaturalNumber0(xn) = all_22_1_28)
% 67.33/29.17 |
% 67.33/29.17 | From (499) and (1182) follows:
% 67.33/29.17 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.17 |
% 67.33/29.17 | Using (53) and (1144) yields:
% 67.33/29.17 | (615) $false
% 67.33/29.17 |
% 67.33/29.17 |-The branch is then unsatisfiable
% 67.33/29.17 |-Branch two:
% 67.33/29.17 | (1185) aNaturalNumber0(xn) = all_22_1_28
% 67.33/29.17 | (2065) all_22_1_28 = all_12_2_8
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (499,2065) yields a new equation:
% 67.33/29.17 | (508) all_12_2_8 = 0
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (508,2065) yields a new equation:
% 67.33/29.17 | (499) all_22_1_28 = 0
% 67.33/29.17 |
% 67.33/29.17 | From (499) and (1185) follows:
% 67.33/29.17 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.17 |
% 67.33/29.17 +-Applying beta-rule and splitting (255), into two cases.
% 67.33/29.17 |-Branch one:
% 67.33/29.17 | (1314) ~ (aNaturalNumber0(xm) = all_41_2_56)
% 67.33/29.17 |
% 67.33/29.17 | From (253) and (1314) follows:
% 67.33/29.17 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.33/29.17 |
% 67.33/29.17 | Using (36) and (1191) yields:
% 67.33/29.17 | (615) $false
% 67.33/29.17 |
% 67.33/29.17 |-The branch is then unsatisfiable
% 67.33/29.17 |-Branch two:
% 67.33/29.17 | (1317) aNaturalNumber0(xm) = all_41_2_56
% 67.33/29.17 | (253) all_41_2_56 = 0
% 67.33/29.17 |
% 67.33/29.17 | From (253) and (1317) follows:
% 67.33/29.17 | (36) aNaturalNumber0(xm) = 0
% 67.33/29.17 |
% 67.33/29.17 +-Applying beta-rule and splitting (413), into two cases.
% 67.33/29.17 |-Branch one:
% 67.33/29.17 | (1354) ~ (aNaturalNumber0(xn) = all_26_0_35)
% 67.33/29.17 |
% 67.33/29.17 | From (594) and (1354) follows:
% 67.33/29.17 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.17 |
% 67.33/29.17 | Using (53) and (1144) yields:
% 67.33/29.17 | (615) $false
% 67.33/29.17 |
% 67.33/29.17 |-The branch is then unsatisfiable
% 67.33/29.17 |-Branch two:
% 67.33/29.17 | (1357) aNaturalNumber0(xn) = all_26_0_35
% 67.33/29.17 | (2079) all_28_2_40 = all_26_0_35
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (514,2079) yields a new equation:
% 67.33/29.17 | (594) all_26_0_35 = 0
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (594,2079) yields a new equation:
% 67.33/29.17 | (514) all_28_2_40 = 0
% 67.33/29.17 |
% 67.33/29.17 | From (594) and (1357) follows:
% 67.33/29.17 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.17 |
% 67.33/29.17 +-Applying beta-rule and splitting (441), into two cases.
% 67.33/29.17 |-Branch one:
% 67.33/29.17 | (1480) ~ (aNaturalNumber0(xn) = all_16_2_14)
% 67.33/29.17 |
% 67.33/29.17 | From (571) and (1480) follows:
% 67.33/29.17 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.17 |
% 67.33/29.17 | Using (53) and (1144) yields:
% 67.33/29.17 | (615) $false
% 67.33/29.17 |
% 67.33/29.17 |-The branch is then unsatisfiable
% 67.33/29.17 |-Branch two:
% 67.33/29.17 | (1483) aNaturalNumber0(xn) = all_16_2_14
% 67.33/29.17 | (2087) all_22_2_29 = all_16_2_14
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (2087,510) yields a new equation:
% 67.33/29.17 | (2088) all_16_2_14 = 0
% 67.33/29.17 |
% 67.33/29.17 | Simplifying 2088 yields:
% 67.33/29.17 | (571) all_16_2_14 = 0
% 67.33/29.17 |
% 67.33/29.17 | From (571) and (1483) follows:
% 67.33/29.17 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.17 |
% 67.33/29.17 +-Applying beta-rule and splitting (474), into two cases.
% 67.33/29.17 |-Branch one:
% 67.33/29.17 | (1229) ~ (aNaturalNumber0(xn) = all_36_2_52)
% 67.33/29.17 |
% 67.33/29.17 | From (979) and (1229) follows:
% 67.33/29.17 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.17 |
% 67.33/29.17 | Using (53) and (1144) yields:
% 67.33/29.17 | (615) $false
% 67.33/29.17 |
% 67.33/29.17 |-The branch is then unsatisfiable
% 67.33/29.17 |-Branch two:
% 67.33/29.17 | (1232) aNaturalNumber0(xn) = all_36_2_52
% 67.33/29.17 | (2095) all_36_2_52 = all_12_2_8
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (979,2095) yields a new equation:
% 67.33/29.17 | (508) all_12_2_8 = 0
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (508,2095) yields a new equation:
% 67.33/29.17 | (979) all_36_2_52 = 0
% 67.33/29.17 |
% 67.33/29.17 | From (979) and (1232) follows:
% 67.33/29.17 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.17 |
% 67.33/29.17 +-Applying beta-rule and splitting (318), into two cases.
% 67.33/29.17 |-Branch one:
% 67.33/29.17 | (1464) ~ (aNaturalNumber0(xp) = all_16_2_14)
% 67.33/29.17 |
% 67.33/29.17 | From (571) and (1464) follows:
% 67.33/29.17 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.33/29.17 |
% 67.33/29.17 | Using (12) and (1198) yields:
% 67.33/29.17 | (615) $false
% 67.33/29.17 |
% 67.33/29.17 |-The branch is then unsatisfiable
% 67.33/29.17 |-Branch two:
% 67.33/29.17 | (1467) aNaturalNumber0(xp) = all_16_2_14
% 67.33/29.17 | (2103) all_24_2_32 = all_16_2_14
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (493,2103) yields a new equation:
% 67.33/29.17 | (571) all_16_2_14 = 0
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (571,2103) yields a new equation:
% 67.33/29.17 | (493) all_24_2_32 = 0
% 67.33/29.17 |
% 67.33/29.17 | From (571) and (1467) follows:
% 67.33/29.17 | (12) aNaturalNumber0(xp) = 0
% 67.33/29.17 |
% 67.33/29.17 +-Applying beta-rule and splitting (464), into two cases.
% 67.33/29.17 |-Branch one:
% 67.33/29.17 | (1294) ~ (aNaturalNumber0(xn) = all_14_1_10)
% 67.33/29.17 |
% 67.33/29.17 | From (503) and (1294) follows:
% 67.33/29.17 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.17 |
% 67.33/29.17 | Using (53) and (1144) yields:
% 67.33/29.17 | (615) $false
% 67.33/29.17 |
% 67.33/29.17 |-The branch is then unsatisfiable
% 67.33/29.17 |-Branch two:
% 67.33/29.17 | (1297) aNaturalNumber0(xn) = all_14_1_10
% 67.33/29.17 | (2111) all_14_1_10 = all_14_2_11
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (503,2111) yields a new equation:
% 67.33/29.17 | (451) all_14_2_11 = 0
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (451,2111) yields a new equation:
% 67.33/29.17 | (503) all_14_1_10 = 0
% 67.33/29.17 |
% 67.33/29.17 | From (503) and (1297) follows:
% 67.33/29.17 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.17 |
% 67.33/29.17 +-Applying beta-rule and splitting (213), into two cases.
% 67.33/29.17 |-Branch one:
% 67.33/29.17 | (2115) ~ (aNaturalNumber0(sz00) = all_36_1_51)
% 67.33/29.17 |
% 67.33/29.17 | From (555) and (2115) follows:
% 67.33/29.17 | (1503) ~ (aNaturalNumber0(sz00) = 0)
% 67.33/29.17 |
% 67.33/29.17 | Using (41) and (1503) yields:
% 67.33/29.17 | (615) $false
% 67.33/29.17 |
% 67.33/29.17 |-The branch is then unsatisfiable
% 67.33/29.17 |-Branch two:
% 67.33/29.17 | (2118) aNaturalNumber0(sz00) = all_36_1_51
% 67.33/29.17 | (555) all_36_1_51 = 0
% 67.33/29.17 |
% 67.33/29.17 | From (555) and (2118) follows:
% 67.33/29.17 | (41) aNaturalNumber0(sz00) = 0
% 67.33/29.17 |
% 67.33/29.17 +-Applying beta-rule and splitting (438), into two cases.
% 67.33/29.17 |-Branch one:
% 67.33/29.17 | (1151) ~ (aNaturalNumber0(xn) = all_22_0_27)
% 67.33/29.17 |
% 67.33/29.17 | From (554) and (1151) follows:
% 67.33/29.17 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.17 |
% 67.33/29.17 | Using (53) and (1144) yields:
% 67.33/29.17 | (615) $false
% 67.33/29.17 |
% 67.33/29.17 |-The branch is then unsatisfiable
% 67.33/29.17 |-Branch two:
% 67.33/29.17 | (1154) aNaturalNumber0(xn) = all_22_0_27
% 67.33/29.17 | (2125) all_22_0_27 = all_22_2_29
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (554,2125) yields a new equation:
% 67.33/29.17 | (510) all_22_2_29 = 0
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (510,2125) yields a new equation:
% 67.33/29.17 | (554) all_22_0_27 = 0
% 67.33/29.17 |
% 67.33/29.17 | From (554) and (1154) follows:
% 67.33/29.17 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.17 |
% 67.33/29.17 +-Applying beta-rule and splitting (355), into two cases.
% 67.33/29.17 |-Branch one:
% 67.33/29.17 | (1386) ~ (aNaturalNumber0(xm) = all_26_2_37)
% 67.33/29.17 |
% 67.33/29.17 | From (572) and (1386) follows:
% 67.33/29.17 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.33/29.17 |
% 67.33/29.17 | Using (36) and (1191) yields:
% 67.33/29.17 | (615) $false
% 67.33/29.17 |
% 67.33/29.17 |-The branch is then unsatisfiable
% 67.33/29.17 |-Branch two:
% 67.33/29.17 | (1389) aNaturalNumber0(xm) = all_26_2_37
% 67.33/29.17 | (2133) all_26_2_37 = all_24_3_33
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (572,2133) yields a new equation:
% 67.33/29.17 | (483) all_24_3_33 = 0
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (483,2133) yields a new equation:
% 67.33/29.17 | (572) all_26_2_37 = 0
% 67.33/29.17 |
% 67.33/29.17 | From (572) and (1389) follows:
% 67.33/29.17 | (36) aNaturalNumber0(xm) = 0
% 67.33/29.17 |
% 67.33/29.17 +-Applying beta-rule and splitting (440), into two cases.
% 67.33/29.17 |-Branch one:
% 67.33/29.17 | (1245) ~ (aNaturalNumber0(xn) = all_26_2_37)
% 67.33/29.17 |
% 67.33/29.17 | From (572) and (1245) follows:
% 67.33/29.17 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.17 |
% 67.33/29.17 | Using (53) and (1144) yields:
% 67.33/29.17 | (615) $false
% 67.33/29.17 |
% 67.33/29.17 |-The branch is then unsatisfiable
% 67.33/29.17 |-Branch two:
% 67.33/29.17 | (1248) aNaturalNumber0(xn) = all_26_2_37
% 67.33/29.17 | (2141) all_26_2_37 = all_22_2_29
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (572,2141) yields a new equation:
% 67.33/29.17 | (510) all_22_2_29 = 0
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (510,2141) yields a new equation:
% 67.33/29.17 | (572) all_26_2_37 = 0
% 67.33/29.17 |
% 67.33/29.17 | From (572) and (1248) follows:
% 67.33/29.17 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.17 |
% 67.33/29.17 +-Applying beta-rule and splitting (336), into two cases.
% 67.33/29.17 |-Branch one:
% 67.33/29.17 | (1386) ~ (aNaturalNumber0(xm) = all_26_2_37)
% 67.33/29.17 |
% 67.33/29.17 | From (572) and (1386) follows:
% 67.33/29.17 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.33/29.17 |
% 67.33/29.17 | Using (36) and (1191) yields:
% 67.33/29.17 | (615) $false
% 67.33/29.17 |
% 67.33/29.17 |-The branch is then unsatisfiable
% 67.33/29.17 |-Branch two:
% 67.33/29.17 | (1389) aNaturalNumber0(xm) = all_26_2_37
% 67.33/29.17 | (2149) all_30_7_48 = all_26_2_37
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (331,2149) yields a new equation:
% 67.33/29.17 | (572) all_26_2_37 = 0
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (572,2149) yields a new equation:
% 67.33/29.17 | (331) all_30_7_48 = 0
% 67.33/29.17 |
% 67.33/29.17 | From (572) and (1389) follows:
% 67.33/29.17 | (36) aNaturalNumber0(xm) = 0
% 67.33/29.17 |
% 67.33/29.17 +-Applying beta-rule and splitting (459), into two cases.
% 67.33/29.17 |-Branch one:
% 67.33/29.17 | (1728) ~ (aNaturalNumber0(xn) = all_36_3_53)
% 67.33/29.17 |
% 67.33/29.17 | From (480) and (1728) follows:
% 67.33/29.17 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.17 |
% 67.33/29.17 | Using (53) and (1144) yields:
% 67.33/29.17 | (615) $false
% 67.33/29.17 |
% 67.33/29.17 |-The branch is then unsatisfiable
% 67.33/29.17 |-Branch two:
% 67.33/29.17 | (1731) aNaturalNumber0(xn) = all_36_3_53
% 67.33/29.17 | (2157) all_36_3_53 = all_14_2_11
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (480,2157) yields a new equation:
% 67.33/29.17 | (451) all_14_2_11 = 0
% 67.33/29.17 |
% 67.33/29.17 | Combining equations (451,2157) yields a new equation:
% 67.33/29.17 | (480) all_36_3_53 = 0
% 67.33/29.17 |
% 67.33/29.17 | From (480) and (1731) follows:
% 67.33/29.17 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.18 |
% 67.33/29.18 +-Applying beta-rule and splitting (337), into two cases.
% 67.33/29.18 |-Branch one:
% 67.33/29.18 | (1562) ~ (aNaturalNumber0(xm) = all_16_2_14)
% 67.33/29.18 |
% 67.33/29.18 | From (571) and (1562) follows:
% 67.33/29.18 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.33/29.18 |
% 67.33/29.18 | Using (36) and (1191) yields:
% 67.33/29.18 | (615) $false
% 67.33/29.18 |
% 67.33/29.18 |-The branch is then unsatisfiable
% 67.33/29.18 |-Branch two:
% 67.33/29.18 | (1565) aNaturalNumber0(xm) = all_16_2_14
% 67.33/29.18 | (2165) all_30_7_48 = all_16_2_14
% 67.33/29.18 |
% 67.33/29.18 | Combining equations (331,2165) yields a new equation:
% 67.33/29.18 | (571) all_16_2_14 = 0
% 67.33/29.18 |
% 67.33/29.18 | Combining equations (571,2165) yields a new equation:
% 67.33/29.18 | (331) all_30_7_48 = 0
% 67.33/29.18 |
% 67.33/29.18 | From (571) and (1565) follows:
% 67.33/29.18 | (36) aNaturalNumber0(xm) = 0
% 67.33/29.18 |
% 67.33/29.18 +-Applying beta-rule and splitting (445), into two cases.
% 67.33/29.18 |-Branch one:
% 67.33/29.18 | (1166) ~ (aNaturalNumber0(xn) = all_30_7_48)
% 67.33/29.18 |
% 67.33/29.18 | From (331) and (1166) follows:
% 67.33/29.18 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.18 |
% 67.33/29.18 | Using (53) and (1144) yields:
% 67.33/29.18 | (615) $false
% 67.33/29.18 |
% 67.33/29.18 |-The branch is then unsatisfiable
% 67.33/29.18 |-Branch two:
% 67.33/29.18 | (1169) aNaturalNumber0(xn) = all_30_7_48
% 67.33/29.18 | (2173) all_30_7_48 = all_22_2_29
% 67.33/29.18 |
% 67.33/29.18 | Combining equations (331,2173) yields a new equation:
% 67.33/29.18 | (510) all_22_2_29 = 0
% 67.33/29.18 |
% 67.33/29.18 | Combining equations (510,2173) yields a new equation:
% 67.33/29.18 | (331) all_30_7_48 = 0
% 67.33/29.18 |
% 67.33/29.18 | From (331) and (1169) follows:
% 67.33/29.18 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.18 |
% 67.33/29.18 +-Applying beta-rule and splitting (447), into two cases.
% 67.33/29.18 |-Branch one:
% 67.33/29.18 | (1568) ~ (aNaturalNumber0(xn) = all_24_3_33)
% 67.33/29.18 |
% 67.33/29.18 | From (483) and (1568) follows:
% 67.33/29.18 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.18 |
% 67.33/29.18 | Using (53) and (1144) yields:
% 67.33/29.18 | (615) $false
% 67.33/29.18 |
% 67.33/29.18 |-The branch is then unsatisfiable
% 67.33/29.18 |-Branch two:
% 67.33/29.18 | (1571) aNaturalNumber0(xn) = all_24_3_33
% 67.33/29.18 | (2181) all_24_3_33 = all_22_2_29
% 67.33/29.18 |
% 67.33/29.18 | Combining equations (483,2181) yields a new equation:
% 67.33/29.18 | (510) all_22_2_29 = 0
% 67.33/29.18 |
% 67.33/29.18 | Combining equations (510,2181) yields a new equation:
% 67.33/29.18 | (483) all_24_3_33 = 0
% 67.33/29.18 |
% 67.33/29.18 | From (483) and (1571) follows:
% 67.33/29.18 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.18 |
% 67.33/29.18 +-Applying beta-rule and splitting (458), into two cases.
% 67.33/29.18 |-Branch one:
% 67.33/29.18 | (1174) ~ (aNaturalNumber0(xn) = all_41_2_56)
% 67.33/29.18 |
% 67.33/29.18 | From (253) and (1174) follows:
% 67.33/29.18 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.18 |
% 67.33/29.18 | Using (53) and (1144) yields:
% 67.33/29.18 | (615) $false
% 67.33/29.18 |
% 67.33/29.18 |-The branch is then unsatisfiable
% 67.33/29.18 |-Branch two:
% 67.33/29.18 | (1177) aNaturalNumber0(xn) = all_41_2_56
% 67.33/29.18 | (2189) all_41_2_56 = all_14_2_11
% 67.33/29.18 |
% 67.33/29.18 | Combining equations (253,2189) yields a new equation:
% 67.33/29.18 | (451) all_14_2_11 = 0
% 67.33/29.18 |
% 67.33/29.18 | Combining equations (451,2189) yields a new equation:
% 67.33/29.18 | (253) all_41_2_56 = 0
% 67.33/29.18 |
% 67.33/29.18 | From (253) and (1177) follows:
% 67.33/29.18 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.18 |
% 67.33/29.18 +-Applying beta-rule and splitting (348), into two cases.
% 67.33/29.18 |-Branch one:
% 67.33/29.18 | (1330) ~ (aNaturalNumber0(xm) = all_36_3_53)
% 67.33/29.18 |
% 67.33/29.18 | From (480) and (1330) follows:
% 67.33/29.18 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.33/29.18 |
% 67.33/29.18 | Using (36) and (1191) yields:
% 67.33/29.18 | (615) $false
% 67.33/29.18 |
% 67.33/29.18 |-The branch is then unsatisfiable
% 67.33/29.18 |-Branch two:
% 67.33/29.18 | (1333) aNaturalNumber0(xm) = all_36_3_53
% 67.33/29.18 | (2197) all_36_3_53 = all_28_1_39
% 67.33/29.18 |
% 67.33/29.18 | Combining equations (480,2197) yields a new equation:
% 67.33/29.18 | (515) all_28_1_39 = 0
% 67.33/29.18 |
% 67.33/29.18 | Combining equations (515,2197) yields a new equation:
% 67.33/29.18 | (480) all_36_3_53 = 0
% 67.33/29.18 |
% 67.33/29.18 | From (480) and (1333) follows:
% 67.33/29.18 | (36) aNaturalNumber0(xm) = 0
% 67.33/29.18 |
% 67.33/29.18 +-Applying beta-rule and splitting (279), into two cases.
% 67.33/29.18 |-Branch one:
% 67.33/29.18 | (2201) ~ (aNaturalNumber0(xk) = all_26_2_37)
% 67.33/29.18 |
% 67.33/29.18 | From (572) and (2201) follows:
% 67.33/29.18 | (974) ~ (aNaturalNumber0(xk) = 0)
% 67.33/29.18 |
% 67.33/29.18 | Using (972) and (974) yields:
% 67.33/29.18 | (615) $false
% 67.33/29.18 |
% 67.33/29.18 |-The branch is then unsatisfiable
% 67.33/29.18 |-Branch two:
% 67.33/29.18 | (2204) aNaturalNumber0(xk) = all_26_2_37
% 67.33/29.18 | (2205) all_41_1_55 = all_26_2_37
% 67.33/29.18 |
% 67.33/29.18 | Combining equations (980,2205) yields a new equation:
% 67.33/29.18 | (572) all_26_2_37 = 0
% 67.33/29.18 |
% 67.33/29.18 | Combining equations (572,2205) yields a new equation:
% 67.33/29.18 | (980) all_41_1_55 = 0
% 67.33/29.18 |
% 67.33/29.18 | From (572) and (2204) follows:
% 67.33/29.18 | (972) aNaturalNumber0(xk) = 0
% 67.33/29.18 |
% 67.33/29.18 +-Applying beta-rule and splitting (263), into two cases.
% 67.33/29.18 |-Branch one:
% 67.33/29.18 | (1330) ~ (aNaturalNumber0(xm) = all_36_3_53)
% 67.33/29.18 |
% 67.33/29.18 | From (480) and (1330) follows:
% 67.33/29.18 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.33/29.18 |
% 67.33/29.18 | Using (36) and (1191) yields:
% 67.33/29.18 | (615) $false
% 67.33/29.18 |
% 67.33/29.18 |-The branch is then unsatisfiable
% 67.33/29.18 |-Branch two:
% 67.33/29.18 | (1333) aNaturalNumber0(xm) = all_36_3_53
% 67.33/29.18 | (480) all_36_3_53 = 0
% 67.33/29.18 |
% 67.33/29.18 | From (480) and (1333) follows:
% 67.33/29.18 | (36) aNaturalNumber0(xm) = 0
% 67.33/29.18 |
% 67.33/29.18 +-Applying beta-rule and splitting (325), into two cases.
% 67.33/29.18 |-Branch one:
% 67.33/29.18 | (1464) ~ (aNaturalNumber0(xp) = all_16_2_14)
% 67.33/29.18 |
% 67.33/29.18 | From (571) and (1464) follows:
% 67.33/29.18 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.33/29.18 |
% 67.33/29.18 | Using (12) and (1198) yields:
% 67.33/29.18 | (615) $false
% 67.33/29.18 |
% 67.33/29.18 |-The branch is then unsatisfiable
% 67.33/29.18 |-Branch two:
% 67.33/29.18 | (1467) aNaturalNumber0(xp) = all_16_2_14
% 67.33/29.18 | (2219) all_16_1_13 = all_16_2_14
% 67.33/29.18 |
% 67.33/29.18 | Combining equations (497,2219) yields a new equation:
% 67.33/29.18 | (571) all_16_2_14 = 0
% 67.33/29.18 |
% 67.33/29.18 | From (571) and (1467) follows:
% 67.33/29.18 | (12) aNaturalNumber0(xp) = 0
% 67.33/29.18 |
% 67.33/29.18 +-Applying beta-rule and splitting (296), into two cases.
% 67.33/29.18 |-Branch one:
% 67.33/29.18 | (1213) ~ (aNaturalNumber0(xp) = all_26_0_35)
% 67.33/29.18 |
% 67.33/29.18 | From (594) and (1213) follows:
% 67.33/29.18 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.33/29.18 |
% 67.33/29.18 | Using (12) and (1198) yields:
% 67.33/29.18 | (615) $false
% 67.33/29.18 |
% 67.33/29.18 |-The branch is then unsatisfiable
% 67.33/29.18 |-Branch two:
% 67.33/29.18 | (1216) aNaturalNumber0(xp) = all_26_0_35
% 67.33/29.18 | (2226) all_30_6_47 = all_26_0_35
% 67.33/29.18 |
% 67.33/29.18 | Combining equations (1242,2226) yields a new equation:
% 67.33/29.18 | (594) all_26_0_35 = 0
% 67.33/29.18 |
% 67.33/29.18 | From (594) and (1216) follows:
% 67.33/29.18 | (12) aNaturalNumber0(xp) = 0
% 67.33/29.18 |
% 67.33/29.18 +-Applying beta-rule and splitting (382), into two cases.
% 67.33/29.18 |-Branch one:
% 67.33/29.18 | (1330) ~ (aNaturalNumber0(xm) = all_36_3_53)
% 67.33/29.18 |
% 67.33/29.18 | From (480) and (1330) follows:
% 67.33/29.18 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.33/29.18 |
% 67.33/29.18 | Using (36) and (1191) yields:
% 67.33/29.18 | (615) $false
% 67.33/29.18 |
% 67.33/29.18 |-The branch is then unsatisfiable
% 67.33/29.18 |-Branch two:
% 67.33/29.18 | (1333) aNaturalNumber0(xm) = all_36_3_53
% 67.33/29.18 | (2233) all_36_3_53 = all_14_1_10
% 67.33/29.18 |
% 67.33/29.18 | Combining equations (480,2233) yields a new equation:
% 67.33/29.18 | (503) all_14_1_10 = 0
% 67.33/29.18 |
% 67.33/29.18 | Combining equations (503,2233) yields a new equation:
% 67.33/29.18 | (480) all_36_3_53 = 0
% 67.33/29.18 |
% 67.33/29.18 | From (480) and (1333) follows:
% 67.33/29.18 | (36) aNaturalNumber0(xm) = 0
% 67.33/29.18 |
% 67.33/29.18 +-Applying beta-rule and splitting (209), into two cases.
% 67.33/29.18 |-Branch one:
% 67.33/29.18 | (1418) ~ (aNaturalNumber0(xp) = all_36_1_51)
% 67.33/29.18 |
% 67.33/29.18 | From (555) and (1418) follows:
% 67.33/29.18 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.33/29.18 |
% 67.33/29.18 | Using (12) and (1198) yields:
% 67.33/29.18 | (615) $false
% 67.33/29.18 |
% 67.33/29.18 |-The branch is then unsatisfiable
% 67.33/29.18 |-Branch two:
% 67.33/29.18 | (1421) aNaturalNumber0(xp) = all_36_1_51
% 67.33/29.18 | (555) all_36_1_51 = 0
% 67.33/29.18 |
% 67.33/29.18 | From (555) and (1421) follows:
% 67.33/29.18 | (12) aNaturalNumber0(xp) = 0
% 67.33/29.18 |
% 67.33/29.18 +-Applying beta-rule and splitting (268), into two cases.
% 67.33/29.18 |-Branch one:
% 67.33/29.18 | (1286) ~ (aNaturalNumber0(xr) = all_26_2_37)
% 67.33/29.18 |
% 67.33/29.18 | From (572) and (1286) follows:
% 67.33/29.18 | (1287) ~ (aNaturalNumber0(xr) = 0)
% 67.33/29.18 |
% 67.33/29.18 | Using (10) and (1287) yields:
% 67.33/29.18 | (615) $false
% 67.33/29.18 |
% 67.33/29.18 |-The branch is then unsatisfiable
% 67.33/29.18 |-Branch two:
% 67.33/29.18 | (1289) aNaturalNumber0(xr) = all_26_2_37
% 67.33/29.18 | (2247) all_36_3_53 = all_26_2_37
% 67.33/29.18 |
% 67.33/29.18 | Combining equations (480,2247) yields a new equation:
% 67.33/29.18 | (572) all_26_2_37 = 0
% 67.33/29.18 |
% 67.33/29.18 | Combining equations (572,2247) yields a new equation:
% 67.33/29.18 | (480) all_36_3_53 = 0
% 67.33/29.18 |
% 67.33/29.18 | From (572) and (1289) follows:
% 67.33/29.18 | (10) aNaturalNumber0(xr) = 0
% 67.33/29.18 |
% 67.33/29.18 +-Applying beta-rule and splitting (409), into two cases.
% 67.33/29.18 |-Branch one:
% 67.33/29.18 | (2251) ~ (aNaturalNumber0(sz10) = all_28_2_40)
% 67.33/29.18 |
% 67.33/29.18 | From (514) and (2251) follows:
% 67.33/29.18 | (1252) ~ (aNaturalNumber0(sz10) = 0)
% 67.33/29.18 |
% 67.33/29.18 | Using (16) and (1252) yields:
% 67.33/29.18 | (615) $false
% 67.33/29.18 |
% 67.33/29.18 |-The branch is then unsatisfiable
% 67.33/29.18 |-Branch two:
% 67.33/29.18 | (2254) aNaturalNumber0(sz10) = all_28_2_40
% 67.33/29.18 | (514) all_28_2_40 = 0
% 67.33/29.18 |
% 67.33/29.18 | From (514) and (2254) follows:
% 67.33/29.18 | (16) aNaturalNumber0(sz10) = 0
% 67.33/29.18 |
% 67.33/29.18 +-Applying beta-rule and splitting (439), into two cases.
% 67.33/29.18 |-Branch one:
% 67.33/29.18 | (1354) ~ (aNaturalNumber0(xn) = all_26_0_35)
% 67.33/29.18 |
% 67.33/29.18 | From (594) and (1354) follows:
% 67.33/29.18 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.18 |
% 67.33/29.18 | Using (53) and (1144) yields:
% 67.33/29.18 | (615) $false
% 67.33/29.18 |
% 67.33/29.18 |-The branch is then unsatisfiable
% 67.33/29.18 |-Branch two:
% 67.33/29.19 | (1357) aNaturalNumber0(xn) = all_26_0_35
% 67.33/29.19 | (2261) all_26_0_35 = all_22_2_29
% 67.33/29.19 |
% 67.33/29.19 | Combining equations (594,2261) yields a new equation:
% 67.33/29.19 | (510) all_22_2_29 = 0
% 67.33/29.19 |
% 67.33/29.19 | Combining equations (510,2261) yields a new equation:
% 67.33/29.19 | (594) all_26_0_35 = 0
% 67.33/29.19 |
% 67.33/29.19 | From (594) and (1357) follows:
% 67.33/29.19 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.19 |
% 67.33/29.19 +-Applying beta-rule and splitting (220), into two cases.
% 67.33/29.19 |-Branch one:
% 67.33/29.19 | (1442) ~ (aNaturalNumber0(xr) = all_26_0_35)
% 67.33/29.19 |
% 67.33/29.19 | From (594) and (1442) follows:
% 67.33/29.19 | (1287) ~ (aNaturalNumber0(xr) = 0)
% 67.33/29.19 |
% 67.33/29.19 | Using (10) and (1287) yields:
% 67.33/29.19 | (615) $false
% 67.33/29.19 |
% 67.33/29.19 |-The branch is then unsatisfiable
% 67.33/29.19 |-Branch two:
% 67.33/29.19 | (1445) aNaturalNumber0(xr) = all_26_0_35
% 67.33/29.19 | (594) all_26_0_35 = 0
% 67.33/29.19 |
% 67.33/29.19 | From (594) and (1445) follows:
% 67.33/29.19 | (10) aNaturalNumber0(xr) = 0
% 67.33/29.19 |
% 67.33/29.19 +-Applying beta-rule and splitting (270), into two cases.
% 67.33/29.19 |-Branch one:
% 67.33/29.19 | (1508) ~ (aNaturalNumber0(xr) = all_12_0_6)
% 67.33/29.19 |
% 67.33/29.19 | From (570) and (1508) follows:
% 67.33/29.19 | (1287) ~ (aNaturalNumber0(xr) = 0)
% 67.33/29.19 |
% 67.33/29.19 | Using (10) and (1287) yields:
% 67.33/29.19 | (615) $false
% 67.33/29.19 |
% 67.33/29.19 |-The branch is then unsatisfiable
% 67.33/29.19 |-Branch two:
% 67.33/29.19 | (1511) aNaturalNumber0(xr) = all_12_0_6
% 67.33/29.19 | (2275) all_36_3_53 = all_12_0_6
% 67.33/29.19 |
% 67.33/29.19 | Combining equations (480,2275) yields a new equation:
% 67.33/29.19 | (570) all_12_0_6 = 0
% 67.33/29.19 |
% 67.33/29.19 | Combining equations (570,2275) yields a new equation:
% 67.33/29.19 | (480) all_36_3_53 = 0
% 67.33/29.19 |
% 67.33/29.19 | From (570) and (1511) follows:
% 67.33/29.19 | (10) aNaturalNumber0(xr) = 0
% 67.33/29.19 |
% 67.33/29.19 +-Applying beta-rule and splitting (289), into two cases.
