TSTP Solution File: NUM503+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM503+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 08:45:12 EDT 2022
% Result : Theorem 42.03s 11.76s
% Output : Proof 91.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM503+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 5 17:31:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.64/0.67 ____ _
% 0.64/0.67 ___ / __ \_____(_)___ ________ __________
% 0.64/0.67 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.64/0.67 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.64/0.67 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.64/0.67
% 0.64/0.67 A Theorem Prover for First-Order Logic
% 0.64/0.67 (ePrincess v.1.0)
% 0.64/0.67
% 0.64/0.67 (c) Philipp Rümmer, 2009-2015
% 0.64/0.67 (c) Peter Backeman, 2014-2015
% 0.64/0.67 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.64/0.67 Free software under GNU Lesser General Public License (LGPL).
% 0.64/0.67 Bug reports to peter@backeman.se
% 0.64/0.67
% 0.64/0.67 For more information, visit http://user.uu.se/~petba168/breu/
% 0.64/0.67
% 0.64/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.74/0.73 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.23/1.18 Prover 0: Preprocessing ...
% 4.89/1.91 Prover 0: Constructing countermodel ...
% 21.24/6.02 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 21.51/6.10 Prover 1: Preprocessing ...
% 22.22/6.30 Prover 1: Constructing countermodel ...
% 32.00/8.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 32.19/8.69 Prover 2: Preprocessing ...
% 33.26/8.96 Prover 2: Warning: ignoring some quantifiers
% 33.54/8.97 Prover 2: Constructing countermodel ...
% 41.91/11.63 Prover 0: stopped
% 42.03/11.76 Prover 1: proved (3119ms)
% 42.03/11.76 Prover 2: stopped
% 42.03/11.76
% 42.03/11.76 No countermodel exists, formula is valid
% 42.03/11.76 % SZS status Theorem for theBenchmark
% 42.03/11.76
% 42.03/11.76 Generating proof ... found it (size 1206)
% 89.97/41.93
% 89.97/41.93 % SZS output start Proof for theBenchmark
% 89.97/41.93 Assumed formulas after preprocessing and simplification:
% 89.97/41.93 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v4 = 0) & ~ (v3 = 0) & ~ (xk = sz10) & ~ (xk = sz00) & ~ (xp = xm) & ~ (xp = xn) & ~ (sz10 = sz00) & isPrime0(xr) = 0 & isPrime0(xp) = 0 & sdtsldt0(v2, xp) = xk & doDivides0(xr, v2) = 0 & doDivides0(xr, xk) = 0 & doDivides0(xp, v2) = 0 & sdtlseqdt0(v5, v7) = v8 & sdtlseqdt0(v2, v5) = v6 & sdtlseqdt0(xr, xk) = 0 & sdtlseqdt0(xp, xk) = 0 & sdtlseqdt0(xp, xm) = v4 & sdtlseqdt0(xp, xn) = v3 & sdtlseqdt0(xm, xp) = 0 & sdtlseqdt0(xn, xp) = 0 & sdtasdt0(xp, xk) = v7 & sdtasdt0(xp, xm) = v5 & 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) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | v9 = sz00 | ~ (sdtlseqdt0(v12, v13) = v14) | ~ (sdtasdt0(v9, v11) = v13) | ~ (sdtasdt0(v9, v10) = v12) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (sdtlseqdt0(v19, v20) = v21 & sdtlseqdt0(v10, v11) = v18 & sdtasdt0(v11, v9) = v20 & sdtasdt0(v10, v9) = v19 & aNaturalNumber0(v11) = v17 & aNaturalNumber0(v10) = v16 & aNaturalNumber0(v9) = v15 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | (v21 = 0 & v14 = 0 & ~ (v20 = v19) & ~ (v13 = v12))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = v9 | ~ (sdtlseqdt0(v12, v13) = v14) | ~ (sdtlseqdt0(v9, v10) = 0) | ~ (sdtpldt0(v10, v11) = v13) | ~ (sdtpldt0(v9, v11) = v12) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((sdtlseqdt0(v16, v17) = v18 & sdtpldt0(v11, v10) = v17 & sdtpldt0(v11, v9) = v16 & aNaturalNumber0(v11) = v15 & ( ~ (v15 = 0) | (v18 = 0 & v14 = 0 & ~ (v17 = v16) & ~ (v13 = v12)))) | (aNaturalNumber0(v10) = v16 & aNaturalNumber0(v9) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v9 = sz00 | ~ (sdtsldt0(v13, v9) = v14) | ~ (sdtsldt0(v10, v9) = v11) | ~ (sdtasdt0(v12, v10) = v13) | ? [v15] : ? [v16] : ? [v17] : ((doDivides0(v9, v10) = v17 & aNaturalNumber0(v10) = v16 & aNaturalNumber0(v9) = v15 & ( ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0))) | (sdtasdt0(v12, v11) = v16 & aNaturalNumber0(v12) = v15 & ( ~ (v15 = 0) | v16 = v14)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtasdt0(v9, v11) = v13) | ~ (sdtasdt0(v9, v10) = v12) | ~ (sdtpldt0(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (sdtasdt0(v18, v9) = v20 & sdtasdt0(v11, v9) = v22 & sdtasdt0(v10, v9) = v21 & sdtasdt0(v9, v18) = v19 & sdtpldt0(v21, v22) = v23 & sdtpldt0(v10, v11) = v18 & aNaturalNumber0(v11) = v17 & aNaturalNumber0(v10) = v16 & aNaturalNumber0(v9) = v15 & ( ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | (v23 = v20 & v19 = v14)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (doDivides0(v9, v12) = v13) | ~ (sdtpldt0(v10, v11) = v12) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (doDivides0(v9, v11) = v18 & doDivides0(v9, v10) = v17 & aNaturalNumber0(v11) = v16 & aNaturalNumber0(v10) = v15 & aNaturalNumber0(v9) = v14 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | v9 = sz00 | ~ (sdtasdt0(v9, v11) = v13) | ~ (sdtasdt0(v9, v10) = v12) | ~ (aNaturalNumber0(v9) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (sdtasdt0(v11, v9) = v17 & sdtasdt0(v10, v9) = v16 & aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | ( ~ (v17 = v16) & ~ (v13 = v12))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtpldt0(v9, v11) = v13) | ~ (sdtpldt0(v9, v10) = v12) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (sdtpldt0(v11, v9) = v18 & sdtpldt0(v10, v9) = v17 & aNaturalNumber0(v11) = v16 & aNaturalNumber0(v10) = v15 & aNaturalNumber0(v9) = v14 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ( ~ (v18 = v17) & ~ (v13 = v12))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtasdt0(v12, v11) = v13) | ~ (sdtasdt0(v9, v10) = v12) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (sdtasdt0(v10, v11) = v17 & sdtasdt0(v9, v17) = v18 & aNaturalNumber0(v11) = v16 & aNaturalNumber0(v10) = v15 & aNaturalNumber0(v9) = v14 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | v18 = v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtpldt0(v12, v11) = v13) | ~ (sdtpldt0(v9, v10) = v12) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (sdtpldt0(v10, v11) = v17 & sdtpldt0(v9, v17) = v18 & aNaturalNumber0(v11) = v16 & aNaturalNumber0(v10) = v15 & aNaturalNumber0(v9) = v14 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | v18 = v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | v9 = sz00 | ~ (sdtsldt0(v10, v9) = v11) | ~ (sdtasdt0(v9, v12) = v10) | ? [v13] : ? [v14] : ? [v15] : (( ~ (v13 = 0) & aNaturalNumber0(v12) = v13) | (doDivides0(v9, v10) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (sdtmndt0(v10, v9) = v11) | ~ (sdtpldt0(v9, v12) = v10) | ? [v13] : ? [v14] : ? [v15] : (( ~ (v13 = 0) & aNaturalNumber0(v12) = v13) | (sdtlseqdt0(v9, v10) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | v9 = sz00 | ~ (sdtsldt0(v10, v9) = v11) | ~ (sdtasdt0(v9, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (doDivides0(v9, v10) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (sdtmndt0(v10, v9) = v11) | ~ (sdtpldt0(v9, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (sdtlseqdt0(v9, v10) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v9 = sz00 | ~ (sdtlseqdt0(v10, v11) = v12) | ~ (sdtasdt0(v10, v9) = v11) | ? [v13] : ? [v14] : (aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (doDivides0(v9, v11) = v12) | ~ (doDivides0(v9, v10) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (doDivides0(v10, v11) = v16 & aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (sdtlseqdt0(v9, v11) = v12) | ~ (sdtlseqdt0(v9, v10) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (sdtlseqdt0(v10, v11) = v16 & aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (doDivides0(v9, v10) = v11) | ~ (sdtasdt0(v9, v12) = v10) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & aNaturalNumber0(v12) = v13) | (aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (sdtlseqdt0(v9, v10) = v11) | ~ (sdtpldt0(v9, v12) = v10) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & aNaturalNumber0(v12) = v13) | (aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (sdtsldt0(v12, v11) = v10) | ~ (sdtsldt0(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (doDivides0(v12, v11) = v10) | ~ (doDivides0(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (iLess0(v12, v11) = v10) | ~ (iLess0(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (sdtmndt0(v12, v11) = v10) | ~ (sdtmndt0(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (sdtlseqdt0(v12, v11) = v10) | ~ (sdtlseqdt0(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (sdtasdt0(v12, v11) = v10) | ~ (sdtasdt0(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (sdtpldt0(v12, v11) = v10) | ~ (sdtpldt0(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = sz00 | ~ (sdtsldt0(v10, v9) = v11) | ~ (sdtasdt0(v9, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ((v13 = 0 & aNaturalNumber0(v11) = 0) | (doDivides0(v9, v10) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (doDivides0(v11, v12) = 0) | ~ (sdtasdt0(v9, v10) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (isPrime0(v11) = v16 & doDivides0(v11, v10) = v21 & doDivides0(v11, v9) = v20 & iLess0(v18, v1) = v19 & sdtpldt0(v17, v11) = v18 & sdtpldt0(v9, v10) = v17 & aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v19 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | v21 = 0 | v20 = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (doDivides0(v9, v12) = 0) | ~ (sdtpldt0(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (doDivides0(v9, v11) = v17 & doDivides0(v9, v10) = v16 & aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | v17 = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtmndt0(v10, v9) = v11) | ~ (sdtpldt0(v9, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ((v13 = 0 & aNaturalNumber0(v11) = 0) | (sdtlseqdt0(v9, v10) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = v9 | ~ (iLess0(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (sdtlseqdt0(v9, v10) = v14 & aNaturalNumber0(v10) = v13 & aNaturalNumber0(v9) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (sdtlseqdt0(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (sdtlseqdt0(v10, v9) = v14 & aNaturalNumber0(v10) = v13 & aNaturalNumber0(v9) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | (v14 = 0 & ~ (v10 = v9))))) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (isPrime0(v11) = v10) | ~ (isPrime0(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (aNaturalNumber0(v11) = v10) | ~ (aNaturalNumber0(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v10, v9) = v14 & aNaturalNumber0(v10) = v13 & aNaturalNumber0(v9) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | v14 = v11))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (aNaturalNumber0(v11) = v14 & aNaturalNumber0(v10) = v13 & aNaturalNumber0(v9) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | v14 = 0))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtpldt0(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (sdtpldt0(v10, v9) = v14 & aNaturalNumber0(v10) = v13 & aNaturalNumber0(v9) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | v14 = v11))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtpldt0(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (aNaturalNumber0(v11) = v14 & aNaturalNumber0(v10) = v13 & aNaturalNumber0(v9) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | v14 = 0))) & ! [v9] : ! [v10] : (v10 = v9 | v10 = sz10 | ~ (isPrime0(v9) = 0) | ~ (doDivides0(v10, v9) = 0) | ? [v11] : (( ~ (v11 = 0) & aNaturalNumber0(v10) = v11) | ( ~ (v11 = 0) & aNaturalNumber0(v9) = v11))) & ! [v9] : ! [v10] : (v10 = v9 | ~ (sdtlseqdt0(v9, v10) = 0) | ? [v11] : ? [v12] : ? [v13] : (sdtlseqdt0(v10, v9) = v13 & aNaturalNumber0(v10) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v9] : ! [v10] : (v10 = sz00 | v9 = sz00 | ~ (sdtasdt0(v9, v10) = sz00) | ? [v11] : ? [v12] : (aNaturalNumber0(v10) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v9] : ! [v10] : (v10 = sz00 | ~ (doDivides0(v9, v10) = 0) | ? [v11] : ? [v12] : ? [v13] : (sdtlseqdt0(v9, v10) = v13 & aNaturalNumber0(v10) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) | v13 = 0))) & ! [v9] : ! [v10] : (v10 = sz00 | ~ (sdtpldt0(v9, v10) = sz00) | ? [v11] : ? [v12] : (aNaturalNumber0(v10) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v9] : ! [v10] : (v10 = 0 | v9 = sz10 | v9 = sz00 | ~ (isPrime0(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & ~ (v11 = v9) & ~ (v11 = sz10) & doDivides0(v11, v9) = 0 & aNaturalNumber0(v11) = 0) | ( ~ (v11 = 0) & aNaturalNumber0(v9) = v11))) & ! [v9] : ! [v10] : (v10 = 0 | v9 = sz10 | v9 = sz00 | ~ (sdtlseqdt0(sz10, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & aNaturalNumber0(v9) = v11)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (sdtlseqdt0(v9, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & aNaturalNumber0(v9) = v11)) & ! [v9] : ! [v10] : (v9 = sz00 | ~ (sdtpldt0(v9, v10) = sz00) | ? [v11] : ? [v12] : (aNaturalNumber0(v10) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v9] : ! [v10] : ( ~ (doDivides0(v9, v10) = 0) | ? [v11] : ? [v12] : ? [v13] : ((v13 = v10 & v12 = 0 & sdtasdt0(v9, v11) = v10 & aNaturalNumber0(v11) = 0) | (aNaturalNumber0(v10) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v9] : ! [v10] : ( ~ (sdtlseqdt0(v9, v10) = 0) | ? [v11] : ? [v12] : ? [v13] : ((v13 = v10 & v12 = 0 & sdtpldt0(v9, v11) = v10 & aNaturalNumber0(v11) = 0) | (aNaturalNumber0(v10) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v9] : ! [v10] : ( ~ (sdtasdt0(sz10, v9) = v10) | ? [v11] : ? [v12] : (sdtasdt0(v9, sz10) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v11 = 0) | (v12 = v9 & v10 = v9)))) & ! [v9] : ! [v10] : ( ~ (sdtasdt0(sz00, v9) = v10) | ? [v11] : ? [v12] : (sdtasdt0(v9, sz00) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v11 = 0) | (v12 = sz00 & v10 = sz00)))) & ! [v9] : ! [v10] : ( ~ (sdtpldt0(sz00, v9) = v10) | ? [v11] : ? [v12] : (sdtpldt0(v9, sz00) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v11 = 0) | (v12 = v9 & v10 = v9)))) & ! [v9] : (v9 = sz10 | v9 = sz00 | ~ (aNaturalNumber0(v9) = 0) | ? [v10] : (isPrime0(v10) = 0 & doDivides0(v10, v9) = 0 & aNaturalNumber0(v10) = 0)) & ( ~ (v8 = 0) | ~ (v6 = 0) | v7 = v5 | v5 = v2))
% 89.97/42.00 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 yields:
% 89.97/42.00 | (1) ~ (all_0_4_4 = 0) & ~ (all_0_5_5 = 0) & ~ (xk = sz10) & ~ (xk = sz00) & ~ (xp = xm) & ~ (xp = xn) & ~ (sz10 = sz00) & isPrime0(xr) = 0 & isPrime0(xp) = 0 & sdtsldt0(all_0_6_6, xp) = xk & doDivides0(xr, all_0_6_6) = 0 & doDivides0(xr, xk) = 0 & doDivides0(xp, all_0_6_6) = 0 & sdtlseqdt0(all_0_3_3, all_0_1_1) = all_0_0_0 & sdtlseqdt0(all_0_6_6, all_0_3_3) = all_0_2_2 & sdtlseqdt0(xr, xk) = 0 & sdtlseqdt0(xp, xk) = 0 & sdtlseqdt0(xp, xm) = all_0_4_4 & sdtlseqdt0(xp, xn) = all_0_5_5 & sdtlseqdt0(xm, xp) = 0 & sdtlseqdt0(xn, xp) = 0 & sdtasdt0(xp, xk) = all_0_1_1 & sdtasdt0(xp, xm) = all_0_3_3 & sdtasdt0(xn, xm) = all_0_6_6 & sdtpldt0(all_0_8_8, xp) = all_0_7_7 & sdtpldt0(xn, xm) = all_0_8_8 & 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_7_7) = v10 & sdtpldt0(v8, v2) = v9 & sdtpldt0(v0, v1) = v8 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v10 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v12 = 0 | v11 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (doDivides0(v0, v3) = 0) | ~ (sdtpldt0(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (doDivides0(v0, v2) = v8 & doDivides0(v0, v1) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (iLess0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtlseqdt0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtlseqdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v5 = 0 & ~ (v1 = v0))))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ (isPrime0(v0) = 0) | ~ (doDivides0(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (sdtlseqdt0(v1, v0) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (doDivides0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (sdtlseqdt0(v0, v1) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0))) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (isPrime0(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & ~ (v2 = v0) & ~ (v2 = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)) & ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (doDivides0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ! [v0] : ! [v1] : ( ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00)))) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0)) & ( ~ (all_0_0_0 = 0) | ~ (all_0_2_2 = 0) | all_0_1_1 = all_0_3_3 | all_0_3_3 = all_0_6_6)
% 90.40/42.03 |
% 90.40/42.03 | Applying alpha-rule on (1) yields:
% 90.40/42.03 | (2) ! [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)))))
% 90.40/42.03 | (3) sdtlseqdt0(xr, xk) = 0
% 90.40/42.03 | (4) sdtlseqdt0(xn, xp) = 0
% 90.40/42.03 | (5) ! [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)))))
% 90.40/42.03 | (6) doDivides0(xp, all_0_6_6) = 0
% 90.40/42.03 | (7) ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 90.40/42.03 | (8) aNaturalNumber0(sz10) = 0
% 90.40/42.03 | (9) doDivides0(xr, xk) = 0
% 90.40/42.03 | (10) ! [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)))))
% 90.40/42.03 | (11) ! [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)))
% 90.40/42.03 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 90.40/42.03 | (13) sdtasdt0(xp, xm) = all_0_3_3
% 90.40/42.03 | (14) ! [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)))))
% 90.40/42.03 | (15) ! [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)))
% 90.40/42.03 | (16) ! [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))))
% 90.40/42.03 | (17) sdtasdt0(xp, xk) = all_0_1_1
% 90.40/42.03 | (18) ! [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)))
% 90.40/42.03 | (19) ! [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)))
% 90.40/42.03 | (20) aNaturalNumber0(xn) = 0
% 90.40/42.03 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 90.40/42.03 | (22) sdtlseqdt0(all_0_3_3, all_0_1_1) = all_0_0_0
% 90.40/42.03 | (23) isPrime0(xr) = 0
% 90.40/42.03 | (24) sdtsldt0(all_0_6_6, xp) = xk
% 90.40/42.03 | (25) sdtlseqdt0(all_0_6_6, all_0_3_3) = all_0_2_2
% 90.40/42.03 | (26) sdtlseqdt0(xp, xk) = 0
% 90.40/42.04 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0))
% 90.40/42.04 | (28) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 90.40/42.04 | (29) aNaturalNumber0(sz00) = 0
% 90.40/42.04 | (30) ~ (isPrime0(sz10) = 0)
% 90.40/42.04 | (31) ~ (xk = sz00)
% 90.40/42.04 | (32) aNaturalNumber0(xm) = 0
% 90.40/42.04 | (33) ! [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)))))
% 90.40/42.04 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (doDivides0(v0, v2) = v3) | ~ (doDivides0(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (doDivides0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 90.40/42.04 | (35) ! [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)))))
% 90.40/42.04 | (36) ! [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)))))
% 90.40/42.04 | (37) ! [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))))
% 90.40/42.04 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0))
% 90.40/42.04 | (39) ! [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)))))
% 90.40/42.04 | (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)))
% 90.40/42.04 | (41) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 90.40/42.04 | (42) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ (isPrime0(v0) = 0) | ~ (doDivides0(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 90.40/42.04 | (43) ! [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)))
% 90.40/42.04 | (44) ~ (all_0_0_0 = 0) | ~ (all_0_2_2 = 0) | all_0_1_1 = all_0_3_3 | all_0_3_3 = all_0_6_6
% 90.40/42.04 | (45) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 90.40/42.04 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 90.40/42.04 | (47) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00))))
% 90.40/42.04 | (48) aNaturalNumber0(xp) = 0
% 90.40/42.04 | (49) ~ (all_0_5_5 = 0)
% 90.40/42.04 | (50) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0))
% 90.40/42.04 | (51) ! [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)))))
% 90.40/42.05 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0))
% 90.40/42.05 | (53) ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 90.40/42.05 | (54) ! [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)))))
% 90.40/42.05 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0))
% 90.40/42.05 | (56) ! [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_7_7) = 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)))
% 90.40/42.05 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 90.40/42.05 | (58) sdtlseqdt0(xp, xn) = all_0_5_5
% 90.40/42.05 | (59) ! [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)))
% 90.40/42.05 | (60) ! [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))))
% 90.40/42.05 | (61) isPrime0(xp) = 0
% 90.40/42.05 | (62) ~ (isPrime0(sz00) = 0)
% 90.40/42.05 | (63) ! [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))))
% 90.40/42.05 | (64) ~ (xp = xm)
% 90.40/42.05 | (65) doDivides0(xr, all_0_6_6) = 0
% 90.40/42.05 | (66) ~ (xp = xn)
% 90.40/42.05 | (67) sdtlseqdt0(xm, xp) = 0
% 90.40/42.05 | (68) sdtpldt0(xn, xm) = all_0_8_8
% 90.40/42.05 | (69) ! [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))))
% 90.40/42.05 | (70) ! [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))))
% 90.40/42.05 | (71) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 90.40/42.05 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0))
% 90.40/42.05 | (73) ~ (sz10 = sz00)
% 90.40/42.05 | (74) ~ (all_0_4_4 = 0)
% 90.40/42.05 | (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))))
% 90.40/42.05 | (76) sdtpldt0(all_0_8_8, xp) = all_0_7_7
% 90.40/42.05 | (77) aNaturalNumber0(xr) = 0
% 90.40/42.05 | (78) ~ (xk = sz10)
% 90.40/42.05 | (79) ! [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)))))
% 90.40/42.05 | (80) ! [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)))
% 90.40/42.06 | (81) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 90.40/42.06 | (82) ! [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)))))
% 90.40/42.06 | (83) ! [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)))))
% 90.40/42.06 | (84) ! [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))))
% 90.40/42.06 | (85) sdtasdt0(xn, xm) = all_0_6_6
% 90.40/42.06 | (86) ! [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)))
% 90.40/42.06 | (87) sdtlseqdt0(xp, xm) = all_0_4_4
% 90.40/42.06 | (88) ! [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))))
% 90.40/42.06 |
% 90.40/42.06 | Using (61) and (30) yields:
% 90.40/42.06 | (89) ~ (xp = sz10)
% 90.40/42.06 |
% 90.40/42.06 | Using (61) and (62) yields:
% 90.40/42.06 | (90) ~ (xp = sz00)
% 90.40/42.06 |
% 90.40/42.06 | Instantiating formula (18) with all_0_6_6, xr and discharging atoms doDivides0(xr, all_0_6_6) = 0, yields:
% 90.40/42.06 | (91) all_0_6_6 = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xr, all_0_6_6) = v2 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 90.40/42.06 |
% 90.40/42.06 | Instantiating formula (79) with all_0_6_6, xr and discharging atoms doDivides0(xr, all_0_6_6) = 0, yields:
% 90.40/42.06 | (92) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_6_6 & v1 = 0 & sdtasdt0(xr, v0) = all_0_6_6 & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 90.40/42.06 |
% 90.40/42.06 | Instantiating formula (79) with xk, xr and discharging atoms doDivides0(xr, xk) = 0, yields:
% 90.40/42.06 | (93) ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & v1 = 0 & sdtasdt0(xr, v0) = xk & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 90.40/42.06 |
% 90.40/42.06 | Instantiating formula (18) with all_0_6_6, xp and discharging atoms doDivides0(xp, all_0_6_6) = 0, yields:
% 90.40/42.06 | (94) all_0_6_6 = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, all_0_6_6) = v2 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 90.40/42.06 |
% 90.40/42.06 | Instantiating formula (79) with all_0_6_6, xp and discharging atoms doDivides0(xp, all_0_6_6) = 0, yields:
% 90.40/42.06 | (95) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_6_6 & v1 = 0 & sdtasdt0(xp, v0) = all_0_6_6 & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 90.40/42.06 |
% 90.40/42.06 | Instantiating formula (35) with xk, xp and discharging atoms sdtlseqdt0(xp, xk) = 0, yields:
% 90.40/42.06 | (96) ? [v0] : ? [v1] : ? [v2] : ((v2 = xk & v1 = 0 & sdtpldt0(xp, v0) = xk & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 90.40/42.06 |
% 90.40/42.06 | Instantiating formula (84) with all_0_4_4, xm, xk, xp and discharging atoms sdtlseqdt0(xp, xk) = 0, sdtlseqdt0(xp, xm) = all_0_4_4, yields:
% 90.40/42.06 | (97) all_0_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtlseqdt0(xk, xm) = v3 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 90.40/42.06 |
% 90.40/42.06 | Instantiating formula (84) with all_0_5_5, xn, xk, xp and discharging atoms sdtlseqdt0(xp, xk) = 0, sdtlseqdt0(xp, xn) = all_0_5_5, yields:
% 90.40/42.06 | (98) all_0_5_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtlseqdt0(xk, xn) = v3 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 90.40/42.06 |
% 90.40/42.06 | Instantiating formula (35) with xp, xm and discharging atoms sdtlseqdt0(xm, xp) = 0, yields:
% 90.40/42.06 | (99) ? [v0] : ? [v1] : ? [v2] : ((v2 = xp & v1 = 0 & sdtpldt0(xm, v0) = xp & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 90.40/42.07 |
% 90.40/42.07 | Instantiating formula (35) with xp, xn and discharging atoms sdtlseqdt0(xn, xp) = 0, yields:
% 90.40/42.07 | (100) ? [v0] : ? [v1] : ? [v2] : ((v2 = xp & v1 = 0 & sdtpldt0(xn, v0) = xp & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xp) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 90.40/42.07 |
% 90.40/42.07 | Instantiating formula (69) with all_0_4_4, xm, xp, xk and discharging atoms sdtlseqdt0(xp, xm) = all_0_4_4, yields:
% 90.40/42.07 | (101) all_0_4_4 = 0 | xk = sz00 | ~ (sdtasdt0(xp, xk) = xm) | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 90.40/42.07 |
% 90.40/42.07 | Instantiating formula (69) with all_0_5_5, xn, xp, xk and discharging atoms sdtlseqdt0(xp, xn) = all_0_5_5, yields:
% 90.40/42.07 | (102) all_0_5_5 = 0 | xk = sz00 | ~ (sdtasdt0(xp, xk) = xn) | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 90.40/42.07 |
% 90.40/42.07 | Instantiating formula (88) with all_0_1_1, xk, all_0_6_6, xp and discharging atoms sdtsldt0(all_0_6_6, xp) = xk, sdtasdt0(xp, xk) = all_0_1_1, yields:
% 90.40/42.07 | (103) all_0_1_1 = all_0_6_6 | xp = sz00 | ? [v0] : ? [v1] : ? [v2] : (doDivides0(xp, all_0_6_6) = v2 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 90.40/42.07 |
% 90.40/42.07 | Instantiating formula (10) with all_0_1_1, xk, all_0_6_6, xp and discharging atoms sdtsldt0(all_0_6_6, xp) = xk, sdtasdt0(xp, xk) = all_0_1_1, yields:
% 90.40/42.07 | (104) xp = sz00 | ? [v0] : ? [v1] : ? [v2] : ((v0 = 0 & aNaturalNumber0(xk) = 0) | (doDivides0(xp, all_0_6_6) = v2 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 90.40/42.07 |
% 90.40/42.07 | Instantiating formula (56) with all_0_6_6, xr, xk, xp and discharging atoms doDivides0(xr, all_0_6_6) = 0, yields:
% 90.40/42.07 | (105) ~ (sdtasdt0(xp, xk) = all_0_6_6) | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xr) = v3 & doDivides0(xr, xk) = v8 & doDivides0(xr, xp) = v7 & iLess0(v5, all_0_7_7) = v6 & sdtpldt0(v4, xr) = v5 & sdtpldt0(xp, xk) = v4 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 90.40/42.07 |
% 90.40/42.07 | Instantiating formula (56) with all_0_6_6, xp, xk, xp and discharging atoms doDivides0(xp, all_0_6_6) = 0, yields:
% 90.40/42.07 | (106) ~ (sdtasdt0(xp, xk) = all_0_6_6) | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, xk) = v8 & doDivides0(xp, xp) = v7 & iLess0(v5, all_0_7_7) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xp, xk) = v4 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 90.40/42.07 |
% 90.40/42.07 | Instantiating formula (45) with xk, xp yields:
% 90.40/42.07 | (107) xk = sz00 | xp = sz00 | ~ (sdtasdt0(xp, xk) = sz00) | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 90.40/42.07 |
% 90.40/42.07 | Instantiating formula (43) with all_0_1_1, xk, xp and discharging atoms sdtasdt0(xp, xk) = all_0_1_1, yields:
% 90.40/42.07 | (108) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xk, xp) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_1_1))
% 90.40/42.07 |
% 90.40/42.07 | Instantiating formula (86) with all_0_1_1, xk, xp and discharging atoms sdtasdt0(xp, xk) = all_0_1_1, yields:
% 90.40/42.07 | (109) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_1_1) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 90.40/42.07 |
% 90.40/42.07 | Instantiating formula (36) with all_0_0_0, all_0_1_1, all_0_3_3, xk, xm, xp and discharging atoms sdtlseqdt0(all_0_3_3, all_0_1_1) = all_0_0_0, sdtasdt0(xp, xk) = all_0_1_1, sdtasdt0(xp, xm) = all_0_3_3, yields:
% 90.40/42.07 | (110) xk = xm | xp = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v4, v5) = v6 & sdtlseqdt0(xm, xk) = v3 & sdtasdt0(xk, xp) = v5 & sdtasdt0(xm, xp) = v4 & aNaturalNumber0(xk) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v6 = 0 & all_0_0_0 = 0 & ~ (v5 = v4) & ~ (all_0_1_1 = all_0_3_3))))
% 90.40/42.07 |
% 90.40/42.07 | Instantiating formula (43) with all_0_3_3, xm, xp and discharging atoms sdtasdt0(xp, xm) = all_0_3_3, yields:
% 90.40/42.07 | (111) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xm, xp) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_3_3))
% 90.40/42.07 |
% 90.40/42.07 | Instantiating formula (86) with all_0_3_3, xm, xp and discharging atoms sdtasdt0(xp, xm) = all_0_3_3, yields:
% 90.40/42.07 | (112) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_3_3) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 90.40/42.07 |
% 90.40/42.07 | Instantiating formula (59) with all_0_6_6, xn, xm, xk, xp and discharging atoms sdtasdt0(xn, xm) = all_0_6_6, yields:
% 90.40/42.07 | (113) ~ (sdtasdt0(xp, xk) = xn) | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(xk, xm) = v3 & sdtasdt0(xp, v3) = v4 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_6_6))
% 90.40/42.07 |
% 90.40/42.07 | Instantiating formula (56) with all_0_6_6, xr, xm, xn and discharging atoms doDivides0(xr, all_0_6_6) = 0, sdtasdt0(xn, xm) = all_0_6_6, yields:
% 90.40/42.07 | (114) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xr) = v3 & doDivides0(xr, xm) = v8 & doDivides0(xr, xn) = v7 & iLess0(v5, all_0_7_7) = v6 & sdtpldt0(v4, xr) = v5 & sdtpldt0(xn, xm) = v4 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 90.40/42.08 |
% 90.40/42.08 | Instantiating formula (56) with all_0_6_6, xp, xm, xn and discharging atoms doDivides0(xp, all_0_6_6) = 0, sdtasdt0(xn, xm) = all_0_6_6, yields:
% 90.40/42.08 | (115) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, xm) = v8 & doDivides0(xp, xn) = v7 & iLess0(v5, all_0_7_7) = 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))
% 90.40/42.08 |
% 90.40/42.08 | Instantiating formula (45) with xm, xn yields:
% 90.40/42.08 | (116) xm = sz00 | xn = sz00 | ~ (sdtasdt0(xn, xm) = sz00) | ? [v0] : ? [v1] : (aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 90.40/42.08 |
% 90.40/42.08 | Instantiating formula (41) with all_0_6_6, xm yields:
% 90.40/42.08 | (117) ~ (sdtasdt0(sz10, xm) = all_0_6_6) | ? [v0] : ? [v1] : (sdtasdt0(xm, sz10) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v0 = 0) | (v1 = xm & all_0_6_6 = xm)))
% 90.40/42.08 |
% 90.40/42.08 | Instantiating formula (47) with all_0_6_6, xm yields:
% 90.40/42.08 | (118) ~ (sdtasdt0(sz00, xm) = all_0_6_6) | ? [v0] : ? [v1] : (sdtasdt0(xm, sz00) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v0 = 0) | (v1 = sz00 & all_0_6_6 = sz00)))
% 90.40/42.08 |
% 90.40/42.08 | Instantiating formula (43) with all_0_6_6, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_6_6, yields:
% 90.40/42.08 | (119) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_6_6))
% 90.40/42.08 |
% 90.40/42.08 | Instantiating formula (86) with all_0_6_6, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_6_6, yields:
% 90.40/42.08 | (120) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_6_6) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 90.40/42.08 |
% 90.40/42.08 | Instantiating formula (80) with all_0_7_7, xp, all_0_8_8 and discharging atoms sdtpldt0(all_0_8_8, xp) = all_0_7_7, yields:
% 90.40/42.08 | (121) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, all_0_8_8) = v2 & aNaturalNumber0(all_0_8_8) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_7_7))
% 90.40/42.08 |
% 90.40/42.08 | Instantiating formula (11) with all_0_7_7, xp, all_0_8_8 and discharging atoms sdtpldt0(all_0_8_8, xp) = all_0_7_7, yields:
% 90.40/42.08 | (122) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_7_7) = v2 & aNaturalNumber0(all_0_8_8) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 90.40/42.08 |
% 90.40/42.08 | Instantiating formula (19) with all_0_7_7, all_0_8_8, xp, xm, xn and discharging atoms sdtpldt0(all_0_8_8, xp) = all_0_7_7, sdtpldt0(xn, xm) = all_0_8_8, yields:
% 90.40/42.08 | (123) ? [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_7_7))
% 90.40/42.08 |
% 90.40/42.08 | Instantiating formula (80) with all_0_8_8, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_8_8, yields:
% 90.40/42.08 | (124) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_8_8))
% 90.40/42.08 |
% 90.40/42.08 | Instantiating formula (11) with all_0_8_8, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_8_8, yields:
% 90.40/42.08 | (125) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_8_8) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 90.40/42.08 |
% 90.40/42.08 | Instantiating formula (39) with all_0_1_1, all_0_3_3, xk, xm, xp and discharging atoms sdtasdt0(xp, xk) = all_0_1_1, sdtasdt0(xp, xm) = all_0_3_3, aNaturalNumber0(xp) = 0, yields:
% 90.40/42.08 | (126) xk = xm | xp = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(xk, xp) = v3 & sdtasdt0(xm, xp) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = v2) & ~ (all_0_1_1 = all_0_3_3))))
% 90.40/42.08 |
% 90.40/42.08 | Instantiating formula (50) with xp and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 90.40/42.08 | (127) xp = sz10 | xp = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 90.40/42.08 |
% 90.40/42.08 | Instantiating formula (50) with xm and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 90.40/42.08 | (128) xm = sz10 | xm = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xm) = 0 & aNaturalNumber0(v0) = 0)
% 90.40/42.08 |
% 90.40/42.08 | Instantiating formula (50) with xn and discharging atoms aNaturalNumber0(xn) = 0, yields:
% 90.40/42.08 | (129) xn = sz10 | xn = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xn) = 0 & aNaturalNumber0(v0) = 0)
% 90.40/42.08 |
% 90.40/42.08 | Instantiating (125) with all_12_0_9, all_12_1_10, all_12_2_11 yields:
% 90.40/42.08 | (130) aNaturalNumber0(all_0_8_8) = all_12_0_9 & aNaturalNumber0(xm) = all_12_1_10 & aNaturalNumber0(xn) = all_12_2_11 & ( ~ (all_12_1_10 = 0) | ~ (all_12_2_11 = 0) | all_12_0_9 = 0)
% 90.40/42.08 |
% 90.40/42.08 | Applying alpha-rule on (130) yields:
% 90.40/42.08 | (131) aNaturalNumber0(all_0_8_8) = all_12_0_9
% 90.40/42.08 | (132) aNaturalNumber0(xm) = all_12_1_10
% 90.40/42.08 | (133) aNaturalNumber0(xn) = all_12_2_11
% 90.40/42.08 | (134) ~ (all_12_1_10 = 0) | ~ (all_12_2_11 = 0) | all_12_0_9 = 0
% 90.40/42.08 |
% 90.40/42.08 | Instantiating (123) with all_14_0_12, all_14_1_13, all_14_2_14, all_14_3_15, all_14_4_16 yields:
% 90.40/42.08 | (135) sdtpldt0(xm, xp) = all_14_1_13 & sdtpldt0(xn, all_14_1_13) = all_14_0_12 & aNaturalNumber0(xp) = all_14_2_14 & aNaturalNumber0(xm) = all_14_3_15 & aNaturalNumber0(xn) = all_14_4_16 & ( ~ (all_14_2_14 = 0) | ~ (all_14_3_15 = 0) | ~ (all_14_4_16 = 0) | all_14_0_12 = all_0_7_7)
% 90.40/42.08 |
% 90.40/42.08 | Applying alpha-rule on (135) yields:
% 90.40/42.08 | (136) sdtpldt0(xm, xp) = all_14_1_13
% 90.40/42.08 | (137) aNaturalNumber0(xn) = all_14_4_16
% 90.40/42.08 | (138) aNaturalNumber0(xp) = all_14_2_14
% 90.40/42.08 | (139) ~ (all_14_2_14 = 0) | ~ (all_14_3_15 = 0) | ~ (all_14_4_16 = 0) | all_14_0_12 = all_0_7_7
% 90.40/42.08 | (140) sdtpldt0(xn, all_14_1_13) = all_14_0_12
% 90.40/42.08 | (141) aNaturalNumber0(xm) = all_14_3_15
% 90.40/42.08 |
% 90.40/42.08 | Instantiating (109) with all_16_0_17, all_16_1_18, all_16_2_19 yields:
% 90.40/42.08 | (142) aNaturalNumber0(all_0_1_1) = all_16_0_17 & aNaturalNumber0(xk) = all_16_1_18 & aNaturalNumber0(xp) = all_16_2_19 & ( ~ (all_16_1_18 = 0) | ~ (all_16_2_19 = 0) | all_16_0_17 = 0)
% 90.40/42.09 |
% 90.40/42.09 | Applying alpha-rule on (142) yields:
% 90.40/42.09 | (143) aNaturalNumber0(all_0_1_1) = all_16_0_17
% 90.40/42.09 | (144) aNaturalNumber0(xk) = all_16_1_18
% 90.40/42.09 | (145) aNaturalNumber0(xp) = all_16_2_19
% 90.40/42.09 | (146) ~ (all_16_1_18 = 0) | ~ (all_16_2_19 = 0) | all_16_0_17 = 0
% 90.40/42.09 |
% 90.40/42.09 | Instantiating (108) with all_19_0_23, all_19_1_24, all_19_2_25 yields:
% 90.40/42.09 | (147) sdtasdt0(xk, xp) = all_19_0_23 & aNaturalNumber0(xk) = all_19_1_24 & aNaturalNumber0(xp) = all_19_2_25 & ( ~ (all_19_1_24 = 0) | ~ (all_19_2_25 = 0) | all_19_0_23 = all_0_1_1)
% 90.40/42.09 |
% 90.40/42.09 | Applying alpha-rule on (147) yields:
% 90.40/42.09 | (148) sdtasdt0(xk, xp) = all_19_0_23
% 90.40/42.09 | (149) aNaturalNumber0(xk) = all_19_1_24
% 90.40/42.09 | (150) aNaturalNumber0(xp) = all_19_2_25
% 90.40/42.09 | (151) ~ (all_19_1_24 = 0) | ~ (all_19_2_25 = 0) | all_19_0_23 = all_0_1_1
% 90.40/42.09 |
% 90.40/42.09 | Instantiating (100) with all_21_0_26, all_21_1_27, all_21_2_28 yields:
% 90.40/42.09 | (152) (all_21_0_26 = xp & all_21_1_27 = 0 & sdtpldt0(xn, all_21_2_28) = xp & aNaturalNumber0(all_21_2_28) = 0) | (aNaturalNumber0(xp) = all_21_1_27 & aNaturalNumber0(xn) = all_21_2_28 & ( ~ (all_21_1_27 = 0) | ~ (all_21_2_28 = 0)))
% 90.40/42.09 |
% 90.40/42.09 | Instantiating (124) with all_22_0_29, all_22_1_30, all_22_2_31 yields:
% 90.40/42.09 | (153) sdtpldt0(xm, xn) = all_22_0_29 & aNaturalNumber0(xm) = all_22_1_30 & aNaturalNumber0(xn) = all_22_2_31 & ( ~ (all_22_1_30 = 0) | ~ (all_22_2_31 = 0) | all_22_0_29 = all_0_8_8)
% 90.40/42.09 |
% 90.40/42.09 | Applying alpha-rule on (153) yields:
% 90.40/42.09 | (154) sdtpldt0(xm, xn) = all_22_0_29
% 90.40/42.09 | (155) aNaturalNumber0(xm) = all_22_1_30
% 90.40/42.09 | (156) aNaturalNumber0(xn) = all_22_2_31
% 90.40/42.09 | (157) ~ (all_22_1_30 = 0) | ~ (all_22_2_31 = 0) | all_22_0_29 = all_0_8_8
% 90.40/42.09 |
% 90.40/42.09 | Instantiating (122) with all_24_0_32, all_24_1_33, all_24_2_34 yields:
% 90.40/42.09 | (158) aNaturalNumber0(all_0_7_7) = all_24_0_32 & aNaturalNumber0(all_0_8_8) = all_24_2_34 & aNaturalNumber0(xp) = all_24_1_33 & ( ~ (all_24_1_33 = 0) | ~ (all_24_2_34 = 0) | all_24_0_32 = 0)
% 90.40/42.09 |
% 90.40/42.09 | Applying alpha-rule on (158) yields:
% 90.40/42.09 | (159) aNaturalNumber0(all_0_7_7) = all_24_0_32
% 90.40/42.09 | (160) aNaturalNumber0(all_0_8_8) = all_24_2_34
% 90.40/42.09 | (161) aNaturalNumber0(xp) = all_24_1_33
% 90.40/42.09 | (162) ~ (all_24_1_33 = 0) | ~ (all_24_2_34 = 0) | all_24_0_32 = 0
% 90.40/42.09 |
% 90.40/42.09 | Instantiating (121) with all_26_0_35, all_26_1_36, all_26_2_37 yields:
% 90.40/42.09 | (163) sdtpldt0(xp, all_0_8_8) = all_26_0_35 & aNaturalNumber0(all_0_8_8) = all_26_2_37 & aNaturalNumber0(xp) = all_26_1_36 & ( ~ (all_26_1_36 = 0) | ~ (all_26_2_37 = 0) | all_26_0_35 = all_0_7_7)
% 90.40/42.09 |
% 90.40/42.09 | Applying alpha-rule on (163) yields:
% 90.40/42.09 | (164) sdtpldt0(xp, all_0_8_8) = all_26_0_35
% 90.40/42.09 | (165) aNaturalNumber0(all_0_8_8) = all_26_2_37
% 90.40/42.09 | (166) aNaturalNumber0(xp) = all_26_1_36
% 90.40/42.09 | (167) ~ (all_26_1_36 = 0) | ~ (all_26_2_37 = 0) | all_26_0_35 = all_0_7_7
% 90.40/42.09 |
% 90.40/42.09 | Instantiating (99) with all_28_0_38, all_28_1_39, all_28_2_40 yields:
% 90.40/42.09 | (168) (all_28_0_38 = xp & all_28_1_39 = 0 & sdtpldt0(xm, all_28_2_40) = xp & aNaturalNumber0(all_28_2_40) = 0) | (aNaturalNumber0(xp) = all_28_1_39 & aNaturalNumber0(xm) = all_28_2_40 & ( ~ (all_28_1_39 = 0) | ~ (all_28_2_40 = 0)))
% 90.40/42.09 |
% 90.40/42.09 | Instantiating (120) with all_29_0_41, all_29_1_42, all_29_2_43 yields:
% 90.40/42.09 | (169) aNaturalNumber0(all_0_6_6) = all_29_0_41 & aNaturalNumber0(xm) = all_29_1_42 & aNaturalNumber0(xn) = all_29_2_43 & ( ~ (all_29_1_42 = 0) | ~ (all_29_2_43 = 0) | all_29_0_41 = 0)
% 90.40/42.09 |
% 90.40/42.09 | Applying alpha-rule on (169) yields:
% 90.40/42.09 | (170) aNaturalNumber0(all_0_6_6) = all_29_0_41
% 90.40/42.09 | (171) aNaturalNumber0(xm) = all_29_1_42
% 90.40/42.09 | (172) aNaturalNumber0(xn) = all_29_2_43
% 90.40/42.09 | (173) ~ (all_29_1_42 = 0) | ~ (all_29_2_43 = 0) | all_29_0_41 = 0
% 90.40/42.09 |
% 90.40/42.09 | Instantiating (119) with all_31_0_44, all_31_1_45, all_31_2_46 yields:
% 90.40/42.09 | (174) sdtasdt0(xm, xn) = all_31_0_44 & aNaturalNumber0(xm) = all_31_1_45 & aNaturalNumber0(xn) = all_31_2_46 & ( ~ (all_31_1_45 = 0) | ~ (all_31_2_46 = 0) | all_31_0_44 = all_0_6_6)
% 90.40/42.09 |
% 90.40/42.09 | Applying alpha-rule on (174) yields:
% 90.40/42.09 | (175) sdtasdt0(xm, xn) = all_31_0_44
% 90.40/42.09 | (176) aNaturalNumber0(xm) = all_31_1_45
% 90.40/42.09 | (177) aNaturalNumber0(xn) = all_31_2_46
% 90.40/42.09 | (178) ~ (all_31_1_45 = 0) | ~ (all_31_2_46 = 0) | all_31_0_44 = all_0_6_6
% 90.40/42.09 |
% 90.40/42.09 | Instantiating (96) with all_33_0_47, all_33_1_48, all_33_2_49 yields:
% 90.40/42.09 | (179) (all_33_0_47 = xk & all_33_1_48 = 0 & sdtpldt0(xp, all_33_2_49) = xk & aNaturalNumber0(all_33_2_49) = 0) | (aNaturalNumber0(xk) = all_33_1_48 & aNaturalNumber0(xp) = all_33_2_49 & ( ~ (all_33_1_48 = 0) | ~ (all_33_2_49 = 0)))
% 90.40/42.09 |
% 90.40/42.09 | Instantiating (115) with all_34_0_50, all_34_1_51, all_34_2_52, all_34_3_53, all_34_4_54, all_34_5_55, all_34_6_56, all_34_7_57, all_34_8_58 yields:
% 90.40/42.09 | (180) isPrime0(xp) = all_34_5_55 & doDivides0(xp, xm) = all_34_0_50 & doDivides0(xp, xn) = all_34_1_51 & iLess0(all_34_3_53, all_0_7_7) = all_34_2_52 & sdtpldt0(all_34_4_54, xp) = all_34_3_53 & sdtpldt0(xn, xm) = all_34_4_54 & aNaturalNumber0(xp) = all_34_6_56 & aNaturalNumber0(xm) = all_34_7_57 & aNaturalNumber0(xn) = all_34_8_58 & ( ~ (all_34_2_52 = 0) | ~ (all_34_5_55 = 0) | ~ (all_34_6_56 = 0) | ~ (all_34_7_57 = 0) | ~ (all_34_8_58 = 0) | all_34_0_50 = 0 | all_34_1_51 = 0)
% 90.40/42.10 |
% 90.40/42.10 | Applying alpha-rule on (180) yields:
% 90.40/42.10 | (181) aNaturalNumber0(xp) = all_34_6_56
% 90.40/42.10 | (182) doDivides0(xp, xm) = all_34_0_50
% 90.40/42.10 | (183) sdtpldt0(all_34_4_54, xp) = all_34_3_53
% 90.40/42.10 | (184) ~ (all_34_2_52 = 0) | ~ (all_34_5_55 = 0) | ~ (all_34_6_56 = 0) | ~ (all_34_7_57 = 0) | ~ (all_34_8_58 = 0) | all_34_0_50 = 0 | all_34_1_51 = 0
% 90.40/42.10 | (185) iLess0(all_34_3_53, all_0_7_7) = all_34_2_52
% 90.40/42.10 | (186) aNaturalNumber0(xm) = all_34_7_57
% 90.40/42.10 | (187) sdtpldt0(xn, xm) = all_34_4_54
% 90.40/42.10 | (188) doDivides0(xp, xn) = all_34_1_51
% 90.40/42.10 | (189) aNaturalNumber0(xn) = all_34_8_58
% 90.40/42.10 | (190) isPrime0(xp) = all_34_5_55
% 90.40/42.10 |
% 90.40/42.10 | Instantiating (114) with all_36_0_59, all_36_1_60, all_36_2_61, all_36_3_62, all_36_4_63, all_36_5_64, all_36_6_65, all_36_7_66, all_36_8_67 yields:
% 90.40/42.10 | (191) isPrime0(xr) = all_36_5_64 & doDivides0(xr, xm) = all_36_0_59 & doDivides0(xr, xn) = all_36_1_60 & iLess0(all_36_3_62, all_0_7_7) = all_36_2_61 & sdtpldt0(all_36_4_63, xr) = all_36_3_62 & sdtpldt0(xn, xm) = all_36_4_63 & aNaturalNumber0(xr) = all_36_6_65 & aNaturalNumber0(xm) = all_36_7_66 & aNaturalNumber0(xn) = all_36_8_67 & ( ~ (all_36_2_61 = 0) | ~ (all_36_5_64 = 0) | ~ (all_36_6_65 = 0) | ~ (all_36_7_66 = 0) | ~ (all_36_8_67 = 0) | all_36_0_59 = 0 | all_36_1_60 = 0)
% 90.40/42.10 |
% 90.40/42.10 | Applying alpha-rule on (191) yields:
% 90.40/42.10 | (192) iLess0(all_36_3_62, all_0_7_7) = all_36_2_61
% 90.40/42.10 | (193) aNaturalNumber0(xn) = all_36_8_67
% 90.40/42.10 | (194) aNaturalNumber0(xr) = all_36_6_65
% 90.40/42.10 | (195) doDivides0(xr, xn) = all_36_1_60
% 90.40/42.10 | (196) doDivides0(xr, xm) = all_36_0_59
% 90.40/42.10 | (197) sdtpldt0(all_36_4_63, xr) = all_36_3_62
% 90.40/42.10 | (198) isPrime0(xr) = all_36_5_64
% 90.40/42.10 | (199) ~ (all_36_2_61 = 0) | ~ (all_36_5_64 = 0) | ~ (all_36_6_65 = 0) | ~ (all_36_7_66 = 0) | ~ (all_36_8_67 = 0) | all_36_0_59 = 0 | all_36_1_60 = 0
% 90.40/42.10 | (200) sdtpldt0(xn, xm) = all_36_4_63
% 90.40/42.10 | (201) aNaturalNumber0(xm) = all_36_7_66
% 90.40/42.10 |
% 90.40/42.10 | Instantiating (112) with all_38_0_68, all_38_1_69, all_38_2_70 yields:
% 90.40/42.10 | (202) aNaturalNumber0(all_0_3_3) = all_38_0_68 & aNaturalNumber0(xp) = all_38_2_70 & aNaturalNumber0(xm) = all_38_1_69 & ( ~ (all_38_1_69 = 0) | ~ (all_38_2_70 = 0) | all_38_0_68 = 0)
% 90.40/42.10 |
% 90.40/42.10 | Applying alpha-rule on (202) yields:
% 90.40/42.10 | (203) aNaturalNumber0(all_0_3_3) = all_38_0_68
% 90.40/42.10 | (204) aNaturalNumber0(xp) = all_38_2_70
% 90.40/42.10 | (205) aNaturalNumber0(xm) = all_38_1_69
% 90.40/42.10 | (206) ~ (all_38_1_69 = 0) | ~ (all_38_2_70 = 0) | all_38_0_68 = 0
% 90.40/42.10 |
% 90.40/42.10 | Instantiating (95) with all_40_0_71, all_40_1_72, all_40_2_73 yields:
% 90.40/42.10 | (207) (all_40_0_71 = all_0_6_6 & all_40_1_72 = 0 & sdtasdt0(xp, all_40_2_73) = all_0_6_6 & aNaturalNumber0(all_40_2_73) = 0) | (aNaturalNumber0(all_0_6_6) = all_40_1_72 & aNaturalNumber0(xp) = all_40_2_73 & ( ~ (all_40_1_72 = 0) | ~ (all_40_2_73 = 0)))
% 90.40/42.10 |
% 90.40/42.10 | Instantiating (93) with all_41_0_74, all_41_1_75, all_41_2_76 yields:
% 90.40/42.10 | (208) (all_41_0_74 = xk & all_41_1_75 = 0 & sdtasdt0(xr, all_41_2_76) = xk & aNaturalNumber0(all_41_2_76) = 0) | (aNaturalNumber0(xr) = all_41_2_76 & aNaturalNumber0(xk) = all_41_1_75 & ( ~ (all_41_1_75 = 0) | ~ (all_41_2_76 = 0)))
% 90.40/42.10 |
% 90.40/42.10 | Instantiating (92) with all_42_0_77, all_42_1_78, all_42_2_79 yields:
% 90.40/42.10 | (209) (all_42_0_77 = all_0_6_6 & all_42_1_78 = 0 & sdtasdt0(xr, all_42_2_79) = all_0_6_6 & aNaturalNumber0(all_42_2_79) = 0) | (aNaturalNumber0(all_0_6_6) = all_42_1_78 & aNaturalNumber0(xr) = all_42_2_79 & ( ~ (all_42_1_78 = 0) | ~ (all_42_2_79 = 0)))
% 90.40/42.10 |
% 90.40/42.10 | Instantiating (111) with all_43_0_80, all_43_1_81, all_43_2_82 yields:
% 90.40/42.10 | (210) sdtasdt0(xm, xp) = all_43_0_80 & aNaturalNumber0(xp) = all_43_2_82 & aNaturalNumber0(xm) = all_43_1_81 & ( ~ (all_43_1_81 = 0) | ~ (all_43_2_82 = 0) | all_43_0_80 = all_0_3_3)
% 90.40/42.10 |
% 90.40/42.10 | Applying alpha-rule on (210) yields:
% 90.40/42.10 | (211) sdtasdt0(xm, xp) = all_43_0_80
% 90.40/42.10 | (212) aNaturalNumber0(xp) = all_43_2_82
% 90.40/42.10 | (213) aNaturalNumber0(xm) = all_43_1_81
% 90.40/42.10 | (214) ~ (all_43_1_81 = 0) | ~ (all_43_2_82 = 0) | all_43_0_80 = all_0_3_3
% 90.40/42.10 |
% 90.82/42.10 +-Applying beta-rule and splitting (104), into two cases.
