TSTP Solution File: NUM508+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM508+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.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 08:45:16 EDT 2022
% Result : Theorem 22.02s 6.62s
% Output : Proof 38.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM508+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n028.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 : Tue Jul 5 11:24:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.65/0.63 ____ _
% 0.65/0.63 ___ / __ \_____(_)___ ________ __________
% 0.65/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.65/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.65/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.65/0.63
% 0.65/0.63 A Theorem Prover for First-Order Logic
% 0.65/0.63 (ePrincess v.1.0)
% 0.65/0.63
% 0.65/0.63 (c) Philipp Rümmer, 2009-2015
% 0.65/0.63 (c) Peter Backeman, 2014-2015
% 0.65/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.65/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.65/0.63 Bug reports to peter@backeman.se
% 0.65/0.63
% 0.65/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.65/0.63
% 0.65/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.92/1.08 Prover 0: Preprocessing ...
% 3.74/1.55 Prover 0: Constructing countermodel ...
% 19.20/5.98 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.59/6.11 Prover 1: Preprocessing ...
% 20.54/6.26 Prover 1: Constructing countermodel ...
% 22.02/6.62 Prover 1: proved (643ms)
% 22.02/6.62 Prover 0: stopped
% 22.02/6.62
% 22.02/6.62 No countermodel exists, formula is valid
% 22.02/6.62 % SZS status Theorem for theBenchmark
% 22.02/6.62
% 22.02/6.62 Generating proof ... found it (size 323)
% 37.57/11.17
% 37.57/11.17 % SZS output start Proof for theBenchmark
% 37.57/11.17 Assumed formulas after preprocessing and simplification:
% 37.57/11.17 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & ~ (v6 = 0) & ~ (v5 = v1) & ~ (v4 = 0) & ~ (v3 = 0) & ~ (xk = xp) & ~ (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(xr, xm) = v7 & doDivides0(xr, xn) = v6 & doDivides0(xp, v2) = 0 & sdtlseqdt0(v5, v1) = 0 & sdtlseqdt0(xr, xk) = 0 & sdtlseqdt0(xk, xp) = 0 & sdtlseqdt0(xp, xm) = v4 & sdtlseqdt0(xp, xn) = v3 & sdtlseqdt0(xm, xp) = 0 & sdtlseqdt0(xn, xp) = 0 & sdtasdt0(xn, xm) = v2 & sdtpldt0(v0, xr) = v5 & 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) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | v8 = sz00 | ~ (sdtlseqdt0(v11, v12) = v13) | ~ (sdtasdt0(v8, v10) = v12) | ~ (sdtasdt0(v8, v9) = v11) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (sdtlseqdt0(v18, v19) = v20 & sdtlseqdt0(v9, v10) = v17 & sdtasdt0(v10, v8) = v19 & sdtasdt0(v9, v8) = v18 & aNaturalNumber0(v10) = v16 & aNaturalNumber0(v9) = v15 & aNaturalNumber0(v8) = v14 & ( ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | (v20 = 0 & v13 = 0 & ~ (v19 = v18) & ~ (v12 = v11))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (sdtlseqdt0(v11, v12) = v13) | ~ (sdtlseqdt0(v8, v9) = 0) | ~ (sdtpldt0(v9, v10) = v12) | ~ (sdtpldt0(v8, v10) = v11) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((sdtlseqdt0(v15, v16) = v17 & sdtpldt0(v10, v9) = v16 & sdtpldt0(v10, v8) = v15 & aNaturalNumber0(v10) = v14 & ( ~ (v14 = 0) | (v17 = 0 & v13 = 0 & ~ (v16 = v15) & ~ (v12 = v11)))) | (aNaturalNumber0(v9) = v15 & aNaturalNumber0(v8) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v8 = sz00 | ~ (sdtsldt0(v12, v8) = v13) | ~ (sdtsldt0(v9, v8) = v10) | ~ (sdtasdt0(v11, v9) = v12) | ? [v14] : ? [v15] : ? [v16] : ((doDivides0(v8, v9) = v16 & aNaturalNumber0(v9) = v15 & aNaturalNumber0(v8) = v14 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0))) | (sdtasdt0(v11, v10) = v15 & aNaturalNumber0(v11) = v14 & ( ~ (v14 = 0) | v15 = v13)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtasdt0(v8, v10) = v12) | ~ (sdtasdt0(v8, v9) = v11) | ~ (sdtpldt0(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (sdtasdt0(v17, v8) = v19 & sdtasdt0(v10, v8) = v21 & sdtasdt0(v9, v8) = v20 & sdtasdt0(v8, v17) = v18 & sdtpldt0(v20, v21) = v22 & sdtpldt0(v9, v10) = v17 & aNaturalNumber0(v10) = v16 & aNaturalNumber0(v9) = v15 & aNaturalNumber0(v8) = v14 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | (v22 = v19 & v18 = v13)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (doDivides0(v8, v11) = v12) | ~ (sdtpldt0(v9, v10) = v11) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (doDivides0(v8, v10) = v17 & doDivides0(v8, v9) = v16 & aNaturalNumber0(v10) = v15 & aNaturalNumber0(v9) = v14 & aNaturalNumber0(v8) = v13 & ( ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | v8 = sz00 | ~ (sdtasdt0(v8, v10) = v12) | ~ (sdtasdt0(v8, v9) = v11) | ~ (aNaturalNumber0(v8) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (sdtasdt0(v10, v8) = v16 & sdtasdt0(v9, v8) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0) | ( ~ (v16 = v15) & ~ (v12 = v11))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (sdtpldt0(v8, v10) = v12) | ~ (sdtpldt0(v8, v9) = v11) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (sdtpldt0(v10, v8) = v17 & sdtpldt0(v9, v8) = v16 & aNaturalNumber0(v10) = v15 & aNaturalNumber0(v9) = v14 & aNaturalNumber0(v8) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | ( ~ (v17 = v16) & ~ (v12 = v11))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtasdt0(v11, v10) = v12) | ~ (sdtasdt0(v8, v9) = v11) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (sdtasdt0(v9, v10) = v16 & sdtasdt0(v8, v16) = v17 & aNaturalNumber0(v10) = v15 & aNaturalNumber0(v9) = v14 & aNaturalNumber0(v8) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | v17 = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtpldt0(v11, v10) = v12) | ~ (sdtpldt0(v8, v9) = v11) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (sdtpldt0(v9, v10) = v16 & sdtpldt0(v8, v16) = v17 & aNaturalNumber0(v10) = v15 & aNaturalNumber0(v9) = v14 & aNaturalNumber0(v8) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | v17 = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | v8 = sz00 | ~ (sdtsldt0(v9, v8) = v10) | ~ (sdtasdt0(v8, v11) = v9) | ? [v12] : ? [v13] : ? [v14] : (( ~ (v12 = 0) & aNaturalNumber0(v11) = v12) | (doDivides0(v8, v9) = v14 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (sdtmndt0(v9, v8) = v10) | ~ (sdtpldt0(v8, v11) = v9) | ? [v12] : ? [v13] : ? [v14] : (( ~ (v12 = 0) & aNaturalNumber0(v11) = v12) | (sdtlseqdt0(v8, v9) = v14 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | v8 = sz00 | ~ (sdtsldt0(v9, v8) = v10) | ~ (sdtasdt0(v8, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (doDivides0(v8, v9) = v14 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (sdtmndt0(v9, v8) = v10) | ~ (sdtpldt0(v8, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (sdtlseqdt0(v8, v9) = v14 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v8 = sz00 | ~ (sdtlseqdt0(v9, v10) = v11) | ~ (sdtasdt0(v9, v8) = v10) | ? [v12] : ? [v13] : (aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (doDivides0(v8, v10) = v11) | ~ (doDivides0(v8, v9) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (doDivides0(v9, v10) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (sdtlseqdt0(v8, v10) = v11) | ~ (sdtlseqdt0(v8, v9) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (sdtlseqdt0(v9, v10) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (doDivides0(v8, v9) = v10) | ~ (sdtasdt0(v8, v11) = v9) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & aNaturalNumber0(v11) = v12) | (aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (sdtlseqdt0(v8, v9) = v10) | ~ (sdtpldt0(v8, v11) = v9) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & aNaturalNumber0(v11) = v12) | (aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (sdtsldt0(v11, v10) = v9) | ~ (sdtsldt0(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (doDivides0(v11, v10) = v9) | ~ (doDivides0(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (iLess0(v11, v10) = v9) | ~ (iLess0(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (sdtmndt0(v11, v10) = v9) | ~ (sdtmndt0(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (sdtlseqdt0(v11, v10) = v9) | ~ (sdtlseqdt0(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (sdtasdt0(v11, v10) = v9) | ~ (sdtasdt0(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (sdtpldt0(v11, v10) = v9) | ~ (sdtpldt0(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = sz00 | ~ (sdtsldt0(v9, v8) = v10) | ~ (sdtasdt0(v8, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ((v12 = 0 & aNaturalNumber0(v10) = 0) | (doDivides0(v8, v9) = v14 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (doDivides0(v10, v11) = 0) | ~ (sdtasdt0(v8, v9) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (isPrime0(v10) = v15 & doDivides0(v10, v9) = v20 & doDivides0(v10, v8) = v19 & iLess0(v17, v1) = v18 & sdtpldt0(v16, v10) = v17 & sdtpldt0(v8, v9) = v16 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & ( ~ (v18 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | v20 = 0 | v19 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (doDivides0(v8, v11) = 0) | ~ (sdtpldt0(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (doDivides0(v8, v10) = v16 & doDivides0(v8, v9) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | v16 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtmndt0(v9, v8) = v10) | ~ (sdtpldt0(v8, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ((v12 = 0 & aNaturalNumber0(v10) = 0) | (sdtlseqdt0(v8, v9) = v14 & aNaturalNumber0(v9) = v13 & aNaturalNumber0(v8) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = v8 | ~ (iLess0(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (sdtlseqdt0(v8, v9) = v13 & aNaturalNumber0(v9) = v12 & aNaturalNumber0(v8) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (sdtlseqdt0(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (sdtlseqdt0(v9, v8) = v13 & aNaturalNumber0(v9) = v12 & aNaturalNumber0(v8) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) | (v13 = 0 & ~ (v9 = v8))))) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (isPrime0(v10) = v9) | ~ (isPrime0(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (aNaturalNumber0(v10) = v9) | ~ (aNaturalNumber0(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (sdtasdt0(v9, v8) = v13 & aNaturalNumber0(v9) = v12 & aNaturalNumber0(v8) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) | v13 = v10))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (aNaturalNumber0(v10) = v13 & aNaturalNumber0(v9) = v12 & aNaturalNumber0(v8) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) | v13 = 0))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt0(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (sdtpldt0(v9, v8) = v13 & aNaturalNumber0(v9) = v12 & aNaturalNumber0(v8) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) | v13 = v10))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt0(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (aNaturalNumber0(v10) = v13 & aNaturalNumber0(v9) = v12 & aNaturalNumber0(v8) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) | v13 = 0))) & ! [v8] : ! [v9] : (v9 = v8 | v9 = sz10 | ~ (isPrime0(v8) = 0) | ~ (doDivides0(v9, v8) = 0) | ? [v10] : (( ~ (v10 = 0) & aNaturalNumber0(v9) = v10) | ( ~ (v10 = 0) & aNaturalNumber0(v8) = v10))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (sdtlseqdt0(v8, v9) = 