TSTP Solution File: NUM504+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM504+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n009.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 08:45:13 EDT 2022
% Result : Theorem 20.50s 6.31s
% Output : Proof 27.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM504+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jul 6 20:03:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.54/0.59 ____ _
% 0.54/0.59 ___ / __ \_____(_)___ ________ __________
% 0.54/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.59
% 0.54/0.59 A Theorem Prover for First-Order Logic
% 0.54/0.59 (ePrincess v.1.0)
% 0.54/0.59
% 0.54/0.59 (c) Philipp Rümmer, 2009-2015
% 0.54/0.59 (c) Peter Backeman, 2014-2015
% 0.54/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.59 Bug reports to peter@backeman.se
% 0.54/0.59
% 0.54/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.59
% 0.54/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.80/0.99 Prover 0: Preprocessing ...
% 3.61/1.48 Prover 0: Constructing countermodel ...
% 18.92/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.15/6.05 Prover 1: Preprocessing ...
% 20.22/6.21 Prover 1: Constructing countermodel ...
% 20.50/6.31 Prover 1: proved (381ms)
% 20.50/6.31 Prover 0: stopped
% 20.50/6.31
% 20.50/6.31 No countermodel exists, formula is valid
% 20.50/6.31 % SZS status Theorem for theBenchmark
% 20.50/6.31
% 20.50/6.31 Generating proof ... found it (size 213)
% 26.31/7.63
% 26.31/7.63 % SZS output start Proof for theBenchmark
% 26.31/7.63 Assumed formulas after preprocessing and simplification:
% 26.31/7.63 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v5 = v2) & ~ (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, v6) = 0 & sdtlseqdt0(v2, v5) = 0 & 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) = v6 & 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) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | v7 = sz00 | ~ (sdtlseqdt0(v10, v11) = v12) | ~ (sdtasdt0(v7, v9) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (sdtlseqdt0(v17, v18) = v19 & sdtlseqdt0(v8, v9) = v16 & sdtasdt0(v9, v7) = v18 & sdtasdt0(v8, v7) = v17 & aNaturalNumber0(v9) = v15 & aNaturalNumber0(v8) = v14 & aNaturalNumber0(v7) = v13 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | (v19 = 0 & v12 = 0 & ~ (v18 = v17) & ~ (v11 = v10))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (sdtlseqdt0(v10, v11) = v12) | ~ (sdtlseqdt0(v7, v8) = 0) | ~ (sdtpldt0(v8, v9) = v11) | ~ (sdtpldt0(v7, v9) = v10) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((sdtlseqdt0(v14, v15) = v16 & sdtpldt0(v9, v8) = v15 & sdtpldt0(v9, v7) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v13 = 0) | (v16 = 0 & v12 = 0 & ~ (v15 = v14) & ~ (v11 = v10)))) | (aNaturalNumber0(v8) = v14 & aNaturalNumber0(v7) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v7 = sz00 | ~ (sdtsldt0(v11, v7) = v12) | ~ (sdtsldt0(v8, v7) = v9) | ~ (sdtasdt0(v10, v8) = v11) | ? [v13] : ? [v14] : ? [v15] : ((doDivides0(v7, v8) = v15 & aNaturalNumber0(v8) = v14 & aNaturalNumber0(v7) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0))) | (sdtasdt0(v10, v9) = v14 & aNaturalNumber0(v10) = v13 & ( ~ (v13 = 0) | v14 = v12)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtasdt0(v7, v9) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ~ (sdtpldt0(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (sdtasdt0(v16, v7) = v18 & sdtasdt0(v9, v7) = v20 & sdtasdt0(v8, v7) = v19 & sdtasdt0(v7, v16) = v17 & sdtpldt0(v19, v20) = v21 & sdtpldt0(v8, v9) = v16 & aNaturalNumber0(v9) = v15 & aNaturalNumber0(v8) = v14 & aNaturalNumber0(v7) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | (v21 = v18 & v17 = v12)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (doDivides0(v7, v10) = v11) | ~ (sdtpldt0(v8, v9) = v10) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (doDivides0(v7, v9) = v16 & doDivides0(v7, v8) = v15 & aNaturalNumber0(v9) = v14 & aNaturalNumber0(v8) = v13 & aNaturalNumber0(v7) = v12 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v7, v9) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ~ (aNaturalNumber0(v7) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (sdtasdt0(v9, v7) = v15 & sdtasdt0(v8, v7) = v14 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | ( ~ (v15 = v14) & ~ (v11 = v10))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (sdtpldt0(v7, v9) = v11) | ~ (sdtpldt0(v7, v8) = v10) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (sdtpldt0(v9, v7) = v16 & sdtpldt0(v8, v7) = v15 & aNaturalNumber0(v9) = v14 & aNaturalNumber0(v8) = v13 & aNaturalNumber0(v7) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ( ~ (v16 = v15) & ~ (v11 = v10))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v10, v9) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (sdtasdt0(v8, v9) = v15 & sdtasdt0(v7, v15) = v16 & aNaturalNumber0(v9) = v14 & aNaturalNumber0(v8) = v13 & aNaturalNumber0(v7) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | v16 = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtpldt0(v10, v9) = v11) | ~ (sdtpldt0(v7, v8) = v10) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (sdtpldt0(v8, v9) = v15 & sdtpldt0(v7, v15) = v16 & aNaturalNumber0(v9) = v14 & aNaturalNumber0(v8) = v13 & aNaturalNumber0(v7) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | v16 = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | v7 = sz00 | ~ (sdtsldt0(v8, v7) = v9) | ~ (sdtasdt0(v7, v10) = v8) | ? [v11] : ? [v12] : ? [v13] : (( ~ (v11 = 0) & aNaturalNumber0(v10) = v11) | (doDivides0(v7, v8) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (sdtmndt0(v8, v7) = v9) | ~ (sdtpldt0(v7, v10) = v8) | ? [v11] : ? [v12] : ? [v13] : (( ~ (v11 = 0) & aNaturalNumber0(v10) = v11) | (sdtlseqdt0(v7, v8) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | v7 = sz00 | ~ (sdtsldt0(v8, v7) = v9) | ~ (sdtasdt0(v7, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (doDivides0(v7, v8) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (sdtmndt0(v8, v7) = v9) | ~ (sdtpldt0(v7, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (sdtlseqdt0(v7, v8) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v7 = sz00 | ~ (sdtlseqdt0(v8, v9) = v10) | ~ (sdtasdt0(v8, v7) = v9) | ? [v11] : ? [v12] : (aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (doDivides0(v7, v9) = v10) | ~ (doDivides0(v7, v8) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (doDivides0(v8, v9) = v14 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (sdtlseqdt0(v7, v9) = v10) | ~ (sdtlseqdt0(v7, v8) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtlseqdt0(v8, v9) = v14 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (doDivides0(v7, v8) = v9) | ~ (sdtasdt0(v7, v10) = v8) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & aNaturalNumber0(v10) = v11) | (aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (sdtlseqdt0(v7, v8) = v9) | ~ (sdtpldt0(v7, v10) = v8) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & aNaturalNumber0(v10) = v11) | (aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtsldt0(v10, v9) = v8) | ~ (sdtsldt0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (doDivides0(v10, v9) = v8) | ~ (doDivides0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (iLess0(v10, v9) = v8) | ~ (iLess0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtmndt0(v10, v9) = v8) | ~ (sdtmndt0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtlseqdt0(v10, v9) = v8) | ~ (sdtlseqdt0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtasdt0(v10, v9) = v8) | ~ (sdtasdt0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v10, v9) = v8) | ~ (sdtpldt0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = sz00 | ~ (sdtsldt0(v8, v7) = v9) | ~ (sdtasdt0(v7, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v11 = 0 & aNaturalNumber0(v9) = 0) | (doDivides0(v7, v8) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (doDivides0(v9, v10) = 0) | ~ (sdtasdt0(v7, v8) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (isPrime0(v9) = v14 & doDivides0(v9, v8) = v19 & doDivides0(v9, v7) = v18 & iLess0(v16, v1) = v17 & sdtpldt0(v15, v9) = v16 & sdtpldt0(v7, v8) = v15 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v17 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | v19 = 0 | v18 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (doDivides0(v7, v10) = 0) | ~ (sdtpldt0(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (doDivides0(v7, v9) = v15 & doDivides0(v7, v8) = v14 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | v15 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtmndt0(v8, v7) = v9) | ~ (sdtpldt0(v7, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v11 = 0 & aNaturalNumber0(v9) = 0) | (sdtlseqdt0(v7, v8) = v13 & aNaturalNumber0(v8) = v12 & aNaturalNumber0(v7) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = v7 | ~ (iLess0(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (sdtlseqdt0(v7, v8) = v12 & aNaturalNumber0(v8) = v11 & aNaturalNumber0(v7) = v10 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (sdtlseqdt0(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (sdtlseqdt0(v8, v7) = v12 & aNaturalNumber0(v8) = v11 & aNaturalNumber0(v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | (v12 = 0 & ~ (v8 = v7))))) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (isPrime0(v9) = v8) | ~ (isPrime0(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (aNaturalNumber0(v9) = v8) | ~ (aNaturalNumber0(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (sdtasdt0(v8, v7) = v12 & aNaturalNumber0(v8) = v11 & aNaturalNumber0(v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | v12 = v9))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (aNaturalNumber0(v9) = v12 & aNaturalNumber0(v8) = v11 & aNaturalNumber0(v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | v12 = 0))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (sdtpldt0(v8, v7) = v12 & aNaturalNumber0(v8) = v11 & aNaturalNumber0(v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | v12 = v9))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (aNaturalNumber0(v9) = v12 & aNaturalNumber0(v8) = v11 & aNaturalNumber0(v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | v12 = 0))) & ! [v7] : ! [v8] : (v8 = v7 | v8 = sz10 | ~ (isPrime0(v7) = 0) | ~ (doDivides0(v8, v7) = 0) | ? [v9] : (( ~ (v9 = 0) & aNaturalNumber0(v8) = v9) | ( ~ (v9 = 0) & aNaturalNumber0(v7) = v9))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (sdtlseqdt0(v7, v8) = 0) | ? [v9] : ? [v10] : ? [v11] : (sdtlseqdt0(v8, v7) = v11 & aNaturalNumber0(v8) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : (v8 = sz00 | v7 = sz00 | ~ (sdtasdt0(v7, v8) = sz00) | ? [v9] : ? [v10] : (aNaturalNumber0(v8) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : (v8 = sz00 | ~ (doDivides0(v7, v8) = 0) | ? [v9] : ? [v10] : ? [v11] : (sdtlseqdt0(v7, v8) = v11 & aNaturalNumber0(v8) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = 0))) & ! [v7] : ! [v8] : (v8 = sz00 | ~ (sdtpldt0(v7, v8) = sz00) | ? [v9] : ? [v10] : (aNaturalNumber0(v8) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : (v8 = 0 | v7 = sz10 | v7 = sz00 | ~ (isPrime0(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & ~ (v9 = v7) & ~ (v9 = sz10) & doDivides0(v9, v7) = 0 & aNaturalNumber0(v9) = 0) | ( ~ (v9 = 0) & aNaturalNumber0(v7) = v9))) & ! [v7] : ! [v8] : (v8 = 0 | v7 = sz10 | v7 = sz00 | ~ (sdtlseqdt0(sz10, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & aNaturalNumber0(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (sdtlseqdt0(v7, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & aNaturalNumber0(v7) = v9)) & ! [v7] : ! [v8] : (v7 = sz00 | ~ (sdtpldt0(v7, v8) = sz00) | ? [v9] : ? [v10] : (aNaturalNumber0(v8) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : ( ~ (doDivides0(v7, v8) = 0) | ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & v10 = 0 & sdtasdt0(v7, v9) = v8 & aNaturalNumber0(v9) = 0) | (aNaturalNumber0(v8) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0))))) & ! [v7] : ! [v8] : ( ~ (sdtlseqdt0(v7, v8) = 0) | ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & v10 = 0 & sdtpldt0(v7, v9) = v8 & aNaturalNumber0(v9) = 0) | (aNaturalNumber0(v8) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0))))) & ! [v7] : ! [v8] : ( ~ (sdtasdt0(sz10, v7) = v8) | ? [v9] : ? [v10] : (sdtasdt0(v7, sz10) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v9 = 0) | (v10 = v7 & v8 = v7)))) & ! [v7] : ! [v8] : ( ~ (sdtasdt0(sz00, v7) = v8) | ? [v9] : ? [v10] : (sdtasdt0(v7, sz00) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v9 = 0) | (v10 = sz00 & v8 = sz00)))) & ! [v7] : ! [v8] : ( ~ (sdtpldt0(sz00, v7) = v8) | ? [v9] : ? [v10] : (sdtpldt0(v7, sz00) = v10 & aNaturalNumber0(v7) = v9 & ( ~ (v9 = 0) | (v10 = v7 & v8 = v7)))) & ! [v7] : (v7 = sz10 | v7 = sz00 | ~ (aNaturalNumber0(v7) = 0) | ? [v8] : (isPrime0(v8) = 0 & doDivides0(v8, v7) = 0 & aNaturalNumber0(v8) = 0)))
% 26.45/7.70 | 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 yields:
% 26.45/7.70 | (1) ~ (all_0_0_0 = all_0_1_1) & ~ (all_0_1_1 = all_0_4_4) & ~ (all_0_2_2 = 0) & ~ (all_0_3_3 = 0) & ~ (xk = sz10) & ~ (xk = sz00) & ~ (xp = xm) & ~ (xp = xn) & ~ (sz10 = sz00) & isPrime0(xr) = 0 & isPrime0(xp) = 0 & sdtsldt0(all_0_4_4, xp) = xk & doDivides0(xr, all_0_4_4) = 0 & doDivides0(xr, xk) = 0 & doDivides0(xp, all_0_4_4) = 0 & sdtlseqdt0(all_0_1_1, all_0_0_0) = 0 & sdtlseqdt0(all_0_4_4, all_0_1_1) = 0 & sdtlseqdt0(xr, xk) = 0 & sdtlseqdt0(xp, xk) = 0 & sdtlseqdt0(xp, xm) = all_0_2_2 & sdtlseqdt0(xp, xn) = all_0_3_3 & sdtlseqdt0(xm, xp) = 0 & sdtlseqdt0(xn, xp) = 0 & sdtasdt0(xp, xk) = all_0_0_0 & sdtasdt0(xp, xm) = all_0_1_1 & sdtasdt0(xn, xm) = all_0_4_4 & sdtpldt0(all_0_6_6, xp) = all_0_5_5 & sdtpldt0(xn, xm) = all_0_6_6 & 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_5_5) = 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))
% 26.45/7.71 |
% 26.45/7.71 | Applying alpha-rule on (1) yields:
% 26.45/7.71 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0))
% 26.45/7.71 | (3) ! [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))))
% 26.45/7.71 | (4) sdtlseqdt0(all_0_1_1, all_0_0_0) = 0
% 26.45/7.71 | (5) sdtpldt0(xn, xm) = all_0_6_6
% 26.45/7.72 | (6) ! [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)))))
% 26.45/7.72 | (7) sdtasdt0(xp, xk) = all_0_0_0
% 26.45/7.72 | (8) ! [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))))
% 26.45/7.72 | (9) ! [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))))
% 26.45/7.72 | (10) sdtsldt0(all_0_4_4, xp) = xk
% 26.45/7.72 | (11) doDivides0(xp, all_0_4_4) = 0
% 26.45/7.72 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 26.45/7.72 | (13) sdtlseqdt0(xp, xk) = 0
% 26.45/7.72 | (14) ! [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)))))
% 26.45/7.72 | (15) aNaturalNumber0(xp) = 0
% 26.45/7.72 | (16) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 26.45/7.72 | (17) ! [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)))
% 26.45/7.72 | (18) ~ (xk = sz00)
% 26.45/7.72 | (19) isPrime0(xr) = 0
% 26.45/7.72 | (20) sdtasdt0(xn, xm) = all_0_4_4
% 26.45/7.72 | (21) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 26.45/7.72 | (22) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 26.45/7.72 | (23) ! [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_5_5) = 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)))
% 26.45/7.72 | (24) ! [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)))
% 26.45/7.72 | (25) ~ (all_0_1_1 = all_0_4_4)
% 26.45/7.72 | (26) ! [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))))
% 26.45/7.72 | (27) aNaturalNumber0(xm) = 0
% 26.45/7.72 | (28) ! [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)))))
% 26.45/7.72 | (29) ! [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)))))
% 26.45/7.72 | (30) sdtpldt0(all_0_6_6, xp) = all_0_5_5
% 26.45/7.72 | (31) aNaturalNumber0(sz00) = 0
% 26.45/7.72 | (32) ! [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)))))