% 67.33/29.19 |-Branch one:
% 67.33/29.19 | (2279) ~ (aNaturalNumber0(xk) = all_16_2_14)
% 67.33/29.19 |
% 67.33/29.19 | From (571) and (2279) follows:
% 67.33/29.19 | (974) ~ (aNaturalNumber0(xk) = 0)
% 67.33/29.19 |
% 67.33/29.19 | Using (972) and (974) yields:
% 67.33/29.19 | (615) $false
% 67.33/29.19 |
% 67.33/29.19 |-The branch is then unsatisfiable
% 67.33/29.19 |-Branch two:
% 67.33/29.19 | (2282) aNaturalNumber0(xk) = all_16_2_14
% 67.33/29.19 | (2283) all_36_2_52 = all_16_2_14
% 67.33/29.19 |
% 67.33/29.19 | Combining equations (979,2283) yields a new equation:
% 67.33/29.19 | (571) all_16_2_14 = 0
% 67.33/29.19 |
% 67.33/29.19 | Combining equations (571,2283) yields a new equation:
% 67.33/29.19 | (979) all_36_2_52 = 0
% 67.33/29.19 |
% 67.33/29.19 | From (571) and (2282) follows:
% 67.33/29.19 | (972) aNaturalNumber0(xk) = 0
% 67.33/29.19 |
% 67.33/29.19 +-Applying beta-rule and splitting (395), into two cases.
% 67.33/29.19 |-Branch one:
% 67.33/29.19 | (2287) ~ (aNaturalNumber0(sz10) = all_30_8_49)
% 67.33/29.19 |
% 67.33/29.19 | From (516) and (2287) follows:
% 67.33/29.19 | (1252) ~ (aNaturalNumber0(sz10) = 0)
% 67.33/29.19 |
% 67.33/29.19 | Using (16) and (1252) yields:
% 67.33/29.19 | (615) $false
% 67.33/29.19 |
% 67.33/29.19 |-The branch is then unsatisfiable
% 67.33/29.19 |-Branch two:
% 67.33/29.19 | (2290) aNaturalNumber0(sz10) = all_30_8_49
% 67.33/29.19 | (516) all_30_8_49 = 0
% 67.33/29.19 |
% 67.33/29.19 | From (516) and (2290) follows:
% 67.33/29.19 | (16) aNaturalNumber0(sz10) = 0
% 67.33/29.19 |
% 67.33/29.19 +-Applying beta-rule and splitting (407), into two cases.
% 67.33/29.19 |-Branch one:
% 67.33/29.19 | (1294) ~ (aNaturalNumber0(xn) = all_14_1_10)
% 67.33/29.19 |
% 67.33/29.19 | From (503) and (1294) follows:
% 67.33/29.19 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.19 |
% 67.33/29.19 | Using (53) and (1144) yields:
% 67.33/29.19 | (615) $false
% 67.33/29.19 |
% 67.33/29.19 |-The branch is then unsatisfiable
% 67.33/29.19 |-Branch two:
% 67.33/29.19 | (1297) aNaturalNumber0(xn) = all_14_1_10
% 67.33/29.19 | (2297) all_30_8_49 = all_14_1_10
% 67.33/29.19 |
% 67.33/29.19 | Combining equations (516,2297) yields a new equation:
% 67.33/29.19 | (503) all_14_1_10 = 0
% 67.33/29.19 |
% 67.33/29.19 | From (503) and (1297) follows:
% 67.33/29.19 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.19 |
% 67.33/29.19 +-Applying beta-rule and splitting (294), into two cases.
% 67.33/29.19 |-Branch one:
% 67.33/29.19 | (1418) ~ (aNaturalNumber0(xp) = all_36_1_51)
% 67.33/29.19 |
% 67.33/29.19 | From (555) and (1418) follows:
% 67.33/29.19 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.33/29.19 |
% 67.33/29.19 | Using (12) and (1198) yields:
% 67.33/29.19 | (615) $false
% 67.33/29.19 |
% 67.33/29.19 |-The branch is then unsatisfiable
% 67.33/29.19 |-Branch two:
% 67.33/29.19 | (1421) aNaturalNumber0(xp) = all_36_1_51
% 67.33/29.19 | (2304) all_36_1_51 = all_30_6_47
% 67.33/29.19 |
% 67.33/29.19 | Combining equations (555,2304) yields a new equation:
% 67.33/29.19 | (1242) all_30_6_47 = 0
% 67.33/29.19 |
% 67.33/29.19 | Combining equations (1242,2304) yields a new equation:
% 67.33/29.19 | (555) all_36_1_51 = 0
% 67.33/29.19 |
% 67.33/29.19 | From (555) and (1421) follows:
% 67.33/29.19 | (12) aNaturalNumber0(xp) = 0
% 67.33/29.19 |
% 67.33/29.19 +-Applying beta-rule and splitting (353), into two cases.
% 67.33/29.19 |-Branch one:
% 67.33/29.19 | (1190) ~ (aNaturalNumber0(xm) = all_22_0_27)
% 67.33/29.19 |
% 67.33/29.19 | From (554) and (1190) follows:
% 67.33/29.19 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.33/29.19 |
% 67.33/29.19 | Using (36) and (1191) yields:
% 67.33/29.19 | (615) $false
% 67.33/29.19 |
% 67.33/29.19 |-The branch is then unsatisfiable
% 67.33/29.19 |-Branch two:
% 67.33/29.19 | (1193) aNaturalNumber0(xm) = all_22_0_27
% 67.33/29.19 | (2312) all_24_3_33 = all_22_0_27
% 67.33/29.19 |
% 67.33/29.19 | Combining equations (483,2312) yields a new equation:
% 67.33/29.19 | (554) all_22_0_27 = 0
% 67.33/29.19 |
% 67.33/29.19 | From (554) and (1193) follows:
% 67.33/29.19 | (36) aNaturalNumber0(xm) = 0
% 67.33/29.19 |
% 67.33/29.19 +-Applying beta-rule and splitting (264), into two cases.
% 67.33/29.19 |-Branch one:
% 67.33/29.19 | (1728) ~ (aNaturalNumber0(xn) = all_36_3_53)
% 67.33/29.19 |
% 67.33/29.19 | From (480) and (1728) follows:
% 67.33/29.19 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.19 |
% 67.33/29.19 | Using (53) and (1144) yields:
% 67.33/29.19 | (615) $false
% 67.33/29.19 |
% 67.33/29.19 |-The branch is then unsatisfiable
% 67.33/29.19 |-Branch two:
% 67.33/29.19 | (1731) aNaturalNumber0(xn) = all_36_3_53
% 67.33/29.19 | (480) all_36_3_53 = 0
% 67.33/29.19 |
% 67.33/29.19 | From (480) and (1731) follows:
% 67.33/29.19 | (53) aNaturalNumber0(xn) = 0
% 67.33/29.19 |
% 67.33/29.19 +-Applying beta-rule and splitting (403), into two cases.
% 67.33/29.19 |-Branch one:
% 67.33/29.19 | (1166) ~ (aNaturalNumber0(xn) = all_30_7_48)
% 67.33/29.19 |
% 67.33/29.19 | From (331) and (1166) follows:
% 67.33/29.19 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.33/29.19 |
% 67.33/29.19 | Using (53) and (1144) yields:
% 67.33/29.19 | (615) $false
% 67.33/29.19 |
% 67.33/29.19 |-The branch is then unsatisfiable
% 67.33/29.19 |-Branch two:
% 67.54/29.19 | (1169) aNaturalNumber0(xn) = all_30_7_48
% 67.54/29.19 | (2325) all_30_7_48 = all_30_8_49
% 67.54/29.19 |
% 67.54/29.19 | Combining equations (331,2325) yields a new equation:
% 67.54/29.19 | (516) all_30_8_49 = 0
% 67.54/29.19 |
% 67.54/29.19 | Combining equations (516,2325) yields a new equation:
% 67.54/29.19 | (331) all_30_7_48 = 0
% 67.54/29.19 |
% 67.54/29.19 | From (331) and (1169) follows:
% 67.54/29.19 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.19 |
% 67.54/29.19 +-Applying beta-rule and splitting (299), into two cases.
% 67.54/29.19 |-Branch one:
% 67.54/29.19 | (2054) ~ (aNaturalNumber0(xp) = all_12_0_6)
% 67.54/29.19 |
% 67.54/29.19 | From (570) and (2054) follows:
% 67.54/29.19 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.54/29.19 |
% 67.54/29.19 | Using (12) and (1198) yields:
% 67.54/29.19 | (615) $false
% 67.54/29.19 |
% 67.54/29.19 |-The branch is then unsatisfiable
% 67.54/29.19 |-Branch two:
% 67.54/29.19 | (2057) aNaturalNumber0(xp) = all_12_0_6
% 67.54/29.19 | (2333) all_30_6_47 = all_12_0_6
% 67.54/29.19 |
% 67.54/29.19 | Combining equations (1242,2333) yields a new equation:
% 67.54/29.19 | (570) all_12_0_6 = 0
% 67.54/29.19 |
% 67.54/29.19 | From (570) and (2057) follows:
% 67.54/29.19 | (12) aNaturalNumber0(xp) = 0
% 67.54/29.19 |
% 67.54/29.19 +-Applying beta-rule and splitting (372), into two cases.
% 67.54/29.19 |-Branch one:
% 67.54/29.19 | (1338) ~ (aNaturalNumber0(xm) = all_36_2_52)
% 67.54/29.19 |
% 67.54/29.19 | From (979) and (1338) follows:
% 67.54/29.19 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.19 |
% 67.54/29.19 | Using (36) and (1191) yields:
% 67.54/29.19 | (615) $false
% 67.54/29.19 |
% 67.54/29.19 |-The branch is then unsatisfiable
% 67.54/29.19 |-Branch two:
% 67.54/29.19 | (1341) aNaturalNumber0(xm) = all_36_2_52
% 67.54/29.19 | (2340) all_36_2_52 = all_22_1_28
% 67.54/29.19 |
% 67.54/29.19 | Combining equations (979,2340) yields a new equation:
% 67.54/29.19 | (499) all_22_1_28 = 0
% 67.54/29.19 |
% 67.54/29.19 | Combining equations (499,2340) yields a new equation:
% 67.54/29.19 | (979) all_36_2_52 = 0
% 67.54/29.19 |
% 67.54/29.19 | From (979) and (1341) follows:
% 67.54/29.19 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.19 |
% 67.54/29.19 +-Applying beta-rule and splitting (387), into two cases.
% 67.54/29.19 |-Branch one:
% 67.54/29.19 | (1516) ~ (aNaturalNumber0(xm) = all_36_1_51)
% 67.54/29.19 |
% 67.54/29.19 | From (555) and (1516) follows:
% 67.54/29.19 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.19 |
% 67.54/29.19 | Using (36) and (1191) yields:
% 67.54/29.19 | (615) $false
% 67.54/29.19 |
% 67.54/29.19 |-The branch is then unsatisfiable
% 67.54/29.19 |-Branch two:
% 67.54/29.19 | (1519) aNaturalNumber0(xm) = all_36_1_51
% 67.54/29.19 | (2348) all_36_1_51 = all_12_1_7
% 67.54/29.19 |
% 67.54/29.19 | Combining equations (555,2348) yields a new equation:
% 67.54/29.19 | (507) all_12_1_7 = 0
% 67.54/29.19 |
% 67.54/29.19 | Combining equations (507,2348) yields a new equation:
% 67.54/29.19 | (555) all_36_1_51 = 0
% 67.54/29.19 |
% 67.54/29.19 | From (555) and (1519) follows:
% 67.54/29.19 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.19 |
% 67.54/29.19 +-Applying beta-rule and splitting (388), into two cases.
% 67.54/29.19 |-Branch one:
% 67.54/29.19 | (1190) ~ (aNaturalNumber0(xm) = all_22_0_27)
% 67.54/29.19 |
% 67.54/29.19 | From (554) and (1190) follows:
% 67.54/29.19 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.19 |
% 67.54/29.19 | Using (36) and (1191) yields:
% 67.54/29.19 | (615) $false
% 67.54/29.19 |
% 67.54/29.19 |-The branch is then unsatisfiable
% 67.54/29.19 |-Branch two:
% 67.54/29.19 | (1193) aNaturalNumber0(xm) = all_22_0_27
% 67.54/29.19 | (2356) all_22_0_27 = all_12_1_7
% 67.54/29.19 |
% 67.54/29.19 | Combining equations (554,2356) yields a new equation:
% 67.54/29.19 | (507) all_12_1_7 = 0
% 67.54/29.19 |
% 67.54/29.19 | Combining equations (507,2356) yields a new equation:
% 67.54/29.19 | (554) all_22_0_27 = 0
% 67.54/29.19 |
% 67.54/29.19 | From (554) and (1193) follows:
% 67.54/29.19 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.19 |
% 67.54/29.19 +-Applying beta-rule and splitting (256), into two cases.
% 67.54/29.19 |-Branch one:
% 67.54/29.20 | (1174) ~ (aNaturalNumber0(xn) = all_41_2_56)
% 67.54/29.20 |
% 67.54/29.20 | From (253) and (1174) follows:
% 67.54/29.20 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.20 |
% 67.54/29.20 | Using (53) and (1144) yields:
% 67.54/29.20 | (615) $false
% 67.54/29.20 |
% 67.54/29.20 |-The branch is then unsatisfiable
% 67.54/29.20 |-Branch two:
% 67.54/29.20 | (1177) aNaturalNumber0(xn) = all_41_2_56
% 67.54/29.20 | (253) all_41_2_56 = 0
% 67.54/29.20 |
% 67.54/29.20 | From (253) and (1177) follows:
% 67.54/29.20 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.20 |
% 67.54/29.20 +-Applying beta-rule and splitting (429), into two cases.
% 67.54/29.20 |-Branch one:
% 67.54/29.20 | (1673) ~ (aNaturalNumber0(xn) = all_41_1_55)
% 67.54/29.20 |
% 67.54/29.20 | From (980) and (1673) follows:
% 67.54/29.20 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.20 |
% 67.54/29.20 | Using (53) and (1144) yields:
% 67.54/29.20 | (615) $false
% 67.54/29.20 |
% 67.54/29.20 |-The branch is then unsatisfiable
% 67.54/29.20 |-Branch two:
% 67.54/29.20 | (1676) aNaturalNumber0(xn) = all_41_1_55
% 67.54/29.20 | (2370) all_41_1_55 = all_24_4_34
% 67.54/29.20 |
% 67.54/29.20 | Combining equations (980,2370) yields a new equation:
% 67.54/29.20 | (511) all_24_4_34 = 0
% 67.54/29.20 |
% 67.54/29.20 | Combining equations (511,2370) yields a new equation:
% 67.54/29.20 | (980) all_41_1_55 = 0
% 67.54/29.20 |
% 67.54/29.20 | From (980) and (1676) follows:
% 67.54/29.20 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.20 |
% 67.54/29.20 +-Applying beta-rule and splitting (422), into two cases.
% 67.54/29.20 |-Branch one:
% 67.54/29.20 | (1182) ~ (aNaturalNumber0(xn) = all_22_1_28)
% 67.54/29.20 |
% 67.54/29.20 | From (499) and (1182) follows:
% 67.54/29.20 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.20 |
% 67.54/29.20 | Using (53) and (1144) yields:
% 67.54/29.20 | (615) $false
% 67.54/29.20 |
% 67.54/29.20 |-The branch is then unsatisfiable
% 67.54/29.20 |-Branch two:
% 67.54/29.20 | (1185) aNaturalNumber0(xn) = all_22_1_28
% 67.54/29.20 | (2378) all_28_2_40 = all_22_1_28
% 67.54/29.20 |
% 67.54/29.20 | Combining equations (514,2378) yields a new equation:
% 67.54/29.20 | (499) all_22_1_28 = 0
% 67.54/29.20 |
% 67.54/29.20 | Combining equations (499,2378) yields a new equation:
% 67.54/29.20 | (514) all_28_2_40 = 0
% 67.54/29.20 |
% 67.54/29.20 | From (499) and (1185) follows:
% 67.54/29.20 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.20 |
% 67.54/29.20 +-Applying beta-rule and splitting (354), into two cases.
% 67.54/29.20 |-Branch one:
% 67.54/29.20 | (1871) ~ (aNaturalNumber0(xm) = all_26_0_35)
% 67.54/29.20 |
% 67.54/29.20 | From (594) and (1871) follows:
% 67.54/29.20 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.20 |
% 67.54/29.20 | Using (36) and (1191) yields:
% 67.54/29.20 | (615) $false
% 67.54/29.20 |
% 67.54/29.20 |-The branch is then unsatisfiable
% 67.54/29.20 |-Branch two:
% 67.54/29.20 | (1874) aNaturalNumber0(xm) = all_26_0_35
% 67.54/29.20 | (2386) all_26_0_35 = all_24_3_33
% 67.54/29.20 |
% 67.54/29.20 | Combining equations (594,2386) yields a new equation:
% 67.54/29.20 | (483) all_24_3_33 = 0
% 67.54/29.20 |
% 67.54/29.20 | Combining equations (483,2386) yields a new equation:
% 67.54/29.20 | (594) all_26_0_35 = 0
% 67.54/29.20 |
% 67.54/29.20 | From (594) and (1874) follows:
% 67.54/29.20 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.20 |
% 67.54/29.20 +-Applying beta-rule and splitting (225), into two cases.
% 67.54/29.20 |-Branch one:
% 67.54/29.20 | (2390) ~ (aNaturalNumber0(all_0_4_4) = all_22_0_27)
% 67.54/29.20 |
% 67.54/29.20 | From (554) and (2390) follows:
% 67.54/29.20 | (2391) ~ (aNaturalNumber0(all_0_4_4) = 0)
% 67.54/29.20 |
% 67.54/29.20 | Using (595) and (2391) yields:
% 67.54/29.20 | (615) $false
% 67.54/29.20 |
% 67.54/29.20 |-The branch is then unsatisfiable
% 67.54/29.20 |-Branch two:
% 67.54/29.20 | (2393) aNaturalNumber0(all_0_4_4) = all_22_0_27
% 67.54/29.20 | (2394) all_26_0_35 = all_22_0_27
% 67.54/29.20 |
% 67.54/29.20 | Combining equations (594,2394) yields a new equation:
% 67.54/29.20 | (554) all_22_0_27 = 0
% 67.54/29.20 |
% 67.54/29.20 | Combining equations (554,2394) yields a new equation:
% 67.54/29.20 | (594) all_26_0_35 = 0
% 67.54/29.20 |
% 67.54/29.20 | From (554) and (2393) follows:
% 67.54/29.20 | (595) aNaturalNumber0(all_0_4_4) = 0
% 67.54/29.20 |
% 67.54/29.20 +-Applying beta-rule and splitting (366), into two cases.
% 67.54/29.20 |-Branch one:
% 67.54/29.20 | (1871) ~ (aNaturalNumber0(xm) = all_26_0_35)
% 67.54/29.20 |
% 67.54/29.20 | From (594) and (1871) follows:
% 67.54/29.20 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.20 |
% 67.54/29.20 | Using (36) and (1191) yields:
% 67.54/29.20 | (615) $false
% 67.54/29.20 |
% 67.54/29.20 |-The branch is then unsatisfiable
% 67.54/29.20 |-Branch two:
% 67.54/29.20 | (1874) aNaturalNumber0(xm) = all_26_0_35
% 67.54/29.20 | (2402) all_26_0_35 = all_22_1_28
% 67.54/29.20 |
% 67.54/29.20 | Combining equations (594,2402) yields a new equation:
% 67.54/29.20 | (499) all_22_1_28 = 0
% 67.54/29.20 |
% 67.54/29.20 | Combining equations (499,2402) yields a new equation:
% 67.54/29.20 | (594) all_26_0_35 = 0
% 67.54/29.20 |
% 67.54/29.20 | From (594) and (1874) follows:
% 67.54/29.20 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.20 |
% 67.54/29.20 +-Applying beta-rule and splitting (310), into two cases.
% 67.54/29.20 |-Branch one:
% 67.54/29.20 | (1197) ~ (aNaturalNumber0(xp) = all_41_2_56)
% 67.54/29.20 |
% 67.54/29.20 | From (253) and (1197) follows:
% 67.54/29.20 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.54/29.20 |
% 67.54/29.20 | Using (12) and (1198) yields:
% 67.54/29.20 | (615) $false
% 67.54/29.20 |
% 67.54/29.20 |-The branch is then unsatisfiable
% 67.54/29.20 |-Branch two:
% 67.54/29.20 | (1200) aNaturalNumber0(xp) = all_41_2_56
% 67.54/29.20 | (2410) all_41_2_56 = all_26_1_36
% 67.54/29.20 |
% 67.54/29.20 | Combining equations (253,2410) yields a new equation:
% 67.54/29.20 | (303) all_26_1_36 = 0
% 67.54/29.20 |
% 67.54/29.20 | Combining equations (303,2410) yields a new equation:
% 67.54/29.20 | (253) all_41_2_56 = 0
% 67.54/29.20 |
% 67.54/29.20 | From (253) and (1200) follows:
% 67.54/29.20 | (12) aNaturalNumber0(xp) = 0
% 67.54/29.20 |
% 67.54/29.20 +-Applying beta-rule and splitting (229), into two cases.
% 67.54/29.20 |-Branch one:
% 67.54/29.20 | (2414) ~ (aNaturalNumber0(sz00) = all_26_2_37)
% 67.54/29.20 |
% 67.54/29.20 | From (572) and (2414) follows:
% 67.54/29.20 | (1503) ~ (aNaturalNumber0(sz00) = 0)
% 67.54/29.20 |
% 67.54/29.20 | Using (41) and (1503) yields:
% 67.54/29.20 | (615) $false
% 67.54/29.20 |
% 67.54/29.20 |-The branch is then unsatisfiable
% 67.54/29.20 |-Branch two:
% 67.54/29.20 | (2417) aNaturalNumber0(sz00) = all_26_2_37
% 67.54/29.20 | (572) all_26_2_37 = 0
% 67.54/29.20 |
% 67.54/29.20 | From (572) and (2417) follows:
% 67.54/29.20 | (41) aNaturalNumber0(sz00) = 0
% 67.54/29.20 |
% 67.54/29.20 +-Applying beta-rule and splitting (280), into two cases.
% 67.54/29.20 |-Branch one:
% 67.54/29.20 | (2279) ~ (aNaturalNumber0(xk) = all_16_2_14)
% 67.54/29.20 |
% 67.54/29.20 | From (571) and (2279) follows:
% 67.54/29.20 | (974) ~ (aNaturalNumber0(xk) = 0)
% 67.54/29.20 |
% 67.54/29.20 | Using (972) and (974) yields:
% 67.54/29.20 | (615) $false
% 67.54/29.20 |
% 67.54/29.20 |-The branch is then unsatisfiable
% 67.54/29.20 |-Branch two:
% 67.54/29.20 | (2282) aNaturalNumber0(xk) = all_16_2_14
% 67.54/29.20 | (2424) all_41_1_55 = all_16_2_14
% 67.54/29.20 |
% 67.54/29.20 | Combining equations (980,2424) yields a new equation:
% 67.54/29.20 | (571) all_16_2_14 = 0
% 67.54/29.20 |
% 67.54/29.20 | Combining equations (571,2424) yields a new equation:
% 67.54/29.20 | (980) all_41_1_55 = 0
% 67.54/29.20 |
% 67.54/29.20 | From (571) and (2282) follows:
% 67.54/29.20 | (972) aNaturalNumber0(xk) = 0
% 67.54/29.20 |
% 67.54/29.20 +-Applying beta-rule and splitting (443), into two cases.
% 67.54/29.20 |-Branch one:
% 67.54/29.20 | (1728) ~ (aNaturalNumber0(xn) = all_36_3_53)
% 67.54/29.20 |
% 67.54/29.20 | From (480) and (1728) follows:
% 67.54/29.20 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.20 |
% 67.54/29.20 | Using (53) and (1144) yields:
% 67.54/29.20 | (615) $false
% 67.54/29.20 |
% 67.54/29.20 |-The branch is then unsatisfiable
% 67.54/29.20 |-Branch two:
% 67.54/29.20 | (1731) aNaturalNumber0(xn) = all_36_3_53
% 67.54/29.20 | (2432) all_36_3_53 = all_22_2_29
% 67.54/29.20 |
% 67.54/29.20 | Combining equations (480,2432) yields a new equation:
% 67.54/29.20 | (510) all_22_2_29 = 0
% 67.54/29.20 |
% 67.54/29.20 | Combining equations (510,2432) yields a new equation:
% 67.54/29.20 | (480) all_36_3_53 = 0
% 67.54/29.20 |
% 67.54/29.20 | From (480) and (1731) follows:
% 67.54/29.20 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.20 |
% 67.54/29.20 +-Applying beta-rule and splitting (278), into two cases.
% 67.54/29.20 |-Branch one:
% 67.54/29.20 | (2436) ~ (aNaturalNumber0(xk) = all_26_0_35)
% 67.54/29.20 |
% 67.54/29.20 | From (594) and (2436) follows:
% 67.54/29.20 | (974) ~ (aNaturalNumber0(xk) = 0)
% 67.54/29.20 |
% 67.54/29.20 | Using (972) and (974) yields:
% 67.54/29.20 | (615) $false
% 67.54/29.20 |
% 67.54/29.20 |-The branch is then unsatisfiable
% 67.54/29.20 |-Branch two:
% 67.54/29.20 | (2439) aNaturalNumber0(xk) = all_26_0_35
% 67.54/29.20 | (2440) all_41_1_55 = all_26_0_35
% 67.54/29.20 |
% 67.54/29.20 | Combining equations (980,2440) yields a new equation:
% 67.54/29.20 | (594) all_26_0_35 = 0
% 67.54/29.20 |
% 67.54/29.20 | Combining equations (594,2440) yields a new equation:
% 67.54/29.20 | (980) all_41_1_55 = 0
% 67.54/29.20 |
% 67.54/29.20 | From (594) and (2439) follows:
% 67.54/29.20 | (972) aNaturalNumber0(xk) = 0
% 67.54/29.20 |
% 67.54/29.20 +-Applying beta-rule and splitting (215), into two cases.
% 67.54/29.20 |-Branch one:
% 67.54/29.20 | (1190) ~ (aNaturalNumber0(xm) = all_22_0_27)
% 67.54/29.20 |
% 67.54/29.20 | From (554) and (1190) follows:
% 67.54/29.20 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.20 |
% 67.54/29.20 | Using (36) and (1191) yields:
% 67.54/29.20 | (615) $false
% 67.54/29.20 |
% 67.54/29.20 |-The branch is then unsatisfiable
% 67.54/29.20 |-Branch two:
% 67.54/29.20 | (1193) aNaturalNumber0(xm) = all_22_0_27
% 67.54/29.20 | (554) all_22_0_27 = 0
% 67.54/29.20 |
% 67.54/29.20 | From (554) and (1193) follows:
% 67.54/29.20 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.20 |
% 67.54/29.20 +-Applying beta-rule and splitting (315), into two cases.
% 67.54/29.20 |-Branch one:
% 67.54/29.20 | (1554) ~ (aNaturalNumber0(xp) = all_22_0_27)
% 67.54/29.20 |
% 67.54/29.20 | From (554) and (1554) follows:
% 67.54/29.20 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.54/29.20 |
% 67.54/29.20 | Using (12) and (1198) yields:
% 67.54/29.20 | (615) $false
% 67.54/29.20 |
% 67.54/29.20 |-The branch is then unsatisfiable
% 67.54/29.20 |-Branch two:
% 67.54/29.20 | (1557) aNaturalNumber0(xp) = all_22_0_27
% 67.54/29.20 | (2454) all_24_2_32 = all_22_0_27
% 67.54/29.20 |
% 67.54/29.20 | Combining equations (493,2454) yields a new equation:
% 67.54/29.20 | (554) all_22_0_27 = 0
% 67.54/29.20 |
% 67.54/29.20 | From (554) and (1557) follows:
% 67.54/29.20 | (12) aNaturalNumber0(xp) = 0
% 67.54/29.21 |
% 67.54/29.21 +-Applying beta-rule and splitting (360), into two cases.
% 67.54/29.21 |-Branch one:
% 67.54/29.21 | (1338) ~ (aNaturalNumber0(xm) = all_36_2_52)
% 67.54/29.21 |
% 67.54/29.21 | From (979) and (1338) follows:
% 67.54/29.21 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.21 |
% 67.54/29.21 | Using (36) and (1191) yields:
% 67.54/29.21 | (615) $false
% 67.54/29.21 |
% 67.54/29.21 |-The branch is then unsatisfiable
% 67.54/29.21 |-Branch two:
% 67.54/29.21 | (1341) aNaturalNumber0(xm) = all_36_2_52
% 67.54/29.21 | (2461) all_36_2_52 = all_24_3_33
% 67.54/29.21 |
% 67.54/29.21 | Combining equations (979,2461) yields a new equation:
% 67.54/29.21 | (483) all_24_3_33 = 0
% 67.54/29.21 |
% 67.54/29.21 | Combining equations (483,2461) yields a new equation:
% 67.54/29.21 | (979) all_36_2_52 = 0
% 67.54/29.21 |
% 67.54/29.21 | From (979) and (1341) follows:
% 67.54/29.21 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.21 |
% 67.54/29.21 +-Applying beta-rule and splitting (276), into two cases.
% 67.54/29.21 |-Branch one:
% 67.54/29.21 | (2465) ~ (aNaturalNumber0(xk) = all_36_1_51)
% 67.54/29.21 |
% 67.54/29.21 | From (555) and (2465) follows:
% 67.54/29.21 | (974) ~ (aNaturalNumber0(xk) = 0)
% 67.54/29.21 |
% 67.54/29.21 | Using (972) and (974) yields:
% 67.54/29.21 | (615) $false
% 67.54/29.21 |
% 67.54/29.21 |-The branch is then unsatisfiable
% 67.54/29.21 |-Branch two:
% 67.54/29.21 | (2468) aNaturalNumber0(xk) = all_36_1_51
% 67.54/29.21 | (2469) all_41_1_55 = all_36_1_51
% 67.54/29.21 |
% 67.54/29.21 | Combining equations (980,2469) yields a new equation:
% 67.54/29.21 | (555) all_36_1_51 = 0
% 67.54/29.21 |
% 67.54/29.21 | Combining equations (555,2469) yields a new equation:
% 67.54/29.21 | (980) all_41_1_55 = 0
% 67.54/29.21 |
% 67.54/29.21 | From (555) and (2468) follows:
% 67.54/29.21 | (972) aNaturalNumber0(xk) = 0
% 67.54/29.21 |
% 67.54/29.21 +-Applying beta-rule and splitting (300), into two cases.
% 67.54/29.21 |-Branch one:
% 67.54/29.21 | (1197) ~ (aNaturalNumber0(xp) = all_41_2_56)
% 67.54/29.21 |
% 67.54/29.21 | From (253) and (1197) follows:
% 67.54/29.21 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.54/29.21 |
% 67.54/29.21 | Using (12) and (1198) yields:
% 67.54/29.21 | (615) $false
% 67.54/29.21 |
% 67.54/29.21 |-The branch is then unsatisfiable
% 67.54/29.21 |-Branch two:
% 67.54/29.21 | (1200) aNaturalNumber0(xp) = all_41_2_56
% 67.54/29.21 | (2477) all_41_2_56 = all_30_6_47
% 67.54/29.21 |
% 67.54/29.21 | Combining equations (253,2477) yields a new equation:
% 67.54/29.21 | (1242) all_30_6_47 = 0
% 67.54/29.21 |
% 67.54/29.21 | Combining equations (1242,2477) yields a new equation:
% 67.54/29.21 | (253) all_41_2_56 = 0
% 67.54/29.21 |
% 67.54/29.21 | From (253) and (1200) follows:
% 67.54/29.21 | (12) aNaturalNumber0(xp) = 0
% 67.54/29.21 |
% 67.54/29.21 +-Applying beta-rule and splitting (281), into two cases.