0) | ? [v10] : ? [v11] : ? [v12] : (sdtlseqdt0(v9, v8) = v12 & aNaturalNumber0(v9) = v11 & aNaturalNumber0(v8) = v10 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : (v9 = sz00 | v8 = sz00 | ~ (sdtasdt0(v8, v9) = sz00) | ? [v10] : ? [v11] : (aNaturalNumber0(v9) = v11 & aNaturalNumber0(v8) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : (v9 = sz00 | ~ (doDivides0(v8, v9) = 0) | ? [v10] : ? [v11] : ? [v12] : (sdtlseqdt0(v8, v9) = v12 & aNaturalNumber0(v9) = v11 & aNaturalNumber0(v8) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | v12 = 0))) & ! [v8] : ! [v9] : (v9 = sz00 | ~ (sdtpldt0(v8, v9) = sz00) | ? [v10] : ? [v11] : (aNaturalNumber0(v9) = v11 & aNaturalNumber0(v8) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : (v9 = 0 | v8 = sz10 | v8 = sz00 | ~ (isPrime0(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & ~ (v10 = v8) & ~ (v10 = sz10) & doDivides0(v10, v8) = 0 & aNaturalNumber0(v10) = 0) | ( ~ (v10 = 0) & aNaturalNumber0(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | v8 = sz10 | v8 = sz00 | ~ (sdtlseqdt0(sz10, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & aNaturalNumber0(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (sdtlseqdt0(v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & aNaturalNumber0(v8) = v10)) & ! [v8] : ! [v9] : (v8 = sz00 | ~ (sdtpldt0(v8, v9) = sz00) | ? [v10] : ? [v11] : (aNaturalNumber0(v9) = v11 & aNaturalNumber0(v8) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : ( ~ (doDivides0(v8, v9) = 0) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v9 & v11 = 0 & sdtasdt0(v8, v10) = v9 & aNaturalNumber0(v10) = 0) | (aNaturalNumber0(v9) = v11 & aNaturalNumber0(v8) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! [v8] : ! [v9] : ( ~ (sdtlseqdt0(v8, v9) = 0) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v9 & v11 = 0 & sdtpldt0(v8, v10) = v9 & aNaturalNumber0(v10) = 0) | (aNaturalNumber0(v9) = v11 & aNaturalNumber0(v8) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! [v8] : ! [v9] : ( ~ (sdtasdt0(sz10, v8) = v9) | ? [v10] : ? [v11] : (sdtasdt0(v8, sz10) = v11 & aNaturalNumber0(v8) = v10 & ( ~ (v10 = 0) | (v11 = v8 & v9 = v8)))) & ! [v8] : ! [v9] : ( ~ (sdtasdt0(sz00, v8) = v9) | ? [v10] : ? [v11] : (sdtasdt0(v8, sz00) = v11 & aNaturalNumber0(v8) = v10 & ( ~ (v10 = 0) | (v11 = sz00 & v9 = sz00)))) & ! [v8] : ! [v9] : ( ~ (sdtpldt0(sz00, v8) = v9) | ? [v10] : ? [v11] : (sdtpldt0(v8, sz00) = v11 & aNaturalNumber0(v8) = v10 & ( ~ (v10 = 0) | (v11 = v8 & v9 = v8)))) & ! [v8] : (v8 = sz10 | v8 = sz00 | ~ (aNaturalNumber0(v8) = 0) | ? [v9] : (isPrime0(v9) = 0 & doDivides0(v9, v8) = 0 & aNaturalNumber0(v9) = 0)))
% 37.83/11.25 | 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 yields:
% 37.83/11.25 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = all_0_6_6) & ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0) & ~ (xk = xp) & ~ (xk = sz10) & ~ (xk = sz00) & ~ (xp = xm) & ~ (xp = xn) & ~ (sz10 = sz00) & isPrime0(xr) = 0 & isPrime0(xp) = 0 & sdtsldt0(all_0_5_5, xp) = xk & doDivides0(xr, all_0_5_5) = 0 & doDivides0(xr, xk) = 0 & doDivides0(xr, xm) = all_0_0_0 & doDivides0(xr, xn) = all_0_1_1 & doDivides0(xp, all_0_5_5) = 0 & sdtlseqdt0(all_0_2_2, all_0_6_6) = 0 & sdtlseqdt0(xr, xk) = 0 & sdtlseqdt0(xk, xp) = 0 & sdtlseqdt0(xp, xm) = all_0_3_3 & sdtlseqdt0(xp, xn) = all_0_4_4 & sdtlseqdt0(xm, xp) = 0 & sdtlseqdt0(xn, xp) = 0 & sdtasdt0(xn, xm) = all_0_5_5 & sdtpldt0(all_0_7_7, xr) = all_0_2_2 & sdtpldt0(all_0_7_7, xp) = all_0_6_6 & sdtpldt0(xn, xm) = all_0_7_7 & 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_6_6) = 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))
% 38.05/11.28 |
% 38.05/11.28 | Applying alpha-rule on (1) yields:
% 38.05/11.28 | (2) ! [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)))