% 26.45/7.73 | (33) ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (isPrime0(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & ~ (v2 = v0) & ~ (v2 = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 26.82/7.73 | (34) ! [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)))))
% 26.82/7.73 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 26.82/7.73 | (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)))))
% 26.82/7.73 | (37) ~ (isPrime0(sz10) = 0)
% 26.82/7.73 | (38) ! [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)))
% 26.82/7.73 | (39) ! [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))))
% 26.82/7.73 | (40) sdtlseqdt0(xm, xp) = 0
% 26.82/7.73 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 26.82/7.73 | (42) ! [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))))
% 26.82/7.73 | (43) ~ (all_0_3_3 = 0)
% 26.82/7.73 | (44) ! [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)))
% 26.82/7.73 | (45) ! [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))))
% 26.82/7.73 | (46) ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 26.82/7.73 | (47) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0))
% 26.82/7.73 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 26.82/7.73 | (49) isPrime0(xp) = 0
% 26.82/7.73 | (50) ! [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)))
% 26.82/7.73 | (51) ! [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)))))
% 26.82/7.73 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0))
% 26.82/7.73 | (53) doDivides0(xr, all_0_4_4) = 0
% 26.82/7.73 | (54) ! [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)))))
% 26.82/7.73 | (55) ! [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)))
% 26.82/7.73 | (56) sdtlseqdt0(all_0_4_4, all_0_1_1) = 0
% 26.82/7.73 | (57) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0))
% 26.82/7.73 | (58) ! [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)))
% 26.82/7.74 | (59) ~ (all_0_0_0 = all_0_1_1)
% 26.82/7.74 | (60) sdtlseqdt0(xr, xk) = 0
% 26.82/7.74 | (61) ! [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))))
% 26.82/7.74 | (62) ! [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)))
% 26.82/7.74 | (63) ~ (sz10 = sz00)
% 26.82/7.74 | (64) aNaturalNumber0(sz10) = 0
% 26.82/7.74 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0))
% 26.82/7.74 | (66) sdtasdt0(xp, xm) = all_0_1_1
% 26.82/7.74 | (67) ! [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))))
% 26.82/7.74 | (68) ! [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)))))
% 26.82/7.74 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0))
% 26.82/7.74 | (70) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00))))
% 26.82/7.74 | (71) ~ (xk = sz10)
% 26.82/7.74 | (72) ~ (isPrime0(sz00) = 0)
% 26.82/7.74 | (73) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ (isPrime0(v0) = 0) | ~ (doDivides0(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 26.82/7.74 | (74) ! [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)))))
% 26.82/7.74 | (75) aNaturalNumber0(xn) = 0
% 26.82/7.74 | (76) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 26.82/7.74 | (77) ! [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)))))
% 26.82/7.74 | (78) ~ (xp = xn)
% 26.82/7.74 | (79) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 26.82/7.74 | (80) ~ (all_0_2_2 = 0)
% 26.82/7.74 | (81) sdtlseqdt0(xp, xn) = all_0_3_3
% 26.82/7.74 | (82) doDivides0(xr, xk) = 0
% 26.82/7.74 | (83) ! [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))))
% 26.82/7.74 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 26.82/7.74 | (85) aNaturalNumber0(xr) = 0
% 26.82/7.74 | (86) ~ (xp = xm)
% 26.82/7.74 | (87) sdtlseqdt0(xp, xm) = all_0_2_2
% 26.82/7.74 | (88) sdtlseqdt0(xn, xp) = 0
% 26.82/7.74 | (89) ! [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)))))
% 26.82/7.75 |
% 26.82/7.75 | Using (49) and (72) yields:
% 26.82/7.75 | (90) ~ (xp = sz00)
% 26.82/7.75 |
% 26.82/7.75 | Instantiating formula (39) with all_0_0_0, all_0_1_1 and discharging atoms sdtlseqdt0(all_0_1_1, all_0_0_0) = 0, yields:
% 26.82/7.75 | (91) all_0_0_0 = all_0_1_1 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_0_0_0, all_0_1_1) = v2 & aNaturalNumber0(all_0_0_0) = v1 & aNaturalNumber0(all_0_1_1) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 26.82/7.75 |
% 26.82/7.75 | Instantiating formula (39) with all_0_1_1, all_0_4_4 and discharging atoms sdtlseqdt0(all_0_4_4, all_0_1_1) = 0, yields:
% 26.82/7.75 | (92) all_0_1_1 = all_0_4_4 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_0_1_1, all_0_4_4) = v2 & aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(all_0_4_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 26.82/7.75 |
% 26.82/7.75 | Instantiating formula (61) with all_0_2_2, xm, xk, xp and discharging atoms sdtlseqdt0(xp, xk) = 0, sdtlseqdt0(xp, xm) = all_0_2_2, yields:
% 26.82/7.75 | (93) all_0_2_2 = 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)))
% 26.82/7.75 |
% 26.82/7.75 | Instantiating formula (61) with all_0_3_3, xn, xk, xp and discharging atoms sdtlseqdt0(xp, xk) = 0, sdtlseqdt0(xp, xn) = all_0_3_3, yields:
% 26.82/7.75 | (94) all_0_3_3 = 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)))
% 26.82/7.75 |
% 26.82/7.75 | Instantiating formula (3) with all_0_0_0, xk, all_0_4_4, xp and discharging atoms sdtsldt0(all_0_4_4, xp) = xk, sdtasdt0(xp, xk) = all_0_0_0, yields:
% 26.82/7.75 | (95) all_0_0_0 = all_0_4_4 | xp = sz00 | ? [v0] : ? [v1] : ? [v2] : (doDivides0(xp, all_0_4_4) = v2 & aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 26.82/7.75 |
% 26.82/7.75 | Instantiating formula (77) with all_0_0_0, xk, all_0_4_4, xp and discharging atoms sdtsldt0(all_0_4_4, xp) = xk, sdtasdt0(xp, xk) = all_0_0_0, yields:
% 26.82/7.75 | (96) xp = sz00 | ? [v0] : ? [v1] : ? [v2] : ((v0 = 0 & aNaturalNumber0(xk) = 0) | (doDivides0(xp, all_0_4_4) = v2 & aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 26.82/7.75 |
% 26.82/7.75 | Instantiating formula (50) with all_0_0_0, xk, xp and discharging atoms sdtasdt0(xp, xk) = all_0_0_0, yields:
% 26.82/7.75 | (97) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xk, xp) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_0_0))
% 26.82/7.75 |
% 26.82/7.75 | Instantiating formula (44) with all_0_0_0, xk, xp and discharging atoms sdtasdt0(xp, xk) = all_0_0_0, yields:
% 26.82/7.75 | (98) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_0_0) = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 26.82/7.75 |
% 26.82/7.75 | Instantiating formula (50) with all_0_1_1, xm, xp and discharging atoms sdtasdt0(xp, xm) = all_0_1_1, yields:
% 26.82/7.75 | (99) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xm, xp) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_1_1))
% 26.82/7.75 |
% 26.82/7.75 | Instantiating formula (44) with all_0_1_1, xm, xp and discharging atoms sdtasdt0(xp, xm) = all_0_1_1, yields:
% 26.82/7.75 | (100) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_1_1) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 26.82/7.75 |
% 26.82/7.75 | Instantiating formula (23) with all_0_4_4, xr, xm, xn and discharging atoms doDivides0(xr, all_0_4_4) = 0, sdtasdt0(xn, xm) = all_0_4_4, yields:
% 26.82/7.75 | (101) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xr) = v3 & doDivides0(xr, xm) = v8 & doDivides0(xr, xn) = v7 & iLess0(v5, all_0_5_5) = 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))
% 26.82/7.75 |
% 26.82/7.75 | Instantiating formula (23) with all_0_4_4, xp, xm, xn and discharging atoms doDivides0(xp, all_0_4_4) = 0, sdtasdt0(xn, xm) = all_0_4_4, yields:
% 26.82/7.75 | (102) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, xm) = v8 & doDivides0(xp, xn) = v7 & iLess0(v5, all_0_5_5) = 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))
% 26.82/7.75 |
% 26.82/7.75 | Instantiating formula (50) with all_0_4_4, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_4_4, yields:
% 26.82/7.75 | (103) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_4_4))
% 26.82/7.75 |
% 26.82/7.75 | Instantiating formula (44) with all_0_4_4, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_4_4, yields:
% 26.82/7.75 | (104) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_4_4) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 26.82/7.75 |
% 26.82/7.75 | Instantiating formula (62) with all_0_5_5, xp, all_0_6_6 and discharging atoms sdtpldt0(all_0_6_6, xp) = all_0_5_5, yields:
% 26.82/7.75 | (105) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, all_0_6_6) = v2 & aNaturalNumber0(all_0_6_6) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_5_5))
% 26.82/7.75 |
% 26.82/7.75 | Instantiating formula (38) with all_0_5_5, xp, all_0_6_6 and discharging atoms sdtpldt0(all_0_6_6, xp) = all_0_5_5, yields:
% 26.82/7.75 | (106) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_5_5) = v2 & aNaturalNumber0(all_0_6_6) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 26.82/7.76 |
% 26.82/7.76 | Instantiating formula (17) with all_0_5_5, all_0_6_6, xp, xm, xn and discharging atoms sdtpldt0(all_0_6_6, xp) = all_0_5_5, sdtpldt0(xn, xm) = all_0_6_6, yields:
% 26.82/7.76 | (107) ? [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_5_5))
% 26.82/7.76 |
% 26.82/7.76 | Instantiating formula (62) with all_0_6_6, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_6_6, yields:
% 26.82/7.76 | (108) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_6_6))
% 26.82/7.76 |
% 26.82/7.76 | Instantiating formula (38) with all_0_6_6, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_6_6, yields:
% 26.82/7.76 | (109) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_6_6) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 26.82/7.76 |
% 26.82/7.76 | Instantiating formula (47) with xp and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 26.82/7.76 | (110) xp = sz10 | xp = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 26.82/7.76 |
% 26.82/7.76 | Instantiating (109) with all_12_0_7, all_12_1_8, all_12_2_9 yields:
% 26.82/7.76 | (111) aNaturalNumber0(all_0_6_6) = all_12_0_7 & aNaturalNumber0(xm) = all_12_1_8 & aNaturalNumber0(xn) = all_12_2_9 & ( ~ (all_12_1_8 = 0) | ~ (all_12_2_9 = 0) | all_12_0_7 = 0)
% 26.82/7.76 |
% 26.82/7.76 | Applying alpha-rule on (111) yields:
% 26.82/7.76 | (112) aNaturalNumber0(all_0_6_6) = all_12_0_7
% 26.82/7.76 | (113) aNaturalNumber0(xm) = all_12_1_8
% 26.82/7.76 | (114) aNaturalNumber0(xn) = all_12_2_9
% 26.82/7.76 | (115) ~ (all_12_1_8 = 0) | ~ (all_12_2_9 = 0) | all_12_0_7 = 0
% 26.82/7.76 |
% 26.82/7.76 | Instantiating (108) with all_14_0_10, all_14_1_11, all_14_2_12 yields:
% 26.82/7.76 | (116) sdtpldt0(xm, xn) = all_14_0_10 & aNaturalNumber0(xm) = all_14_1_11 & aNaturalNumber0(xn) = all_14_2_12 & ( ~ (all_14_1_11 = 0) | ~ (all_14_2_12 = 0) | all_14_0_10 = all_0_6_6)
% 26.82/7.76 |
% 26.82/7.76 | Applying alpha-rule on (116) yields:
% 26.82/7.76 | (117) sdtpldt0(xm, xn) = all_14_0_10
% 26.82/7.76 | (118) aNaturalNumber0(xm) = all_14_1_11
% 26.82/7.76 | (119) aNaturalNumber0(xn) = all_14_2_12
% 26.82/7.76 | (120) ~ (all_14_1_11 = 0) | ~ (all_14_2_12 = 0) | all_14_0_10 = all_0_6_6
% 26.82/7.76 |
% 26.82/7.76 | Instantiating (103) with all_16_0_13, all_16_1_14, all_16_2_15 yields:
% 26.82/7.76 | (121) sdtasdt0(xm, xn) = all_16_0_13 & aNaturalNumber0(xm) = all_16_1_14 & aNaturalNumber0(xn) = all_16_2_15 & ( ~ (all_16_1_14 = 0) | ~ (all_16_2_15 = 0) | all_16_0_13 = all_0_4_4)
% 26.82/7.76 |
% 26.82/7.76 | Applying alpha-rule on (121) yields:
% 26.82/7.76 | (122) sdtasdt0(xm, xn) = all_16_0_13
% 26.82/7.76 | (123) aNaturalNumber0(xm) = all_16_1_14
% 26.82/7.76 | (124) aNaturalNumber0(xn) = all_16_2_15
% 26.82/7.76 | (125) ~ (all_16_1_14 = 0) | ~ (all_16_2_15 = 0) | all_16_0_13 = all_0_4_4
% 26.82/7.76 |
% 26.82/7.76 | Instantiating (102) with all_18_0_16, all_18_1_17, all_18_2_18, all_18_3_19, all_18_4_20, all_18_5_21, all_18_6_22, all_18_7_23, all_18_8_24 yields:
% 26.82/7.76 | (126) isPrime0(xp) = all_18_5_21 & doDivides0(xp, xm) = all_18_0_16 & doDivides0(xp, xn) = all_18_1_17 & iLess0(all_18_3_19, all_0_5_5) = all_18_2_18 & sdtpldt0(all_18_4_20, xp) = all_18_3_19 & sdtpldt0(xn, xm) = all_18_4_20 & aNaturalNumber0(xp) = all_18_6_22 & aNaturalNumber0(xm) = all_18_7_23 & aNaturalNumber0(xn) = all_18_8_24 & ( ~ (all_18_2_18 = 0) | ~ (all_18_5_21 = 0) | ~ (all_18_6_22 = 0) | ~ (all_18_7_23 = 0) | ~ (all_18_8_24 = 0) | all_18_0_16 = 0 | all_18_1_17 = 0)
% 26.82/7.76 |
% 26.82/7.76 | Applying alpha-rule on (126) yields:
% 26.82/7.76 | (127) doDivides0(xp, xm) = all_18_0_16
% 26.82/7.76 | (128) aNaturalNumber0(xm) = all_18_7_23
% 26.82/7.76 | (129) doDivides0(xp, xn) = all_18_1_17
% 26.82/7.76 | (130) iLess0(all_18_3_19, all_0_5_5) = all_18_2_18
% 26.82/7.76 | (131) sdtpldt0(all_18_4_20, xp) = all_18_3_19
% 26.82/7.76 | (132) isPrime0(xp) = all_18_5_21
% 26.82/7.76 | (133) ~ (all_18_2_18 = 0) | ~ (all_18_5_21 = 0) | ~ (all_18_6_22 = 0) | ~ (all_18_7_23 = 0) | ~ (all_18_8_24 = 0) | all_18_0_16 = 0 | all_18_1_17 = 0
% 26.82/7.76 | (134) sdtpldt0(xn, xm) = all_18_4_20
% 26.82/7.76 | (135) aNaturalNumber0(xn) = all_18_8_24
% 26.82/7.76 | (136) aNaturalNumber0(xp) = all_18_6_22
% 26.82/7.76 |
% 26.82/7.76 | Instantiating (101) with all_20_0_25, all_20_1_26, all_20_2_27, all_20_3_28, all_20_4_29, all_20_5_30, all_20_6_31, all_20_7_32, all_20_8_33 yields:
% 26.82/7.76 | (137) isPrime0(xr) = all_20_5_30 & doDivides0(xr, xm) = all_20_0_25 & doDivides0(xr, xn) = all_20_1_26 & iLess0(all_20_3_28, all_0_5_5) = all_20_2_27 & sdtpldt0(all_20_4_29, xr) = all_20_3_28 & sdtpldt0(xn, xm) = all_20_4_29 & aNaturalNumber0(xr) = all_20_6_31 & aNaturalNumber0(xm) = all_20_7_32 & aNaturalNumber0(xn) = all_20_8_33 & ( ~ (all_20_2_27 = 0) | ~ (all_20_5_30 = 0) | ~ (all_20_6_31 = 0) | ~ (all_20_7_32 = 0) | ~ (all_20_8_33 = 0) | all_20_0_25 = 0 | all_20_1_26 = 0)
% 26.82/7.76 |
% 26.82/7.76 | Applying alpha-rule on (137) yields:
% 26.82/7.76 | (138) sdtpldt0(xn, xm) = all_20_4_29
% 26.82/7.76 | (139) ~ (all_20_2_27 = 0) | ~ (all_20_5_30 = 0) | ~ (all_20_6_31 = 0) | ~ (all_20_7_32 = 0) | ~ (all_20_8_33 = 0) | all_20_0_25 = 0 | all_20_1_26 = 0
% 26.82/7.76 | (140) sdtpldt0(all_20_4_29, xr) = all_20_3_28
% 26.82/7.76 | (141) doDivides0(xr, xm) = all_20_0_25
% 26.82/7.76 | (142) doDivides0(xr, xn) = all_20_1_26
% 26.82/7.76 | (143) iLess0(all_20_3_28, all_0_5_5) = all_20_2_27
% 26.82/7.76 | (144) aNaturalNumber0(xr) = all_20_6_31
% 26.82/7.76 | (145) isPrime0(xr) = all_20_5_30
% 26.82/7.76 | (146) aNaturalNumber0(xm) = all_20_7_32
% 26.82/7.76 | (147) aNaturalNumber0(xn) = all_20_8_33
% 26.82/7.76 |
% 26.82/7.76 | Instantiating (107) with all_22_0_34, all_22_1_35, all_22_2_36, all_22_3_37, all_22_4_38 yields:
% 26.82/7.76 | (148) sdtpldt0(xm, xp) = all_22_1_35 & sdtpldt0(xn, all_22_1_35) = all_22_0_34 & aNaturalNumber0(xp) = all_22_2_36 & aNaturalNumber0(xm) = all_22_3_37 & aNaturalNumber0(xn) = all_22_4_38 & ( ~ (all_22_2_36 = 0) | ~ (all_22_3_37 = 0) | ~ (all_22_4_38 = 0) | all_22_0_34 = all_0_5_5)
% 26.82/7.76 |
% 26.82/7.76 | Applying alpha-rule on (148) yields:
% 26.82/7.76 | (149) ~ (all_22_2_36 = 0) | ~ (all_22_3_37 = 0) | ~ (all_22_4_38 = 0) | all_22_0_34 = all_0_5_5
% 26.82/7.76 | (150) aNaturalNumber0(xp) = all_22_2_36
% 26.82/7.76 | (151) aNaturalNumber0(xm) = all_22_3_37
% 26.82/7.76 | (152) aNaturalNumber0(xn) = all_22_4_38
% 26.82/7.76 | (153) sdtpldt0(xm, xp) = all_22_1_35
% 26.82/7.76 | (154) sdtpldt0(xn, all_22_1_35) = all_22_0_34
% 26.82/7.76 |
% 26.82/7.76 | Instantiating (100) with all_28_0_51, all_28_1_52, all_28_2_53 yields:
% 26.82/7.76 | (155) aNaturalNumber0(all_0_1_1) = all_28_0_51 & aNaturalNumber0(xp) = all_28_2_53 & aNaturalNumber0(xm) = all_28_1_52 & ( ~ (all_28_1_52 = 0) | ~ (all_28_2_53 = 0) | all_28_0_51 = 0)
% 26.82/7.76 |
% 26.82/7.76 | Applying alpha-rule on (155) yields:
% 26.82/7.76 | (156) aNaturalNumber0(all_0_1_1) = all_28_0_51
% 26.82/7.76 | (157) aNaturalNumber0(xp) = all_28_2_53
% 26.82/7.76 | (158) aNaturalNumber0(xm) = all_28_1_52
% 26.82/7.76 | (159) ~ (all_28_1_52 = 0) | ~ (all_28_2_53 = 0) | all_28_0_51 = 0
% 26.82/7.76 |
% 26.82/7.76 | Instantiating (106) with all_32_0_60, all_32_1_61, all_32_2_62 yields:
% 26.82/7.76 | (160) aNaturalNumber0(all_0_5_5) = all_32_0_60 & aNaturalNumber0(all_0_6_6) = all_32_2_62 & aNaturalNumber0(xp) = all_32_1_61 & ( ~ (all_32_1_61 = 0) | ~ (all_32_2_62 = 0) | all_32_0_60 = 0)
% 26.82/7.76 |
% 26.82/7.76 | Applying alpha-rule on (160) yields:
% 26.82/7.76 | (161) aNaturalNumber0(all_0_5_5) = all_32_0_60
% 26.82/7.76 | (162) aNaturalNumber0(all_0_6_6) = all_32_2_62
% 26.82/7.76 | (163) aNaturalNumber0(xp) = all_32_1_61
% 26.82/7.76 | (164) ~ (all_32_1_61 = 0) | ~ (all_32_2_62 = 0) | all_32_0_60 = 0
% 26.82/7.76 |
% 26.82/7.76 | Instantiating (105) with all_34_0_63, all_34_1_64, all_34_2_65 yields:
% 26.82/7.76 | (165) sdtpldt0(xp, all_0_6_6) = all_34_0_63 & aNaturalNumber0(all_0_6_6) = all_34_2_65 & aNaturalNumber0(xp) = all_34_1_64 & ( ~ (all_34_1_64 = 0) | ~ (all_34_2_65 = 0) | all_34_0_63 = all_0_5_5)
% 26.82/7.76 |
% 26.82/7.76 | Applying alpha-rule on (165) yields:
% 26.82/7.76 | (166) sdtpldt0(xp, all_0_6_6) = all_34_0_63
% 26.82/7.76 | (167) aNaturalNumber0(all_0_6_6) = all_34_2_65
% 26.82/7.76 | (168) aNaturalNumber0(xp) = all_34_1_64
% 26.82/7.76 | (169) ~ (all_34_1_64 = 0) | ~ (all_34_2_65 = 0) | all_34_0_63 = all_0_5_5
% 26.82/7.76 |
% 26.82/7.76 | Instantiating (98) with all_36_0_66, all_36_1_67, all_36_2_68 yields:
% 26.82/7.76 | (170) aNaturalNumber0(all_0_0_0) = all_36_0_66 & aNaturalNumber0(xk) = all_36_1_67 & aNaturalNumber0(xp) = all_36_2_68 & ( ~ (all_36_1_67 = 0) | ~ (all_36_2_68 = 0) | all_36_0_66 = 0)
% 26.82/7.77 |
% 26.82/7.77 | Applying alpha-rule on (170) yields:
% 26.82/7.77 | (171) aNaturalNumber0(all_0_0_0) = all_36_0_66
% 26.82/7.77 | (172) aNaturalNumber0(xk) = all_36_1_67
% 26.82/7.77 | (173) aNaturalNumber0(xp) = all_36_2_68
% 26.82/7.77 | (174) ~ (all_36_1_67 = 0) | ~ (all_36_2_68 = 0) | all_36_0_66 = 0
% 26.82/7.77 |
% 26.82/7.77 | Instantiating (97) with all_38_0_69, all_38_1_70, all_38_2_71 yields:
% 26.82/7.77 | (175) sdtasdt0(xk, xp) = all_38_0_69 & aNaturalNumber0(xk) = all_38_1_70 & aNaturalNumber0(xp) = all_38_2_71 & ( ~ (all_38_1_70 = 0) | ~ (all_38_2_71 = 0) | all_38_0_69 = all_0_0_0)
% 26.82/7.77 |
% 26.82/7.77 | Applying alpha-rule on (175) yields:
% 26.82/7.77 | (176) sdtasdt0(xk, xp) = all_38_0_69
% 26.82/7.77 | (177) aNaturalNumber0(xk) = all_38_1_70
% 26.82/7.77 | (178) aNaturalNumber0(xp) = all_38_2_71
% 26.82/7.77 | (179) ~ (all_38_1_70 = 0) | ~ (all_38_2_71 = 0) | all_38_0_69 = all_0_0_0
% 26.82/7.77 |
% 26.82/7.77 | Instantiating (104) with all_40_0_72, all_40_1_73, all_40_2_74 yields:
% 26.82/7.77 | (180) aNaturalNumber0(all_0_4_4) = all_40_0_72 & aNaturalNumber0(xm) = all_40_1_73 & aNaturalNumber0(xn) = all_40_2_74 & ( ~ (all_40_1_73 = 0) | ~ (all_40_2_74 = 0) | all_40_0_72 = 0)
% 26.82/7.77 |
% 26.82/7.77 | Applying alpha-rule on (180) yields:
% 26.82/7.77 | (181) aNaturalNumber0(all_0_4_4) = all_40_0_72
% 26.82/7.77 | (182) aNaturalNumber0(xm) = all_40_1_73
% 26.82/7.77 | (183) aNaturalNumber0(xn) = all_40_2_74
% 26.82/7.77 | (184) ~ (all_40_1_73 = 0) | ~ (all_40_2_74 = 0) | all_40_0_72 = 0
% 26.82/7.77 |
% 26.82/7.77 | Instantiating (99) with all_45_0_84, all_45_1_85, all_45_2_86 yields:
% 26.82/7.77 | (185) sdtasdt0(xm, xp) = all_45_0_84 & aNaturalNumber0(xp) = all_45_2_86 & aNaturalNumber0(xm) = all_45_1_85 & ( ~ (all_45_1_85 = 0) | ~ (all_45_2_86 = 0) | all_45_0_84 = all_0_1_1)
% 26.82/7.77 |
% 26.82/7.77 | Applying alpha-rule on (185) yields:
% 26.82/7.77 | (186) sdtasdt0(xm, xp) = all_45_0_84
% 26.82/7.77 | (187) aNaturalNumber0(xp) = all_45_2_86
% 26.82/7.77 | (188) aNaturalNumber0(xm) = all_45_1_85
% 26.82/7.77 | (189) ~ (all_45_1_85 = 0) | ~ (all_45_2_86 = 0) | all_45_0_84 = all_0_1_1
% 26.82/7.77 |
% 26.82/7.77 +-Applying beta-rule and splitting (91), into two cases.
% 26.82/7.77 |-Branch one:
% 26.82/7.77 | (190) all_0_0_0 = all_0_1_1
% 26.82/7.77 |
% 26.82/7.77 | Equations (190) can reduce 59 to:
% 26.82/7.77 | (191) $false
% 26.82/7.77 |
% 26.82/7.77 |-The branch is then unsatisfiable
% 26.82/7.77 |-Branch two:
% 26.82/7.77 | (59) ~ (all_0_0_0 = all_0_1_1)
% 26.82/7.77 | (193) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_0_0_0, all_0_1_1) = v2 & aNaturalNumber0(all_0_0_0) = v1 & aNaturalNumber0(all_0_1_1) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 26.82/7.77 |
% 26.82/7.77 | Instantiating (193) with all_51_0_87, all_51_1_88, all_51_2_89 yields:
% 26.82/7.77 | (194) sdtlseqdt0(all_0_0_0, all_0_1_1) = all_51_0_87 & aNaturalNumber0(all_0_0_0) = all_51_1_88 & aNaturalNumber0(all_0_1_1) = all_51_2_89 & ( ~ (all_51_0_87 = 0) | ~ (all_51_1_88 = 0) | ~ (all_51_2_89 = 0))
% 26.82/7.77 |
% 26.82/7.77 | Applying alpha-rule on (194) yields:
% 26.82/7.77 | (195) sdtlseqdt0(all_0_0_0, all_0_1_1) = all_51_0_87
% 26.82/7.77 | (196) aNaturalNumber0(all_0_0_0) = all_51_1_88
% 26.82/7.77 | (197) aNaturalNumber0(all_0_1_1) = all_51_2_89
% 26.82/7.77 | (198) ~ (all_51_0_87 = 0) | ~ (all_51_1_88 = 0) | ~ (all_51_2_89 = 0)
% 26.82/7.77 |
% 26.82/7.77 +-Applying beta-rule and splitting (93), into two cases.
% 26.82/7.77 |-Branch one:
% 26.82/7.77 | (199) all_0_2_2 = 0
% 26.82/7.77 |
% 26.82/7.77 | Equations (199) can reduce 80 to:
% 26.82/7.77 | (191) $false
% 26.82/7.77 |
% 26.82/7.77 |-The branch is then unsatisfiable
% 26.82/7.77 |-Branch two:
% 26.82/7.77 | (80) ~ (all_0_2_2 = 0)
% 26.82/7.77 | (202) ? [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)))
% 26.82/7.77 |
% 26.82/7.77 | Instantiating (202) with all_56_0_90, all_56_1_91, all_56_2_92, all_56_3_93 yields:
% 26.82/7.77 | (203) sdtlseqdt0(xk, xm) = all_56_0_90 & aNaturalNumber0(xk) = all_56_2_92 & aNaturalNumber0(xp) = all_56_3_93 & aNaturalNumber0(xm) = all_56_1_91 & ( ~ (all_56_0_90 = 0) | ~ (all_56_1_91 = 0) | ~ (all_56_2_92 = 0) | ~ (all_56_3_93 = 0))
% 26.82/7.77 |
% 26.82/7.77 | Applying alpha-rule on (203) yields:
% 26.82/7.77 | (204) sdtlseqdt0(xk, xm) = all_56_0_90
% 26.82/7.77 | (205) aNaturalNumber0(xm) = all_56_1_91
% 26.82/7.77 | (206) aNaturalNumber0(xp) = all_56_3_93
% 26.82/7.77 | (207) aNaturalNumber0(xk) = all_56_2_92
% 26.82/7.77 | (208) ~ (all_56_0_90 = 0) | ~ (all_56_1_91 = 0) | ~ (all_56_2_92 = 0) | ~ (all_56_3_93 = 0)
% 26.82/7.77 |
% 26.82/7.77 +-Applying beta-rule and splitting (92), into two cases.
% 26.82/7.77 |-Branch one:
% 26.82/7.77 | (209) all_0_1_1 = all_0_4_4
% 26.82/7.77 |
% 26.82/7.77 | Equations (209) can reduce 25 to:
% 26.82/7.77 | (191) $false
% 26.82/7.77 |
% 26.82/7.77 |-The branch is then unsatisfiable
% 26.82/7.77 |-Branch two:
% 26.82/7.77 | (25) ~ (all_0_1_1 = all_0_4_4)
% 26.82/7.77 | (212) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_0_1_1, all_0_4_4) = v2 & aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(all_0_4_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 26.82/7.77 |
% 26.82/7.77 | Instantiating (212) with all_61_0_94, all_61_1_95, all_61_2_96 yields:
% 26.82/7.77 | (213) sdtlseqdt0(all_0_1_1, all_0_4_4) = all_61_0_94 & aNaturalNumber0(all_0_1_1) = all_61_1_95 & aNaturalNumber0(all_0_4_4) = all_61_2_96 & ( ~ (all_61_0_94 = 0) | ~ (all_61_1_95 = 0) | ~ (all_61_2_96 = 0))
% 26.82/7.77 |
% 26.82/7.77 | Applying alpha-rule on (213) yields:
% 26.82/7.77 | (214) sdtlseqdt0(all_0_1_1, all_0_4_4) = all_61_0_94
% 26.82/7.77 | (215) aNaturalNumber0(all_0_1_1) = all_61_1_95
% 26.82/7.77 | (216) aNaturalNumber0(all_0_4_4) = all_61_2_96
% 26.82/7.77 | (217) ~ (all_61_0_94 = 0) | ~ (all_61_1_95 = 0) | ~ (all_61_2_96 = 0)
% 26.82/7.77 |
% 26.82/7.77 +-Applying beta-rule and splitting (96), into two cases.
% 26.82/7.77 |-Branch one:
% 26.82/7.77 | (218) xp = sz00
% 26.82/7.77 |
% 26.82/7.77 | Equations (218) can reduce 90 to:
% 26.82/7.77 | (191) $false
% 26.82/7.77 |
% 26.82/7.77 |-The branch is then unsatisfiable
% 26.82/7.77 |-Branch two:
% 26.82/7.77 | (90) ~ (xp = sz00)
% 26.82/7.77 | (221) ? [v0] : ? [v1] : ? [v2] : ((v0 = 0 & aNaturalNumber0(xk) = 0) | (doDivides0(xp, all_0_4_4) = v2 & aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 26.82/7.77 |
% 26.82/7.77 +-Applying beta-rule and splitting (94), into two cases.