% 67.54/29.21 |-Branch one:
% 67.54/29.21 | (2012) ~ (aNaturalNumber0(xk) = all_41_2_56)
% 67.54/29.21 |
% 67.54/29.21 | From (253) and (2012) follows:
% 67.54/29.21 | (974) ~ (aNaturalNumber0(xk) = 0)
% 67.54/29.21 |
% 67.54/29.21 | Using (972) and (974) yields:
% 67.54/29.21 | (615) $false
% 67.54/29.21 |
% 67.54/29.21 |-The branch is then unsatisfiable
% 67.54/29.21 |-Branch two:
% 67.54/29.21 | (2015) aNaturalNumber0(xk) = all_41_2_56
% 67.54/29.21 | (2485) all_41_1_55 = all_41_2_56
% 67.54/29.21 |
% 67.54/29.21 | Combining equations (980,2485) yields a new equation:
% 67.54/29.21 | (253) all_41_2_56 = 0
% 67.54/29.21 |
% 67.54/29.21 | Combining equations (253,2485) yields a new equation:
% 67.54/29.21 | (980) all_41_1_55 = 0
% 67.54/29.21 |
% 67.54/29.21 | From (253) and (2015) follows:
% 67.54/29.21 | (972) aNaturalNumber0(xk) = 0
% 67.54/29.21 |
% 67.54/29.21 +-Applying beta-rule and splitting (247), into two cases.
% 67.54/29.21 |-Branch one:
% 67.54/29.21 | (2489) ~ (aNaturalNumber0(sz10) = all_12_0_6)
% 67.54/29.21 |
% 67.54/29.21 | From (570) and (2489) follows:
% 67.54/29.21 | (1252) ~ (aNaturalNumber0(sz10) = 0)
% 67.54/29.21 |
% 67.54/29.21 | Using (16) and (1252) yields:
% 67.54/29.21 | (615) $false
% 67.54/29.21 |
% 67.54/29.21 |-The branch is then unsatisfiable
% 67.54/29.21 |-Branch two:
% 67.54/29.21 | (2492) aNaturalNumber0(sz10) = all_12_0_6
% 67.54/29.21 | (570) all_12_0_6 = 0
% 67.54/29.21 |
% 67.54/29.21 | From (570) and (2492) follows:
% 67.54/29.21 | (16) aNaturalNumber0(sz10) = 0
% 67.54/29.21 |
% 67.54/29.21 +-Applying beta-rule and splitting (224), into two cases.
% 67.54/29.21 |-Branch one:
% 67.54/29.21 | (2495) ~ (aNaturalNumber0(all_0_4_4) = all_36_1_51)
% 67.54/29.21 |
% 67.54/29.21 | From (555) and (2495) follows:
% 67.54/29.21 | (2391) ~ (aNaturalNumber0(all_0_4_4) = 0)
% 67.54/29.21 |
% 67.54/29.21 | Using (595) and (2391) yields:
% 67.54/29.21 | (615) $false
% 67.54/29.21 |
% 67.54/29.21 |-The branch is then unsatisfiable
% 67.54/29.21 |-Branch two:
% 67.54/29.21 | (2498) aNaturalNumber0(all_0_4_4) = all_36_1_51
% 67.54/29.21 | (2499) all_36_1_51 = all_26_0_35
% 67.54/29.21 |
% 67.54/29.21 | Combining equations (555,2499) yields a new equation:
% 67.54/29.21 | (594) all_26_0_35 = 0
% 67.54/29.21 |
% 67.54/29.21 | Combining equations (594,2499) yields a new equation:
% 67.54/29.21 | (555) all_36_1_51 = 0
% 67.54/29.21 |
% 67.54/29.21 | From (555) and (2498) follows:
% 67.54/29.21 | (595) aNaturalNumber0(all_0_4_4) = 0
% 67.54/29.21 |
% 67.54/29.21 +-Applying beta-rule and splitting (223), into two cases.
% 67.54/29.21 |-Branch one:
% 67.54/29.21 | (2391) ~ (aNaturalNumber0(all_0_4_4) = 0)
% 67.54/29.21 |
% 67.54/29.21 | Using (595) and (2391) yields:
% 67.54/29.21 | (615) $false
% 67.54/29.21 |
% 67.54/29.21 |-The branch is then unsatisfiable
% 67.54/29.21 |-Branch two:
% 67.54/29.21 | (595) aNaturalNumber0(all_0_4_4) = 0
% 67.54/29.21 | (594) all_26_0_35 = 0
% 67.54/29.21 |
% 67.54/29.21 +-Applying beta-rule and splitting (453), into two cases.
% 67.54/29.21 |-Branch one:
% 67.54/29.21 | (2507) ~ (aNaturalNumber0(sz00) = all_14_2_11)
% 67.54/29.21 |
% 67.54/29.21 | From (451) and (2507) follows:
% 67.54/29.21 | (1503) ~ (aNaturalNumber0(sz00) = 0)
% 67.54/29.21 |
% 67.54/29.21 | Using (41) and (1503) yields:
% 67.54/29.21 | (615) $false
% 67.54/29.21 |
% 67.54/29.21 |-The branch is then unsatisfiable
% 67.54/29.21 |-Branch two:
% 67.54/29.21 | (2510) aNaturalNumber0(sz00) = all_14_2_11
% 67.54/29.21 | (451) all_14_2_11 = 0
% 67.54/29.21 |
% 67.54/29.21 | From (451) and (2510) follows:
% 67.54/29.21 | (41) aNaturalNumber0(sz00) = 0
% 67.54/29.21 |
% 67.54/29.21 +-Applying beta-rule and splitting (262), into two cases.
% 67.54/29.21 |-Branch one:
% 67.54/29.21 | (1272) ~ (aNaturalNumber0(xp) = all_36_3_53)
% 67.54/29.21 |
% 67.54/29.21 | From (480) and (1272) follows:
% 67.54/29.21 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.54/29.21 |
% 67.54/29.21 | Using (12) and (1198) yields:
% 67.54/29.21 | (615) $false
% 67.54/29.21 |
% 67.54/29.21 |-The branch is then unsatisfiable
% 67.54/29.21 |-Branch two:
% 67.54/29.21 | (1275) aNaturalNumber0(xp) = all_36_3_53
% 67.54/29.21 | (480) all_36_3_53 = 0
% 67.54/29.21 |
% 67.54/29.21 | From (480) and (1275) follows:
% 67.54/29.21 | (12) aNaturalNumber0(xp) = 0
% 67.54/29.21 |
% 67.54/29.21 +-Applying beta-rule and splitting (381), into two cases.
% 67.54/29.21 |-Branch one:
% 67.54/29.21 | (1314) ~ (aNaturalNumber0(xm) = all_41_2_56)
% 67.54/29.21 |
% 67.54/29.21 | From (253) and (1314) follows:
% 67.54/29.21 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.21 |
% 67.54/29.21 | Using (36) and (1191) yields:
% 67.54/29.21 | (615) $false
% 67.54/29.21 |
% 67.54/29.21 |-The branch is then unsatisfiable
% 67.54/29.21 |-Branch two:
% 67.54/29.21 | (1317) aNaturalNumber0(xm) = all_41_2_56
% 67.54/29.21 | (2523) all_41_2_56 = all_14_1_10
% 67.54/29.21 |
% 67.54/29.21 | Combining equations (253,2523) yields a new equation:
% 67.54/29.21 | (503) all_14_1_10 = 0
% 67.54/29.21 |
% 67.54/29.21 | Combining equations (503,2523) yields a new equation:
% 67.54/29.21 | (253) all_41_2_56 = 0
% 67.54/29.21 |
% 67.54/29.21 | From (253) and (1317) follows:
% 67.54/29.21 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.21 |
% 67.54/29.21 +-Applying beta-rule and splitting (428), into two cases.
% 67.54/29.21 |-Branch one:
% 67.54/29.21 | (1646) ~ (aNaturalNumber0(xn) = all_12_0_6)
% 67.54/29.21 |
% 67.54/29.21 | From (570) and (1646) follows:
% 67.54/29.21 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.21 |
% 67.54/29.21 | Using (53) and (1144) yields:
% 67.54/29.21 | (615) $false
% 67.54/29.21 |
% 67.54/29.21 |-The branch is then unsatisfiable
% 67.54/29.21 |-Branch two:
% 67.54/29.21 | (1649) aNaturalNumber0(xn) = all_12_0_6
% 67.54/29.21 | (2531) all_24_4_34 = all_12_0_6
% 67.54/29.21 |
% 67.54/29.21 | Combining equations (511,2531) yields a new equation:
% 67.54/29.21 | (570) all_12_0_6 = 0
% 67.54/29.21 |
% 67.54/29.21 | From (570) and (1649) follows:
% 67.54/29.21 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.21 |
% 67.54/29.21 +-Applying beta-rule and splitting (446), into two cases.
% 67.54/29.21 |-Branch one:
% 67.54/29.21 | (1143) ~ (aNaturalNumber0(xn) = all_28_1_39)
% 67.54/29.21 |
% 67.54/29.21 | From (515) and (1143) follows:
% 67.54/29.21 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.21 |
% 67.54/29.21 | Using (53) and (1144) yields:
% 67.54/29.21 | (615) $false
% 67.54/29.21 |
% 67.54/29.21 |-The branch is then unsatisfiable
% 67.54/29.21 |-Branch two:
% 67.54/29.21 | (1146) aNaturalNumber0(xn) = all_28_1_39
% 67.54/29.21 | (2538) all_28_1_39 = all_22_2_29
% 67.54/29.21 |
% 67.54/29.21 | Combining equations (515,2538) yields a new equation:
% 67.54/29.21 | (510) all_22_2_29 = 0
% 67.54/29.21 |
% 67.54/29.21 | Combining equations (510,2538) yields a new equation:
% 67.54/29.21 | (515) all_28_1_39 = 0
% 67.54/29.21 |
% 67.54/29.21 | From (515) and (1146) follows:
% 67.54/29.21 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.21 |
% 67.54/29.21 +-Applying beta-rule and splitting (212), into two cases.
% 67.54/29.21 |-Branch one:
% 67.54/29.21 | (2542) ~ (aNaturalNumber0(sz10) = all_36_1_51)
% 67.54/29.21 |
% 67.54/29.21 | From (555) and (2542) follows:
% 67.54/29.21 | (1252) ~ (aNaturalNumber0(sz10) = 0)
% 67.54/29.21 |
% 67.54/29.21 | Using (16) and (1252) yields:
% 67.54/29.21 | (615) $false
% 67.54/29.21 |
% 67.54/29.21 |-The branch is then unsatisfiable
% 67.54/29.21 |-Branch two:
% 67.54/29.21 | (2545) aNaturalNumber0(sz10) = all_36_1_51
% 67.54/29.21 | (555) all_36_1_51 = 0
% 67.54/29.21 |
% 67.54/29.21 | From (555) and (2545) follows:
% 67.54/29.21 | (16) aNaturalNumber0(sz10) = 0
% 67.54/29.21 |
% 67.54/29.21 +-Applying beta-rule and splitting (425), into two cases.
% 67.54/29.21 |-Branch one:
% 67.54/29.21 | (1370) ~ (aNaturalNumber0(xn) = all_36_1_51)
% 67.54/29.21 |
% 67.54/29.21 | From (555) and (1370) follows:
% 67.54/29.21 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.21 |
% 67.54/29.21 | Using (53) and (1144) yields:
% 67.54/29.21 | (615) $false
% 67.54/29.21 |
% 67.54/29.21 |-The branch is then unsatisfiable
% 67.54/29.21 |-Branch two:
% 67.54/29.21 | (1373) aNaturalNumber0(xn) = all_36_1_51
% 67.54/29.21 | (2552) all_36_1_51 = all_24_4_34
% 67.54/29.21 |
% 67.54/29.21 | Combining equations (555,2552) yields a new equation:
% 67.54/29.21 | (511) all_24_4_34 = 0
% 67.54/29.21 |
% 67.54/29.21 | Combining equations (511,2552) yields a new equation:
% 67.54/29.21 | (555) all_36_1_51 = 0
% 67.54/29.21 |
% 67.54/29.21 | From (555) and (1373) follows:
% 67.54/29.21 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.21 |
% 67.54/29.21 +-Applying beta-rule and splitting (230), into two cases.
% 67.54/29.21 |-Branch one:
% 67.54/29.22 | (1258) ~ (aNaturalNumber0(all_0_5_5) = 0)
% 67.54/29.22 |
% 67.54/29.22 | Using (573) and (1258) yields:
% 67.54/29.22 | (615) $false
% 67.54/29.22 |
% 67.54/29.22 |-The branch is then unsatisfiable
% 67.54/29.22 |-Branch two:
% 67.54/29.22 | (573) aNaturalNumber0(all_0_5_5) = 0
% 67.54/29.22 | (572) all_26_2_37 = 0
% 67.54/29.22 |
% 67.54/29.22 +-Applying beta-rule and splitting (221), into two cases.
% 67.54/29.22 |-Branch one:
% 67.54/29.22 | (1213) ~ (aNaturalNumber0(xp) = all_26_0_35)
% 67.54/29.22 |
% 67.54/29.22 | From (594) and (1213) follows:
% 67.54/29.22 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.54/29.22 |
% 67.54/29.22 | Using (12) and (1198) yields:
% 67.54/29.22 | (615) $false
% 67.54/29.22 |
% 67.54/29.22 |-The branch is then unsatisfiable
% 67.54/29.22 |-Branch two:
% 67.54/29.22 | (1216) aNaturalNumber0(xp) = all_26_0_35
% 67.54/29.22 | (594) all_26_0_35 = 0
% 67.54/29.22 |
% 67.54/29.22 | From (594) and (1216) follows:
% 67.54/29.22 | (12) aNaturalNumber0(xp) = 0
% 67.54/29.22 |
% 67.54/29.22 +-Applying beta-rule and splitting (389), into two cases.
% 67.54/29.22 |-Branch one:
% 67.54/29.22 | (1871) ~ (aNaturalNumber0(xm) = all_26_0_35)
% 67.54/29.22 |
% 67.54/29.22 | From (594) and (1871) follows:
% 67.54/29.22 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.22 |
% 67.54/29.22 | Using (36) and (1191) yields:
% 67.54/29.22 | (615) $false
% 67.54/29.22 |
% 67.54/29.22 |-The branch is then unsatisfiable
% 67.54/29.22 |-Branch two:
% 67.54/29.22 | (1874) aNaturalNumber0(xm) = all_26_0_35
% 67.54/29.22 | (2570) all_26_0_35 = all_12_1_7
% 67.54/29.22 |
% 67.54/29.22 | Combining equations (594,2570) yields a new equation:
% 67.54/29.22 | (507) all_12_1_7 = 0
% 67.54/29.22 |
% 67.54/29.22 | Combining equations (507,2570) yields a new equation:
% 67.54/29.22 | (594) all_26_0_35 = 0
% 67.54/29.22 |
% 67.54/29.22 | From (594) and (1874) follows:
% 67.54/29.22 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.22 |
% 67.54/29.22 +-Applying beta-rule and splitting (365), into two cases.
% 67.54/29.22 |-Branch one:
% 67.54/29.22 | (1190) ~ (aNaturalNumber0(xm) = all_22_0_27)
% 67.54/29.22 |
% 67.54/29.22 | From (554) and (1190) follows:
% 67.54/29.22 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.22 |
% 67.54/29.22 | Using (36) and (1191) yields:
% 67.54/29.22 | (615) $false
% 67.54/29.22 |
% 67.54/29.22 |-The branch is then unsatisfiable
% 67.54/29.22 |-Branch two:
% 67.54/29.22 | (1193) aNaturalNumber0(xm) = all_22_0_27
% 67.54/29.22 | (2578) all_22_0_27 = all_22_1_28
% 67.54/29.22 |
% 67.54/29.22 | Combining equations (554,2578) yields a new equation:
% 67.54/29.22 | (499) all_22_1_28 = 0
% 67.54/29.22 |
% 67.54/29.22 | Combining equations (499,2578) yields a new equation:
% 67.54/29.22 | (554) all_22_0_27 = 0
% 67.54/29.22 |
% 67.54/29.22 | From (554) and (1193) follows:
% 67.54/29.22 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.22 |
% 67.54/29.22 +-Applying beta-rule and splitting (285), into two cases.
% 67.54/29.22 |-Branch one:
% 67.54/29.22 | (1338) ~ (aNaturalNumber0(xm) = all_36_2_52)
% 67.54/29.22 |
% 67.54/29.22 | From (979) and (1338) follows:
% 67.54/29.22 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.22 |
% 67.54/29.22 | Using (36) and (1191) yields:
% 67.54/29.22 | (615) $false
% 67.54/29.22 |
% 67.54/29.22 |-The branch is then unsatisfiable
% 67.54/29.22 |-Branch two:
% 67.54/29.22 | (1341) aNaturalNumber0(xm) = all_36_2_52
% 67.54/29.22 | (979) all_36_2_52 = 0
% 67.54/29.22 |
% 67.54/29.22 | From (979) and (1341) follows:
% 67.54/29.22 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.22 |
% 67.54/29.22 +-Applying beta-rule and splitting (468), into two cases.
% 67.54/29.22 |-Branch one:
% 67.54/29.22 | (1370) ~ (aNaturalNumber0(xn) = all_36_1_51)
% 67.54/29.22 |
% 67.54/29.22 | From (555) and (1370) follows:
% 67.54/29.22 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.22 |
% 67.54/29.22 | Using (53) and (1144) yields:
% 67.54/29.22 | (615) $false
% 67.54/29.22 |
% 67.54/29.22 |-The branch is then unsatisfiable
% 67.54/29.22 |-Branch two:
% 67.54/29.22 | (1373) aNaturalNumber0(xn) = all_36_1_51
% 67.54/29.22 | (2592) all_36_1_51 = all_12_2_8
% 67.54/29.22 |
% 67.54/29.22 | Combining equations (555,2592) yields a new equation:
% 67.54/29.22 | (508) all_12_2_8 = 0
% 67.54/29.22 |
% 67.54/29.22 | Combining equations (508,2592) yields a new equation:
% 67.54/29.22 | (555) all_36_1_51 = 0
% 67.54/29.22 |
% 67.54/29.22 | From (555) and (1373) follows:
% 67.54/29.22 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.22 |
% 67.54/29.22 +-Applying beta-rule and splitting (328), into two cases.
% 67.54/29.22 |-Branch one:
% 67.54/29.22 | (1272) ~ (aNaturalNumber0(xp) = all_36_3_53)
% 67.54/29.22 |
% 67.54/29.22 | From (480) and (1272) follows:
% 67.54/29.22 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.54/29.22 |
% 67.54/29.22 | Using (12) and (1198) yields:
% 67.54/29.22 | (615) $false
% 67.54/29.22 |
% 67.54/29.22 |-The branch is then unsatisfiable
% 67.54/29.22 |-Branch two:
% 67.54/29.22 | (1275) aNaturalNumber0(xp) = all_36_3_53
% 67.54/29.22 | (2600) all_36_3_53 = all_16_1_13
% 67.54/29.22 |
% 67.54/29.22 | Combining equations (480,2600) yields a new equation:
% 67.54/29.22 | (497) all_16_1_13 = 0
% 67.54/29.22 |
% 67.54/29.22 | Combining equations (497,2600) yields a new equation:
% 67.54/29.22 | (480) all_36_3_53 = 0
% 67.54/29.22 |
% 67.54/29.22 | From (480) and (1275) follows:
% 67.54/29.22 | (12) aNaturalNumber0(xp) = 0
% 67.54/29.22 |
% 67.54/29.22 +-Applying beta-rule and splitting (257), into two cases.
% 67.54/29.22 |-Branch one:
% 67.54/29.22 | (1524) ~ (aNaturalNumber0(xr) = all_36_1_51)
% 67.54/29.22 |
% 67.54/29.22 | From (555) and (1524) follows:
% 67.54/29.22 | (1287) ~ (aNaturalNumber0(xr) = 0)
% 67.54/29.22 |
% 67.54/29.22 | Using (10) and (1287) yields:
% 67.54/29.22 | (615) $false
% 67.54/29.22 |
% 67.54/29.22 |-The branch is then unsatisfiable
% 67.54/29.22 |-Branch two:
% 67.54/29.22 | (1527) aNaturalNumber0(xr) = all_36_1_51
% 67.54/29.22 | (2608) all_41_2_56 = all_36_1_51
% 67.54/29.22 |
% 67.54/29.22 | Combining equations (253,2608) yields a new equation:
% 67.54/29.22 | (555) all_36_1_51 = 0
% 67.54/29.22 |
% 67.54/29.22 | Combining equations (555,2608) yields a new equation:
% 67.54/29.22 | (253) all_41_2_56 = 0
% 67.54/29.22 |
% 67.54/29.22 | From (555) and (1527) follows:
% 67.54/29.22 | (10) aNaturalNumber0(xr) = 0
% 67.54/29.22 |
% 67.54/29.22 +-Applying beta-rule and splitting (351), into two cases.
% 67.54/29.22 |-Branch one:
% 67.54/29.22 | (1568) ~ (aNaturalNumber0(xn) = all_24_3_33)
% 67.54/29.22 |
% 67.54/29.22 | From (483) and (1568) follows:
% 67.54/29.22 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.22 |
% 67.54/29.22 | Using (53) and (1144) yields:
% 67.54/29.22 | (615) $false
% 67.54/29.22 |
% 67.54/29.22 |-The branch is then unsatisfiable
% 67.54/29.22 |-Branch two:
% 67.54/29.22 | (1571) aNaturalNumber0(xn) = all_24_3_33
% 67.54/29.22 | (483) all_24_3_33 = 0
% 67.54/29.22 |
% 67.54/29.22 | From (483) and (1571) follows:
% 67.54/29.22 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.22 |
% 67.54/29.22 +-Applying beta-rule and splitting (391), into two cases.
% 67.54/29.22 |-Branch one:
% 67.54/29.22 | (1306) ~ (aNaturalNumber0(xm) = all_12_0_6)
% 67.54/29.22 |
% 67.54/29.22 | From (570) and (1306) follows:
% 67.54/29.22 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.22 |
% 67.54/29.22 | Using (36) and (1191) yields:
% 67.54/29.22 | (615) $false
% 67.54/29.22 |
% 67.54/29.22 |-The branch is then unsatisfiable
% 67.54/29.22 |-Branch two:
% 67.54/29.22 | (1309) aNaturalNumber0(xm) = all_12_0_6
% 67.54/29.22 | (2622) all_12_0_6 = all_12_1_7
% 67.54/29.22 |
% 67.54/29.22 | Combining equations (2622,570) yields a new equation:
% 67.54/29.22 | (506) all_12_1_7 = 0
% 67.54/29.22 |
% 67.54/29.22 | Simplifying 506 yields:
% 67.54/29.22 | (507) all_12_1_7 = 0
% 67.54/29.22 |
% 67.54/29.22 | From (570) and (1309) follows:
% 67.54/29.22 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.22 |
% 67.54/29.22 +-Applying beta-rule and splitting (452), into two cases.
% 67.54/29.22 |-Branch one:
% 67.54/29.22 | (2626) ~ (aNaturalNumber0(sz10) = all_14_2_11)
% 67.54/29.22 |
% 67.54/29.22 | From (451) and (2626) follows:
% 67.54/29.22 | (1252) ~ (aNaturalNumber0(sz10) = 0)
% 67.54/29.22 |
% 67.54/29.22 | Using (16) and (1252) yields:
% 67.54/29.22 | (615) $false
% 67.54/29.22 |
% 67.54/29.22 |-The branch is then unsatisfiable
% 67.54/29.22 |-Branch two:
% 67.54/29.22 | (2629) aNaturalNumber0(sz10) = all_14_2_11
% 67.54/29.22 | (451) all_14_2_11 = 0
% 67.54/29.22 |
% 67.54/29.22 | From (451) and (2629) follows:
% 67.54/29.22 | (16) aNaturalNumber0(sz10) = 0
% 67.54/29.22 |
% 67.54/29.22 +-Applying beta-rule and splitting (426), into two cases.
% 67.54/29.22 |-Branch one:
% 67.54/29.22 | (1151) ~ (aNaturalNumber0(xn) = all_22_0_27)
% 67.54/29.22 |
% 67.54/29.22 | From (554) and (1151) follows:
% 67.54/29.22 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.22 |
% 67.54/29.22 | Using (53) and (1144) yields:
% 67.54/29.22 | (615) $false
% 67.54/29.22 |
% 67.54/29.22 |-The branch is then unsatisfiable
% 67.54/29.22 |-Branch two:
% 67.54/29.22 | (1154) aNaturalNumber0(xn) = all_22_0_27
% 67.54/29.22 | (2636) all_24_4_34 = all_22_0_27
% 67.54/29.22 |
% 67.54/29.22 | Combining equations (511,2636) yields a new equation:
% 67.54/29.22 | (554) all_22_0_27 = 0
% 67.54/29.22 |
% 67.54/29.22 | Combining equations (554,2636) yields a new equation:
% 67.54/29.22 | (511) all_24_4_34 = 0
% 67.54/29.22 |
% 67.54/29.22 | From (554) and (1154) follows:
% 67.54/29.22 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.22 |
% 67.54/29.22 +-Applying beta-rule and splitting (234), into two cases.
% 67.54/29.22 |-Branch one:
% 67.54/29.22 | (1720) ~ (aNaturalNumber0(xr) = all_16_2_14)
% 67.54/29.22 |
% 67.54/29.22 | From (571) and (1720) follows:
% 67.54/29.22 | (1287) ~ (aNaturalNumber0(xr) = 0)
% 67.54/29.22 |
% 67.54/29.22 | Using (10) and (1287) yields:
% 67.54/29.22 | (615) $false
% 67.54/29.22 |
% 67.54/29.22 |-The branch is then unsatisfiable
% 67.54/29.22 |-Branch two:
% 67.54/29.22 | (1723) aNaturalNumber0(xr) = all_16_2_14
% 67.54/29.22 | (571) all_16_2_14 = 0
% 67.54/29.22 |
% 67.54/29.22 | From (571) and (1723) follows:
% 67.54/29.22 | (10) aNaturalNumber0(xr) = 0
% 67.54/29.22 |
% 67.54/29.22 +-Applying beta-rule and splitting (359), into two cases.
% 67.54/29.22 |-Branch one:
% 67.54/29.22 | (1851) ~ (aNaturalNumber0(xm) = all_41_1_55)
% 67.54/29.22 |
% 67.54/29.22 | From (980) and (1851) follows:
% 67.54/29.22 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.22 |
% 67.54/29.22 | Using (36) and (1191) yields:
% 67.54/29.22 | (615) $false
% 67.54/29.22 |
% 67.54/29.22 |-The branch is then unsatisfiable
% 67.54/29.22 |-Branch two:
% 67.54/29.22 | (1854) aNaturalNumber0(xm) = all_41_1_55
% 67.54/29.22 | (2650) all_41_1_55 = all_24_3_33
% 67.54/29.22 |
% 67.54/29.22 | Combining equations (980,2650) yields a new equation:
% 67.54/29.22 | (483) all_24_3_33 = 0
% 67.54/29.22 |
% 67.54/29.22 | Combining equations (483,2650) yields a new equation:
% 67.54/29.22 | (980) all_41_1_55 = 0
% 67.54/29.22 |
% 67.54/29.22 | From (980) and (1854) follows:
% 67.54/29.22 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.22 |
% 67.54/29.22 +-Applying beta-rule and splitting (208), into two cases.
% 67.54/29.22 |-Branch one:
% 67.54/29.22 | (1524) ~ (aNaturalNumber0(xr) = all_36_1_51)
% 67.54/29.22 |
% 67.54/29.22 | From (555) and (1524) follows:
% 67.54/29.22 | (1287) ~ (aNaturalNumber0(xr) = 0)
% 67.54/29.22 |
% 67.54/29.22 | Using (10) and (1287) yields:
% 67.54/29.22 | (615) $false
% 67.54/29.22 |
% 67.54/29.22 |-The branch is then unsatisfiable
% 67.54/29.22 |-Branch two:
% 67.54/29.22 | (1527) aNaturalNumber0(xr) = all_36_1_51
% 67.54/29.22 | (555) all_36_1_51 = 0
% 67.54/29.22 |
% 67.54/29.22 | From (555) and (1527) follows:
% 67.54/29.22 | (10) aNaturalNumber0(xr) = 0
% 67.54/29.22 |
% 67.54/29.22 +-Applying beta-rule and splitting (210), into two cases.
% 67.54/29.22 |-Branch one:
% 67.54/29.22 | (1516) ~ (aNaturalNumber0(xm) = all_36_1_51)
% 67.54/29.22 |
% 67.54/29.22 | From (555) and (1516) follows:
% 67.54/29.22 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.22 |
% 67.54/29.22 | Using (36) and (1191) yields:
% 67.54/29.22 | (615) $false
% 67.54/29.22 |
% 67.54/29.22 |-The branch is then unsatisfiable
% 67.54/29.22 |-Branch two:
% 67.54/29.23 | (1519) aNaturalNumber0(xm) = all_36_1_51
% 67.54/29.23 | (555) all_36_1_51 = 0
% 67.54/29.23 |
% 67.54/29.23 | From (555) and (1519) follows:
% 67.54/29.23 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.23 |
% 67.54/29.23 +-Applying beta-rule and splitting (378), into two cases.
% 67.54/29.23 |-Branch one:
% 67.54/29.23 | (1386) ~ (aNaturalNumber0(xm) = all_26_2_37)
% 67.54/29.23 |
% 67.54/29.23 | From (572) and (1386) follows:
% 67.54/29.23 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.23 |
% 67.54/29.23 | Using (36) and (1191) yields:
% 67.54/29.23 | (615) $false
% 67.54/29.23 |
% 67.54/29.23 |-The branch is then unsatisfiable
% 67.54/29.23 |-Branch two:
% 67.54/29.23 | (1389) aNaturalNumber0(xm) = all_26_2_37
% 67.54/29.23 | (2670) all_26_2_37 = all_14_1_10
% 67.54/29.23 |
% 67.54/29.23 | Combining equations (572,2670) yields a new equation:
% 67.54/29.23 | (503) all_14_1_10 = 0
% 67.54/29.23 |
% 67.54/29.23 | Combining equations (503,2670) yields a new equation:
% 67.54/29.23 | (572) all_26_2_37 = 0
% 67.54/29.23 |
% 67.54/29.23 | From (572) and (1389) follows:
% 67.54/29.23 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.23 |
% 67.54/29.23 +-Applying beta-rule and splitting (416), into two cases.
% 67.54/29.23 |-Branch one:
% 67.54/29.23 | (1646) ~ (aNaturalNumber0(xn) = all_12_0_6)
% 67.54/29.23 |
% 67.54/29.23 | From (570) and (1646) follows:
% 67.54/29.23 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.23 |
% 67.54/29.23 | Using (53) and (1144) yields:
% 67.54/29.23 | (615) $false
% 67.54/29.23 |
% 67.54/29.23 |-The branch is then unsatisfiable
% 67.54/29.23 |-Branch two:
% 67.54/29.23 | (1649) aNaturalNumber0(xn) = all_12_0_6
% 67.54/29.23 | (2678) all_28_2_40 = all_12_0_6
% 67.54/29.23 |
% 67.54/29.23 | Combining equations (514,2678) yields a new equation:
% 67.54/29.23 | (570) all_12_0_6 = 0
% 67.54/29.23 |
% 67.54/29.23 | Combining equations (570,2678) yields a new equation:
% 67.54/29.23 | (514) all_28_2_40 = 0
% 67.54/29.23 |
% 67.54/29.23 | From (570) and (1649) follows:
% 67.54/29.23 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.23 |
% 67.54/29.23 +-Applying beta-rule and splitting (462), into two cases.
% 67.54/29.23 |-Branch one:
% 67.54/29.23 | (1568) ~ (aNaturalNumber0(xn) = all_24_3_33)
% 67.54/29.23 |
% 67.54/29.23 | From (483) and (1568) follows:
% 67.54/29.23 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.23 |
% 67.54/29.23 | Using (53) and (1144) yields:
% 67.54/29.23 | (615) $false
% 67.54/29.23 |
% 67.54/29.23 |-The branch is then unsatisfiable
% 67.54/29.23 |-Branch two:
% 67.54/29.23 | (1571) aNaturalNumber0(xn) = all_24_3_33
% 67.54/29.23 | (2686) all_24_3_33 = all_14_2_11
% 67.54/29.23 |
% 67.54/29.23 | Combining equations (483,2686) yields a new equation:
% 67.54/29.23 | (451) all_14_2_11 = 0
% 67.54/29.23 |
% 67.54/29.23 | Combining equations (451,2686) yields a new equation:
% 67.54/29.23 | (483) all_24_3_33 = 0
% 67.54/29.23 |
% 67.54/29.23 | From (483) and (1571) follows:
% 67.54/29.23 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.23 |
% 67.54/29.23 +-Applying beta-rule and splitting (344), into two cases.