% 90.82/42.10 |-Branch one:
% 90.82/42.10 | (215) xp = sz00
% 90.82/42.10 |
% 90.82/42.10 | Equations (215) can reduce 90 to:
% 90.82/42.10 | (216) $false
% 90.82/42.10 |
% 90.82/42.10 |-The branch is then unsatisfiable
% 90.82/42.10 |-Branch two:
% 90.82/42.10 | (90) ~ (xp = sz00)
% 90.82/42.10 | (218) ? [v0] : ? [v1] : ? [v2] : ((v0 = 0 & aNaturalNumber0(xk) = 0) | (doDivides0(xp, all_0_6_6) = v2 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 90.82/42.10 |
% 90.82/42.10 | Instantiating (218) with all_49_0_83, all_49_1_84, all_49_2_85 yields:
% 90.82/42.10 | (219) (all_49_2_85 = 0 & aNaturalNumber0(xk) = 0) | (doDivides0(xp, all_0_6_6) = all_49_0_83 & aNaturalNumber0(all_0_6_6) = all_49_1_84 & aNaturalNumber0(xp) = all_49_2_85 & ( ~ (all_49_0_83 = 0) | ~ (all_49_1_84 = 0) | ~ (all_49_2_85 = 0)))
% 90.82/42.10 |
% 90.82/42.10 +-Applying beta-rule and splitting (97), into two cases.
% 90.82/42.10 |-Branch one:
% 90.82/42.10 | (220) all_0_4_4 = 0
% 90.82/42.10 |
% 90.82/42.10 | Equations (220) can reduce 74 to:
% 90.82/42.10 | (216) $false
% 90.82/42.10 |
% 90.82/42.10 |-The branch is then unsatisfiable
% 90.82/42.10 |-Branch two:
% 90.82/42.10 | (74) ~ (all_0_4_4 = 0)
% 90.82/42.10 | (223) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtlseqdt0(xk, xm) = v3 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 90.82/42.10 |
% 90.82/42.10 | Instantiating (223) with all_53_0_86, all_53_1_87, all_53_2_88, all_53_3_89 yields:
% 90.82/42.10 | (224) sdtlseqdt0(xk, xm) = all_53_0_86 & aNaturalNumber0(xk) = all_53_2_88 & aNaturalNumber0(xp) = all_53_3_89 & aNaturalNumber0(xm) = all_53_1_87 & ( ~ (all_53_0_86 = 0) | ~ (all_53_1_87 = 0) | ~ (all_53_2_88 = 0) | ~ (all_53_3_89 = 0))
% 90.82/42.10 |
% 90.82/42.10 | Applying alpha-rule on (224) yields:
% 90.82/42.10 | (225) ~ (all_53_0_86 = 0) | ~ (all_53_1_87 = 0) | ~ (all_53_2_88 = 0) | ~ (all_53_3_89 = 0)
% 90.82/42.11 | (226) aNaturalNumber0(xk) = all_53_2_88
% 90.82/42.11 | (227) aNaturalNumber0(xp) = all_53_3_89
% 90.82/42.11 | (228) sdtlseqdt0(xk, xm) = all_53_0_86
% 90.82/42.11 | (229) aNaturalNumber0(xm) = all_53_1_87
% 90.82/42.11 |
% 90.82/42.11 +-Applying beta-rule and splitting (98), into two cases.
% 90.82/42.11 |-Branch one:
% 90.82/42.11 | (230) all_0_5_5 = 0
% 90.82/42.11 |
% 90.82/42.11 | Equations (230) can reduce 49 to:
% 90.82/42.11 | (216) $false
% 90.82/42.11 |
% 90.82/42.11 |-The branch is then unsatisfiable
% 90.82/42.11 |-Branch two:
% 90.82/42.11 | (49) ~ (all_0_5_5 = 0)
% 90.82/42.11 | (233) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtlseqdt0(xk, xn) = v3 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 90.82/42.11 |
% 90.82/42.11 | Instantiating (233) with all_58_0_90, all_58_1_91, all_58_2_92, all_58_3_93 yields:
% 90.82/42.11 | (234) sdtlseqdt0(xk, xn) = all_58_0_90 & aNaturalNumber0(xk) = all_58_2_92 & aNaturalNumber0(xp) = all_58_3_93 & aNaturalNumber0(xn) = all_58_1_91 & ( ~ (all_58_0_90 = 0) | ~ (all_58_1_91 = 0) | ~ (all_58_2_92 = 0) | ~ (all_58_3_93 = 0))
% 90.82/42.11 |
% 90.82/42.11 | Applying alpha-rule on (234) yields:
% 90.82/42.11 | (235) ~ (all_58_0_90 = 0) | ~ (all_58_1_91 = 0) | ~ (all_58_2_92 = 0) | ~ (all_58_3_93 = 0)
% 90.82/42.11 | (236) aNaturalNumber0(xk) = all_58_2_92
% 90.82/42.11 | (237) aNaturalNumber0(xp) = all_58_3_93
% 90.82/42.11 | (238) sdtlseqdt0(xk, xn) = all_58_0_90
% 90.82/42.11 | (239) aNaturalNumber0(xn) = all_58_1_91
% 90.82/42.11 |
% 90.82/42.11 +-Applying beta-rule and splitting (127), into two cases.
% 90.82/42.11 |-Branch one:
% 90.82/42.11 | (215) xp = sz00
% 90.82/42.11 |
% 90.82/42.11 | Equations (215) can reduce 90 to:
% 90.82/42.11 | (216) $false
% 90.82/42.11 |
% 90.82/42.11 |-The branch is then unsatisfiable
% 90.82/42.11 |-Branch two:
% 90.82/42.11 | (90) ~ (xp = sz00)
% 90.82/42.11 | (243) xp = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 90.82/42.11 |
% 90.82/42.11 +-Applying beta-rule and splitting (243), into two cases.
% 90.82/42.11 |-Branch one:
% 90.82/42.11 | (244) xp = sz10
% 90.82/42.11 |
% 90.82/42.11 | Equations (244) can reduce 89 to:
% 90.82/42.11 | (216) $false
% 90.82/42.11 |
% 90.82/42.11 |-The branch is then unsatisfiable
% 90.82/42.11 |-Branch two:
% 90.82/42.11 | (89) ~ (xp = sz10)
% 90.82/42.11 | (247) ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 90.82/42.11 |
% 90.82/42.11 | Instantiating (247) with all_70_0_94 yields:
% 90.82/42.11 | (248) isPrime0(all_70_0_94) = 0 & doDivides0(all_70_0_94, xp) = 0 & aNaturalNumber0(all_70_0_94) = 0
% 90.82/42.11 |
% 90.82/42.11 | Applying alpha-rule on (248) yields:
% 90.82/42.11 | (249) isPrime0(all_70_0_94) = 0
% 90.82/42.11 | (250) doDivides0(all_70_0_94, xp) = 0
% 90.82/42.11 | (251) aNaturalNumber0(all_70_0_94) = 0
% 90.82/42.11 |
% 90.82/42.11 | Using (249) and (30) yields:
% 90.82/42.11 | (252) ~ (all_70_0_94 = sz10)
% 90.82/42.11 |
% 90.82/42.11 | Using (249) and (62) yields:
% 90.82/42.11 | (253) ~ (all_70_0_94 = sz00)
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (27) with xp, all_34_5_55, 0 and discharging atoms isPrime0(xp) = all_34_5_55, isPrime0(xp) = 0, yields:
% 90.82/42.11 | (254) all_34_5_55 = 0
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (57) with all_0_8_8, xp, all_34_3_53, all_0_7_7 and discharging atoms sdtpldt0(all_0_8_8, xp) = all_0_7_7, yields:
% 90.82/42.11 | (255) all_34_3_53 = all_0_7_7 | ~ (sdtpldt0(all_0_8_8, xp) = all_34_3_53)
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (57) with xn, xm, all_36_4_63, all_0_8_8 and discharging atoms sdtpldt0(xn, xm) = all_36_4_63, sdtpldt0(xn, xm) = all_0_8_8, yields:
% 90.82/42.11 | (256) all_36_4_63 = all_0_8_8
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (57) with xn, xm, all_34_4_54, all_36_4_63 and discharging atoms sdtpldt0(xn, xm) = all_36_4_63, sdtpldt0(xn, xm) = all_34_4_54, yields:
% 90.82/42.11 | (257) all_36_4_63 = all_34_4_54
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (55) with all_0_8_8, all_24_2_34, all_26_2_37 and discharging atoms aNaturalNumber0(all_0_8_8) = all_26_2_37, aNaturalNumber0(all_0_8_8) = all_24_2_34, yields:
% 90.82/42.11 | (258) all_26_2_37 = all_24_2_34
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (55) with all_0_8_8, all_12_0_9, all_26_2_37 and discharging atoms aNaturalNumber0(all_0_8_8) = all_26_2_37, aNaturalNumber0(all_0_8_8) = all_12_0_9, yields:
% 90.82/42.11 | (259) all_26_2_37 = all_12_0_9
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (55) with xr, all_36_6_65, 0 and discharging atoms aNaturalNumber0(xr) = all_36_6_65, aNaturalNumber0(xr) = 0, yields:
% 90.82/42.11 | (260) all_36_6_65 = 0
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (55) with xk, all_58_2_92, 0 and discharging atoms aNaturalNumber0(xk) = all_58_2_92, yields:
% 90.82/42.11 | (261) all_58_2_92 = 0 | ~ (aNaturalNumber0(xk) = 0)
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (55) with xk, all_53_2_88, all_58_2_92 and discharging atoms aNaturalNumber0(xk) = all_58_2_92, aNaturalNumber0(xk) = all_53_2_88, yields:
% 90.82/42.11 | (262) all_58_2_92 = all_53_2_88
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (55) with xk, all_19_1_24, all_58_2_92 and discharging atoms aNaturalNumber0(xk) = all_58_2_92, aNaturalNumber0(xk) = all_19_1_24, yields:
% 90.82/42.11 | (263) all_58_2_92 = all_19_1_24
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (55) with xk, all_16_1_18, all_58_2_92 and discharging atoms aNaturalNumber0(xk) = all_58_2_92, aNaturalNumber0(xk) = all_16_1_18, yields:
% 90.82/42.11 | (264) all_58_2_92 = all_16_1_18
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (55) with xp, all_58_3_93, 0 and discharging atoms aNaturalNumber0(xp) = all_58_3_93, aNaturalNumber0(xp) = 0, yields:
% 90.82/42.11 | (265) all_58_3_93 = 0
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (55) with xp, all_43_2_82, all_53_3_89 and discharging atoms aNaturalNumber0(xp) = all_53_3_89, aNaturalNumber0(xp) = all_43_2_82, yields:
% 90.82/42.11 | (266) all_53_3_89 = all_43_2_82
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (55) with xp, all_38_2_70, all_53_3_89 and discharging atoms aNaturalNumber0(xp) = all_53_3_89, aNaturalNumber0(xp) = all_38_2_70, yields:
% 90.82/42.11 | (267) all_53_3_89 = all_38_2_70
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (55) with xp, all_34_6_56, all_58_3_93 and discharging atoms aNaturalNumber0(xp) = all_58_3_93, aNaturalNumber0(xp) = all_34_6_56, yields:
% 90.82/42.11 | (268) all_58_3_93 = all_34_6_56
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (55) with xp, all_34_6_56, all_43_2_82 and discharging atoms aNaturalNumber0(xp) = all_43_2_82, aNaturalNumber0(xp) = all_34_6_56, yields:
% 90.82/42.11 | (269) all_43_2_82 = all_34_6_56
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (55) with xp, all_26_1_36, all_43_2_82 and discharging atoms aNaturalNumber0(xp) = all_43_2_82, aNaturalNumber0(xp) = all_26_1_36, yields:
% 90.82/42.11 | (270) all_43_2_82 = all_26_1_36
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (55) with xp, all_24_1_33, all_43_2_82 and discharging atoms aNaturalNumber0(xp) = all_43_2_82, aNaturalNumber0(xp) = all_24_1_33, yields:
% 90.82/42.11 | (271) all_43_2_82 = all_24_1_33
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (55) with xp, all_19_2_25, all_24_1_33 and discharging atoms aNaturalNumber0(xp) = all_24_1_33, aNaturalNumber0(xp) = all_19_2_25, yields:
% 90.82/42.11 | (272) all_24_1_33 = all_19_2_25
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (55) with xp, all_16_2_19, all_19_2_25 and discharging atoms aNaturalNumber0(xp) = all_19_2_25, aNaturalNumber0(xp) = all_16_2_19, yields:
% 90.82/42.11 | (273) all_19_2_25 = all_16_2_19
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (55) with xp, all_14_2_14, all_16_2_19 and discharging atoms aNaturalNumber0(xp) = all_16_2_19, aNaturalNumber0(xp) = all_14_2_14, yields:
% 90.82/42.11 | (274) all_16_2_19 = all_14_2_14
% 90.82/42.11 |
% 90.82/42.11 | Instantiating formula (55) with xm, all_43_1_81, all_53_1_87 and discharging atoms aNaturalNumber0(xm) = all_53_1_87, aNaturalNumber0(xm) = all_43_1_81, yields:
% 90.82/42.12 | (275) all_53_1_87 = all_43_1_81
% 90.82/42.12 |
% 90.82/42.12 | Instantiating formula (55) with xm, all_38_1_69, all_43_1_81 and discharging atoms aNaturalNumber0(xm) = all_43_1_81, aNaturalNumber0(xm) = all_38_1_69, yields:
% 90.82/42.12 | (276) all_43_1_81 = all_38_1_69
% 90.82/42.12 |
% 90.82/42.12 | Instantiating formula (55) with xm, all_36_7_66, all_38_1_69 and discharging atoms aNaturalNumber0(xm) = all_38_1_69, aNaturalNumber0(xm) = all_36_7_66, yields:
% 90.82/42.12 | (277) all_38_1_69 = all_36_7_66
% 90.82/42.12 |
% 90.82/42.12 | Instantiating formula (55) with xm, all_34_7_57, all_36_7_66 and discharging atoms aNaturalNumber0(xm) = all_36_7_66, aNaturalNumber0(xm) = all_34_7_57, yields:
% 90.82/42.12 | (278) all_36_7_66 = all_34_7_57
% 90.82/42.12 |
% 90.82/42.12 | Instantiating formula (55) with xm, all_31_1_45, all_34_7_57 and discharging atoms aNaturalNumber0(xm) = all_34_7_57, aNaturalNumber0(xm) = all_31_1_45, yields:
% 90.82/42.12 | (279) all_34_7_57 = all_31_1_45
% 90.82/42.12 |
% 90.82/42.12 | Instantiating formula (55) with xm, all_29_1_42, all_31_1_45 and discharging atoms aNaturalNumber0(xm) = all_31_1_45, aNaturalNumber0(xm) = all_29_1_42, yields:
% 90.82/42.12 | (280) all_31_1_45 = all_29_1_42
% 90.82/42.12 |
% 90.82/42.12 | Instantiating formula (55) with xm, all_22_1_30, all_29_1_42 and discharging atoms aNaturalNumber0(xm) = all_29_1_42, aNaturalNumber0(xm) = all_22_1_30, yields:
% 90.82/42.12 | (281) all_29_1_42 = all_22_1_30
% 90.82/42.12 |
% 90.82/42.12 | Instantiating formula (55) with xm, all_14_3_15, 0 and discharging atoms aNaturalNumber0(xm) = all_14_3_15, aNaturalNumber0(xm) = 0, yields:
% 90.82/42.12 | (282) all_14_3_15 = 0
% 90.82/42.12 |
% 90.82/42.12 | Instantiating formula (55) with xm, all_14_3_15, all_22_1_30 and discharging atoms aNaturalNumber0(xm) = all_22_1_30, aNaturalNumber0(xm) = all_14_3_15, yields:
% 90.82/42.12 | (283) all_22_1_30 = all_14_3_15
% 90.82/42.12 |
% 90.82/42.12 | Instantiating formula (55) with xm, all_12_1_10, all_53_1_87 and discharging atoms aNaturalNumber0(xm) = all_53_1_87, aNaturalNumber0(xm) = all_12_1_10, yields:
% 90.82/42.12 | (284) all_53_1_87 = all_12_1_10
% 90.82/42.12 |
% 90.82/42.12 | Instantiating formula (55) with xn, all_34_8_58, 0 and discharging atoms aNaturalNumber0(xn) = all_34_8_58, aNaturalNumber0(xn) = 0, yields:
% 90.82/42.12 | (285) all_34_8_58 = 0
% 90.82/42.12 |
% 90.82/42.12 | Instantiating formula (55) with xn, all_34_8_58, all_36_8_67 and discharging atoms aNaturalNumber0(xn) = all_36_8_67, aNaturalNumber0(xn) = all_34_8_58, yields:
% 90.82/42.12 | (286) all_36_8_67 = all_34_8_58
% 90.82/42.12 |
% 90.82/42.12 | Instantiating formula (55) with xn, all_31_2_46, all_36_8_67 and discharging atoms aNaturalNumber0(xn) = all_36_8_67, aNaturalNumber0(xn) = all_31_2_46, yields:
% 90.82/42.12 | (287) all_36_8_67 = all_31_2_46
% 90.82/42.12 |
% 90.82/42.12 | Instantiating formula (55) with xn, all_29_2_43, all_58_1_91 and discharging atoms aNaturalNumber0(xn) = all_58_1_91, aNaturalNumber0(xn) = all_29_2_43, yields:
% 90.82/42.12 | (288) all_58_1_91 = all_29_2_43
% 90.82/42.12 |
% 90.82/42.12 | Instantiating formula (55) with xn, all_29_2_43, all_34_8_58 and discharging atoms aNaturalNumber0(xn) = all_34_8_58, aNaturalNumber0(xn) = all_29_2_43, yields:
% 90.82/42.12 | (289) all_34_8_58 = all_29_2_43
% 90.82/42.12 |
% 90.82/42.12 | Instantiating formula (55) with xn, all_22_2_31, all_34_8_58 and discharging atoms aNaturalNumber0(xn) = all_34_8_58, aNaturalNumber0(xn) = all_22_2_31, yields:
% 90.82/42.12 | (290) all_34_8_58 = all_22_2_31
% 90.82/42.12 |
% 90.82/42.12 | Instantiating formula (55) with xn, all_14_4_16, all_58_1_91 and discharging atoms aNaturalNumber0(xn) = all_58_1_91, aNaturalNumber0(xn) = all_14_4_16, yields:
% 90.82/42.12 | (291) all_58_1_91 = all_14_4_16
% 90.82/42.12 |
% 90.82/42.12 | Instantiating formula (55) with xn, all_12_2_11, all_34_8_58 and discharging atoms aNaturalNumber0(xn) = all_34_8_58, aNaturalNumber0(xn) = all_12_2_11, yields:
% 90.82/42.12 | (292) all_34_8_58 = all_12_2_11
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (288,291) yields a new equation:
% 90.82/42.12 | (293) all_29_2_43 = all_14_4_16
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 293 yields:
% 90.82/42.12 | (294) all_29_2_43 = all_14_4_16
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (264,262) yields a new equation:
% 90.82/42.12 | (295) all_53_2_88 = all_16_1_18
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (263,262) yields a new equation:
% 90.82/42.12 | (296) all_53_2_88 = all_19_1_24
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (268,265) yields a new equation:
% 90.82/42.12 | (297) all_34_6_56 = 0
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 297 yields:
% 90.82/42.12 | (298) all_34_6_56 = 0
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (275,284) yields a new equation:
% 90.82/42.12 | (299) all_43_1_81 = all_12_1_10
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 299 yields:
% 90.82/42.12 | (300) all_43_1_81 = all_12_1_10
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (295,296) yields a new equation:
% 90.82/42.12 | (301) all_19_1_24 = all_16_1_18
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (266,267) yields a new equation:
% 90.82/42.12 | (302) all_43_2_82 = all_38_2_70
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 302 yields:
% 90.82/42.12 | (303) all_43_2_82 = all_38_2_70
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (276,300) yields a new equation:
% 90.82/42.12 | (304) all_38_1_69 = all_12_1_10
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 304 yields:
% 90.82/42.12 | (305) all_38_1_69 = all_12_1_10
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (271,303) yields a new equation:
% 90.82/42.12 | (306) all_38_2_70 = all_24_1_33
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (270,303) yields a new equation:
% 90.82/42.12 | (307) all_38_2_70 = all_26_1_36
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (269,303) yields a new equation:
% 90.82/42.12 | (308) all_38_2_70 = all_34_6_56
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (277,305) yields a new equation:
% 90.82/42.12 | (309) all_36_7_66 = all_12_1_10
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 309 yields:
% 90.82/42.12 | (310) all_36_7_66 = all_12_1_10
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (306,307) yields a new equation:
% 90.82/42.12 | (311) all_26_1_36 = all_24_1_33
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (308,307) yields a new equation:
% 90.82/42.12 | (312) all_34_6_56 = all_26_1_36
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 312 yields:
% 90.82/42.12 | (313) all_34_6_56 = all_26_1_36
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (256,257) yields a new equation:
% 90.82/42.12 | (314) all_34_4_54 = all_0_8_8
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (278,310) yields a new equation:
% 90.82/42.12 | (315) all_34_7_57 = all_12_1_10
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 315 yields:
% 90.82/42.12 | (316) all_34_7_57 = all_12_1_10
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (286,287) yields a new equation:
% 90.82/42.12 | (317) all_34_8_58 = all_31_2_46
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 317 yields:
% 90.82/42.12 | (318) all_34_8_58 = all_31_2_46
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (313,298) yields a new equation:
% 90.82/42.12 | (319) all_26_1_36 = 0
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 319 yields:
% 90.82/42.12 | (320) all_26_1_36 = 0
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (279,316) yields a new equation:
% 90.82/42.12 | (321) all_31_1_45 = all_12_1_10
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 321 yields:
% 90.82/42.12 | (322) all_31_1_45 = all_12_1_10
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (292,318) yields a new equation:
% 90.82/42.12 | (323) all_31_2_46 = all_12_2_11
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (290,318) yields a new equation:
% 90.82/42.12 | (324) all_31_2_46 = all_22_2_31
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (285,318) yields a new equation:
% 90.82/42.12 | (325) all_31_2_46 = 0
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (289,318) yields a new equation:
% 90.82/42.12 | (326) all_31_2_46 = all_29_2_43
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (280,322) yields a new equation:
% 90.82/42.12 | (327) all_29_1_42 = all_12_1_10
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 327 yields:
% 90.82/42.12 | (328) all_29_1_42 = all_12_1_10
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (323,324) yields a new equation:
% 90.82/42.12 | (329) all_22_2_31 = all_12_2_11
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (325,324) yields a new equation:
% 90.82/42.12 | (330) all_22_2_31 = 0
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (326,324) yields a new equation:
% 90.82/42.12 | (331) all_29_2_43 = all_22_2_31
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 331 yields:
% 90.82/42.12 | (332) all_29_2_43 = all_22_2_31
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (281,328) yields a new equation:
% 90.82/42.12 | (333) all_22_1_30 = all_12_1_10
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 333 yields:
% 90.82/42.12 | (334) all_22_1_30 = all_12_1_10
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (332,294) yields a new equation:
% 90.82/42.12 | (335) all_22_2_31 = all_14_4_16
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 335 yields:
% 90.82/42.12 | (336) all_22_2_31 = all_14_4_16
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (311,320) yields a new equation:
% 90.82/42.12 | (337) all_24_1_33 = 0
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 337 yields:
% 90.82/42.12 | (338) all_24_1_33 = 0
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (259,258) yields a new equation:
% 90.82/42.12 | (339) all_24_2_34 = all_12_0_9
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (272,338) yields a new equation:
% 90.82/42.12 | (340) all_19_2_25 = 0
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 340 yields:
% 90.82/42.12 | (341) all_19_2_25 = 0
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (283,334) yields a new equation:
% 90.82/42.12 | (342) all_14_3_15 = all_12_1_10
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 342 yields:
% 90.82/42.12 | (343) all_14_3_15 = all_12_1_10
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (329,336) yields a new equation:
% 90.82/42.12 | (344) all_14_4_16 = all_12_2_11
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (330,336) yields a new equation:
% 90.82/42.12 | (345) all_14_4_16 = 0
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (273,341) yields a new equation:
% 90.82/42.12 | (346) all_16_2_19 = 0
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 346 yields:
% 90.82/42.12 | (347) all_16_2_19 = 0
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (274,347) yields a new equation:
% 90.82/42.12 | (348) all_14_2_14 = 0
% 90.82/42.12 |
% 90.82/42.12 | Simplifying 348 yields:
% 90.82/42.12 | (349) all_14_2_14 = 0
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (282,343) yields a new equation:
% 90.82/42.12 | (350) all_12_1_10 = 0
% 90.82/42.12 |
% 90.82/42.12 | Combining equations (344,345) yields a new equation:
% 90.82/42.13 | (351) all_12_2_11 = 0
% 90.82/42.13 |
% 90.82/42.13 | Simplifying 351 yields:
% 90.82/42.13 | (352) all_12_2_11 = 0
% 90.82/42.13 |
% 90.82/42.13 | Combining equations (350,343) yields a new equation:
% 90.82/42.13 | (282) all_14_3_15 = 0
% 90.82/42.13 |
% 90.82/42.13 | Combining equations (345,336) yields a new equation:
% 90.82/42.13 | (330) all_22_2_31 = 0
% 90.82/42.13 |
% 90.82/42.13 | Combining equations (350,334) yields a new equation:
% 90.82/42.13 | (355) all_22_1_30 = 0
% 90.82/42.13 |
% 90.82/42.13 | Combining equations (339,258) yields a new equation:
% 90.82/42.13 | (259) all_26_2_37 = all_12_0_9
% 90.82/42.13 |
% 90.82/42.13 | Combining equations (345,294) yields a new equation:
% 90.82/42.13 | (357) all_29_2_43 = 0
% 90.82/42.13 |
% 90.82/42.13 | Combining equations (350,328) yields a new equation:
% 90.82/42.13 | (358) all_29_1_42 = 0
% 90.82/42.13 |
% 90.82/42.13 | Combining equations (330,324) yields a new equation:
% 90.82/42.13 | (325) all_31_2_46 = 0
% 90.82/42.13 |
% 90.82/42.13 | Combining equations (350,322) yields a new equation:
% 90.82/42.13 | (360) all_31_1_45 = 0
% 90.82/42.13 |
% 90.82/42.13 | Combining equations (314,257) yields a new equation:
% 90.82/42.13 | (256) all_36_4_63 = all_0_8_8
% 90.82/42.13 |
% 90.82/42.13 | Combining equations (320,307) yields a new equation:
% 90.82/42.13 | (362) all_38_2_70 = 0
% 90.82/42.13 |
% 90.82/42.13 | Combining equations (362,303) yields a new equation:
% 90.82/42.13 | (363) all_43_2_82 = 0
% 90.82/42.13 |
% 90.82/42.13 | Combining equations (350,300) yields a new equation:
% 90.82/42.13 | (364) all_43_1_81 = 0
% 90.82/42.13 |
% 90.82/42.13 | Combining equations (362,267) yields a new equation:
% 90.82/42.13 | (365) all_53_3_89 = 0
% 90.82/42.13 |
% 90.82/42.13 | Combining equations (301,296) yields a new equation:
% 90.82/42.13 | (295) all_53_2_88 = all_16_1_18
% 90.82/42.13 |
% 90.82/42.13 | Combining equations (350,284) yields a new equation:
% 90.82/42.13 | (367) all_53_1_87 = 0
% 90.82/42.13 |
% 90.82/42.13 | Combining equations (295,262) yields a new equation:
% 90.82/42.13 | (264) all_58_2_92 = all_16_1_18
% 90.82/42.13 |
% 90.82/42.13 | Combining equations (345,291) yields a new equation:
% 90.82/42.13 | (369) all_58_1_91 = 0
% 90.82/42.13 |
% 90.82/42.13 | From (254) and (190) follows:
% 90.82/42.13 | (61) isPrime0(xp) = 0
% 90.82/42.13 |
% 90.82/42.13 | From (256) and (197) follows:
% 90.82/42.13 | (371) sdtpldt0(all_0_8_8, xr) = all_36_3_62
% 90.82/42.13 |
% 90.82/42.13 | From (314) and (183) follows:
% 90.82/42.13 | (372) sdtpldt0(all_0_8_8, xp) = all_34_3_53
% 90.82/42.13 |
% 90.82/42.13 | From (314) and (187) follows:
% 90.82/42.13 | (68) sdtpldt0(xn, xm) = all_0_8_8
% 90.82/42.13 |
% 90.82/42.13 | From (260) and (194) follows:
% 90.82/42.13 | (77) aNaturalNumber0(xr) = 0
% 90.82/42.13 |
% 90.82/42.13 | From (301) and (149) follows:
% 90.82/42.13 | (144) aNaturalNumber0(xk) = all_16_1_18
% 90.82/42.13 |
% 90.82/42.13 | From (349) and (138) follows:
% 90.82/42.13 | (48) aNaturalNumber0(xp) = 0
% 90.82/42.13 |
% 90.82/42.13 | From (350) and (132) follows:
% 90.82/42.13 | (32) aNaturalNumber0(xm) = 0
% 90.82/42.13 |
% 90.82/42.13 | From (352) and (133) follows:
% 90.82/42.13 | (20) aNaturalNumber0(xn) = 0
% 90.82/42.13 |
% 90.82/42.13 +-Applying beta-rule and splitting (139), into two cases.
% 90.82/42.13 |-Branch one:
% 90.82/42.13 | (379) ~ (all_14_2_14 = 0)
% 90.82/42.13 |
% 90.82/42.13 | Equations (349) can reduce 379 to:
% 90.82/42.13 | (216) $false
% 90.82/42.13 |
% 90.82/42.13 |-The branch is then unsatisfiable
% 90.82/42.13 |-Branch two:
% 90.82/42.13 | (349) all_14_2_14 = 0
% 90.82/42.13 | (382) ~ (all_14_3_15 = 0) | ~ (all_14_4_16 = 0) | all_14_0_12 = all_0_7_7
% 90.82/42.13 |
% 90.82/42.13 +-Applying beta-rule and splitting (152), into two cases.
% 90.82/42.13 |-Branch one:
% 90.82/42.13 | (383) all_21_0_26 = xp & all_21_1_27 = 0 & sdtpldt0(xn, all_21_2_28) = xp & aNaturalNumber0(all_21_2_28) = 0
% 90.82/42.13 |
% 90.82/42.13 | Applying alpha-rule on (383) yields:
% 90.82/42.13 | (384) all_21_0_26 = xp
% 90.82/42.13 | (385) all_21_1_27 = 0
% 90.82/42.13 | (386) sdtpldt0(xn, all_21_2_28) = xp
% 90.82/42.13 | (387) aNaturalNumber0(all_21_2_28) = 0
% 90.82/42.13 |
% 90.82/42.13 +-Applying beta-rule and splitting (173), into two cases.
% 90.82/42.13 |-Branch one:
% 90.82/42.13 | (388) ~ (all_29_1_42 = 0)
% 90.82/42.13 |
% 90.82/42.13 | Equations (358) can reduce 388 to:
% 90.82/42.13 | (216) $false
% 90.82/42.13 |
% 90.82/42.13 |-The branch is then unsatisfiable
% 90.82/42.13 |-Branch two:
% 90.82/42.13 | (358) all_29_1_42 = 0
% 90.82/42.13 | (391) ~ (all_29_2_43 = 0) | all_29_0_41 = 0
% 90.82/42.13 |
% 90.82/42.13 +-Applying beta-rule and splitting (134), into two cases.
% 90.82/42.13 |-Branch one:
% 90.82/42.13 | (392) ~ (all_12_1_10 = 0)
% 90.82/42.13 |
% 90.82/42.13 | Equations (350) can reduce 392 to:
% 90.82/42.13 | (216) $false
% 90.82/42.13 |
% 90.82/42.13 |-The branch is then unsatisfiable
% 90.82/42.13 |-Branch two:
% 90.82/42.13 | (350) all_12_1_10 = 0
% 90.82/42.13 | (395) ~ (all_12_2_11 = 0) | all_12_0_9 = 0
% 90.82/42.13 |
% 90.82/42.13 +-Applying beta-rule and splitting (395), into two cases.
% 90.82/42.13 |-Branch one:
% 90.82/42.13 | (396) ~ (all_12_2_11 = 0)
% 90.82/42.13 |
% 90.82/42.13 | Equations (352) can reduce 396 to:
% 90.82/42.13 | (216) $false
% 90.82/42.13 |
% 90.82/42.13 |-The branch is then unsatisfiable
% 90.82/42.13 |-Branch two:
% 90.82/42.13 | (352) all_12_2_11 = 0
% 90.82/42.13 | (399) all_12_0_9 = 0
% 90.82/42.13 |
% 90.82/42.13 | Combining equations (399,259) yields a new equation:
% 90.82/42.13 | (400) all_26_2_37 = 0
% 90.82/42.13 |
% 90.82/42.13 +-Applying beta-rule and splitting (167), into two cases.
% 90.82/42.13 |-Branch one:
% 90.82/42.13 | (401) ~ (all_26_1_36 = 0)
% 90.82/42.13 |
% 90.82/42.13 | Equations (320) can reduce 401 to:
% 90.82/42.13 | (216) $false
% 90.82/42.13 |
% 90.82/42.13 |-The branch is then unsatisfiable
% 90.82/42.13 |-Branch two:
% 90.82/42.13 | (320) all_26_1_36 = 0
% 90.82/42.13 | (404) ~ (all_26_2_37 = 0) | all_26_0_35 = all_0_7_7
% 90.82/42.13 |
% 90.82/42.13 +-Applying beta-rule and splitting (404), into two cases.
% 90.82/42.13 |-Branch one:
% 90.82/42.13 | (405) ~ (all_26_2_37 = 0)
% 90.82/42.13 |
% 90.82/42.13 | Equations (400) can reduce 405 to:
% 90.82/42.13 | (216) $false
% 90.82/42.13 |
% 90.82/42.13 |-The branch is then unsatisfiable
% 90.82/42.13 |-Branch two:
% 90.82/42.13 | (400) all_26_2_37 = 0
% 90.82/42.13 | (408) all_26_0_35 = all_0_7_7
% 90.82/42.13 |
% 90.82/42.13 | From (408) and (164) follows:
% 90.82/42.13 | (409) sdtpldt0(xp, all_0_8_8) = all_0_7_7
% 90.82/42.13 |
% 90.82/42.13 +-Applying beta-rule and splitting (214), into two cases.
% 90.82/42.13 |-Branch one:
% 90.82/42.13 | (410) ~ (all_43_1_81 = 0)
% 90.82/42.13 |
% 90.82/42.13 | Equations (364) can reduce 410 to:
% 90.82/42.13 | (216) $false
% 90.82/42.13 |
% 90.82/42.13 |-The branch is then unsatisfiable
% 90.82/42.13 |-Branch two:
% 90.82/42.13 | (364) all_43_1_81 = 0
% 90.82/42.13 | (413) ~ (all_43_2_82 = 0) | all_43_0_80 = all_0_3_3
% 90.82/42.13 |
% 90.82/42.13 +-Applying beta-rule and splitting (157), into two cases.
% 90.82/42.13 |-Branch one:
% 90.82/42.13 | (414) ~ (all_22_1_30 = 0)
% 90.82/42.13 |
% 90.82/42.13 | Equations (355) can reduce 414 to:
% 90.82/42.13 | (216) $false
% 90.82/42.13 |
% 90.82/42.13 |-The branch is then unsatisfiable
% 90.82/42.13 |-Branch two:
% 90.82/42.13 | (355) all_22_1_30 = 0
% 90.82/42.13 | (417) ~ (all_22_2_31 = 0) | all_22_0_29 = all_0_8_8
% 90.82/42.13 |
% 90.82/42.13 +-Applying beta-rule and splitting (255), into two cases.
% 90.82/42.13 |-Branch one:
% 90.82/42.13 | (418) ~ (sdtpldt0(all_0_8_8, xp) = all_34_3_53)
% 90.82/42.13 |
% 90.82/42.13 | Using (372) and (418) yields:
% 90.82/42.13 | (419) $false
% 90.82/42.13 |
% 90.82/42.13 |-The branch is then unsatisfiable
% 90.82/42.13 |-Branch two:
% 90.82/42.13 | (372) sdtpldt0(all_0_8_8, xp) = all_34_3_53
% 90.82/42.13 | (421) all_34_3_53 = all_0_7_7
% 90.82/42.13 |
% 90.82/42.13 | From (421) and (372) follows:
% 90.82/42.13 | (76) sdtpldt0(all_0_8_8, xp) = all_0_7_7
% 90.82/42.13 |
% 90.82/42.13 +-Applying beta-rule and splitting (413), into two cases.
% 90.82/42.13 |-Branch one:
% 90.82/42.13 | (423) ~ (all_43_2_82 = 0)
% 90.82/42.13 |
% 90.82/42.13 | Equations (363) can reduce 423 to:
% 90.82/42.13 | (216) $false
% 90.82/42.13 |
% 90.82/42.13 |-The branch is then unsatisfiable
% 90.82/42.13 |-Branch two:
% 90.82/42.13 | (363) all_43_2_82 = 0
% 90.82/42.13 | (426) all_43_0_80 = all_0_3_3
% 90.82/42.13 |
% 90.82/42.13 | From (426) and (211) follows:
% 90.82/42.13 | (427) sdtasdt0(xm, xp) = all_0_3_3
% 90.82/42.13 |
% 90.82/42.13 +-Applying beta-rule and splitting (417), into two cases.
% 90.82/42.13 |-Branch one:
% 90.82/42.13 | (428) ~ (all_22_2_31 = 0)
% 90.82/42.13 |
% 90.82/42.13 | Equations (330) can reduce 428 to:
% 90.82/42.13 | (216) $false
% 90.82/42.13 |
% 90.82/42.13 |-The branch is then unsatisfiable
% 90.82/42.13 |-Branch two:
% 90.82/42.13 | (330) all_22_2_31 = 0
% 90.82/42.13 | (431) all_22_0_29 = all_0_8_8
% 90.82/42.13 |
% 90.82/42.13 | From (431) and (154) follows:
% 90.82/42.13 | (432) sdtpldt0(xm, xn) = all_0_8_8
% 90.82/42.13 |
% 90.82/42.13 +-Applying beta-rule and splitting (391), into two cases.