% 26.82/7.77 |-Branch one:
% 26.82/7.77 | (222) all_0_3_3 = 0
% 26.82/7.77 |
% 26.82/7.77 | Equations (222) can reduce 43 to:
% 26.82/7.77 | (191) $false
% 26.82/7.77 |
% 26.82/7.77 |-The branch is then unsatisfiable
% 26.82/7.77 |-Branch two:
% 26.82/7.77 | (43) ~ (all_0_3_3 = 0)
% 26.82/7.77 | (225) ? [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)))
% 26.82/7.77 |
% 26.82/7.77 | Instantiating (225) with all_70_0_100, all_70_1_101, all_70_2_102, all_70_3_103 yields:
% 26.82/7.77 | (226) sdtlseqdt0(xk, xn) = all_70_0_100 & aNaturalNumber0(xk) = all_70_2_102 & aNaturalNumber0(xp) = all_70_3_103 & aNaturalNumber0(xn) = all_70_1_101 & ( ~ (all_70_0_100 = 0) | ~ (all_70_1_101 = 0) | ~ (all_70_2_102 = 0) | ~ (all_70_3_103 = 0))
% 26.82/7.77 |
% 26.82/7.77 | Applying alpha-rule on (226) yields:
% 26.82/7.77 | (227) sdtlseqdt0(xk, xn) = all_70_0_100
% 26.82/7.77 | (228) aNaturalNumber0(xk) = all_70_2_102
% 26.82/7.77 | (229) aNaturalNumber0(xn) = all_70_1_101
% 26.82/7.77 | (230) aNaturalNumber0(xp) = all_70_3_103
% 26.82/7.77 | (231) ~ (all_70_0_100 = 0) | ~ (all_70_1_101 = 0) | ~ (all_70_2_102 = 0) | ~ (all_70_3_103 = 0)
% 26.82/7.77 |
% 26.82/7.77 +-Applying beta-rule and splitting (110), into two cases.
% 26.82/7.77 |-Branch one:
% 26.82/7.77 | (218) xp = sz00
% 26.82/7.77 |
% 26.82/7.77 | Equations (218) can reduce 90 to:
% 26.82/7.77 | (191) $false
% 26.82/7.77 |
% 26.82/7.77 |-The branch is then unsatisfiable
% 26.82/7.77 |-Branch two:
% 26.82/7.77 | (90) ~ (xp = sz00)
% 26.82/7.77 | (235) xp = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 26.82/7.77 |
% 26.82/7.77 | Instantiating formula (2) with all_0_1_1, all_0_4_4, all_61_0_94, 0 and discharging atoms sdtlseqdt0(all_0_1_1, all_0_4_4) = all_61_0_94, yields:
% 26.82/7.77 | (236) all_61_0_94 = 0 | ~ (sdtlseqdt0(all_0_1_1, all_0_4_4) = 0)
% 26.82/7.77 |
% 26.82/7.77 | Instantiating formula (52) with all_0_1_1, all_51_2_89, all_61_1_95 and discharging atoms aNaturalNumber0(all_0_1_1) = all_61_1_95, aNaturalNumber0(all_0_1_1) = all_51_2_89, yields:
% 26.82/7.77 | (237) all_61_1_95 = all_51_2_89
% 26.82/7.77 |
% 26.82/7.77 | Instantiating formula (52) with all_0_1_1, all_28_0_51, all_61_1_95 and discharging atoms aNaturalNumber0(all_0_1_1) = all_61_1_95, aNaturalNumber0(all_0_1_1) = all_28_0_51, yields:
% 26.82/7.77 | (238) all_61_1_95 = all_28_0_51
% 26.82/7.77 |
% 26.82/7.77 | Instantiating formula (52) with all_0_4_4, all_40_0_72, all_61_2_96 and discharging atoms aNaturalNumber0(all_0_4_4) = all_61_2_96, aNaturalNumber0(all_0_4_4) = all_40_0_72, yields:
% 26.82/7.77 | (239) all_61_2_96 = all_40_0_72
% 26.82/7.77 |
% 26.82/7.77 | Instantiating formula (52) with xp, all_45_2_86, all_56_3_93 and discharging atoms aNaturalNumber0(xp) = all_56_3_93, aNaturalNumber0(xp) = all_45_2_86, yields:
% 26.82/7.77 | (240) all_56_3_93 = all_45_2_86
% 26.82/7.77 |
% 26.82/7.77 | Instantiating formula (52) with xp, all_38_2_71, all_70_3_103 and discharging atoms aNaturalNumber0(xp) = all_70_3_103, aNaturalNumber0(xp) = all_38_2_71, yields:
% 26.82/7.77 | (241) all_70_3_103 = all_38_2_71
% 26.82/7.77 |
% 26.82/7.77 | Instantiating formula (52) with xp, all_36_2_68, 0 and discharging atoms aNaturalNumber0(xp) = all_36_2_68, aNaturalNumber0(xp) = 0, yields:
% 26.82/7.78 | (242) all_36_2_68 = 0
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xp, all_36_2_68, all_70_3_103 and discharging atoms aNaturalNumber0(xp) = all_70_3_103, aNaturalNumber0(xp) = all_36_2_68, yields:
% 26.82/7.78 | (243) all_70_3_103 = all_36_2_68
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xp, all_34_1_64, all_45_2_86 and discharging atoms aNaturalNumber0(xp) = all_45_2_86, aNaturalNumber0(xp) = all_34_1_64, yields:
% 26.82/7.78 | (244) all_45_2_86 = all_34_1_64
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xp, all_32_1_61, all_70_3_103 and discharging atoms aNaturalNumber0(xp) = all_70_3_103, aNaturalNumber0(xp) = all_32_1_61, yields:
% 26.82/7.78 | (245) all_70_3_103 = all_32_1_61
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xp, all_28_2_53, all_70_3_103 and discharging atoms aNaturalNumber0(xp) = all_70_3_103, aNaturalNumber0(xp) = all_28_2_53, yields:
% 26.82/7.78 | (246) all_70_3_103 = all_28_2_53
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xp, all_22_2_36, all_34_1_64 and discharging atoms aNaturalNumber0(xp) = all_34_1_64, aNaturalNumber0(xp) = all_22_2_36, yields:
% 26.82/7.78 | (247) all_34_1_64 = all_22_2_36
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xp, all_22_2_36, all_28_2_53 and discharging atoms aNaturalNumber0(xp) = all_28_2_53, aNaturalNumber0(xp) = all_22_2_36, yields:
% 26.82/7.78 | (248) all_28_2_53 = all_22_2_36
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xp, all_18_6_22, all_56_3_93 and discharging atoms aNaturalNumber0(xp) = all_56_3_93, aNaturalNumber0(xp) = all_18_6_22, yields:
% 26.82/7.78 | (249) all_56_3_93 = all_18_6_22
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xm, all_40_1_73, all_45_1_85 and discharging atoms aNaturalNumber0(xm) = all_45_1_85, aNaturalNumber0(xm) = all_40_1_73, yields:
% 26.82/7.78 | (250) all_45_1_85 = all_40_1_73
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xm, all_28_1_52, 0 and discharging atoms aNaturalNumber0(xm) = all_28_1_52, aNaturalNumber0(xm) = 0, yields:
% 26.82/7.78 | (251) all_28_1_52 = 0
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xm, all_28_1_52, all_56_1_91 and discharging atoms aNaturalNumber0(xm) = all_56_1_91, aNaturalNumber0(xm) = all_28_1_52, yields:
% 26.82/7.78 | (252) all_56_1_91 = all_28_1_52
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xm, all_22_3_37, all_56_1_91 and discharging atoms aNaturalNumber0(xm) = all_56_1_91, aNaturalNumber0(xm) = all_22_3_37, yields:
% 26.82/7.78 | (253) all_56_1_91 = all_22_3_37
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xm, all_20_7_32, all_28_1_52 and discharging atoms aNaturalNumber0(xm) = all_28_1_52, aNaturalNumber0(xm) = all_20_7_32, yields:
% 26.82/7.78 | (254) all_28_1_52 = all_20_7_32
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xm, all_18_7_23, all_40_1_73 and discharging atoms aNaturalNumber0(xm) = all_40_1_73, aNaturalNumber0(xm) = all_18_7_23, yields:
% 26.82/7.78 | (255) all_40_1_73 = all_18_7_23
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xm, all_18_7_23, all_20_7_32 and discharging atoms aNaturalNumber0(xm) = all_20_7_32, aNaturalNumber0(xm) = all_18_7_23, yields:
% 26.82/7.78 | (256) all_20_7_32 = all_18_7_23
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xm, all_16_1_14, all_20_7_32 and discharging atoms aNaturalNumber0(xm) = all_20_7_32, aNaturalNumber0(xm) = all_16_1_14, yields:
% 26.82/7.78 | (257) all_20_7_32 = all_16_1_14
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xm, all_14_1_11, all_28_1_52 and discharging atoms aNaturalNumber0(xm) = all_28_1_52, aNaturalNumber0(xm) = all_14_1_11, yields:
% 26.82/7.78 | (258) all_28_1_52 = all_14_1_11
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xm, all_12_1_8, all_45_1_85 and discharging atoms aNaturalNumber0(xm) = all_45_1_85, aNaturalNumber0(xm) = all_12_1_8, yields:
% 26.82/7.78 | (259) all_45_1_85 = all_12_1_8
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xn, all_40_2_74, all_70_1_101 and discharging atoms aNaturalNumber0(xn) = all_70_1_101, aNaturalNumber0(xn) = all_40_2_74, yields:
% 26.82/7.78 | (260) all_70_1_101 = all_40_2_74
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xn, all_22_4_38, 0 and discharging atoms aNaturalNumber0(xn) = all_22_4_38, aNaturalNumber0(xn) = 0, yields:
% 26.82/7.78 | (261) all_22_4_38 = 0
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xn, all_20_8_33, all_70_1_101 and discharging atoms aNaturalNumber0(xn) = all_70_1_101, aNaturalNumber0(xn) = all_20_8_33, yields:
% 26.82/7.78 | (262) all_70_1_101 = all_20_8_33
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xn, all_18_8_24, all_22_4_38 and discharging atoms aNaturalNumber0(xn) = all_22_4_38, aNaturalNumber0(xn) = all_18_8_24, yields:
% 26.82/7.78 | (263) all_22_4_38 = all_18_8_24
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xn, all_16_2_15, all_20_8_33 and discharging atoms aNaturalNumber0(xn) = all_20_8_33, aNaturalNumber0(xn) = all_16_2_15, yields:
% 26.82/7.78 | (264) all_20_8_33 = all_16_2_15
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xn, all_14_2_12, all_18_8_24 and discharging atoms aNaturalNumber0(xn) = all_18_8_24, aNaturalNumber0(xn) = all_14_2_12, yields:
% 26.82/7.78 | (265) all_18_8_24 = all_14_2_12