% 67.54/29.23 |-Branch one:
% 67.54/29.23 | (2690) ~ (aNaturalNumber0(sz10) = all_28_1_39)
% 67.54/29.23 |
% 67.54/29.23 | From (515) and (2690) follows:
% 67.54/29.23 | (1252) ~ (aNaturalNumber0(sz10) = 0)
% 67.54/29.23 |
% 67.54/29.23 | Using (16) and (1252) yields:
% 67.54/29.23 | (615) $false
% 67.54/29.23 |
% 67.54/29.23 |-The branch is then unsatisfiable
% 67.54/29.23 |-Branch two:
% 67.54/29.23 | (2693) aNaturalNumber0(sz10) = all_28_1_39
% 67.54/29.23 | (515) all_28_1_39 = 0
% 67.54/29.23 |
% 67.54/29.23 +-Applying beta-rule and splitting (282), into two cases.
% 67.54/29.23 |-Branch one:
% 67.54/29.23 | (2695) ~ (aNaturalNumber0(xk) = all_36_3_53)
% 67.54/29.23 |
% 67.54/29.23 | From (480) and (2695) follows:
% 67.54/29.23 | (974) ~ (aNaturalNumber0(xk) = 0)
% 67.54/29.23 |
% 67.54/29.23 | Using (972) and (974) yields:
% 67.54/29.23 | (615) $false
% 67.54/29.23 |
% 67.54/29.23 |-The branch is then unsatisfiable
% 67.54/29.23 |-Branch two:
% 67.54/29.23 | (2698) aNaturalNumber0(xk) = all_36_3_53
% 67.54/29.23 | (2699) all_41_1_55 = all_36_3_53
% 67.54/29.23 |
% 67.54/29.23 | Combining equations (980,2699) yields a new equation:
% 67.54/29.23 | (480) all_36_3_53 = 0
% 67.54/29.23 |
% 67.54/29.23 | Combining equations (480,2699) yields a new equation:
% 67.54/29.23 | (980) all_41_1_55 = 0
% 67.54/29.23 |
% 67.54/29.23 | From (480) and (2698) follows:
% 67.54/29.23 | (972) aNaturalNumber0(xk) = 0
% 67.54/29.23 |
% 67.54/29.23 +-Applying beta-rule and splitting (465), into two cases.
% 67.54/29.23 |-Branch one:
% 67.54/29.23 | (1159) ~ (aNaturalNumber0(xn) = all_12_1_7)
% 67.54/29.23 |
% 67.54/29.23 | From (507) and (1159) follows:
% 67.54/29.23 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.23 |
% 67.54/29.23 | Using (53) and (1144) yields:
% 67.54/29.23 | (615) $false
% 67.54/29.23 |
% 67.54/29.23 |-The branch is then unsatisfiable
% 67.54/29.23 |-Branch two:
% 67.54/29.23 | (1162) aNaturalNumber0(xn) = all_12_1_7
% 67.54/29.23 | (2707) all_14_2_11 = all_12_1_7
% 67.54/29.23 |
% 67.54/29.23 | Combining equations (451,2707) yields a new equation:
% 67.54/29.23 | (507) all_12_1_7 = 0
% 67.54/29.23 |
% 67.54/29.23 | From (507) and (1162) follows:
% 67.54/29.23 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.23 |
% 67.54/29.23 +-Applying beta-rule and splitting (346), into two cases.
% 67.54/29.23 |-Branch one:
% 67.54/29.23 | (1190) ~ (aNaturalNumber0(xm) = all_22_0_27)
% 67.54/29.23 |
% 67.54/29.23 | From (554) and (1190) follows:
% 67.54/29.23 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.23 |
% 67.54/29.23 | Using (36) and (1191) yields:
% 67.54/29.23 | (615) $false
% 67.54/29.23 |
% 67.54/29.23 |-The branch is then unsatisfiable
% 67.54/29.23 |-Branch two:
% 67.54/29.23 | (1193) aNaturalNumber0(xm) = all_22_0_27
% 67.54/29.23 | (2714) all_28_1_39 = all_22_0_27
% 67.54/29.23 |
% 67.54/29.23 | Combining equations (515,2714) yields a new equation:
% 67.54/29.23 | (554) all_22_0_27 = 0
% 67.54/29.23 |
% 67.54/29.23 | Combining equations (554,2714) yields a new equation:
% 67.54/29.23 | (515) all_28_1_39 = 0
% 67.54/29.23 |
% 67.54/29.23 | From (554) and (1193) follows:
% 67.54/29.23 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.23 |
% 67.54/29.23 +-Applying beta-rule and splitting (343), into two cases.
% 67.54/29.23 |-Branch one:
% 67.54/29.23 | (1143) ~ (aNaturalNumber0(xn) = all_28_1_39)
% 67.54/29.23 |
% 67.54/29.23 | From (515) and (1143) follows:
% 67.54/29.23 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.23 |
% 67.54/29.23 | Using (53) and (1144) yields:
% 67.54/29.23 | (615) $false
% 67.54/29.23 |
% 67.54/29.23 |-The branch is then unsatisfiable
% 67.54/29.23 |-Branch two:
% 67.54/29.23 | (1146) aNaturalNumber0(xn) = all_28_1_39
% 67.54/29.23 | (515) all_28_1_39 = 0
% 67.54/29.23 |
% 67.54/29.23 | From (515) and (1146) follows:
% 67.54/29.23 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.23 |
% 67.54/29.23 +-Applying beta-rule and splitting (319), into two cases.
% 67.54/29.23 |-Branch one:
% 67.54/29.23 | (1197) ~ (aNaturalNumber0(xp) = all_41_2_56)
% 67.54/29.23 |
% 67.54/29.23 | From (253) and (1197) follows:
% 67.54/29.23 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.54/29.23 |
% 67.54/29.23 | Using (12) and (1198) yields:
% 67.54/29.23 | (615) $false
% 67.54/29.23 |
% 67.54/29.23 |-The branch is then unsatisfiable
% 67.54/29.23 |-Branch two:
% 67.54/29.23 | (1200) aNaturalNumber0(xp) = all_41_2_56
% 67.54/29.23 | (2728) all_41_2_56 = all_24_2_32
% 67.54/29.23 |
% 67.54/29.23 | Combining equations (253,2728) yields a new equation:
% 67.54/29.23 | (493) all_24_2_32 = 0
% 67.54/29.23 |
% 67.54/29.23 | Combining equations (493,2728) yields a new equation:
% 67.54/29.23 | (253) all_41_2_56 = 0
% 67.54/29.23 |
% 67.54/29.23 | From (253) and (1200) follows:
% 67.54/29.23 | (12) aNaturalNumber0(xp) = 0
% 67.54/29.23 |
% 67.54/29.23 +-Applying beta-rule and splitting (254), into two cases.
% 67.54/29.23 |-Branch one:
% 67.54/29.23 | (1197) ~ (aNaturalNumber0(xp) = all_41_2_56)
% 67.54/29.23 |
% 67.54/29.23 | From (253) and (1197) follows:
% 67.54/29.23 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.54/29.23 |
% 67.54/29.23 | Using (12) and (1198) yields:
% 67.54/29.23 | (615) $false
% 67.54/29.23 |
% 67.54/29.23 |-The branch is then unsatisfiable
% 67.54/29.23 |-Branch two:
% 67.54/29.23 | (1200) aNaturalNumber0(xp) = all_41_2_56
% 67.54/29.23 | (253) all_41_2_56 = 0
% 67.54/29.23 |
% 67.54/29.23 | From (253) and (1200) follows:
% 67.54/29.23 | (12) aNaturalNumber0(xp) = 0
% 67.54/29.23 |
% 67.54/29.23 +-Applying beta-rule and splitting (377), into two cases.
% 67.54/29.23 |-Branch one:
% 67.54/29.23 | (1871) ~ (aNaturalNumber0(xm) = all_26_0_35)
% 67.54/29.23 |
% 67.54/29.23 | From (594) and (1871) follows:
% 67.54/29.23 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.23 |
% 67.54/29.23 | Using (36) and (1191) yields:
% 67.54/29.23 | (615) $false
% 67.54/29.23 |
% 67.54/29.23 |-The branch is then unsatisfiable
% 67.54/29.23 |-Branch two:
% 67.54/29.23 | (1874) aNaturalNumber0(xm) = all_26_0_35
% 67.54/29.23 | (2742) all_26_0_35 = all_14_1_10
% 67.54/29.23 |
% 67.54/29.23 | Combining equations (594,2742) yields a new equation:
% 67.54/29.23 | (503) all_14_1_10 = 0
% 67.54/29.23 |
% 67.54/29.23 | Combining equations (503,2742) yields a new equation:
% 67.54/29.23 | (594) all_26_0_35 = 0
% 67.54/29.23 |
% 67.54/29.23 | From (594) and (1874) follows:
% 67.54/29.23 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.23 |
% 67.54/29.23 +-Applying beta-rule and splitting (251), into two cases.
% 67.54/29.23 |-Branch one:
% 67.54/29.23 | (1603) ~ (aNaturalNumber0(all_0_5_5) = all_26_0_35)
% 67.54/29.23 |
% 67.54/29.23 | From (594) and (1603) follows:
% 67.54/29.23 | (1258) ~ (aNaturalNumber0(all_0_5_5) = 0)
% 67.54/29.23 |
% 67.54/29.23 | Using (573) and (1258) yields:
% 67.54/29.23 | (615) $false
% 67.54/29.23 |
% 67.54/29.23 |-The branch is then unsatisfiable
% 67.54/29.23 |-Branch two:
% 67.54/29.23 | (1606) aNaturalNumber0(all_0_5_5) = all_26_0_35
% 67.54/29.23 | (2750) all_26_0_35 = all_12_0_6
% 67.54/29.23 |
% 67.54/29.23 | Combining equations (594,2750) yields a new equation:
% 67.54/29.23 | (570) all_12_0_6 = 0
% 67.54/29.23 |
% 67.54/29.23 | Combining equations (570,2750) yields a new equation:
% 67.54/29.23 | (594) all_26_0_35 = 0
% 67.54/29.23 |
% 67.54/29.23 +-Applying beta-rule and splitting (427), into two cases.
% 67.54/29.23 |-Branch one:
% 67.54/29.23 | (1480) ~ (aNaturalNumber0(xn) = all_16_2_14)
% 67.54/29.23 |
% 67.54/29.23 | From (571) and (1480) follows:
% 67.54/29.23 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.23 |
% 67.54/29.23 | Using (53) and (1144) yields:
% 67.54/29.23 | (615) $false
% 67.54/29.23 |
% 67.54/29.23 |-The branch is then unsatisfiable
% 67.54/29.23 |-Branch two:
% 67.54/29.23 | (1483) aNaturalNumber0(xn) = all_16_2_14
% 67.54/29.23 | (2757) all_24_4_34 = all_16_2_14
% 67.54/29.23 |
% 67.54/29.23 | Combining equations (511,2757) yields a new equation:
% 67.54/29.23 | (571) all_16_2_14 = 0
% 67.54/29.23 |
% 67.54/29.23 | From (571) and (1483) follows:
% 67.54/29.23 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.23 |
% 67.54/29.23 +-Applying beta-rule and splitting (295), into two cases.
% 67.54/29.23 |-Branch one:
% 67.54/29.23 | (1554) ~ (aNaturalNumber0(xp) = all_22_0_27)
% 67.54/29.23 |
% 67.54/29.23 | From (554) and (1554) follows:
% 67.54/29.24 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.54/29.24 |
% 67.54/29.24 | Using (12) and (1198) yields:
% 67.54/29.24 | (615) $false
% 67.54/29.24 |
% 67.54/29.24 |-The branch is then unsatisfiable
% 67.54/29.24 |-Branch two:
% 67.54/29.24 | (1557) aNaturalNumber0(xp) = all_22_0_27
% 67.54/29.24 | (2764) all_30_6_47 = all_22_0_27
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (1242,2764) yields a new equation:
% 67.54/29.24 | (554) all_22_0_27 = 0
% 67.54/29.24 |
% 67.54/29.24 | From (554) and (1557) follows:
% 67.54/29.24 | (12) aNaturalNumber0(xp) = 0
% 67.54/29.24 |
% 67.54/29.24 +-Applying beta-rule and splitting (410), into two cases.
% 67.54/29.24 |-Branch one:
% 67.54/29.24 | (2767) ~ (aNaturalNumber0(sz00) = all_28_2_40)
% 67.54/29.24 |
% 67.54/29.24 | From (514) and (2767) follows:
% 67.54/29.24 | (1503) ~ (aNaturalNumber0(sz00) = 0)
% 67.54/29.24 |
% 67.54/29.24 | Using (41) and (1503) yields:
% 67.54/29.24 | (615) $false
% 67.54/29.24 |
% 67.54/29.24 |-The branch is then unsatisfiable
% 67.54/29.24 |-Branch two:
% 67.54/29.24 | (2770) aNaturalNumber0(sz00) = all_28_2_40
% 67.54/29.24 | (514) all_28_2_40 = 0
% 67.54/29.24 |
% 67.54/29.24 +-Applying beta-rule and splitting (414), into two cases.
% 67.54/29.24 |-Branch one:
% 67.54/29.24 | (1245) ~ (aNaturalNumber0(xn) = all_26_2_37)
% 67.54/29.24 |
% 67.54/29.24 | From (572) and (1245) follows:
% 67.54/29.24 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.24 |
% 67.54/29.24 | Using (53) and (1144) yields:
% 67.54/29.24 | (615) $false
% 67.54/29.24 |
% 67.54/29.24 |-The branch is then unsatisfiable
% 67.54/29.24 |-Branch two:
% 67.54/29.24 | (1248) aNaturalNumber0(xn) = all_26_2_37
% 67.54/29.24 | (2776) all_28_2_40 = all_26_2_37
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (514,2776) yields a new equation:
% 67.54/29.24 | (572) all_26_2_37 = 0
% 67.54/29.24 |
% 67.54/29.24 | From (572) and (1248) follows:
% 67.54/29.24 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.24 |
% 67.54/29.24 +-Applying beta-rule and splitting (308), into two cases.
% 67.54/29.24 |-Branch one:
% 67.54/29.24 | (1464) ~ (aNaturalNumber0(xp) = all_16_2_14)
% 67.54/29.24 |
% 67.54/29.24 | From (571) and (1464) follows:
% 67.54/29.24 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.54/29.24 |
% 67.54/29.24 | Using (12) and (1198) yields:
% 67.54/29.24 | (615) $false
% 67.54/29.24 |
% 67.54/29.24 |-The branch is then unsatisfiable
% 67.54/29.24 |-Branch two:
% 67.54/29.24 | (1467) aNaturalNumber0(xp) = all_16_2_14
% 67.54/29.24 | (2783) all_26_1_36 = all_16_2_14
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (303,2783) yields a new equation:
% 67.54/29.24 | (571) all_16_2_14 = 0
% 67.54/29.24 |
% 67.54/29.24 | From (571) and (1467) follows:
% 67.54/29.24 | (12) aNaturalNumber0(xp) = 0
% 67.54/29.24 |
% 67.54/29.24 +-Applying beta-rule and splitting (399), into two cases.
% 67.54/29.24 |-Branch one:
% 67.54/29.24 | (1646) ~ (aNaturalNumber0(xn) = all_12_0_6)
% 67.54/29.24 |
% 67.54/29.24 | From (570) and (1646) follows:
% 67.54/29.24 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.24 |
% 67.54/29.24 | Using (53) and (1144) yields:
% 67.54/29.24 | (615) $false
% 67.54/29.24 |
% 67.54/29.24 |-The branch is then unsatisfiable
% 67.54/29.24 |-Branch two:
% 67.54/29.24 | (1649) aNaturalNumber0(xn) = all_12_0_6
% 67.54/29.24 | (2790) all_30_8_49 = all_12_0_6
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (516,2790) yields a new equation:
% 67.54/29.24 | (570) all_12_0_6 = 0
% 67.54/29.24 |
% 67.54/29.24 | From (570) and (1649) follows:
% 67.54/29.24 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.24 |
% 67.54/29.24 +-Applying beta-rule and splitting (216), into two cases.
% 67.54/29.24 |-Branch one:
% 67.54/29.24 | (1151) ~ (aNaturalNumber0(xn) = all_22_0_27)
% 67.54/29.24 |
% 67.54/29.24 | From (554) and (1151) follows:
% 67.54/29.24 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.24 |
% 67.54/29.24 | Using (53) and (1144) yields:
% 67.54/29.24 | (615) $false
% 67.54/29.24 |
% 67.54/29.24 |-The branch is then unsatisfiable
% 67.54/29.24 |-Branch two:
% 67.54/29.24 | (1154) aNaturalNumber0(xn) = all_22_0_27
% 67.54/29.24 | (554) all_22_0_27 = 0
% 67.54/29.24 |
% 67.54/29.24 | From (554) and (1154) follows:
% 67.54/29.24 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.24 |
% 67.54/29.24 +-Applying beta-rule and splitting (432), into two cases.
% 67.54/29.24 |-Branch one:
% 67.54/29.24 | (1143) ~ (aNaturalNumber0(xn) = all_28_1_39)
% 67.54/29.24 |
% 67.54/29.24 | From (515) and (1143) follows:
% 67.54/29.24 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.24 |
% 67.54/29.24 | Using (53) and (1144) yields:
% 67.54/29.24 | (615) $false
% 67.54/29.24 |
% 67.54/29.24 |-The branch is then unsatisfiable
% 67.54/29.24 |-Branch two:
% 67.54/29.24 | (1146) aNaturalNumber0(xn) = all_28_1_39
% 67.54/29.24 | (2803) all_28_1_39 = all_24_4_34
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (515,2803) yields a new equation:
% 67.54/29.24 | (511) all_24_4_34 = 0
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (511,2803) yields a new equation:
% 67.54/29.24 | (515) all_28_1_39 = 0
% 67.54/29.24 |
% 67.54/29.24 | From (515) and (1146) follows:
% 67.54/29.24 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.24 |
% 67.54/29.24 +-Applying beta-rule and splitting (258), into two cases.
% 67.54/29.24 |-Branch one:
% 67.54/29.24 | (1532) ~ (aNaturalNumber0(xr) = all_22_0_27)
% 67.54/29.24 |
% 67.54/29.24 | From (554) and (1532) follows:
% 67.54/29.24 | (1287) ~ (aNaturalNumber0(xr) = 0)
% 67.54/29.24 |
% 67.54/29.24 | Using (10) and (1287) yields:
% 67.54/29.24 | (615) $false
% 67.54/29.24 |
% 67.54/29.24 |-The branch is then unsatisfiable
% 67.54/29.24 |-Branch two:
% 67.54/29.24 | (1535) aNaturalNumber0(xr) = all_22_0_27
% 67.54/29.24 | (2811) all_41_2_56 = all_22_0_27
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (253,2811) yields a new equation:
% 67.54/29.24 | (554) all_22_0_27 = 0
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (554,2811) yields a new equation:
% 67.54/29.24 | (253) all_41_2_56 = 0
% 67.54/29.24 |
% 67.54/29.24 +-Applying beta-rule and splitting (341), into two cases.
% 67.54/29.24 |-Branch one:
% 67.54/29.24 | (1851) ~ (aNaturalNumber0(xm) = all_41_1_55)
% 67.54/29.24 |
% 67.54/29.24 | From (980) and (1851) follows:
% 67.54/29.24 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.24 |
% 67.54/29.24 | Using (36) and (1191) yields:
% 67.54/29.24 | (615) $false
% 67.54/29.24 |
% 67.54/29.24 |-The branch is then unsatisfiable
% 67.54/29.24 |-Branch two:
% 67.54/29.24 | (1854) aNaturalNumber0(xm) = all_41_1_55
% 67.54/29.24 | (2818) all_41_1_55 = all_30_7_48
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (980,2818) yields a new equation:
% 67.54/29.24 | (331) all_30_7_48 = 0
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (331,2818) yields a new equation:
% 67.54/29.24 | (980) all_41_1_55 = 0
% 67.54/29.24 |
% 67.54/29.24 | From (980) and (1854) follows:
% 67.54/29.24 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.24 |
% 67.54/29.24 +-Applying beta-rule and splitting (292), into two cases.
% 67.54/29.24 |-Branch one:
% 67.54/29.24 | (2695) ~ (aNaturalNumber0(xk) = all_36_3_53)
% 67.54/29.24 |
% 67.54/29.24 | From (480) and (2695) follows:
% 67.54/29.24 | (974) ~ (aNaturalNumber0(xk) = 0)
% 67.54/29.24 |
% 67.54/29.24 | Using (972) and (974) yields:
% 67.54/29.24 | (615) $false
% 67.54/29.24 |
% 67.54/29.24 |-The branch is then unsatisfiable
% 67.54/29.24 |-Branch two:
% 67.54/29.24 | (2698) aNaturalNumber0(xk) = all_36_3_53
% 67.54/29.24 | (2826) all_36_2_52 = all_36_3_53
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (979,2826) yields a new equation:
% 67.54/29.24 | (480) all_36_3_53 = 0
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (480,2826) yields a new equation:
% 67.54/29.24 | (979) all_36_2_52 = 0
% 67.54/29.24 |
% 67.54/29.24 | From (480) and (2698) follows:
% 67.54/29.24 | (972) aNaturalNumber0(xk) = 0
% 67.54/29.24 |
% 67.54/29.24 +-Applying beta-rule and splitting (288), into two cases.
% 67.54/29.24 |-Branch one:
% 67.54/29.24 | (2436) ~ (aNaturalNumber0(xk) = all_26_0_35)
% 67.54/29.24 |
% 67.54/29.24 | From (594) and (2436) follows:
% 67.54/29.24 | (974) ~ (aNaturalNumber0(xk) = 0)
% 67.54/29.24 |
% 67.54/29.24 | Using (972) and (974) yields:
% 67.54/29.24 | (615) $false
% 67.54/29.24 |
% 67.54/29.24 |-The branch is then unsatisfiable
% 67.54/29.24 |-Branch two:
% 67.54/29.24 | (2439) aNaturalNumber0(xk) = all_26_0_35
% 67.54/29.24 | (2834) all_36_2_52 = all_26_0_35
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (979,2834) yields a new equation:
% 67.54/29.24 | (594) all_26_0_35 = 0
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (594,2834) yields a new equation:
% 67.54/29.24 | (979) all_36_2_52 = 0
% 67.54/29.24 |
% 67.54/29.24 | From (594) and (2439) follows:
% 67.54/29.24 | (972) aNaturalNumber0(xk) = 0
% 67.54/29.24 |
% 67.54/29.24 +-Applying beta-rule and splitting (380), into two cases.
% 67.54/29.24 |-Branch one:
% 67.54/29.24 | (1306) ~ (aNaturalNumber0(xm) = all_12_0_6)
% 67.54/29.24 |
% 67.54/29.24 | From (570) and (1306) follows:
% 67.54/29.24 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.24 |
% 67.54/29.24 | Using (36) and (1191) yields:
% 67.54/29.24 | (615) $false
% 67.54/29.24 |
% 67.54/29.24 |-The branch is then unsatisfiable
% 67.54/29.24 |-Branch two:
% 67.54/29.24 | (1309) aNaturalNumber0(xm) = all_12_0_6
% 67.54/29.24 | (2842) all_14_1_10 = all_12_0_6
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (503,2842) yields a new equation:
% 67.54/29.24 | (570) all_12_0_6 = 0
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (570,2842) yields a new equation:
% 67.54/29.24 | (503) all_14_1_10 = 0
% 67.54/29.24 |
% 67.54/29.24 | From (570) and (1309) follows:
% 67.54/29.24 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.24 |
% 67.54/29.24 +-Applying beta-rule and splitting (323), into two cases.
% 67.54/29.24 |-Branch one:
% 67.54/29.24 | (1213) ~ (aNaturalNumber0(xp) = all_26_0_35)
% 67.54/29.24 |
% 67.54/29.24 | From (594) and (1213) follows:
% 67.54/29.24 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.54/29.24 |
% 67.54/29.24 | Using (12) and (1198) yields:
% 67.54/29.24 | (615) $false
% 67.54/29.24 |
% 67.54/29.24 |-The branch is then unsatisfiable
% 67.54/29.24 |-Branch two:
% 67.54/29.24 | (1216) aNaturalNumber0(xp) = all_26_0_35
% 67.54/29.24 | (2850) all_26_0_35 = all_16_1_13
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (594,2850) yields a new equation:
% 67.54/29.24 | (497) all_16_1_13 = 0
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (497,2850) yields a new equation:
% 67.54/29.24 | (594) all_26_0_35 = 0
% 67.54/29.24 |
% 67.54/29.24 | From (594) and (1216) follows:
% 67.54/29.24 | (12) aNaturalNumber0(xp) = 0
% 67.54/29.24 |
% 67.54/29.24 +-Applying beta-rule and splitting (478), into two cases.
% 67.54/29.24 |-Branch one:
% 67.54/29.24 | (1294) ~ (aNaturalNumber0(xn) = all_14_1_10)
% 67.54/29.24 |
% 67.54/29.24 | From (503) and (1294) follows:
% 67.54/29.24 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.24 |
% 67.54/29.24 | Using (53) and (1144) yields:
% 67.54/29.24 | (615) $false
% 67.54/29.24 |
% 67.54/29.24 |-The branch is then unsatisfiable
% 67.54/29.24 |-Branch two:
% 67.54/29.24 | (1297) aNaturalNumber0(xn) = all_14_1_10
% 67.54/29.24 | (2858) all_14_1_10 = all_12_2_8
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (503,2858) yields a new equation:
% 67.54/29.24 | (508) all_12_2_8 = 0
% 67.54/29.24 |
% 67.54/29.24 | Combining equations (508,2858) yields a new equation:
% 67.54/29.24 | (503) all_14_1_10 = 0
% 67.54/29.24 |
% 67.54/29.24 | From (503) and (1297) follows:
% 67.54/29.24 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.24 |
% 67.54/29.24 +-Applying beta-rule and splitting (472), into two cases.
% 67.54/29.24 |-Branch one:
% 67.54/29.24 | (1174) ~ (aNaturalNumber0(xn) = all_41_2_56)
% 67.54/29.24 |
% 67.54/29.24 | From (253) and (1174) follows:
% 67.54/29.25 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.25 |
% 67.54/29.25 | Using (53) and (1144) yields:
% 67.54/29.25 | (615) $false
% 67.54/29.25 |
% 67.54/29.25 |-The branch is then unsatisfiable
% 67.54/29.25 |-Branch two:
% 67.54/29.25 | (1177) aNaturalNumber0(xn) = all_41_2_56
% 67.54/29.25 | (2866) all_41_2_56 = all_12_2_8
% 67.54/29.25 |
% 67.54/29.25 | Combining equations (253,2866) yields a new equation:
% 67.54/29.25 | (508) all_12_2_8 = 0
% 67.54/29.25 |
% 67.54/29.25 | Combining equations (508,2866) yields a new equation:
% 67.54/29.25 | (253) all_41_2_56 = 0
% 67.54/29.25 |
% 67.54/29.25 | From (253) and (1177) follows:
% 67.54/29.25 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.25 |
% 67.54/29.25 +-Applying beta-rule and splitting (317), into two cases.
% 67.54/29.25 |-Branch one:
% 67.54/29.25 | (1205) ~ (aNaturalNumber0(xp) = all_26_2_37)
% 67.54/29.25 |
% 67.54/29.25 | From (572) and (1205) follows:
% 67.54/29.25 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.54/29.25 |
% 67.54/29.25 | Using (12) and (1198) yields:
% 67.54/29.25 | (615) $false
% 67.54/29.25 |
% 67.54/29.25 |-The branch is then unsatisfiable
% 67.54/29.25 |-Branch two:
% 67.54/29.25 | (1208) aNaturalNumber0(xp) = all_26_2_37
% 67.54/29.25 | (2874) all_26_2_37 = all_24_2_32
% 67.54/29.25 |
% 67.54/29.25 | Combining equations (572,2874) yields a new equation:
% 67.54/29.25 | (493) all_24_2_32 = 0
% 67.54/29.25 |
% 67.54/29.25 | Combining equations (493,2874) yields a new equation:
% 67.54/29.25 | (572) all_26_2_37 = 0
% 67.54/29.25 |
% 67.54/29.25 | From (572) and (1208) follows:
% 67.54/29.25 | (12) aNaturalNumber0(xp) = 0
% 67.54/29.25 |
% 67.54/29.25 +-Applying beta-rule and splitting (392), into two cases.
% 67.54/29.25 |-Branch one:
% 67.54/29.25 | (1314) ~ (aNaturalNumber0(xm) = all_41_2_56)
% 67.54/29.25 |
% 67.54/29.25 | From (253) and (1314) follows:
% 67.54/29.25 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.25 |
% 67.54/29.25 | Using (36) and (1191) yields:
% 67.54/29.25 | (615) $false
% 67.54/29.25 |
% 67.54/29.25 |-The branch is then unsatisfiable
% 67.54/29.25 |-Branch two:
% 67.54/29.25 | (1317) aNaturalNumber0(xm) = all_41_2_56
% 67.54/29.25 | (2882) all_41_2_56 = all_12_1_7
% 67.54/29.25 |
% 67.54/29.25 | Combining equations (253,2882) yields a new equation:
% 67.54/29.25 | (507) all_12_1_7 = 0
% 67.54/29.25 |
% 67.54/29.25 | Combining equations (507,2882) yields a new equation:
% 67.54/29.25 | (253) all_41_2_56 = 0
% 67.54/29.25 |
% 67.54/29.25 | From (253) and (1317) follows:
% 67.54/29.25 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.25 |
% 67.54/29.25 +-Applying beta-rule and splitting (379), into two cases.
% 67.54/29.25 |-Branch one:
% 67.54/29.25 | (1562) ~ (aNaturalNumber0(xm) = all_16_2_14)
% 67.54/29.25 |
% 67.54/29.25 | From (571) and (1562) follows:
% 67.54/29.25 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.25 |
% 67.54/29.25 | Using (36) and (1191) yields:
% 67.54/29.25 | (615) $false
% 67.54/29.25 |
% 67.54/29.25 |-The branch is then unsatisfiable
% 67.54/29.25 |-Branch two:
% 67.54/29.25 | (1565) aNaturalNumber0(xm) = all_16_2_14
% 67.54/29.25 | (2890) all_16_2_14 = all_14_1_10
% 67.54/29.25 |
% 67.54/29.25 | From (571) and (1565) follows:
% 67.54/29.25 | (36) aNaturalNumber0(xm) = 0
% 67.54/29.25 |
% 67.54/29.25 +-Applying beta-rule and splitting (370), into two cases.
% 67.54/29.25 |-Branch one:
% 67.54/29.25 | (1330) ~ (aNaturalNumber0(xm) = all_36_3_53)
% 67.54/29.25 |
% 67.54/29.25 | From (480) and (1330) follows:
% 67.54/29.25 | (1191) ~ (aNaturalNumber0(xm) = 0)
% 67.54/29.25 |
% 67.54/29.25 | Using (36) and (1191) yields:
% 67.54/29.25 | (615) $false
% 67.54/29.25 |
% 67.54/29.25 |-The branch is then unsatisfiable
% 67.54/29.25 |-Branch two:
% 67.54/29.25 | (1333) aNaturalNumber0(xm) = all_36_3_53
% 67.54/29.25 | (2896) all_36_3_53 = all_22_1_28
% 67.54/29.25 |
% 67.54/29.25 | Combining equations (480,2896) yields a new equation:
% 67.54/29.25 | (499) all_22_1_28 = 0
% 67.54/29.25 |
% 67.54/29.25 | Combining equations (499,2896) yields a new equation:
% 67.54/29.25 | (480) all_36_3_53 = 0
% 67.54/29.25 |
% 67.54/29.25 +-Applying beta-rule and splitting (326), into two cases.