% 90.82/42.13 |-Branch one:
% 90.82/42.13 | (433) ~ (all_29_2_43 = 0)
% 90.82/42.13 |
% 90.82/42.13 | Equations (357) can reduce 433 to:
% 90.82/42.13 | (216) $false
% 90.82/42.13 |
% 90.82/42.13 |-The branch is then unsatisfiable
% 90.82/42.13 |-Branch two:
% 90.82/42.13 | (357) all_29_2_43 = 0
% 90.82/42.13 | (436) all_29_0_41 = 0
% 90.82/42.13 |
% 90.82/42.13 | From (436) and (170) follows:
% 90.82/42.13 | (437) aNaturalNumber0(all_0_6_6) = 0
% 90.82/42.13 |
% 90.82/42.13 +-Applying beta-rule and splitting (219), into two cases.
% 90.82/42.13 |-Branch one:
% 90.82/42.13 | (438) all_49_2_85 = 0 & aNaturalNumber0(xk) = 0
% 90.82/42.13 |
% 90.82/42.13 | Applying alpha-rule on (438) yields:
% 90.82/42.13 | (439) all_49_2_85 = 0
% 90.82/42.13 | (440) aNaturalNumber0(xk) = 0
% 90.82/42.13 |
% 90.82/42.13 +-Applying beta-rule and splitting (382), into two cases.
% 90.82/42.13 |-Branch one:
% 90.82/42.14 | (441) ~ (all_14_3_15 = 0)
% 90.82/42.14 |
% 90.82/42.14 | Equations (282) can reduce 441 to:
% 90.82/42.14 | (216) $false
% 90.82/42.14 |
% 90.82/42.14 |-The branch is then unsatisfiable
% 90.82/42.14 |-Branch two:
% 90.82/42.14 | (282) all_14_3_15 = 0
% 90.82/42.14 | (444) ~ (all_14_4_16 = 0) | all_14_0_12 = all_0_7_7
% 90.82/42.14 |
% 90.82/42.14 +-Applying beta-rule and splitting (261), into two cases.
% 90.82/42.14 |-Branch one:
% 90.82/42.14 | (445) ~ (aNaturalNumber0(xk) = 0)
% 90.82/42.14 |
% 90.82/42.14 | Using (440) and (445) yields:
% 90.82/42.14 | (419) $false
% 90.82/42.14 |
% 90.82/42.14 |-The branch is then unsatisfiable
% 90.82/42.14 |-Branch two:
% 90.82/42.14 | (440) aNaturalNumber0(xk) = 0
% 90.82/42.14 | (448) all_58_2_92 = 0
% 90.82/42.14 |
% 90.82/42.14 | Combining equations (448,264) yields a new equation:
% 90.82/42.14 | (449) all_16_1_18 = 0
% 90.82/42.14 |
% 90.82/42.14 | Combining equations (449,301) yields a new equation:
% 90.82/42.14 | (450) all_19_1_24 = 0
% 90.82/42.14 |
% 90.82/42.14 | Combining equations (449,295) yields a new equation:
% 90.82/42.14 | (451) all_53_2_88 = 0
% 90.82/42.14 |
% 90.82/42.14 | Combining equations (449,264) yields a new equation:
% 90.82/42.14 | (448) all_58_2_92 = 0
% 90.82/42.14 |
% 90.82/42.14 | From (449) and (144) follows:
% 90.82/42.14 | (440) aNaturalNumber0(xk) = 0
% 90.82/42.14 |
% 90.82/42.14 +-Applying beta-rule and splitting (107), into two cases.
% 90.82/42.14 |-Branch one:
% 90.82/42.14 | (454) ~ (sdtasdt0(xp, xk) = sz00)
% 90.82/42.14 |
% 90.82/42.14 +-Applying beta-rule and splitting (178), into two cases.
% 90.82/42.14 |-Branch one:
% 90.82/42.14 | (455) ~ (all_31_1_45 = 0)
% 90.82/42.14 |
% 90.82/42.14 | Equations (360) can reduce 455 to:
% 90.82/42.14 | (216) $false
% 90.82/42.14 |
% 90.82/42.14 |-The branch is then unsatisfiable
% 90.82/42.14 |-Branch two:
% 90.82/42.14 | (360) all_31_1_45 = 0
% 90.82/42.14 | (458) ~ (all_31_2_46 = 0) | all_31_0_44 = all_0_6_6
% 90.82/42.14 |
% 90.82/42.14 +-Applying beta-rule and splitting (458), into two cases.
% 90.82/42.14 |-Branch one:
% 90.82/42.14 | (459) ~ (all_31_2_46 = 0)
% 90.82/42.14 |
% 90.82/42.14 | Equations (325) can reduce 459 to:
% 90.82/42.14 | (216) $false
% 90.82/42.14 |
% 90.82/42.14 |-The branch is then unsatisfiable
% 90.82/42.14 |-Branch two:
% 90.82/42.14 | (325) all_31_2_46 = 0
% 90.82/42.14 | (462) all_31_0_44 = all_0_6_6
% 90.82/42.14 |
% 90.82/42.14 | From (462) and (175) follows:
% 90.82/42.14 | (463) sdtasdt0(xm, xn) = all_0_6_6
% 90.82/42.14 |
% 90.82/42.14 +-Applying beta-rule and splitting (209), into two cases.
% 90.82/42.14 |-Branch one:
% 90.82/42.14 | (464) all_42_0_77 = all_0_6_6 & all_42_1_78 = 0 & sdtasdt0(xr, all_42_2_79) = all_0_6_6 & aNaturalNumber0(all_42_2_79) = 0
% 90.82/42.14 |
% 90.82/42.14 | Applying alpha-rule on (464) yields:
% 90.82/42.14 | (465) all_42_0_77 = all_0_6_6
% 90.82/42.14 | (466) all_42_1_78 = 0
% 90.82/42.14 | (467) sdtasdt0(xr, all_42_2_79) = all_0_6_6
% 90.82/42.14 | (468) aNaturalNumber0(all_42_2_79) = 0
% 90.82/42.14 |
% 90.82/42.14 +-Applying beta-rule and splitting (168), into two cases.
% 90.82/42.14 |-Branch one:
% 90.82/42.14 | (469) all_28_0_38 = xp & all_28_1_39 = 0 & sdtpldt0(xm, all_28_2_40) = xp & aNaturalNumber0(all_28_2_40) = 0
% 90.82/42.14 |
% 90.82/42.14 | Applying alpha-rule on (469) yields:
% 90.82/42.14 | (470) all_28_0_38 = xp
% 90.82/42.14 | (471) all_28_1_39 = 0
% 90.82/42.14 | (472) sdtpldt0(xm, all_28_2_40) = xp
% 90.82/42.14 | (473) aNaturalNumber0(all_28_2_40) = 0
% 90.82/42.14 |
% 90.82/42.14 +-Applying beta-rule and splitting (146), into two cases.
% 90.82/42.14 |-Branch one:
% 90.82/42.14 | (474) ~ (all_16_1_18 = 0)
% 90.82/42.14 |
% 90.82/42.14 | Equations (449) can reduce 474 to:
% 90.82/42.14 | (216) $false
% 90.82/42.14 |
% 90.82/42.14 |-The branch is then unsatisfiable
% 90.82/42.14 |-Branch two:
% 90.82/42.14 | (449) all_16_1_18 = 0
% 90.82/42.14 | (477) ~ (all_16_2_19 = 0) | all_16_0_17 = 0
% 90.82/42.14 |
% 90.82/42.14 +-Applying beta-rule and splitting (477), into two cases.
% 90.82/42.14 |-Branch one:
% 90.82/42.14 | (478) ~ (all_16_2_19 = 0)
% 90.82/42.14 |
% 90.82/42.14 | Equations (347) can reduce 478 to:
% 90.82/42.14 | (216) $false
% 90.82/42.14 |
% 90.82/42.14 |-The branch is then unsatisfiable
% 90.82/42.14 |-Branch two:
% 90.82/42.14 | (347) all_16_2_19 = 0
% 90.82/42.14 | (481) all_16_0_17 = 0
% 90.82/42.14 |
% 90.82/42.14 | From (481) and (143) follows:
% 90.82/42.14 | (482) aNaturalNumber0(all_0_1_1) = 0
% 90.82/42.14 |
% 90.82/42.14 +-Applying beta-rule and splitting (101), into two cases.
% 90.82/42.14 |-Branch one:
% 90.82/42.14 | (483) ~ (sdtasdt0(xp, xk) = xm)
% 90.82/42.14 |
% 90.82/42.14 +-Applying beta-rule and splitting (103), into two cases.
% 90.82/42.14 |-Branch one:
% 90.82/42.14 | (215) xp = sz00
% 90.82/42.14 |
% 90.82/42.14 | Equations (215) can reduce 90 to:
% 90.82/42.14 | (216) $false
% 90.82/42.14 |
% 90.82/42.14 |-The branch is then unsatisfiable
% 90.82/42.14 |-Branch two:
% 90.82/42.14 | (90) ~ (xp = sz00)
% 90.82/42.14 | (487) all_0_1_1 = all_0_6_6 | ? [v0] : ? [v1] : ? [v2] : (doDivides0(xp, all_0_6_6) = v2 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 90.82/42.14 |
% 90.82/42.14 +-Applying beta-rule and splitting (487), into two cases.
% 90.82/42.14 |-Branch one:
% 90.82/42.14 | (488) all_0_1_1 = all_0_6_6
% 90.82/42.14 |
% 90.82/42.14 | From (488) and (22) follows:
% 90.82/42.14 | (489) sdtlseqdt0(all_0_3_3, all_0_6_6) = all_0_0_0
% 90.82/42.14 |
% 90.82/42.14 | From (488) and (17) follows:
% 90.82/42.14 | (490) sdtasdt0(xp, xk) = all_0_6_6
% 90.82/42.14 |
% 90.82/42.14 | From (488) and (482) follows:
% 90.82/42.14 | (437) aNaturalNumber0(all_0_6_6) = 0
% 90.82/42.14 |
% 90.82/42.14 +-Applying beta-rule and splitting (207), into two cases.
% 90.82/42.14 |-Branch one:
% 90.82/42.14 | (492) all_40_0_71 = all_0_6_6 & all_40_1_72 = 0 & sdtasdt0(xp, all_40_2_73) = all_0_6_6 & aNaturalNumber0(all_40_2_73) = 0
% 90.82/42.14 |
% 90.82/42.14 | Applying alpha-rule on (492) yields:
% 90.82/42.14 | (493) all_40_0_71 = all_0_6_6
% 90.82/42.14 | (494) all_40_1_72 = 0
% 90.82/42.14 | (495) sdtasdt0(xp, all_40_2_73) = all_0_6_6
% 90.82/42.14 | (496) aNaturalNumber0(all_40_2_73) = 0
% 90.82/42.14 |
% 90.82/42.14 +-Applying beta-rule and splitting (105), into two cases.
% 90.82/42.14 |-Branch one:
% 90.82/42.14 | (497) ~ (sdtasdt0(xp, xk) = all_0_6_6)
% 90.82/42.14 |
% 90.82/42.14 | Using (490) and (497) yields:
% 90.82/42.14 | (419) $false
% 90.82/42.14 |
% 90.82/42.14 |-The branch is then unsatisfiable
% 90.82/42.14 |-Branch two:
% 90.82/42.14 | (490) sdtasdt0(xp, xk) = all_0_6_6
% 90.82/42.14 | (500) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xr) = v3 & doDivides0(xr, xk) = v8 & doDivides0(xr, xp) = v7 & iLess0(v5, all_0_7_7) = v6 & sdtpldt0(v4, xr) = v5 & sdtpldt0(xp, xk) = v4 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 90.82/42.14 |
% 90.82/42.14 | Instantiating (500) with all_216_0_96, all_216_1_97, all_216_2_98, all_216_3_99, all_216_4_100, all_216_5_101, all_216_6_102, all_216_7_103, all_216_8_104 yields:
% 90.82/42.14 | (501) isPrime0(xr) = all_216_5_101 & doDivides0(xr, xk) = all_216_0_96 & doDivides0(xr, xp) = all_216_1_97 & iLess0(all_216_3_99, all_0_7_7) = all_216_2_98 & sdtpldt0(all_216_4_100, xr) = all_216_3_99 & sdtpldt0(xp, xk) = all_216_4_100 & aNaturalNumber0(xr) = all_216_6_102 & aNaturalNumber0(xk) = all_216_7_103 & aNaturalNumber0(xp) = all_216_8_104 & ( ~ (all_216_2_98 = 0) | ~ (all_216_5_101 = 0) | ~ (all_216_6_102 = 0) | ~ (all_216_7_103 = 0) | ~ (all_216_8_104 = 0) | all_216_0_96 = 0 | all_216_1_97 = 0)
% 90.82/42.14 |
% 90.82/42.14 | Applying alpha-rule on (501) yields:
% 90.82/42.14 | (502) sdtpldt0(xp, xk) = all_216_4_100
% 90.82/42.14 | (503) ~ (all_216_2_98 = 0) | ~ (all_216_5_101 = 0) | ~ (all_216_6_102 = 0) | ~ (all_216_7_103 = 0) | ~ (all_216_8_104 = 0) | all_216_0_96 = 0 | all_216_1_97 = 0
% 90.82/42.14 | (504) aNaturalNumber0(xk) = all_216_7_103
% 90.82/42.14 | (505) doDivides0(xr, xp) = all_216_1_97
% 90.82/42.14 | (506) sdtpldt0(all_216_4_100, xr) = all_216_3_99
% 90.82/42.14 | (507) aNaturalNumber0(xp) = all_216_8_104
% 90.82/42.14 | (508) doDivides0(xr, xk) = all_216_0_96
% 90.82/42.14 | (509) aNaturalNumber0(xr) = all_216_6_102
% 90.82/42.14 | (510) iLess0(all_216_3_99, all_0_7_7) = all_216_2_98
% 90.82/42.14 | (511) isPrime0(xr) = all_216_5_101
% 90.82/42.14 |
% 90.82/42.14 +-Applying beta-rule and splitting (225), into two cases.
% 90.82/42.14 |-Branch one:
% 90.82/42.14 | (512) ~ (all_53_0_86 = 0)
% 90.82/42.14 |
% 90.82/42.14 +-Applying beta-rule and splitting (235), into two cases.
% 90.82/42.14 |-Branch one:
% 90.82/42.14 | (513) ~ (all_58_0_90 = 0)
% 90.82/42.14 |
% 90.82/42.14 +-Applying beta-rule and splitting (151), into two cases.
% 90.82/42.14 |-Branch one:
% 90.82/42.14 | (514) ~ (all_19_1_24 = 0)
% 90.82/42.14 |
% 90.82/42.14 | Equations (450) can reduce 514 to:
% 90.82/42.14 | (216) $false
% 90.82/42.14 |
% 90.82/42.14 |-The branch is then unsatisfiable
% 90.82/42.14 |-Branch two:
% 90.82/42.14 | (450) all_19_1_24 = 0
% 90.82/42.14 | (517) ~ (all_19_2_25 = 0) | all_19_0_23 = all_0_1_1
% 90.82/42.14 |
% 90.82/42.14 +-Applying beta-rule and splitting (106), into two cases.
% 90.82/42.14 |-Branch one:
% 90.82/42.14 | (497) ~ (sdtasdt0(xp, xk) = all_0_6_6)
% 90.82/42.14 |
% 90.82/42.14 | Using (490) and (497) yields:
% 90.82/42.14 | (419) $false
% 90.82/42.14 |
% 90.82/42.14 |-The branch is then unsatisfiable
% 90.82/42.14 |-Branch two:
% 90.82/42.14 | (490) sdtasdt0(xp, xk) = all_0_6_6
% 90.82/42.14 | (521) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, xk) = v8 & doDivides0(xp, xp) = v7 & iLess0(v5, all_0_7_7) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xp, xk) = v4 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 90.82/42.14 |
% 90.82/42.14 | Instantiating (521) with all_233_0_105, all_233_1_106, all_233_2_107, all_233_3_108, all_233_4_109, all_233_5_110, all_233_6_111, all_233_7_112, all_233_8_113 yields:
% 90.82/42.14 | (522) isPrime0(xp) = all_233_5_110 & doDivides0(xp, xk) = all_233_0_105 & doDivides0(xp, xp) = all_233_1_106 & iLess0(all_233_3_108, all_0_7_7) = all_233_2_107 & sdtpldt0(all_233_4_109, xp) = all_233_3_108 & sdtpldt0(xp, xk) = all_233_4_109 & aNaturalNumber0(xk) = all_233_7_112 & aNaturalNumber0(xp) = all_233_6_111 & aNaturalNumber0(xp) = all_233_8_113 & ( ~ (all_233_2_107 = 0) | ~ (all_233_5_110 = 0) | ~ (all_233_6_111 = 0) | ~ (all_233_7_112 = 0) | ~ (all_233_8_113 = 0) | all_233_0_105 = 0 | all_233_1_106 = 0)
% 90.82/42.14 |
% 90.82/42.14 | Applying alpha-rule on (522) yields:
% 90.82/42.14 | (523) iLess0(all_233_3_108, all_0_7_7) = all_233_2_107
% 90.82/42.15 | (524) aNaturalNumber0(xk) = all_233_7_112
% 90.82/42.15 | (525) sdtpldt0(xp, xk) = all_233_4_109
% 90.82/42.15 | (526) ~ (all_233_2_107 = 0) | ~ (all_233_5_110 = 0) | ~ (all_233_6_111 = 0) | ~ (all_233_7_112 = 0) | ~ (all_233_8_113 = 0) | all_233_0_105 = 0 | all_233_1_106 = 0
% 90.82/42.15 | (527) isPrime0(xp) = all_233_5_110
% 90.82/42.15 | (528) doDivides0(xp, xp) = all_233_1_106
% 90.82/42.15 | (529) aNaturalNumber0(xp) = all_233_8_113
% 90.82/42.15 | (530) doDivides0(xp, xk) = all_233_0_105
% 90.82/42.15 | (531) sdtpldt0(all_233_4_109, xp) = all_233_3_108
% 90.82/42.15 | (532) aNaturalNumber0(xp) = all_233_6_111
% 90.82/42.15 |
% 90.82/42.15 +-Applying beta-rule and splitting (517), into two cases.
% 90.82/42.15 |-Branch one:
% 90.82/42.15 | (533) ~ (all_19_2_25 = 0)
% 90.82/42.15 |
% 90.82/42.15 | Equations (341) can reduce 533 to:
% 90.82/42.15 | (216) $false
% 90.82/42.15 |
% 90.82/42.15 |-The branch is then unsatisfiable
% 90.82/42.15 |-Branch two:
% 90.82/42.15 | (341) all_19_2_25 = 0
% 90.82/42.15 | (536) all_19_0_23 = all_0_1_1
% 90.82/42.15 |
% 90.82/42.15 | Combining equations (488,536) yields a new equation:
% 90.82/42.15 | (537) all_19_0_23 = all_0_6_6
% 90.82/42.15 |
% 90.82/42.15 | From (537) and (148) follows:
% 90.82/42.15 | (538) sdtasdt0(xk, xp) = all_0_6_6
% 90.82/42.15 |
% 90.82/42.15 +-Applying beta-rule and splitting (444), into two cases.
% 90.82/42.15 |-Branch one:
% 90.82/42.15 | (539) ~ (all_14_4_16 = 0)
% 90.82/42.15 |
% 90.82/42.15 | Equations (345) can reduce 539 to:
% 90.82/42.15 | (216) $false
% 90.82/42.15 |
% 90.82/42.15 |-The branch is then unsatisfiable
% 90.82/42.15 |-Branch two:
% 90.82/42.15 | (345) all_14_4_16 = 0
% 90.82/42.15 | (542) all_14_0_12 = all_0_7_7
% 90.82/42.15 |
% 90.82/42.15 | From (542) and (140) follows:
% 90.82/42.15 | (543) sdtpldt0(xn, all_14_1_13) = all_0_7_7
% 90.82/42.15 |
% 90.82/42.15 | Instantiating formula (27) with xp, all_233_5_110, 0 and discharging atoms isPrime0(xp) = all_233_5_110, isPrime0(xp) = 0, yields:
% 90.82/42.15 | (544) all_233_5_110 = 0
% 90.82/42.15 |
% 90.82/42.15 | Instantiating formula (72) with xr, xk, all_216_0_96, 0 and discharging atoms doDivides0(xr, xk) = all_216_0_96, doDivides0(xr, xk) = 0, yields:
% 90.82/42.15 | (545) all_216_0_96 = 0
% 90.82/42.15 |
% 90.82/42.15 | Instantiating formula (57) with xp, xk, all_216_4_100, all_233_4_109 and discharging atoms sdtpldt0(xp, xk) = all_233_4_109, sdtpldt0(xp, xk) = all_216_4_100, yields:
% 90.82/42.15 | (546) all_233_4_109 = all_216_4_100
% 90.82/42.15 |
% 90.82/42.15 | Instantiating formula (55) with xr, all_216_6_102, 0 and discharging atoms aNaturalNumber0(xr) = all_216_6_102, aNaturalNumber0(xr) = 0, yields:
% 90.82/42.15 | (547) all_216_6_102 = 0
% 90.82/42.15 |
% 90.82/42.15 | Instantiating formula (55) with xk, all_233_7_112, 0 and discharging atoms aNaturalNumber0(xk) = all_233_7_112, aNaturalNumber0(xk) = 0, yields:
% 90.82/42.15 | (548) all_233_7_112 = 0
% 90.82/42.15 |
% 90.82/42.15 | Instantiating formula (55) with xk, all_216_7_103, all_233_7_112 and discharging atoms aNaturalNumber0(xk) = all_233_7_112, aNaturalNumber0(xk) = all_216_7_103, yields:
% 90.82/42.15 | (549) all_233_7_112 = all_216_7_103
% 90.82/42.15 |
% 90.82/42.15 | Instantiating formula (55) with xp, all_233_6_111, 0 and discharging atoms aNaturalNumber0(xp) = all_233_6_111, aNaturalNumber0(xp) = 0, yields:
% 90.82/42.15 | (550) all_233_6_111 = 0
% 90.82/42.15 |
% 90.82/42.15 | Instantiating formula (55) with xp, all_233_8_113, all_233_6_111 and discharging atoms aNaturalNumber0(xp) = all_233_6_111, aNaturalNumber0(xp) = all_233_8_113, yields:
% 90.82/42.15 | (551) all_233_6_111 = all_233_8_113
% 90.82/42.15 |
% 90.82/42.15 | Instantiating formula (55) with xp, all_216_8_104, all_233_6_111 and discharging atoms aNaturalNumber0(xp) = all_233_6_111, aNaturalNumber0(xp) = all_216_8_104, yields:
% 90.82/42.15 | (552) all_233_6_111 = all_216_8_104
% 90.82/42.15 |
% 90.82/42.15 | Using (490) and (483) yields:
% 90.82/42.15 | (553) ~ (all_0_6_6 = xm)
% 90.82/42.15 |
% 90.82/42.15 | Using (490) and (454) yields:
% 90.82/42.15 | (554) ~ (all_0_6_6 = sz00)
% 90.82/42.15 |
% 90.82/42.15 | Combining equations (552,551) yields a new equation:
% 90.82/42.15 | (555) all_233_8_113 = all_216_8_104
% 90.82/42.15 |
% 90.82/42.15 | Combining equations (550,551) yields a new equation:
% 90.82/42.15 | (556) all_233_8_113 = 0
% 90.82/42.15 |
% 90.82/42.15 | Combining equations (549,548) yields a new equation:
% 90.82/42.15 | (557) all_216_7_103 = 0
% 90.82/42.15 |
% 90.82/42.15 | Simplifying 557 yields:
% 90.82/42.15 | (558) all_216_7_103 = 0
% 90.82/42.15 |
% 90.82/42.15 | Combining equations (556,555) yields a new equation:
% 90.82/42.15 | (559) all_216_8_104 = 0
% 90.82/42.15 |
% 90.82/42.15 | From (544) and (527) follows:
% 90.82/42.15 | (61) isPrime0(xp) = 0
% 90.82/42.15 |
% 90.82/42.15 | From (545) and (508) follows:
% 90.82/42.15 | (9) doDivides0(xr, xk) = 0
% 90.82/42.15 |
% 90.82/42.15 | From (546) and (531) follows:
% 90.82/42.15 | (562) sdtpldt0(all_216_4_100, xp) = all_233_3_108
% 90.82/42.15 |
% 90.82/42.15 | From (546) and (525) follows:
% 90.82/42.15 | (502) sdtpldt0(xp, xk) = all_216_4_100
% 90.82/42.15 |
% 90.82/42.15 | From (547) and (509) follows:
% 90.82/42.15 | (77) aNaturalNumber0(xr) = 0
% 90.82/42.15 |
% 90.82/42.15 | From (558) and (504) follows:
% 90.82/42.15 | (440) aNaturalNumber0(xk) = 0
% 90.82/42.15 |
% 90.82/42.15 | From (559) and (507) follows:
% 90.82/42.15 | (48) aNaturalNumber0(xp) = 0
% 90.82/42.15 |
% 90.82/42.15 +-Applying beta-rule and splitting (117), into two cases.
% 90.82/42.15 |-Branch one:
% 90.82/42.15 | (567) ~ (sdtasdt0(sz10, xm) = all_0_6_6)
% 90.82/42.15 |
% 90.82/42.15 +-Applying beta-rule and splitting (91), into two cases.
% 90.82/42.15 |-Branch one:
% 90.82/42.15 | (568) all_0_6_6 = sz00
% 90.82/42.15 |
% 90.82/42.15 | Equations (568) can reduce 554 to:
% 90.82/42.15 | (216) $false
% 90.82/42.15 |
% 90.82/42.15 |-The branch is then unsatisfiable
% 90.82/42.15 |-Branch two:
% 90.82/42.15 | (554) ~ (all_0_6_6 = sz00)
% 90.82/42.15 | (571) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xr, all_0_6_6) = v2 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 90.82/42.15 |
% 90.82/42.15 | Instantiating (571) with all_259_0_114, all_259_1_115, all_259_2_116 yields:
% 90.82/42.15 | (572) sdtlseqdt0(xr, all_0_6_6) = all_259_0_114 & aNaturalNumber0(all_0_6_6) = all_259_1_115 & aNaturalNumber0(xr) = all_259_2_116 & ( ~ (all_259_1_115 = 0) | ~ (all_259_2_116 = 0) | all_259_0_114 = 0)
% 90.82/42.15 |
% 90.82/42.15 | Applying alpha-rule on (572) yields:
% 90.82/42.15 | (573) sdtlseqdt0(xr, all_0_6_6) = all_259_0_114
% 90.82/42.15 | (574) aNaturalNumber0(all_0_6_6) = all_259_1_115
% 90.82/42.15 | (575) aNaturalNumber0(xr) = all_259_2_116
% 90.82/42.15 | (576) ~ (all_259_1_115 = 0) | ~ (all_259_2_116 = 0) | all_259_0_114 = 0
% 90.82/42.15 |
% 90.82/42.15 +-Applying beta-rule and splitting (118), into two cases.
% 90.82/42.15 |-Branch one:
% 90.82/42.15 | (577) ~ (sdtasdt0(sz00, xm) = all_0_6_6)
% 90.82/42.15 |
% 90.82/42.15 +-Applying beta-rule and splitting (179), into two cases.
% 90.82/42.15 |-Branch one:
% 90.82/42.15 | (578) all_33_0_47 = xk & all_33_1_48 = 0 & sdtpldt0(xp, all_33_2_49) = xk & aNaturalNumber0(all_33_2_49) = 0
% 90.82/42.15 |
% 90.82/42.15 | Applying alpha-rule on (578) yields:
% 90.82/42.15 | (579) all_33_0_47 = xk
% 90.82/42.15 | (580) all_33_1_48 = 0
% 90.82/42.15 | (581) sdtpldt0(xp, all_33_2_49) = xk
% 90.82/42.15 | (582) aNaturalNumber0(all_33_2_49) = 0
% 90.82/42.15 |
% 90.82/42.15 +-Applying beta-rule and splitting (94), into two cases.
% 90.82/42.15 |-Branch one:
% 90.82/42.15 | (568) all_0_6_6 = sz00
% 90.82/42.15 |
% 90.82/42.15 | Equations (568) can reduce 554 to:
% 90.82/42.15 | (216) $false
% 90.82/42.15 |
% 90.82/42.15 |-The branch is then unsatisfiable
% 90.82/42.15 |-Branch two:
% 90.82/42.15 | (554) ~ (all_0_6_6 = sz00)
% 90.82/42.15 | (586) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, all_0_6_6) = v2 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 90.82/42.15 |
% 90.82/42.15 | Instantiating (586) with all_273_0_117, all_273_1_118, all_273_2_119 yields:
% 90.82/42.15 | (587) sdtlseqdt0(xp, all_0_6_6) = all_273_0_117 & aNaturalNumber0(all_0_6_6) = all_273_1_118 & aNaturalNumber0(xp) = all_273_2_119 & ( ~ (all_273_1_118 = 0) | ~ (all_273_2_119 = 0) | all_273_0_117 = 0)
% 90.82/42.15 |
% 90.82/42.15 | Applying alpha-rule on (587) yields:
% 90.82/42.15 | (588) sdtlseqdt0(xp, all_0_6_6) = all_273_0_117
% 90.82/42.15 | (589) aNaturalNumber0(all_0_6_6) = all_273_1_118
% 90.82/42.15 | (590) aNaturalNumber0(xp) = all_273_2_119
% 90.82/42.15 | (591) ~ (all_273_1_118 = 0) | ~ (all_273_2_119 = 0) | all_273_0_117 = 0
% 90.82/42.15 |
% 90.82/42.15 | Instantiating formula (55) with all_0_6_6, all_273_1_118, 0 and discharging atoms aNaturalNumber0(all_0_6_6) = all_273_1_118, aNaturalNumber0(all_0_6_6) = 0, yields:
% 90.82/42.15 | (592) all_273_1_118 = 0
% 90.82/42.15 |
% 90.82/42.15 | Instantiating formula (55) with xr, all_259_2_116, 0 and discharging atoms aNaturalNumber0(xr) = all_259_2_116, aNaturalNumber0(xr) = 0, yields:
% 90.82/42.15 | (593) all_259_2_116 = 0
% 90.82/42.15 |
% 90.82/42.15 | Instantiating formula (55) with xp, all_273_2_119, 0 and discharging atoms aNaturalNumber0(xp) = all_273_2_119, aNaturalNumber0(xp) = 0, yields:
% 90.82/42.15 | (594) all_273_2_119 = 0
% 90.82/42.15 |
% 90.82/42.15 | Using (85) and (567) yields:
% 90.82/42.15 | (595) ~ (xn = sz10)
% 90.82/42.15 |
% 90.82/42.15 | Using (85) and (577) yields:
% 90.82/42.15 | (596) ~ (xn = sz00)
% 90.82/42.15 |
% 90.82/42.15 | From (593) and (575) follows:
% 90.82/42.15 | (77) aNaturalNumber0(xr) = 0
% 90.82/42.15 |
% 90.82/42.15 | From (594) and (590) follows:
% 90.82/42.15 | (48) aNaturalNumber0(xp) = 0
% 90.82/42.15 |
% 90.82/42.15 +-Applying beta-rule and splitting (591), into two cases.
% 90.82/42.15 |-Branch one:
% 90.82/42.15 | (599) ~ (all_273_1_118 = 0)
% 90.82/42.16 |
% 90.82/42.16 | Equations (592) can reduce 599 to:
% 90.82/42.16 | (216) $false
% 90.82/42.16 |
% 90.82/42.16 |-The branch is then unsatisfiable
% 90.82/42.16 |-Branch two:
% 90.82/42.16 | (592) all_273_1_118 = 0
% 90.82/42.16 | (602) ~ (all_273_2_119 = 0) | all_273_0_117 = 0
% 90.82/42.16 |
% 90.82/42.16 +-Applying beta-rule and splitting (602), into two cases.
% 90.82/42.16 |-Branch one:
% 90.82/42.16 | (603) ~ (all_273_2_119 = 0)
% 90.82/42.16 |
% 90.82/42.16 | Equations (594) can reduce 603 to:
% 90.82/42.16 | (216) $false
% 90.82/42.16 |
% 90.82/42.16 |-The branch is then unsatisfiable
% 90.82/42.16 |-Branch two:
% 90.82/42.16 | (594) all_273_2_119 = 0
% 90.82/42.16 | (606) all_273_0_117 = 0
% 90.82/42.16 |
% 90.82/42.16 | From (606) and (588) follows:
% 90.82/42.16 | (607) sdtlseqdt0(xp, all_0_6_6) = 0
% 90.82/42.16 |
% 90.82/42.16 +-Applying beta-rule and splitting (129), into two cases.
% 90.82/42.16 |-Branch one:
% 90.82/42.16 | (608) xn = sz00
% 90.82/42.16 |
% 90.82/42.16 | Equations (608) can reduce 596 to:
% 90.82/42.16 | (216) $false
% 90.82/42.16 |
% 90.82/42.16 |-The branch is then unsatisfiable
% 90.82/42.16 |-Branch two:
% 90.82/42.16 | (596) ~ (xn = sz00)
% 90.82/42.16 | (611) xn = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xn) = 0 & aNaturalNumber0(v0) = 0)
% 90.82/42.16 |
% 90.82/42.16 +-Applying beta-rule and splitting (208), into two cases.
% 90.82/42.16 |-Branch one:
% 90.82/42.16 | (612) all_41_0_74 = xk & all_41_1_75 = 0 & sdtasdt0(xr, all_41_2_76) = xk & aNaturalNumber0(all_41_2_76) = 0
% 90.82/42.16 |
% 90.82/42.16 | Applying alpha-rule on (612) yields:
% 90.82/42.16 | (613) all_41_0_74 = xk
% 90.82/42.16 | (614) all_41_1_75 = 0
% 90.82/42.16 | (615) sdtasdt0(xr, all_41_2_76) = xk
% 90.82/42.16 | (616) aNaturalNumber0(all_41_2_76) = 0
% 90.82/42.16 |
% 90.82/42.16 +-Applying beta-rule and splitting (611), into two cases.