% 38.05/11.28 | (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))))
% 38.05/11.28 | (4) ! [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_6_6) = 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)))
% 38.05/11.28 | (5) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 38.05/11.28 | (6) ! [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)))))
% 38.05/11.28 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 38.05/11.28 | (8) ! [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))))
% 38.05/11.28 | (9) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 38.05/11.28 | (10) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ (isPrime0(v0) = 0) | ~ (doDivides0(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 38.05/11.29 | (11) ~ (all_0_3_3 = 0)
% 38.05/11.29 | (12) sdtsldt0(all_0_5_5, xp) = xk
% 38.05/11.29 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0))
% 38.05/11.29 | (14) sdtasdt0(xn, xm) = all_0_5_5
% 38.05/11.29 | (15) ~ (xk = sz00)
% 38.05/11.29 | (16) sdtlseqdt0(xp, xn) = all_0_4_4
% 38.05/11.29 | (17) ! [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)))))
% 38.05/11.29 | (18) doDivides0(xr, xm) = all_0_0_0
% 38.05/11.29 | (19) ~ (all_0_1_1 = 0)
% 38.05/11.29 | (20) doDivides0(xr, all_0_5_5) = 0
% 38.05/11.29 | (21) ! [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)))))
% 38.05/11.29 | (22) ! [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)))))
% 38.05/11.29 | (23) sdtpldt0(xn, xm) = all_0_7_7
% 38.05/11.29 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0))
% 38.05/11.29 | (25) ! [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))))
% 38.05/11.29 | (26) ~ (xk = xp)
% 38.05/11.29 | (27) ! [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)))
% 38.05/11.29 | (28) ! [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)))
% 38.05/11.29 | (29) doDivides0(xp, all_0_5_5) = 0
% 38.05/11.29 | (30) aNaturalNumber0(xm) = 0
% 38.05/11.29 | (31) sdtpldt0(all_0_7_7, xp) = all_0_6_6
% 38.05/11.29 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 38.05/11.29 | (33) isPrime0(xp) = 0
% 38.05/11.29 | (34) ! [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)))
% 38.05/11.29 | (35) aNaturalNumber0(xp) = 0
% 38.05/11.29 | (36) ! [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))))
% 38.05/11.29 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0))
% 38.05/11.29 | (38) ~ (all_0_4_4 = 0)
% 38.05/11.29 | (39) sdtlseqdt0(xk, xp) = 0
% 38.05/11.29 | (40) ! [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)))))
% 38.05/11.29 | (41) ! [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)))
% 38.05/11.29 | (42) ! [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)))))
% 38.05/11.29 | (43) sdtlseqdt0(all_0_2_2, all_0_6_6) = 0
% 38.05/11.29 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0))
% 38.05/11.29 | (45) ! [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))))
% 38.05/11.30 | (46) sdtlseqdt0(xr, xk) = 0
% 38.05/11.30 | (47) ! [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))))
% 38.05/11.30 | (48) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00))))
% 38.05/11.30 | (49) ! [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)))))
% 38.05/11.30 | (50) ! [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))))
% 38.05/11.30 | (51) ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 38.05/11.30 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0))
% 38.05/11.30 | (53) ! [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)))))
% 38.05/11.30 | (54) ! [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)))
% 38.05/11.30 | (55) ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 38.05/11.30 | (56) ! [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)))
% 38.05/11.30 | (57) ~ (isPrime0(sz10) = 0)