% 67.54/29.25 |-Branch one:
% 67.54/29.25 | (2054) ~ (aNaturalNumber0(xp) = all_12_0_6)
% 67.54/29.25 |
% 67.54/29.25 | From (570) and (2054) follows:
% 67.54/29.25 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.54/29.25 |
% 67.54/29.25 | Using (12) and (1198) yields:
% 67.54/29.25 | (615) $false
% 67.54/29.25 |
% 67.54/29.25 |-The branch is then unsatisfiable
% 67.54/29.25 |-Branch two:
% 67.54/29.25 | (2057) aNaturalNumber0(xp) = all_12_0_6
% 67.54/29.25 | (2903) all_16_1_13 = all_12_0_6
% 67.54/29.25 |
% 67.54/29.25 | Combining equations (497,2903) yields a new equation:
% 67.54/29.25 | (570) all_12_0_6 = 0
% 67.54/29.25 |
% 67.54/29.25 | From (570) and (2057) follows:
% 67.54/29.25 | (12) aNaturalNumber0(xp) = 0
% 67.54/29.25 |
% 67.54/29.25 +-Applying beta-rule and splitting (314), into two cases.
% 67.54/29.25 |-Branch one:
% 67.54/29.25 | (1418) ~ (aNaturalNumber0(xp) = all_36_1_51)
% 67.54/29.25 |
% 67.54/29.25 | From (555) and (1418) follows:
% 67.54/29.25 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.54/29.25 |
% 67.54/29.25 | Using (12) and (1198) yields:
% 67.54/29.25 | (615) $false
% 67.54/29.25 |
% 67.54/29.25 |-The branch is then unsatisfiable
% 67.54/29.25 |-Branch two:
% 67.54/29.25 | (1421) aNaturalNumber0(xp) = all_36_1_51
% 67.54/29.25 | (2910) all_36_1_51 = all_24_2_32
% 67.54/29.25 |
% 67.54/29.25 | Combining equations (555,2910) yields a new equation:
% 67.54/29.25 | (493) all_24_2_32 = 0
% 67.54/29.25 |
% 67.54/29.25 | Combining equations (493,2910) yields a new equation:
% 67.54/29.25 | (555) all_36_1_51 = 0
% 67.54/29.25 |
% 67.54/29.25 | From (555) and (1421) follows:
% 67.54/29.25 | (12) aNaturalNumber0(xp) = 0
% 67.54/29.25 |
% 67.54/29.25 +-Applying beta-rule and splitting (385), into two cases.
% 67.54/29.25 |-Branch one:
% 67.54/29.25 | (1159) ~ (aNaturalNumber0(xn) = all_12_1_7)
% 67.54/29.25 |
% 67.54/29.25 | From (507) and (1159) follows:
% 67.54/29.25 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.25 |
% 67.54/29.25 | Using (53) and (1144) yields:
% 67.54/29.25 | (615) $false
% 67.54/29.25 |
% 67.54/29.25 |-The branch is then unsatisfiable
% 67.54/29.25 |-Branch two:
% 67.54/29.25 | (1162) aNaturalNumber0(xn) = all_12_1_7
% 67.54/29.25 | (507) all_12_1_7 = 0
% 67.54/29.25 |
% 67.54/29.25 | From (507) and (1162) follows:
% 67.54/29.25 | (53) aNaturalNumber0(xn) = 0
% 67.54/29.25 |
% 67.54/29.25 +-Applying beta-rule and splitting (290), into two cases.
% 67.54/29.25 |-Branch one:
% 67.54/29.25 | (2920) ~ (aNaturalNumber0(xk) = all_12_0_6)
% 67.54/29.25 |
% 67.54/29.25 | From (570) and (2920) follows:
% 67.54/29.25 | (974) ~ (aNaturalNumber0(xk) = 0)
% 67.54/29.25 |
% 67.54/29.25 | Using (972) and (974) yields:
% 67.54/29.25 | (615) $false
% 67.54/29.25 |
% 67.54/29.25 |-The branch is then unsatisfiable
% 67.54/29.25 |-Branch two:
% 67.54/29.25 | (2923) aNaturalNumber0(xk) = all_12_0_6
% 67.54/29.25 | (2924) all_36_2_52 = all_12_0_6
% 67.54/29.25 |
% 67.54/29.25 | Combining equations (979,2924) yields a new equation:
% 67.54/29.25 | (570) all_12_0_6 = 0
% 67.54/29.25 |
% 67.54/29.25 | From (570) and (2923) follows:
% 67.54/29.25 | (972) aNaturalNumber0(xk) = 0
% 67.54/29.25 |
% 67.54/29.25 +-Applying beta-rule and splitting (442), into two cases.
% 67.54/29.25 |-Branch one:
% 67.54/29.25 | (1646) ~ (aNaturalNumber0(xn) = all_12_0_6)
% 67.54/29.25 |
% 67.54/29.25 | From (570) and (1646) follows:
% 67.54/29.25 | (1144) ~ (aNaturalNumber0(xn) = 0)
% 67.54/29.25 |
% 67.54/29.25 | Using (53) and (1144) yields:
% 67.54/29.25 | (615) $false
% 67.54/29.25 |
% 67.54/29.25 |-The branch is then unsatisfiable
% 67.54/29.25 |-Branch two:
% 67.54/29.25 | (1649) aNaturalNumber0(xn) = all_12_0_6
% 67.54/29.25 | (2931) all_22_2_29 = all_12_0_6
% 67.54/29.25 |
% 67.54/29.25 | Combining equations (2931,510) yields a new equation:
% 67.54/29.25 | (2932) all_12_0_6 = 0
% 67.54/29.25 |
% 67.54/29.25 | Simplifying 2932 yields:
% 67.54/29.25 | (570) all_12_0_6 = 0
% 67.54/29.25 |
% 67.54/29.25 +-Applying beta-rule and splitting (322), into two cases.
% 67.54/29.25 |-Branch one:
% 67.54/29.25 | (1554) ~ (aNaturalNumber0(xp) = all_22_0_27)
% 67.54/29.25 |
% 67.54/29.25 | From (554) and (1554) follows:
% 67.54/29.25 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.54/29.25 |
% 67.54/29.25 | Using (12) and (1198) yields:
% 67.54/29.25 | (615) $false
% 67.54/29.25 |
% 67.54/29.25 |-The branch is then unsatisfiable
% 67.54/29.25 |-Branch two:
% 67.54/29.25 | (1557) aNaturalNumber0(xp) = all_22_0_27
% 67.54/29.25 | (2938) all_22_0_27 = all_16_1_13
% 67.54/29.25 |
% 67.54/29.25 | Combining equations (554,2938) yields a new equation:
% 67.54/29.25 | (497) all_16_1_13 = 0
% 67.54/29.25 |
% 67.54/29.25 | Combining equations (497,2938) yields a new equation:
% 67.54/29.25 | (554) all_22_0_27 = 0
% 67.54/29.25 |
% 67.54/29.25 | From (554) and (1557) follows:
% 67.54/29.25 | (12) aNaturalNumber0(xp) = 0
% 67.54/29.25 |
% 67.54/29.25 +-Applying beta-rule and splitting (311), into two cases.
% 67.54/29.25 |-Branch one:
% 67.54/29.25 | (1272) ~ (aNaturalNumber0(xp) = all_36_3_53)
% 67.54/29.25 |
% 67.54/29.25 | From (480) and (1272) follows:
% 67.54/29.25 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.54/29.25 |
% 67.54/29.25 | Using (12) and (1198) yields:
% 67.54/29.25 | (615) $false
% 67.54/29.25 |
% 67.54/29.25 |-The branch is then unsatisfiable
% 67.54/29.25 |-Branch two:
% 67.54/29.25 | (1275) aNaturalNumber0(xp) = all_36_3_53
% 67.54/29.25 | (2946) all_36_3_53 = all_26_1_36
% 67.54/29.25 |
% 67.54/29.25 | Combining equations (480,2946) yields a new equation:
% 67.54/29.25 | (303) all_26_1_36 = 0
% 67.54/29.25 |
% 67.54/29.25 | Combining equations (303,2946) yields a new equation:
% 67.54/29.25 | (480) all_36_3_53 = 0
% 67.54/29.25 |
% 67.54/29.25 | From (480) and (1275) follows:
% 67.54/29.25 | (12) aNaturalNumber0(xp) = 0
% 67.54/29.25 |
% 67.54/29.25 +-Applying beta-rule and splitting (244), into two cases.
% 67.54/29.25 |-Branch one:
% 67.54/29.25 | (2054) ~ (aNaturalNumber0(xp) = all_12_0_6)
% 67.54/29.25 |
% 67.54/29.25 | From (570) and (2054) follows:
% 67.54/29.25 | (1198) ~ (aNaturalNumber0(xp) = 0)
% 67.54/29.25 |
% 67.54/29.25 | Using (12) and (1198) yields:
% 67.54/29.25 | (615) $false
% 67.54/29.25 |
% 67.54/29.25 |-The branch is then unsatisfiable
% 67.54/29.25 |-Branch two:
% 67.54/29.25 | (2057) aNaturalNumber0(xp) = all_12_0_6
% 67.54/29.25 | (570) all_12_0_6 = 0
% 67.54/29.25 |
% 67.54/29.25 | From (570) and (2057) follows:
% 67.54/29.25 | (12) aNaturalNumber0(xp) = 0
% 67.54/29.25 |
% 67.54/29.25 +-Applying beta-rule and splitting (218), into two cases.
% 67.54/29.25 |-Branch one:
% 67.54/29.25 | (1937) ~ (aNaturalNumber0(all_0_3_3) = 0)
% 67.54/29.25 |
% 67.54/29.25 | Using (556) and (1937) yields:
% 67.54/29.25 | (615) $false
% 67.54/29.25 |
% 67.54/29.25 |-The branch is then unsatisfiable
% 67.54/29.25 |-Branch two:
% 67.54/29.25 | (556) aNaturalNumber0(all_0_3_3) = 0
% 67.54/29.25 | (554) all_22_0_27 = 0
% 67.54/29.25 |
% 67.54/29.25 | Instantiating formula (81) with xk, all_432_0_148 and discharging atoms doDivides0(all_432_0_148, xk) = 0, yields:
% 67.70/29.25 | (2960) xk = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_432_0_148, xk) = v2 & aNaturalNumber0(all_432_0_148) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 67.70/29.25 |
% 67.70/29.25 | Instantiating formula (81) with xk, all_386_0_142 and discharging atoms doDivides0(all_386_0_142, xk) = 0, yields:
% 67.70/29.26 | (2961) xk = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_386_0_142, xk) = v2 & aNaturalNumber0(all_386_0_142) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 67.70/29.26 |
% 67.70/29.26 | Instantiating formula (45) with all_0_3_3, xk, xp, all_21_2_26, xr and discharging atoms sdtasdt0(xr, all_21_2_26) = xk, sdtasdt0(xk, xp) = all_0_3_3, yields:
% 67.70/29.26 | (2962) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_21_2_26, xp) = v3 & sdtasdt0(xr, v3) = v4 & aNaturalNumber0(all_21_2_26) = v1 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xp) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_3_3))
% 67.70/29.26 |
% 67.70/29.26 | Instantiating formula (37) with xp, all_36_0_50, all_0_3_3, xk and discharging atoms doDivides0(xk, all_0_3_3) = all_36_0_50, sdtasdt0(xk, xp) = all_0_3_3, yields:
% 67.70/29.26 | (2963) all_36_0_50 = 0 | ? [v0] : ? [v1] : (( ~ (v0 = 0) & aNaturalNumber0(xp) = v0) | (aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xk) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 67.70/29.26 |
% 67.70/29.26 | Instantiating formula (7) with all_0_3_3, xp, xp, xk and discharging atoms doDivides0(xp, all_0_3_3) = 0, sdtasdt0(xk, xp) = all_0_3_3, yields:
% 67.70/29.26 | (2964) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, xk) = v7 & doDivides0(xp, xp) = v8 & iLess0(v5, all_0_4_4) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xk, xp) = v4 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v1 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 67.70/29.26 |
% 67.70/29.26 | Instantiating formula (45) with xp, xp, all_186_2_128, all_186_2_128, xp and discharging atoms sdtasdt0(xp, all_186_2_128) = xp, yields:
% 67.70/29.26 | (2965) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_186_2_128, all_186_2_128) = v3 & sdtasdt0(xp, v3) = v4 & aNaturalNumber0(all_186_2_128) = v2 & aNaturalNumber0(all_186_2_128) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = xp))
% 67.70/29.26 |
% 67.70/29.26 | Instantiating formula (7) with xp, xp, all_186_2_128, xp and discharging atoms doDivides0(xp, xp) = 0, sdtasdt0(xp, all_186_2_128) = xp, yields:
% 67.70/29.26 | (2966) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, all_186_2_128) = v8 & doDivides0(xp, xp) = v7 & iLess0(v5, all_0_4_4) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xp, all_186_2_128) = v4 & aNaturalNumber0(all_186_2_128) = v1 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 67.70/29.26 |
% 67.70/29.26 | Instantiating formula (7) with xp, all_208_0_135, all_186_2_128, xp and discharging atoms doDivides0(all_208_0_135, xp) = 0, sdtasdt0(xp, all_186_2_128) = xp, yields:
% 67.70/29.26 | (2967) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(all_208_0_135) = v3 & doDivides0(all_208_0_135, all_186_2_128) = v8 & doDivides0(all_208_0_135, xp) = v7 & iLess0(v5, all_0_4_4) = v6 & sdtpldt0(v4, all_208_0_135) = v5 & sdtpldt0(xp, all_186_2_128) = v4 & aNaturalNumber0(all_208_0_135) = v2 & aNaturalNumber0(all_186_2_128) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 67.70/29.26 |
% 67.70/29.26 | Instantiating formula (27) with xp, all_186_2_128, xp and discharging atoms sdtasdt0(xp, all_186_2_128) = xp, yields:
% 67.70/29.26 | (2968) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_186_2_128, xp) = v2 & aNaturalNumber0(all_186_2_128) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xp))
% 67.70/29.26 |
% 67.70/29.26 | Instantiating formula (45) with all_0_3_3, xp, xk, all_186_2_128, xp and discharging atoms sdtasdt0(xp, all_186_2_128) = xp, sdtasdt0(xp, xk) = all_0_3_3, yields:
% 67.70/29.26 | (2969) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_186_2_128, xk) = v3 & sdtasdt0(xp, v3) = v4 & aNaturalNumber0(all_186_2_128) = v1 & aNaturalNumber0(xk) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_3_3))
% 67.70/29.26 |
% 67.70/29.26 | Instantiating formula (78) with all_179_3_103, xp, all_179_4_104 and discharging atoms sdtpldt0(all_179_4_104, xp) = all_179_3_103, yields:
% 67.70/29.26 | (2970) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, all_179_4_104) = v2 & aNaturalNumber0(all_179_4_104) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_179_3_103))
% 67.70/29.26 |
% 67.70/29.26 | Instantiating formula (43) with all_179_3_103, xp, all_179_4_104 and discharging atoms sdtpldt0(all_179_4_104, xp) = all_179_3_103, yields:
% 67.70/29.26 | (2971) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_179_3_103) = v2 & aNaturalNumber0(all_179_4_104) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 67.70/29.26 |
% 67.70/29.26 | Instantiating formula (49) with all_0_4_4, all_24_1_31, xn, xp, xm and discharging atoms sdtpldt0(all_24_1_31, xn) = all_0_4_4, sdtpldt0(xm, xp) = all_24_1_31, yields:
% 67.70/29.26 | (2972) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xp, xn) = v3 & sdtpldt0(xm, v3) = v4 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_4_4))
% 67.70/29.26 |
% 67.70/29.26 | Instantiating formula (40) with xp, xm, all_19_2_20, xp and discharging atoms doDivides0(xp, xp) = 0, sdtpldt0(all_19_2_20, xm) = xp, yields:
% 67.70/29.26 | (2973) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(xp, all_19_2_20) = v3 & doDivides0(xp, xm) = v4 & aNaturalNumber0(all_19_2_20) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 67.70/29.26 |
% 67.70/29.26 | Instantiating formula (40) with xp, xn, all_18_2_17, xp and discharging atoms doDivides0(xp, xp) = 0, sdtpldt0(all_18_2_17, xn) = xp, yields:
% 67.70/29.26 | (2974) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(xp, all_18_2_17) = v3 & doDivides0(xp, xn) = v4 & aNaturalNumber0(all_18_2_17) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 67.70/29.26 |
% 67.70/29.26 | Instantiating formula (49) with all_179_4_104, xp, xk, all_19_2_20, xm and discharging atoms sdtpldt0(xp, xk) = all_179_4_104, sdtpldt0(xm, all_19_2_20) = xp, yields:
% 67.70/29.26 | (2975) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_19_2_20, xk) = v3 & sdtpldt0(xm, v3) = v4 & aNaturalNumber0(all_19_2_20) = v1 & aNaturalNumber0(xk) = v2 & aNaturalNumber0(xm) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_179_4_104))
% 67.70/29.26 |
% 67.70/29.26 | Instantiating formula (49) with all_179_4_104, xp, xk, all_18_2_17, xn and discharging atoms sdtpldt0(xp, xk) = all_179_4_104, sdtpldt0(xn, all_18_2_17) = xp, yields:
% 67.70/29.26 | (2976) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_18_2_17, xk) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(all_18_2_17) = v1 & aNaturalNumber0(xk) = v2 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_179_4_104))
% 67.70/29.26 |
% 67.70/29.26 | Instantiating formula (49) with all_179_3_103, all_179_4_104, xp, xk, xp and discharging atoms sdtpldt0(all_179_4_104, xp) = all_179_3_103, sdtpldt0(xp, xk) = all_179_4_104, yields:
% 67.70/29.26 | (2977) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xk, xp) = v3 & sdtpldt0(xp, v3) = v4 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_179_3_103))
% 67.70/29.26 |
% 67.70/29.26 | Instantiating formula (49) with all_179_4_104, xp, xk, xm, all_19_2_20 and discharging atoms sdtpldt0(all_19_2_20, xm) = xp, sdtpldt0(xp, xk) = all_179_4_104, yields:
% 67.70/29.26 | (2978) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_19_2_20, v3) = v4 & sdtpldt0(xm, xk) = v3 & aNaturalNumber0(all_19_2_20) = v0 & aNaturalNumber0(xk) = v2 & aNaturalNumber0(xm) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_179_4_104))
% 67.70/29.26 |
% 67.70/29.26 | Instantiating formula (49) with all_179_4_104, xp, xk, xn, all_18_2_17 and discharging atoms sdtpldt0(all_18_2_17, xn) = xp, sdtpldt0(xp, xk) = all_179_4_104, yields:
% 67.71/29.26 | (2979) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_18_2_17, v3) = v4 & sdtpldt0(xn, xk) = v3 & aNaturalNumber0(all_18_2_17) = v0 & aNaturalNumber0(xk) = v2 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_179_4_104))
% 67.71/29.26 |
% 67.71/29.26 | Instantiating formula (78) with all_179_4_104, xk, xp and discharging atoms sdtpldt0(xp, xk) = all_179_4_104, yields:
% 67.71/29.26 | (2980) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xk, xp) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_179_4_104))
% 67.71/29.26 |
% 67.71/29.26 | Instantiating formula (43) with all_179_4_104, xk, xp and discharging atoms sdtpldt0(xp, xk) = all_179_4_104, yields:
% 67.71/29.26 | (2981) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_179_4_104) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 67.71/29.26 |
% 67.71/29.26 | Instantiating formula (24) with all_161_1_68, all_0_5_5, xp, xm, xn and discharging atoms sdtpldt0(xn, xp) = all_161_1_68, sdtpldt0(xn, xm) = all_0_5_5, yields:
% 67.71/29.26 | (2982) xp = xm | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xp, xn) = v4 & sdtpldt0(xm, xn) = v3 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v4 = v3) & ~ (all_161_1_68 = all_0_5_5))))
% 67.71/29.26 |
% 67.71/29.26 | Instantiating formula (78) with all_161_1_68, xp, xn and discharging atoms sdtpldt0(xn, xp) = all_161_1_68, yields:
% 67.71/29.26 | (2983) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, xn) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_161_1_68))
% 67.71/29.26 |
% 67.71/29.26 | Instantiating formula (43) with all_161_1_68, xp, xn and discharging atoms sdtpldt0(xn, xp) = all_161_1_68, yields:
% 67.71/29.26 | (2984) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_161_1_68) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 67.71/29.26 |
% 67.71/29.26 | Instantiating (2984) with all_2334_0_168, all_2334_1_169, all_2334_2_170 yields:
% 67.71/29.26 | (2985) aNaturalNumber0(all_161_1_68) = all_2334_0_168 & aNaturalNumber0(xp) = all_2334_1_169 & aNaturalNumber0(xn) = all_2334_2_170 & ( ~ (all_2334_1_169 = 0) | ~ (all_2334_2_170 = 0) | all_2334_0_168 = 0)
% 67.71/29.26 |
% 67.71/29.26 | Applying alpha-rule on (2985) yields:
% 67.71/29.26 | (2986) aNaturalNumber0(all_161_1_68) = all_2334_0_168
% 67.71/29.26 | (2987) aNaturalNumber0(xp) = all_2334_1_169
% 67.71/29.26 | (2988) aNaturalNumber0(xn) = all_2334_2_170
% 67.71/29.26 | (2989) ~ (all_2334_1_169 = 0) | ~ (all_2334_2_170 = 0) | all_2334_0_168 = 0
% 67.71/29.26 |
% 67.71/29.26 | Instantiating (2983) with all_2336_0_171, all_2336_1_172, all_2336_2_173 yields:
% 67.71/29.26 | (2990) sdtpldt0(xp, xn) = all_2336_0_171 & aNaturalNumber0(xp) = all_2336_1_172 & aNaturalNumber0(xn) = all_2336_2_173 & ( ~ (all_2336_1_172 = 0) | ~ (all_2336_2_173 = 0) | all_2336_0_171 = all_161_1_68)
% 67.71/29.26 |
% 67.71/29.26 | Applying alpha-rule on (2990) yields:
% 67.71/29.26 | (2991) sdtpldt0(xp, xn) = all_2336_0_171
% 67.71/29.26 | (2992) aNaturalNumber0(xp) = all_2336_1_172
% 67.71/29.26 | (2993) aNaturalNumber0(xn) = all_2336_2_173
% 67.71/29.26 | (2994) ~ (all_2336_1_172 = 0) | ~ (all_2336_2_173 = 0) | all_2336_0_171 = all_161_1_68
% 67.71/29.26 |
% 67.71/29.26 | Instantiating (2976) with all_2352_0_197, all_2352_1_198, all_2352_2_199, all_2352_3_200, all_2352_4_201 yields:
% 67.71/29.26 | (2995) sdtpldt0(all_18_2_17, xk) = all_2352_1_198 & sdtpldt0(xn, all_2352_1_198) = all_2352_0_197 & aNaturalNumber0(all_18_2_17) = all_2352_3_200 & aNaturalNumber0(xk) = all_2352_2_199 & aNaturalNumber0(xn) = all_2352_4_201 & ( ~ (all_2352_2_199 = 0) | ~ (all_2352_3_200 = 0) | ~ (all_2352_4_201 = 0) | all_2352_0_197 = all_179_4_104)
% 67.71/29.26 |
% 67.71/29.26 | Applying alpha-rule on (2995) yields:
% 67.71/29.26 | (2996) aNaturalNumber0(all_18_2_17) = all_2352_3_200
% 67.71/29.26 | (2997) aNaturalNumber0(xk) = all_2352_2_199
% 67.71/29.26 | (2998) sdtpldt0(xn, all_2352_1_198) = all_2352_0_197
% 67.71/29.26 | (2999) sdtpldt0(all_18_2_17, xk) = all_2352_1_198
% 67.71/29.26 | (3000) aNaturalNumber0(xn) = all_2352_4_201
% 67.71/29.26 | (3001) ~ (all_2352_2_199 = 0) | ~ (all_2352_3_200 = 0) | ~ (all_2352_4_201 = 0) | all_2352_0_197 = all_179_4_104
% 67.71/29.26 |
% 67.71/29.26 | Instantiating (2981) with all_2356_0_205, all_2356_1_206, all_2356_2_207 yields:
% 67.71/29.26 | (3002) aNaturalNumber0(all_179_4_104) = all_2356_0_205 & aNaturalNumber0(xk) = all_2356_1_206 & aNaturalNumber0(xp) = all_2356_2_207 & ( ~ (all_2356_1_206 = 0) | ~ (all_2356_2_207 = 0) | all_2356_0_205 = 0)
% 67.71/29.26 |
% 67.71/29.26 | Applying alpha-rule on (3002) yields:
% 67.71/29.26 | (3003) aNaturalNumber0(all_179_4_104) = all_2356_0_205
% 67.71/29.26 | (3004) aNaturalNumber0(xk) = all_2356_1_206
% 67.71/29.26 | (3005) aNaturalNumber0(xp) = all_2356_2_207
% 67.71/29.26 | (3006) ~ (all_2356_1_206 = 0) | ~ (all_2356_2_207 = 0) | all_2356_0_205 = 0
% 67.71/29.26 |
% 67.71/29.26 | Instantiating (2980) with all_2358_0_208, all_2358_1_209, all_2358_2_210 yields:
% 67.71/29.26 | (3007) sdtpldt0(xk, xp) = all_2358_0_208 & aNaturalNumber0(xk) = all_2358_1_209 & aNaturalNumber0(xp) = all_2358_2_210 & ( ~ (all_2358_1_209 = 0) | ~ (all_2358_2_210 = 0) | all_2358_0_208 = all_179_4_104)
% 67.71/29.26 |
% 67.71/29.26 | Applying alpha-rule on (3007) yields:
% 67.71/29.26 | (3008) sdtpldt0(xk, xp) = all_2358_0_208
% 67.71/29.27 | (3009) aNaturalNumber0(xk) = all_2358_1_209
% 67.71/29.27 | (3010) aNaturalNumber0(xp) = all_2358_2_210
% 67.71/29.27 | (3011) ~ (all_2358_1_209 = 0) | ~ (all_2358_2_210 = 0) | all_2358_0_208 = all_179_4_104
% 67.71/29.27 |
% 67.71/29.27 | Instantiating (2978) with all_2360_0_211, all_2360_1_212, all_2360_2_213, all_2360_3_214, all_2360_4_215 yields:
% 67.71/29.27 | (3012) sdtpldt0(all_19_2_20, all_2360_1_212) = all_2360_0_211 & sdtpldt0(xm, xk) = all_2360_1_212 & aNaturalNumber0(all_19_2_20) = all_2360_4_215 & aNaturalNumber0(xk) = all_2360_2_213 & aNaturalNumber0(xm) = all_2360_3_214 & ( ~ (all_2360_2_213 = 0) | ~ (all_2360_3_214 = 0) | ~ (all_2360_4_215 = 0) | all_2360_0_211 = all_179_4_104)
% 67.71/29.27 |
% 67.71/29.27 | Applying alpha-rule on (3012) yields:
% 67.71/29.27 | (3013) aNaturalNumber0(xm) = all_2360_3_214
% 67.71/29.27 | (3014) sdtpldt0(xm, xk) = all_2360_1_212
% 67.71/29.27 | (3015) sdtpldt0(all_19_2_20, all_2360_1_212) = all_2360_0_211
% 67.71/29.27 | (3016) aNaturalNumber0(all_19_2_20) = all_2360_4_215
% 67.71/29.27 | (3017) ~ (all_2360_2_213 = 0) | ~ (all_2360_3_214 = 0) | ~ (all_2360_4_215 = 0) | all_2360_0_211 = all_179_4_104
% 67.71/29.27 | (3018) aNaturalNumber0(xk) = all_2360_2_213
% 67.71/29.27 |
% 67.71/29.27 | Instantiating (2975) with all_2364_0_219, all_2364_1_220, all_2364_2_221, all_2364_3_222, all_2364_4_223 yields:
% 67.71/29.27 | (3019) sdtpldt0(all_19_2_20, xk) = all_2364_1_220 & sdtpldt0(xm, all_2364_1_220) = all_2364_0_219 & aNaturalNumber0(all_19_2_20) = all_2364_3_222 & aNaturalNumber0(xk) = all_2364_2_221 & aNaturalNumber0(xm) = all_2364_4_223 & ( ~ (all_2364_2_221 = 0) | ~ (all_2364_3_222 = 0) | ~ (all_2364_4_223 = 0) | all_2364_0_219 = all_179_4_104)
% 67.71/29.27 |
% 67.71/29.27 | Applying alpha-rule on (3019) yields:
% 67.71/29.27 | (3020) aNaturalNumber0(xk) = all_2364_2_221
% 67.71/29.27 | (3021) sdtpldt0(all_19_2_20, xk) = all_2364_1_220
% 67.71/29.27 | (3022) ~ (all_2364_2_221 = 0) | ~ (all_2364_3_222 = 0) | ~ (all_2364_4_223 = 0) | all_2364_0_219 = all_179_4_104
% 67.71/29.27 | (3023) aNaturalNumber0(xm) = all_2364_4_223
% 67.71/29.27 | (3024) aNaturalNumber0(all_19_2_20) = all_2364_3_222
% 67.71/29.27 | (3025) sdtpldt0(xm, all_2364_1_220) = all_2364_0_219
% 67.71/29.27 |
% 67.71/29.27 | Instantiating (2974) with all_2376_0_249, all_2376_1_250, all_2376_2_251, all_2376_3_252, all_2376_4_253 yields:
% 67.71/29.27 | (3026) doDivides0(xp, all_18_2_17) = all_2376_1_250 & doDivides0(xp, xn) = all_2376_0_249 & aNaturalNumber0(all_18_2_17) = all_2376_3_252 & aNaturalNumber0(xp) = all_2376_4_253 & aNaturalNumber0(xn) = all_2376_2_251 & ( ~ (all_2376_1_250 = 0) | ~ (all_2376_2_251 = 0) | ~ (all_2376_3_252 = 0) | ~ (all_2376_4_253 = 0) | all_2376_0_249 = 0)
% 67.71/29.27 |
% 67.71/29.27 | Applying alpha-rule on (3026) yields:
% 67.71/29.27 | (3027) ~ (all_2376_1_250 = 0) | ~ (all_2376_2_251 = 0) | ~ (all_2376_3_252 = 0) | ~ (all_2376_4_253 = 0) | all_2376_0_249 = 0
% 67.71/29.27 | (3028) doDivides0(xp, all_18_2_17) = all_2376_1_250
% 67.71/29.27 | (3029) aNaturalNumber0(xn) = all_2376_2_251
% 67.71/29.27 | (3030) doDivides0(xp, xn) = all_2376_0_249
% 67.71/29.27 | (3031) aNaturalNumber0(xp) = all_2376_4_253
% 67.71/29.27 | (3032) aNaturalNumber0(all_18_2_17) = all_2376_3_252
% 67.71/29.27 |
% 67.71/29.27 | Instantiating (2972) with all_2378_0_254, all_2378_1_255, all_2378_2_256, all_2378_3_257, all_2378_4_258 yields:
% 67.71/29.27 | (3033) sdtpldt0(xp, xn) = all_2378_1_255 & sdtpldt0(xm, all_2378_1_255) = all_2378_0_254 & aNaturalNumber0(xp) = all_2378_3_257 & aNaturalNumber0(xm) = all_2378_4_258 & aNaturalNumber0(xn) = all_2378_2_256 & ( ~ (all_2378_2_256 = 0) | ~ (all_2378_3_257 = 0) | ~ (all_2378_4_258 = 0) | all_2378_0_254 = all_0_4_4)
% 67.71/29.27 |
% 67.71/29.27 | Applying alpha-rule on (3033) yields:
% 67.71/29.27 | (3034) aNaturalNumber0(xm) = all_2378_4_258
% 67.71/29.27 | (3035) ~ (all_2378_2_256 = 0) | ~ (all_2378_3_257 = 0) | ~ (all_2378_4_258 = 0) | all_2378_0_254 = all_0_4_4
% 67.71/29.27 | (3036) sdtpldt0(xm, all_2378_1_255) = all_2378_0_254
% 67.71/29.27 | (3037) aNaturalNumber0(xn) = all_2378_2_256
% 67.71/29.27 | (3038) sdtpldt0(xp, xn) = all_2378_1_255
% 67.71/29.27 | (3039) aNaturalNumber0(xp) = all_2378_3_257
% 67.71/29.27 |
% 67.71/29.27 | Instantiating (2968) with all_2380_0_259, all_2380_1_260, all_2380_2_261 yields:
% 67.71/29.27 | (3040) sdtasdt0(all_186_2_128, xp) = all_2380_0_259 & aNaturalNumber0(all_186_2_128) = all_2380_1_260 & aNaturalNumber0(xp) = all_2380_2_261 & ( ~ (all_2380_1_260 = 0) | ~ (all_2380_2_261 = 0) | all_2380_0_259 = xp)
% 67.71/29.27 |
% 67.71/29.27 | Applying alpha-rule on (3040) yields:
% 67.71/29.27 | (3041) sdtasdt0(all_186_2_128, xp) = all_2380_0_259
% 67.71/29.27 | (3042) aNaturalNumber0(all_186_2_128) = all_2380_1_260
% 67.71/29.27 | (3043) aNaturalNumber0(xp) = all_2380_2_261
% 67.71/29.27 | (3044) ~ (all_2380_1_260 = 0) | ~ (all_2380_2_261 = 0) | all_2380_0_259 = xp
% 67.71/29.27 |
% 67.71/29.27 | Instantiating (2967) with all_2382_0_262, all_2382_1_263, all_2382_2_264, all_2382_3_265, all_2382_4_266, all_2382_5_267, all_2382_6_268, all_2382_7_269, all_2382_8_270 yields:
% 67.71/29.27 | (3045) isPrime0(all_208_0_135) = all_2382_5_267 & doDivides0(all_208_0_135, all_186_2_128) = all_2382_0_262 & doDivides0(all_208_0_135, xp) = all_2382_1_263 & iLess0(all_2382_3_265, all_0_4_4) = all_2382_2_264 & sdtpldt0(all_2382_4_266, all_208_0_135) = all_2382_3_265 & sdtpldt0(xp, all_186_2_128) = all_2382_4_266 & aNaturalNumber0(all_208_0_135) = all_2382_6_268 & aNaturalNumber0(all_186_2_128) = all_2382_7_269 & aNaturalNumber0(xp) = all_2382_8_270 & ( ~ (all_2382_2_264 = 0) | ~ (all_2382_5_267 = 0) | ~ (all_2382_6_268 = 0) | ~ (all_2382_7_269 = 0) | ~ (all_2382_8_270 = 0) | all_2382_0_262 = 0 | all_2382_1_263 = 0)