% 90.82/42.16 |-Branch one:
% 90.82/42.16 | (617) xn = sz10
% 90.82/42.16 |
% 90.82/42.16 | Equations (617) can reduce 595 to:
% 90.82/42.16 | (216) $false
% 90.82/42.16 |
% 90.82/42.16 |-The branch is then unsatisfiable
% 90.82/42.16 |-Branch two:
% 90.82/42.16 | (595) ~ (xn = sz10)
% 90.82/42.16 | (620) ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xn) = 0 & aNaturalNumber0(v0) = 0)
% 90.82/42.16 |
% 90.82/42.16 | Instantiating (620) with all_310_0_120 yields:
% 90.82/42.16 | (621) isPrime0(all_310_0_120) = 0 & doDivides0(all_310_0_120, xn) = 0 & aNaturalNumber0(all_310_0_120) = 0
% 90.82/42.16 |
% 90.82/42.16 | Applying alpha-rule on (621) yields:
% 90.82/42.16 | (622) isPrime0(all_310_0_120) = 0
% 90.82/42.16 | (623) doDivides0(all_310_0_120, xn) = 0
% 90.82/42.16 | (624) aNaturalNumber0(all_310_0_120) = 0
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (18) with xn, all_310_0_120 and discharging atoms doDivides0(all_310_0_120, xn) = 0, yields:
% 90.82/42.16 | (625) xn = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_310_0_120, xn) = v2 & aNaturalNumber0(all_310_0_120) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (42) with all_70_0_94, xp and discharging atoms isPrime0(xp) = 0, doDivides0(all_70_0_94, xp) = 0, yields:
% 90.82/42.16 | (626) all_70_0_94 = xp | all_70_0_94 = sz10 | ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_70_0_94) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (18) with xp, all_70_0_94 and discharging atoms doDivides0(all_70_0_94, xp) = 0, yields:
% 90.82/42.16 | (627) xp = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_70_0_94, xp) = v2 & aNaturalNumber0(all_70_0_94) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (84) with all_0_4_4, xm, all_0_6_6, xp and discharging atoms sdtlseqdt0(xp, all_0_6_6) = 0, sdtlseqdt0(xp, xm) = all_0_4_4, yields:
% 90.82/42.16 | (628) all_0_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtlseqdt0(all_0_6_6, xm) = v3 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (84) with all_0_5_5, xn, all_0_6_6, xp and discharging atoms sdtlseqdt0(xp, all_0_6_6) = 0, sdtlseqdt0(xp, xn) = all_0_5_5, yields:
% 90.82/42.16 | (629) all_0_5_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtlseqdt0(all_0_6_6, xn) = v3 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (2) with all_53_0_86, xm, xk and discharging atoms sdtlseqdt0(xk, xm) = all_53_0_86, yields:
% 90.82/42.16 | (630) all_53_0_86 = 0 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xm, xk) = v2 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xk = xm))))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (2) with all_58_0_90, xn, xk and discharging atoms sdtlseqdt0(xk, xn) = all_58_0_90, yields:
% 90.82/42.16 | (631) all_58_0_90 = 0 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xn, xk) = v2 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xk = xn))))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (56) with all_0_6_6, xp, all_42_2_79, xr and discharging atoms doDivides0(xp, all_0_6_6) = 0, sdtasdt0(xr, all_42_2_79) = all_0_6_6, yields:
% 90.82/42.16 | (632) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, all_42_2_79) = v8 & doDivides0(xp, xr) = v7 & iLess0(v5, all_0_7_7) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xr, all_42_2_79) = v4 & aNaturalNumber0(all_42_2_79) = v1 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xp) = v2 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (59) with all_0_6_6, xk, xp, all_41_2_76, xr and discharging atoms sdtasdt0(xr, all_41_2_76) = xk, sdtasdt0(xk, xp) = all_0_6_6, yields:
% 90.82/42.16 | (633) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_41_2_76, xp) = v3 & sdtasdt0(xr, v3) = v4 & aNaturalNumber0(all_41_2_76) = v1 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xp) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_6_6))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (56) with all_0_6_6, xr, xp, xk and discharging atoms doDivides0(xr, all_0_6_6) = 0, sdtasdt0(xk, xp) = all_0_6_6, yields:
% 90.82/42.16 | (634) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xr) = v3 & doDivides0(xr, xk) = v7 & doDivides0(xr, xp) = v8 & iLess0(v5, all_0_7_7) = v6 & sdtpldt0(v4, xr) = v5 & sdtpldt0(xk, xp) = v4 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (56) with all_0_6_6, xp, xp, xk and discharging atoms doDivides0(xp, all_0_6_6) = 0, sdtasdt0(xk, xp) = all_0_6_6, yields:
% 90.82/42.16 | (635) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, xk) = v7 & doDivides0(xp, xp) = v8 & iLess0(v5, all_0_7_7) = 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))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (36) with all_0_0_0, all_0_6_6, all_0_3_3, all_40_2_73, xm, xp and discharging atoms sdtlseqdt0(all_0_3_3, all_0_6_6) = all_0_0_0, sdtasdt0(xp, all_40_2_73) = all_0_6_6, sdtasdt0(xp, xm) = all_0_3_3, yields:
% 90.82/42.16 | (636) all_40_2_73 = xm | xp = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v4, v5) = v6 & sdtlseqdt0(xm, all_40_2_73) = v3 & sdtasdt0(all_40_2_73, xp) = v5 & sdtasdt0(xm, xp) = v4 & aNaturalNumber0(all_40_2_73) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v6 = 0 & all_0_0_0 = 0 & ~ (v5 = v4) & ~ (all_0_3_3 = all_0_6_6))))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (39) with all_0_6_6, all_0_3_3, all_40_2_73, xm, xp and discharging atoms sdtasdt0(xp, all_40_2_73) = all_0_6_6, sdtasdt0(xp, xm) = all_0_3_3, aNaturalNumber0(xp) = 0, yields:
% 90.82/42.16 | (637) all_40_2_73 = xm | xp = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_40_2_73, xp) = v3 & sdtasdt0(xm, xp) = v2 & aNaturalNumber0(all_40_2_73) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = v2) & ~ (all_0_3_3 = all_0_6_6))))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (56) with all_0_6_6, xr, all_40_2_73, xp and discharging atoms doDivides0(xr, all_0_6_6) = 0, sdtasdt0(xp, all_40_2_73) = all_0_6_6, yields:
% 90.82/42.16 | (638) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xr) = v3 & doDivides0(xr, all_40_2_73) = v8 & doDivides0(xr, xp) = v7 & iLess0(v5, all_0_7_7) = v6 & sdtpldt0(v4, xr) = v5 & sdtpldt0(xp, all_40_2_73) = v4 & aNaturalNumber0(all_40_2_73) = v1 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (56) with all_0_6_6, xp, all_40_2_73, xp and discharging atoms doDivides0(xp, all_0_6_6) = 0, sdtasdt0(xp, all_40_2_73) = all_0_6_6, yields:
% 90.82/42.16 | (639) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, all_40_2_73) = v8 & doDivides0(xp, xp) = v7 & iLess0(v5, all_0_7_7) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xp, all_40_2_73) = v4 & aNaturalNumber0(all_40_2_73) = v1 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (43) with all_0_6_6, all_40_2_73, xp and discharging atoms sdtasdt0(xp, all_40_2_73) = all_0_6_6, yields:
% 90.82/42.16 | (640) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_40_2_73, xp) = v2 & aNaturalNumber0(all_40_2_73) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_6_6))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (39) with all_0_6_6, all_0_6_6, xk, all_40_2_73, xp and discharging atoms sdtasdt0(xp, all_40_2_73) = all_0_6_6, sdtasdt0(xp, xk) = all_0_6_6, aNaturalNumber0(xp) = 0, yields:
% 90.82/42.16 | (641) all_40_2_73 = xk | xp = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_40_2_73, xp) = v2 & sdtasdt0(xk, xp) = v3 & aNaturalNumber0(all_40_2_73) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (36) with all_0_2_2, all_0_3_3, all_0_6_6, xp, xn, xm and discharging atoms sdtlseqdt0(all_0_6_6, all_0_3_3) = all_0_2_2, sdtasdt0(xm, xp) = all_0_3_3, sdtasdt0(xm, xn) = all_0_6_6, yields:
% 90.82/42.16 | (642) xp = xn | xm = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v4, v5) = v6 & sdtlseqdt0(xn, xp) = v3 & sdtasdt0(xp, xm) = v5 & sdtasdt0(xn, xm) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v6 = 0 & all_0_2_2 = 0 & ~ (v5 = v4) & ~ (all_0_3_3 = all_0_6_6))))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (56) with all_0_6_6, xr, xn, xm and discharging atoms doDivides0(xr, all_0_6_6) = 0, sdtasdt0(xm, xn) = all_0_6_6, yields:
% 90.82/42.16 | (643) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xr) = v3 & doDivides0(xr, xm) = v7 & doDivides0(xr, xn) = v8 & iLess0(v5, all_0_7_7) = v6 & sdtpldt0(v4, xr) = v5 & sdtpldt0(xm, xn) = v4 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (56) with all_0_6_6, xp, xn, xm and discharging atoms doDivides0(xp, all_0_6_6) = 0, sdtasdt0(xm, xn) = all_0_6_6, yields:
% 90.82/42.16 | (644) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, xm) = v7 & doDivides0(xp, xn) = v8 & iLess0(v5, all_0_7_7) = 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))
% 90.82/42.16 |
% 90.82/42.16 | Instantiating formula (47) with all_0_6_6, xn yields:
% 90.82/42.16 | (645) ~ (sdtasdt0(sz00, xn) = all_0_6_6) | ? [v0] : ? [v1] : (sdtasdt0(xn, sz00) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v0 = 0) | (v1 = sz00 & all_0_6_6 = sz00)))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (80) with all_233_3_108, xp, all_216_4_100 and discharging atoms sdtpldt0(all_216_4_100, xp) = all_233_3_108, yields:
% 90.82/42.17 | (646) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, all_216_4_100) = v2 & aNaturalNumber0(all_216_4_100) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_233_3_108))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (11) with all_233_3_108, xp, all_216_4_100 and discharging atoms sdtpldt0(all_216_4_100, xp) = all_233_3_108, yields:
% 90.82/42.17 | (647) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_233_3_108) = v2 & aNaturalNumber0(all_216_4_100) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (19) with all_36_3_62, all_0_8_8, xr, xm, xn and discharging atoms sdtpldt0(all_0_8_8, xr) = all_36_3_62, sdtpldt0(xn, xm) = all_0_8_8, yields:
% 90.82/42.17 | (648) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xm, xr) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_36_3_62))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (40) with xk, all_33_2_49, xp, xr and discharging atoms doDivides0(xr, xk) = 0, sdtpldt0(xp, all_33_2_49) = xk, yields:
% 90.82/42.17 | (649) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(xr, all_33_2_49) = v4 & doDivides0(xr, xp) = v3 & aNaturalNumber0(all_33_2_49) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (80) with xk, all_33_2_49, xp and discharging atoms sdtpldt0(xp, all_33_2_49) = xk, yields:
% 90.82/42.17 | (650) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_33_2_49, xp) = v2 & aNaturalNumber0(all_33_2_49) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xk))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (19) with all_216_3_99, all_216_4_100, xr, xk, xp and discharging atoms sdtpldt0(all_216_4_100, xr) = all_216_3_99, sdtpldt0(xp, xk) = all_216_4_100, yields:
% 90.82/42.17 | (651) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xk, xr) = v3 & sdtpldt0(xp, v3) = v4 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_216_3_99))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (19) with all_233_3_108, all_216_4_100, xp, xk, xp and discharging atoms sdtpldt0(all_216_4_100, xp) = all_233_3_108, sdtpldt0(xp, xk) = all_216_4_100, yields:
% 90.82/42.17 | (652) ? [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_233_3_108))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (80) with all_216_4_100, xk, xp and discharging atoms sdtpldt0(xp, xk) = all_216_4_100, yields:
% 90.82/42.17 | (653) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xk, xp) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_216_4_100))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (11) with all_216_4_100, xk, xp and discharging atoms sdtpldt0(xp, xk) = all_216_4_100, yields:
% 90.82/42.17 | (654) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_216_4_100) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (40) with xp, all_28_2_40, xm, all_70_0_94 and discharging atoms doDivides0(all_70_0_94, xp) = 0, sdtpldt0(xm, all_28_2_40) = xp, yields:
% 90.82/42.17 | (655) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(all_70_0_94, all_28_2_40) = v4 & doDivides0(all_70_0_94, xm) = v3 & aNaturalNumber0(all_70_0_94) = v0 & aNaturalNumber0(all_28_2_40) = v2 & aNaturalNumber0(xm) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (19) with xk, xp, all_33_2_49, all_28_2_40, xm and discharging atoms sdtpldt0(xp, all_33_2_49) = xk, sdtpldt0(xm, all_28_2_40) = xp, yields:
% 90.82/42.17 | (656) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_28_2_40, all_33_2_49) = v3 & sdtpldt0(xm, v3) = v4 & aNaturalNumber0(all_33_2_49) = v2 & aNaturalNumber0(all_28_2_40) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = xk))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (19) with all_0_7_7, xp, all_0_8_8, all_28_2_40, xm and discharging atoms sdtpldt0(xp, all_0_8_8) = all_0_7_7, sdtpldt0(xm, all_28_2_40) = xp, yields:
% 90.82/42.17 | (657) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_28_2_40, all_0_8_8) = v3 & sdtpldt0(xm, v3) = v4 & aNaturalNumber0(all_28_2_40) = v1 & aNaturalNumber0(all_0_8_8) = v2 & aNaturalNumber0(xm) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_7_7))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (19) with all_216_4_100, xp, xk, all_28_2_40, xm and discharging atoms sdtpldt0(xp, xk) = all_216_4_100, sdtpldt0(xm, all_28_2_40) = xp, yields:
% 90.82/42.17 | (658) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_28_2_40, xk) = v3 & sdtpldt0(xm, v3) = v4 & aNaturalNumber0(all_28_2_40) = v1 & aNaturalNumber0(xk) = v2 & aNaturalNumber0(xm) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_216_4_100))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (80) with xp, all_28_2_40, xm and discharging atoms sdtpldt0(xm, all_28_2_40) = xp, yields:
% 90.82/42.17 | (659) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_28_2_40, xm) = v2 & aNaturalNumber0(all_28_2_40) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xp))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (80) with all_14_1_13, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_14_1_13, yields:
% 90.82/42.17 | (660) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, xm) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_14_1_13))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (11) with all_14_1_13, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_14_1_13, yields:
% 90.82/42.17 | (661) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_14_1_13) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (19) with all_0_7_7, all_0_8_8, xp, xn, xm and discharging atoms sdtpldt0(all_0_8_8, xp) = all_0_7_7, sdtpldt0(xm, xn) = all_0_8_8, yields:
% 90.82/42.17 | (662) ? [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_7_7))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (19) with all_36_3_62, all_0_8_8, xr, xn, xm and discharging atoms sdtpldt0(all_0_8_8, xr) = all_36_3_62, sdtpldt0(xm, xn) = all_0_8_8, yields:
% 90.82/42.17 | (663) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xm, v3) = v4 & sdtpldt0(xn, xr) = v3 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_36_3_62))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (83) with all_0_8_8, all_14_1_13, xn, xp, xm and discharging atoms sdtpldt0(xm, xp) = all_14_1_13, sdtpldt0(xm, xn) = all_0_8_8, yields:
% 90.82/42.17 | (664) 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_14_1_13 = all_0_8_8))))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (40) with xp, all_21_2_28, xn, all_70_0_94 and discharging atoms doDivides0(all_70_0_94, xp) = 0, sdtpldt0(xn, all_21_2_28) = xp, yields:
% 90.82/42.17 | (665) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (doDivides0(all_70_0_94, all_21_2_28) = v4 & doDivides0(all_70_0_94, xn) = v3 & aNaturalNumber0(all_70_0_94) = v0 & aNaturalNumber0(all_21_2_28) = v2 & aNaturalNumber0(xn) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (19) with xk, xp, all_33_2_49, all_21_2_28, xn and discharging atoms sdtpldt0(xp, all_33_2_49) = xk, sdtpldt0(xn, all_21_2_28) = xp, yields:
% 90.82/42.17 | (666) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_21_2_28, all_33_2_49) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(all_33_2_49) = v2 & aNaturalNumber0(all_21_2_28) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = xk))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (19) with all_0_7_7, xp, all_0_8_8, all_21_2_28, xn and discharging atoms sdtpldt0(xp, all_0_8_8) = all_0_7_7, sdtpldt0(xn, all_21_2_28) = xp, yields:
% 90.82/42.17 | (667) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_21_2_28, all_0_8_8) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(all_21_2_28) = v1 & aNaturalNumber0(all_0_8_8) = v2 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_7_7))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (19) with all_216_4_100, xp, xk, all_21_2_28, xn and discharging atoms sdtpldt0(xp, xk) = all_216_4_100, sdtpldt0(xn, all_21_2_28) = xp, yields:
% 90.82/42.17 | (668) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_21_2_28, xk) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(all_21_2_28) = v1 & aNaturalNumber0(xk) = v2 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_216_4_100))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (80) with xp, all_21_2_28, xn and discharging atoms sdtpldt0(xn, all_21_2_28) = xp, yields:
% 90.82/42.17 | (669) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_21_2_28, xn) = v2 & aNaturalNumber0(all_21_2_28) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xp))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (80) with all_0_7_7, all_14_1_13, xn and discharging atoms sdtpldt0(xn, all_14_1_13) = all_0_7_7, yields:
% 90.82/42.17 | (670) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_14_1_13, xn) = v2 & aNaturalNumber0(all_14_1_13) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_7_7))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (11) with all_0_7_7, all_14_1_13, xn and discharging atoms sdtpldt0(xn, all_14_1_13) = all_0_7_7, yields:
% 90.82/42.17 | (671) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_14_1_13) = v1 & aNaturalNumber0(all_0_7_7) = v2 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 90.82/42.17 |
% 90.82/42.17 | Instantiating formula (50) with all_70_0_94 and discharging atoms aNaturalNumber0(all_70_0_94) = 0, yields:
% 90.82/42.17 | (672) all_70_0_94 = sz10 | all_70_0_94 = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_70_0_94) = 0 & aNaturalNumber0(v0) = 0)
% 90.82/42.17 |
% 90.82/42.17 | Instantiating (671) with all_321_0_121, all_321_1_122, all_321_2_123 yields:
% 90.82/42.17 | (673) aNaturalNumber0(all_14_1_13) = all_321_1_122 & aNaturalNumber0(all_0_7_7) = all_321_0_121 & aNaturalNumber0(xn) = all_321_2_123 & ( ~ (all_321_1_122 = 0) | ~ (all_321_2_123 = 0) | all_321_0_121 = 0)
% 90.82/42.17 |
% 90.82/42.17 | Applying alpha-rule on (673) yields:
% 90.82/42.17 | (674) aNaturalNumber0(all_14_1_13) = all_321_1_122
% 90.82/42.17 | (675) aNaturalNumber0(all_0_7_7) = all_321_0_121
% 90.82/42.17 | (676) aNaturalNumber0(xn) = all_321_2_123
% 90.82/42.17 | (677) ~ (all_321_1_122 = 0) | ~ (all_321_2_123 = 0) | all_321_0_121 = 0
% 90.82/42.17 |
% 90.82/42.17 | Instantiating (670) with all_323_0_124, all_323_1_125, all_323_2_126 yields:
% 90.82/42.17 | (678) sdtpldt0(all_14_1_13, xn) = all_323_0_124 & aNaturalNumber0(all_14_1_13) = all_323_1_125 & aNaturalNumber0(xn) = all_323_2_126 & ( ~ (all_323_1_125 = 0) | ~ (all_323_2_126 = 0) | all_323_0_124 = all_0_7_7)
% 90.82/42.17 |
% 90.82/42.17 | Applying alpha-rule on (678) yields:
% 90.82/42.17 | (679) sdtpldt0(all_14_1_13, xn) = all_323_0_124
% 90.82/42.17 | (680) aNaturalNumber0(all_14_1_13) = all_323_1_125
% 90.82/42.17 | (681) aNaturalNumber0(xn) = all_323_2_126
% 90.82/42.17 | (682) ~ (all_323_1_125 = 0) | ~ (all_323_2_126 = 0) | all_323_0_124 = all_0_7_7
% 90.82/42.17 |
% 90.82/42.17 | Instantiating (655) with all_325_0_127, all_325_1_128, all_325_2_129, all_325_3_130, all_325_4_131 yields:
% 90.82/42.17 | (683) doDivides0(all_70_0_94, all_28_2_40) = all_325_0_127 & doDivides0(all_70_0_94, xm) = all_325_1_128 & aNaturalNumber0(all_70_0_94) = all_325_4_131 & aNaturalNumber0(all_28_2_40) = all_325_2_129 & aNaturalNumber0(xm) = all_325_3_130 & ( ~ (all_325_1_128 = 0) | ~ (all_325_2_129 = 0) | ~ (all_325_3_130 = 0) | ~ (all_325_4_131 = 0) | all_325_0_127 = 0)
% 90.82/42.17 |
% 90.82/42.17 | Applying alpha-rule on (683) yields:
% 90.82/42.17 | (684) aNaturalNumber0(all_28_2_40) = all_325_2_129
% 90.82/42.17 | (685) aNaturalNumber0(all_70_0_94) = all_325_4_131
% 90.82/42.17 | (686) doDivides0(all_70_0_94, xm) = all_325_1_128
% 90.82/42.17 | (687) doDivides0(all_70_0_94, all_28_2_40) = all_325_0_127
% 90.82/42.17 | (688) aNaturalNumber0(xm) = all_325_3_130
% 90.82/42.17 | (689) ~ (all_325_1_128 = 0) | ~ (all_325_2_129 = 0) | ~ (all_325_3_130 = 0) | ~ (all_325_4_131 = 0) | all_325_0_127 = 0
% 90.82/42.17 |
% 90.82/42.17 | Instantiating (650) with all_327_0_132, all_327_1_133, all_327_2_134 yields:
% 90.82/42.17 | (690) sdtpldt0(all_33_2_49, xp) = all_327_0_132 & aNaturalNumber0(all_33_2_49) = all_327_1_133 & aNaturalNumber0(xp) = all_327_2_134 & ( ~ (all_327_1_133 = 0) | ~ (all_327_2_134 = 0) | all_327_0_132 = xk)
% 90.82/42.18 |
% 90.82/42.18 | Applying alpha-rule on (690) yields:
% 90.82/42.18 | (691) sdtpldt0(all_33_2_49, xp) = all_327_0_132
% 90.82/42.18 | (692) aNaturalNumber0(all_33_2_49) = all_327_1_133
% 90.82/42.18 | (693) aNaturalNumber0(xp) = all_327_2_134
% 90.82/42.18 | (694) ~ (all_327_1_133 = 0) | ~ (all_327_2_134 = 0) | all_327_0_132 = xk
% 90.82/42.18 |
% 90.82/42.18 | Instantiating (665) with all_329_0_135, all_329_1_136, all_329_2_137, all_329_3_138, all_329_4_139 yields:
% 90.82/42.18 | (695) doDivides0(all_70_0_94, all_21_2_28) = all_329_0_135 & doDivides0(all_70_0_94, xn) = all_329_1_136 & aNaturalNumber0(all_70_0_94) = all_329_4_139 & aNaturalNumber0(all_21_2_28) = all_329_2_137 & aNaturalNumber0(xn) = all_329_3_138 & ( ~ (all_329_1_136 = 0) | ~ (all_329_2_137 = 0) | ~ (all_329_3_138 = 0) | ~ (all_329_4_139 = 0) | all_329_0_135 = 0)
% 90.82/42.18 |
% 90.82/42.18 | Applying alpha-rule on (695) yields:
% 90.82/42.18 | (696) ~ (all_329_1_136 = 0) | ~ (all_329_2_137 = 0) | ~ (all_329_3_138 = 0) | ~ (all_329_4_139 = 0) | all_329_0_135 = 0
% 90.82/42.18 | (697) aNaturalNumber0(xn) = all_329_3_138
% 90.82/42.18 | (698) aNaturalNumber0(all_21_2_28) = all_329_2_137
% 90.82/42.18 | (699) doDivides0(all_70_0_94, all_21_2_28) = all_329_0_135
% 90.82/42.18 | (700) aNaturalNumber0(all_70_0_94) = all_329_4_139
% 90.82/42.18 | (701) doDivides0(all_70_0_94, xn) = all_329_1_136
% 90.82/42.18 |
% 90.82/42.18 | Instantiating (659) with all_331_0_140, all_331_1_141, all_331_2_142 yields:
% 90.82/42.18 | (702) sdtpldt0(all_28_2_40, xm) = all_331_0_140 & aNaturalNumber0(all_28_2_40) = all_331_1_141 & aNaturalNumber0(xm) = all_331_2_142 & ( ~ (all_331_1_141 = 0) | ~ (all_331_2_142 = 0) | all_331_0_140 = xp)
% 90.82/42.18 |
% 90.82/42.18 | Applying alpha-rule on (702) yields:
% 90.82/42.18 | (703) sdtpldt0(all_28_2_40, xm) = all_331_0_140
% 90.82/42.18 | (704) aNaturalNumber0(all_28_2_40) = all_331_1_141
% 90.82/42.18 | (705) aNaturalNumber0(xm) = all_331_2_142
% 90.82/42.18 | (706) ~ (all_331_1_141 = 0) | ~ (all_331_2_142 = 0) | all_331_0_140 = xp
% 90.82/42.18 |
% 90.82/42.18 | Instantiating (663) with all_333_0_143, all_333_1_144, all_333_2_145, all_333_3_146, all_333_4_147 yields:
% 90.82/42.18 | (707) sdtpldt0(xm, all_333_1_144) = all_333_0_143 & sdtpldt0(xn, xr) = all_333_1_144 & aNaturalNumber0(xr) = all_333_2_145 & aNaturalNumber0(xm) = all_333_4_147 & aNaturalNumber0(xn) = all_333_3_146 & ( ~ (all_333_2_145 = 0) | ~ (all_333_3_146 = 0) | ~ (all_333_4_147 = 0) | all_333_0_143 = all_36_3_62)
% 90.82/42.18 |
% 90.82/42.18 | Applying alpha-rule on (707) yields:
% 90.82/42.18 | (708) aNaturalNumber0(xn) = all_333_3_146
% 90.82/42.18 | (709) sdtpldt0(xn, xr) = all_333_1_144
% 90.82/42.18 | (710) sdtpldt0(xm, all_333_1_144) = all_333_0_143
% 90.82/42.18 | (711) aNaturalNumber0(xr) = all_333_2_145
% 90.82/42.18 | (712) aNaturalNumber0(xm) = all_333_4_147
% 90.82/42.18 | (713) ~ (all_333_2_145 = 0) | ~ (all_333_3_146 = 0) | ~ (all_333_4_147 = 0) | all_333_0_143 = all_36_3_62
% 90.82/42.18 |
% 90.82/42.18 | Instantiating (662) with all_335_0_148, all_335_1_149, all_335_2_150, all_335_3_151, all_335_4_152 yields:
% 90.82/42.18 | (714) sdtpldt0(xm, all_335_1_149) = all_335_0_148 & sdtpldt0(xn, xp) = all_335_1_149 & aNaturalNumber0(xp) = all_335_2_150 & aNaturalNumber0(xm) = all_335_4_152 & aNaturalNumber0(xn) = all_335_3_151 & ( ~ (all_335_2_150 = 0) | ~ (all_335_3_151 = 0) | ~ (all_335_4_152 = 0) | all_335_0_148 = all_0_7_7)
% 90.82/42.18 |
% 90.82/42.18 | Applying alpha-rule on (714) yields:
% 90.82/42.18 | (715) sdtpldt0(xm, all_335_1_149) = all_335_0_148
% 90.82/42.18 | (716) aNaturalNumber0(xp) = all_335_2_150
% 90.82/42.18 | (717) aNaturalNumber0(xm) = all_335_4_152
% 90.82/42.18 | (718) aNaturalNumber0(xn) = all_335_3_151
% 90.82/42.18 | (719) sdtpldt0(xn, xp) = all_335_1_149
% 90.82/42.18 | (720) ~ (all_335_2_150 = 0) | ~ (all_335_3_151 = 0) | ~ (all_335_4_152 = 0) | all_335_0_148 = all_0_7_7
% 90.82/42.18 |
% 90.82/42.18 | Instantiating (661) with all_337_0_153, all_337_1_154, all_337_2_155 yields:
% 90.82/42.18 | (721) aNaturalNumber0(all_14_1_13) = all_337_0_153 & aNaturalNumber0(xp) = all_337_1_154 & aNaturalNumber0(xm) = all_337_2_155 & ( ~ (all_337_1_154 = 0) | ~ (all_337_2_155 = 0) | all_337_0_153 = 0)
% 90.82/42.18 |
% 90.82/42.18 | Applying alpha-rule on (721) yields:
% 90.82/42.18 | (722) aNaturalNumber0(all_14_1_13) = all_337_0_153
% 90.82/42.18 | (723) aNaturalNumber0(xp) = all_337_1_154
% 90.82/42.18 | (724) aNaturalNumber0(xm) = all_337_2_155
% 90.82/42.18 | (725) ~ (all_337_1_154 = 0) | ~ (all_337_2_155 = 0) | all_337_0_153 = 0
% 90.82/42.18 |
% 90.82/42.18 | Instantiating (660) with all_339_0_156, all_339_1_157, all_339_2_158 yields:
% 90.82/42.18 | (726) sdtpldt0(xp, xm) = all_339_0_156 & aNaturalNumber0(xp) = all_339_1_157 & aNaturalNumber0(xm) = all_339_2_158 & ( ~ (all_339_1_157 = 0) | ~ (all_339_2_158 = 0) | all_339_0_156 = all_14_1_13)
% 90.82/42.18 |
% 90.82/42.18 | Applying alpha-rule on (726) yields:
% 90.82/42.18 | (727) sdtpldt0(xp, xm) = all_339_0_156
% 90.82/42.18 | (728) aNaturalNumber0(xp) = all_339_1_157
% 90.82/42.18 | (729) aNaturalNumber0(xm) = all_339_2_158
% 90.82/42.18 | (730) ~ (all_339_1_157 = 0) | ~ (all_339_2_158 = 0) | all_339_0_156 = all_14_1_13
% 90.82/42.18 |
% 90.82/42.18 | Instantiating (658) with all_341_0_159, all_341_1_160, all_341_2_161, all_341_3_162, all_341_4_163 yields:
% 90.82/42.18 | (731) sdtpldt0(all_28_2_40, xk) = all_341_1_160 & sdtpldt0(xm, all_341_1_160) = all_341_0_159 & aNaturalNumber0(all_28_2_40) = all_341_3_162 & aNaturalNumber0(xk) = all_341_2_161 & aNaturalNumber0(xm) = all_341_4_163 & ( ~ (all_341_2_161 = 0) | ~ (all_341_3_162 = 0) | ~ (all_341_4_163 = 0) | all_341_0_159 = all_216_4_100)
% 90.82/42.18 |
% 90.82/42.18 | Applying alpha-rule on (731) yields:
% 90.82/42.18 | (732) ~ (all_341_2_161 = 0) | ~ (all_341_3_162 = 0) | ~ (all_341_4_163 = 0) | all_341_0_159 = all_216_4_100
% 90.82/42.18 | (733) aNaturalNumber0(xk) = all_341_2_161
% 90.82/42.18 | (734) aNaturalNumber0(all_28_2_40) = all_341_3_162
% 90.82/42.18 | (735) sdtpldt0(all_28_2_40, xk) = all_341_1_160
% 90.82/42.18 | (736) sdtpldt0(xm, all_341_1_160) = all_341_0_159
% 90.82/42.18 | (737) aNaturalNumber0(xm) = all_341_4_163
% 90.82/42.18 |
% 90.82/42.18 | Instantiating (657) with all_343_0_164, all_343_1_165, all_343_2_166, all_343_3_167, all_343_4_168 yields:
% 90.82/42.18 | (738) sdtpldt0(all_28_2_40, all_0_8_8) = all_343_1_165 & sdtpldt0(xm, all_343_1_165) = all_343_0_164 & aNaturalNumber0(all_28_2_40) = all_343_3_167 & aNaturalNumber0(all_0_8_8) = all_343_2_166 & aNaturalNumber0(xm) = all_343_4_168 & ( ~ (all_343_2_166 = 0) | ~ (all_343_3_167 = 0) | ~ (all_343_4_168 = 0) | all_343_0_164 = all_0_7_7)
% 90.82/42.18 |
% 90.82/42.18 | Applying alpha-rule on (738) yields:
% 90.82/42.18 | (739) sdtpldt0(xm, all_343_1_165) = all_343_0_164
% 90.82/42.18 | (740) ~ (all_343_2_166 = 0) | ~ (all_343_3_167 = 0) | ~ (all_343_4_168 = 0) | all_343_0_164 = all_0_7_7
% 90.82/42.18 | (741) sdtpldt0(all_28_2_40, all_0_8_8) = all_343_1_165
% 90.82/42.18 | (742) aNaturalNumber0(xm) = all_343_4_168
% 90.82/42.18 | (743) aNaturalNumber0(all_28_2_40) = all_343_3_167
% 90.82/42.18 | (744) aNaturalNumber0(all_0_8_8) = all_343_2_166
% 90.82/42.18 |
% 90.82/42.18 | Instantiating (644) with all_345_0_169, all_345_1_170, all_345_2_171, all_345_3_172, all_345_4_173, all_345_5_174, all_345_6_175, all_345_7_176, all_345_8_177 yields:
% 90.82/42.18 | (745) isPrime0(xp) = all_345_5_174 & doDivides0(xp, xm) = all_345_1_170 & doDivides0(xp, xn) = all_345_0_169 & iLess0(all_345_3_172, all_0_7_7) = all_345_2_171 & sdtpldt0(all_345_4_173, xp) = all_345_3_172 & sdtpldt0(xm, xn) = all_345_4_173 & aNaturalNumber0(xp) = all_345_6_175 & aNaturalNumber0(xm) = all_345_8_177 & aNaturalNumber0(xn) = all_345_7_176 & ( ~ (all_345_2_171 = 0) | ~ (all_345_5_174 = 0) | ~ (all_345_6_175 = 0) | ~ (all_345_7_176 = 0) | ~ (all_345_8_177 = 0) | all_345_0_169 = 0 | all_345_1_170 = 0)
% 90.82/42.18 |
% 90.82/42.18 | Applying alpha-rule on (745) yields:
% 90.82/42.18 | (746) sdtpldt0(xm, xn) = all_345_4_173
% 90.82/42.18 | (747) doDivides0(xp, xm) = all_345_1_170
% 90.82/42.18 | (748) aNaturalNumber0(xn) = all_345_7_176
% 90.82/42.18 | (749) iLess0(all_345_3_172, all_0_7_7) = all_345_2_171
% 90.82/42.18 | (750) isPrime0(xp) = all_345_5_174
% 90.82/42.18 | (751) ~ (all_345_2_171 = 0) | ~ (all_345_5_174 = 0) | ~ (all_345_6_175 = 0) | ~ (all_345_7_176 = 0) | ~ (all_345_8_177 = 0) | all_345_0_169 = 0 | all_345_1_170 = 0
% 90.82/42.18 | (752) aNaturalNumber0(xp) = all_345_6_175
% 90.82/42.18 | (753) aNaturalNumber0(xm) = all_345_8_177
% 90.82/42.18 | (754) sdtpldt0(all_345_4_173, xp) = all_345_3_172
% 90.82/42.18 | (755) doDivides0(xp, xn) = all_345_0_169
% 90.82/42.18 |
% 90.82/42.18 | Instantiating (643) with all_347_0_178, all_347_1_179, all_347_2_180, all_347_3_181, all_347_4_182, all_347_5_183, all_347_6_184, all_347_7_185, all_347_8_186 yields:
% 90.82/42.18 | (756) isPrime0(xr) = all_347_5_183 & doDivides0(xr, xm) = all_347_1_179 & doDivides0(xr, xn) = all_347_0_178 & iLess0(all_347_3_181, all_0_7_7) = all_347_2_180 & sdtpldt0(all_347_4_182, xr) = all_347_3_181 & sdtpldt0(xm, xn) = all_347_4_182 & aNaturalNumber0(xr) = all_347_6_184 & aNaturalNumber0(xm) = all_347_8_186 & aNaturalNumber0(xn) = all_347_7_185 & ( ~ (all_347_2_180 = 0) | ~ (all_347_5_183 = 0) | ~ (all_347_6_184 = 0) | ~ (all_347_7_185 = 0) | ~ (all_347_8_186 = 0) | all_347_0_178 = 0 | all_347_1_179 = 0)
% 90.82/42.18 |
% 90.82/42.18 | Applying alpha-rule on (756) yields:
% 91.22/42.18 | (757) doDivides0(xr, xm) = all_347_1_179
% 91.22/42.18 | (758) ~ (all_347_2_180 = 0) | ~ (all_347_5_183 = 0) | ~ (all_347_6_184 = 0) | ~ (all_347_7_185 = 0) | ~ (all_347_8_186 = 0) | all_347_0_178 = 0 | all_347_1_179 = 0
% 91.22/42.18 | (759) sdtpldt0(all_347_4_182, xr) = all_347_3_181
% 91.22/42.18 | (760) iLess0(all_347_3_181, all_0_7_7) = all_347_2_180
% 91.22/42.18 | (761) aNaturalNumber0(xm) = all_347_8_186
% 91.22/42.18 | (762) sdtpldt0(xm, xn) = all_347_4_182
% 91.22/42.18 | (763) doDivides0(xr, xn) = all_347_0_178
% 91.22/42.18 | (764) isPrime0(xr) = all_347_5_183
% 91.22/42.19 | (765) aNaturalNumber0(xr) = all_347_6_184
% 91.22/42.19 | (766) aNaturalNumber0(xn) = all_347_7_185
% 91.22/42.19 |
% 91.22/42.19 | Instantiating (640) with all_349_0_187, all_349_1_188, all_349_2_189 yields:
% 91.22/42.19 | (767) sdtasdt0(all_40_2_73, xp) = all_349_0_187 & aNaturalNumber0(all_40_2_73) = all_349_1_188 & aNaturalNumber0(xp) = all_349_2_189 & ( ~ (all_349_1_188 = 0) | ~ (all_349_2_189 = 0) | all_349_0_187 = all_0_6_6)
% 91.22/42.19 |
% 91.22/42.19 | Applying alpha-rule on (767) yields:
% 91.22/42.19 | (768) sdtasdt0(all_40_2_73, xp) = all_349_0_187
% 91.22/42.19 | (769) aNaturalNumber0(all_40_2_73) = all_349_1_188
% 91.22/42.19 | (770) aNaturalNumber0(xp) = all_349_2_189
% 91.22/42.19 | (771) ~ (all_349_1_188 = 0) | ~ (all_349_2_189 = 0) | all_349_0_187 = all_0_6_6
% 91.22/42.19 |
% 91.22/42.19 | Instantiating (656) with all_351_0_190, all_351_1_191, all_351_2_192, all_351_3_193, all_351_4_194 yields:
% 91.22/42.19 | (772) sdtpldt0(all_28_2_40, all_33_2_49) = all_351_1_191 & sdtpldt0(xm, all_351_1_191) = all_351_0_190 & aNaturalNumber0(all_33_2_49) = all_351_2_192 & aNaturalNumber0(all_28_2_40) = all_351_3_193 & aNaturalNumber0(xm) = all_351_4_194 & ( ~ (all_351_2_192 = 0) | ~ (all_351_3_193 = 0) | ~ (all_351_4_194 = 0) | all_351_0_190 = xk)
% 91.22/42.19 |
% 91.22/42.19 | Applying alpha-rule on (772) yields:
% 91.22/42.19 | (773) aNaturalNumber0(xm) = all_351_4_194
% 91.22/42.19 | (774) aNaturalNumber0(all_33_2_49) = all_351_2_192
% 91.22/42.19 | (775) sdtpldt0(xm, all_351_1_191) = all_351_0_190
% 91.22/42.19 | (776) ~ (all_351_2_192 = 0) | ~ (all_351_3_193 = 0) | ~ (all_351_4_194 = 0) | all_351_0_190 = xk
% 91.22/42.19 | (777) sdtpldt0(all_28_2_40, all_33_2_49) = all_351_1_191
% 91.22/42.19 | (778) aNaturalNumber0(all_28_2_40) = all_351_3_193
% 91.22/42.19 |
% 91.22/42.19 | Instantiating (669) with all_353_0_195, all_353_1_196, all_353_2_197 yields:
% 91.22/42.19 | (779) sdtpldt0(all_21_2_28, xn) = all_353_0_195 & aNaturalNumber0(all_21_2_28) = all_353_1_196 & aNaturalNumber0(xn) = all_353_2_197 & ( ~ (all_353_1_196 = 0) | ~ (all_353_2_197 = 0) | all_353_0_195 = xp)
% 91.22/42.19 |
% 91.22/42.19 | Applying alpha-rule on (779) yields:
% 91.22/42.19 | (780) sdtpldt0(all_21_2_28, xn) = all_353_0_195
% 91.22/42.19 | (781) aNaturalNumber0(all_21_2_28) = all_353_1_196
% 91.22/42.19 | (782) aNaturalNumber0(xn) = all_353_2_197
% 91.22/42.19 | (783) ~ (all_353_1_196 = 0) | ~ (all_353_2_197 = 0) | all_353_0_195 = xp
% 91.22/42.19 |
% 91.22/42.19 | Instantiating (632) with all_357_0_201, all_357_1_202, all_357_2_203, all_357_3_204, all_357_4_205, all_357_5_206, all_357_6_207, all_357_7_208, all_357_8_209 yields:
% 91.22/42.19 | (784) isPrime0(xp) = all_357_5_206 & doDivides0(xp, all_42_2_79) = all_357_0_201 & doDivides0(xp, xr) = all_357_1_202 & iLess0(all_357_3_204, all_0_7_7) = all_357_2_203 & sdtpldt0(all_357_4_205, xp) = all_357_3_204 & sdtpldt0(xr, all_42_2_79) = all_357_4_205 & aNaturalNumber0(all_42_2_79) = all_357_7_208 & aNaturalNumber0(xr) = all_357_8_209 & aNaturalNumber0(xp) = all_357_6_207 & ( ~ (all_357_2_203 = 0) | ~ (all_357_5_206 = 0) | ~ (all_357_6_207 = 0) | ~ (all_357_7_208 = 0) | ~ (all_357_8_209 = 0) | all_357_0_201 = 0 | all_357_1_202 = 0)
% 91.22/42.19 |
% 91.22/42.19 | Applying alpha-rule on (784) yields:
% 91.22/42.19 | (785) aNaturalNumber0(all_42_2_79) = all_357_7_208
% 91.22/42.19 | (786) aNaturalNumber0(xp) = all_357_6_207
% 91.22/42.19 | (787) isPrime0(xp) = all_357_5_206
% 91.22/42.19 | (788) iLess0(all_357_3_204, all_0_7_7) = all_357_2_203
% 91.22/42.19 | (789) doDivides0(xp, xr) = all_357_1_202
% 91.22/42.19 | (790) sdtpldt0(xr, all_42_2_79) = all_357_4_205
% 91.22/42.19 | (791) doDivides0(xp, all_42_2_79) = all_357_0_201
% 91.22/42.19 | (792) aNaturalNumber0(xr) = all_357_8_209
% 91.22/42.19 | (793) sdtpldt0(all_357_4_205, xp) = all_357_3_204
% 91.22/42.19 | (794) ~ (all_357_2_203 = 0) | ~ (all_357_5_206 = 0) | ~ (all_357_6_207 = 0) | ~ (all_357_7_208 = 0) | ~ (all_357_8_209 = 0) | all_357_0_201 = 0 | all_357_1_202 = 0
% 91.22/42.19 |
% 91.22/42.19 | Instantiating (639) with all_362_0_219, all_362_1_220, all_362_2_221, all_362_3_222, all_362_4_223, all_362_5_224, all_362_6_225, all_362_7_226, all_362_8_227 yields:
% 91.22/42.19 | (795) isPrime0(xp) = all_362_5_224 & doDivides0(xp, all_40_2_73) = all_362_0_219 & doDivides0(xp, xp) = all_362_1_220 & iLess0(all_362_3_222, all_0_7_7) = all_362_2_221 & sdtpldt0(all_362_4_223, xp) = all_362_3_222 & sdtpldt0(xp, all_40_2_73) = all_362_4_223 & aNaturalNumber0(all_40_2_73) = all_362_7_226 & aNaturalNumber0(xp) = all_362_6_225 & aNaturalNumber0(xp) = all_362_8_227 & ( ~ (all_362_2_221 = 0) | ~ (all_362_5_224 = 0) | ~ (all_362_6_225 = 0) | ~ (all_362_7_226 = 0) | ~ (all_362_8_227 = 0) | all_362_0_219 = 0 | all_362_1_220 = 0)
% 91.22/42.19 |
% 91.22/42.19 | Applying alpha-rule on (795) yields:
% 91.22/42.19 | (796) aNaturalNumber0(all_40_2_73) = all_362_7_226
% 91.22/42.19 | (797) ~ (all_362_2_221 = 0) | ~ (all_362_5_224 = 0) | ~ (all_362_6_225 = 0) | ~ (all_362_7_226 = 0) | ~ (all_362_8_227 = 0) | all_362_0_219 = 0 | all_362_1_220 = 0
% 91.22/42.19 | (798) iLess0(all_362_3_222, all_0_7_7) = all_362_2_221
% 91.22/42.19 | (799) sdtpldt0(all_362_4_223, xp) = all_362_3_222
% 91.22/42.19 | (800) sdtpldt0(xp, all_40_2_73) = all_362_4_223
% 91.22/42.19 | (801) doDivides0(xp, all_40_2_73) = all_362_0_219
% 91.22/42.19 | (802) isPrime0(xp) = all_362_5_224
% 91.22/42.19 | (803) aNaturalNumber0(xp) = all_362_6_225
% 91.22/42.19 | (804) doDivides0(xp, xp) = all_362_1_220
% 91.22/42.19 | (805) aNaturalNumber0(xp) = all_362_8_227
% 91.22/42.19 |
% 91.22/42.19 | Instantiating (638) with all_364_0_228, all_364_1_229, all_364_2_230, all_364_3_231, all_364_4_232, all_364_5_233, all_364_6_234, all_364_7_235, all_364_8_236 yields:
% 91.22/42.19 | (806) isPrime0(xr) = all_364_5_233 & doDivides0(xr, all_40_2_73) = all_364_0_228 & doDivides0(xr, xp) = all_364_1_229 & iLess0(all_364_3_231, all_0_7_7) = all_364_2_230 & sdtpldt0(all_364_4_232, xr) = all_364_3_231 & sdtpldt0(xp, all_40_2_73) = all_364_4_232 & aNaturalNumber0(all_40_2_73) = all_364_7_235 & aNaturalNumber0(xr) = all_364_6_234 & aNaturalNumber0(xp) = all_364_8_236 & ( ~ (all_364_2_230 = 0) | ~ (all_364_5_233 = 0) | ~ (all_364_6_234 = 0) | ~ (all_364_7_235 = 0) | ~ (all_364_8_236 = 0) | all_364_0_228 = 0 | all_364_1_229 = 0)
% 91.22/42.19 |
% 91.22/42.19 | Applying alpha-rule on (806) yields:
% 91.22/42.19 | (807) iLess0(all_364_3_231, all_0_7_7) = all_364_2_230
% 91.22/42.19 | (808) doDivides0(xr, all_40_2_73) = all_364_0_228
% 91.22/42.19 | (809) sdtpldt0(all_364_4_232, xr) = all_364_3_231
% 91.22/42.19 | (810) doDivides0(xr, xp) = all_364_1_229
% 91.22/42.19 | (811) ~ (all_364_2_230 = 0) | ~ (all_364_5_233 = 0) | ~ (all_364_6_234 = 0) | ~ (all_364_7_235 = 0) | ~ (all_364_8_236 = 0) | all_364_0_228 = 0 | all_364_1_229 = 0
% 91.22/42.19 | (812) sdtpldt0(xp, all_40_2_73) = all_364_4_232
% 91.22/42.19 | (813) aNaturalNumber0(xp) = all_364_8_236
% 91.22/42.19 | (814) isPrime0(xr) = all_364_5_233
% 91.22/42.19 | (815) aNaturalNumber0(all_40_2_73) = all_364_7_235
% 91.22/42.19 | (816) aNaturalNumber0(xr) = all_364_6_234
% 91.22/42.19 |
% 91.22/42.19 | Instantiating (654) with all_366_0_237, all_366_1_238, all_366_2_239 yields:
% 91.22/42.19 | (817) aNaturalNumber0(all_216_4_100) = all_366_0_237 & aNaturalNumber0(xk) = all_366_1_238 & aNaturalNumber0(xp) = all_366_2_239 & ( ~ (all_366_1_238 = 0) | ~ (all_366_2_239 = 0) | all_366_0_237 = 0)
% 91.22/42.19 |
% 91.22/42.19 | Applying alpha-rule on (817) yields:
% 91.22/42.19 | (818) aNaturalNumber0(all_216_4_100) = all_366_0_237
% 91.22/42.19 | (819) aNaturalNumber0(xk) = all_366_1_238
% 91.22/42.19 | (820) aNaturalNumber0(xp) = all_366_2_239
% 91.22/42.19 | (821) ~ (all_366_1_238 = 0) | ~ (all_366_2_239 = 0) | all_366_0_237 = 0
% 91.22/42.19 |
% 91.22/42.19 | Instantiating (649) with all_368_0_240, all_368_1_241, all_368_2_242, all_368_3_243, all_368_4_244 yields:
% 91.22/42.19 | (822) doDivides0(xr, all_33_2_49) = all_368_0_240 & doDivides0(xr, xp) = all_368_1_241 & aNaturalNumber0(all_33_2_49) = all_368_2_242 & aNaturalNumber0(xr) = all_368_4_244 & aNaturalNumber0(xp) = all_368_3_243 & ( ~ (all_368_1_241 = 0) | ~ (all_368_2_242 = 0) | ~ (all_368_3_243 = 0) | ~ (all_368_4_244 = 0) | all_368_0_240 = 0)
% 91.22/42.19 |
% 91.22/42.19 | Applying alpha-rule on (822) yields:
% 91.22/42.19 | (823) aNaturalNumber0(all_33_2_49) = all_368_2_242
% 91.22/42.19 | (824) doDivides0(xr, xp) = all_368_1_241
% 91.22/42.19 | (825) aNaturalNumber0(xr) = all_368_4_244
% 91.22/42.19 | (826) doDivides0(xr, all_33_2_49) = all_368_0_240
% 91.22/42.19 | (827) aNaturalNumber0(xp) = all_368_3_243
% 91.22/42.19 | (828) ~ (all_368_1_241 = 0) | ~ (all_368_2_242 = 0) | ~ (all_368_3_243 = 0) | ~ (all_368_4_244 = 0) | all_368_0_240 = 0
% 91.22/42.19 |
% 91.22/42.19 | Instantiating (653) with all_372_0_248, all_372_1_249, all_372_2_250 yields:
% 91.22/42.19 | (829) sdtpldt0(xk, xp) = all_372_0_248 & aNaturalNumber0(xk) = all_372_1_249 & aNaturalNumber0(xp) = all_372_2_250 & ( ~ (all_372_1_249 = 0) | ~ (all_372_2_250 = 0) | all_372_0_248 = all_216_4_100)
% 91.22/42.19 |
% 91.22/42.19 | Applying alpha-rule on (829) yields:
% 91.22/42.19 | (830) sdtpldt0(xk, xp) = all_372_0_248
% 91.22/42.19 | (831) aNaturalNumber0(xk) = all_372_1_249
% 91.22/42.19 | (832) aNaturalNumber0(xp) = all_372_2_250
% 91.22/42.19 | (833) ~ (all_372_1_249 = 0) | ~ (all_372_2_250 = 0) | all_372_0_248 = all_216_4_100
% 91.22/42.19 |
% 91.22/42.19 | Instantiating (652) with all_374_0_251, all_374_1_252, all_374_2_253, all_374_3_254, all_374_4_255 yields:
% 91.22/42.19 | (834) sdtpldt0(xk, xp) = all_374_1_252 & sdtpldt0(xp, all_374_1_252) = all_374_0_251 & aNaturalNumber0(xk) = all_374_3_254 & aNaturalNumber0(xp) = all_374_2_253 & aNaturalNumber0(xp) = all_374_4_255 & ( ~ (all_374_2_253 = 0) | ~ (all_374_3_254 = 0) | ~ (all_374_4_255 = 0) | all_374_0_251 = all_233_3_108)
% 91.22/42.20 |
% 91.22/42.20 | Applying alpha-rule on (834) yields:
% 91.22/42.20 | (835) aNaturalNumber0(xp) = all_374_2_253
% 91.22/42.20 | (836) aNaturalNumber0(xp) = all_374_4_255
% 91.22/42.20 | (837) ~ (all_374_2_253 = 0) | ~ (all_374_3_254 = 0) | ~ (all_374_4_255 = 0) | all_374_0_251 = all_233_3_108
% 91.22/42.20 | (838) sdtpldt0(xp, all_374_1_252) = all_374_0_251
% 91.22/42.20 | (839) sdtpldt0(xk, xp) = all_374_1_252
% 91.22/42.20 | (840) aNaturalNumber0(xk) = all_374_3_254
% 91.22/42.20 |
% 91.22/42.20 | Instantiating (647) with all_376_0_256, all_376_1_257, all_376_2_258 yields:
% 91.22/42.20 | (841) aNaturalNumber0(all_233_3_108) = all_376_0_256 & aNaturalNumber0(all_216_4_100) = all_376_2_258 & aNaturalNumber0(xp) = all_376_1_257 & ( ~ (all_376_1_257 = 0) | ~ (all_376_2_258 = 0) | all_376_0_256 = 0)
% 91.22/42.20 |
% 91.22/42.20 | Applying alpha-rule on (841) yields:
% 91.22/42.20 | (842) aNaturalNumber0(all_233_3_108) = all_376_0_256
% 91.22/42.20 | (843) aNaturalNumber0(all_216_4_100) = all_376_2_258
% 91.22/42.20 | (844) aNaturalNumber0(xp) = all_376_1_257
% 91.22/42.20 | (845) ~ (all_376_1_257 = 0) | ~ (all_376_2_258 = 0) | all_376_0_256 = 0
% 91.22/42.20 |
% 91.22/42.20 | Instantiating (646) with all_378_0_259, all_378_1_260, all_378_2_261 yields:
% 91.22/42.20 | (846) sdtpldt0(xp, all_216_4_100) = all_378_0_259 & aNaturalNumber0(all_216_4_100) = all_378_2_261 & aNaturalNumber0(xp) = all_378_1_260 & ( ~ (all_378_1_260 = 0) | ~ (all_378_2_261 = 0) | all_378_0_259 = all_233_3_108)
% 91.22/42.20 |
% 91.22/42.20 | Applying alpha-rule on (846) yields:
% 91.22/42.20 | (847) sdtpldt0(xp, all_216_4_100) = all_378_0_259
% 91.22/42.20 | (848) aNaturalNumber0(all_216_4_100) = all_378_2_261
% 91.22/42.20 | (849) aNaturalNumber0(xp) = all_378_1_260
% 91.22/42.20 | (850) ~ (all_378_1_260 = 0) | ~ (all_378_2_261 = 0) | all_378_0_259 = all_233_3_108
% 91.22/42.20 |
% 91.22/42.20 | Instantiating (648) with all_388_0_276, all_388_1_277, all_388_2_278, all_388_3_279, all_388_4_280 yields:
% 91.22/42.20 | (851) sdtpldt0(xm, xr) = all_388_1_277 & sdtpldt0(xn, all_388_1_277) = all_388_0_276 & aNaturalNumber0(xr) = all_388_2_278 & aNaturalNumber0(xm) = all_388_3_279 & aNaturalNumber0(xn) = all_388_4_280 & ( ~ (all_388_2_278 = 0) | ~ (all_388_3_279 = 0) | ~ (all_388_4_280 = 0) | all_388_0_276 = all_36_3_62)
% 91.22/42.20 |
% 91.22/42.20 | Applying alpha-rule on (851) yields:
% 91.22/42.20 | (852) aNaturalNumber0(xn) = all_388_4_280
% 91.22/42.20 | (853) sdtpldt0(xn, all_388_1_277) = all_388_0_276
% 91.22/42.20 | (854) aNaturalNumber0(xm) = all_388_3_279
% 91.22/42.20 | (855) aNaturalNumber0(xr) = all_388_2_278
% 91.22/42.20 | (856) sdtpldt0(xm, xr) = all_388_1_277
% 91.22/42.20 | (857) ~ (all_388_2_278 = 0) | ~ (all_388_3_279 = 0) | ~ (all_388_4_280 = 0) | all_388_0_276 = all_36_3_62
% 91.22/42.20 |
% 91.22/42.20 | Instantiating (651) with all_392_0_284, all_392_1_285, all_392_2_286, all_392_3_287, all_392_4_288 yields:
% 91.22/42.20 | (858) sdtpldt0(xk, xr) = all_392_1_285 & sdtpldt0(xp, all_392_1_285) = all_392_0_284 & aNaturalNumber0(xr) = all_392_2_286 & aNaturalNumber0(xk) = all_392_3_287 & aNaturalNumber0(xp) = all_392_4_288 & ( ~ (all_392_2_286 = 0) | ~ (all_392_3_287 = 0) | ~ (all_392_4_288 = 0) | all_392_0_284 = all_216_3_99)
% 91.22/42.20 |
% 91.22/42.20 | Applying alpha-rule on (858) yields:
% 91.22/42.20 | (859) ~ (all_392_2_286 = 0) | ~ (all_392_3_287 = 0) | ~ (all_392_4_288 = 0) | all_392_0_284 = all_216_3_99
% 91.22/42.20 | (860) sdtpldt0(xp, all_392_1_285) = all_392_0_284
% 91.22/42.20 | (861) sdtpldt0(xk, xr) = all_392_1_285
% 91.22/42.20 | (862) aNaturalNumber0(xp) = all_392_4_288
% 91.22/42.20 | (863) aNaturalNumber0(xk) = all_392_3_287
% 91.22/42.20 | (864) aNaturalNumber0(xr) = all_392_2_286
% 91.22/42.20 |
% 91.22/42.20 | Instantiating (633) with all_394_0_289, all_394_1_290, all_394_2_291, all_394_3_292, all_394_4_293 yields:
% 91.22/42.20 | (865) sdtasdt0(all_41_2_76, xp) = all_394_1_290 & sdtasdt0(xr, all_394_1_290) = all_394_0_289 & aNaturalNumber0(all_41_2_76) = all_394_3_292 & aNaturalNumber0(xr) = all_394_4_293 & aNaturalNumber0(xp) = all_394_2_291 & ( ~ (all_394_2_291 = 0) | ~ (all_394_3_292 = 0) | ~ (all_394_4_293 = 0) | all_394_0_289 = all_0_6_6)
% 91.22/42.20 |
% 91.22/42.20 | Applying alpha-rule on (865) yields:
% 91.22/42.20 | (866) aNaturalNumber0(xp) = all_394_2_291
% 91.22/42.20 | (867) ~ (all_394_2_291 = 0) | ~ (all_394_3_292 = 0) | ~ (all_394_4_293 = 0) | all_394_0_289 = all_0_6_6
% 91.22/42.20 | (868) aNaturalNumber0(xr) = all_394_4_293
% 91.22/42.20 | (869) sdtasdt0(xr, all_394_1_290) = all_394_0_289
% 91.22/42.20 | (870) aNaturalNumber0(all_41_2_76) = all_394_3_292
% 91.22/42.20 | (871) sdtasdt0(all_41_2_76, xp) = all_394_1_290
% 91.22/42.20 |
% 91.22/42.20 | Instantiating (635) with all_400_0_306, all_400_1_307, all_400_2_308, all_400_3_309, all_400_4_310, all_400_5_311, all_400_6_312, all_400_7_313, all_400_8_314 yields:
% 91.22/42.20 | (872) isPrime0(xp) = all_400_5_311 & doDivides0(xp, xk) = all_400_1_307 & doDivides0(xp, xp) = all_400_0_306 & iLess0(all_400_3_309, all_0_7_7) = all_400_2_308 & sdtpldt0(all_400_4_310, xp) = all_400_3_309 & sdtpldt0(xk, xp) = all_400_4_310 & aNaturalNumber0(xk) = all_400_8_314 & aNaturalNumber0(xp) = all_400_6_312 & aNaturalNumber0(xp) = all_400_7_313 & ( ~ (all_400_2_308 = 0) | ~ (all_400_5_311 = 0) | ~ (all_400_6_312 = 0) | ~ (all_400_7_313 = 0) | ~ (all_400_8_314 = 0) | all_400_0_306 = 0 | all_400_1_307 = 0)
% 91.22/42.20 |
% 91.22/42.20 | Applying alpha-rule on (872) yields:
% 91.22/42.20 | (873) aNaturalNumber0(xp) = all_400_6_312
% 91.22/42.20 | (874) aNaturalNumber0(xp) = all_400_7_313
% 91.22/42.20 | (875) sdtpldt0(xk, xp) = all_400_4_310
% 91.22/42.20 | (876) sdtpldt0(all_400_4_310, xp) = all_400_3_309
% 91.22/42.20 | (877) doDivides0(xp, xk) = all_400_1_307
% 91.22/42.20 | (878) doDivides0(xp, xp) = all_400_0_306
% 91.22/42.20 | (879) aNaturalNumber0(xk) = all_400_8_314
% 91.22/42.20 | (880) isPrime0(xp) = all_400_5_311
% 91.22/42.20 | (881) iLess0(all_400_3_309, all_0_7_7) = all_400_2_308
% 91.22/42.20 | (882) ~ (all_400_2_308 = 0) | ~ (all_400_5_311 = 0) | ~ (all_400_6_312 = 0) | ~ (all_400_7_313 = 0) | ~ (all_400_8_314 = 0) | all_400_0_306 = 0 | all_400_1_307 = 0
% 91.22/42.20 |
% 91.22/42.20 | Instantiating (634) with all_403_0_318, all_403_1_319, all_403_2_320, all_403_3_321, all_403_4_322, all_403_5_323, all_403_6_324, all_403_7_325, all_403_8_326 yields:
% 91.22/42.20 | (883) isPrime0(xr) = all_403_5_323 & doDivides0(xr, xk) = all_403_1_319 & doDivides0(xr, xp) = all_403_0_318 & iLess0(all_403_3_321, all_0_7_7) = all_403_2_320 & sdtpldt0(all_403_4_322, xr) = all_403_3_321 & sdtpldt0(xk, xp) = all_403_4_322 & aNaturalNumber0(xr) = all_403_6_324 & aNaturalNumber0(xk) = all_403_8_326 & aNaturalNumber0(xp) = all_403_7_325 & ( ~ (all_403_2_320 = 0) | ~ (all_403_5_323 = 0) | ~ (all_403_6_324 = 0) | ~ (all_403_7_325 = 0) | ~ (all_403_8_326 = 0) | all_403_0_318 = 0 | all_403_1_319 = 0)
% 91.22/42.20 |
% 91.22/42.20 | Applying alpha-rule on (883) yields:
% 91.22/42.20 | (884) doDivides0(xr, xk) = all_403_1_319
% 91.22/42.20 | (885) isPrime0(xr) = all_403_5_323
% 91.22/42.20 | (886) aNaturalNumber0(xr) = all_403_6_324
% 91.22/42.20 | (887) sdtpldt0(all_403_4_322, xr) = all_403_3_321
% 91.22/42.20 | (888) aNaturalNumber0(xk) = all_403_8_326
% 91.22/42.20 | (889) ~ (all_403_2_320 = 0) | ~ (all_403_5_323 = 0) | ~ (all_403_6_324 = 0) | ~ (all_403_7_325 = 0) | ~ (all_403_8_326 = 0) | all_403_0_318 = 0 | all_403_1_319 = 0
% 91.22/42.20 | (890) doDivides0(xr, xp) = all_403_0_318
% 91.22/42.20 | (891) sdtpldt0(xk, xp) = all_403_4_322
% 91.22/42.20 | (892) aNaturalNumber0(xp) = all_403_7_325
% 91.22/42.20 | (893) iLess0(all_403_3_321, all_0_7_7) = all_403_2_320
% 91.22/42.20 |
% 91.22/42.20 | Instantiating (668) with all_408_0_339, all_408_1_340, all_408_2_341, all_408_3_342, all_408_4_343 yields:
% 91.22/42.20 | (894) sdtpldt0(all_21_2_28, xk) = all_408_1_340 & sdtpldt0(xn, all_408_1_340) = all_408_0_339 & aNaturalNumber0(all_21_2_28) = all_408_3_342 & aNaturalNumber0(xk) = all_408_2_341 & aNaturalNumber0(xn) = all_408_4_343 & ( ~ (all_408_2_341 = 0) | ~ (all_408_3_342 = 0) | ~ (all_408_4_343 = 0) | all_408_0_339 = all_216_4_100)
% 91.22/42.20 |
% 91.22/42.20 | Applying alpha-rule on (894) yields:
% 91.22/42.20 | (895) aNaturalNumber0(all_21_2_28) = all_408_3_342
% 91.22/42.20 | (896) aNaturalNumber0(xn) = all_408_4_343
% 91.22/42.20 | (897) sdtpldt0(xn, all_408_1_340) = all_408_0_339
% 91.22/42.20 | (898) aNaturalNumber0(xk) = all_408_2_341
% 91.22/42.20 | (899) ~ (all_408_2_341 = 0) | ~ (all_408_3_342 = 0) | ~ (all_408_4_343 = 0) | all_408_0_339 = all_216_4_100
% 91.22/42.21 | (900) sdtpldt0(all_21_2_28, xk) = all_408_1_340
% 91.22/42.21 |
% 91.22/42.21 | Instantiating (667) with all_410_0_344, all_410_1_345, all_410_2_346, all_410_3_347, all_410_4_348 yields:
% 91.22/42.21 | (901) sdtpldt0(all_21_2_28, all_0_8_8) = all_410_1_345 & sdtpldt0(xn, all_410_1_345) = all_410_0_344 & aNaturalNumber0(all_21_2_28) = all_410_3_347 & aNaturalNumber0(all_0_8_8) = all_410_2_346 & aNaturalNumber0(xn) = all_410_4_348 & ( ~ (all_410_2_346 = 0) | ~ (all_410_3_347 = 0) | ~ (all_410_4_348 = 0) | all_410_0_344 = all_0_7_7)
% 91.22/42.21 |
% 91.22/42.21 | Applying alpha-rule on (901) yields:
% 91.22/42.21 | (902) aNaturalNumber0(all_21_2_28) = all_410_3_347
% 91.22/42.21 | (903) aNaturalNumber0(xn) = all_410_4_348
% 91.22/42.21 | (904) ~ (all_410_2_346 = 0) | ~ (all_410_3_347 = 0) | ~ (all_410_4_348 = 0) | all_410_0_344 = all_0_7_7
% 91.22/42.21 | (905) sdtpldt0(all_21_2_28, all_0_8_8) = all_410_1_345
% 91.22/42.21 | (906) aNaturalNumber0(all_0_8_8) = all_410_2_346
% 91.22/42.21 | (907) sdtpldt0(xn, all_410_1_345) = all_410_0_344
% 91.22/42.21 |
% 91.22/42.21 | Instantiating (666) with all_412_0_349, all_412_1_350, all_412_2_351, all_412_3_352, all_412_4_353 yields:
% 91.22/42.21 | (908) sdtpldt0(all_21_2_28, all_33_2_49) = all_412_1_350 & sdtpldt0(xn, all_412_1_350) = all_412_0_349 & aNaturalNumber0(all_33_2_49) = all_412_2_351 & aNaturalNumber0(all_21_2_28) = all_412_3_352 & aNaturalNumber0(xn) = all_412_4_353 & ( ~ (all_412_2_351 = 0) | ~ (all_412_3_352 = 0) | ~ (all_412_4_353 = 0) | all_412_0_349 = xk)
% 91.22/42.21 |
% 91.22/42.21 | Applying alpha-rule on (908) yields:
% 91.22/42.21 | (909) aNaturalNumber0(xn) = all_412_4_353
% 91.22/42.21 | (910) sdtpldt0(xn, all_412_1_350) = all_412_0_349
% 91.22/42.21 | (911) sdtpldt0(all_21_2_28, all_33_2_49) = all_412_1_350
% 91.22/42.21 | (912) ~ (all_412_2_351 = 0) | ~ (all_412_3_352 = 0) | ~ (all_412_4_353 = 0) | all_412_0_349 = xk
% 91.22/42.21 | (913) aNaturalNumber0(all_33_2_49) = all_412_2_351
% 91.22/42.21 | (914) aNaturalNumber0(all_21_2_28) = all_412_3_352
% 91.22/42.21 |
% 91.22/42.21 +-Applying beta-rule and splitting (628), into two cases.