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xn, all_14_2_12, all_16_2_15 and discharging atoms aNaturalNumber0(xn) = all_16_2_15, aNaturalNumber0(xn) = all_14_2_12, yields:
% 26.82/7.78 | (266) all_16_2_15 = all_14_2_12
% 26.82/7.78 |
% 26.82/7.78 | Instantiating formula (52) with xn, all_12_2_9, all_70_1_101 and discharging atoms aNaturalNumber0(xn) = all_70_1_101, aNaturalNumber0(xn) = all_12_2_9, yields:
% 26.82/7.78 | (267) all_70_1_101 = all_12_2_9
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (262,260) yields a new equation:
% 26.82/7.78 | (268) all_40_2_74 = all_20_8_33
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (267,260) yields a new equation:
% 26.82/7.78 | (269) all_40_2_74 = all_12_2_9
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (246,241) yields a new equation:
% 26.82/7.78 | (270) all_38_2_71 = all_28_2_53
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (245,241) yields a new equation:
% 26.82/7.78 | (271) all_38_2_71 = all_32_1_61
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (243,241) yields a new equation:
% 26.82/7.78 | (272) all_38_2_71 = all_36_2_68
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (238,237) yields a new equation:
% 26.82/7.78 | (273) all_51_2_89 = all_28_0_51
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (252,253) yields a new equation:
% 26.82/7.78 | (274) all_28_1_52 = all_22_3_37
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 274 yields:
% 26.82/7.78 | (275) all_28_1_52 = all_22_3_37
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (240,249) yields a new equation:
% 26.82/7.78 | (276) all_45_2_86 = all_18_6_22
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 276 yields:
% 26.82/7.78 | (277) all_45_2_86 = all_18_6_22
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (250,259) yields a new equation:
% 26.82/7.78 | (278) all_40_1_73 = all_12_1_8
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 278 yields:
% 26.82/7.78 | (279) all_40_1_73 = all_12_1_8
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (244,277) yields a new equation:
% 26.82/7.78 | (280) all_34_1_64 = all_18_6_22
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 280 yields:
% 26.82/7.78 | (281) all_34_1_64 = all_18_6_22
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (255,279) yields a new equation:
% 26.82/7.78 | (282) all_18_7_23 = all_12_1_8
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 282 yields:
% 26.82/7.78 | (283) all_18_7_23 = all_12_1_8
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (268,269) yields a new equation:
% 26.82/7.78 | (284) all_20_8_33 = all_12_2_9
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 284 yields:
% 26.82/7.78 | (285) all_20_8_33 = all_12_2_9
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (270,271) yields a new equation:
% 26.82/7.78 | (286) all_32_1_61 = all_28_2_53
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (272,271) yields a new equation:
% 26.82/7.78 | (287) all_36_2_68 = all_32_1_61
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 287 yields:
% 26.82/7.78 | (288) all_36_2_68 = all_32_1_61
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (288,242) yields a new equation:
% 26.82/7.78 | (289) all_32_1_61 = 0
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 289 yields:
% 26.82/7.78 | (290) all_32_1_61 = 0
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (247,281) yields a new equation:
% 26.82/7.78 | (291) all_22_2_36 = all_18_6_22
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 291 yields:
% 26.82/7.78 | (292) all_22_2_36 = all_18_6_22
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (286,290) yields a new equation:
% 26.82/7.78 | (293) all_28_2_53 = 0
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 293 yields:
% 26.82/7.78 | (294) all_28_2_53 = 0
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (251,275) yields a new equation:
% 26.82/7.78 | (295) all_22_3_37 = 0
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (258,275) yields a new equation:
% 26.82/7.78 | (296) all_22_3_37 = all_14_1_11
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (254,275) yields a new equation:
% 26.82/7.78 | (297) all_22_3_37 = all_20_7_32
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (248,294) yields a new equation:
% 26.82/7.78 | (298) all_22_2_36 = 0
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 298 yields:
% 26.82/7.78 | (299) all_22_2_36 = 0
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (292,299) yields a new equation:
% 26.82/7.78 | (300) all_18_6_22 = 0
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 300 yields:
% 26.82/7.78 | (301) all_18_6_22 = 0
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (297,296) yields a new equation:
% 26.82/7.78 | (302) all_20_7_32 = all_14_1_11
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 302 yields:
% 26.82/7.78 | (303) all_20_7_32 = all_14_1_11
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (295,296) yields a new equation:
% 26.82/7.78 | (304) all_14_1_11 = 0
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (263,261) yields a new equation:
% 26.82/7.78 | (305) all_18_8_24 = 0
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 305 yields:
% 26.82/7.78 | (306) all_18_8_24 = 0
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (303,257) yields a new equation:
% 26.82/7.78 | (307) all_16_1_14 = all_14_1_11
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (256,257) yields a new equation:
% 26.82/7.78 | (308) all_18_7_23 = all_16_1_14
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 308 yields:
% 26.82/7.78 | (309) all_18_7_23 = all_16_1_14
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (264,285) yields a new equation:
% 26.82/7.78 | (310) all_16_2_15 = all_12_2_9
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 310 yields:
% 26.82/7.78 | (311) all_16_2_15 = all_12_2_9
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (309,283) yields a new equation:
% 26.82/7.78 | (312) all_16_1_14 = all_12_1_8
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 312 yields:
% 26.82/7.78 | (313) all_16_1_14 = all_12_1_8
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (265,306) yields a new equation:
% 26.82/7.78 | (314) all_14_2_12 = 0
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 314 yields:
% 26.82/7.78 | (315) all_14_2_12 = 0
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (307,313) yields a new equation:
% 26.82/7.78 | (316) all_14_1_11 = all_12_1_8
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 316 yields:
% 26.82/7.78 | (317) all_14_1_11 = all_12_1_8
% 26.82/7.78 |
% 26.82/7.78 | Combining equations (266,311) yields a new equation:
% 26.82/7.78 | (318) all_14_2_12 = all_12_2_9
% 26.82/7.78 |
% 26.82/7.78 | Simplifying 318 yields:
% 26.82/7.78 | (319) all_14_2_12 = all_12_2_9
% 26.82/7.78 |
% 26.82/7.79 | Combining equations (304,317) yields a new equation:
% 26.82/7.79 | (320) all_12_1_8 = 0
% 26.82/7.79 |
% 26.82/7.79 | Combining equations (315,319) yields a new equation:
% 26.82/7.79 | (321) all_12_2_9 = 0
% 26.82/7.79 |
% 26.82/7.79 | Combining equations (320,317) yields a new equation:
% 26.82/7.79 | (304) all_14_1_11 = 0
% 26.82/7.79 |
% 26.82/7.79 | Combining equations (304,296) yields a new equation:
% 26.82/7.79 | (295) all_22_3_37 = 0
% 26.82/7.79 |
% 26.82/7.79 | Combining equations (295,275) yields a new equation:
% 26.82/7.79 | (251) all_28_1_52 = 0
% 26.82/7.79 |
% 26.82/7.79 | Combining equations (321,269) yields a new equation:
% 26.82/7.79 | (325) all_40_2_74 = 0
% 26.82/7.79 |
% 26.82/7.79 | Combining equations (320,279) yields a new equation:
% 26.82/7.79 | (326) all_40_1_73 = 0
% 26.82/7.79 |
% 26.82/7.79 | Combining equations (273,237) yields a new equation:
% 26.82/7.79 | (238) all_61_1_95 = all_28_0_51
% 26.82/7.79 |
% 26.82/7.79 | From (239) and (216) follows:
% 26.82/7.79 | (181) aNaturalNumber0(all_0_4_4) = all_40_0_72
% 26.82/7.79 |
% 26.82/7.79 | From (301) and (136) follows:
% 26.82/7.79 | (15) aNaturalNumber0(xp) = 0
% 26.82/7.79 |
% 26.82/7.79 +-Applying beta-rule and splitting (159), into two cases.
% 26.82/7.79 |-Branch one:
% 26.82/7.79 | (330) ~ (all_28_1_52 = 0)
% 26.82/7.79 |
% 26.82/7.79 | Equations (251) can reduce 330 to:
% 26.82/7.79 | (191) $false
% 26.82/7.79 |
% 26.82/7.79 |-The branch is then unsatisfiable
% 26.82/7.79 |-Branch two:
% 26.82/7.79 | (251) all_28_1_52 = 0
% 26.82/7.79 | (333) ~ (all_28_2_53 = 0) | all_28_0_51 = 0
% 26.82/7.79 |
% 26.82/7.79 +-Applying beta-rule and splitting (333), into two cases.