% 67.71/29.27 |
% 67.71/29.27 | Applying alpha-rule on (3045) yields:
% 67.71/29.27 | (3046) aNaturalNumber0(xp) = all_2382_8_270
% 67.71/29.27 | (3047) sdtpldt0(xp, all_186_2_128) = all_2382_4_266
% 67.71/29.27 | (3048) sdtpldt0(all_2382_4_266, all_208_0_135) = all_2382_3_265
% 67.71/29.27 | (3049) aNaturalNumber0(all_208_0_135) = all_2382_6_268
% 67.71/29.27 | (3050) doDivides0(all_208_0_135, xp) = all_2382_1_263
% 67.71/29.27 | (3051) iLess0(all_2382_3_265, all_0_4_4) = all_2382_2_264
% 67.71/29.27 | (3052) doDivides0(all_208_0_135, all_186_2_128) = all_2382_0_262
% 67.71/29.27 | (3053) isPrime0(all_208_0_135) = all_2382_5_267
% 67.71/29.27 | (3054) ~ (all_2382_2_264 = 0) | ~ (all_2382_5_267 = 0) | ~ (all_2382_6_268 = 0) | ~ (all_2382_7_269 = 0) | ~ (all_2382_8_270 = 0) | all_2382_0_262 = 0 | all_2382_1_263 = 0
% 67.71/29.27 | (3055) aNaturalNumber0(all_186_2_128) = all_2382_7_269
% 67.71/29.27 |
% 67.71/29.27 | Instantiating (2966) with all_2384_0_271, all_2384_1_272, all_2384_2_273, all_2384_3_274, all_2384_4_275, all_2384_5_276, all_2384_6_277, all_2384_7_278, all_2384_8_279 yields:
% 67.71/29.27 | (3056) isPrime0(xp) = all_2384_5_276 & doDivides0(xp, all_186_2_128) = all_2384_0_271 & doDivides0(xp, xp) = all_2384_1_272 & iLess0(all_2384_3_274, all_0_4_4) = all_2384_2_273 & sdtpldt0(all_2384_4_275, xp) = all_2384_3_274 & sdtpldt0(xp, all_186_2_128) = all_2384_4_275 & aNaturalNumber0(all_186_2_128) = all_2384_7_278 & aNaturalNumber0(xp) = all_2384_6_277 & aNaturalNumber0(xp) = all_2384_8_279 & ( ~ (all_2384_2_273 = 0) | ~ (all_2384_5_276 = 0) | ~ (all_2384_6_277 = 0) | ~ (all_2384_7_278 = 0) | ~ (all_2384_8_279 = 0) | all_2384_0_271 = 0 | all_2384_1_272 = 0)
% 67.71/29.27 |
% 67.71/29.27 | Applying alpha-rule on (3056) yields:
% 67.71/29.27 | (3057) aNaturalNumber0(all_186_2_128) = all_2384_7_278
% 67.71/29.27 | (3058) isPrime0(xp) = all_2384_5_276
% 67.71/29.27 | (3059) aNaturalNumber0(xp) = all_2384_6_277
% 67.71/29.27 | (3060) ~ (all_2384_2_273 = 0) | ~ (all_2384_5_276 = 0) | ~ (all_2384_6_277 = 0) | ~ (all_2384_7_278 = 0) | ~ (all_2384_8_279 = 0) | all_2384_0_271 = 0 | all_2384_1_272 = 0
% 67.71/29.27 | (3061) doDivides0(xp, all_186_2_128) = all_2384_0_271
% 67.71/29.27 | (3062) doDivides0(xp, xp) = all_2384_1_272
% 67.71/29.27 | (3063) iLess0(all_2384_3_274, all_0_4_4) = all_2384_2_273
% 67.71/29.27 | (3064) sdtpldt0(all_2384_4_275, xp) = all_2384_3_274
% 67.71/29.27 | (3065) aNaturalNumber0(xp) = all_2384_8_279
% 67.71/29.27 | (3066) sdtpldt0(xp, all_186_2_128) = all_2384_4_275
% 67.71/29.27 |
% 67.71/29.27 | Instantiating (2977) with all_2388_0_283, all_2388_1_284, all_2388_2_285, all_2388_3_286, all_2388_4_287 yields:
% 67.71/29.27 | (3067) sdtpldt0(xk, xp) = all_2388_1_284 & sdtpldt0(xp, all_2388_1_284) = all_2388_0_283 & aNaturalNumber0(xk) = all_2388_3_286 & aNaturalNumber0(xp) = all_2388_2_285 & aNaturalNumber0(xp) = all_2388_4_287 & ( ~ (all_2388_2_285 = 0) | ~ (all_2388_3_286 = 0) | ~ (all_2388_4_287 = 0) | all_2388_0_283 = all_179_3_103)
% 67.71/29.27 |
% 67.71/29.27 | Applying alpha-rule on (3067) yields:
% 67.71/29.27 | (3068) sdtpldt0(xk, xp) = all_2388_1_284
% 67.71/29.27 | (3069) aNaturalNumber0(xk) = all_2388_3_286
% 67.71/29.27 | (3070) sdtpldt0(xp, all_2388_1_284) = all_2388_0_283
% 67.71/29.27 | (3071) aNaturalNumber0(xp) = all_2388_2_285
% 67.71/29.27 | (3072) aNaturalNumber0(xp) = all_2388_4_287
% 67.71/29.28 | (3073) ~ (all_2388_2_285 = 0) | ~ (all_2388_3_286 = 0) | ~ (all_2388_4_287 = 0) | all_2388_0_283 = all_179_3_103
% 67.71/29.28 |
% 67.71/29.28 | Instantiating (2979) with all_2399_0_312, all_2399_1_313, all_2399_2_314, all_2399_3_315, all_2399_4_316 yields:
% 67.71/29.28 | (3074) sdtpldt0(all_18_2_17, all_2399_1_313) = all_2399_0_312 & sdtpldt0(xn, xk) = all_2399_1_313 & aNaturalNumber0(all_18_2_17) = all_2399_4_316 & aNaturalNumber0(xk) = all_2399_2_314 & aNaturalNumber0(xn) = all_2399_3_315 & ( ~ (all_2399_2_314 = 0) | ~ (all_2399_3_315 = 0) | ~ (all_2399_4_316 = 0) | all_2399_0_312 = all_179_4_104)
% 67.71/29.28 |
% 67.71/29.28 | Applying alpha-rule on (3074) yields:
% 67.71/29.28 | (3075) sdtpldt0(xn, xk) = all_2399_1_313
% 67.71/29.28 | (3076) aNaturalNumber0(all_18_2_17) = all_2399_4_316
% 67.71/29.28 | (3077) aNaturalNumber0(xn) = all_2399_3_315
% 67.71/29.28 | (3078) ~ (all_2399_2_314 = 0) | ~ (all_2399_3_315 = 0) | ~ (all_2399_4_316 = 0) | all_2399_0_312 = all_179_4_104
% 67.71/29.28 | (3079) sdtpldt0(all_18_2_17, all_2399_1_313) = all_2399_0_312
% 67.71/29.28 | (3080) aNaturalNumber0(xk) = all_2399_2_314
% 67.71/29.28 |
% 67.71/29.28 | Instantiating (2964) with all_2408_0_336, all_2408_1_337, all_2408_2_338, all_2408_3_339, all_2408_4_340, all_2408_5_341, all_2408_6_342, all_2408_7_343, all_2408_8_344 yields:
% 67.71/29.28 | (3081) isPrime0(xp) = all_2408_5_341 & doDivides0(xp, xk) = all_2408_1_337 & doDivides0(xp, xp) = all_2408_0_336 & iLess0(all_2408_3_339, all_0_4_4) = all_2408_2_338 & sdtpldt0(all_2408_4_340, xp) = all_2408_3_339 & sdtpldt0(xk, xp) = all_2408_4_340 & aNaturalNumber0(xk) = all_2408_8_344 & aNaturalNumber0(xp) = all_2408_6_342 & aNaturalNumber0(xp) = all_2408_7_343 & ( ~ (all_2408_2_338 = 0) | ~ (all_2408_5_341 = 0) | ~ (all_2408_6_342 = 0) | ~ (all_2408_7_343 = 0) | ~ (all_2408_8_344 = 0) | all_2408_0_336 = 0 | all_2408_1_337 = 0)
% 67.71/29.28 |
% 67.71/29.28 | Applying alpha-rule on (3081) yields:
% 67.71/29.28 | (3082) isPrime0(xp) = all_2408_5_341
% 67.71/29.28 | (3083) aNaturalNumber0(xp) = all_2408_6_342
% 67.71/29.28 | (3084) iLess0(all_2408_3_339, all_0_4_4) = all_2408_2_338
% 67.71/29.28 | (3085) doDivides0(xp, xk) = all_2408_1_337
% 67.71/29.28 | (3086) ~ (all_2408_2_338 = 0) | ~ (all_2408_5_341 = 0) | ~ (all_2408_6_342 = 0) | ~ (all_2408_7_343 = 0) | ~ (all_2408_8_344 = 0) | all_2408_0_336 = 0 | all_2408_1_337 = 0
% 67.71/29.28 | (3087) sdtpldt0(xk, xp) = all_2408_4_340
% 67.71/29.28 | (3088) aNaturalNumber0(xk) = all_2408_8_344
% 67.71/29.28 | (3089) aNaturalNumber0(xp) = all_2408_7_343
% 67.71/29.28 | (3090) sdtpldt0(all_2408_4_340, xp) = all_2408_3_339
% 67.71/29.28 | (3091) doDivides0(xp, xp) = all_2408_0_336
% 67.71/29.28 |
% 67.71/29.28 | Instantiating (2962) with all_2410_0_345, all_2410_1_346, all_2410_2_347, all_2410_3_348, all_2410_4_349 yields:
% 67.71/29.28 | (3092) sdtasdt0(all_21_2_26, xp) = all_2410_1_346 & sdtasdt0(xr, all_2410_1_346) = all_2410_0_345 & aNaturalNumber0(all_21_2_26) = all_2410_3_348 & aNaturalNumber0(xr) = all_2410_4_349 & aNaturalNumber0(xp) = all_2410_2_347 & ( ~ (all_2410_2_347 = 0) | ~ (all_2410_3_348 = 0) | ~ (all_2410_4_349 = 0) | all_2410_0_345 = all_0_3_3)
% 67.71/29.28 |
% 67.71/29.28 | Applying alpha-rule on (3092) yields:
% 67.71/29.28 | (3093) ~ (all_2410_2_347 = 0) | ~ (all_2410_3_348 = 0) | ~ (all_2410_4_349 = 0) | all_2410_0_345 = all_0_3_3
% 67.71/29.28 | (3094) sdtasdt0(all_21_2_26, xp) = all_2410_1_346
% 67.71/29.28 | (3095) aNaturalNumber0(xp) = all_2410_2_347
% 67.71/29.28 | (3096) aNaturalNumber0(all_21_2_26) = all_2410_3_348
% 67.71/29.28 | (3097) sdtasdt0(xr, all_2410_1_346) = all_2410_0_345
% 67.71/29.28 | (3098) aNaturalNumber0(xr) = all_2410_4_349
% 67.71/29.28 |
% 67.71/29.28 | Instantiating (2965) with all_2414_0_359, all_2414_1_360, all_2414_2_361, all_2414_3_362, all_2414_4_363 yields:
% 67.71/29.28 | (3099) sdtasdt0(all_186_2_128, all_186_2_128) = all_2414_1_360 & sdtasdt0(xp, all_2414_1_360) = all_2414_0_359 & aNaturalNumber0(all_186_2_128) = all_2414_2_361 & aNaturalNumber0(all_186_2_128) = all_2414_3_362 & aNaturalNumber0(xp) = all_2414_4_363 & ( ~ (all_2414_2_361 = 0) | ~ (all_2414_3_362 = 0) | ~ (all_2414_4_363 = 0) | all_2414_0_359 = xp)
% 67.71/29.28 |
% 67.71/29.28 | Applying alpha-rule on (3099) yields:
% 67.71/29.28 | (3100) aNaturalNumber0(xp) = all_2414_4_363
% 67.71/29.28 | (3101) sdtasdt0(xp, all_2414_1_360) = all_2414_0_359
% 67.71/29.28 | (3102) ~ (all_2414_2_361 = 0) | ~ (all_2414_3_362 = 0) | ~ (all_2414_4_363 = 0) | all_2414_0_359 = xp
% 67.71/29.28 | (3103) aNaturalNumber0(all_186_2_128) = all_2414_3_362
% 67.71/29.28 | (3104) sdtasdt0(all_186_2_128, all_186_2_128) = all_2414_1_360
% 67.71/29.28 | (3105) aNaturalNumber0(all_186_2_128) = all_2414_2_361
% 67.71/29.28 |
% 67.71/29.28 | Instantiating (2971) with all_2421_0_379, all_2421_1_380, all_2421_2_381 yields:
% 67.71/29.28 | (3106) aNaturalNumber0(all_179_3_103) = all_2421_0_379 & aNaturalNumber0(all_179_4_104) = all_2421_2_381 & aNaturalNumber0(xp) = all_2421_1_380 & ( ~ (all_2421_1_380 = 0) | ~ (all_2421_2_381 = 0) | all_2421_0_379 = 0)
% 67.71/29.28 |
% 67.71/29.28 | Applying alpha-rule on (3106) yields:
% 67.71/29.28 | (3107) aNaturalNumber0(all_179_3_103) = all_2421_0_379
% 67.71/29.28 | (3108) aNaturalNumber0(all_179_4_104) = all_2421_2_381
% 67.71/29.28 | (3109) aNaturalNumber0(xp) = all_2421_1_380
% 67.71/29.28 | (3110) ~ (all_2421_1_380 = 0) | ~ (all_2421_2_381 = 0) | all_2421_0_379 = 0
% 67.71/29.28 |
% 67.71/29.28 | Instantiating (2969) with all_2423_0_382, all_2423_1_383, all_2423_2_384, all_2423_3_385, all_2423_4_386 yields:
% 67.71/29.28 | (3111) sdtasdt0(all_186_2_128, xk) = all_2423_1_383 & sdtasdt0(xp, all_2423_1_383) = all_2423_0_382 & aNaturalNumber0(all_186_2_128) = all_2423_3_385 & aNaturalNumber0(xk) = all_2423_2_384 & aNaturalNumber0(xp) = all_2423_4_386 & ( ~ (all_2423_2_384 = 0) | ~ (all_2423_3_385 = 0) | ~ (all_2423_4_386 = 0) | all_2423_0_382 = all_0_3_3)
% 67.71/29.28 |
% 67.71/29.28 | Applying alpha-rule on (3111) yields:
% 67.71/29.28 | (3112) aNaturalNumber0(all_186_2_128) = all_2423_3_385
% 67.71/29.28 | (3113) aNaturalNumber0(xp) = all_2423_4_386
% 67.71/29.28 | (3114) aNaturalNumber0(xk) = all_2423_2_384
% 67.71/29.28 | (3115) ~ (all_2423_2_384 = 0) | ~ (all_2423_3_385 = 0) | ~ (all_2423_4_386 = 0) | all_2423_0_382 = all_0_3_3
% 67.71/29.28 | (3116) sdtasdt0(all_186_2_128, xk) = all_2423_1_383
% 67.71/29.28 | (3117) sdtasdt0(xp, all_2423_1_383) = all_2423_0_382
% 67.71/29.28 |
% 67.71/29.28 | Instantiating (2970) with all_2425_0_387, all_2425_1_388, all_2425_2_389 yields:
% 67.71/29.28 | (3118) sdtpldt0(xp, all_179_4_104) = all_2425_0_387 & aNaturalNumber0(all_179_4_104) = all_2425_2_389 & aNaturalNumber0(xp) = all_2425_1_388 & ( ~ (all_2425_1_388 = 0) | ~ (all_2425_2_389 = 0) | all_2425_0_387 = all_179_3_103)
% 67.71/29.28 |
% 67.71/29.28 | Applying alpha-rule on (3118) yields:
% 67.71/29.28 | (3119) sdtpldt0(xp, all_179_4_104) = all_2425_0_387
% 67.71/29.28 | (3120) aNaturalNumber0(all_179_4_104) = all_2425_2_389
% 67.71/29.28 | (3121) aNaturalNumber0(xp) = all_2425_1_388
% 67.71/29.28 | (3122) ~ (all_2425_1_388 = 0) | ~ (all_2425_2_389 = 0) | all_2425_0_387 = all_179_3_103
% 67.71/29.28 |
% 67.71/29.28 | Instantiating (2973) with all_2435_0_412, all_2435_1_413, all_2435_2_414, all_2435_3_415, all_2435_4_416 yields:
% 67.71/29.28 | (3123) doDivides0(xp, all_19_2_20) = all_2435_1_413 & doDivides0(xp, xm) = all_2435_0_412 & aNaturalNumber0(all_19_2_20) = all_2435_3_415 & aNaturalNumber0(xp) = all_2435_4_416 & aNaturalNumber0(xm) = all_2435_2_414 & ( ~ (all_2435_1_413 = 0) | ~ (all_2435_2_414 = 0) | ~ (all_2435_3_415 = 0) | ~ (all_2435_4_416 = 0) | all_2435_0_412 = 0)
% 67.71/29.28 |
% 67.71/29.28 | Applying alpha-rule on (3123) yields:
% 67.71/29.28 | (3124) aNaturalNumber0(xm) = all_2435_2_414
% 67.71/29.28 | (3125) doDivides0(xp, xm) = all_2435_0_412
% 67.71/29.28 | (3126) aNaturalNumber0(all_19_2_20) = all_2435_3_415
% 67.71/29.28 | (3127) ~ (all_2435_1_413 = 0) | ~ (all_2435_2_414 = 0) | ~ (all_2435_3_415 = 0) | ~ (all_2435_4_416 = 0) | all_2435_0_412 = 0
% 67.71/29.28 | (3128) doDivides0(xp, all_19_2_20) = all_2435_1_413
% 67.71/29.28 | (3129) aNaturalNumber0(xp) = all_2435_4_416
% 67.71/29.28 |
% 67.71/29.28 | Instantiating formula (46) with xk, all_2408_8_344, all_2423_2_384 and discharging atoms aNaturalNumber0(xk) = all_2423_2_384, aNaturalNumber0(xk) = all_2408_8_344, yields:
% 67.71/29.28 | (3130) all_2423_2_384 = all_2408_8_344
% 67.71/29.28 |
% 67.71/29.28 | Instantiating formula (46) with xk, all_2388_3_286, all_2408_8_344 and discharging atoms aNaturalNumber0(xk) = all_2408_8_344, aNaturalNumber0(xk) = all_2388_3_286, yields:
% 67.71/29.28 | (3131) all_2408_8_344 = all_2388_3_286
% 67.71/29.28 |
% 67.71/29.28 | Instantiating formula (46) with xk, all_2364_2_221, all_2399_2_314 and discharging atoms aNaturalNumber0(xk) = all_2399_2_314, aNaturalNumber0(xk) = all_2364_2_221, yields:
% 67.71/29.28 | (3132) all_2399_2_314 = all_2364_2_221
% 67.71/29.28 |
% 67.71/29.28 | Instantiating formula (46) with xk, all_2364_2_221, all_2388_3_286 and discharging atoms aNaturalNumber0(xk) = all_2388_3_286, aNaturalNumber0(xk) = all_2364_2_221, yields:
% 67.71/29.29 | (3133) all_2388_3_286 = all_2364_2_221
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xk, all_2360_2_213, all_2364_2_221 and discharging atoms aNaturalNumber0(xk) = all_2364_2_221, aNaturalNumber0(xk) = all_2360_2_213, yields:
% 67.71/29.29 | (3134) all_2364_2_221 = all_2360_2_213
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xk, all_2358_1_209, all_2399_2_314 and discharging atoms aNaturalNumber0(xk) = all_2399_2_314, aNaturalNumber0(xk) = all_2358_1_209, yields:
% 67.71/29.29 | (3135) all_2399_2_314 = all_2358_1_209
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xk, all_2356_1_206, 0 and discharging atoms aNaturalNumber0(xk) = all_2356_1_206, aNaturalNumber0(xk) = 0, yields:
% 67.71/29.29 | (3136) all_2356_1_206 = 0
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xk, all_2356_1_206, all_2399_2_314 and discharging atoms aNaturalNumber0(xk) = all_2399_2_314, aNaturalNumber0(xk) = all_2356_1_206, yields:
% 67.71/29.29 | (3137) all_2399_2_314 = all_2356_1_206
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xk, all_2352_2_199, all_2423_2_384 and discharging atoms aNaturalNumber0(xk) = all_2423_2_384, aNaturalNumber0(xk) = all_2352_2_199, yields:
% 67.71/29.29 | (3138) all_2423_2_384 = all_2352_2_199
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2425_1_388, all_2435_4_416 and discharging atoms aNaturalNumber0(xp) = all_2435_4_416, aNaturalNumber0(xp) = all_2425_1_388, yields:
% 67.71/29.29 | (3139) all_2435_4_416 = all_2425_1_388
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2423_4_386, all_2435_4_416 and discharging atoms aNaturalNumber0(xp) = all_2435_4_416, aNaturalNumber0(xp) = all_2423_4_386, yields:
% 67.71/29.29 | (3140) all_2435_4_416 = all_2423_4_386
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2421_1_380, all_2423_4_386 and discharging atoms aNaturalNumber0(xp) = all_2423_4_386, aNaturalNumber0(xp) = all_2421_1_380, yields:
% 67.71/29.29 | (3141) all_2423_4_386 = all_2421_1_380
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2410_2_347, all_2414_4_363 and discharging atoms aNaturalNumber0(xp) = all_2414_4_363, aNaturalNumber0(xp) = all_2410_2_347, yields:
% 67.71/29.29 | (3142) all_2414_4_363 = all_2410_2_347
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2408_6_342, 0 and discharging atoms aNaturalNumber0(xp) = all_2408_6_342, aNaturalNumber0(xp) = 0, yields:
% 67.71/29.29 | (3143) all_2408_6_342 = 0
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2408_7_343, all_2410_2_347 and discharging atoms aNaturalNumber0(xp) = all_2410_2_347, aNaturalNumber0(xp) = all_2408_7_343, yields:
% 67.71/29.29 | (3144) all_2410_2_347 = all_2408_7_343
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2388_2_285, all_2408_6_342 and discharging atoms aNaturalNumber0(xp) = all_2408_6_342, aNaturalNumber0(xp) = all_2388_2_285, yields:
% 67.71/29.29 | (3145) all_2408_6_342 = all_2388_2_285
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2388_4_287, all_2421_1_380 and discharging atoms aNaturalNumber0(xp) = all_2421_1_380, aNaturalNumber0(xp) = all_2388_4_287, yields:
% 67.71/29.29 | (3146) all_2421_1_380 = all_2388_4_287
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2388_4_287, all_2408_7_343 and discharging atoms aNaturalNumber0(xp) = all_2408_7_343, aNaturalNumber0(xp) = all_2388_4_287, yields:
% 67.71/29.29 | (3147) all_2408_7_343 = all_2388_4_287
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2384_6_277, all_2435_4_416 and discharging atoms aNaturalNumber0(xp) = all_2435_4_416, aNaturalNumber0(xp) = all_2384_6_277, yields:
% 67.71/29.29 | (3148) all_2435_4_416 = all_2384_6_277
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2384_8_279, all_2388_2_285 and discharging atoms aNaturalNumber0(xp) = all_2388_2_285, aNaturalNumber0(xp) = all_2384_8_279, yields:
% 67.71/29.29 | (3149) all_2388_2_285 = all_2384_8_279
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2382_8_270, all_2414_4_363 and discharging atoms aNaturalNumber0(xp) = all_2414_4_363, aNaturalNumber0(xp) = all_2382_8_270, yields:
% 67.71/29.29 | (3150) all_2414_4_363 = all_2382_8_270
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2380_2_261, all_2384_8_279 and discharging atoms aNaturalNumber0(xp) = all_2384_8_279, aNaturalNumber0(xp) = all_2380_2_261, yields:
% 67.71/29.29 | (3151) all_2384_8_279 = all_2380_2_261
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2378_3_257, all_2380_2_261 and discharging atoms aNaturalNumber0(xp) = all_2380_2_261, aNaturalNumber0(xp) = all_2378_3_257, yields:
% 67.71/29.29 | (3152) all_2380_2_261 = all_2378_3_257
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2358_2_210, all_2378_3_257 and discharging atoms aNaturalNumber0(xp) = all_2378_3_257, aNaturalNumber0(xp) = all_2358_2_210, yields:
% 67.71/29.29 | (3153) all_2378_3_257 = all_2358_2_210
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2358_2_210, all_2376_4_253 and discharging atoms aNaturalNumber0(xp) = all_2376_4_253, aNaturalNumber0(xp) = all_2358_2_210, yields:
% 67.71/29.29 | (3154) all_2376_4_253 = all_2358_2_210
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2356_2_207, all_2376_4_253 and discharging atoms aNaturalNumber0(xp) = all_2376_4_253, aNaturalNumber0(xp) = all_2356_2_207, yields:
% 67.71/29.29 | (3155) all_2376_4_253 = all_2356_2_207
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2336_1_172, all_2388_4_287 and discharging atoms aNaturalNumber0(xp) = all_2388_4_287, aNaturalNumber0(xp) = all_2336_1_172, yields:
% 67.71/29.29 | (3156) all_2388_4_287 = all_2336_1_172
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2336_1_172, all_2376_4_253 and discharging atoms aNaturalNumber0(xp) = all_2376_4_253, aNaturalNumber0(xp) = all_2336_1_172, yields:
% 67.71/29.29 | (3157) all_2376_4_253 = all_2336_1_172
% 67.71/29.29 |
% 67.71/29.29 | Instantiating formula (46) with xp, all_2334_1_169, all_2388_4_287 and discharging atoms aNaturalNumber0(xp) = all_2388_4_287, aNaturalNumber0(xp) = all_2334_1_169, yields:
% 67.71/29.29 | (3158) all_2388_4_287 = all_2334_1_169
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3148,3139) yields a new equation:
% 67.71/29.29 | (3159) all_2425_1_388 = all_2384_6_277
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3140,3139) yields a new equation:
% 67.71/29.29 | (3160) all_2425_1_388 = all_2423_4_386
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3160,3159) yields a new equation:
% 67.71/29.29 | (3161) all_2423_4_386 = all_2384_6_277
% 67.71/29.29 |
% 67.71/29.29 | Simplifying 3161 yields:
% 67.71/29.29 | (3162) all_2423_4_386 = all_2384_6_277
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3130,3138) yields a new equation:
% 67.71/29.29 | (3163) all_2408_8_344 = all_2352_2_199
% 67.71/29.29 |
% 67.71/29.29 | Simplifying 3163 yields:
% 67.71/29.29 | (3164) all_2408_8_344 = all_2352_2_199
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3141,3162) yields a new equation:
% 67.71/29.29 | (3165) all_2421_1_380 = all_2384_6_277
% 67.71/29.29 |
% 67.71/29.29 | Simplifying 3165 yields:
% 67.71/29.29 | (3166) all_2421_1_380 = all_2384_6_277
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3146,3166) yields a new equation:
% 67.71/29.29 | (3167) all_2388_4_287 = all_2384_6_277
% 67.71/29.29 |
% 67.71/29.29 | Simplifying 3167 yields:
% 67.71/29.29 | (3168) all_2388_4_287 = all_2384_6_277
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3142,3150) yields a new equation:
% 67.71/29.29 | (3169) all_2410_2_347 = all_2382_8_270
% 67.71/29.29 |
% 67.71/29.29 | Simplifying 3169 yields:
% 67.71/29.29 | (3170) all_2410_2_347 = all_2382_8_270
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3144,3170) yields a new equation:
% 67.71/29.29 | (3171) all_2408_7_343 = all_2382_8_270
% 67.71/29.29 |
% 67.71/29.29 | Simplifying 3171 yields:
% 67.71/29.29 | (3172) all_2408_7_343 = all_2382_8_270
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3145,3143) yields a new equation:
% 67.71/29.29 | (3173) all_2388_2_285 = 0
% 67.71/29.29 |
% 67.71/29.29 | Simplifying 3173 yields:
% 67.71/29.29 | (3174) all_2388_2_285 = 0
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3147,3172) yields a new equation:
% 67.71/29.29 | (3175) all_2388_4_287 = all_2382_8_270
% 67.71/29.29 |
% 67.71/29.29 | Simplifying 3175 yields:
% 67.71/29.29 | (3176) all_2388_4_287 = all_2382_8_270
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3131,3164) yields a new equation:
% 67.71/29.29 | (3177) all_2388_3_286 = all_2352_2_199
% 67.71/29.29 |
% 67.71/29.29 | Simplifying 3177 yields:
% 67.71/29.29 | (3178) all_2388_3_286 = all_2352_2_199
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3137,3135) yields a new equation:
% 67.71/29.29 | (3179) all_2358_1_209 = all_2356_1_206
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3132,3135) yields a new equation:
% 67.71/29.29 | (3180) all_2364_2_221 = all_2358_1_209
% 67.71/29.29 |
% 67.71/29.29 | Simplifying 3180 yields:
% 67.71/29.29 | (3181) all_2364_2_221 = all_2358_1_209
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3149,3174) yields a new equation:
% 67.71/29.29 | (3182) all_2384_8_279 = 0
% 67.71/29.29 |
% 67.71/29.29 | Simplifying 3182 yields:
% 67.71/29.29 | (3183) all_2384_8_279 = 0
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3133,3178) yields a new equation:
% 67.71/29.29 | (3184) all_2364_2_221 = all_2352_2_199
% 67.71/29.29 |
% 67.71/29.29 | Simplifying 3184 yields:
% 67.71/29.29 | (3185) all_2364_2_221 = all_2352_2_199
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3158,3168) yields a new equation:
% 67.71/29.29 | (3186) all_2384_6_277 = all_2334_1_169
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3156,3168) yields a new equation:
% 67.71/29.29 | (3187) all_2384_6_277 = all_2336_1_172
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3176,3168) yields a new equation:
% 67.71/29.29 | (3188) all_2384_6_277 = all_2382_8_270
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3186,3188) yields a new equation:
% 67.71/29.29 | (3189) all_2382_8_270 = all_2334_1_169
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3187,3188) yields a new equation:
% 67.71/29.29 | (3190) all_2382_8_270 = all_2336_1_172
% 67.71/29.29 |
% 67.71/29.29 | Combining equations (3151,3183) yields a new equation:
% 67.71/29.29 | (3191) all_2380_2_261 = 0
% 67.71/29.29 |
% 67.71/29.30 | Simplifying 3191 yields:
% 67.71/29.30 | (3192) all_2380_2_261 = 0
% 67.71/29.30 |
% 67.71/29.30 | Combining equations (3190,3189) yields a new equation:
% 67.71/29.30 | (3193) all_2336_1_172 = all_2334_1_169
% 67.71/29.30 |
% 67.71/29.30 | Simplifying 3193 yields:
% 67.71/29.30 | (3194) all_2336_1_172 = all_2334_1_169
% 67.71/29.30 |
% 67.71/29.30 | Combining equations (3152,3192) yields a new equation:
% 67.71/29.30 | (3195) all_2378_3_257 = 0
% 67.71/29.30 |
% 67.71/29.30 | Simplifying 3195 yields:
% 67.71/29.30 | (3196) all_2378_3_257 = 0
% 67.71/29.30 |
% 67.71/29.30 | Combining equations (3153,3196) yields a new equation:
% 67.71/29.30 | (3197) all_2358_2_210 = 0
% 67.71/29.30 |
% 67.71/29.30 | Simplifying 3197 yields:
% 67.71/29.30 | (3198) all_2358_2_210 = 0
% 67.71/29.30 |
% 67.71/29.30 | Combining equations (3157,3155) yields a new equation:
% 67.71/29.30 | (3199) all_2356_2_207 = all_2336_1_172
% 67.71/29.30 |
% 67.71/29.30 | Combining equations (3154,3155) yields a new equation:
% 67.71/29.30 | (3200) all_2358_2_210 = all_2356_2_207
% 67.71/29.30 |
% 67.71/29.30 | Simplifying 3200 yields:
% 67.71/29.30 | (3201) all_2358_2_210 = all_2356_2_207
% 67.71/29.30 |
% 67.71/29.30 | Combining equations (3181,3134) yields a new equation:
% 67.71/29.30 | (3202) all_2360_2_213 = all_2358_1_209
% 67.71/29.30 |
% 67.71/29.30 | Combining equations (3185,3134) yields a new equation:
% 67.71/29.30 | (3203) all_2360_2_213 = all_2352_2_199
% 67.71/29.30 |
% 67.71/29.30 | Combining equations (3202,3203) yields a new equation:
% 67.71/29.30 | (3204) all_2358_1_209 = all_2352_2_199
% 67.71/29.30 |
% 67.71/29.30 | Simplifying 3204 yields:
% 67.71/29.30 | (3205) all_2358_1_209 = all_2352_2_199
% 67.71/29.30 |
% 67.71/29.30 | Combining equations (3179,3205) yields a new equation:
% 67.71/29.30 | (3206) all_2356_1_206 = all_2352_2_199
% 67.71/29.30 |
% 67.71/29.30 | Simplifying 3206 yields:
% 67.71/29.30 | (3207) all_2356_1_206 = all_2352_2_199
% 67.71/29.30 |
% 67.71/29.30 | Combining equations (3201,3198) yields a new equation:
% 67.71/29.30 | (3208) all_2356_2_207 = 0
% 67.71/29.30 |
% 67.71/29.30 | Simplifying 3208 yields:
% 67.71/29.30 | (3209) all_2356_2_207 = 0
% 67.71/29.30 |
% 67.71/29.30 | Combining equations (3136,3207) yields a new equation:
% 67.71/29.30 | (3210) all_2352_2_199 = 0
% 67.71/29.30 |
% 67.71/29.30 | Combining equations (3199,3209) yields a new equation:
% 67.71/29.30 | (3211) all_2336_1_172 = 0
% 67.71/29.30 |
% 67.71/29.30 | Simplifying 3211 yields:
% 67.71/29.30 | (3212) all_2336_1_172 = 0
% 67.71/29.30 |
% 67.71/29.30 | Combining equations (3194,3212) yields a new equation:
% 67.71/29.30 | (3213) all_2334_1_169 = 0
% 67.71/29.30 |
% 67.71/29.30 | Simplifying 3213 yields:
% 67.71/29.30 | (3214) all_2334_1_169 = 0
% 67.71/29.30 |
% 67.71/29.30 | From (3210) and (2997) follows:
% 67.71/29.30 | (972) aNaturalNumber0(xk) = 0
% 67.71/29.30 |
% 67.71/29.30 | From (3214) and (2987) follows:
% 67.71/29.30 | (12) aNaturalNumber0(xp) = 0
% 67.71/29.30 |
% 67.71/29.30 +-Applying beta-rule and splitting (2982), into two cases.