% 91.22/42.21 |-Branch one:
% 91.22/42.21 | (220) all_0_4_4 = 0
% 91.22/42.21 |
% 91.22/42.21 | Equations (220) can reduce 74 to:
% 91.22/42.21 | (216) $false
% 91.22/42.21 |
% 91.22/42.21 |-The branch is then unsatisfiable
% 91.22/42.21 |-Branch two:
% 91.22/42.21 | (74) ~ (all_0_4_4 = 0)
% 91.22/42.21 | (918) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtlseqdt0(all_0_6_6, xm) = v3 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 91.22/42.21 |
% 91.22/42.21 | Instantiating (918) with all_418_0_354, all_418_1_355, all_418_2_356, all_418_3_357 yields:
% 91.22/42.21 | (919) sdtlseqdt0(all_0_6_6, xm) = all_418_0_354 & aNaturalNumber0(all_0_6_6) = all_418_2_356 & aNaturalNumber0(xp) = all_418_3_357 & aNaturalNumber0(xm) = all_418_1_355 & ( ~ (all_418_0_354 = 0) | ~ (all_418_1_355 = 0) | ~ (all_418_2_356 = 0) | ~ (all_418_3_357 = 0))
% 91.22/42.21 |
% 91.22/42.21 | Applying alpha-rule on (919) yields:
% 91.22/42.21 | (920) aNaturalNumber0(xp) = all_418_3_357
% 91.22/42.21 | (921) aNaturalNumber0(xm) = all_418_1_355
% 91.22/42.21 | (922) sdtlseqdt0(all_0_6_6, xm) = all_418_0_354
% 91.22/42.21 | (923) aNaturalNumber0(all_0_6_6) = all_418_2_356
% 91.22/42.21 | (924) ~ (all_418_0_354 = 0) | ~ (all_418_1_355 = 0) | ~ (all_418_2_356 = 0) | ~ (all_418_3_357 = 0)
% 91.22/42.21 |
% 91.22/42.21 +-Applying beta-rule and splitting (629), into two cases.
% 91.22/42.21 |-Branch one:
% 91.22/42.21 | (230) all_0_5_5 = 0
% 91.22/42.21 |
% 91.22/42.21 | Equations (230) can reduce 49 to:
% 91.22/42.21 | (216) $false
% 91.22/42.21 |
% 91.22/42.21 |-The branch is then unsatisfiable
% 91.22/42.21 |-Branch two:
% 91.22/42.21 | (49) ~ (all_0_5_5 = 0)
% 91.22/42.21 | (928) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtlseqdt0(all_0_6_6, xn) = v3 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 91.22/42.21 |
% 91.22/42.21 | Instantiating (928) with all_423_0_358, all_423_1_359, all_423_2_360, all_423_3_361 yields:
% 91.22/42.21 | (929) sdtlseqdt0(all_0_6_6, xn) = all_423_0_358 & aNaturalNumber0(all_0_6_6) = all_423_2_360 & aNaturalNumber0(xp) = all_423_3_361 & aNaturalNumber0(xn) = all_423_1_359 & ( ~ (all_423_0_358 = 0) | ~ (all_423_1_359 = 0) | ~ (all_423_2_360 = 0) | ~ (all_423_3_361 = 0))
% 91.22/42.21 |
% 91.22/42.21 | Applying alpha-rule on (929) yields:
% 91.22/42.21 | (930) aNaturalNumber0(all_0_6_6) = all_423_2_360
% 91.22/42.21 | (931) aNaturalNumber0(xp) = all_423_3_361
% 91.22/42.21 | (932) ~ (all_423_0_358 = 0) | ~ (all_423_1_359 = 0) | ~ (all_423_2_360 = 0) | ~ (all_423_3_361 = 0)
% 91.22/42.21 | (933) sdtlseqdt0(all_0_6_6, xn) = all_423_0_358
% 91.22/42.21 | (934) aNaturalNumber0(xn) = all_423_1_359
% 91.22/42.21 |
% 91.22/42.21 +-Applying beta-rule and splitting (625), into two cases.
% 91.22/42.21 |-Branch one:
% 91.22/42.21 | (608) xn = sz00
% 91.22/42.21 |
% 91.22/42.21 | Equations (608) can reduce 596 to:
% 91.22/42.21 | (216) $false
% 91.22/42.21 |
% 91.22/42.21 |-The branch is then unsatisfiable
% 91.22/42.21 |-Branch two:
% 91.22/42.21 | (596) ~ (xn = sz00)
% 91.22/42.21 | (938) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_310_0_120, xn) = v2 & aNaturalNumber0(all_310_0_120) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 91.22/42.21 |
% 91.22/42.21 | Instantiating (938) with all_428_0_362, all_428_1_363, all_428_2_364 yields:
% 91.22/42.21 | (939) sdtlseqdt0(all_310_0_120, xn) = all_428_0_362 & aNaturalNumber0(all_310_0_120) = all_428_2_364 & aNaturalNumber0(xn) = all_428_1_363 & ( ~ (all_428_1_363 = 0) | ~ (all_428_2_364 = 0) | all_428_0_362 = 0)
% 91.22/42.21 |
% 91.22/42.21 | Applying alpha-rule on (939) yields:
% 91.22/42.21 | (940) sdtlseqdt0(all_310_0_120, xn) = all_428_0_362
% 91.22/42.21 | (941) aNaturalNumber0(all_310_0_120) = all_428_2_364
% 91.22/42.21 | (942) aNaturalNumber0(xn) = all_428_1_363
% 91.22/42.21 | (943) ~ (all_428_1_363 = 0) | ~ (all_428_2_364 = 0) | all_428_0_362 = 0
% 91.22/42.21 |
% 91.22/42.21 +-Applying beta-rule and splitting (627), into two cases.
% 91.22/42.21 |-Branch one:
% 91.22/42.21 | (215) xp = sz00
% 91.22/42.21 |
% 91.22/42.21 | Equations (215) can reduce 90 to:
% 91.22/42.21 | (216) $false
% 91.22/42.21 |
% 91.22/42.21 |-The branch is then unsatisfiable
% 91.22/42.21 |-Branch two:
% 91.22/42.21 | (90) ~ (xp = sz00)
% 91.22/42.21 | (947) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_70_0_94, xp) = v2 & aNaturalNumber0(all_70_0_94) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 91.22/42.21 |
% 91.22/42.21 | Instantiating (947) with all_438_0_368, all_438_1_369, all_438_2_370 yields:
% 91.22/42.21 | (948) sdtlseqdt0(all_70_0_94, xp) = all_438_0_368 & aNaturalNumber0(all_70_0_94) = all_438_2_370 & aNaturalNumber0(xp) = all_438_1_369 & ( ~ (all_438_1_369 = 0) | ~ (all_438_2_370 = 0) | all_438_0_368 = 0)
% 91.22/42.21 |
% 91.22/42.21 | Applying alpha-rule on (948) yields:
% 91.22/42.21 | (949) sdtlseqdt0(all_70_0_94, xp) = all_438_0_368
% 91.22/42.21 | (950) aNaturalNumber0(all_70_0_94) = all_438_2_370
% 91.22/42.21 | (951) aNaturalNumber0(xp) = all_438_1_369
% 91.22/42.21 | (952) ~ (all_438_1_369 = 0) | ~ (all_438_2_370 = 0) | all_438_0_368 = 0
% 91.22/42.21 |
% 91.22/42.21 +-Applying beta-rule and splitting (630), into two cases.
% 91.22/42.21 |-Branch one:
% 91.22/42.21 | (953) all_53_0_86 = 0
% 91.22/42.21 |
% 91.22/42.21 | Equations (953) can reduce 512 to:
% 91.22/42.21 | (216) $false
% 91.22/42.21 |
% 91.22/42.21 |-The branch is then unsatisfiable
% 91.22/42.21 |-Branch two:
% 91.22/42.21 | (512) ~ (all_53_0_86 = 0)
% 91.22/42.21 | (956) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xm, xk) = v2 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xk = xm))))
% 91.22/42.21 |
% 91.22/42.21 | Instantiating (956) with all_443_0_371, all_443_1_372, all_443_2_373 yields:
% 91.22/42.21 | (957) sdtlseqdt0(xm, xk) = all_443_0_371 & aNaturalNumber0(xk) = all_443_2_373 & aNaturalNumber0(xm) = all_443_1_372 & ( ~ (all_443_1_372 = 0) | ~ (all_443_2_373 = 0) | (all_443_0_371 = 0 & ~ (xk = xm)))
% 91.22/42.21 |
% 91.22/42.21 | Applying alpha-rule on (957) yields:
% 91.22/42.21 | (958) sdtlseqdt0(xm, xk) = all_443_0_371
% 91.22/42.21 | (959) aNaturalNumber0(xk) = all_443_2_373
% 91.22/42.21 | (960) aNaturalNumber0(xm) = all_443_1_372
% 91.22/42.21 | (961) ~ (all_443_1_372 = 0) | ~ (all_443_2_373 = 0) | (all_443_0_371 = 0 & ~ (xk = xm))
% 91.22/42.21 |
% 91.22/42.21 +-Applying beta-rule and splitting (631), into two cases.
% 91.22/42.21 |-Branch one:
% 91.22/42.21 | (962) all_58_0_90 = 0
% 91.22/42.21 |
% 91.22/42.21 | Equations (962) can reduce 513 to:
% 91.22/42.21 | (216) $false
% 91.22/42.21 |
% 91.22/42.21 |-The branch is then unsatisfiable
% 91.22/42.21 |-Branch two:
% 91.22/42.21 | (513) ~ (all_58_0_90 = 0)
% 91.22/42.21 | (965) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xn, xk) = v2 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xk = xn))))
% 91.22/42.21 |
% 91.22/42.21 | Instantiating (965) with all_448_0_374, all_448_1_375, all_448_2_376 yields:
% 91.22/42.21 | (966) sdtlseqdt0(xn, xk) = all_448_0_374 & aNaturalNumber0(xk) = all_448_2_376 & aNaturalNumber0(xn) = all_448_1_375 & ( ~ (all_448_1_375 = 0) | ~ (all_448_2_376 = 0) | (all_448_0_374 = 0 & ~ (xk = xn)))
% 91.22/42.21 |
% 91.22/42.21 | Applying alpha-rule on (966) yields:
% 91.22/42.21 | (967) sdtlseqdt0(xn, xk) = all_448_0_374
% 91.22/42.21 | (968) aNaturalNumber0(xk) = all_448_2_376
% 91.22/42.21 | (969) aNaturalNumber0(xn) = all_448_1_375
% 91.22/42.21 | (970) ~ (all_448_1_375 = 0) | ~ (all_448_2_376 = 0) | (all_448_0_374 = 0 & ~ (xk = xn))
% 91.22/42.21 |
% 91.22/42.21 +-Applying beta-rule and splitting (672), into two cases.
% 91.22/42.21 |-Branch one:
% 91.22/42.21 | (971) all_70_0_94 = sz00
% 91.22/42.21 |
% 91.22/42.21 | Equations (971) can reduce 253 to:
% 91.22/42.21 | (216) $false
% 91.22/42.21 |
% 91.22/42.21 |-The branch is then unsatisfiable
% 91.22/42.21 |-Branch two:
% 91.22/42.21 | (253) ~ (all_70_0_94 = sz00)
% 91.22/42.21 | (974) all_70_0_94 = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_70_0_94) = 0 & aNaturalNumber0(v0) = 0)
% 91.22/42.21 |
% 91.22/42.21 +-Applying beta-rule and splitting (974), into two cases.
% 91.22/42.21 |-Branch one:
% 91.22/42.21 | (975) all_70_0_94 = sz10
% 91.22/42.21 |
% 91.22/42.21 | Equations (975) can reduce 252 to:
% 91.22/42.21 | (216) $false
% 91.22/42.21 |
% 91.22/42.21 |-The branch is then unsatisfiable
% 91.22/42.21 |-Branch two:
% 91.22/42.21 | (252) ~ (all_70_0_94 = sz10)
% 91.22/42.21 | (978) ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, all_70_0_94) = 0 & aNaturalNumber0(v0) = 0)
% 91.22/42.21 |
% 91.22/42.21 | Instantiating formula (55) with all_70_0_94, all_438_2_370, 0 and discharging atoms aNaturalNumber0(all_70_0_94) = all_438_2_370, aNaturalNumber0(all_70_0_94) = 0, yields:
% 91.22/42.21 | (979) all_438_2_370 = 0
% 91.22/42.21 |
% 91.22/42.21 | Instantiating formula (55) with all_70_0_94, all_329_4_139, all_438_2_370 and discharging atoms aNaturalNumber0(all_70_0_94) = all_438_2_370, aNaturalNumber0(all_70_0_94) = all_329_4_139, yields:
% 91.22/42.21 | (980) all_438_2_370 = all_329_4_139
% 91.22/42.21 |
% 91.22/42.21 | Instantiating formula (55) with all_70_0_94, all_325_4_131, all_438_2_370 and discharging atoms aNaturalNumber0(all_70_0_94) = all_438_2_370, aNaturalNumber0(all_70_0_94) = all_325_4_131, yields:
% 91.22/42.21 | (981) all_438_2_370 = all_325_4_131
% 91.22/42.21 |
% 91.22/42.21 | Instantiating formula (55) with all_40_2_73, all_364_7_235, 0 and discharging atoms aNaturalNumber0(all_40_2_73) = all_364_7_235, aNaturalNumber0(all_40_2_73) = 0, yields:
% 91.22/42.21 | (982) all_364_7_235 = 0
% 91.22/42.21 |
% 91.22/42.21 | Instantiating formula (55) with all_40_2_73, all_362_7_226, all_364_7_235 and discharging atoms aNaturalNumber0(all_40_2_73) = all_364_7_235, aNaturalNumber0(all_40_2_73) = all_362_7_226, yields:
% 91.22/42.21 | (983) all_364_7_235 = all_362_7_226
% 91.22/42.21 |
% 91.22/42.21 | Instantiating formula (55) with all_40_2_73, all_349_1_188, all_364_7_235 and discharging atoms aNaturalNumber0(all_40_2_73) = all_364_7_235, aNaturalNumber0(all_40_2_73) = all_349_1_188, yields:
% 91.22/42.21 | (984) all_364_7_235 = all_349_1_188
% 91.22/42.21 |
% 91.22/42.21 | Instantiating formula (55) with xk, all_443_2_373, all_448_2_376 and discharging atoms aNaturalNumber0(xk) = all_448_2_376, aNaturalNumber0(xk) = all_443_2_373, yields:
% 91.22/42.21 | (985) all_448_2_376 = all_443_2_373
% 91.22/42.21 |
% 91.22/42.21 | Instantiating formula (55) with xk, all_408_2_341, all_443_2_373 and discharging atoms aNaturalNumber0(xk) = all_443_2_373, aNaturalNumber0(xk) = all_408_2_341, yields:
% 91.22/42.21 | (986) all_443_2_373 = all_408_2_341
% 91.22/42.21 |
% 91.22/42.21 | Instantiating formula (55) with xk, all_403_8_326, all_448_2_376 and discharging atoms aNaturalNumber0(xk) = all_448_2_376, aNaturalNumber0(xk) = all_403_8_326, yields:
% 91.22/42.21 | (987) all_448_2_376 = all_403_8_326
% 91.22/42.21 |
% 91.22/42.21 | Instantiating formula (55) with xk, all_400_8_314, all_408_2_341 and discharging atoms aNaturalNumber0(xk) = all_408_2_341, aNaturalNumber0(xk) = all_400_8_314, yields:
% 91.22/42.21 | (988) all_408_2_341 = all_400_8_314
% 91.22/42.21 |
% 91.22/42.21 | Instantiating formula (55) with xk, all_392_3_287, all_408_2_341 and discharging atoms aNaturalNumber0(xk) = all_408_2_341, aNaturalNumber0(xk) = all_392_3_287, yields:
% 91.22/42.21 | (989) all_408_2_341 = all_392_3_287
% 91.22/42.21 |
% 91.22/42.21 | Instantiating formula (55) with xk, all_374_3_254, 0 and discharging atoms aNaturalNumber0(xk) = all_374_3_254, aNaturalNumber0(xk) = 0, yields:
% 91.22/42.21 | (990) all_374_3_254 = 0
% 91.22/42.21 |
% 91.22/42.21 | Instantiating formula (55) with xk, all_374_3_254, all_408_2_341 and discharging atoms aNaturalNumber0(xk) = all_408_2_341, aNaturalNumber0(xk) = all_374_3_254, yields:
% 91.22/42.21 | (991) all_408_2_341 = all_374_3_254
% 91.22/42.21 |
% 91.22/42.21 | Instantiating formula (55) with xk, all_372_1_249, all_408_2_341 and discharging atoms aNaturalNumber0(xk) = all_408_2_341, aNaturalNumber0(xk) = all_372_1_249, yields:
% 91.22/42.21 | (992) all_408_2_341 = all_372_1_249
% 91.22/42.21 |
% 91.22/42.21 | Instantiating formula (55) with xk, all_366_1_238, all_392_3_287 and discharging atoms aNaturalNumber0(xk) = all_392_3_287, aNaturalNumber0(xk) = all_366_1_238, yields:
% 91.22/42.21 | (993) all_392_3_287 = all_366_1_238
% 91.22/42.21 |
% 91.22/42.21 | Instantiating formula (55) with xk, all_341_2_161, all_408_2_341 and discharging atoms aNaturalNumber0(xk) = all_408_2_341, aNaturalNumber0(xk) = all_341_2_161, yields:
% 91.22/42.21 | (994) all_408_2_341 = all_341_2_161
% 91.22/42.21 |
% 91.22/42.21 | Instantiating formula (55) with xp, all_418_3_357, all_423_3_361 and discharging atoms aNaturalNumber0(xp) = all_423_3_361, aNaturalNumber0(xp) = all_418_3_357, yields:
% 91.22/42.22 | (995) all_423_3_361 = all_418_3_357
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_403_7_325, all_418_3_357 and discharging atoms aNaturalNumber0(xp) = all_418_3_357, aNaturalNumber0(xp) = all_403_7_325, yields:
% 91.22/42.22 | (996) all_418_3_357 = all_403_7_325
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_400_7_313, 0 and discharging atoms aNaturalNumber0(xp) = all_400_7_313, aNaturalNumber0(xp) = 0, yields:
% 91.22/42.22 | (997) all_400_7_313 = 0
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_394_2_291, all_403_7_325 and discharging atoms aNaturalNumber0(xp) = all_403_7_325, aNaturalNumber0(xp) = all_394_2_291, yields:
% 91.22/42.22 | (998) all_403_7_325 = all_394_2_291
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_392_4_288, all_394_2_291 and discharging atoms aNaturalNumber0(xp) = all_394_2_291, aNaturalNumber0(xp) = all_392_4_288, yields:
% 91.22/42.22 | (999) all_394_2_291 = all_392_4_288
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_378_1_260, all_392_4_288 and discharging atoms aNaturalNumber0(xp) = all_392_4_288, aNaturalNumber0(xp) = all_378_1_260, yields:
% 91.22/42.22 | (1000) all_392_4_288 = all_378_1_260
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_376_1_257, all_378_1_260 and discharging atoms aNaturalNumber0(xp) = all_378_1_260, aNaturalNumber0(xp) = all_376_1_257, yields:
% 91.22/42.22 | (1001) all_378_1_260 = all_376_1_257
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_374_2_253, all_438_1_369 and discharging atoms aNaturalNumber0(xp) = all_438_1_369, aNaturalNumber0(xp) = all_374_2_253, yields:
% 91.22/42.22 | (1002) all_438_1_369 = all_374_2_253
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_374_2_253, all_376_1_257 and discharging atoms aNaturalNumber0(xp) = all_376_1_257, aNaturalNumber0(xp) = all_374_2_253, yields:
% 91.22/42.22 | (1003) all_376_1_257 = all_374_2_253
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_374_4_255, all_438_1_369 and discharging atoms aNaturalNumber0(xp) = all_438_1_369, aNaturalNumber0(xp) = all_374_4_255, yields:
% 91.22/42.22 | (1004) all_438_1_369 = all_374_4_255
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_372_2_250, all_438_1_369 and discharging atoms aNaturalNumber0(xp) = all_438_1_369, aNaturalNumber0(xp) = all_372_2_250, yields:
% 91.22/42.22 | (1005) all_438_1_369 = all_372_2_250
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_368_3_243, all_438_1_369 and discharging atoms aNaturalNumber0(xp) = all_438_1_369, aNaturalNumber0(xp) = all_368_3_243, yields:
% 91.22/42.22 | (1006) all_438_1_369 = all_368_3_243
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_366_2_239, all_368_3_243 and discharging atoms aNaturalNumber0(xp) = all_368_3_243, aNaturalNumber0(xp) = all_366_2_239, yields:
% 91.22/42.22 | (1007) all_368_3_243 = all_366_2_239
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_364_8_236, all_366_2_239 and discharging atoms aNaturalNumber0(xp) = all_366_2_239, aNaturalNumber0(xp) = all_364_8_236, yields:
% 91.22/42.22 | (1008) all_366_2_239 = all_364_8_236
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_362_6_225, all_400_6_312 and discharging atoms aNaturalNumber0(xp) = all_400_6_312, aNaturalNumber0(xp) = all_362_6_225, yields:
% 91.22/42.22 | (1009) all_400_6_312 = all_362_6_225
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_362_6_225, all_364_8_236 and discharging atoms aNaturalNumber0(xp) = all_364_8_236, aNaturalNumber0(xp) = all_362_6_225, yields:
% 91.22/42.22 | (1010) all_364_8_236 = all_362_6_225
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_362_8_227, all_423_3_361 and discharging atoms aNaturalNumber0(xp) = all_423_3_361, aNaturalNumber0(xp) = all_362_8_227, yields:
% 91.22/42.22 | (1011) all_423_3_361 = all_362_8_227
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_357_6_207, all_400_7_313 and discharging atoms aNaturalNumber0(xp) = all_400_7_313, aNaturalNumber0(xp) = all_357_6_207, yields:
% 91.22/42.22 | (1012) all_400_7_313 = all_357_6_207
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_349_2_189, all_400_6_312 and discharging atoms aNaturalNumber0(xp) = all_400_6_312, aNaturalNumber0(xp) = all_349_2_189, yields:
% 91.22/42.22 | (1013) all_400_6_312 = all_349_2_189
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_345_6_175, all_364_8_236 and discharging atoms aNaturalNumber0(xp) = all_364_8_236, aNaturalNumber0(xp) = all_345_6_175, yields:
% 91.22/42.22 | (1014) all_364_8_236 = all_345_6_175
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_339_1_157, all_364_8_236 and discharging atoms aNaturalNumber0(xp) = all_364_8_236, aNaturalNumber0(xp) = all_339_1_157, yields:
% 91.22/42.22 | (1015) all_364_8_236 = all_339_1_157
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_337_1_154, all_339_1_157 and discharging atoms aNaturalNumber0(xp) = all_339_1_157, aNaturalNumber0(xp) = all_337_1_154, yields:
% 91.22/42.22 | (1016) all_339_1_157 = all_337_1_154
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_335_2_150, all_400_7_313 and discharging atoms aNaturalNumber0(xp) = all_400_7_313, aNaturalNumber0(xp) = all_335_2_150, yields:
% 91.22/42.22 | (1017) all_400_7_313 = all_335_2_150
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_335_2_150, all_337_1_154 and discharging atoms aNaturalNumber0(xp) = all_337_1_154, aNaturalNumber0(xp) = all_335_2_150, yields:
% 91.22/42.22 | (1018) all_337_1_154 = all_335_2_150
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xp, all_327_2_134, all_362_6_225 and discharging atoms aNaturalNumber0(xp) = all_362_6_225, aNaturalNumber0(xp) = all_327_2_134, yields:
% 91.22/42.22 | (1019) all_362_6_225 = all_327_2_134
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xm, all_443_1_372, 0 and discharging atoms aNaturalNumber0(xm) = all_443_1_372, aNaturalNumber0(xm) = 0, yields:
% 91.22/42.22 | (1020) all_443_1_372 = 0
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xm, all_418_1_355, all_443_1_372 and discharging atoms aNaturalNumber0(xm) = all_443_1_372, aNaturalNumber0(xm) = all_418_1_355, yields:
% 91.22/42.22 | (1021) all_443_1_372 = all_418_1_355
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xm, all_351_4_194, all_388_3_279 and discharging atoms aNaturalNumber0(xm) = all_388_3_279, aNaturalNumber0(xm) = all_351_4_194, yields:
% 91.22/42.22 | (1022) all_388_3_279 = all_351_4_194
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xm, all_345_8_177, all_347_8_186 and discharging atoms aNaturalNumber0(xm) = all_347_8_186, aNaturalNumber0(xm) = all_345_8_177, yields:
% 91.22/42.22 | (1023) all_347_8_186 = all_345_8_177
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xm, all_343_4_168, all_443_1_372 and discharging atoms aNaturalNumber0(xm) = all_443_1_372, aNaturalNumber0(xm) = all_343_4_168, yields:
% 91.22/42.22 | (1024) all_443_1_372 = all_343_4_168
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xm, all_343_4_168, all_351_4_194 and discharging atoms aNaturalNumber0(xm) = all_351_4_194, aNaturalNumber0(xm) = all_343_4_168, yields:
% 91.22/42.22 | (1025) all_351_4_194 = all_343_4_168
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xm, all_341_4_163, all_388_3_279 and discharging atoms aNaturalNumber0(xm) = all_388_3_279, aNaturalNumber0(xm) = all_341_4_163, yields:
% 91.22/42.22 | (1026) all_388_3_279 = all_341_4_163
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xm, all_339_2_158, all_345_8_177 and discharging atoms aNaturalNumber0(xm) = all_345_8_177, aNaturalNumber0(xm) = all_339_2_158, yields:
% 91.22/42.22 | (1027) all_345_8_177 = all_339_2_158
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xm, all_337_2_155, all_339_2_158 and discharging atoms aNaturalNumber0(xm) = all_339_2_158, aNaturalNumber0(xm) = all_337_2_155, yields:
% 91.22/42.22 | (1028) all_339_2_158 = all_337_2_155
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xm, all_335_4_152, all_343_4_168 and discharging atoms aNaturalNumber0(xm) = all_343_4_168, aNaturalNumber0(xm) = all_335_4_152, yields:
% 91.22/42.22 | (1029) all_343_4_168 = all_335_4_152
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xm, all_333_4_147, all_343_4_168 and discharging atoms aNaturalNumber0(xm) = all_343_4_168, aNaturalNumber0(xm) = all_333_4_147, yields:
% 91.22/42.22 | (1030) all_343_4_168 = all_333_4_147
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xm, all_333_4_147, all_337_2_155 and discharging atoms aNaturalNumber0(xm) = all_337_2_155, aNaturalNumber0(xm) = all_333_4_147, yields:
% 91.22/42.22 | (1031) all_337_2_155 = all_333_4_147
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xm, all_331_2_142, all_347_8_186 and discharging atoms aNaturalNumber0(xm) = all_347_8_186, aNaturalNumber0(xm) = all_331_2_142, yields:
% 91.22/42.22 | (1032) all_347_8_186 = all_331_2_142
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xm, all_325_3_130, all_333_4_147 and discharging atoms aNaturalNumber0(xm) = all_333_4_147, aNaturalNumber0(xm) = all_325_3_130, yields:
% 91.22/42.22 | (1033) all_333_4_147 = all_325_3_130
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xn, all_428_1_363, all_448_1_375 and discharging atoms aNaturalNumber0(xn) = all_448_1_375, aNaturalNumber0(xn) = all_428_1_363, yields:
% 91.22/42.22 | (1034) all_448_1_375 = all_428_1_363
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xn, all_423_1_359, 0 and discharging atoms aNaturalNumber0(xn) = all_423_1_359, aNaturalNumber0(xn) = 0, yields:
% 91.22/42.22 | (1035) all_423_1_359 = 0
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xn, all_412_4_353, all_428_1_363 and discharging atoms aNaturalNumber0(xn) = all_428_1_363, aNaturalNumber0(xn) = all_412_4_353, yields:
% 91.22/42.22 | (1036) all_428_1_363 = all_412_4_353
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xn, all_410_4_348, all_423_1_359 and discharging atoms aNaturalNumber0(xn) = all_423_1_359, aNaturalNumber0(xn) = all_410_4_348, yields:
% 91.22/42.22 | (1037) all_423_1_359 = all_410_4_348
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xn, all_408_4_343, all_412_4_353 and discharging atoms aNaturalNumber0(xn) = all_412_4_353, aNaturalNumber0(xn) = all_408_4_343, yields:
% 91.22/42.22 | (1038) all_412_4_353 = all_408_4_343
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xn, all_388_4_280, all_423_1_359 and discharging atoms aNaturalNumber0(xn) = all_423_1_359, aNaturalNumber0(xn) = all_388_4_280, yields:
% 91.22/42.22 | (1039) all_423_1_359 = all_388_4_280
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xn, all_347_7_185, all_408_4_343 and discharging atoms aNaturalNumber0(xn) = all_408_4_343, aNaturalNumber0(xn) = all_347_7_185, yields:
% 91.22/42.22 | (1040) all_408_4_343 = all_347_7_185
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xn, all_347_7_185, all_353_2_197 and discharging atoms aNaturalNumber0(xn) = all_353_2_197, aNaturalNumber0(xn) = all_347_7_185, yields:
% 91.22/42.22 | (1041) all_353_2_197 = all_347_7_185
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xn, all_345_7_176, all_347_7_185 and discharging atoms aNaturalNumber0(xn) = all_347_7_185, aNaturalNumber0(xn) = all_345_7_176, yields:
% 91.22/42.22 | (1042) all_347_7_185 = all_345_7_176
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xn, all_335_3_151, all_388_4_280 and discharging atoms aNaturalNumber0(xn) = all_388_4_280, aNaturalNumber0(xn) = all_335_3_151, yields:
% 91.22/42.22 | (1043) all_388_4_280 = all_335_3_151
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xn, all_333_3_146, all_335_3_151 and discharging atoms aNaturalNumber0(xn) = all_335_3_151, aNaturalNumber0(xn) = all_333_3_146, yields:
% 91.22/42.22 | (1044) all_335_3_151 = all_333_3_146
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xn, all_329_3_138, all_353_2_197 and discharging atoms aNaturalNumber0(xn) = all_353_2_197, aNaturalNumber0(xn) = all_329_3_138, yields:
% 91.22/42.22 | (1045) all_353_2_197 = all_329_3_138
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xn, all_323_2_126, all_347_7_185 and discharging atoms aNaturalNumber0(xn) = all_347_7_185, aNaturalNumber0(xn) = all_323_2_126, yields:
% 91.22/42.22 | (1046) all_347_7_185 = all_323_2_126
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xn, all_323_2_126, all_335_3_151 and discharging atoms aNaturalNumber0(xn) = all_335_3_151, aNaturalNumber0(xn) = all_323_2_126, yields:
% 91.22/42.22 | (1047) all_335_3_151 = all_323_2_126
% 91.22/42.22 |
% 91.22/42.22 | Instantiating formula (55) with xn, all_321_2_123, all_448_1_375 and discharging atoms aNaturalNumber0(xn) = all_448_1_375, aNaturalNumber0(xn) = all_321_2_123, yields:
% 91.22/42.22 | (1048) all_448_1_375 = all_321_2_123
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1034,1048) yields a new equation:
% 91.22/42.22 | (1049) all_428_1_363 = all_321_2_123
% 91.22/42.22 |
% 91.22/42.22 | Simplifying 1049 yields:
% 91.22/42.22 | (1050) all_428_1_363 = all_321_2_123
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (985,987) yields a new equation:
% 91.22/42.22 | (1051) all_443_2_373 = all_403_8_326
% 91.22/42.22 |
% 91.22/42.22 | Simplifying 1051 yields:
% 91.22/42.22 | (1052) all_443_2_373 = all_403_8_326
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1020,1021) yields a new equation:
% 91.22/42.22 | (1053) all_418_1_355 = 0
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1024,1021) yields a new equation:
% 91.22/42.22 | (1054) all_418_1_355 = all_343_4_168
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (986,1052) yields a new equation:
% 91.22/42.22 | (1055) all_408_2_341 = all_403_8_326
% 91.22/42.22 |
% 91.22/42.22 | Simplifying 1055 yields:
% 91.22/42.22 | (1056) all_408_2_341 = all_403_8_326
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1002,1004) yields a new equation:
% 91.22/42.22 | (1057) all_374_2_253 = all_374_4_255
% 91.22/42.22 |
% 91.22/42.22 | Simplifying 1057 yields:
% 91.22/42.22 | (1058) all_374_2_253 = all_374_4_255
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1005,1004) yields a new equation:
% 91.22/42.22 | (1059) all_374_4_255 = all_372_2_250
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1006,1004) yields a new equation:
% 91.22/42.22 | (1060) all_374_4_255 = all_368_3_243
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (981,980) yields a new equation:
% 91.22/42.22 | (1061) all_329_4_139 = all_325_4_131
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (979,980) yields a new equation:
% 91.22/42.22 | (1062) all_329_4_139 = 0
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1036,1050) yields a new equation:
% 91.22/42.22 | (1063) all_412_4_353 = all_321_2_123
% 91.22/42.22 |
% 91.22/42.22 | Simplifying 1063 yields:
% 91.22/42.22 | (1064) all_412_4_353 = all_321_2_123
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1039,1037) yields a new equation:
% 91.22/42.22 | (1065) all_410_4_348 = all_388_4_280
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1035,1037) yields a new equation:
% 91.22/42.22 | (1066) all_410_4_348 = 0
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (995,1011) yields a new equation:
% 91.22/42.22 | (1067) all_418_3_357 = all_362_8_227
% 91.22/42.22 |
% 91.22/42.22 | Simplifying 1067 yields:
% 91.22/42.22 | (1068) all_418_3_357 = all_362_8_227
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1054,1053) yields a new equation:
% 91.22/42.22 | (1069) all_343_4_168 = 0
% 91.22/42.22 |
% 91.22/42.22 | Simplifying 1069 yields:
% 91.22/42.22 | (1070) all_343_4_168 = 0
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (996,1068) yields a new equation:
% 91.22/42.22 | (1071) all_403_7_325 = all_362_8_227
% 91.22/42.22 |
% 91.22/42.22 | Simplifying 1071 yields:
% 91.22/42.22 | (1072) all_403_7_325 = all_362_8_227
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1038,1064) yields a new equation:
% 91.22/42.22 | (1073) all_408_4_343 = all_321_2_123
% 91.22/42.22 |
% 91.22/42.22 | Simplifying 1073 yields:
% 91.22/42.22 | (1074) all_408_4_343 = all_321_2_123
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1065,1066) yields a new equation:
% 91.22/42.22 | (1075) all_388_4_280 = 0
% 91.22/42.22 |
% 91.22/42.22 | Simplifying 1075 yields:
% 91.22/42.22 | (1076) all_388_4_280 = 0
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (991,1056) yields a new equation:
% 91.22/42.22 | (1077) all_403_8_326 = all_374_3_254
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (992,1056) yields a new equation:
% 91.22/42.22 | (1078) all_403_8_326 = all_372_1_249
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (994,1056) yields a new equation:
% 91.22/42.22 | (1079) all_403_8_326 = all_341_2_161
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (989,1056) yields a new equation:
% 91.22/42.22 | (1080) all_403_8_326 = all_392_3_287
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (988,1056) yields a new equation:
% 91.22/42.22 | (1081) all_403_8_326 = all_400_8_314
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1040,1074) yields a new equation:
% 91.22/42.22 | (1082) all_347_7_185 = all_321_2_123
% 91.22/42.22 |
% 91.22/42.22 | Simplifying 1082 yields:
% 91.22/42.22 | (1083) all_347_7_185 = all_321_2_123
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (998,1072) yields a new equation:
% 91.22/42.22 | (1084) all_394_2_291 = all_362_8_227
% 91.22/42.22 |
% 91.22/42.22 | Simplifying 1084 yields:
% 91.22/42.22 | (1085) all_394_2_291 = all_362_8_227
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1078,1081) yields a new equation:
% 91.22/42.22 | (1086) all_400_8_314 = all_372_1_249
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1079,1081) yields a new equation:
% 91.22/42.22 | (1087) all_400_8_314 = all_341_2_161
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1080,1081) yields a new equation:
% 91.22/42.22 | (1088) all_400_8_314 = all_392_3_287
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1077,1081) yields a new equation:
% 91.22/42.22 | (1089) all_400_8_314 = all_374_3_254
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1009,1013) yields a new equation:
% 91.22/42.22 | (1090) all_362_6_225 = all_349_2_189
% 91.22/42.22 |
% 91.22/42.22 | Simplifying 1090 yields:
% 91.22/42.22 | (1091) all_362_6_225 = all_349_2_189
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (997,1012) yields a new equation:
% 91.22/42.22 | (1092) all_357_6_207 = 0
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1017,1012) yields a new equation:
% 91.22/42.22 | (1093) all_357_6_207 = all_335_2_150
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1087,1086) yields a new equation:
% 91.22/42.22 | (1094) all_372_1_249 = all_341_2_161
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1089,1086) yields a new equation:
% 91.22/42.22 | (1095) all_374_3_254 = all_372_1_249
% 91.22/42.22 |
% 91.22/42.22 | Simplifying 1095 yields:
% 91.22/42.22 | (1096) all_374_3_254 = all_372_1_249
% 91.22/42.22 |
% 91.22/42.22 | Combining equations (1088,1086) yields a new equation:
% 91.22/42.22 | (1097) all_392_3_287 = all_372_1_249
% 91.22/42.22 |
% 91.22/42.22 | Simplifying 1097 yields:
% 91.22/42.23 | (1098) all_392_3_287 = all_372_1_249
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (999,1085) yields a new equation:
% 91.22/42.23 | (1099) all_392_4_288 = all_362_8_227
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1099 yields:
% 91.22/42.23 | (1100) all_392_4_288 = all_362_8_227
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1098,993) yields a new equation:
% 91.22/42.23 | (1101) all_372_1_249 = all_366_1_238
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1101 yields:
% 91.22/42.23 | (1102) all_372_1_249 = all_366_1_238
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1000,1100) yields a new equation:
% 91.22/42.23 | (1103) all_378_1_260 = all_362_8_227
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1103 yields:
% 91.22/42.23 | (1104) all_378_1_260 = all_362_8_227
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1022,1026) yields a new equation:
% 91.22/42.23 | (1105) all_351_4_194 = all_341_4_163
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1105 yields:
% 91.22/42.23 | (1106) all_351_4_194 = all_341_4_163
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1043,1076) yields a new equation:
% 91.22/42.23 | (1107) all_335_3_151 = 0
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1107 yields:
% 91.22/42.23 | (1108) all_335_3_151 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1001,1104) yields a new equation:
% 91.22/42.23 | (1109) all_376_1_257 = all_362_8_227
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1109 yields:
% 91.22/42.23 | (1110) all_376_1_257 = all_362_8_227
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1003,1110) yields a new equation:
% 91.22/42.23 | (1111) all_374_2_253 = all_362_8_227
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1111 yields:
% 91.22/42.23 | (1112) all_374_2_253 = all_362_8_227
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1058,1112) yields a new equation:
% 91.22/42.23 | (1113) all_374_4_255 = all_362_8_227
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1113 yields:
% 91.22/42.23 | (1114) all_374_4_255 = all_362_8_227
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1096,990) yields a new equation:
% 91.22/42.23 | (1115) all_372_1_249 = 0
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1115 yields:
% 91.22/42.23 | (1116) all_372_1_249 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1060,1059) yields a new equation:
% 91.22/42.23 | (1117) all_372_2_250 = all_368_3_243
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1114,1059) yields a new equation:
% 91.22/42.23 | (1118) all_372_2_250 = all_362_8_227
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1094,1102) yields a new equation:
% 91.22/42.23 | (1119) all_366_1_238 = all_341_2_161
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1116,1102) yields a new equation:
% 91.22/42.23 | (1120) all_366_1_238 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1117,1118) yields a new equation:
% 91.22/42.23 | (1121) all_368_3_243 = all_362_8_227
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1121 yields:
% 91.22/42.23 | (1122) all_368_3_243 = all_362_8_227
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1007,1122) yields a new equation:
% 91.22/42.23 | (1123) all_366_2_239 = all_362_8_227
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1123 yields:
% 91.22/42.23 | (1124) all_366_2_239 = all_362_8_227
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1119,1120) yields a new equation:
% 91.22/42.23 | (1125) all_341_2_161 = 0
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1125 yields:
% 91.22/42.23 | (1126) all_341_2_161 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1008,1124) yields a new equation:
% 91.22/42.23 | (1127) all_364_8_236 = all_362_8_227
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1127 yields:
% 91.22/42.23 | (1128) all_364_8_236 = all_362_8_227
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (982,983) yields a new equation:
% 91.22/42.23 | (1129) all_362_7_226 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (984,983) yields a new equation:
% 91.22/42.23 | (1130) all_362_7_226 = all_349_1_188
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1015,1128) yields a new equation:
% 91.22/42.23 | (1131) all_362_8_227 = all_339_1_157
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1010,1128) yields a new equation:
% 91.22/42.23 | (1132) all_362_6_225 = all_362_8_227
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1132 yields:
% 91.22/42.23 | (1133) all_362_6_225 = all_362_8_227
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1014,1128) yields a new equation:
% 91.22/42.23 | (1134) all_362_8_227 = all_345_6_175
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1019,1091) yields a new equation:
% 91.22/42.23 | (1135) all_349_2_189 = all_327_2_134
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1133,1091) yields a new equation:
% 91.22/42.23 | (1136) all_362_8_227 = all_349_2_189
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1136 yields:
% 91.22/42.23 | (1137) all_362_8_227 = all_349_2_189
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1130,1129) yields a new equation:
% 91.22/42.23 | (1138) all_349_1_188 = 0
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1138 yields:
% 91.22/42.23 | (1139) all_349_1_188 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1131,1134) yields a new equation:
% 91.22/42.23 | (1140) all_345_6_175 = all_339_1_157
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1137,1134) yields a new equation:
% 91.22/42.23 | (1141) all_349_2_189 = all_345_6_175
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1141 yields:
% 91.22/42.23 | (1142) all_349_2_189 = all_345_6_175
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1093,1092) yields a new equation:
% 91.22/42.23 | (1143) all_335_2_150 = 0
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1143 yields:
% 91.22/42.23 | (1144) all_335_2_150 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1041,1045) yields a new equation:
% 91.22/42.23 | (1145) all_347_7_185 = all_329_3_138
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1145 yields:
% 91.22/42.23 | (1146) all_347_7_185 = all_329_3_138
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1025,1106) yields a new equation:
% 91.22/42.23 | (1147) all_343_4_168 = all_341_4_163
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1147 yields:
% 91.22/42.23 | (1148) all_343_4_168 = all_341_4_163
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1142,1135) yields a new equation:
% 91.22/42.23 | (1149) all_345_6_175 = all_327_2_134
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1149 yields:
% 91.22/42.23 | (1150) all_345_6_175 = all_327_2_134
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1146,1042) yields a new equation:
% 91.22/42.23 | (1151) all_345_7_176 = all_329_3_138
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1046,1042) yields a new equation:
% 91.22/42.23 | (1152) all_345_7_176 = all_323_2_126
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1083,1042) yields a new equation:
% 91.22/42.23 | (1153) all_345_7_176 = all_321_2_123
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1023,1032) yields a new equation:
% 91.22/42.23 | (1154) all_345_8_177 = all_331_2_142
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1154 yields:
% 91.22/42.23 | (1155) all_345_8_177 = all_331_2_142
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1140,1150) yields a new equation:
% 91.22/42.23 | (1156) all_339_1_157 = all_327_2_134
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1156 yields:
% 91.22/42.23 | (1157) all_339_1_157 = all_327_2_134
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1152,1151) yields a new equation:
% 91.22/42.23 | (1158) all_329_3_138 = all_323_2_126
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1153,1151) yields a new equation:
% 91.22/42.23 | (1159) all_329_3_138 = all_321_2_123
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1027,1155) yields a new equation:
% 91.22/42.23 | (1160) all_339_2_158 = all_331_2_142
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1160 yields:
% 91.22/42.23 | (1161) all_339_2_158 = all_331_2_142
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1029,1148) yields a new equation:
% 91.22/42.23 | (1162) all_341_4_163 = all_335_4_152
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1030,1148) yields a new equation:
% 91.22/42.23 | (1163) all_341_4_163 = all_333_4_147
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1070,1148) yields a new equation:
% 91.22/42.23 | (1164) all_341_4_163 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1163,1162) yields a new equation:
% 91.22/42.23 | (1165) all_335_4_152 = all_333_4_147
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1164,1162) yields a new equation:
% 91.22/42.23 | (1166) all_335_4_152 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1016,1157) yields a new equation:
% 91.22/42.23 | (1167) all_337_1_154 = all_327_2_134
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1167 yields:
% 91.22/42.23 | (1168) all_337_1_154 = all_327_2_134
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1028,1161) yields a new equation:
% 91.22/42.23 | (1169) all_337_2_155 = all_331_2_142
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1169 yields:
% 91.22/42.23 | (1170) all_337_2_155 = all_331_2_142
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1018,1168) yields a new equation:
% 91.22/42.23 | (1171) all_335_2_150 = all_327_2_134
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1171 yields:
% 91.22/42.23 | (1172) all_335_2_150 = all_327_2_134
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1031,1170) yields a new equation:
% 91.22/42.23 | (1173) all_333_4_147 = all_331_2_142
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1173 yields:
% 91.22/42.23 | (1174) all_333_4_147 = all_331_2_142
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1144,1172) yields a new equation:
% 91.22/42.23 | (1175) all_327_2_134 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1047,1044) yields a new equation:
% 91.22/42.23 | (1176) all_333_3_146 = all_323_2_126
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1108,1044) yields a new equation:
% 91.22/42.23 | (1177) all_333_3_146 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1165,1166) yields a new equation:
% 91.22/42.23 | (1178) all_333_4_147 = 0
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1178 yields:
% 91.22/42.23 | (1179) all_333_4_147 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1176,1177) yields a new equation:
% 91.22/42.23 | (1180) all_323_2_126 = 0
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1180 yields:
% 91.22/42.23 | (1181) all_323_2_126 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1033,1174) yields a new equation:
% 91.22/42.23 | (1182) all_331_2_142 = all_325_3_130
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1179,1174) yields a new equation:
% 91.22/42.23 | (1183) all_331_2_142 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1182,1183) yields a new equation:
% 91.22/42.23 | (1184) all_325_3_130 = 0
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1184 yields:
% 91.22/42.23 | (1185) all_325_3_130 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1158,1159) yields a new equation:
% 91.22/42.23 | (1186) all_323_2_126 = all_321_2_123
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1186 yields:
% 91.22/42.23 | (1187) all_323_2_126 = all_321_2_123
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1061,1062) yields a new equation:
% 91.22/42.23 | (1188) all_325_4_131 = 0
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1188 yields:
% 91.22/42.23 | (1189) all_325_4_131 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1187,1181) yields a new equation:
% 91.22/42.23 | (1190) all_321_2_123 = 0
% 91.22/42.23 |
% 91.22/42.23 | Simplifying 1190 yields:
% 91.22/42.23 | (1191) all_321_2_123 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1120,1102) yields a new equation:
% 91.22/42.23 | (1116) all_372_1_249 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1116,1086) yields a new equation:
% 91.22/42.23 | (1193) all_400_8_314 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1193,1081) yields a new equation:
% 91.22/42.23 | (1194) all_403_8_326 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1194,1052) yields a new equation:
% 91.22/42.23 | (1195) all_443_2_373 = 0
% 91.22/42.23 |
% 91.22/42.23 | Combining equations (1053,1021) yields a new equation:
% 91.22/42.23 | (1020) all_443_1_372 = 0
% 91.22/42.23 |
% 91.22/42.23 | From (1189) and (685) follows:
% 91.22/42.23 | (251) aNaturalNumber0(all_70_0_94) = 0
% 91.22/42.23 |
% 91.22/42.23 | From (1139) and (769) follows:
% 91.22/42.23 | (496) aNaturalNumber0(all_40_2_73) = 0
% 91.22/42.23 |
% 91.22/42.23 | From (1126) and (733) follows:
% 91.22/42.23 | (440) aNaturalNumber0(xk) = 0
% 91.22/42.23 |
% 91.22/42.23 | From (1175) and (693) follows:
% 91.22/42.23 | (48) aNaturalNumber0(xp) = 0
% 91.22/42.23 |
% 91.22/42.23 | From (1185) and (688) follows:
% 91.22/42.23 | (32) aNaturalNumber0(xm) = 0
% 91.22/42.23 |
% 91.22/42.23 | From (1191) and (676) follows:
% 91.22/42.23 | (20) aNaturalNumber0(xn) = 0
% 91.22/42.23 |
% 91.22/42.23 +-Applying beta-rule and splitting (664), into two cases.