% 26.82/7.79 |-Branch one:
% 26.82/7.79 | (334) ~ (all_28_2_53 = 0)
% 26.82/7.79 |
% 26.82/7.79 | Equations (294) can reduce 334 to:
% 26.82/7.79 | (191) $false
% 26.82/7.79 |
% 26.82/7.79 |-The branch is then unsatisfiable
% 26.82/7.79 |-Branch two:
% 26.82/7.79 | (294) all_28_2_53 = 0
% 26.82/7.79 | (337) all_28_0_51 = 0
% 26.82/7.79 |
% 26.82/7.79 | Combining equations (337,238) yields a new equation:
% 26.82/7.79 | (338) all_61_1_95 = 0
% 26.82/7.79 |
% 26.82/7.79 +-Applying beta-rule and splitting (184), into two cases.
% 26.82/7.79 |-Branch one:
% 26.82/7.79 | (339) ~ (all_40_1_73 = 0)
% 26.82/7.79 |
% 26.82/7.79 | Equations (326) can reduce 339 to:
% 26.82/7.79 | (191) $false
% 27.11/7.79 |
% 27.11/7.79 |-The branch is then unsatisfiable
% 27.11/7.79 |-Branch two:
% 27.11/7.79 | (326) all_40_1_73 = 0
% 27.11/7.79 | (342) ~ (all_40_2_74 = 0) | all_40_0_72 = 0
% 27.11/7.79 |
% 27.11/7.79 +-Applying beta-rule and splitting (342), into two cases.
% 27.11/7.79 |-Branch one:
% 27.11/7.79 | (343) ~ (all_40_2_74 = 0)
% 27.11/7.79 |
% 27.11/7.79 | Equations (325) can reduce 343 to:
% 27.11/7.79 | (191) $false
% 27.11/7.79 |
% 27.11/7.79 |-The branch is then unsatisfiable
% 27.11/7.79 |-Branch two:
% 27.11/7.79 | (325) all_40_2_74 = 0
% 27.11/7.79 | (346) all_40_0_72 = 0
% 27.11/7.79 |
% 27.11/7.79 | Combining equations (346,239) yields a new equation:
% 27.11/7.79 | (347) all_61_2_96 = 0
% 27.11/7.79 |
% 27.11/7.79 | From (346) and (181) follows:
% 27.11/7.79 | (348) aNaturalNumber0(all_0_4_4) = 0
% 27.11/7.79 |
% 27.11/7.79 +-Applying beta-rule and splitting (217), into two cases.
% 27.11/7.79 |-Branch one:
% 27.11/7.79 | (349) ~ (all_61_0_94 = 0)
% 27.11/7.79 |
% 27.11/7.79 +-Applying beta-rule and splitting (95), into two cases.
% 27.11/7.79 |-Branch one:
% 27.11/7.79 | (218) xp = sz00
% 27.11/7.79 |
% 27.11/7.79 | Equations (218) can reduce 90 to:
% 27.11/7.79 | (191) $false
% 27.11/7.79 |
% 27.11/7.79 |-The branch is then unsatisfiable
% 27.11/7.79 |-Branch two:
% 27.11/7.79 | (90) ~ (xp = sz00)
% 27.11/7.79 | (353) all_0_0_0 = all_0_4_4 | ? [v0] : ? [v1] : ? [v2] : (doDivides0(xp, all_0_4_4) = v2 & aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 27.11/7.79 |
% 27.11/7.79 +-Applying beta-rule and splitting (353), into two cases.
% 27.11/7.79 |-Branch one:
% 27.11/7.79 | (354) all_0_0_0 = all_0_4_4
% 27.11/7.79 |
% 27.11/7.79 | From (354) and (4) follows:
% 27.11/7.79 | (355) sdtlseqdt0(all_0_1_1, all_0_4_4) = 0
% 27.11/7.79 |
% 27.11/7.79 +-Applying beta-rule and splitting (236), into two cases.
% 27.11/7.79 |-Branch one:
% 27.11/7.79 | (356) ~ (sdtlseqdt0(all_0_1_1, all_0_4_4) = 0)
% 27.11/7.79 |
% 27.11/7.79 | Using (355) and (356) yields:
% 27.11/7.79 | (357) $false
% 27.11/7.79 |
% 27.11/7.79 |-The branch is then unsatisfiable
% 27.11/7.79 |-Branch two:
% 27.11/7.79 | (355) sdtlseqdt0(all_0_1_1, all_0_4_4) = 0
% 27.11/7.79 | (359) all_61_0_94 = 0
% 27.11/7.79 |
% 27.11/7.79 | Equations (359) can reduce 349 to:
% 27.11/7.79 | (191) $false
% 27.11/7.79 |
% 27.11/7.79 |-The branch is then unsatisfiable
% 27.11/7.79 |-Branch two:
% 27.11/7.79 | (361) ~ (all_0_0_0 = all_0_4_4)
% 27.11/7.79 | (362) ? [v0] : ? [v1] : ? [v2] : (doDivides0(xp, all_0_4_4) = v2 & aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 27.11/7.79 |
% 27.11/7.79 | Instantiating (362) with all_189_0_124, all_189_1_125, all_189_2_126 yields:
% 27.11/7.79 | (363) doDivides0(xp, all_0_4_4) = all_189_0_124 & aNaturalNumber0(all_0_4_4) = all_189_1_125 & aNaturalNumber0(xp) = all_189_2_126 & ( ~ (all_189_0_124 = 0) | ~ (all_189_1_125 = 0) | ~ (all_189_2_126 = 0))
% 27.11/7.79 |
% 27.11/7.79 | Applying alpha-rule on (363) yields:
% 27.11/7.79 | (364) doDivides0(xp, all_0_4_4) = all_189_0_124
% 27.11/7.79 | (365) aNaturalNumber0(all_0_4_4) = all_189_1_125
% 27.11/7.79 | (366) aNaturalNumber0(xp) = all_189_2_126
% 27.11/7.79 | (367) ~ (all_189_0_124 = 0) | ~ (all_189_1_125 = 0) | ~ (all_189_2_126 = 0)
% 27.11/7.79 |
% 27.11/7.79 | Instantiating formula (65) with xp, all_0_4_4, all_189_0_124, 0 and discharging atoms doDivides0(xp, all_0_4_4) = all_189_0_124, doDivides0(xp, all_0_4_4) = 0, yields:
% 27.11/7.79 | (368) all_189_0_124 = 0
% 27.11/7.79 |
% 27.11/7.79 | Instantiating formula (52) with all_0_4_4, all_189_1_125, 0 and discharging atoms aNaturalNumber0(all_0_4_4) = all_189_1_125, aNaturalNumber0(all_0_4_4) = 0, yields:
% 27.11/7.79 | (369) all_189_1_125 = 0
% 27.11/7.79 |
% 27.11/7.79 | Instantiating formula (52) with xp, all_189_2_126, 0 and discharging atoms aNaturalNumber0(xp) = all_189_2_126, aNaturalNumber0(xp) = 0, yields:
% 27.11/7.79 | (370) all_189_2_126 = 0
% 27.11/7.79 |
% 27.11/7.79 +-Applying beta-rule and splitting (367), into two cases.
% 27.11/7.79 |-Branch one:
% 27.11/7.79 | (371) ~ (all_189_0_124 = 0)
% 27.11/7.79 |
% 27.11/7.79 | Equations (368) can reduce 371 to:
% 27.11/7.79 | (191) $false
% 27.11/7.79 |
% 27.11/7.79 |-The branch is then unsatisfiable
% 27.11/7.79 |-Branch two:
% 27.11/7.79 | (368) all_189_0_124 = 0
% 27.11/7.79 | (374) ~ (all_189_1_125 = 0) | ~ (all_189_2_126 = 0)
% 27.11/7.79 |
% 27.11/7.79 +-Applying beta-rule and splitting (374), into two cases.
% 27.11/7.79 |-Branch one:
% 27.11/7.79 | (375) ~ (all_189_1_125 = 0)
% 27.11/7.79 |
% 27.11/7.79 | Equations (369) can reduce 375 to:
% 27.11/7.79 | (191) $false
% 27.11/7.79 |
% 27.11/7.79 |-The branch is then unsatisfiable
% 27.11/7.79 |-Branch two:
% 27.11/7.79 | (369) all_189_1_125 = 0
% 27.11/7.79 | (378) ~ (all_189_2_126 = 0)
% 27.11/7.79 |
% 27.11/7.79 | Equations (370) can reduce 378 to:
% 27.11/7.79 | (191) $false
% 27.11/7.79 |
% 27.11/7.79 |-The branch is then unsatisfiable
% 27.11/7.79 |-Branch two:
% 27.11/7.79 | (359) all_61_0_94 = 0
% 27.11/7.79 | (381) ~ (all_61_1_95 = 0) | ~ (all_61_2_96 = 0)
% 27.11/7.79 |
% 27.11/7.79 +-Applying beta-rule and splitting (381), into two cases.
% 27.11/7.79 |-Branch one:
% 27.11/7.79 | (382) ~ (all_61_1_95 = 0)
% 27.11/7.79 |
% 27.11/7.79 | Equations (338) can reduce 382 to:
% 27.11/7.79 | (191) $false
% 27.11/7.79 |
% 27.11/7.79 |-The branch is then unsatisfiable
% 27.11/7.79 |-Branch two:
% 27.11/7.79 | (338) all_61_1_95 = 0
% 27.11/7.79 | (385) ~ (all_61_2_96 = 0)
% 27.11/7.79 |
% 27.11/7.79 | Equations (347) can reduce 385 to:
% 27.11/7.79 | (191) $false
% 27.11/7.79 |
% 27.11/7.79 |-The branch is then unsatisfiable
% 27.11/7.79 % SZS output end Proof for theBenchmark
% 27.11/7.79
% 27.11/7.79 7195ms
%------------------------------------------------------------------------------