% 67.71/29.30 |-Branch one:
% 67.71/29.30 | (3217) xp = xm
% 67.71/29.30 |
% 67.71/29.30 | Equations (3217) can reduce 80 to:
% 67.71/29.30 | (159) $false
% 67.71/29.30 |
% 67.71/29.30 |-The branch is then unsatisfiable
% 67.71/29.30 |-Branch two:
% 67.71/29.30 | (80) ~ (xp = xm)
% 67.71/29.30 | (3220) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xp, xn) = v4 & sdtpldt0(xm, xn) = v3 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v4 = v3) & ~ (all_161_1_68 = all_0_5_5))))
% 67.71/29.30 |
% 67.71/29.30 | Instantiating (3220) with all_2473_0_452, all_2473_1_453, all_2473_2_454, all_2473_3_455, all_2473_4_456 yields:
% 67.71/29.30 | (3221) sdtpldt0(xp, xn) = all_2473_0_452 & sdtpldt0(xm, xn) = all_2473_1_453 & aNaturalNumber0(xp) = all_2473_2_454 & aNaturalNumber0(xm) = all_2473_3_455 & aNaturalNumber0(xn) = all_2473_4_456 & ( ~ (all_2473_2_454 = 0) | ~ (all_2473_3_455 = 0) | ~ (all_2473_4_456 = 0) | ( ~ (all_2473_0_452 = all_2473_1_453) & ~ (all_161_1_68 = all_0_5_5)))
% 67.71/29.30 |
% 67.71/29.30 | Applying alpha-rule on (3221) yields:
% 67.71/29.30 | (3222) aNaturalNumber0(xp) = all_2473_2_454
% 67.71/29.30 | (3223) sdtpldt0(xm, xn) = all_2473_1_453
% 67.71/29.30 | (3224) ~ (all_2473_2_454 = 0) | ~ (all_2473_3_455 = 0) | ~ (all_2473_4_456 = 0) | ( ~ (all_2473_0_452 = all_2473_1_453) & ~ (all_161_1_68 = all_0_5_5))
% 67.71/29.30 | (3225) sdtpldt0(xp, xn) = all_2473_0_452
% 67.71/29.30 | (3226) aNaturalNumber0(xn) = all_2473_4_456
% 67.71/29.30 | (3227) aNaturalNumber0(xm) = all_2473_3_455
% 67.71/29.30 |
% 67.71/29.30 +-Applying beta-rule and splitting (2963), into two cases.
% 67.71/29.30 |-Branch one:
% 67.71/29.30 | (3228) all_36_0_50 = 0
% 67.71/29.30 |
% 67.80/29.30 | Equations (3228) can reduce 1051 to:
% 67.80/29.30 | (159) $false
% 67.80/29.30 |
% 67.80/29.30 |-The branch is then unsatisfiable
% 67.80/29.30 |-Branch two:
% 67.80/29.30 | (1051) ~ (all_36_0_50 = 0)
% 67.80/29.30 | (3231) ? [v0] : ? [v1] : (( ~ (v0 = 0) & aNaturalNumber0(xp) = v0) | (aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xk) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 67.80/29.30 |
% 67.80/29.30 | Instantiating (3231) with all_2495_0_457, all_2495_1_458 yields:
% 67.80/29.30 | (3232) ( ~ (all_2495_1_458 = 0) & aNaturalNumber0(xp) = all_2495_1_458) | (aNaturalNumber0(all_0_3_3) = all_2495_0_457 & aNaturalNumber0(xk) = all_2495_1_458 & ( ~ (all_2495_0_457 = 0) | ~ (all_2495_1_458 = 0)))
% 67.80/29.30 |
% 67.80/29.30 +-Applying beta-rule and splitting (2961), into two cases.
% 67.80/29.30 |-Branch one:
% 67.80/29.30 | (168) xk = sz00
% 67.80/29.30 |
% 67.80/29.30 | Equations (168) can reduce 13 to:
% 67.80/29.30 | (159) $false
% 67.80/29.30 |
% 67.80/29.30 |-The branch is then unsatisfiable
% 67.80/29.30 |-Branch two:
% 67.80/29.30 | (13) ~ (xk = sz00)
% 67.80/29.30 | (3236) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_386_0_142, xk) = v2 & aNaturalNumber0(all_386_0_142) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 67.80/29.30 |
% 67.80/29.30 | Instantiating (3236) with all_2542_0_462, all_2542_1_463, all_2542_2_464 yields:
% 67.80/29.30 | (3237) sdtlseqdt0(all_386_0_142, xk) = all_2542_0_462 & aNaturalNumber0(all_386_0_142) = all_2542_2_464 & aNaturalNumber0(xk) = all_2542_1_463 & ( ~ (all_2542_1_463 = 0) | ~ (all_2542_2_464 = 0) | all_2542_0_462 = 0)
% 67.80/29.30 |
% 67.80/29.30 | Applying alpha-rule on (3237) yields:
% 67.80/29.30 | (3238) sdtlseqdt0(all_386_0_142, xk) = all_2542_0_462
% 67.80/29.30 | (3239) aNaturalNumber0(all_386_0_142) = all_2542_2_464
% 67.80/29.30 | (3240) aNaturalNumber0(xk) = all_2542_1_463
% 67.80/29.30 | (3241) ~ (all_2542_1_463 = 0) | ~ (all_2542_2_464 = 0) | all_2542_0_462 = 0
% 67.80/29.30 |
% 67.80/29.30 | Instantiating formula (46) with xk, all_2542_1_463, 0 and discharging atoms aNaturalNumber0(xk) = all_2542_1_463, aNaturalNumber0(xk) = 0, yields:
% 67.80/29.30 | (3242) all_2542_1_463 = 0
% 67.80/29.30 |
% 67.80/29.30 | Instantiating formula (46) with xp, all_2473_2_454, 0 and discharging atoms aNaturalNumber0(xp) = all_2473_2_454, aNaturalNumber0(xp) = 0, yields:
% 67.80/29.30 | (3243) all_2473_2_454 = 0
% 67.80/29.30 |
% 67.80/29.30 | From (3242) and (3240) follows:
% 67.80/29.30 | (972) aNaturalNumber0(xk) = 0
% 67.80/29.30 |
% 67.80/29.30 | From (3243) and (3222) follows:
% 67.80/29.30 | (12) aNaturalNumber0(xp) = 0
% 67.80/29.30 |
% 67.80/29.30 +-Applying beta-rule and splitting (2960), into two cases.
% 67.80/29.30 |-Branch one:
% 67.80/29.30 | (168) xk = sz00
% 67.80/29.30 |
% 67.80/29.30 | Equations (168) can reduce 13 to:
% 67.80/29.30 | (159) $false
% 67.80/29.30 |
% 67.80/29.30 |-The branch is then unsatisfiable
% 67.80/29.30 |-Branch two:
% 67.80/29.30 | (13) ~ (xk = sz00)
% 67.80/29.30 | (3249) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_432_0_148, xk) = v2 & aNaturalNumber0(all_432_0_148) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 67.80/29.30 |
% 67.80/29.30 | Instantiating (3249) with all_2924_0_473, all_2924_1_474, all_2924_2_475 yields:
% 67.80/29.30 | (3250) sdtlseqdt0(all_432_0_148, xk) = all_2924_0_473 & aNaturalNumber0(all_432_0_148) = all_2924_2_475 & aNaturalNumber0(xk) = all_2924_1_474 & ( ~ (all_2924_1_474 = 0) | ~ (all_2924_2_475 = 0) | all_2924_0_473 = 0)
% 67.80/29.30 |
% 67.80/29.31 | Applying alpha-rule on (3250) yields:
% 67.80/29.31 | (3251) sdtlseqdt0(all_432_0_148, xk) = all_2924_0_473
% 67.80/29.31 | (3252) aNaturalNumber0(all_432_0_148) = all_2924_2_475
% 67.80/29.31 | (3253) aNaturalNumber0(xk) = all_2924_1_474
% 67.80/29.31 | (3254) ~ (all_2924_1_474 = 0) | ~ (all_2924_2_475 = 0) | all_2924_0_473 = 0
% 67.80/29.31 |
% 67.80/29.31 +-Applying beta-rule and splitting (3232), into two cases.
% 67.80/29.31 |-Branch one:
% 67.80/29.31 | (3255) ~ (all_2495_1_458 = 0) & aNaturalNumber0(xp) = all_2495_1_458
% 67.80/29.31 |
% 67.80/29.31 | Applying alpha-rule on (3255) yields:
% 67.80/29.31 | (3256) ~ (all_2495_1_458 = 0)
% 67.80/29.31 | (3257) aNaturalNumber0(xp) = all_2495_1_458
% 67.80/29.31 |
% 67.80/29.31 | Instantiating formula (46) with xp, all_2495_1_458, 0 and discharging atoms aNaturalNumber0(xp) = all_2495_1_458, aNaturalNumber0(xp) = 0, yields:
% 67.80/29.31 | (3258) all_2495_1_458 = 0
% 67.80/29.31 |
% 67.80/29.31 | Equations (3258) can reduce 3256 to:
% 67.80/29.31 | (159) $false
% 67.80/29.31 |
% 67.80/29.31 |-The branch is then unsatisfiable
% 67.80/29.31 |-Branch two:
% 67.80/29.31 | (3260) aNaturalNumber0(all_0_3_3) = all_2495_0_457 & aNaturalNumber0(xk) = all_2495_1_458 & ( ~ (all_2495_0_457 = 0) | ~ (all_2495_1_458 = 0))
% 67.80/29.31 |
% 67.80/29.31 | Applying alpha-rule on (3260) yields:
% 67.80/29.31 | (3261) aNaturalNumber0(all_0_3_3) = all_2495_0_457
% 67.80/29.31 | (3262) aNaturalNumber0(xk) = all_2495_1_458
% 67.80/29.31 | (3263) ~ (all_2495_0_457 = 0) | ~ (all_2495_1_458 = 0)
% 67.80/29.31 |
% 67.80/29.31 | Instantiating formula (46) with all_0_3_3, all_2495_0_457, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_2495_0_457, aNaturalNumber0(all_0_3_3) = 0, yields:
% 67.80/29.31 | (3264) all_2495_0_457 = 0
% 67.80/29.31 |
% 67.80/29.31 | Instantiating formula (46) with xk, all_2924_1_474, 0 and discharging atoms aNaturalNumber0(xk) = all_2924_1_474, aNaturalNumber0(xk) = 0, yields:
% 67.80/29.31 | (3265) all_2924_1_474 = 0
% 67.80/29.31 |
% 67.80/29.31 | Instantiating formula (46) with xk, all_2495_1_458, all_2924_1_474 and discharging atoms aNaturalNumber0(xk) = all_2924_1_474, aNaturalNumber0(xk) = all_2495_1_458, yields:
% 67.80/29.31 | (3266) all_2924_1_474 = all_2495_1_458
% 67.80/29.31 |
% 67.80/29.31 | Combining equations (3266,3265) yields a new equation:
% 67.80/29.31 | (3267) all_2495_1_458 = 0
% 67.80/29.31 |
% 67.80/29.31 | Simplifying 3267 yields:
% 67.80/29.31 | (3258) all_2495_1_458 = 0
% 67.80/29.31 |
% 67.80/29.31 +-Applying beta-rule and splitting (3263), into two cases.
% 67.80/29.31 |-Branch one:
% 67.80/29.31 | (3269) ~ (all_2495_0_457 = 0)
% 67.80/29.31 |
% 67.80/29.31 | Equations (3264) can reduce 3269 to:
% 67.80/29.31 | (159) $false
% 67.80/29.31 |
% 67.80/29.31 |-The branch is then unsatisfiable
% 67.80/29.31 |-Branch two:
% 67.80/29.31 | (3264) all_2495_0_457 = 0
% 67.80/29.31 | (3256) ~ (all_2495_1_458 = 0)
% 67.80/29.31 |
% 67.80/29.31 | Equations (3258) can reduce 3256 to:
% 67.80/29.31 | (159) $false
% 67.80/29.31 |
% 67.80/29.31 |-The branch is then unsatisfiable
% 67.80/29.32 |-Branch two:
% 67.80/29.32 | (3274) doDivides0(xp, xm) = 0
% 67.80/29.33 | (3275) xm = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, xm) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 67.80/29.33 |
% 67.80/29.33 +-Applying beta-rule and splitting (3275), into two cases.
% 67.80/29.33 |-Branch one:
% 67.80/29.33 | (3276) xm = sz00
% 67.80/29.33 |
% 67.80/29.33 | Equations (3276) can reduce 1102 to:
% 67.80/29.33 | (159) $false
% 67.80/29.33 |
% 67.80/29.33 |-The branch is then unsatisfiable
% 67.80/29.33 |-Branch two:
% 67.80/29.33 | (1102) ~ (xm = sz00)
% 67.80/29.33 | (3279) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, xm) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 67.80/29.33 |
% 67.80/29.33 | Instantiating (3279) with all_542_0_479, all_542_1_480, all_542_2_481 yields:
% 67.80/29.33 | (3280) sdtlseqdt0(xp, xm) = all_542_0_479 & aNaturalNumber0(xp) = all_542_2_481 & aNaturalNumber0(xm) = all_542_1_480 & ( ~ (all_542_1_480 = 0) | ~ (all_542_2_481 = 0) | all_542_0_479 = 0)
% 67.80/29.33 |
% 67.80/29.33 | Applying alpha-rule on (3280) yields:
% 67.80/29.33 | (3281) sdtlseqdt0(xp, xm) = all_542_0_479
% 67.80/29.33 | (3282) aNaturalNumber0(xp) = all_542_2_481
% 67.80/29.33 | (3283) aNaturalNumber0(xm) = all_542_1_480
% 67.80/29.33 | (3284) ~ (all_542_1_480 = 0) | ~ (all_542_2_481 = 0) | all_542_0_479 = 0
% 67.80/29.33 |
% 67.80/29.33 | Instantiating formula (17) with xp, xm, all_542_0_479, all_0_1_1 and discharging atoms sdtlseqdt0(xp, xm) = all_542_0_479, sdtlseqdt0(xp, xm) = all_0_1_1, yields:
% 67.80/29.33 | (3285) all_542_0_479 = all_0_1_1
% 67.80/29.33 |
% 67.80/29.33 | Instantiating formula (46) with xp, all_542_2_481, 0 and discharging atoms aNaturalNumber0(xp) = all_542_2_481, aNaturalNumber0(xp) = 0, yields:
% 67.80/29.33 | (3286) all_542_2_481 = 0
% 67.80/29.33 |
% 67.80/29.33 | Instantiating formula (46) with xm, all_542_1_480, 0 and discharging atoms aNaturalNumber0(xm) = all_542_1_480, aNaturalNumber0(xm) = 0, yields:
% 67.80/29.33 | (3287) all_542_1_480 = 0
% 67.80/29.33 |
% 67.80/29.33 +-Applying beta-rule and splitting (3284), into two cases.
% 67.80/29.33 |-Branch one:
% 67.80/29.33 | (3288) ~ (all_542_1_480 = 0)
% 67.80/29.33 |
% 67.80/29.33 | Equations (3287) can reduce 3288 to:
% 67.80/29.33 | (159) $false
% 67.80/29.33 |
% 67.80/29.33 |-The branch is then unsatisfiable
% 67.80/29.33 |-Branch two:
% 67.80/29.33 | (3287) all_542_1_480 = 0
% 67.80/29.33 | (3291) ~ (all_542_2_481 = 0) | all_542_0_479 = 0
% 67.80/29.33 |
% 67.80/29.33 +-Applying beta-rule and splitting (3291), into two cases.
% 67.80/29.33 |-Branch one:
% 67.80/29.33 | (3292) ~ (all_542_2_481 = 0)
% 67.80/29.33 |
% 67.80/29.33 | Equations (3286) can reduce 3292 to:
% 67.80/29.33 | (159) $false
% 67.80/29.33 |
% 67.80/29.33 |-The branch is then unsatisfiable
% 67.80/29.33 |-Branch two:
% 67.80/29.33 | (3286) all_542_2_481 = 0
% 67.80/29.33 | (3295) all_542_0_479 = 0
% 67.80/29.33 |
% 67.80/29.33 | Combining equations (3295,3285) yields a new equation:
% 67.80/29.33 | (3296) all_0_1_1 = 0
% 67.80/29.33 |
% 67.80/29.33 | Equations (3296) can reduce 23 to:
% 67.80/29.33 | (159) $false
% 67.80/29.33 |
% 67.80/29.33 |-The branch is then unsatisfiable
% 67.80/29.33 |-Branch two:
% 67.80/29.33 | (3298) doDivides0(xp, xn) = 0
% 67.80/29.33 | (3299) xn = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, xn) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 67.80/29.33 |
% 67.80/29.33 +-Applying beta-rule and splitting (105), into two cases.
% 67.80/29.33 |-Branch one:
% 67.80/29.33 | (3300) xn = sz00
% 67.80/29.33 |
% 67.80/29.33 | Equations (3300) can reduce 1101 to:
% 67.80/29.33 | (159) $false
% 67.80/29.33 |
% 67.80/29.33 |-The branch is then unsatisfiable
% 67.80/29.33 |-Branch two:
% 67.80/29.33 | (1101) ~ (xn = sz00)
% 67.80/29.33 | (3303) xn = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xn) = 0 & aNaturalNumber0(v0) = 0)
% 67.80/29.33 |
% 67.80/29.33 +-Applying beta-rule and splitting (3299), into two cases.
% 67.80/29.33 |-Branch one:
% 67.80/29.33 | (3300) xn = sz00
% 67.80/29.33 |
% 67.80/29.33 | Equations (3300) can reduce 1101 to:
% 67.80/29.33 | (159) $false
% 67.80/29.33 |
% 67.80/29.33 |-The branch is then unsatisfiable
% 67.80/29.33 |-Branch two:
% 67.80/29.33 | (1101) ~ (xn = sz00)
% 67.80/29.33 | (3307) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, xn) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 67.80/29.33 |
% 67.80/29.33 | Instantiating (3307) with all_538_0_487, all_538_1_488, all_538_2_489 yields:
% 67.80/29.33 | (3308) sdtlseqdt0(xp, xn) = all_538_0_487 & aNaturalNumber0(xp) = all_538_2_489 & aNaturalNumber0(xn) = all_538_1_488 & ( ~ (all_538_1_488 = 0) | ~ (all_538_2_489 = 0) | all_538_0_487 = 0)
% 67.80/29.33 |
% 67.80/29.33 | Applying alpha-rule on (3308) yields:
% 67.80/29.33 | (3309) sdtlseqdt0(xp, xn) = all_538_0_487
% 67.80/29.33 | (3310) aNaturalNumber0(xp) = all_538_2_489
% 67.80/29.33 | (3311) aNaturalNumber0(xn) = all_538_1_488
% 67.80/29.33 | (3312) ~ (all_538_1_488 = 0) | ~ (all_538_2_489 = 0) | all_538_0_487 = 0
% 67.80/29.33 |
% 67.80/29.33 | Instantiating formula (17) with xp, xn, all_538_0_487, all_0_2_2 and discharging atoms sdtlseqdt0(xp, xn) = all_538_0_487, sdtlseqdt0(xp, xn) = all_0_2_2, yields:
% 67.80/29.33 | (3313) all_538_0_487 = all_0_2_2
% 67.80/29.33 |
% 67.80/29.33 | Instantiating formula (46) with xp, all_538_2_489, 0 and discharging atoms aNaturalNumber0(xp) = all_538_2_489, aNaturalNumber0(xp) = 0, yields:
% 67.80/29.33 | (3314) all_538_2_489 = 0
% 67.80/29.33 |
% 67.80/29.33 | Instantiating formula (46) with xn, all_538_1_488, 0 and discharging atoms aNaturalNumber0(xn) = all_538_1_488, aNaturalNumber0(xn) = 0, yields:
% 67.80/29.33 | (3315) all_538_1_488 = 0
% 67.80/29.33 |
% 67.80/29.33 +-Applying beta-rule and splitting (3312), into two cases.
% 67.80/29.33 |-Branch one:
% 67.80/29.33 | (3316) ~ (all_538_1_488 = 0)
% 67.80/29.33 |
% 67.80/29.33 | Equations (3315) can reduce 3316 to:
% 67.80/29.33 | (159) $false
% 67.80/29.33 |
% 67.80/29.33 |-The branch is then unsatisfiable
% 67.80/29.33 |-Branch two:
% 67.80/29.33 | (3315) all_538_1_488 = 0
% 67.80/29.33 | (3319) ~ (all_538_2_489 = 0) | all_538_0_487 = 0
% 67.80/29.33 |
% 67.80/29.33 +-Applying beta-rule and splitting (3319), into two cases.
% 67.80/29.33 |-Branch one:
% 67.80/29.33 | (3320) ~ (all_538_2_489 = 0)
% 67.80/29.33 |
% 67.80/29.33 | Equations (3314) can reduce 3320 to:
% 67.80/29.33 | (159) $false
% 67.80/29.33 |
% 67.80/29.33 |-The branch is then unsatisfiable
% 67.80/29.33 |-Branch two:
% 67.80/29.33 | (3314) all_538_2_489 = 0
% 67.80/29.33 | (3323) all_538_0_487 = 0
% 67.80/29.33 |
% 67.80/29.33 | Combining equations (3323,3313) yields a new equation:
% 67.80/29.33 | (3324) all_0_2_2 = 0
% 67.80/29.33 |
% 67.80/29.33 | Equations (3324) can reduce 39 to:
% 67.80/29.33 | (159) $false
% 67.80/29.33 |
% 67.80/29.33 |-The branch is then unsatisfiable
% 67.80/29.33 |-Branch two:
% 67.80/29.33 | (3326) sdtasdt0(sz00, xn) = all_0_3_3
% 67.80/29.33 | (3327) ? [v0] : ? [v1] : (sdtasdt0(xn, sz00) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v0 = 0) | (v1 = sz00 & all_0_3_3 = sz00)))
% 67.80/29.33 |
% 67.80/29.33 | Instantiating (3327) with all_523_0_495, all_523_1_496 yields:
% 67.80/29.33 | (3328) sdtasdt0(xn, sz00) = all_523_0_495 & aNaturalNumber0(xn) = all_523_1_496 & ( ~ (all_523_1_496 = 0) | (all_523_0_495 = sz00 & all_0_3_3 = sz00))
% 67.80/29.33 |
% 67.80/29.33 | Applying alpha-rule on (3328) yields:
% 67.80/29.33 | (3329) sdtasdt0(xn, sz00) = all_523_0_495
% 67.80/29.33 | (3330) aNaturalNumber0(xn) = all_523_1_496
% 67.80/29.33 | (3331) ~ (all_523_1_496 = 0) | (all_523_0_495 = sz00 & all_0_3_3 = sz00)
% 67.80/29.33 |
% 67.80/29.33 +-Applying beta-rule and splitting (3331), into two cases.
% 67.80/29.33 |-Branch one:
% 67.80/29.33 | (3332) ~ (all_523_1_496 = 0)
% 67.80/29.33 |
% 67.80/29.33 | Instantiating formula (46) with xn, all_523_1_496, 0 and discharging atoms aNaturalNumber0(xn) = all_523_1_496, aNaturalNumber0(xn) = 0, yields:
% 67.80/29.33 | (3333) all_523_1_496 = 0
% 67.80/29.33 |
% 67.80/29.33 | Equations (3333) can reduce 3332 to:
% 67.80/29.33 | (159) $false
% 67.80/29.33 |
% 67.80/29.33 |-The branch is then unsatisfiable
% 67.80/29.33 |-Branch two:
% 67.80/29.33 | (3333) all_523_1_496 = 0
% 67.80/29.33 | (3336) all_523_0_495 = sz00 & all_0_3_3 = sz00
% 67.80/29.33 |
% 67.80/29.33 | Applying alpha-rule on (3336) yields:
% 67.80/29.33 | (3337) all_523_0_495 = sz00
% 67.80/29.33 | (1089) all_0_3_3 = sz00
% 67.80/29.33 |
% 67.80/29.34 | Equations (1089) can reduce 1087 to:
% 67.80/29.34 | (159) $false
% 67.80/29.34 |
% 67.80/29.34 |-The branch is then unsatisfiable
% 67.80/29.34 |-Branch two:
% 67.80/29.34 | (3340) sdtasdt0(sz00, xm) = all_0_3_3
% 67.80/29.34 | (3341) ? [v0] : ? [v1] : (sdtasdt0(xm, sz00) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v0 = 0) | (v1 = sz00 & all_0_3_3 = sz00)))
% 67.80/29.34 |
% 67.80/29.34 | Instantiating (3341) with all_509_0_497, all_509_1_498 yields:
% 67.80/29.34 | (3342) sdtasdt0(xm, sz00) = all_509_0_497 & aNaturalNumber0(xm) = all_509_1_498 & ( ~ (all_509_1_498 = 0) | (all_509_0_497 = sz00 & all_0_3_3 = sz00))
% 67.80/29.34 |
% 67.80/29.34 | Applying alpha-rule on (3342) yields:
% 67.80/29.34 | (3343) sdtasdt0(xm, sz00) = all_509_0_497
% 67.80/29.34 | (3344) aNaturalNumber0(xm) = all_509_1_498
% 67.80/29.34 | (3345) ~ (all_509_1_498 = 0) | (all_509_0_497 = sz00 & all_0_3_3 = sz00)
% 67.80/29.34 |
% 67.80/29.34 +-Applying beta-rule and splitting (90), into two cases.
% 67.80/29.34 |-Branch one:
% 67.80/29.34 | (1089) all_0_3_3 = sz00
% 67.80/29.34 |
% 67.80/29.34 | Equations (1089) can reduce 1087 to:
% 67.80/29.34 | (159) $false
% 67.80/29.34 |
% 67.80/29.34 |-The branch is then unsatisfiable
% 67.80/29.34 |-Branch two:
% 67.80/29.34 | (1087) ~ (all_0_3_3 = sz00)
% 67.80/29.34 | (1092) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 67.80/29.34 |
% 67.80/29.34 +-Applying beta-rule and splitting (3345), into two cases.
% 67.80/29.34 |-Branch one:
% 67.80/29.34 | (3350) ~ (all_509_1_498 = 0)
% 67.80/29.34 |
% 67.80/29.34 | Instantiating formula (46) with xm, all_509_1_498, 0 and discharging atoms aNaturalNumber0(xm) = all_509_1_498, aNaturalNumber0(xm) = 0, yields:
% 67.80/29.34 | (3351) all_509_1_498 = 0
% 67.80/29.34 |
% 67.80/29.34 | Equations (3351) can reduce 3350 to:
% 67.80/29.34 | (159) $false
% 67.80/29.34 |
% 67.80/29.34 |-The branch is then unsatisfiable
% 67.80/29.34 |-Branch two:
% 67.80/29.34 | (3351) all_509_1_498 = 0
% 67.80/29.34 | (3354) all_509_0_497 = sz00 & all_0_3_3 = sz00
% 67.80/29.34 |
% 67.80/29.34 | Applying alpha-rule on (3354) yields:
% 67.80/29.34 | (3355) all_509_0_497 = sz00
% 67.80/29.34 | (1089) all_0_3_3 = sz00
% 67.80/29.34 |
% 67.80/29.34 | Equations (1089) can reduce 1087 to:
% 67.80/29.34 | (159) $false
% 67.80/29.34 |
% 67.80/29.34 |-The branch is then unsatisfiable
% 67.80/29.34 |-Branch two:
% 67.80/29.34 | (3358) doDivides0(xp, all_0_3_3) = all_456_0_152 & aNaturalNumber0(all_0_3_3) = all_456_1_153 & aNaturalNumber0(xp) = all_456_2_154 & ( ~ (all_456_0_152 = 0) | ~ (all_456_1_153 = 0) | ~ (all_456_2_154 = 0))
% 67.80/29.34 |
% 67.80/29.34 | Applying alpha-rule on (3358) yields:
% 67.80/29.34 | (3359) doDivides0(xp, all_0_3_3) = all_456_0_152
% 67.80/29.34 | (3360) aNaturalNumber0(all_0_3_3) = all_456_1_153
% 67.80/29.34 | (3361) aNaturalNumber0(xp) = all_456_2_154
% 67.80/29.34 | (3362) ~ (all_456_0_152 = 0) | ~ (all_456_1_153 = 0) | ~ (all_456_2_154 = 0)
% 67.80/29.34 |
% 67.80/29.34 | Instantiating formula (32) with xp, all_0_3_3, all_456_0_152, 0 and discharging atoms doDivides0(xp, all_0_3_3) = all_456_0_152, doDivides0(xp, all_0_3_3) = 0, yields:
% 67.80/29.34 | (3363) all_456_0_152 = 0
% 67.80/29.34 |
% 67.80/29.34 | Instantiating formula (46) with all_0_3_3, all_456_1_153, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_456_1_153, aNaturalNumber0(all_0_3_3) = 0, yields:
% 67.80/29.34 | (3364) all_456_1_153 = 0
% 67.80/29.34 |
% 67.80/29.34 | Instantiating formula (46) with xp, all_456_2_154, 0 and discharging atoms aNaturalNumber0(xp) = all_456_2_154, aNaturalNumber0(xp) = 0, yields:
% 67.80/29.34 | (1085) all_456_2_154 = 0
% 67.80/29.34 |
% 67.80/29.34 +-Applying beta-rule and splitting (3362), into two cases.