% 91.22/42.23 |-Branch one:
% 91.22/42.23 | (1203) xp = xn
% 91.22/42.23 |
% 91.22/42.23 | Equations (1203) can reduce 66 to:
% 91.22/42.23 | (216) $false
% 91.22/42.23 |
% 91.22/42.23 |-The branch is then unsatisfiable
% 91.22/42.23 |-Branch two:
% 91.22/42.23 | (66) ~ (xp = xn)
% 91.22/42.23 | (1206) ? [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_14_1_13 = all_0_8_8))))
% 91.22/42.23 |
% 91.22/42.23 | Instantiating (1206) with all_535_0_381, all_535_1_382, all_535_2_383, all_535_3_384, all_535_4_385 yields:
% 91.22/42.23 | (1207) sdtpldt0(xp, xm) = all_535_1_382 & sdtpldt0(xn, xm) = all_535_0_381 & aNaturalNumber0(xp) = all_535_3_384 & aNaturalNumber0(xm) = all_535_4_385 & aNaturalNumber0(xn) = all_535_2_383 & ( ~ (all_535_2_383 = 0) | ~ (all_535_3_384 = 0) | ~ (all_535_4_385 = 0) | ( ~ (all_535_0_381 = all_535_1_382) & ~ (all_14_1_13 = all_0_8_8)))
% 91.22/42.23 |
% 91.22/42.23 | Applying alpha-rule on (1207) yields:
% 91.22/42.23 | (1208) aNaturalNumber0(xn) = all_535_2_383
% 91.22/42.23 | (1209) aNaturalNumber0(xm) = all_535_4_385
% 91.22/42.24 | (1210) ~ (all_535_2_383 = 0) | ~ (all_535_3_384 = 0) | ~ (all_535_4_385 = 0) | ( ~ (all_535_0_381 = all_535_1_382) & ~ (all_14_1_13 = all_0_8_8))
% 91.22/42.24 | (1211) sdtpldt0(xn, xm) = all_535_0_381
% 91.22/42.24 | (1212) sdtpldt0(xp, xm) = all_535_1_382
% 91.22/42.24 | (1213) aNaturalNumber0(xp) = all_535_3_384
% 91.22/42.24 |
% 91.22/42.24 +-Applying beta-rule and splitting (961), into two cases.
% 91.22/42.24 |-Branch one:
% 91.22/42.24 | (1214) ~ (all_443_1_372 = 0)
% 91.22/42.24 |
% 91.22/42.24 | Equations (1020) can reduce 1214 to:
% 91.22/42.24 | (216) $false
% 91.22/42.24 |
% 91.22/42.24 |-The branch is then unsatisfiable
% 91.22/42.24 |-Branch two:
% 91.22/42.24 | (1020) all_443_1_372 = 0
% 91.22/42.24 | (1217) ~ (all_443_2_373 = 0) | (all_443_0_371 = 0 & ~ (xk = xm))
% 91.22/42.24 |
% 91.22/42.24 +-Applying beta-rule and splitting (1217), into two cases.
% 91.22/42.24 |-Branch one:
% 91.22/42.24 | (1218) ~ (all_443_2_373 = 0)
% 91.22/42.24 |
% 91.22/42.24 | Equations (1195) can reduce 1218 to:
% 91.22/42.24 | (216) $false
% 91.22/42.24 |
% 91.22/42.24 |-The branch is then unsatisfiable
% 91.22/42.24 |-Branch two:
% 91.22/42.24 | (1195) all_443_2_373 = 0
% 91.22/42.24 | (1221) all_443_0_371 = 0 & ~ (xk = xm)
% 91.22/42.24 |
% 91.22/42.24 | Applying alpha-rule on (1221) yields:
% 91.22/42.24 | (1222) all_443_0_371 = 0
% 91.22/42.24 | (1223) ~ (xk = xm)
% 91.22/42.24 |
% 91.22/42.24 | From (1222) and (958) follows:
% 91.22/42.24 | (1224) sdtlseqdt0(xm, xk) = 0
% 91.22/42.24 |
% 91.22/42.24 +-Applying beta-rule and splitting (641), into two cases.
% 91.22/42.24 |-Branch one:
% 91.22/42.24 | (215) xp = sz00
% 91.22/42.24 |
% 91.22/42.24 | Equations (215) can reduce 90 to:
% 91.22/42.24 | (216) $false
% 91.22/42.24 |
% 91.22/42.24 |-The branch is then unsatisfiable
% 91.22/42.24 |-Branch two:
% 91.22/42.24 | (90) ~ (xp = sz00)
% 91.22/42.24 | (1228) all_40_2_73 = xk | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_40_2_73, xp) = v2 & sdtasdt0(xk, xp) = v3 & aNaturalNumber0(all_40_2_73) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 91.22/42.24 |
% 91.22/42.24 +-Applying beta-rule and splitting (1228), into two cases.
% 91.22/42.24 |-Branch one:
% 91.22/42.24 | (1229) all_40_2_73 = xk
% 91.22/42.24 |
% 91.22/42.24 | From (1229) and (496) follows:
% 91.22/42.24 | (440) aNaturalNumber0(xk) = 0
% 91.22/42.24 |
% 91.22/42.24 | Instantiating formula (55) with xp, all_535_3_384, 0 and discharging atoms aNaturalNumber0(xp) = all_535_3_384, aNaturalNumber0(xp) = 0, yields:
% 91.22/42.24 | (1231) all_535_3_384 = 0
% 91.22/42.24 |
% 91.22/42.24 | Instantiating formula (55) with xm, all_535_4_385, 0 and discharging atoms aNaturalNumber0(xm) = all_535_4_385, aNaturalNumber0(xm) = 0, yields:
% 91.22/42.24 | (1232) all_535_4_385 = 0
% 91.22/42.24 |
% 91.22/42.24 | Instantiating formula (55) with xn, all_535_2_383, 0 and discharging atoms aNaturalNumber0(xn) = all_535_2_383, aNaturalNumber0(xn) = 0, yields:
% 91.22/42.24 | (1233) all_535_2_383 = 0
% 91.22/42.24 |
% 91.22/42.24 | From (1231) and (1213) follows:
% 91.22/42.24 | (48) aNaturalNumber0(xp) = 0
% 91.22/42.24 |
% 91.22/42.24 | From (1232) and (1209) follows:
% 91.22/42.24 | (32) aNaturalNumber0(xm) = 0
% 91.22/42.24 |
% 91.22/42.24 | From (1233) and (1208) follows:
% 91.22/42.24 | (20) aNaturalNumber0(xn) = 0
% 91.22/42.24 |
% 91.22/42.24 +-Applying beta-rule and splitting (637), into two cases.
% 91.22/42.24 |-Branch one:
% 91.22/42.24 | (215) xp = sz00
% 91.22/42.24 |
% 91.22/42.24 | Equations (215) can reduce 90 to:
% 91.22/42.24 | (216) $false
% 91.22/42.24 |
% 91.22/42.24 |-The branch is then unsatisfiable
% 91.22/42.24 |-Branch two:
% 91.22/42.24 | (90) ~ (xp = sz00)
% 91.22/42.24 | (1240) all_40_2_73 = xm | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_40_2_73, xp) = v3 & sdtasdt0(xm, xp) = v2 & aNaturalNumber0(all_40_2_73) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = v2) & ~ (all_0_3_3 = all_0_6_6))))
% 91.22/42.24 |
% 91.22/42.24 +-Applying beta-rule and splitting (110), into two cases.
% 91.22/42.24 |-Branch one:
% 91.22/42.24 | (215) xp = sz00
% 91.22/42.24 |
% 91.22/42.24 | Equations (215) can reduce 90 to:
% 91.22/42.24 | (216) $false
% 91.22/42.24 |
% 91.22/42.24 |-The branch is then unsatisfiable
% 91.22/42.24 |-Branch two:
% 91.22/42.24 | (90) ~ (xp = sz00)
% 91.22/42.24 | (1244) xk = xm | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v4, v5) = v6 & sdtlseqdt0(xm, xk) = v3 & sdtasdt0(xk, xp) = v5 & sdtasdt0(xm, xp) = v4 & aNaturalNumber0(xk) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v6 = 0 & all_0_0_0 = 0 & ~ (v5 = v4) & ~ (all_0_1_1 = all_0_3_3))))
% 91.22/42.24 |
% 91.22/42.24 +-Applying beta-rule and splitting (1244), into two cases.
% 91.22/42.24 |-Branch one:
% 91.22/42.24 | (1245) xk = xm
% 91.22/42.24 |
% 91.22/42.24 | Equations (1245) can reduce 1223 to:
% 91.22/42.24 | (216) $false
% 91.22/42.24 |
% 91.22/42.24 |-The branch is then unsatisfiable
% 91.22/42.24 |-Branch two:
% 91.22/42.24 | (1223) ~ (xk = xm)
% 91.22/42.24 | (1248) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v4, v5) = v6 & sdtlseqdt0(xm, xk) = v3 & sdtasdt0(xk, xp) = v5 & sdtasdt0(xm, xp) = v4 & aNaturalNumber0(xk) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v6 = 0 & all_0_0_0 = 0 & ~ (v5 = v4) & ~ (all_0_1_1 = all_0_3_3))))
% 91.22/42.24 |
% 91.22/42.24 | Instantiating (1248) with all_958_0_387, all_958_1_388, all_958_2_389, all_958_3_390, all_958_4_391, all_958_5_392, all_958_6_393 yields:
% 91.22/42.24 | (1249) sdtlseqdt0(all_958_2_389, all_958_1_388) = all_958_0_387 & sdtlseqdt0(xm, xk) = all_958_3_390 & sdtasdt0(xk, xp) = all_958_1_388 & sdtasdt0(xm, xp) = all_958_2_389 & aNaturalNumber0(xk) = all_958_4_391 & aNaturalNumber0(xp) = all_958_6_393 & aNaturalNumber0(xm) = all_958_5_392 & ( ~ (all_958_3_390 = 0) | ~ (all_958_4_391 = 0) | ~ (all_958_5_392 = 0) | ~ (all_958_6_393 = 0) | (all_958_0_387 = 0 & all_0_0_0 = 0 & ~ (all_958_1_388 = all_958_2_389) & ~ (all_0_1_1 = all_0_3_3)))
% 91.22/42.24 |
% 91.22/42.24 | Applying alpha-rule on (1249) yields:
% 91.22/42.24 | (1250) sdtlseqdt0(all_958_2_389, all_958_1_388) = all_958_0_387
% 91.22/42.24 | (1251) aNaturalNumber0(xp) = all_958_6_393
% 91.22/42.24 | (1252) sdtlseqdt0(xm, xk) = all_958_3_390
% 91.22/42.24 | (1253) aNaturalNumber0(xm) = all_958_5_392
% 91.22/42.24 | (1254) ~ (all_958_3_390 = 0) | ~ (all_958_4_391 = 0) | ~ (all_958_5_392 = 0) | ~ (all_958_6_393 = 0) | (all_958_0_387 = 0 & all_0_0_0 = 0 & ~ (all_958_1_388 = all_958_2_389) & ~ (all_0_1_1 = all_0_3_3))
% 91.22/42.24 | (1255) sdtasdt0(xk, xp) = all_958_1_388
% 91.22/42.24 | (1256) aNaturalNumber0(xk) = all_958_4_391
% 91.22/42.24 | (1257) sdtasdt0(xm, xp) = all_958_2_389
% 91.22/42.24 |
% 91.22/42.24 +-Applying beta-rule and splitting (645), into two cases.
% 91.22/42.24 |-Branch one:
% 91.22/42.24 | (1258) ~ (sdtasdt0(sz00, xn) = all_0_6_6)
% 91.22/42.24 |
% 91.22/42.24 | Instantiating formula (38) with xm, xk, all_958_3_390, 0 and discharging atoms sdtlseqdt0(xm, xk) = all_958_3_390, sdtlseqdt0(xm, xk) = 0, yields:
% 91.22/42.24 | (1259) all_958_3_390 = 0
% 91.22/42.24 |
% 91.22/42.24 | Instantiating formula (55) with xk, all_958_4_391, 0 and discharging atoms aNaturalNumber0(xk) = all_958_4_391, aNaturalNumber0(xk) = 0, yields:
% 91.22/42.24 | (1260) all_958_4_391 = 0
% 91.22/42.24 |
% 91.22/42.24 | Instantiating formula (55) with xp, all_958_6_393, 0 and discharging atoms aNaturalNumber0(xp) = all_958_6_393, aNaturalNumber0(xp) = 0, yields:
% 91.22/42.24 | (1261) all_958_6_393 = 0
% 91.22/42.24 |
% 91.22/42.24 | Instantiating formula (55) with xm, all_958_5_392, 0 and discharging atoms aNaturalNumber0(xm) = all_958_5_392, aNaturalNumber0(xm) = 0, yields:
% 91.22/42.24 | (1262) all_958_5_392 = 0
% 91.22/42.24 |
% 91.22/42.24 | Using (463) and (1258) yields:
% 91.22/42.24 | (1263) ~ (xm = sz00)
% 91.22/42.24 |
% 91.22/42.24 | From (1261) and (1251) follows:
% 91.22/42.24 | (48) aNaturalNumber0(xp) = 0
% 91.22/42.24 |
% 91.22/42.24 | From (1262) and (1253) follows:
% 91.22/42.24 | (32) aNaturalNumber0(xm) = 0
% 91.22/42.24 |
% 91.22/42.24 +-Applying beta-rule and splitting (128), into two cases.
% 91.22/42.24 |-Branch one:
% 91.22/42.24 | (1266) xm = sz00
% 91.22/42.24 |
% 91.22/42.24 | Equations (1266) can reduce 1263 to:
% 91.22/42.24 | (216) $false
% 91.22/42.24 |
% 91.22/42.24 |-The branch is then unsatisfiable
% 91.22/42.24 |-Branch two:
% 91.22/42.24 | (1263) ~ (xm = sz00)
% 91.22/42.24 | (1269) xm = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xm) = 0 & aNaturalNumber0(v0) = 0)
% 91.22/42.24 |
% 91.22/42.24 +-Applying beta-rule and splitting (626), into two cases.
% 91.22/42.24 |-Branch one:
% 91.22/42.24 | (1270) all_70_0_94 = xp
% 91.22/42.24 |
% 91.22/42.24 | Equations (1270) can reduce 253 to:
% 91.22/42.24 | (90) ~ (xp = sz00)
% 91.22/42.24 |
% 91.22/42.24 | From (1270) and (251) follows:
% 91.22/42.24 | (48) aNaturalNumber0(xp) = 0
% 91.22/42.24 |
% 91.22/42.24 +-Applying beta-rule and splitting (1240), into two cases.
% 91.22/42.24 |-Branch one:
% 91.22/42.24 | (1273) all_40_2_73 = xm
% 91.22/42.24 |
% 91.22/42.24 | Combining equations (1273,1229) yields a new equation:
% 91.22/42.24 | (1245) xk = xm
% 91.22/42.24 |
% 91.22/42.24 | Equations (1245) can reduce 1223 to:
% 91.22/42.24 | (216) $false
% 91.22/42.24 |
% 91.22/42.24 |-The branch is then unsatisfiable
% 91.22/42.24 |-Branch two:
% 91.22/42.24 | (1276) ~ (all_40_2_73 = xm)
% 91.22/42.24 | (1277) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_40_2_73, xp) = v3 & sdtasdt0(xm, xp) = v2 & aNaturalNumber0(all_40_2_73) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = v2) & ~ (all_0_3_3 = all_0_6_6))))
% 91.22/42.24 |
% 91.22/42.24 | Instantiating (1277) with all_1040_0_395, all_1040_1_396, all_1040_2_397, all_1040_3_398 yields:
% 91.22/42.24 | (1278) sdtasdt0(all_40_2_73, xp) = all_1040_0_395 & sdtasdt0(xm, xp) = all_1040_1_396 & aNaturalNumber0(all_40_2_73) = all_1040_2_397 & aNaturalNumber0(xm) = all_1040_3_398 & ( ~ (all_1040_2_397 = 0) | ~ (all_1040_3_398 = 0) | ( ~ (all_1040_0_395 = all_1040_1_396) & ~ (all_0_3_3 = all_0_6_6)))
% 91.22/42.24 |
% 91.22/42.24 | Applying alpha-rule on (1278) yields:
% 91.22/42.24 | (1279) sdtasdt0(xm, xp) = all_1040_1_396
% 91.22/42.24 | (1280) sdtasdt0(all_40_2_73, xp) = all_1040_0_395
% 91.22/42.24 | (1281) aNaturalNumber0(xm) = all_1040_3_398
% 91.22/42.24 | (1282) ~ (all_1040_2_397 = 0) | ~ (all_1040_3_398 = 0) | ( ~ (all_1040_0_395 = all_1040_1_396) & ~ (all_0_3_3 = all_0_6_6))
% 91.22/42.24 | (1283) aNaturalNumber0(all_40_2_73) = all_1040_2_397
% 91.22/42.24 |
% 91.22/42.24 | Equations (1229) can reduce 1276 to:
% 91.22/42.24 | (1223) ~ (xk = xm)
% 91.22/42.24 |
% 91.22/42.24 +-Applying beta-rule and splitting (1254), into two cases.
% 91.22/42.24 |-Branch one:
% 91.22/42.24 | (1285) ~ (all_958_3_390 = 0)
% 91.22/42.24 |
% 91.22/42.24 | Equations (1259) can reduce 1285 to:
% 91.22/42.24 | (216) $false
% 91.22/42.24 |
% 91.22/42.24 |-The branch is then unsatisfiable
% 91.22/42.24 |-Branch two:
% 91.22/42.24 | (1259) all_958_3_390 = 0
% 91.22/42.24 | (1288) ~ (all_958_4_391 = 0) | ~ (all_958_5_392 = 0) | ~ (all_958_6_393 = 0) | (all_958_0_387 = 0 & all_0_0_0 = 0 & ~ (all_958_1_388 = all_958_2_389) & ~ (all_0_1_1 = all_0_3_3))
% 91.22/42.24 |
% 91.22/42.24 +-Applying beta-rule and splitting (1288), into two cases.
% 91.22/42.24 |-Branch one:
% 91.22/42.24 | (1289) ~ (all_958_4_391 = 0)
% 91.22/42.24 |
% 91.22/42.24 | Equations (1260) can reduce 1289 to:
% 91.22/42.24 | (216) $false
% 91.22/42.24 |
% 91.22/42.24 |-The branch is then unsatisfiable
% 91.22/42.24 |-Branch two:
% 91.22/42.24 | (1260) all_958_4_391 = 0
% 91.22/42.24 | (1292) ~ (all_958_5_392 = 0) | ~ (all_958_6_393 = 0) | (all_958_0_387 = 0 & all_0_0_0 = 0 & ~ (all_958_1_388 = all_958_2_389) & ~ (all_0_1_1 = all_0_3_3))
% 91.22/42.24 |
% 91.22/42.24 +-Applying beta-rule and splitting (1292), into two cases.
% 91.22/42.24 |-Branch one:
% 91.22/42.24 | (1293) ~ (all_958_5_392 = 0)
% 91.22/42.24 |
% 91.22/42.24 | Equations (1262) can reduce 1293 to:
% 91.22/42.24 | (216) $false
% 91.22/42.24 |
% 91.22/42.24 |-The branch is then unsatisfiable
% 91.22/42.24 |-Branch two:
% 91.22/42.24 | (1262) all_958_5_392 = 0
% 91.22/42.24 | (1296) ~ (all_958_6_393 = 0) | (all_958_0_387 = 0 & all_0_0_0 = 0 & ~ (all_958_1_388 = all_958_2_389) & ~ (all_0_1_1 = all_0_3_3))
% 91.22/42.24 |
% 91.22/42.24 +-Applying beta-rule and splitting (1296), into two cases.
% 91.22/42.24 |-Branch one:
% 91.22/42.24 | (1297) ~ (all_958_6_393 = 0)
% 91.22/42.24 |
% 91.22/42.24 | Equations (1261) can reduce 1297 to:
% 91.22/42.24 | (216) $false
% 91.22/42.24 |
% 91.22/42.24 |-The branch is then unsatisfiable
% 91.22/42.24 |-Branch two:
% 91.22/42.24 | (1261) all_958_6_393 = 0
% 91.22/42.24 | (1300) all_958_0_387 = 0 & all_0_0_0 = 0 & ~ (all_958_1_388 = all_958_2_389) & ~ (all_0_1_1 = all_0_3_3)
% 91.22/42.24 |
% 91.22/42.24 | Applying alpha-rule on (1300) yields:
% 91.22/42.24 | (1301) all_958_0_387 = 0
% 91.22/42.24 | (1302) all_0_0_0 = 0
% 91.22/42.24 | (1303) ~ (all_958_1_388 = all_958_2_389)
% 91.22/42.24 | (1304) ~ (all_0_1_1 = all_0_3_3)
% 91.22/42.24 |
% 91.22/42.24 | Equations (488) can reduce 1304 to:
% 91.22/42.24 | (1305) ~ (all_0_3_3 = all_0_6_6)
% 91.22/42.24 |
% 91.22/42.24 | Simplifying 1305 yields:
% 91.22/42.24 | (1306) ~ (all_0_3_3 = all_0_6_6)
% 91.22/42.24 |
% 91.22/42.24 +-Applying beta-rule and splitting (44), into two cases.
% 91.22/42.24 |-Branch one:
% 91.22/42.24 | (1307) ~ (all_0_0_0 = 0)
% 91.22/42.24 |
% 91.22/42.24 | Equations (1302) can reduce 1307 to:
% 91.22/42.24 | (216) $false
% 91.22/42.24 |
% 91.22/42.24 |-The branch is then unsatisfiable
% 91.22/42.24 |-Branch two:
% 91.22/42.24 | (1302) all_0_0_0 = 0
% 91.22/42.24 | (1310) ~ (all_0_2_2 = 0) | all_0_1_1 = all_0_3_3 | all_0_3_3 = all_0_6_6
% 91.22/42.24 |
% 91.22/42.25 +-Applying beta-rule and splitting (1310), into two cases.
% 91.22/42.25 |-Branch one:
% 91.22/42.25 | (1311) ~ (all_0_2_2 = 0)
% 91.22/42.25 |
% 91.22/42.25 +-Applying beta-rule and splitting (642), into two cases.
% 91.22/42.25 |-Branch one:
% 91.22/42.25 | (1266) xm = sz00
% 91.22/42.25 |
% 91.22/42.25 | Equations (1266) can reduce 1263 to:
% 91.22/42.25 | (216) $false
% 91.22/42.25 |
% 91.22/42.25 |-The branch is then unsatisfiable
% 91.22/42.25 |-Branch two:
% 91.22/42.25 | (1263) ~ (xm = sz00)
% 91.22/42.25 | (1315) xp = xn | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v4, v5) = v6 & sdtlseqdt0(xn, xp) = v3 & sdtasdt0(xp, xm) = v5 & sdtasdt0(xn, xm) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v6 = 0 & all_0_2_2 = 0 & ~ (v5 = v4) & ~ (all_0_3_3 = all_0_6_6))))
% 91.22/42.25 |
% 91.22/42.25 +-Applying beta-rule and splitting (1315), into two cases.
% 91.22/42.25 |-Branch one:
% 91.22/42.25 | (1203) xp = xn
% 91.22/42.25 |
% 91.22/42.25 | Equations (1203) can reduce 66 to:
% 91.22/42.25 | (216) $false
% 91.22/42.25 |
% 91.22/42.25 |-The branch is then unsatisfiable
% 91.22/42.25 |-Branch two:
% 91.22/42.25 | (66) ~ (xp = xn)
% 91.22/42.25 | (1319) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v4, v5) = v6 & sdtlseqdt0(xn, xp) = v3 & sdtasdt0(xp, xm) = v5 & sdtasdt0(xn, xm) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v6 = 0 & all_0_2_2 = 0 & ~ (v5 = v4) & ~ (all_0_3_3 = all_0_6_6))))
% 91.22/42.25 |
% 91.22/42.25 | Instantiating (1319) with all_1106_0_405, all_1106_1_406, all_1106_2_407, all_1106_3_408, all_1106_4_409, all_1106_5_410, all_1106_6_411 yields:
% 91.22/42.25 | (1320) sdtlseqdt0(all_1106_2_407, all_1106_1_406) = all_1106_0_405 & sdtlseqdt0(xn, xp) = all_1106_3_408 & sdtasdt0(xp, xm) = all_1106_1_406 & sdtasdt0(xn, xm) = all_1106_2_407 & aNaturalNumber0(xp) = all_1106_4_409 & aNaturalNumber0(xm) = all_1106_6_411 & aNaturalNumber0(xn) = all_1106_5_410 & ( ~ (all_1106_3_408 = 0) | ~ (all_1106_4_409 = 0) | ~ (all_1106_5_410 = 0) | ~ (all_1106_6_411 = 0) | (all_1106_0_405 = 0 & all_0_2_2 = 0 & ~ (all_1106_1_406 = all_1106_2_407) & ~ (all_0_3_3 = all_0_6_6)))
% 91.22/42.25 |
% 91.22/42.25 | Applying alpha-rule on (1320) yields:
% 91.22/42.25 | (1321) sdtlseqdt0(all_1106_2_407, all_1106_1_406) = all_1106_0_405
% 91.22/42.25 | (1322) aNaturalNumber0(xn) = all_1106_5_410
% 91.22/42.25 | (1323) sdtlseqdt0(xn, xp) = all_1106_3_408
% 91.22/42.25 | (1324) sdtasdt0(xn, xm) = all_1106_2_407
% 91.22/42.25 | (1325) aNaturalNumber0(xm) = all_1106_6_411
% 91.22/42.25 | (1326) aNaturalNumber0(xp) = all_1106_4_409
% 91.22/42.25 | (1327) ~ (all_1106_3_408 = 0) | ~ (all_1106_4_409 = 0) | ~ (all_1106_5_410 = 0) | ~ (all_1106_6_411 = 0) | (all_1106_0_405 = 0 & all_0_2_2 = 0 & ~ (all_1106_1_406 = all_1106_2_407) & ~ (all_0_3_3 = all_0_6_6))
% 91.22/42.25 | (1328) sdtasdt0(xp, xm) = all_1106_1_406
% 91.22/42.25 |
% 91.22/42.25 +-Applying beta-rule and splitting (636), into two cases.
% 91.22/42.25 |-Branch one:
% 91.22/42.25 | (215) xp = sz00
% 91.22/42.25 |
% 91.22/42.25 | Equations (215) can reduce 90 to:
% 91.22/42.25 | (216) $false
% 91.22/42.25 |
% 91.22/42.25 |-The branch is then unsatisfiable
% 91.22/42.25 |-Branch two:
% 91.22/42.25 | (90) ~ (xp = sz00)
% 91.22/42.25 | (1332) all_40_2_73 = xm | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v4, v5) = v6 & sdtlseqdt0(xm, all_40_2_73) = v3 & sdtasdt0(all_40_2_73, xp) = v5 & sdtasdt0(xm, xp) = v4 & aNaturalNumber0(all_40_2_73) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v6 = 0 & all_0_0_0 = 0 & ~ (v5 = v4) & ~ (all_0_3_3 = all_0_6_6))))
% 91.22/42.25 |
% 91.22/42.25 +-Applying beta-rule and splitting (1332), into two cases.
% 91.22/42.25 |-Branch one:
% 91.22/42.25 | (1273) all_40_2_73 = xm
% 91.22/42.25 |
% 91.22/42.25 | Combining equations (1273,1229) yields a new equation:
% 91.22/42.25 | (1245) xk = xm
% 91.22/42.25 |
% 91.22/42.25 | Equations (1245) can reduce 1223 to:
% 91.22/42.25 | (216) $false
% 91.22/42.25 |
% 91.22/42.25 |-The branch is then unsatisfiable
% 91.22/42.25 |-Branch two:
% 91.22/42.25 | (1276) ~ (all_40_2_73 = xm)
% 91.22/42.25 | (1337) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v4, v5) = v6 & sdtlseqdt0(xm, all_40_2_73) = v3 & sdtasdt0(all_40_2_73, xp) = v5 & sdtasdt0(xm, xp) = v4 & aNaturalNumber0(all_40_2_73) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v6 = 0 & all_0_0_0 = 0 & ~ (v5 = v4) & ~ (all_0_3_3 = all_0_6_6))))
% 91.22/42.25 |
% 91.22/42.25 | Instantiating (1337) with all_1115_0_412, all_1115_1_413, all_1115_2_414, all_1115_3_415, all_1115_4_416, all_1115_5_417, all_1115_6_418 yields:
% 91.22/42.25 | (1338) sdtlseqdt0(all_1115_2_414, all_1115_1_413) = all_1115_0_412 & sdtlseqdt0(xm, all_40_2_73) = all_1115_3_415 & sdtasdt0(all_40_2_73, xp) = all_1115_1_413 & sdtasdt0(xm, xp) = all_1115_2_414 & aNaturalNumber0(all_40_2_73) = all_1115_4_416 & aNaturalNumber0(xp) = all_1115_6_418 & aNaturalNumber0(xm) = all_1115_5_417 & ( ~ (all_1115_3_415 = 0) | ~ (all_1115_4_416 = 0) | ~ (all_1115_5_417 = 0) | ~ (all_1115_6_418 = 0) | (all_1115_0_412 = 0 & all_0_0_0 = 0 & ~ (all_1115_1_413 = all_1115_2_414) & ~ (all_0_3_3 = all_0_6_6)))
% 91.22/42.25 |
% 91.22/42.25 | Applying alpha-rule on (1338) yields:
% 91.22/42.25 | (1339) aNaturalNumber0(all_40_2_73) = all_1115_4_416
% 91.22/42.25 | (1340) sdtasdt0(all_40_2_73, xp) = all_1115_1_413
% 91.22/42.25 | (1341) aNaturalNumber0(xp) = all_1115_6_418
% 91.22/42.25 | (1342) sdtlseqdt0(xm, all_40_2_73) = all_1115_3_415
% 91.22/42.25 | (1343) aNaturalNumber0(xm) = all_1115_5_417
% 91.22/42.25 | (1344) sdtasdt0(xm, xp) = all_1115_2_414
% 91.22/42.25 | (1345) sdtlseqdt0(all_1115_2_414, all_1115_1_413) = all_1115_0_412
% 91.22/42.25 | (1346) ~ (all_1115_3_415 = 0) | ~ (all_1115_4_416 = 0) | ~ (all_1115_5_417 = 0) | ~ (all_1115_6_418 = 0) | (all_1115_0_412 = 0 & all_0_0_0 = 0 & ~ (all_1115_1_413 = all_1115_2_414) & ~ (all_0_3_3 = all_0_6_6))
% 91.22/42.25 |
% 91.22/42.25 | Instantiating formula (38) with xn, xp, all_1106_3_408, 0 and discharging atoms sdtlseqdt0(xn, xp) = all_1106_3_408, sdtlseqdt0(xn, xp) = 0, yields:
% 91.22/42.25 | (1347) all_1106_3_408 = 0
% 91.22/42.25 |
% 91.22/42.25 | Instantiating formula (55) with xp, all_1115_6_418, 0 and discharging atoms aNaturalNumber0(xp) = all_1115_6_418, aNaturalNumber0(xp) = 0, yields:
% 91.22/42.25 | (1348) all_1115_6_418 = 0
% 91.22/42.25 |
% 91.22/42.25 | Instantiating formula (55) with xp, all_1106_4_409, all_1115_6_418 and discharging atoms aNaturalNumber0(xp) = all_1115_6_418, aNaturalNumber0(xp) = all_1106_4_409, yields:
% 91.22/42.25 | (1349) all_1115_6_418 = all_1106_4_409
% 91.22/42.25 |
% 91.22/42.25 | Instantiating formula (55) with xm, all_1115_5_417, 0 and discharging atoms aNaturalNumber0(xm) = all_1115_5_417, aNaturalNumber0(xm) = 0, yields:
% 91.22/42.25 | (1350) all_1115_5_417 = 0
% 91.22/42.25 |
% 91.22/42.25 | Instantiating formula (55) with xm, all_1106_6_411, all_1115_5_417 and discharging atoms aNaturalNumber0(xm) = all_1115_5_417, aNaturalNumber0(xm) = all_1106_6_411, yields:
% 91.22/42.25 | (1351) all_1115_5_417 = all_1106_6_411
% 91.22/42.25 |
% 91.22/42.25 | Instantiating formula (55) with xm, all_1040_3_398, all_1106_6_411 and discharging atoms aNaturalNumber0(xm) = all_1106_6_411, aNaturalNumber0(xm) = all_1040_3_398, yields:
% 91.22/42.25 | (1352) all_1106_6_411 = all_1040_3_398
% 91.22/42.25 |
% 91.22/42.25 | Instantiating formula (55) with xn, all_1106_5_410, 0 and discharging atoms aNaturalNumber0(xn) = all_1106_5_410, aNaturalNumber0(xn) = 0, yields:
% 91.22/42.25 | (1353) all_1106_5_410 = 0
% 91.22/42.25 |
% 91.22/42.25 | Combining equations (1351,1350) yields a new equation:
% 91.22/42.25 | (1354) all_1106_6_411 = 0
% 91.22/42.25 |
% 91.22/42.25 | Simplifying 1354 yields:
% 91.22/42.25 | (1355) all_1106_6_411 = 0
% 91.22/42.25 |
% 91.22/42.25 | Combining equations (1348,1349) yields a new equation:
% 91.22/42.25 | (1356) all_1106_4_409 = 0
% 91.22/42.25 |
% 91.22/42.25 | Combining equations (1355,1352) yields a new equation:
% 91.22/42.25 | (1357) all_1040_3_398 = 0
% 91.22/42.25 |
% 91.22/42.25 | Combining equations (1357,1352) yields a new equation:
% 91.22/42.25 | (1355) all_1106_6_411 = 0
% 91.22/42.25 |
% 91.22/42.25 +-Applying beta-rule and splitting (1327), into two cases.
% 91.22/42.25 |-Branch one:
% 91.22/42.25 | (1359) ~ (all_1106_3_408 = 0)
% 91.22/42.25 |
% 91.22/42.25 | Equations (1347) can reduce 1359 to:
% 91.22/42.25 | (216) $false
% 91.22/42.25 |
% 91.22/42.25 |-The branch is then unsatisfiable
% 91.22/42.25 |-Branch two:
% 91.22/42.25 | (1347) all_1106_3_408 = 0
% 91.22/42.25 | (1362) ~ (all_1106_4_409 = 0) | ~ (all_1106_5_410 = 0) | ~ (all_1106_6_411 = 0) | (all_1106_0_405 = 0 & all_0_2_2 = 0 & ~ (all_1106_1_406 = all_1106_2_407) & ~ (all_0_3_3 = all_0_6_6))
% 91.22/42.25 |
% 91.22/42.25 +-Applying beta-rule and splitting (1362), into two cases.
% 91.22/42.25 |-Branch one:
% 91.22/42.25 | (1363) ~ (all_1106_4_409 = 0)
% 91.22/42.25 |
% 91.22/42.25 | Equations (1356) can reduce 1363 to:
% 91.22/42.25 | (216) $false
% 91.22/42.25 |
% 91.22/42.25 |-The branch is then unsatisfiable
% 91.22/42.25 |-Branch two:
% 91.22/42.25 | (1356) all_1106_4_409 = 0
% 91.22/42.25 | (1366) ~ (all_1106_5_410 = 0) | ~ (all_1106_6_411 = 0) | (all_1106_0_405 = 0 & all_0_2_2 = 0 & ~ (all_1106_1_406 = all_1106_2_407) & ~ (all_0_3_3 = all_0_6_6))
% 91.22/42.25 |
% 91.22/42.25 +-Applying beta-rule and splitting (1366), into two cases.