% 67.80/29.34 |-Branch one:
% 67.80/29.34 | (3366) ~ (all_456_0_152 = 0)
% 67.80/29.34 |
% 67.80/29.34 | Equations (3363) can reduce 3366 to:
% 67.80/29.34 | (159) $false
% 67.80/29.34 |
% 67.80/29.34 |-The branch is then unsatisfiable
% 67.80/29.34 |-Branch two:
% 67.80/29.34 | (3363) all_456_0_152 = 0
% 67.80/29.34 | (3369) ~ (all_456_1_153 = 0) | ~ (all_456_2_154 = 0)
% 67.80/29.34 |
% 67.80/29.34 +-Applying beta-rule and splitting (3369), into two cases.
% 67.80/29.34 |-Branch one:
% 67.80/29.34 | (3370) ~ (all_456_1_153 = 0)
% 67.80/29.34 |
% 67.80/29.34 | Equations (3364) can reduce 3370 to:
% 67.80/29.34 | (159) $false
% 67.80/29.34 |
% 67.80/29.34 |-The branch is then unsatisfiable
% 67.80/29.34 |-Branch two:
% 67.80/29.34 | (3364) all_456_1_153 = 0
% 67.80/29.34 | (3373) ~ (all_456_2_154 = 0)
% 67.80/29.34 |
% 67.80/29.34 | Equations (1085) can reduce 3373 to:
% 67.80/29.34 | (159) $false
% 67.80/29.34 |
% 67.80/29.34 |-The branch is then unsatisfiable
% 67.80/29.34 |-Branch two:
% 67.80/29.34 | (3375) sdtasdt0(xp, all_20_2_23) = sz00
% 67.80/29.34 | (3376) all_20_2_23 = sz00 | xp = sz00 | ? [v0] : ? [v1] : (aNaturalNumber0(all_20_2_23) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 67.80/29.34 |
% 67.80/29.34 +-Applying beta-rule and splitting (3376), into two cases.
% 67.80/29.34 |-Branch one:
% 67.80/29.34 | (982) all_20_2_23 = sz00
% 67.80/29.34 |
% 67.80/29.34 | Combining equations (982,968) yields a new equation:
% 67.80/29.34 | (168) xk = sz00
% 67.80/29.34 |
% 67.80/29.34 | Equations (168) can reduce 13 to:
% 67.80/29.34 | (159) $false
% 67.80/29.34 |
% 67.80/29.34 |-The branch is then unsatisfiable
% 67.80/29.34 |-Branch two:
% 67.80/29.34 | (985) ~ (all_20_2_23 = sz00)
% 67.80/29.34 | (3381) xp = sz00 | ? [v0] : ? [v1] : (aNaturalNumber0(all_20_2_23) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 67.80/29.34 |
% 67.80/29.34 +-Applying beta-rule and splitting (3381), into two cases.
% 67.80/29.34 |-Branch one:
% 67.80/29.34 | (181) xp = sz00
% 67.80/29.34 |
% 67.80/29.34 | Equations (181) can reduce 86 to:
% 67.80/29.34 | (159) $false
% 67.80/29.34 |
% 67.80/29.34 |-The branch is then unsatisfiable
% 67.80/29.34 |-Branch two:
% 67.80/29.34 | (86) ~ (xp = sz00)
% 67.80/29.34 | (3385) ? [v0] : ? [v1] : (aNaturalNumber0(all_20_2_23) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 67.80/29.34 |
% 67.80/29.34 | Instantiating (3385) with all_489_0_505, all_489_1_506 yields:
% 67.80/29.34 | (3386) aNaturalNumber0(all_20_2_23) = all_489_0_505 & aNaturalNumber0(xp) = all_489_1_506 & ( ~ (all_489_0_505 = 0) | ~ (all_489_1_506 = 0))
% 67.80/29.34 |
% 67.80/29.34 | Applying alpha-rule on (3386) yields:
% 67.80/29.34 | (3387) aNaturalNumber0(all_20_2_23) = all_489_0_505
% 67.80/29.34 | (3388) aNaturalNumber0(xp) = all_489_1_506
% 67.80/29.34 | (3389) ~ (all_489_0_505 = 0) | ~ (all_489_1_506 = 0)
% 67.80/29.34 |
% 67.80/29.34 | From (968) and (3387) follows:
% 67.80/29.34 | (3390) aNaturalNumber0(xk) = all_489_0_505
% 67.80/29.34 |
% 67.80/29.34 | Instantiating formula (46) with xk, all_489_0_505, 0 and discharging atoms aNaturalNumber0(xk) = all_489_0_505, aNaturalNumber0(xk) = 0, yields:
% 67.80/29.34 | (3391) all_489_0_505 = 0
% 67.80/29.34 |
% 67.80/29.34 | Instantiating formula (46) with xp, all_489_1_506, 0 and discharging atoms aNaturalNumber0(xp) = all_489_1_506, aNaturalNumber0(xp) = 0, yields:
% 67.80/29.34 | (3392) all_489_1_506 = 0
% 67.80/29.34 |
% 67.80/29.34 +-Applying beta-rule and splitting (3389), into two cases.
% 67.80/29.34 |-Branch one:
% 67.80/29.34 | (3393) ~ (all_489_0_505 = 0)
% 67.80/29.34 |
% 67.80/29.34 | Equations (3391) can reduce 3393 to:
% 67.80/29.34 | (159) $false
% 67.80/29.34 |
% 67.80/29.34 |-The branch is then unsatisfiable
% 67.80/29.34 |-Branch two:
% 67.80/29.34 | (3391) all_489_0_505 = 0
% 67.80/29.34 | (3396) ~ (all_489_1_506 = 0)
% 67.80/29.34 |
% 67.80/29.34 | Equations (3392) can reduce 3396 to:
% 67.80/29.34 | (159) $false
% 67.80/29.34 |
% 67.80/29.34 |-The branch is then unsatisfiable
% 67.80/29.34 |-Branch two:
% 67.80/29.34 | (3228) all_36_0_50 = 0
% 67.80/29.34 | (3399) ~ (all_36_1_51 = 0) | ~ (all_36_2_52 = 0) | ~ (all_36_3_53 = 0)
% 67.80/29.34 |
% 67.80/29.34 +-Applying beta-rule and splitting (3399), into two cases.
% 67.80/29.34 |-Branch one:
% 67.80/29.34 | (3400) ~ (all_36_1_51 = 0)
% 67.80/29.34 |
% 67.80/29.34 | Equations (555) can reduce 3400 to:
% 67.80/29.34 | (159) $false
% 67.80/29.34 |
% 67.80/29.34 |-The branch is then unsatisfiable
% 67.80/29.34 |-Branch two:
% 67.80/29.34 | (555) all_36_1_51 = 0
% 67.80/29.34 | (3403) ~ (all_36_2_52 = 0) | ~ (all_36_3_53 = 0)
% 67.80/29.34 |
% 67.80/29.34 +-Applying beta-rule and splitting (3403), into two cases.
% 67.80/29.34 |-Branch one:
% 67.80/29.34 | (3404) ~ (all_36_2_52 = 0)
% 67.80/29.34 |
% 67.80/29.34 | Equations (979) can reduce 3404 to:
% 67.80/29.34 | (159) $false
% 67.80/29.34 |
% 67.80/29.34 |-The branch is then unsatisfiable
% 67.80/29.34 |-Branch two:
% 67.80/29.34 | (979) all_36_2_52 = 0
% 67.80/29.34 | (3407) ~ (all_36_3_53 = 0)
% 67.80/29.34 |
% 67.80/29.34 | Equations (480) can reduce 3407 to:
% 67.80/29.34 | (159) $false
% 67.80/29.34 |
% 67.80/29.34 |-The branch is then unsatisfiable
% 67.80/29.35 |-Branch two:
% 67.80/29.35 | (3409) ~ (all_58_0_58 = xp)
% 67.80/29.35 | (3410) all_58_0_58 = sz10 | ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_58_0_58) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0))
% 67.80/29.35 |
% 67.80/29.35 +-Applying beta-rule and splitting (3410), into two cases.
% 67.80/29.35 |-Branch one:
% 67.80/29.35 | (771) all_58_0_58 = sz10
% 67.80/29.35 |
% 67.80/29.35 | Equations (771) can reduce 201 to:
% 67.80/29.35 | (159) $false
% 67.80/29.35 |
% 67.80/29.35 |-The branch is then unsatisfiable
% 67.80/29.35 |-Branch two:
% 67.80/29.35 | (201) ~ (all_58_0_58 = sz10)
% 67.80/29.35 | (3414) ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_58_0_58) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0))
% 67.80/29.35 |
% 67.80/29.35 | Instantiating (3414) with all_433_0_552 yields:
% 67.80/29.35 | (3415) ( ~ (all_433_0_552 = 0) & aNaturalNumber0(all_58_0_58) = all_433_0_552) | ( ~ (all_433_0_552 = 0) & aNaturalNumber0(xp) = all_433_0_552)
% 67.80/29.35 |
% 67.80/29.35 +-Applying beta-rule and splitting (3415), into two cases.
% 67.80/29.35 |-Branch one:
% 67.80/29.35 | (3416) ~ (all_433_0_552 = 0) & aNaturalNumber0(all_58_0_58) = all_433_0_552
% 67.80/29.35 |
% 67.80/29.35 | Applying alpha-rule on (3416) yields:
% 67.80/29.35 | (3417) ~ (all_433_0_552 = 0)
% 67.80/29.35 | (3418) aNaturalNumber0(all_58_0_58) = all_433_0_552
% 67.80/29.35 |
% 67.80/29.35 | Instantiating formula (46) with all_58_0_58, all_433_0_552, 0 and discharging atoms aNaturalNumber0(all_58_0_58) = all_433_0_552, aNaturalNumber0(all_58_0_58) = 0, yields:
% 67.80/29.35 | (3419) all_433_0_552 = 0
% 67.80/29.35 |
% 67.80/29.35 | Equations (3419) can reduce 3417 to:
% 67.80/29.35 | (159) $false
% 67.80/29.35 |
% 67.80/29.35 |-The branch is then unsatisfiable
% 67.80/29.35 |-Branch two:
% 67.80/29.35 | (3421) ~ (all_433_0_552 = 0) & aNaturalNumber0(xp) = all_433_0_552
% 67.80/29.35 |
% 67.80/29.35 | Applying alpha-rule on (3421) yields:
% 67.80/29.35 | (3417) ~ (all_433_0_552 = 0)
% 67.80/29.35 | (3423) aNaturalNumber0(xp) = all_433_0_552
% 67.80/29.35 |
% 67.80/29.35 | Instantiating formula (46) with xp, all_433_0_552, 0 and discharging atoms aNaturalNumber0(xp) = all_433_0_552, aNaturalNumber0(xp) = 0, yields:
% 67.80/29.35 | (3419) all_433_0_552 = 0
% 67.80/29.35 |
% 67.80/29.35 | Equations (3419) can reduce 3417 to:
% 67.80/29.35 | (159) $false
% 67.80/29.35 |
% 67.80/29.35 |-The branch is then unsatisfiable
% 67.80/29.35 |-Branch two:
% 67.80/29.35 | (3426) aNaturalNumber0(xr) = all_21_2_26 & aNaturalNumber0(xk) = all_21_1_25 & ( ~ (all_21_1_25 = 0) | ~ (all_21_2_26 = 0))
% 67.80/29.35 |
% 67.80/29.35 | Applying alpha-rule on (3426) yields:
% 67.80/29.35 | (3427) aNaturalNumber0(xr) = all_21_2_26
% 67.80/29.35 | (3428) aNaturalNumber0(xk) = all_21_1_25
% 67.80/29.35 | (3429) ~ (all_21_1_25 = 0) | ~ (all_21_2_26 = 0)
% 67.80/29.35 |
% 67.80/29.35 +-Applying beta-rule and splitting (651), into two cases.
% 67.80/29.35 |-Branch one:
% 67.80/29.35 | (974) ~ (aNaturalNumber0(xk) = 0)
% 67.80/29.35 |
% 67.80/29.35 | Using (972) and (974) yields:
% 67.80/29.35 | (615) $false
% 67.80/29.35 |
% 67.80/29.35 |-The branch is then unsatisfiable
% 67.80/29.35 |-Branch two:
% 67.80/29.35 | (972) aNaturalNumber0(xk) = 0
% 67.80/29.35 | (996) xk = sz10 | xk = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xk) = 0 & aNaturalNumber0(v0) = 0)
% 67.80/29.35 |
% 67.80/29.35 | Instantiating formula (46) with xr, all_21_2_26, 0 and discharging atoms aNaturalNumber0(xr) = all_21_2_26, aNaturalNumber0(xr) = 0, yields:
% 67.80/29.35 | (3434) all_21_2_26 = 0
% 67.80/29.35 |
% 67.80/29.35 | Instantiating formula (46) with xk, all_21_1_25, 0 and discharging atoms aNaturalNumber0(xk) = all_21_1_25, aNaturalNumber0(xk) = 0, yields:
% 67.80/29.35 | (990) all_21_1_25 = 0
% 67.80/29.35 |
% 67.80/29.35 +-Applying beta-rule and splitting (3429), into two cases.
% 67.80/29.35 |-Branch one:
% 67.80/29.35 | (3436) ~ (all_21_1_25 = 0)
% 67.80/29.35 |
% 67.80/29.35 | Equations (990) can reduce 3436 to:
% 67.80/29.35 | (159) $false
% 67.80/29.35 |
% 67.80/29.35 |-The branch is then unsatisfiable
% 67.80/29.35 |-Branch two:
% 67.80/29.35 | (990) all_21_1_25 = 0
% 67.80/29.35 | (3439) ~ (all_21_2_26 = 0)
% 67.80/29.35 |
% 67.80/29.35 | Equations (3434) can reduce 3439 to:
% 67.80/29.35 | (159) $false
% 67.80/29.35 |
% 67.80/29.35 |-The branch is then unsatisfiable
% 67.80/29.35 |-Branch two:
% 67.80/29.35 | (3441) ~ (all_20_2_23 = xk)
% 67.80/29.35 | (3442) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_20_2_23) = v0) | (doDivides0(xp, all_0_3_3) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 67.80/29.35 |
% 67.80/29.35 | Instantiating (3442) with all_369_0_572, all_369_1_573, all_369_2_574 yields:
% 67.80/29.35 | (3443) ( ~ (all_369_2_574 = 0) & aNaturalNumber0(all_20_2_23) = all_369_2_574) | (doDivides0(xp, all_0_3_3) = all_369_0_572 & aNaturalNumber0(all_0_3_3) = all_369_1_573 & aNaturalNumber0(xp) = all_369_2_574 & ( ~ (all_369_0_572 = 0) | ~ (all_369_1_573 = 0) | ~ (all_369_2_574 = 0)))
% 67.80/29.35 |
% 67.80/29.35 +-Applying beta-rule and splitting (3443), into two cases.
% 67.80/29.35 |-Branch one:
% 67.80/29.35 | (3444) ~ (all_369_2_574 = 0) & aNaturalNumber0(all_20_2_23) = all_369_2_574
% 67.80/29.35 |
% 67.80/29.35 | Applying alpha-rule on (3444) yields:
% 67.80/29.35 | (3445) ~ (all_369_2_574 = 0)
% 67.80/29.35 | (3446) aNaturalNumber0(all_20_2_23) = all_369_2_574
% 67.80/29.35 |
% 67.80/29.35 | Instantiating formula (46) with all_20_2_23, all_369_2_574, 0 and discharging atoms aNaturalNumber0(all_20_2_23) = all_369_2_574, aNaturalNumber0(all_20_2_23) = 0, yields:
% 67.80/29.35 | (3447) all_369_2_574 = 0
% 67.80/29.35 |
% 67.80/29.35 | Equations (3447) can reduce 3445 to:
% 67.80/29.35 | (159) $false
% 67.80/29.35 |
% 67.80/29.35 |-The branch is then unsatisfiable
% 67.80/29.35 |-Branch two:
% 67.80/29.35 | (3449) doDivides0(xp, all_0_3_3) = all_369_0_572 & aNaturalNumber0(all_0_3_3) = all_369_1_573 & aNaturalNumber0(xp) = all_369_2_574 & ( ~ (all_369_0_572 = 0) | ~ (all_369_1_573 = 0) | ~ (all_369_2_574 = 0))
% 67.80/29.35 |
% 67.80/29.35 | Applying alpha-rule on (3449) yields:
% 67.80/29.35 | (3450) doDivides0(xp, all_0_3_3) = all_369_0_572
% 67.80/29.35 | (3451) aNaturalNumber0(all_0_3_3) = all_369_1_573
% 67.80/29.35 | (3452) aNaturalNumber0(xp) = all_369_2_574
% 67.80/29.35 | (3453) ~ (all_369_0_572 = 0) | ~ (all_369_1_573 = 0) | ~ (all_369_2_574 = 0)
% 67.80/29.35 |
% 67.80/29.35 | Instantiating formula (32) with xp, all_0_3_3, all_369_0_572, 0 and discharging atoms doDivides0(xp, all_0_3_3) = all_369_0_572, doDivides0(xp, all_0_3_3) = 0, yields:
% 67.80/29.35 | (3454) all_369_0_572 = 0
% 67.80/29.35 |
% 67.80/29.35 | Instantiating formula (46) with all_0_3_3, all_369_1_573, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_369_1_573, aNaturalNumber0(all_0_3_3) = 0, yields:
% 67.80/29.35 | (3455) all_369_1_573 = 0
% 67.80/29.35 |
% 67.80/29.35 | Instantiating formula (46) with xp, all_369_2_574, 0 and discharging atoms aNaturalNumber0(xp) = all_369_2_574, aNaturalNumber0(xp) = 0, yields:
% 67.80/29.35 | (3447) all_369_2_574 = 0
% 67.80/29.35 |
% 67.80/29.35 +-Applying beta-rule and splitting (3453), into two cases.
% 67.80/29.35 |-Branch one:
% 67.80/29.35 | (3457) ~ (all_369_0_572 = 0)
% 67.80/29.35 |
% 67.80/29.35 | Equations (3454) can reduce 3457 to:
% 67.80/29.35 | (159) $false
% 67.80/29.35 |
% 67.80/29.35 |-The branch is then unsatisfiable
% 67.80/29.35 |-Branch two:
% 67.80/29.35 | (3454) all_369_0_572 = 0
% 67.80/29.35 | (3460) ~ (all_369_1_573 = 0) | ~ (all_369_2_574 = 0)
% 67.80/29.35 |
% 67.80/29.35 +-Applying beta-rule and splitting (3460), into two cases.
% 67.80/29.35 |-Branch one:
% 67.80/29.35 | (3461) ~ (all_369_1_573 = 0)
% 67.80/29.35 |
% 67.88/29.35 | Equations (3455) can reduce 3461 to:
% 67.88/29.35 | (159) $false
% 67.88/29.35 |
% 67.88/29.35 |-The branch is then unsatisfiable
% 67.88/29.35 |-Branch two:
% 67.88/29.35 | (3455) all_369_1_573 = 0
% 67.88/29.35 | (3445) ~ (all_369_2_574 = 0)
% 67.88/29.35 |
% 67.88/29.35 | Equations (3447) can reduce 3445 to:
% 67.88/29.35 | (159) $false
% 67.88/29.35 |
% 67.88/29.35 |-The branch is then unsatisfiable
% 67.88/29.36 |-Branch two:
% 67.88/29.36 | (3466) aNaturalNumber0(all_58_0_58) = all_186_2_128 & aNaturalNumber0(xp) = all_186_1_127 & ( ~ (all_186_1_127 = 0) | ~ (all_186_2_128 = 0))
% 67.88/29.36 |
% 67.88/29.36 | Applying alpha-rule on (3466) yields:
% 67.88/29.36 | (3467) aNaturalNumber0(all_58_0_58) = all_186_2_128
% 67.88/29.36 | (3468) aNaturalNumber0(xp) = all_186_1_127
% 67.88/29.36 | (3469) ~ (all_186_1_127 = 0) | ~ (all_186_2_128 = 0)
% 67.88/29.36 |
% 67.88/29.36 | Instantiating formula (46) with all_58_0_58, all_186_2_128, 0 and discharging atoms aNaturalNumber0(all_58_0_58) = all_186_2_128, aNaturalNumber0(all_58_0_58) = 0, yields:
% 67.88/29.36 | (3470) all_186_2_128 = 0
% 67.88/29.36 |
% 67.88/29.36 | Instantiating formula (46) with xp, all_186_1_127, 0 and discharging atoms aNaturalNumber0(xp) = all_186_1_127, aNaturalNumber0(xp) = 0, yields:
% 67.88/29.36 | (961) all_186_1_127 = 0
% 67.88/29.36 |
% 67.88/29.36 +-Applying beta-rule and splitting (3469), into two cases.
% 67.88/29.36 |-Branch one:
% 67.88/29.36 | (3472) ~ (all_186_1_127 = 0)
% 67.88/29.36 |
% 67.88/29.36 | Equations (961) can reduce 3472 to:
% 67.88/29.36 | (159) $false
% 67.88/29.36 |
% 67.88/29.36 |-The branch is then unsatisfiable
% 67.88/29.36 |-Branch two:
% 67.88/29.36 | (961) all_186_1_127 = 0
% 67.88/29.36 | (3475) ~ (all_186_2_128 = 0)
% 67.88/29.36 |
% 67.88/29.36 | Equations (3470) can reduce 3475 to:
% 67.88/29.36 | (159) $false
% 67.88/29.36 |
% 67.88/29.36 |-The branch is then unsatisfiable
% 67.88/29.36 |-Branch two:
% 67.88/29.36 | (3477) ~ (all_53_0_57 = xr)
% 67.88/29.36 | (3478) all_53_0_57 = sz10 | ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_53_0_57) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xr) = v0))
% 67.88/29.36 |
% 67.88/29.36 +-Applying beta-rule and splitting (3478), into two cases.
% 67.88/29.36 |-Branch one:
% 67.88/29.36 | (779) all_53_0_57 = sz10
% 67.88/29.36 |
% 67.88/29.36 | Equations (779) can reduce 203 to:
% 67.88/29.36 | (159) $false
% 67.88/29.36 |
% 67.88/29.36 |-The branch is then unsatisfiable
% 67.88/29.36 |-Branch two:
% 67.88/29.36 | (203) ~ (all_53_0_57 = sz10)
% 67.88/29.36 | (3482) ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_53_0_57) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xr) = v0))
% 67.88/29.36 |
% 67.88/29.36 | Instantiating (3482) with all_241_0_575 yields:
% 67.88/29.36 | (3483) ( ~ (all_241_0_575 = 0) & aNaturalNumber0(all_53_0_57) = all_241_0_575) | ( ~ (all_241_0_575 = 0) & aNaturalNumber0(xr) = all_241_0_575)
% 67.88/29.36 |
% 67.88/29.36 +-Applying beta-rule and splitting (3483), into two cases.
% 67.88/29.36 |-Branch one:
% 67.88/29.36 | (3484) ~ (all_241_0_575 = 0) & aNaturalNumber0(all_53_0_57) = all_241_0_575
% 67.88/29.36 |
% 67.88/29.36 | Applying alpha-rule on (3484) yields:
% 67.88/29.36 | (3485) ~ (all_241_0_575 = 0)
% 67.88/29.36 | (3486) aNaturalNumber0(all_53_0_57) = all_241_0_575
% 67.88/29.36 |
% 67.88/29.36 | Instantiating formula (46) with all_53_0_57, all_241_0_575, 0 and discharging atoms aNaturalNumber0(all_53_0_57) = all_241_0_575, aNaturalNumber0(all_53_0_57) = 0, yields:
% 67.88/29.36 | (3487) all_241_0_575 = 0
% 67.88/29.36 |
% 67.88/29.36 | Equations (3487) can reduce 3485 to:
% 67.88/29.36 | (159) $false
% 67.88/29.36 |
% 67.88/29.36 |-The branch is then unsatisfiable
% 67.88/29.36 |-Branch two:
% 67.88/29.36 | (3489) ~ (all_241_0_575 = 0) & aNaturalNumber0(xr) = all_241_0_575
% 67.88/29.36 |
% 67.88/29.36 | Applying alpha-rule on (3489) yields:
% 67.88/29.36 | (3485) ~ (all_241_0_575 = 0)
% 67.88/29.36 | (3491) aNaturalNumber0(xr) = all_241_0_575
% 67.88/29.36 |
% 67.88/29.36 | Instantiating formula (46) with xr, all_241_0_575, 0 and discharging atoms aNaturalNumber0(xr) = all_241_0_575, aNaturalNumber0(xr) = 0, yields:
% 67.88/29.36 | (3487) all_241_0_575 = 0
% 67.88/29.36 |
% 67.88/29.36 | Equations (3487) can reduce 3485 to:
% 67.88/29.36 | (159) $false
% 67.88/29.36 |
% 67.88/29.36 |-The branch is then unsatisfiable
% 67.88/29.36 |-Branch two:
% 67.88/29.36 | (3494) aNaturalNumber0(all_0_3_3) = all_20_1_22 & aNaturalNumber0(xp) = all_20_2_23 & ( ~ (all_20_1_22 = 0) | ~ (all_20_2_23 = 0))
% 67.88/29.36 |
% 67.88/29.36 | Applying alpha-rule on (3494) yields:
% 67.88/29.36 | (3495) aNaturalNumber0(all_0_3_3) = all_20_1_22
% 67.88/29.36 | (3496) aNaturalNumber0(xp) = all_20_2_23
% 67.88/29.36 | (3497) ~ (all_20_1_22 = 0) | ~ (all_20_2_23 = 0)
% 67.88/29.36 |
% 67.88/29.36 | Instantiating formula (46) with all_0_3_3, all_20_1_22, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_20_1_22, aNaturalNumber0(all_0_3_3) = 0, yields:
% 67.88/29.36 | (559) all_20_1_22 = 0
% 67.88/29.36 |
% 67.88/29.36 | Instantiating formula (46) with xp, all_20_2_23, 0 and discharging atoms aNaturalNumber0(xp) = all_20_2_23, aNaturalNumber0(xp) = 0, yields:
% 67.88/29.36 | (3499) all_20_2_23 = 0
% 67.88/29.36 |
% 67.88/29.36 +-Applying beta-rule and splitting (3497), into two cases.
% 67.88/29.36 |-Branch one:
% 67.88/29.36 | (3500) ~ (all_20_1_22 = 0)
% 67.88/29.36 |
% 67.88/29.36 | Equations (559) can reduce 3500 to:
% 67.88/29.36 | (159) $false
% 67.88/29.36 |
% 67.88/29.36 |-The branch is then unsatisfiable
% 67.88/29.36 |-Branch two:
% 67.88/29.36 | (559) all_20_1_22 = 0
% 67.88/29.36 | (3503) ~ (all_20_2_23 = 0)
% 67.88/29.36 |
% 67.88/29.36 | Equations (3499) can reduce 3503 to:
% 67.88/29.36 | (159) $false
% 67.88/29.36 |
% 67.88/29.36 |-The branch is then unsatisfiable
% 67.88/29.36 |-Branch two:
% 67.88/29.36 | (3505) aNaturalNumber0(xp) = all_19_1_19 & aNaturalNumber0(xm) = all_19_2_20 & ( ~ (all_19_1_19 = 0) | ~ (all_19_2_20 = 0))
% 67.88/29.36 |
% 67.88/29.36 | Applying alpha-rule on (3505) yields:
% 67.88/29.36 | (3506) aNaturalNumber0(xp) = all_19_1_19
% 67.88/29.36 | (3507) aNaturalNumber0(xm) = all_19_2_20
% 67.88/29.36 | (3508) ~ (all_19_1_19 = 0) | ~ (all_19_2_20 = 0)
% 67.88/29.36 |
% 67.88/29.36 | Instantiating formula (46) with xp, all_19_1_19, 0 and discharging atoms aNaturalNumber0(xp) = all_19_1_19, aNaturalNumber0(xp) = 0, yields:
% 67.88/29.36 | (540) all_19_1_19 = 0
% 67.88/29.36 |
% 67.88/29.36 | Instantiating formula (46) with xm, all_19_2_20, 0 and discharging atoms aNaturalNumber0(xm) = all_19_2_20, aNaturalNumber0(xm) = 0, yields:
% 67.88/29.36 | (3510) all_19_2_20 = 0
% 67.88/29.36 |
% 67.88/29.36 +-Applying beta-rule and splitting (3508), into two cases.
% 67.88/29.36 |-Branch one:
% 67.88/29.36 | (3511) ~ (all_19_1_19 = 0)
% 67.88/29.36 |
% 67.88/29.36 | Equations (540) can reduce 3511 to:
% 67.88/29.36 | (159) $false
% 67.88/29.36 |
% 67.88/29.36 |-The branch is then unsatisfiable
% 67.88/29.36 |-Branch two:
% 67.88/29.36 | (540) all_19_1_19 = 0
% 67.88/29.36 | (3514) ~ (all_19_2_20 = 0)
% 67.88/29.36 |
% 67.88/29.36 | Equations (3510) can reduce 3514 to:
% 67.88/29.36 | (159) $false
% 67.88/29.36 |
% 67.88/29.36 |-The branch is then unsatisfiable
% 67.88/29.36 |-Branch two:
% 67.88/29.36 | (3516) aNaturalNumber0(xp) = all_18_1_16 & aNaturalNumber0(xn) = all_18_2_17 & ( ~ (all_18_1_16 = 0) | ~ (all_18_2_17 = 0))
% 67.88/29.36 |
% 67.88/29.36 | Applying alpha-rule on (3516) yields:
% 67.88/29.36 | (3517) aNaturalNumber0(xp) = all_18_1_16
% 67.88/29.36 | (3518) aNaturalNumber0(xn) = all_18_2_17
% 67.88/29.36 | (3519) ~ (all_18_1_16 = 0) | ~ (all_18_2_17 = 0)
% 67.88/29.36 |
% 67.88/29.36 | Instantiating formula (46) with xp, all_18_1_16, 0 and discharging atoms aNaturalNumber0(xp) = all_18_1_16, aNaturalNumber0(xp) = 0, yields:
% 67.88/29.36 | (531) all_18_1_16 = 0
% 67.88/29.36 |
% 67.88/29.36 | Instantiating formula (46) with xn, all_18_2_17, 0 and discharging atoms aNaturalNumber0(xn) = all_18_2_17, aNaturalNumber0(xn) = 0, yields:
% 67.88/29.36 | (3521) all_18_2_17 = 0
% 67.88/29.36 |
% 67.88/29.36 +-Applying beta-rule and splitting (3519), into two cases.
% 67.88/29.36 |-Branch one:
% 67.88/29.36 | (3522) ~ (all_18_1_16 = 0)
% 67.88/29.36 |
% 67.88/29.36 | Equations (531) can reduce 3522 to:
% 67.88/29.36 | (159) $false
% 67.88/29.36 |
% 67.88/29.36 |-The branch is then unsatisfiable
% 67.88/29.36 |-Branch two:
% 67.88/29.36 | (531) all_18_1_16 = 0
% 67.88/29.36 | (3525) ~ (all_18_2_17 = 0)
% 67.88/29.36 |
% 67.88/29.37 | Equations (3521) can reduce 3525 to:
% 67.88/29.37 | (159) $false
% 67.88/29.37 |
% 67.88/29.37 |-The branch is then unsatisfiable
% 67.88/29.37 % SZS output end Proof for theBenchmark
% 67.88/29.37
% 67.88/29.37 28710ms
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