% 91.22/42.25 |-Branch one:
% 91.22/42.25 | (1367) ~ (all_1106_5_410 = 0)
% 91.22/42.25 |
% 91.22/42.25 | Equations (1353) can reduce 1367 to:
% 91.22/42.25 | (216) $false
% 91.22/42.25 |
% 91.22/42.25 |-The branch is then unsatisfiable
% 91.22/42.25 |-Branch two:
% 91.22/42.25 | (1353) all_1106_5_410 = 0
% 91.22/42.25 | (1370) ~ (all_1106_6_411 = 0) | (all_1106_0_405 = 0 & all_0_2_2 = 0 & ~ (all_1106_1_406 = all_1106_2_407) & ~ (all_0_3_3 = all_0_6_6))
% 91.22/42.25 |
% 91.22/42.25 +-Applying beta-rule and splitting (1370), into two cases.
% 91.22/42.25 |-Branch one:
% 91.22/42.25 | (1371) ~ (all_1106_6_411 = 0)
% 91.22/42.25 |
% 91.22/42.25 | Equations (1355) can reduce 1371 to:
% 91.22/42.25 | (216) $false
% 91.22/42.25 |
% 91.22/42.25 |-The branch is then unsatisfiable
% 91.22/42.25 |-Branch two:
% 91.22/42.25 | (1355) all_1106_6_411 = 0
% 91.22/42.25 | (1374) all_1106_0_405 = 0 & all_0_2_2 = 0 & ~ (all_1106_1_406 = all_1106_2_407) & ~ (all_0_3_3 = all_0_6_6)
% 91.22/42.25 |
% 91.22/42.25 | Applying alpha-rule on (1374) yields:
% 91.22/42.25 | (1375) all_1106_0_405 = 0
% 91.22/42.25 | (1376) all_0_2_2 = 0
% 91.22/42.25 | (1377) ~ (all_1106_1_406 = all_1106_2_407)
% 91.22/42.25 | (1306) ~ (all_0_3_3 = all_0_6_6)
% 91.22/42.25 |
% 91.22/42.25 | Equations (1376) can reduce 1311 to:
% 91.22/42.25 | (216) $false
% 91.22/42.25 |
% 91.22/42.25 |-The branch is then unsatisfiable
% 91.22/42.25 |-Branch two:
% 91.22/42.25 | (1376) all_0_2_2 = 0
% 91.22/42.25 | (1381) all_0_1_1 = all_0_3_3 | all_0_3_3 = all_0_6_6
% 91.22/42.25 |
% 91.22/42.25 +-Applying beta-rule and splitting (1381), into two cases.
% 91.22/42.25 |-Branch one:
% 91.22/42.25 | (1382) all_0_1_1 = all_0_3_3
% 91.22/42.25 |
% 91.22/42.25 | Combining equations (1382,488) yields a new equation:
% 91.22/42.25 | (1383) all_0_3_3 = all_0_6_6
% 91.22/42.25 |
% 91.22/42.25 | Simplifying 1383 yields:
% 91.22/42.25 | (1384) all_0_3_3 = all_0_6_6
% 91.22/42.25 |
% 91.22/42.25 | Equations (1384) can reduce 1306 to:
% 91.22/42.25 | (216) $false
% 91.22/42.25 |
% 91.22/42.25 |-The branch is then unsatisfiable
% 91.22/42.25 |-Branch two:
% 91.22/42.25 | (1304) ~ (all_0_1_1 = all_0_3_3)
% 91.22/42.25 | (1384) all_0_3_3 = all_0_6_6
% 91.22/42.25 |
% 91.22/42.25 | Equations (1384) can reduce 1306 to:
% 91.22/42.25 | (216) $false
% 91.22/42.25 |
% 91.22/42.25 |-The branch is then unsatisfiable
% 91.22/42.25 |-Branch two:
% 91.22/42.25 | (1389) ~ (all_70_0_94 = xp)
% 91.22/42.25 | (1390) all_70_0_94 = sz10 | ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_70_0_94) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0))
% 91.22/42.25 |
% 91.22/42.25 +-Applying beta-rule and splitting (1390), into two cases.
% 91.22/42.25 |-Branch one:
% 91.22/42.25 | (975) all_70_0_94 = sz10
% 91.22/42.25 |
% 91.22/42.25 | Equations (975) can reduce 252 to:
% 91.22/42.25 | (216) $false
% 91.22/42.25 |
% 91.22/42.25 |-The branch is then unsatisfiable
% 91.22/42.25 |-Branch two:
% 91.22/42.25 | (252) ~ (all_70_0_94 = sz10)
% 91.22/42.25 | (1394) ? [v0] : (( ~ (v0 = 0) & aNaturalNumber0(all_70_0_94) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0))
% 91.22/42.25 |
% 91.22/42.25 | Instantiating (1394) with all_1016_0_424 yields:
% 91.22/42.25 | (1395) ( ~ (all_1016_0_424 = 0) & aNaturalNumber0(all_70_0_94) = all_1016_0_424) | ( ~ (all_1016_0_424 = 0) & aNaturalNumber0(xp) = all_1016_0_424)
% 91.22/42.25 |
% 91.22/42.25 +-Applying beta-rule and splitting (126), into two cases.
% 91.22/42.25 |-Branch one:
% 91.22/42.25 | (215) xp = sz00
% 91.22/42.25 |
% 91.22/42.25 | Equations (215) can reduce 90 to:
% 91.22/42.25 | (216) $false
% 91.22/42.25 |
% 91.22/42.25 |-The branch is then unsatisfiable
% 91.22/42.25 |-Branch two:
% 91.22/42.25 | (90) ~ (xp = sz00)
% 91.22/42.25 | (1399) xk = xm | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(xk, xp) = v3 & sdtasdt0(xm, xp) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = v2) & ~ (all_0_1_1 = all_0_3_3))))
% 91.22/42.25 |
% 91.22/42.25 +-Applying beta-rule and splitting (1395), into two cases.
% 91.22/42.25 |-Branch one:
% 91.22/42.25 | (1400) ~ (all_1016_0_424 = 0) & aNaturalNumber0(all_70_0_94) = all_1016_0_424
% 91.22/42.25 |
% 91.22/42.25 | Applying alpha-rule on (1400) yields:
% 91.22/42.25 | (1401) ~ (all_1016_0_424 = 0)
% 91.22/42.25 | (1402) aNaturalNumber0(all_70_0_94) = all_1016_0_424
% 91.22/42.25 |
% 91.22/42.25 | Instantiating formula (55) with all_70_0_94, all_1016_0_424, 0 and discharging atoms aNaturalNumber0(all_70_0_94) = all_1016_0_424, aNaturalNumber0(all_70_0_94) = 0, yields:
% 91.22/42.26 | (1403) all_1016_0_424 = 0
% 91.22/42.26 |
% 91.22/42.26 | Equations (1403) can reduce 1401 to:
% 91.22/42.26 | (216) $false
% 91.22/42.26 |
% 91.22/42.26 |-The branch is then unsatisfiable
% 91.22/42.26 |-Branch two:
% 91.22/42.26 | (1405) ~ (all_1016_0_424 = 0) & aNaturalNumber0(xp) = all_1016_0_424
% 91.22/42.26 |
% 91.22/42.26 | Applying alpha-rule on (1405) yields:
% 91.22/42.26 | (1401) ~ (all_1016_0_424 = 0)
% 91.22/42.26 | (1407) aNaturalNumber0(xp) = all_1016_0_424
% 91.22/42.26 |
% 91.22/42.26 +-Applying beta-rule and splitting (1399), into two cases.
% 91.22/42.26 |-Branch one:
% 91.22/42.26 | (1245) xk = xm
% 91.22/42.26 |
% 91.22/42.26 | Equations (1245) can reduce 1223 to:
% 91.22/42.26 | (216) $false
% 91.22/42.26 |
% 91.22/42.26 |-The branch is then unsatisfiable
% 91.22/42.26 |-Branch two:
% 91.22/42.26 | (1223) ~ (xk = xm)
% 91.22/42.26 | (1411) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(xk, xp) = v3 & sdtasdt0(xm, xp) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = v2) & ~ (all_0_1_1 = all_0_3_3))))
% 91.22/42.26 |
% 91.22/42.26 +-Applying beta-rule and splitting (636), into two cases.
% 91.22/42.26 |-Branch one:
% 91.22/42.26 | (215) xp = sz00
% 91.22/42.26 |
% 91.22/42.26 | Equations (215) can reduce 90 to:
% 91.22/42.26 | (216) $false
% 91.22/42.26 |
% 91.22/42.26 |-The branch is then unsatisfiable
% 91.22/42.26 |-Branch two:
% 91.22/42.26 | (90) ~ (xp = sz00)
% 91.22/42.26 | (1332) all_40_2_73 = xm | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v4, v5) = v6 & sdtlseqdt0(xm, all_40_2_73) = v3 & sdtasdt0(all_40_2_73, xp) = v5 & sdtasdt0(xm, xp) = v4 & aNaturalNumber0(all_40_2_73) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v6 = 0 & all_0_0_0 = 0 & ~ (v5 = v4) & ~ (all_0_3_3 = all_0_6_6))))
% 91.22/42.26 |
% 91.22/42.26 +-Applying beta-rule and splitting (1332), into two cases.
% 91.22/42.26 |-Branch one:
% 91.22/42.26 | (1273) all_40_2_73 = xm
% 91.22/42.26 |
% 91.22/42.26 | Combining equations (1273,1229) yields a new equation:
% 91.22/42.26 | (1245) xk = xm
% 91.22/42.26 |
% 91.22/42.26 | Equations (1245) can reduce 1223 to:
% 91.22/42.26 | (216) $false
% 91.22/42.26 |
% 91.22/42.26 |-The branch is then unsatisfiable
% 91.22/42.26 |-Branch two:
% 91.22/42.26 | (1276) ~ (all_40_2_73 = xm)
% 91.22/42.26 | (1337) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v4, v5) = v6 & sdtlseqdt0(xm, all_40_2_73) = v3 & sdtasdt0(all_40_2_73, xp) = v5 & sdtasdt0(xm, xp) = v4 & aNaturalNumber0(all_40_2_73) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v6 = 0 & all_0_0_0 = 0 & ~ (v5 = v4) & ~ (all_0_3_3 = all_0_6_6))))
% 91.22/42.26 |
% 91.22/42.26 | Instantiating (1337) with all_1085_0_454, all_1085_1_455, all_1085_2_456, all_1085_3_457, all_1085_4_458, all_1085_5_459, all_1085_6_460 yields:
% 91.22/42.26 | (1421) sdtlseqdt0(all_1085_2_456, all_1085_1_455) = all_1085_0_454 & sdtlseqdt0(xm, all_40_2_73) = all_1085_3_457 & sdtasdt0(all_40_2_73, xp) = all_1085_1_455 & sdtasdt0(xm, xp) = all_1085_2_456 & aNaturalNumber0(all_40_2_73) = all_1085_4_458 & aNaturalNumber0(xp) = all_1085_6_460 & aNaturalNumber0(xm) = all_1085_5_459 & ( ~ (all_1085_3_457 = 0) | ~ (all_1085_4_458 = 0) | ~ (all_1085_5_459 = 0) | ~ (all_1085_6_460 = 0) | (all_1085_0_454 = 0 & all_0_0_0 = 0 & ~ (all_1085_1_455 = all_1085_2_456) & ~ (all_0_3_3 = all_0_6_6)))
% 91.22/42.26 |
% 91.22/42.26 | Applying alpha-rule on (1421) yields:
% 91.22/42.26 | (1422) aNaturalNumber0(xp) = all_1085_6_460
% 91.22/42.26 | (1423) ~ (all_1085_3_457 = 0) | ~ (all_1085_4_458 = 0) | ~ (all_1085_5_459 = 0) | ~ (all_1085_6_460 = 0) | (all_1085_0_454 = 0 & all_0_0_0 = 0 & ~ (all_1085_1_455 = all_1085_2_456) & ~ (all_0_3_3 = all_0_6_6))
% 91.22/42.26 | (1424) sdtlseqdt0(xm, all_40_2_73) = all_1085_3_457
% 91.22/42.26 | (1425) aNaturalNumber0(xm) = all_1085_5_459
% 91.22/42.26 | (1426) sdtasdt0(xm, xp) = all_1085_2_456
% 91.22/42.26 | (1427) sdtlseqdt0(all_1085_2_456, all_1085_1_455) = all_1085_0_454
% 91.22/42.26 | (1428) sdtasdt0(all_40_2_73, xp) = all_1085_1_455
% 91.22/42.26 | (1429) aNaturalNumber0(all_40_2_73) = all_1085_4_458
% 91.22/42.26 |
% 91.22/42.26 | Instantiating formula (55) with xp, all_1085_6_460, 0 and discharging atoms aNaturalNumber0(xp) = all_1085_6_460, aNaturalNumber0(xp) = 0, yields:
% 91.22/42.26 | (1430) all_1085_6_460 = 0
% 91.22/42.26 |
% 91.22/42.26 | Instantiating formula (55) with xp, all_1016_0_424, all_1085_6_460 and discharging atoms aNaturalNumber0(xp) = all_1085_6_460, aNaturalNumber0(xp) = all_1016_0_424, yields:
% 91.22/42.26 | (1431) all_1085_6_460 = all_1016_0_424
% 91.22/42.26 |
% 91.22/42.26 | Combining equations (1431,1430) yields a new equation:
% 91.22/42.26 | (1432) all_1016_0_424 = 0
% 91.22/42.26 |
% 91.22/42.26 | Simplifying 1432 yields:
% 91.22/42.26 | (1403) all_1016_0_424 = 0
% 91.22/42.26 |
% 91.22/42.26 | Equations (1403) can reduce 1401 to:
% 91.22/42.26 | (216) $false
% 91.22/42.26 |
% 91.22/42.26 |-The branch is then unsatisfiable
% 91.22/42.26 |-Branch two:
% 91.22/42.26 | (1435) sdtasdt0(sz00, xn) = all_0_6_6
% 91.22/42.26 | (1436) ? [v0] : ? [v1] : (sdtasdt0(xn, sz00) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v0 = 0) | (v1 = sz00 & all_0_6_6 = sz00)))
% 91.22/42.26 |
% 91.22/42.26 | Instantiating (1436) with all_976_0_464, all_976_1_465 yields:
% 91.22/42.26 | (1437) sdtasdt0(xn, sz00) = all_976_0_464 & aNaturalNumber0(xn) = all_976_1_465 & ( ~ (all_976_1_465 = 0) | (all_976_0_464 = sz00 & all_0_6_6 = sz00))
% 91.22/42.26 |
% 91.22/42.26 | Applying alpha-rule on (1437) yields:
% 91.22/42.26 | (1438) sdtasdt0(xn, sz00) = all_976_0_464
% 91.22/42.26 | (1439) aNaturalNumber0(xn) = all_976_1_465
% 91.22/42.26 | (1440) ~ (all_976_1_465 = 0) | (all_976_0_464 = sz00 & all_0_6_6 = sz00)
% 91.22/42.26 |
% 91.22/42.26 +-Applying beta-rule and splitting (1440), into two cases.
% 91.22/42.26 |-Branch one:
% 91.22/42.26 | (1441) ~ (all_976_1_465 = 0)
% 91.22/42.26 |
% 91.22/42.26 | Instantiating formula (55) with xn, all_976_1_465, 0 and discharging atoms aNaturalNumber0(xn) = all_976_1_465, aNaturalNumber0(xn) = 0, yields:
% 91.22/42.26 | (1442) all_976_1_465 = 0
% 91.22/42.26 |
% 91.22/42.26 | Equations (1442) can reduce 1441 to:
% 91.22/42.26 | (216) $false
% 91.22/42.26 |
% 91.22/42.26 |-The branch is then unsatisfiable
% 91.22/42.26 |-Branch two:
% 91.22/42.26 | (1442) all_976_1_465 = 0
% 91.22/42.26 | (1445) all_976_0_464 = sz00 & all_0_6_6 = sz00
% 91.22/42.26 |
% 91.22/42.26 | Applying alpha-rule on (1445) yields:
% 91.22/42.26 | (1446) all_976_0_464 = sz00
% 91.22/42.26 | (568) all_0_6_6 = sz00
% 91.22/42.26 |
% 91.22/42.26 | Equations (568) can reduce 554 to:
% 91.22/42.26 | (216) $false
% 91.22/42.26 |
% 91.22/42.26 |-The branch is then unsatisfiable
% 91.22/42.26 |-Branch two:
% 91.22/42.26 | (1449) ~ (all_40_2_73 = xk)
% 91.22/42.26 | (1450) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_40_2_73, xp) = v2 & sdtasdt0(xk, xp) = v3 & aNaturalNumber0(all_40_2_73) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 91.22/42.26 |
% 91.22/42.26 | Instantiating (1450) with all_841_0_466, all_841_1_467, all_841_2_468, all_841_3_469 yields:
% 91.22/42.26 | (1451) sdtasdt0(all_40_2_73, xp) = all_841_1_467 & sdtasdt0(xk, xp) = all_841_0_466 & aNaturalNumber0(all_40_2_73) = all_841_3_469 & aNaturalNumber0(xk) = all_841_2_468 & ( ~ (all_841_2_468 = 0) | ~ (all_841_3_469 = 0))
% 91.22/42.26 |
% 91.22/42.26 | Applying alpha-rule on (1451) yields:
% 91.22/42.26 | (1452) sdtasdt0(xk, xp) = all_841_0_466
% 91.22/42.26 | (1453) aNaturalNumber0(all_40_2_73) = all_841_3_469
% 91.22/42.26 | (1454) aNaturalNumber0(xk) = all_841_2_468
% 91.22/42.26 | (1455) ~ (all_841_2_468 = 0) | ~ (all_841_3_469 = 0)
% 91.22/42.26 | (1456) sdtasdt0(all_40_2_73, xp) = all_841_1_467
% 91.22/42.26 |
% 91.22/42.26 +-Applying beta-rule and splitting (110), into two cases.
% 91.22/42.26 |-Branch one:
% 91.22/42.26 | (215) xp = sz00
% 91.22/42.26 |
% 91.22/42.26 | Equations (215) can reduce 90 to:
% 91.22/42.26 | (216) $false
% 91.22/42.26 |
% 91.22/42.26 |-The branch is then unsatisfiable
% 91.22/42.26 |-Branch two:
% 91.22/42.26 | (90) ~ (xp = sz00)
% 91.22/42.26 | (1244) xk = xm | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v4, v5) = v6 & sdtlseqdt0(xm, xk) = v3 & sdtasdt0(xk, xp) = v5 & sdtasdt0(xm, xp) = v4 & aNaturalNumber0(xk) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v6 = 0 & all_0_0_0 = 0 & ~ (v5 = v4) & ~ (all_0_1_1 = all_0_3_3))))
% 91.22/42.26 |
% 91.22/42.26 +-Applying beta-rule and splitting (1244), into two cases.
% 91.22/42.26 |-Branch one:
% 91.22/42.26 | (1245) xk = xm
% 91.22/42.26 |
% 91.22/42.26 | Equations (1245) can reduce 1223 to:
% 91.22/42.26 | (216) $false
% 91.22/42.26 |
% 91.22/42.26 |-The branch is then unsatisfiable
% 91.22/42.26 |-Branch two:
% 91.22/42.26 | (1223) ~ (xk = xm)
% 91.22/42.26 | (1248) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v4, v5) = v6 & sdtlseqdt0(xm, xk) = v3 & sdtasdt0(xk, xp) = v5 & sdtasdt0(xm, xp) = v4 & aNaturalNumber0(xk) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v6 = 0 & all_0_0_0 = 0 & ~ (v5 = v4) & ~ (all_0_1_1 = all_0_3_3))))
% 91.22/42.26 |
% 91.22/42.26 | Instantiating (1248) with all_864_0_470, all_864_1_471, all_864_2_472, all_864_3_473, all_864_4_474, all_864_5_475, all_864_6_476 yields:
% 91.22/42.26 | (1465) sdtlseqdt0(all_864_2_472, all_864_1_471) = all_864_0_470 & sdtlseqdt0(xm, xk) = all_864_3_473 & sdtasdt0(xk, xp) = all_864_1_471 & sdtasdt0(xm, xp) = all_864_2_472 & aNaturalNumber0(xk) = all_864_4_474 & aNaturalNumber0(xp) = all_864_6_476 & aNaturalNumber0(xm) = all_864_5_475 & ( ~ (all_864_3_473 = 0) | ~ (all_864_4_474 = 0) | ~ (all_864_5_475 = 0) | ~ (all_864_6_476 = 0) | (all_864_0_470 = 0 & all_0_0_0 = 0 & ~ (all_864_1_471 = all_864_2_472) & ~ (all_0_1_1 = all_0_3_3)))
% 91.22/42.26 |
% 91.22/42.26 | Applying alpha-rule on (1465) yields:
% 91.22/42.26 | (1466) ~ (all_864_3_473 = 0) | ~ (all_864_4_474 = 0) | ~ (all_864_5_475 = 0) | ~ (all_864_6_476 = 0) | (all_864_0_470 = 0 & all_0_0_0 = 0 & ~ (all_864_1_471 = all_864_2_472) & ~ (all_0_1_1 = all_0_3_3))
% 91.22/42.26 | (1467) aNaturalNumber0(xm) = all_864_5_475
% 91.22/42.26 | (1468) aNaturalNumber0(xp) = all_864_6_476
% 91.22/42.26 | (1469) sdtasdt0(xk, xp) = all_864_1_471
% 91.22/42.26 | (1470) sdtasdt0(xm, xp) = all_864_2_472
% 91.22/42.26 | (1471) sdtlseqdt0(all_864_2_472, all_864_1_471) = all_864_0_470
% 91.22/42.26 | (1472) sdtlseqdt0(xm, xk) = all_864_3_473
% 91.22/42.26 | (1473) aNaturalNumber0(xk) = all_864_4_474
% 91.22/42.26 |
% 91.22/42.26 | Instantiating formula (55) with all_40_2_73, all_841_3_469, 0 and discharging atoms aNaturalNumber0(all_40_2_73) = all_841_3_469, aNaturalNumber0(all_40_2_73) = 0, yields:
% 91.22/42.26 | (1474) all_841_3_469 = 0
% 91.22/42.26 |
% 91.22/42.26 | Instantiating formula (55) with xk, all_864_4_474, 0 and discharging atoms aNaturalNumber0(xk) = all_864_4_474, aNaturalNumber0(xk) = 0, yields:
% 91.22/42.26 | (1475) all_864_4_474 = 0
% 91.22/42.26 |
% 91.22/42.26 | Instantiating formula (55) with xk, all_841_2_468, all_864_4_474 and discharging atoms aNaturalNumber0(xk) = all_864_4_474, aNaturalNumber0(xk) = all_841_2_468, yields:
% 91.22/42.26 | (1476) all_864_4_474 = all_841_2_468
% 91.22/42.26 |
% 91.22/42.26 | Combining equations (1475,1476) yields a new equation:
% 91.22/42.26 | (1477) all_841_2_468 = 0
% 91.22/42.26 |
% 91.22/42.26 +-Applying beta-rule and splitting (1455), into two cases.
% 91.22/42.26 |-Branch one:
% 91.22/42.26 | (1478) ~ (all_841_2_468 = 0)
% 91.22/42.26 |
% 91.22/42.26 | Equations (1477) can reduce 1478 to:
% 91.22/42.26 | (216) $false
% 91.22/42.26 |
% 91.22/42.26 |-The branch is then unsatisfiable
% 91.22/42.26 |-Branch two:
% 91.22/42.26 | (1477) all_841_2_468 = 0
% 91.22/42.26 | (1481) ~ (all_841_3_469 = 0)
% 91.22/42.26 |
% 91.22/42.26 | Equations (1474) can reduce 1481 to:
% 91.22/42.26 | (216) $false
% 91.22/42.26 |
% 91.22/42.26 |-The branch is then unsatisfiable
% 91.22/42.26 |-Branch two:
% 91.22/42.26 | (1483) aNaturalNumber0(xr) = all_41_2_76 & aNaturalNumber0(xk) = all_41_1_75 & ( ~ (all_41_1_75 = 0) | ~ (all_41_2_76 = 0))
% 91.22/42.26 |
% 91.22/42.26 | Applying alpha-rule on (1483) yields:
% 91.22/42.26 | (1484) aNaturalNumber0(xr) = all_41_2_76
% 91.22/42.26 | (1485) aNaturalNumber0(xk) = all_41_1_75
% 91.22/42.26 | (1486) ~ (all_41_1_75 = 0) | ~ (all_41_2_76 = 0)
% 91.22/42.27 |
% 91.22/42.27 | Instantiating formula (55) with xr, all_41_2_76, 0 and discharging atoms aNaturalNumber0(xr) = all_41_2_76, aNaturalNumber0(xr) = 0, yields:
% 91.22/42.27 | (1487) all_41_2_76 = 0
% 91.22/42.27 |
% 91.22/42.27 | Instantiating formula (55) with xk, all_41_1_75, 0 and discharging atoms aNaturalNumber0(xk) = all_41_1_75, aNaturalNumber0(xk) = 0, yields:
% 91.22/42.27 | (614) all_41_1_75 = 0
% 91.22/42.27 |
% 91.22/42.27 +-Applying beta-rule and splitting (1486), into two cases.
% 91.22/42.27 |-Branch one:
% 91.22/42.27 | (1489) ~ (all_41_1_75 = 0)
% 91.22/42.27 |
% 91.22/42.27 | Equations (614) can reduce 1489 to:
% 91.22/42.27 | (216) $false
% 91.22/42.27 |
% 91.22/42.27 |-The branch is then unsatisfiable
% 91.22/42.27 |-Branch two:
% 91.22/42.27 | (614) all_41_1_75 = 0
% 91.22/42.27 | (1492) ~ (all_41_2_76 = 0)
% 91.22/42.27 |
% 91.22/42.27 | Equations (1487) can reduce 1492 to:
% 91.22/42.27 | (216) $false
% 91.22/42.27 |
% 91.22/42.27 |-The branch is then unsatisfiable
% 91.22/42.27 |-Branch two:
% 91.22/42.27 | (1494) aNaturalNumber0(xk) = all_33_1_48 & aNaturalNumber0(xp) = all_33_2_49 & ( ~ (all_33_1_48 = 0) | ~ (all_33_2_49 = 0))
% 91.22/42.27 |
% 91.22/42.27 | Applying alpha-rule on (1494) yields:
% 91.22/42.27 | (1495) aNaturalNumber0(xk) = all_33_1_48
% 91.22/42.27 | (1496) aNaturalNumber0(xp) = all_33_2_49
% 91.22/42.27 | (1497) ~ (all_33_1_48 = 0) | ~ (all_33_2_49 = 0)
% 91.22/42.27 |
% 91.22/42.27 +-Applying beta-rule and splitting (94), into two cases.
% 91.22/42.27 |-Branch one:
% 91.22/42.27 | (568) all_0_6_6 = sz00
% 91.22/42.27 |
% 91.22/42.27 | Equations (568) can reduce 554 to:
% 91.22/42.27 | (216) $false
% 91.22/42.27 |
% 91.22/42.27 |-The branch is then unsatisfiable
% 91.22/42.27 |-Branch two:
% 91.22/42.27 | (554) ~ (all_0_6_6 = sz00)
% 91.22/42.27 | (586) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, all_0_6_6) = v2 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 91.22/42.27 |
% 91.22/42.27 | Instantiating (586) with all_273_0_485, all_273_1_486, all_273_2_487 yields:
% 91.22/42.27 | (1502) sdtlseqdt0(xp, all_0_6_6) = all_273_0_485 & aNaturalNumber0(all_0_6_6) = all_273_1_486 & aNaturalNumber0(xp) = all_273_2_487 & ( ~ (all_273_1_486 = 0) | ~ (all_273_2_487 = 0) | all_273_0_485 = 0)
% 91.22/42.27 |
% 91.22/42.27 | Applying alpha-rule on (1502) yields:
% 91.22/42.27 | (1503) sdtlseqdt0(xp, all_0_6_6) = all_273_0_485
% 91.22/42.27 | (1504) aNaturalNumber0(all_0_6_6) = all_273_1_486
% 91.22/42.27 | (1505) aNaturalNumber0(xp) = all_273_2_487
% 91.22/42.27 | (1506) ~ (all_273_1_486 = 0) | ~ (all_273_2_487 = 0) | all_273_0_485 = 0
% 91.22/42.27 |
% 91.22/42.27 | Instantiating formula (55) with xk, all_33_1_48, 0 and discharging atoms aNaturalNumber0(xk) = all_33_1_48, aNaturalNumber0(xk) = 0, yields:
% 91.22/42.27 | (580) all_33_1_48 = 0
% 91.22/42.27 |
% 91.22/42.27 | Instantiating formula (55) with xp, all_273_2_487, 0 and discharging atoms aNaturalNumber0(xp) = all_273_2_487, aNaturalNumber0(xp) = 0, yields:
% 91.22/42.27 | (1508) all_273_2_487 = 0
% 91.22/42.27 |
% 91.22/42.27 | Instantiating formula (55) with xp, all_33_2_49, all_273_2_487 and discharging atoms aNaturalNumber0(xp) = all_273_2_487, aNaturalNumber0(xp) = all_33_2_49, yields:
% 91.22/42.27 | (1509) all_273_2_487 = all_33_2_49
% 91.22/42.27 |
% 91.22/42.27 | Combining equations (1508,1509) yields a new equation:
% 91.22/42.27 | (1510) all_33_2_49 = 0
% 91.22/42.27 |
% 91.22/42.27 +-Applying beta-rule and splitting (1497), into two cases.
% 91.22/42.27 |-Branch one:
% 91.22/42.27 | (1511) ~ (all_33_1_48 = 0)
% 91.22/42.27 |
% 91.22/42.27 | Equations (580) can reduce 1511 to:
% 91.22/42.27 | (216) $false
% 91.22/42.27 |
% 91.22/42.27 |-The branch is then unsatisfiable
% 91.22/42.27 |-Branch two:
% 91.22/42.27 | (580) all_33_1_48 = 0
% 91.22/42.27 | (1514) ~ (all_33_2_49 = 0)
% 91.22/42.27 |
% 91.22/42.27 | Equations (1510) can reduce 1514 to:
% 91.22/42.27 | (216) $false
% 91.22/42.27 |
% 91.22/42.27 |-The branch is then unsatisfiable
% 91.22/42.27 |-Branch two:
% 91.22/42.27 | (1516) sdtasdt0(sz00, xm) = all_0_6_6
% 91.22/42.27 | (1517) ? [v0] : ? [v1] : (sdtasdt0(xm, sz00) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v0 = 0) | (v1 = sz00 & all_0_6_6 = sz00)))
% 91.22/42.27 |
% 91.22/42.27 | Instantiating (1517) with all_265_0_488, all_265_1_489 yields:
% 91.22/42.27 | (1518) sdtasdt0(xm, sz00) = all_265_0_488 & aNaturalNumber0(xm) = all_265_1_489 & ( ~ (all_265_1_489 = 0) | (all_265_0_488 = sz00 & all_0_6_6 = sz00))
% 91.22/42.27 |
% 91.22/42.27 | Applying alpha-rule on (1518) yields:
% 91.22/42.27 | (1519) sdtasdt0(xm, sz00) = all_265_0_488
% 91.22/42.27 | (1520) aNaturalNumber0(xm) = all_265_1_489
% 91.22/42.27 | (1521) ~ (all_265_1_489 = 0) | (all_265_0_488 = sz00 & all_0_6_6 = sz00)
% 91.22/42.27 |
% 91.22/42.27 +-Applying beta-rule and splitting (1521), into two cases.
% 91.22/42.27 |-Branch one:
% 91.22/42.27 | (1522) ~ (all_265_1_489 = 0)
% 91.22/42.27 |
% 91.22/42.27 | Instantiating formula (55) with xm, all_265_1_489, 0 and discharging atoms aNaturalNumber0(xm) = all_265_1_489, aNaturalNumber0(xm) = 0, yields:
% 91.22/42.27 | (1523) all_265_1_489 = 0
% 91.22/42.27 |
% 91.22/42.27 | Equations (1523) can reduce 1522 to:
% 91.22/42.27 | (216) $false
% 91.22/42.27 |
% 91.22/42.27 |-The branch is then unsatisfiable
% 91.22/42.27 |-Branch two:
% 91.22/42.27 | (1523) all_265_1_489 = 0
% 91.22/42.27 | (1526) all_265_0_488 = sz00 & all_0_6_6 = sz00
% 91.22/42.27 |
% 91.22/42.27 | Applying alpha-rule on (1526) yields:
% 91.22/42.27 | (1527) all_265_0_488 = sz00
% 91.22/42.27 | (568) all_0_6_6 = sz00
% 91.22/42.27 |
% 91.22/42.27 | Equations (568) can reduce 554 to:
% 91.22/42.27 | (216) $false
% 91.22/42.27 |
% 91.22/42.27 |-The branch is then unsatisfiable
% 91.22/42.27 |-Branch two:
% 91.22/42.27 | (1530) sdtasdt0(sz10, xm) = all_0_6_6
% 91.22/42.27 | (1531) ? [v0] : ? [v1] : (sdtasdt0(xm, sz10) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v0 = 0) | (v1 = xm & all_0_6_6 = xm)))
% 91.22/42.27 |
% 91.22/42.27 | Instantiating (1531) with all_255_0_493, all_255_1_494 yields:
% 91.22/42.27 | (1532) sdtasdt0(xm, sz10) = all_255_0_493 & aNaturalNumber0(xm) = all_255_1_494 & ( ~ (all_255_1_494 = 0) | (all_255_0_493 = xm & all_0_6_6 = xm))
% 91.22/42.27 |
% 91.22/42.27 | Applying alpha-rule on (1532) yields:
% 91.22/42.27 | (1533) sdtasdt0(xm, sz10) = all_255_0_493
% 91.22/42.27 | (1534) aNaturalNumber0(xm) = all_255_1_494
% 91.22/42.27 | (1535) ~ (all_255_1_494 = 0) | (all_255_0_493 = xm & all_0_6_6 = xm)
% 91.22/42.27 |
% 91.22/42.27 +-Applying beta-rule and splitting (1535), into two cases.
% 91.22/42.27 |-Branch one:
% 91.22/42.27 | (1536) ~ (all_255_1_494 = 0)
% 91.22/42.27 |
% 91.22/42.27 | Instantiating formula (55) with xm, all_255_1_494, 0 and discharging atoms aNaturalNumber0(xm) = all_255_1_494, aNaturalNumber0(xm) = 0, yields:
% 91.22/42.27 | (1537) all_255_1_494 = 0
% 91.22/42.27 |
% 91.22/42.27 | Equations (1537) can reduce 1536 to:
% 91.22/42.27 | (216) $false
% 91.22/42.27 |
% 91.22/42.27 |-The branch is then unsatisfiable
% 91.22/42.27 |-Branch two:
% 91.22/42.27 | (1537) all_255_1_494 = 0
% 91.22/42.27 | (1540) all_255_0_493 = xm & all_0_6_6 = xm
% 91.22/42.27 |
% 91.22/42.27 | Applying alpha-rule on (1540) yields:
% 91.22/42.27 | (1541) all_255_0_493 = xm
% 91.22/42.27 | (1542) all_0_6_6 = xm
% 91.22/42.27 |
% 91.22/42.27 | Equations (1542) can reduce 553 to:
% 91.22/42.27 | (216) $false
% 91.22/42.27 |
% 91.22/42.27 |-The branch is then unsatisfiable
% 91.22/42.27 |-Branch two:
% 91.22/42.27 | (962) all_58_0_90 = 0
% 91.22/42.27 | (1545) ~ (all_58_1_91 = 0) | ~ (all_58_2_92 = 0) | ~ (all_58_3_93 = 0)
% 91.22/42.27 |
% 91.22/42.27 +-Applying beta-rule and splitting (1545), into two cases.
% 91.22/42.27 |-Branch one:
% 91.22/42.27 | (1546) ~ (all_58_1_91 = 0)
% 91.22/42.27 |
% 91.22/42.27 | Equations (369) can reduce 1546 to:
% 91.22/42.27 | (216) $false
% 91.22/42.27 |
% 91.22/42.27 |-The branch is then unsatisfiable
% 91.22/42.27 |-Branch two:
% 91.22/42.27 | (369) all_58_1_91 = 0
% 91.22/42.27 | (1549) ~ (all_58_2_92 = 0) | ~ (all_58_3_93 = 0)
% 91.22/42.27 |
% 91.22/42.27 +-Applying beta-rule and splitting (1549), into two cases.
% 91.22/42.27 |-Branch one:
% 91.22/42.27 | (1550) ~ (all_58_2_92 = 0)
% 91.22/42.27 |
% 91.22/42.27 | Equations (448) can reduce 1550 to:
% 91.22/42.27 | (216) $false
% 91.22/42.27 |
% 91.22/42.27 |-The branch is then unsatisfiable
% 91.22/42.27 |-Branch two:
% 91.22/42.27 | (448) all_58_2_92 = 0
% 91.22/42.27 | (1553) ~ (all_58_3_93 = 0)
% 91.22/42.27 |
% 91.22/42.27 | Equations (265) can reduce 1553 to:
% 91.22/42.27 | (216) $false
% 91.22/42.27 |
% 91.22/42.27 |-The branch is then unsatisfiable
% 91.22/42.27 |-Branch two:
% 91.22/42.27 | (953) all_53_0_86 = 0
% 91.22/42.27 | (1556) ~ (all_53_1_87 = 0) | ~ (all_53_2_88 = 0) | ~ (all_53_3_89 = 0)
% 91.22/42.27 |
% 91.22/42.27 +-Applying beta-rule and splitting (1556), into two cases.
% 91.22/42.27 |-Branch one:
% 91.22/42.27 | (1557) ~ (all_53_1_87 = 0)
% 91.22/42.27 |
% 91.22/42.27 | Equations (367) can reduce 1557 to:
% 91.22/42.27 | (216) $false
% 91.22/42.27 |
% 91.22/42.27 |-The branch is then unsatisfiable
% 91.22/42.27 |-Branch two:
% 91.22/42.27 | (367) all_53_1_87 = 0
% 91.22/42.27 | (1560) ~ (all_53_2_88 = 0) | ~ (all_53_3_89 = 0)
% 91.22/42.27 |
% 91.22/42.27 +-Applying beta-rule and splitting (1560), into two cases.
% 91.22/42.27 |-Branch one:
% 91.22/42.27 | (1561) ~ (all_53_2_88 = 0)
% 91.22/42.27 |
% 91.22/42.27 | Equations (451) can reduce 1561 to:
% 91.22/42.27 | (216) $false
% 91.22/42.27 |
% 91.22/42.27 |-The branch is then unsatisfiable
% 91.22/42.27 |-Branch two:
% 91.22/42.27 | (451) all_53_2_88 = 0
% 91.22/42.27 | (1564) ~ (all_53_3_89 = 0)
% 91.22/42.27 |
% 91.22/42.27 | Equations (365) can reduce 1564 to:
% 91.22/42.27 | (216) $false
% 91.22/42.27 |
% 91.22/42.27 |-The branch is then unsatisfiable
% 91.22/42.27 |-Branch two:
% 91.22/42.27 | (1566) aNaturalNumber0(all_0_6_6) = all_40_1_72 & aNaturalNumber0(xp) = all_40_2_73 & ( ~ (all_40_1_72 = 0) | ~ (all_40_2_73 = 0))
% 91.22/42.27 |
% 91.22/42.27 | Applying alpha-rule on (1566) yields:
% 91.22/42.27 | (1567) aNaturalNumber0(all_0_6_6) = all_40_1_72
% 91.22/42.27 | (1568) aNaturalNumber0(xp) = all_40_2_73
% 91.22/42.27 | (1569) ~ (all_40_1_72 = 0) | ~ (all_40_2_73 = 0)
% 91.22/42.27 |
% 91.22/42.27 +-Applying beta-rule and splitting (105), into two cases.
% 91.22/42.27 |-Branch one:
% 91.22/42.27 | (497) ~ (sdtasdt0(xp, xk) = all_0_6_6)
% 91.22/42.27 |
% 91.22/42.27 | Using (490) and (497) yields:
% 91.22/42.27 | (419) $false
% 91.22/42.27 |
% 91.22/42.27 |-The branch is then unsatisfiable
% 91.22/42.27 |-Branch two:
% 91.22/42.27 | (490) sdtasdt0(xp, xk) = all_0_6_6
% 91.22/42.27 | (500) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xr) = v3 & doDivides0(xr, xk) = v8 & doDivides0(xr, xp) = v7 & iLess0(v5, all_0_7_7) = v6 & sdtpldt0(v4, xr) = v5 & sdtpldt0(xp, xk) = v4 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 91.22/42.27 |
% 91.22/42.27 | Instantiating (500) with all_216_0_510, all_216_1_511, all_216_2_512, all_216_3_513, all_216_4_514, all_216_5_515, all_216_6_516, all_216_7_517, all_216_8_518 yields:
% 91.22/42.27 | (1574) isPrime0(xr) = all_216_5_515 & doDivides0(xr, xk) = all_216_0_510 & doDivides0(xr, xp) = all_216_1_511 & iLess0(all_216_3_513, all_0_7_7) = all_216_2_512 & sdtpldt0(all_216_4_514, xr) = all_216_3_513 & sdtpldt0(xp, xk) = all_216_4_514 & aNaturalNumber0(xr) = all_216_6_516 & aNaturalNumber0(xk) = all_216_7_517 & aNaturalNumber0(xp) = all_216_8_518 & ( ~ (all_216_2_512 = 0) | ~ (all_216_5_515 = 0) | ~ (all_216_6_516 = 0) | ~ (all_216_7_517 = 0) | ~ (all_216_8_518 = 0) | all_216_0_510 = 0 | all_216_1_511 = 0)
% 91.22/42.27 |
% 91.22/42.27 | Applying alpha-rule on (1574) yields:
% 91.22/42.27 | (1575) ~ (all_216_2_512 = 0) | ~ (all_216_5_515 = 0) | ~ (all_216_6_516 = 0) | ~ (all_216_7_517 = 0) | ~ (all_216_8_518 = 0) | all_216_0_510 = 0 | all_216_1_511 = 0
% 91.22/42.27 | (1576) isPrime0(xr) = all_216_5_515
% 91.22/42.27 | (1577) aNaturalNumber0(xk) = all_216_7_517
% 91.22/42.27 | (1578) sdtpldt0(all_216_4_514, xr) = all_216_3_513
% 91.22/42.27 | (1579) doDivides0(xr, xk) = all_216_0_510
% 91.22/42.27 | (1580) sdtpldt0(xp, xk) = all_216_4_514
% 91.22/42.27 | (1581) doDivides0(xr, xp) = all_216_1_511
% 91.22/42.27 | (1582) aNaturalNumber0(xp) = all_216_8_518
% 91.22/42.28 | (1583) aNaturalNumber0(xr) = all_216_6_516
% 91.22/42.28 | (1584) iLess0(all_216_3_513, all_0_7_7) = all_216_2_512
% 91.22/42.28 |
% 91.22/42.28 +-Applying beta-rule and splitting (106), into two cases.
% 91.22/42.28 |-Branch one:
% 91.22/42.28 | (497) ~ (sdtasdt0(xp, xk) = all_0_6_6)
% 91.22/42.28 |
% 91.22/42.28 | Using (490) and (497) yields:
% 91.22/42.28 | (419) $false
% 91.22/42.28 |
% 91.22/42.28 |-The branch is then unsatisfiable
% 91.22/42.28 |-Branch two:
% 91.22/42.28 | (490) sdtasdt0(xp, xk) = all_0_6_6
% 91.22/42.28 | (521) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, xk) = v8 & doDivides0(xp, xp) = v7 & iLess0(v5, all_0_7_7) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xp, xk) = v4 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 91.22/42.28 |
% 91.22/42.28 | Instantiating (521) with all_233_0_519, all_233_1_520, all_233_2_521, all_233_3_522, all_233_4_523, all_233_5_524, all_233_6_525, all_233_7_526, all_233_8_527 yields:
% 91.22/42.28 | (1589) isPrime0(xp) = all_233_5_524 & doDivides0(xp, xk) = all_233_0_519 & doDivides0(xp, xp) = all_233_1_520 & iLess0(all_233_3_522, all_0_7_7) = all_233_2_521 & sdtpldt0(all_233_4_523, xp) = all_233_3_522 & sdtpldt0(xp, xk) = all_233_4_523 & aNaturalNumber0(xk) = all_233_7_526 & aNaturalNumber0(xp) = all_233_6_525 & aNaturalNumber0(xp) = all_233_8_527 & ( ~ (all_233_2_521 = 0) | ~ (all_233_5_524 = 0) | ~ (all_233_6_525 = 0) | ~ (all_233_7_526 = 0) | ~ (all_233_8_527 = 0) | all_233_0_519 = 0 | all_233_1_520 = 0)
% 91.22/42.28 |
% 91.22/42.28 | Applying alpha-rule on (1589) yields:
% 91.22/42.28 | (1590) aNaturalNumber0(xp) = all_233_6_525
% 91.22/42.28 | (1591) isPrime0(xp) = all_233_5_524
% 91.22/42.28 | (1592) doDivides0(xp, xp) = all_233_1_520
% 91.22/42.28 | (1593) ~ (all_233_2_521 = 0) | ~ (all_233_5_524 = 0) | ~ (all_233_6_525 = 0) | ~ (all_233_7_526 = 0) | ~ (all_233_8_527 = 0) | all_233_0_519 = 0 | all_233_1_520 = 0
% 91.22/42.28 | (1594) sdtpldt0(xp, xk) = all_233_4_523
% 91.22/42.28 | (1595) aNaturalNumber0(xk) = all_233_7_526
% 91.22/42.28 | (1596) sdtpldt0(all_233_4_523, xp) = all_233_3_522
% 91.22/42.28 | (1597) doDivides0(xp, xk) = all_233_0_519
% 91.22/42.28 | (1598) iLess0(all_233_3_522, all_0_7_7) = all_233_2_521
% 91.22/42.28 | (1599) aNaturalNumber0(xp) = all_233_8_527
% 91.22/42.28 |
% 91.22/42.28 | Instantiating formula (55) with all_0_6_6, all_40_1_72, 0 and discharging atoms aNaturalNumber0(all_0_6_6) = all_40_1_72, aNaturalNumber0(all_0_6_6) = 0, yields:
% 91.22/42.28 | (494) all_40_1_72 = 0
% 91.22/42.28 |
% 91.22/42.28 | Instantiating formula (55) with xp, all_233_6_525, 0 and discharging atoms aNaturalNumber0(xp) = all_233_6_525, aNaturalNumber0(xp) = 0, yields:
% 91.22/42.28 | (1601) all_233_6_525 = 0
% 91.22/42.28 |
% 91.22/42.28 | Instantiating formula (55) with xp, all_216_8_518, all_233_6_525 and discharging atoms aNaturalNumber0(xp) = all_233_6_525, aNaturalNumber0(xp) = all_216_8_518, yields:
% 91.22/42.28 | (1602) all_233_6_525 = all_216_8_518
% 91.22/42.28 |
% 91.22/42.28 | Instantiating formula (55) with xp, all_216_8_518, all_233_8_527 and discharging atoms aNaturalNumber0(xp) = all_233_8_527, aNaturalNumber0(xp) = all_216_8_518, yields:
% 91.22/42.28 | (1603) all_233_8_527 = all_216_8_518
% 91.22/42.28 |
% 91.22/42.28 | Instantiating formula (55) with xp, all_40_2_73, all_233_8_527 and discharging atoms aNaturalNumber0(xp) = all_233_8_527, aNaturalNumber0(xp) = all_40_2_73, yields:
% 91.22/42.28 | (1604) all_233_8_527 = all_40_2_73
% 91.22/42.28 |
% 91.22/42.28 | Combining equations (1602,1601) yields a new equation:
% 91.22/42.28 | (1605) all_216_8_518 = 0
% 91.22/42.28 |
% 91.22/42.28 | Simplifying 1605 yields:
% 91.22/42.28 | (1606) all_216_8_518 = 0
% 91.22/42.28 |
% 91.22/42.28 | Combining equations (1603,1604) yields a new equation:
% 91.22/42.28 | (1607) all_216_8_518 = all_40_2_73
% 91.22/42.28 |
% 91.22/42.28 | Simplifying 1607 yields:
% 91.22/42.28 | (1608) all_216_8_518 = all_40_2_73
% 91.22/42.28 |
% 91.22/42.28 | Combining equations (1608,1606) yields a new equation:
% 91.22/42.28 | (1609) all_40_2_73 = 0
% 91.22/42.28 |
% 91.22/42.28 | Simplifying 1609 yields:
% 91.22/42.28 | (1610) all_40_2_73 = 0
% 91.22/42.28 |
% 91.22/42.28 +-Applying beta-rule and splitting (1569), into two cases.
% 91.22/42.28 |-Branch one:
% 91.22/42.28 | (1611) ~ (all_40_1_72 = 0)
% 91.22/42.28 |
% 91.22/42.28 | Equations (494) can reduce 1611 to:
% 91.22/42.28 | (216) $false
% 91.22/42.28 |
% 91.22/42.28 |-The branch is then unsatisfiable
% 91.22/42.28 |-Branch two:
% 91.22/42.28 | (494) all_40_1_72 = 0
% 91.22/42.28 | (1614) ~ (all_40_2_73 = 0)
% 91.22/42.28 |
% 91.22/42.28 | Equations (1610) can reduce 1614 to:
% 91.22/42.28 | (216) $false
% 91.22/42.28 |
% 91.22/42.28 |-The branch is then unsatisfiable
% 91.22/42.28 |-Branch two:
% 91.22/42.28 | (1616) ~ (all_0_1_1 = all_0_6_6)
% 91.22/42.28 | (1617) ? [v0] : ? [v1] : ? [v2] : (doDivides0(xp, all_0_6_6) = v2 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 91.22/42.28 |
% 91.22/42.28 | Instantiating (1617) with all_205_0_528, all_205_1_529, all_205_2_530 yields:
% 91.22/42.28 | (1618) doDivides0(xp, all_0_6_6) = all_205_0_528 & aNaturalNumber0(all_0_6_6) = all_205_1_529 & aNaturalNumber0(xp) = all_205_2_530 & ( ~ (all_205_0_528 = 0) | ~ (all_205_1_529 = 0) | ~ (all_205_2_530 = 0))
% 91.22/42.28 |
% 91.22/42.28 | Applying alpha-rule on (1618) yields:
% 91.22/42.28 | (1619) doDivides0(xp, all_0_6_6) = all_205_0_528
% 91.22/42.28 | (1620) aNaturalNumber0(all_0_6_6) = all_205_1_529
% 91.22/42.28 | (1621) aNaturalNumber0(xp) = all_205_2_530
% 91.22/42.28 | (1622) ~ (all_205_0_528 = 0) | ~ (all_205_1_529 = 0) | ~ (all_205_2_530 = 0)
% 91.62/42.28 |
% 91.62/42.28 | Instantiating formula (72) with xp, all_0_6_6, all_205_0_528, 0 and discharging atoms doDivides0(xp, all_0_6_6) = all_205_0_528, doDivides0(xp, all_0_6_6) = 0, yields:
% 91.62/42.28 | (1623) all_205_0_528 = 0
% 91.62/42.28 |
% 91.62/42.28 | Instantiating formula (55) with all_0_6_6, all_205_1_529, 0 and discharging atoms aNaturalNumber0(all_0_6_6) = all_205_1_529, aNaturalNumber0(all_0_6_6) = 0, yields:
% 91.62/42.28 | (1624) all_205_1_529 = 0
% 91.62/42.28 |
% 91.62/42.28 | Instantiating formula (55) with xp, all_205_2_530, 0 and discharging atoms aNaturalNumber0(xp) = all_205_2_530, aNaturalNumber0(xp) = 0, yields:
% 91.62/42.28 | (1625) all_205_2_530 = 0
% 91.62/42.28 |
% 91.62/42.28 +-Applying beta-rule and splitting (1622), into two cases.
% 91.62/42.28 |-Branch one:
% 91.62/42.28 | (1626) ~ (all_205_0_528 = 0)
% 91.62/42.28 |
% 91.62/42.28 | Equations (1623) can reduce 1626 to:
% 91.62/42.28 | (216) $false
% 91.62/42.28 |
% 91.62/42.28 |-The branch is then unsatisfiable
% 91.62/42.28 |-Branch two:
% 91.62/42.28 | (1623) all_205_0_528 = 0
% 91.62/42.28 | (1629) ~ (all_205_1_529 = 0) | ~ (all_205_2_530 = 0)
% 91.62/42.28 |
% 91.62/42.28 +-Applying beta-rule and splitting (1629), into two cases.
% 91.62/42.28 |-Branch one:
% 91.62/42.28 | (1630) ~ (all_205_1_529 = 0)
% 91.62/42.28 |
% 91.62/42.28 | Equations (1624) can reduce 1630 to:
% 91.62/42.28 | (216) $false
% 91.62/42.28 |
% 91.62/42.28 |-The branch is then unsatisfiable
% 91.62/42.28 |-Branch two:
% 91.62/42.28 | (1624) all_205_1_529 = 0
% 91.62/42.28 | (1633) ~ (all_205_2_530 = 0)
% 91.62/42.28 |
% 91.62/42.28 | Equations (1625) can reduce 1633 to:
% 91.62/42.28 | (216) $false
% 91.62/42.28 |
% 91.62/42.28 |-The branch is then unsatisfiable
% 91.62/42.28 |-Branch two:
% 91.62/42.28 | (1635) sdtasdt0(xp, xk) = xm
% 91.62/42.28 | (1636) all_0_4_4 = 0 | xk = sz00 | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 91.62/42.28 |
% 91.62/42.28 +-Applying beta-rule and splitting (1636), into two cases.
% 91.62/42.28 |-Branch one:
% 91.62/42.28 | (1637) xk = sz00
% 91.62/42.28 |
% 91.62/42.28 | Equations (1637) can reduce 31 to:
% 91.62/42.28 | (216) $false
% 91.62/42.28 |
% 91.62/42.28 |-The branch is then unsatisfiable
% 91.62/42.28 |-Branch two:
% 91.62/42.28 | (31) ~ (xk = sz00)
% 91.62/42.28 | (1640) all_0_4_4 = 0 | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 91.62/42.28 |
% 91.62/42.28 +-Applying beta-rule and splitting (1640), into two cases.
% 91.62/42.28 |-Branch one:
% 91.62/42.28 | (220) all_0_4_4 = 0
% 91.62/42.28 |
% 91.62/42.28 | Equations (220) can reduce 74 to:
% 91.62/42.28 | (216) $false
% 91.62/42.28 |
% 91.62/42.28 |-The branch is then unsatisfiable
% 91.62/42.28 |-Branch two:
% 91.62/42.28 | (74) ~ (all_0_4_4 = 0)
% 91.62/42.28 | (1644) ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 91.62/42.28 |
% 91.62/42.28 | Instantiating (1644) with all_205_0_531, all_205_1_532 yields:
% 91.62/42.28 | (1645) aNaturalNumber0(xk) = all_205_1_532 & aNaturalNumber0(xp) = all_205_0_531 & ( ~ (all_205_0_531 = 0) | ~ (all_205_1_532 = 0))
% 91.62/42.28 |
% 91.62/42.28 | Applying alpha-rule on (1645) yields:
% 91.62/42.28 | (1646) aNaturalNumber0(xk) = all_205_1_532
% 91.62/42.28 | (1647) aNaturalNumber0(xp) = all_205_0_531
% 91.62/42.28 | (1648) ~ (all_205_0_531 = 0) | ~ (all_205_1_532 = 0)
% 91.62/42.28 |
% 91.62/42.28 | Instantiating formula (55) with xk, all_205_1_532, 0 and discharging atoms aNaturalNumber0(xk) = all_205_1_532, aNaturalNumber0(xk) = 0, yields:
% 91.62/42.28 | (1649) all_205_1_532 = 0
% 91.62/42.28 |
% 91.62/42.28 | Instantiating formula (55) with xp, all_205_0_531, 0 and discharging atoms aNaturalNumber0(xp) = all_205_0_531, aNaturalNumber0(xp) = 0, yields:
% 91.62/42.28 | (1650) all_205_0_531 = 0
% 91.62/42.28 |
% 91.62/42.28 +-Applying beta-rule and splitting (1648), into two cases.
% 91.62/42.28 |-Branch one:
% 91.62/42.28 | (1651) ~ (all_205_0_531 = 0)
% 91.62/42.28 |
% 91.62/42.28 | Equations (1650) can reduce 1651 to:
% 91.62/42.28 | (216) $false
% 91.62/42.28 |
% 91.62/42.28 |-The branch is then unsatisfiable
% 91.62/42.28 |-Branch two:
% 91.62/42.28 | (1650) all_205_0_531 = 0
% 91.62/42.28 | (1654) ~ (all_205_1_532 = 0)
% 91.62/42.28 |
% 91.62/42.28 | Equations (1649) can reduce 1654 to:
% 91.62/42.28 | (216) $false
% 91.62/42.28 |
% 91.62/42.28 |-The branch is then unsatisfiable
% 91.62/42.28 |-Branch two:
% 91.62/42.28 | (1656) aNaturalNumber0(xp) = all_28_1_39 & aNaturalNumber0(xm) = all_28_2_40 & ( ~ (all_28_1_39 = 0) | ~ (all_28_2_40 = 0))
% 91.62/42.28 |
% 91.62/42.28 | Applying alpha-rule on (1656) yields:
% 91.62/42.28 | (1657) aNaturalNumber0(xp) = all_28_1_39
% 91.62/42.28 | (1658) aNaturalNumber0(xm) = all_28_2_40
% 91.62/42.28 | (1659) ~ (all_28_1_39 = 0) | ~ (all_28_2_40 = 0)
% 91.62/42.28 |
% 91.62/42.28 | Instantiating formula (55) with xp, all_28_1_39, 0 and discharging atoms aNaturalNumber0(xp) = all_28_1_39, aNaturalNumber0(xp) = 0, yields:
% 91.62/42.28 | (471) all_28_1_39 = 0
% 91.62/42.28 |
% 91.62/42.28 | Instantiating formula (55) with xm, all_28_2_40, 0 and discharging atoms aNaturalNumber0(xm) = all_28_2_40, aNaturalNumber0(xm) = 0, yields:
% 91.62/42.28 | (1661) all_28_2_40 = 0
% 91.62/42.28 |
% 91.62/42.28 +-Applying beta-rule and splitting (1659), into two cases.
% 91.62/42.28 |-Branch one:
% 91.62/42.28 | (1662) ~ (all_28_1_39 = 0)
% 91.62/42.28 |
% 91.62/42.28 | Equations (471) can reduce 1662 to:
% 91.62/42.28 | (216) $false
% 91.62/42.28 |
% 91.62/42.28 |-The branch is then unsatisfiable
% 91.62/42.28 |-Branch two:
% 91.62/42.28 | (471) all_28_1_39 = 0
% 91.62/42.28 | (1665) ~ (all_28_2_40 = 0)
% 91.62/42.28 |
% 91.62/42.28 | Equations (1661) can reduce 1665 to:
% 91.62/42.28 | (216) $false
% 91.62/42.28 |
% 91.62/42.28 |-The branch is then unsatisfiable
% 91.62/42.28 |-Branch two:
% 91.62/42.28 | (1667) aNaturalNumber0(all_0_6_6) = all_42_1_78 & aNaturalNumber0(xr) = all_42_2_79 & ( ~ (all_42_1_78 = 0) | ~ (all_42_2_79 = 0))
% 91.62/42.28 |
% 91.62/42.28 | Applying alpha-rule on (1667) yields:
% 91.62/42.28 | (1668) aNaturalNumber0(all_0_6_6) = all_42_1_78
% 91.62/42.28 | (1669) aNaturalNumber0(xr) = all_42_2_79
% 91.62/42.28 | (1670) ~ (all_42_1_78 = 0) | ~ (all_42_2_79 = 0)
% 91.62/42.28 |
% 91.62/42.28 | Instantiating formula (55) with all_0_6_6, all_42_1_78, 0 and discharging atoms aNaturalNumber0(all_0_6_6) = all_42_1_78, aNaturalNumber0(all_0_6_6) = 0, yields:
% 91.62/42.28 | (466) all_42_1_78 = 0
% 91.62/42.28 |
% 91.62/42.28 | Instantiating formula (55) with xr, all_42_2_79, 0 and discharging atoms aNaturalNumber0(xr) = all_42_2_79, aNaturalNumber0(xr) = 0, yields:
% 91.62/42.29 | (1672) all_42_2_79 = 0
% 91.62/42.29 |
% 91.62/42.29 +-Applying beta-rule and splitting (1670), into two cases.
% 91.62/42.29 |-Branch one:
% 91.62/42.29 | (1673) ~ (all_42_1_78 = 0)
% 91.62/42.29 |
% 91.62/42.29 | Equations (466) can reduce 1673 to:
% 91.62/42.29 | (216) $false
% 91.62/42.29 |
% 91.62/42.29 |-The branch is then unsatisfiable
% 91.62/42.29 |-Branch two:
% 91.62/42.29 | (466) all_42_1_78 = 0
% 91.62/42.29 | (1676) ~ (all_42_2_79 = 0)
% 91.62/42.29 |
% 91.62/42.29 | Equations (1672) can reduce 1676 to:
% 91.62/42.29 | (216) $false
% 91.62/42.29 |
% 91.62/42.29 |-The branch is then unsatisfiable
% 91.62/42.29 |-Branch two:
% 91.62/42.29 | (1678) sdtasdt0(xp, xk) = sz00
% 91.62/42.29 | (1679) xk = sz00 | xp = sz00 | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 91.62/42.29 |
% 91.62/42.29 +-Applying beta-rule and splitting (102), into two cases.
% 91.62/42.29 |-Branch one:
% 91.62/42.29 | (1680) ~ (sdtasdt0(xp, xk) = xn)
% 91.62/42.29 |
% 91.62/42.29 +-Applying beta-rule and splitting (101), into two cases.
% 91.62/42.29 |-Branch one:
% 91.62/42.29 | (483) ~ (sdtasdt0(xp, xk) = xm)
% 91.62/42.29 |
% 91.62/42.29 +-Applying beta-rule and splitting (103), into two cases.
% 91.62/42.29 |-Branch one:
% 91.62/42.29 | (215) xp = sz00
% 91.62/42.29 |
% 91.62/42.29 | Equations (215) can reduce 90 to:
% 91.62/42.29 | (216) $false
% 91.62/42.29 |
% 91.62/42.29 |-The branch is then unsatisfiable
% 91.62/42.29 |-Branch two:
% 91.62/42.29 | (90) ~ (xp = sz00)
% 91.62/42.29 | (487) all_0_1_1 = all_0_6_6 | ? [v0] : ? [v1] : ? [v2] : (doDivides0(xp, all_0_6_6) = v2 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 91.62/42.29 |
% 91.62/42.29 +-Applying beta-rule and splitting (487), into two cases.
% 91.62/42.29 |-Branch one:
% 91.62/42.29 | (488) all_0_1_1 = all_0_6_6
% 91.62/42.29 |
% 91.62/42.29 | From (488) and (17) follows:
% 91.62/42.29 | (490) sdtasdt0(xp, xk) = all_0_6_6
% 91.62/42.29 |
% 91.62/42.29 +-Applying beta-rule and splitting (105), into two cases.
% 91.62/42.29 |-Branch one:
% 91.62/42.29 | (497) ~ (sdtasdt0(xp, xk) = all_0_6_6)
% 91.62/42.29 |
% 91.62/42.29 | Using (490) and (497) yields:
% 91.62/42.29 | (419) $false
% 91.62/42.29 |
% 91.62/42.29 |-The branch is then unsatisfiable
% 91.62/42.29 |-Branch two:
% 91.62/42.29 | (490) sdtasdt0(xp, xk) = all_0_6_6
% 91.62/42.29 | (500) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xr) = v3 & doDivides0(xr, xk) = v8 & doDivides0(xr, xp) = v7 & iLess0(v5, all_0_7_7) = v6 & sdtpldt0(v4, xr) = v5 & sdtpldt0(xp, xk) = v4 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 91.62/42.29 |
% 91.62/42.29 +-Applying beta-rule and splitting (106), into two cases.
% 91.62/42.29 |-Branch one:
% 91.62/42.29 | (497) ~ (sdtasdt0(xp, xk) = all_0_6_6)
% 91.62/42.29 |
% 91.62/42.29 | Using (490) and (497) yields:
% 91.62/42.29 | (419) $false
% 91.62/42.29 |
% 91.62/42.29 |-The branch is then unsatisfiable
% 91.62/42.29 |-Branch two:
% 91.62/42.29 | (490) sdtasdt0(xp, xk) = all_0_6_6
% 91.62/42.29 | (521) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, xk) = v8 & doDivides0(xp, xp) = v7 & iLess0(v5, all_0_7_7) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xp, xk) = v4 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 91.62/42.29 |
% 91.62/42.29 | Instantiating formula (46) with xp, xk, sz00, all_0_6_6 and discharging atoms sdtasdt0(xp, xk) = all_0_6_6, sdtasdt0(xp, xk) = sz00, yields:
% 91.62/42.29 | (568) all_0_6_6 = sz00
% 91.62/42.29 |
% 91.62/42.29 | Using (490) and (483) yields:
% 91.62/42.29 | (553) ~ (all_0_6_6 = xm)
% 91.62/42.29 |
% 91.62/42.29 | Using (490) and (1680) yields:
% 91.62/42.29 | (1698) ~ (all_0_6_6 = xn)
% 91.62/42.29 |
% 91.62/42.29 | Equations (568) can reduce 553 to:
% 91.62/42.29 | (1699) ~ (xm = sz00)
% 91.62/42.29 |
% 91.62/42.29 | Simplifying 1699 yields:
% 91.62/42.29 | (1263) ~ (xm = sz00)
% 91.62/42.29 |
% 91.62/42.29 | Equations (568) can reduce 1698 to:
% 91.62/42.29 | (1701) ~ (xn = sz00)
% 91.62/42.29 |
% 91.62/42.29 | Simplifying 1701 yields:
% 91.62/42.29 | (596) ~ (xn = sz00)
% 91.62/42.29 |
% 91.62/42.29 | From (568) and (85) follows:
% 91.62/42.29 | (1703) sdtasdt0(xn, xm) = sz00
% 91.62/42.29 |
% 91.62/42.29 +-Applying beta-rule and splitting (116), into two cases.
% 91.62/42.29 |-Branch one:
% 91.62/42.29 | (1704) ~ (sdtasdt0(xn, xm) = sz00)
% 91.62/42.29 |
% 91.62/42.29 | Using (1703) and (1704) yields:
% 91.62/42.29 | (419) $false
% 91.62/42.29 |
% 91.62/42.29 |-The branch is then unsatisfiable
% 91.62/42.29 |-Branch two:
% 91.62/42.29 | (1703) sdtasdt0(xn, xm) = sz00
% 91.62/42.29 | (1707) xm = sz00 | xn = sz00 | ? [v0] : ? [v1] : (aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 91.62/42.29 |
% 91.62/42.29 +-Applying beta-rule and splitting (1707), into two cases.
% 91.62/42.29 |-Branch one:
% 91.62/42.29 | (1266) xm = sz00
% 91.62/42.29 |
% 91.62/42.29 | Equations (1266) can reduce 1263 to:
% 91.62/42.29 | (216) $false
% 91.62/42.29 |
% 91.62/42.29 |-The branch is then unsatisfiable
% 91.62/42.29 |-Branch two:
% 91.62/42.29 | (1263) ~ (xm = sz00)
% 91.62/42.29 | (1711) xn = sz00 | ? [v0] : ? [v1] : (aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 91.62/42.29 |
% 91.62/42.29 +-Applying beta-rule and splitting (1711), into two cases.
% 91.62/42.29 |-Branch one:
% 91.62/42.29 | (608) xn = sz00
% 91.62/42.29 |
% 91.62/42.29 | Equations (608) can reduce 596 to:
% 91.62/42.29 | (216) $false
% 91.62/42.29 |
% 91.62/42.29 |-The branch is then unsatisfiable
% 91.62/42.29 |-Branch two:
% 91.62/42.29 | (596) ~ (xn = sz00)
% 91.62/42.29 | (1715) ? [v0] : ? [v1] : (aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 91.62/42.29 |
% 91.62/42.29 | Instantiating (1715) with all_285_0_571, all_285_1_572 yields:
% 91.62/42.29 | (1716) aNaturalNumber0(xm) = all_285_0_571 & aNaturalNumber0(xn) = all_285_1_572 & ( ~ (all_285_0_571 = 0) | ~ (all_285_1_572 = 0))
% 91.62/42.29 |
% 91.62/42.29 | Applying alpha-rule on (1716) yields:
% 91.62/42.29 | (1717) aNaturalNumber0(xm) = all_285_0_571
% 91.62/42.29 | (1718) aNaturalNumber0(xn) = all_285_1_572
% 91.62/42.29 | (1719) ~ (all_285_0_571 = 0) | ~ (all_285_1_572 = 0)
% 91.62/42.29 |
% 91.62/42.29 | Instantiating formula (55) with xm, all_285_0_571, 0 and discharging atoms aNaturalNumber0(xm) = all_285_0_571, aNaturalNumber0(xm) = 0, yields:
% 91.62/42.29 | (1720) all_285_0_571 = 0
% 91.62/42.29 |
% 91.62/42.29 | Instantiating formula (55) with xn, all_285_1_572, 0 and discharging atoms aNaturalNumber0(xn) = all_285_1_572, aNaturalNumber0(xn) = 0, yields:
% 91.62/42.29 | (1721) all_285_1_572 = 0
% 91.62/42.29 |
% 91.62/42.29 +-Applying beta-rule and splitting (1719), into two cases.
% 91.62/42.29 |-Branch one:
% 91.62/42.29 | (1722) ~ (all_285_0_571 = 0)
% 91.62/42.29 |
% 91.62/42.29 | Equations (1720) can reduce 1722 to:
% 91.62/42.29 | (216) $false
% 91.62/42.29 |
% 91.62/42.29 |-The branch is then unsatisfiable
% 91.62/42.29 |-Branch two:
% 91.62/42.29 | (1720) all_285_0_571 = 0
% 91.62/42.29 | (1725) ~ (all_285_1_572 = 0)
% 91.62/42.29 |
% 91.62/42.29 | Equations (1721) can reduce 1725 to:
% 91.62/42.29 | (216) $false
% 91.62/42.29 |
% 91.62/42.29 |-The branch is then unsatisfiable
% 91.62/42.29 |-Branch two:
% 91.62/42.29 | (1616) ~ (all_0_1_1 = all_0_6_6)
% 91.62/42.29 | (1617) ? [v0] : ? [v1] : ? [v2] : (doDivides0(xp, all_0_6_6) = v2 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 91.62/42.29 |
% 91.62/42.29 | Instantiating (1617) with all_225_0_574, all_225_1_575, all_225_2_576 yields:
% 91.62/42.29 | (1729) doDivides0(xp, all_0_6_6) = all_225_0_574 & aNaturalNumber0(all_0_6_6) = all_225_1_575 & aNaturalNumber0(xp) = all_225_2_576 & ( ~ (all_225_0_574 = 0) | ~ (all_225_1_575 = 0) | ~ (all_225_2_576 = 0))
% 91.62/42.29 |
% 91.62/42.29 | Applying alpha-rule on (1729) yields:
% 91.62/42.29 | (1730) doDivides0(xp, all_0_6_6) = all_225_0_574
% 91.62/42.29 | (1731) aNaturalNumber0(all_0_6_6) = all_225_1_575
% 91.62/42.29 | (1732) aNaturalNumber0(xp) = all_225_2_576
% 91.62/42.29 | (1733) ~ (all_225_0_574 = 0) | ~ (all_225_1_575 = 0) | ~ (all_225_2_576 = 0)
% 91.62/42.29 |
% 91.62/42.29 +-Applying beta-rule and splitting (1679), into two cases.
% 91.62/42.29 |-Branch one:
% 91.62/42.29 | (1637) xk = sz00
% 91.62/42.29 |
% 91.62/42.29 | Equations (1637) can reduce 31 to:
% 91.62/42.29 | (216) $false
% 91.62/42.29 |
% 91.62/42.29 |-The branch is then unsatisfiable
% 91.62/42.29 |-Branch two:
% 91.62/42.29 | (31) ~ (xk = sz00)
% 91.62/42.29 | (1737) xp = sz00 | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 91.62/42.29 |
% 91.62/42.29 +-Applying beta-rule and splitting (1737), into two cases.
% 91.62/42.29 |-Branch one:
% 91.62/42.29 | (215) xp = sz00
% 91.62/42.29 |
% 91.62/42.29 | Equations (215) can reduce 90 to:
% 91.62/42.29 | (216) $false
% 91.67/42.29 |
% 91.67/42.29 |-The branch is then unsatisfiable
% 91.67/42.29 |-Branch two:
% 91.67/42.29 | (90) ~ (xp = sz00)
% 91.67/42.29 | (1741) ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 91.67/42.29 |
% 91.67/42.29 | Instantiating (1741) with all_247_0_577, all_247_1_578 yields:
% 91.67/42.29 | (1742) aNaturalNumber0(xk) = all_247_0_577 & aNaturalNumber0(xp) = all_247_1_578 & ( ~ (all_247_0_577 = 0) | ~ (all_247_1_578 = 0))
% 91.67/42.29 |
% 91.67/42.29 | Applying alpha-rule on (1742) yields:
% 91.67/42.29 | (1743) aNaturalNumber0(xk) = all_247_0_577
% 91.67/42.29 | (1744) aNaturalNumber0(xp) = all_247_1_578
% 91.67/42.29 | (1745) ~ (all_247_0_577 = 0) | ~ (all_247_1_578 = 0)
% 91.67/42.29 |
% 91.67/42.29 | Instantiating formula (72) with xp, all_0_6_6, all_225_0_574, 0 and discharging atoms doDivides0(xp, all_0_6_6) = all_225_0_574, doDivides0(xp, all_0_6_6) = 0, yields:
% 91.67/42.29 | (1746) all_225_0_574 = 0
% 91.67/42.29 |
% 91.67/42.29 | Instantiating formula (55) with all_0_6_6, all_225_1_575, 0 and discharging atoms aNaturalNumber0(all_0_6_6) = all_225_1_575, aNaturalNumber0(all_0_6_6) = 0, yields:
% 91.67/42.29 | (1747) all_225_1_575 = 0
% 91.67/42.29 |
% 91.67/42.29 | Instantiating formula (55) with xp, all_247_1_578, 0 and discharging atoms aNaturalNumber0(xp) = all_247_1_578, aNaturalNumber0(xp) = 0, yields:
% 91.67/42.29 | (1748) all_247_1_578 = 0
% 91.67/42.29 |
% 91.67/42.29 | Instantiating formula (55) with xp, all_225_2_576, all_247_1_578 and discharging atoms aNaturalNumber0(xp) = all_247_1_578, aNaturalNumber0(xp) = all_225_2_576, yields:
% 91.67/42.29 | (1749) all_247_1_578 = all_225_2_576
% 91.67/42.29 |
% 91.67/42.29 | Combining equations (1748,1749) yields a new equation:
% 91.67/42.29 | (1750) all_225_2_576 = 0
% 91.67/42.29 |
% 91.67/42.29 +-Applying beta-rule and splitting (1733), into two cases.
% 91.67/42.29 |-Branch one:
% 91.67/42.29 | (1751) ~ (all_225_0_574 = 0)
% 91.67/42.29 |
% 91.67/42.29 | Equations (1746) can reduce 1751 to:
% 91.67/42.29 | (216) $false
% 91.67/42.29 |
% 91.67/42.29 |-The branch is then unsatisfiable
% 91.67/42.29 |-Branch two:
% 91.67/42.29 | (1746) all_225_0_574 = 0
% 91.67/42.29 | (1754) ~ (all_225_1_575 = 0) | ~ (all_225_2_576 = 0)
% 91.67/42.29 |
% 91.67/42.29 +-Applying beta-rule and splitting (1754), into two cases.
% 91.67/42.29 |-Branch one:
% 91.67/42.29 | (1755) ~ (all_225_1_575 = 0)
% 91.67/42.29 |
% 91.67/42.29 | Equations (1747) can reduce 1755 to:
% 91.67/42.29 | (216) $false
% 91.67/42.29 |
% 91.67/42.29 |-The branch is then unsatisfiable
% 91.67/42.29 |-Branch two:
% 91.67/42.29 | (1747) all_225_1_575 = 0
% 91.67/42.29 | (1758) ~ (all_225_2_576 = 0)
% 91.67/42.29 |
% 91.67/42.29 | Equations (1750) can reduce 1758 to:
% 91.67/42.29 | (216) $false
% 91.67/42.29 |
% 91.67/42.29 |-The branch is then unsatisfiable
% 91.67/42.29 |-Branch two:
% 91.67/42.29 | (1635) sdtasdt0(xp, xk) = xm
% 91.67/42.29 | (1636) all_0_4_4 = 0 | xk = sz00 | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 91.67/42.29 |
% 91.67/42.29 +-Applying beta-rule and splitting (1636), into two cases.
% 91.67/42.29 |-Branch one:
% 91.67/42.30 | (1637) xk = sz00
% 91.67/42.30 |
% 91.67/42.30 | Equations (1637) can reduce 31 to:
% 91.67/42.30 | (216) $false
% 91.67/42.30 |
% 91.67/42.30 |-The branch is then unsatisfiable
% 91.67/42.30 |-Branch two:
% 91.67/42.30 | (31) ~ (xk = sz00)
% 91.67/42.30 | (1640) all_0_4_4 = 0 | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 91.67/42.30 |
% 91.67/42.30 +-Applying beta-rule and splitting (1640), into two cases.
% 91.67/42.30 |-Branch one:
% 91.67/42.30 | (220) all_0_4_4 = 0
% 91.67/42.30 |
% 91.67/42.30 | Equations (220) can reduce 74 to:
% 91.67/42.30 | (216) $false
% 91.67/42.30 |
% 91.67/42.30 |-The branch is then unsatisfiable
% 91.67/42.30 |-Branch two:
% 91.67/42.30 | (74) ~ (all_0_4_4 = 0)
% 91.67/42.30 | (1644) ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 91.67/42.30 |
% 91.67/42.30 | Instantiating (1644) with all_209_0_585, all_209_1_586 yields:
% 91.67/42.30 | (1770) aNaturalNumber0(xk) = all_209_1_586 & aNaturalNumber0(xp) = all_209_0_585 & ( ~ (all_209_0_585 = 0) | ~ (all_209_1_586 = 0))
% 91.67/42.30 |
% 91.67/42.30 | Applying alpha-rule on (1770) yields:
% 91.67/42.30 | (1771) aNaturalNumber0(xk) = all_209_1_586
% 91.67/42.30 | (1772) aNaturalNumber0(xp) = all_209_0_585
% 91.67/42.30 | (1773) ~ (all_209_0_585 = 0) | ~ (all_209_1_586 = 0)
% 91.67/42.30 |
% 91.67/42.30 | Instantiating formula (55) with xk, all_209_1_586, 0 and discharging atoms aNaturalNumber0(xk) = all_209_1_586, aNaturalNumber0(xk) = 0, yields:
% 91.67/42.30 | (1774) all_209_1_586 = 0
% 91.67/42.30 |
% 91.67/42.30 | Instantiating formula (55) with xp, all_209_0_585, 0 and discharging atoms aNaturalNumber0(xp) = all_209_0_585, aNaturalNumber0(xp) = 0, yields:
% 91.67/42.30 | (1775) all_209_0_585 = 0
% 91.67/42.30 |
% 91.67/42.30 +-Applying beta-rule and splitting (1773), into two cases.
% 91.67/42.30 |-Branch one:
% 91.67/42.30 | (1776) ~ (all_209_0_585 = 0)
% 91.67/42.30 |
% 91.67/42.30 | Equations (1775) can reduce 1776 to:
% 91.67/42.30 | (216) $false
% 91.67/42.30 |
% 91.67/42.30 |-The branch is then unsatisfiable
% 91.67/42.30 |-Branch two:
% 91.67/42.30 | (1775) all_209_0_585 = 0
% 91.67/42.30 | (1779) ~ (all_209_1_586 = 0)
% 91.67/42.30 |
% 91.67/42.30 | Equations (1774) can reduce 1779 to:
% 91.67/42.30 | (216) $false
% 91.67/42.30 |
% 91.67/42.30 |-The branch is then unsatisfiable
% 91.67/42.30 |-Branch two:
% 91.67/42.30 | (1781) sdtasdt0(xp, xk) = xn
% 91.67/42.30 | (1782) all_0_5_5 = 0 | xk = sz00 | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 91.67/42.30 |
% 91.67/42.30 +-Applying beta-rule and splitting (1782), into two cases.
% 91.67/42.30 |-Branch one:
% 91.67/42.30 | (1637) xk = sz00
% 91.67/42.30 |
% 91.67/42.30 | Equations (1637) can reduce 31 to:
% 91.67/42.30 | (216) $false
% 91.67/42.30 |
% 91.67/42.30 |-The branch is then unsatisfiable
% 91.67/42.30 |-Branch two:
% 91.67/42.30 | (31) ~ (xk = sz00)
% 91.67/42.30 | (1786) all_0_5_5 = 0 | ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 91.67/42.30 |
% 91.67/42.30 +-Applying beta-rule and splitting (1786), into two cases.
% 91.67/42.30 |-Branch one:
% 91.67/42.30 | (230) all_0_5_5 = 0
% 91.67/42.30 |
% 91.67/42.30 | Equations (230) can reduce 49 to:
% 91.67/42.30 | (216) $false
% 91.67/42.30 |
% 91.67/42.30 |-The branch is then unsatisfiable
% 91.67/42.30 |-Branch two:
% 91.67/42.30 | (49) ~ (all_0_5_5 = 0)
% 91.67/42.30 | (1644) ? [v0] : ? [v1] : (aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 91.67/42.30 |
% 91.67/42.30 | Instantiating (1644) with all_173_0_593, all_173_1_594 yields:
% 91.67/42.30 | (1791) aNaturalNumber0(xk) = all_173_1_594 & aNaturalNumber0(xp) = all_173_0_593 & ( ~ (all_173_0_593 = 0) | ~ (all_173_1_594 = 0))
% 91.67/42.30 |
% 91.67/42.30 | Applying alpha-rule on (1791) yields:
% 91.67/42.30 | (1792) aNaturalNumber0(xk) = all_173_1_594
% 91.67/42.30 | (1793) aNaturalNumber0(xp) = all_173_0_593
% 91.67/42.30 | (1794) ~ (all_173_0_593 = 0) | ~ (all_173_1_594 = 0)
% 91.67/42.30 |
% 91.67/42.30 +-Applying beta-rule and splitting (113), into two cases.
% 91.67/42.30 |-Branch one:
% 91.67/42.30 | (1680) ~ (sdtasdt0(xp, xk) = xn)
% 91.67/42.30 |
% 91.67/42.30 | Using (1781) and (1680) yields:
% 91.67/42.30 | (419) $false
% 91.67/42.30 |
% 91.67/42.30 |-The branch is then unsatisfiable
% 91.67/42.30 |-Branch two:
% 91.67/42.30 | (1781) sdtasdt0(xp, xk) = xn
% 91.67/42.30 | (1798) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(xk, xm) = v3 & sdtasdt0(xp, v3) = v4 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_6_6))
% 91.67/42.30 |
% 91.67/42.30 | Instantiating (1798) with all_206_0_595, all_206_1_596, all_206_2_597, all_206_3_598, all_206_4_599 yields:
% 91.67/42.30 | (1799) sdtasdt0(xk, xm) = all_206_1_596 & sdtasdt0(xp, all_206_1_596) = all_206_0_595 & aNaturalNumber0(xk) = all_206_3_598 & aNaturalNumber0(xp) = all_206_4_599 & aNaturalNumber0(xm) = all_206_2_597 & ( ~ (all_206_2_597 = 0) | ~ (all_206_3_598 = 0) | ~ (all_206_4_599 = 0) | all_206_0_595 = all_0_6_6)
% 91.67/42.30 |
% 91.67/42.30 | Applying alpha-rule on (1799) yields:
% 91.67/42.30 | (1800) sdtasdt0(xk, xm) = all_206_1_596
% 91.67/42.30 | (1801) ~ (all_206_2_597 = 0) | ~ (all_206_3_598 = 0) | ~ (all_206_4_599 = 0) | all_206_0_595 = all_0_6_6
% 91.67/42.30 | (1802) sdtasdt0(xp, all_206_1_596) = all_206_0_595
% 91.67/42.30 | (1803) aNaturalNumber0(xm) = all_206_2_597
% 91.67/42.30 | (1804) aNaturalNumber0(xk) = all_206_3_598
% 91.67/42.30 | (1805) aNaturalNumber0(xp) = all_206_4_599
% 91.67/42.30 |
% 91.67/42.30 | Instantiating formula (55) with xk, all_206_3_598, 0 and discharging atoms aNaturalNumber0(xk) = all_206_3_598, aNaturalNumber0(xk) = 0, yields:
% 91.67/42.30 | (1806) all_206_3_598 = 0
% 91.67/42.30 |
% 91.67/42.30 | Instantiating formula (55) with xk, all_173_1_594, all_206_3_598 and discharging atoms aNaturalNumber0(xk) = all_206_3_598, aNaturalNumber0(xk) = all_173_1_594, yields:
% 91.67/42.30 | (1807) all_206_3_598 = all_173_1_594
% 91.67/42.30 |
% 91.67/42.30 | Instantiating formula (55) with xp, all_206_4_599, 0 and discharging atoms aNaturalNumber0(xp) = all_206_4_599, aNaturalNumber0(xp) = 0, yields:
% 91.67/42.30 | (1808) all_206_4_599 = 0
% 91.67/42.30 |
% 91.67/42.30 | Instantiating formula (55) with xp, all_173_0_593, all_206_4_599 and discharging atoms aNaturalNumber0(xp) = all_206_4_599, aNaturalNumber0(xp) = all_173_0_593, yields:
% 91.67/42.30 | (1809) all_206_4_599 = all_173_0_593
% 91.67/42.30 |
% 91.67/42.30 | Combining equations (1807,1806) yields a new equation:
% 91.67/42.30 | (1810) all_173_1_594 = 0
% 91.67/42.30 |
% 91.67/42.30 | Simplifying 1810 yields:
% 91.67/42.30 | (1811) all_173_1_594 = 0
% 91.67/42.30 |
% 91.67/42.30 | Combining equations (1808,1809) yields a new equation:
% 91.67/42.30 | (1812) all_173_0_593 = 0
% 91.67/42.30 |
% 91.67/42.30 +-Applying beta-rule and splitting (1794), into two cases.
% 91.67/42.30 |-Branch one:
% 91.67/42.30 | (1813) ~ (all_173_0_593 = 0)
% 91.67/42.30 |
% 91.67/42.30 | Equations (1812) can reduce 1813 to:
% 91.67/42.30 | (216) $false
% 91.67/42.30 |
% 91.67/42.30 |-The branch is then unsatisfiable
% 91.67/42.30 |-Branch two:
% 91.67/42.30 | (1812) all_173_0_593 = 0
% 91.67/42.30 | (1816) ~ (all_173_1_594 = 0)
% 91.67/42.30 |
% 91.67/42.30 | Equations (1811) can reduce 1816 to:
% 91.67/42.30 | (216) $false
% 91.67/42.30 |
% 91.67/42.30 |-The branch is then unsatisfiable
% 91.67/42.30 |-Branch two:
% 91.67/42.30 | (1818) doDivides0(xp, all_0_6_6) = all_49_0_83 & aNaturalNumber0(all_0_6_6) = all_49_1_84 & aNaturalNumber0(xp) = all_49_2_85 & ( ~ (all_49_0_83 = 0) | ~ (all_49_1_84 = 0) | ~ (all_49_2_85 = 0))
% 91.67/42.30 |
% 91.67/42.30 | Applying alpha-rule on (1818) yields:
% 91.67/42.30 | (1819) doDivides0(xp, all_0_6_6) = all_49_0_83
% 91.67/42.30 | (1820) aNaturalNumber0(all_0_6_6) = all_49_1_84
% 91.67/42.30 | (1821) aNaturalNumber0(xp) = all_49_2_85
% 91.67/42.30 | (1822) ~ (all_49_0_83 = 0) | ~ (all_49_1_84 = 0) | ~ (all_49_2_85 = 0)
% 91.67/42.30 |
% 91.67/42.30 | Instantiating formula (72) with xp, all_0_6_6, all_49_0_83, 0 and discharging atoms doDivides0(xp, all_0_6_6) = all_49_0_83, doDivides0(xp, all_0_6_6) = 0, yields:
% 91.67/42.30 | (1823) all_49_0_83 = 0
% 91.67/42.30 |
% 91.67/42.30 | Instantiating formula (55) with all_0_6_6, all_49_1_84, 0 and discharging atoms aNaturalNumber0(all_0_6_6) = all_49_1_84, aNaturalNumber0(all_0_6_6) = 0, yields:
% 91.67/42.30 | (1824) all_49_1_84 = 0
% 91.67/42.30 |
% 91.67/42.30 | Instantiating formula (55) with xp, all_49_2_85, 0 and discharging atoms aNaturalNumber0(xp) = all_49_2_85, aNaturalNumber0(xp) = 0, yields:
% 91.67/42.30 | (439) all_49_2_85 = 0
% 91.67/42.30 |
% 91.67/42.30 +-Applying beta-rule and splitting (1822), into two cases.
% 91.67/42.30 |-Branch one:
% 91.67/42.30 | (1826) ~ (all_49_0_83 = 0)
% 91.67/42.30 |
% 91.67/42.30 | Equations (1823) can reduce 1826 to:
% 91.67/42.30 | (216) $false
% 91.67/42.30 |
% 91.67/42.30 |-The branch is then unsatisfiable
% 91.67/42.30 |-Branch two:
% 91.67/42.30 | (1823) all_49_0_83 = 0
% 91.67/42.30 | (1829) ~ (all_49_1_84 = 0) | ~ (all_49_2_85 = 0)
% 91.67/42.30 |
% 91.67/42.30 +-Applying beta-rule and splitting (1829), into two cases.
% 91.67/42.30 |-Branch one:
% 91.67/42.30 | (1830) ~ (all_49_1_84 = 0)
% 91.67/42.30 |
% 91.67/42.30 | Equations (1824) can reduce 1830 to:
% 91.67/42.30 | (216) $false
% 91.67/42.30 |
% 91.67/42.30 |-The branch is then unsatisfiable
% 91.67/42.30 |-Branch two:
% 91.67/42.30 | (1824) all_49_1_84 = 0
% 91.67/42.30 | (1833) ~ (all_49_2_85 = 0)
% 91.67/42.30 |
% 91.67/42.30 | Equations (439) can reduce 1833 to:
% 91.67/42.30 | (216) $false
% 91.67/42.30 |
% 91.67/42.30 |-The branch is then unsatisfiable
% 91.67/42.30 |-Branch two:
% 91.67/42.30 | (1835) aNaturalNumber0(xp) = all_21_1_27 & aNaturalNumber0(xn) = all_21_2_28 & ( ~ (all_21_1_27 = 0) | ~ (all_21_2_28 = 0))
% 91.67/42.30 |
% 91.67/42.30 | Applying alpha-rule on (1835) yields:
% 91.67/42.30 | (1836) aNaturalNumber0(xp) = all_21_1_27
% 91.67/42.30 | (1837) aNaturalNumber0(xn) = all_21_2_28
% 91.67/42.30 | (1838) ~ (all_21_1_27 = 0) | ~ (all_21_2_28 = 0)
% 91.67/42.30 |
% 91.67/42.30 | Instantiating formula (55) with xp, all_21_1_27, 0 and discharging atoms aNaturalNumber0(xp) = all_21_1_27, aNaturalNumber0(xp) = 0, yields:
% 91.67/42.30 | (385) all_21_1_27 = 0
% 91.67/42.30 |
% 91.67/42.30 | Instantiating formula (55) with xn, all_21_2_28, 0 and discharging atoms aNaturalNumber0(xn) = all_21_2_28, aNaturalNumber0(xn) = 0, yields:
% 91.67/42.30 | (1840) all_21_2_28 = 0
% 91.67/42.30 |
% 91.67/42.30 +-Applying beta-rule and splitting (1838), into two cases.
% 91.67/42.30 |-Branch one:
% 91.67/42.30 | (1841) ~ (all_21_1_27 = 0)
% 91.67/42.30 |
% 91.67/42.30 | Equations (385) can reduce 1841 to:
% 91.67/42.30 | (216) $false
% 91.67/42.30 |
% 91.67/42.31 |-The branch is then unsatisfiable
% 91.67/42.31 |-Branch two:
% 91.67/42.31 | (385) all_21_1_27 = 0
% 91.67/42.31 | (1844) ~ (all_21_2_28 = 0)
% 91.67/42.31 |
% 91.67/42.31 | Equations (1840) can reduce 1844 to:
% 91.67/42.31 | (216) $false
% 91.67/42.31 |
% 91.67/42.31 |-The branch is then unsatisfiable
% 91.67/42.31 % SZS output end Proof for theBenchmark
% 91.67/42.31
% 91.67/42.31 41621ms
%------------------------------------------------------------------------------