% 38.05/11.30 | (58) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 38.05/11.30 | (59) ~ (isPrime0(sz00) = 0)
% 38.05/11.30 | (60) ! [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)))
% 38.05/11.30 | (61) ~ (sz10 = sz00)
% 38.05/11.30 | (62) ! [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)))))
% 38.05/11.30 | (63) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 38.05/11.30 | (64) ! [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)))
% 38.05/11.30 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 38.05/11.30 | (66) ! [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)))))
% 38.05/11.30 | (67) sdtlseqdt0(xn, xp) = 0
% 38.05/11.30 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 38.05/11.30 | (69) aNaturalNumber0(sz10) = 0
% 38.05/11.31 | (70) ! [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)))))
% 38.05/11.31 | (71) aNaturalNumber0(sz00) = 0
% 38.05/11.31 | (72) ~ (xk = sz10)
% 38.05/11.31 | (73) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0))
% 38.05/11.31 | (74) ! [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))))
% 38.05/11.31 | (75) ~ (all_0_2_2 = all_0_6_6)
% 38.05/11.31 | (76) ~ (xp = xn)
% 38.05/11.31 | (77) ! [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)))))
% 38.05/11.31 | (78) ~ (all_0_0_0 = 0)
% 38.05/11.31 | (79) doDivides0(xr, xn) = all_0_1_1
% 38.05/11.31 | (80) aNaturalNumber0(xn) = 0
% 38.05/11.31 | (81) ! [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)))))
% 38.05/11.31 | (82) isPrime0(xr) = 0
% 38.05/11.31 | (83) sdtpldt0(all_0_7_7, xr) = all_0_2_2
% 38.05/11.31 | (84) ! [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))))
% 38.05/11.31 | (85) ~ (xp = xm)
% 38.05/11.31 | (86) ! [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))))
% 38.05/11.31 | (87) sdtlseqdt0(xm, xp) = 0
% 38.05/11.31 | (88) doDivides0(xr, xk) = 0
% 38.05/11.31 | (89) aNaturalNumber0(xr) = 0
% 38.05/11.31 | (90) sdtlseqdt0(xp, xm) = all_0_3_3
% 38.05/11.31 | (91) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 38.05/11.31 |
% 38.05/11.31 | Instantiating formula (60) with xk, xr and discharging atoms doDivides0(xr, xk) = 0, yields:
% 38.05/11.31 | (92) xk = sz00 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xr, xk) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 38.05/11.31 |
% 38.05/11.31 | Instantiating formula (25) with all_0_0_0, xm, all_0_5_5, xr and discharging atoms doDivides0(xr, all_0_5_5) = 0, doDivides0(xr, xm) = all_0_0_0, yields:
% 38.05/11.31 | (93) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_5_5, xm) = v3 & aNaturalNumber0(all_0_5_5) = v1 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 38.05/11.31 |
% 38.05/11.31 | Instantiating formula (25) with all_0_0_0, xm, xk, xr and discharging atoms doDivides0(xr, xk) = 0, doDivides0(xr, xm) = all_0_0_0, yields:
% 38.05/11.31 | (94) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(xk, xm) = v3 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 38.05/11.31 |
% 38.05/11.31 | Instantiating formula (25) with all_0_1_1, xn, all_0_5_5, xr and discharging atoms doDivides0(xr, all_0_5_5) = 0, doDivides0(xr, xn) = all_0_1_1, yields:
% 38.05/11.31 | (95) all_0_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_5_5, xn) = v3 & aNaturalNumber0(all_0_5_5) = v1 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 38.05/11.31 |
% 38.05/11.31 | Instantiating formula (25) with all_0_1_1, xn, xk, xr and discharging atoms doDivides0(xr, xk) = 0, doDivides0(xr, xn) = all_0_1_1, yields:
% 38.05/11.31 | (96) all_0_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(xk, xn) = v3 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 38.05/11.31 |
% 38.05/11.31 | Instantiating formula (45) with all_0_6_6, all_0_2_2 and discharging atoms sdtlseqdt0(all_0_2_2, all_0_6_6) = 0, yields:
% 38.05/11.31 | (97) all_0_2_2 = all_0_6_6 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_0_6_6, all_0_2_2) = v2 & aNaturalNumber0(all_0_2_2) = v0 & aNaturalNumber0(all_0_6_6) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 38.05/11.32 |
% 38.05/11.32 | Instantiating formula (49) with all_0_6_6, all_0_2_2 and discharging atoms sdtlseqdt0(all_0_2_2, all_0_6_6) = 0, yields:
% 38.05/11.32 | (98) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_6_6 & v1 = 0 & sdtpldt0(all_0_2_2, v0) = all_0_6_6 & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_0_2_2) = v0 & aNaturalNumber0(all_0_6_6) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 38.05/11.32 |
% 38.05/11.32 | Instantiating formula (45) with xp, xk and discharging atoms sdtlseqdt0(xk, xp) = 0, yields:
% 38.05/11.32 | (99) xk = xp | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, xk) = v2 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 38.05/11.32 |
% 38.05/11.32 | Instantiating formula (4) with all_0_5_5, xr, xm, xn and discharging atoms doDivides0(xr, all_0_5_5) = 0, sdtasdt0(xn, xm) = all_0_5_5, yields:
% 38.05/11.32 | (100) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xr) = v3 & doDivides0(xr, xm) = v8 & doDivides0(xr, xn) = v7 & iLess0(v5, all_0_6_6) = 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))
% 38.05/11.32 |
% 38.05/11.32 | Instantiating formula (4) with all_0_5_5, xp, xm, xn and discharging atoms doDivides0(xp, all_0_5_5) = 0, sdtasdt0(xn, xm) = all_0_5_5, yields:
% 38.05/11.32 | (101) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, xm) = v8 & doDivides0(xp, xn) = v7 & iLess0(v5, all_0_6_6) = 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))
% 38.05/11.32 |
% 38.05/11.32 | Instantiating formula (2) with all_0_5_5, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_5_5, yields:
% 38.05/11.32 | (102) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_5_5))
% 38.05/11.32 |
% 38.05/11.32 | Instantiating formula (54) with all_0_5_5, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_5_5, yields:
% 38.05/11.32 | (103) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_5_5) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 38.05/11.32 |
% 38.05/11.32 | Instantiating formula (27) with all_0_2_2, xr, all_0_7_7 and discharging atoms sdtpldt0(all_0_7_7, xr) = all_0_2_2, yields:
% 38.05/11.32 | (104) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xr, all_0_7_7) = v2 & aNaturalNumber0(all_0_7_7) = v0 & aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_2_2))
% 38.05/11.32 |
% 38.05/11.32 | Instantiating formula (41) with all_0_2_2, xr, all_0_7_7 and discharging atoms sdtpldt0(all_0_7_7, xr) = all_0_2_2, yields:
% 38.05/11.32 | (105) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_2_2) = v2 & aNaturalNumber0(all_0_7_7) = v0 & aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 38.05/11.32 |
% 38.05/11.32 | Instantiating formula (27) with all_0_6_6, xp, all_0_7_7 and discharging atoms sdtpldt0(all_0_7_7, xp) = all_0_6_6, yields:
% 38.05/11.32 | (106) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, all_0_7_7) = v2 & aNaturalNumber0(all_0_7_7) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_6_6))
% 38.05/11.32 |
% 38.05/11.32 | Instantiating formula (41) with all_0_6_6, xp, all_0_7_7 and discharging atoms sdtpldt0(all_0_7_7, xp) = all_0_6_6, yields:
% 38.05/11.32 | (107) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_6_6) = v2 & aNaturalNumber0(all_0_7_7) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 38.05/11.32 |
% 38.05/11.32 | Instantiating formula (28) with all_0_2_2, all_0_7_7, xr, xm, xn and discharging atoms sdtpldt0(all_0_7_7, xr) = all_0_2_2, sdtpldt0(xn, xm) = all_0_7_7, yields:
% 38.05/11.32 | (108) ? [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_0_2_2))
% 38.05/11.32 |
% 38.05/11.32 | Instantiating formula (28) with all_0_6_6, all_0_7_7, xp, xm, xn and discharging atoms sdtpldt0(all_0_7_7, xp) = all_0_6_6, sdtpldt0(xn, xm) = all_0_7_7, yields:
% 38.05/11.32 | (109) ? [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_6_6))
% 38.05/11.32 |
% 38.05/11.32 | Instantiating formula (27) with all_0_7_7, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_7_7, yields:
% 38.05/11.32 | (110) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_7_7))
% 38.05/11.32 |
% 38.05/11.32 | Instantiating formula (41) with all_0_7_7, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_7_7, yields:
% 38.05/11.32 | (111) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_7_7) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 38.05/11.32 |
% 38.05/11.32 | Instantiating (111) with all_12_0_8, all_12_1_9, all_12_2_10 yields:
% 38.05/11.32 | (112) aNaturalNumber0(all_0_7_7) = all_12_0_8 & aNaturalNumber0(xm) = all_12_1_9 & aNaturalNumber0(xn) = all_12_2_10 & ( ~ (all_12_1_9 = 0) | ~ (all_12_2_10 = 0) | all_12_0_8 = 0)
% 38.05/11.32 |
% 38.05/11.32 | Applying alpha-rule on (112) yields:
% 38.05/11.32 | (113) aNaturalNumber0(all_0_7_7) = all_12_0_8
% 38.05/11.32 | (114) aNaturalNumber0(xm) = all_12_1_9
% 38.05/11.32 | (115) aNaturalNumber0(xn) = all_12_2_10
% 38.05/11.32 | (116) ~ (all_12_1_9 = 0) | ~ (all_12_2_10 = 0) | all_12_0_8 = 0
% 38.05/11.32 |
% 38.05/11.32 | Instantiating (109) with all_14_0_11, all_14_1_12, all_14_2_13, all_14_3_14, all_14_4_15 yields:
% 38.05/11.32 | (117) sdtpldt0(xm, xp) = all_14_1_12 & sdtpldt0(xn, all_14_1_12) = all_14_0_11 & aNaturalNumber0(xp) = all_14_2_13 & aNaturalNumber0(xm) = all_14_3_14 & aNaturalNumber0(xn) = all_14_4_15 & ( ~ (all_14_2_13 = 0) | ~ (all_14_3_14 = 0) | ~ (all_14_4_15 = 0) | all_14_0_11 = all_0_6_6)
% 38.05/11.32 |
% 38.05/11.32 | Applying alpha-rule on (117) yields:
% 38.05/11.32 | (118) aNaturalNumber0(xm) = all_14_3_14
% 38.05/11.32 | (119) ~ (all_14_2_13 = 0) | ~ (all_14_3_14 = 0) | ~ (all_14_4_15 = 0) | all_14_0_11 = all_0_6_6
% 38.05/11.32 | (120) aNaturalNumber0(xp) = all_14_2_13
% 38.05/11.32 | (121) sdtpldt0(xm, xp) = all_14_1_12
% 38.05/11.33 | (122) aNaturalNumber0(xn) = all_14_4_15
% 38.05/11.33 | (123) sdtpldt0(xn, all_14_1_12) = all_14_0_11
% 38.05/11.33 |
% 38.05/11.33 | Instantiating (108) with all_16_0_16, all_16_1_17, all_16_2_18, all_16_3_19, all_16_4_20 yields:
% 38.05/11.33 | (124) sdtpldt0(xm, xr) = all_16_1_17 & sdtpldt0(xn, all_16_1_17) = all_16_0_16 & aNaturalNumber0(xr) = all_16_2_18 & aNaturalNumber0(xm) = all_16_3_19 & aNaturalNumber0(xn) = all_16_4_20 & ( ~ (all_16_2_18 = 0) | ~ (all_16_3_19 = 0) | ~ (all_16_4_20 = 0) | all_16_0_16 = all_0_2_2)
% 38.05/11.33 |
% 38.05/11.33 | Applying alpha-rule on (124) yields:
% 38.05/11.33 | (125) sdtpldt0(xm, xr) = all_16_1_17
% 38.05/11.33 | (126) sdtpldt0(xn, all_16_1_17) = all_16_0_16
% 38.05/11.33 | (127) ~ (all_16_2_18 = 0) | ~ (all_16_3_19 = 0) | ~ (all_16_4_20 = 0) | all_16_0_16 = all_0_2_2
% 38.05/11.33 | (128) aNaturalNumber0(xm) = all_16_3_19
% 38.05/11.33 | (129) aNaturalNumber0(xn) = all_16_4_20
% 38.05/11.33 | (130) aNaturalNumber0(xr) = all_16_2_18
% 38.05/11.33 |
% 38.05/11.33 | Instantiating (107) with all_18_0_21, all_18_1_22, all_18_2_23 yields:
% 38.05/11.33 | (131) aNaturalNumber0(all_0_6_6) = all_18_0_21 & aNaturalNumber0(all_0_7_7) = all_18_2_23 & aNaturalNumber0(xp) = all_18_1_22 & ( ~ (all_18_1_22 = 0) | ~ (all_18_2_23 = 0) | all_18_0_21 = 0)
% 38.05/11.33 |
% 38.05/11.33 | Applying alpha-rule on (131) yields:
% 38.05/11.33 | (132) aNaturalNumber0(all_0_6_6) = all_18_0_21
% 38.05/11.33 | (133) aNaturalNumber0(all_0_7_7) = all_18_2_23
% 38.05/11.33 | (134) aNaturalNumber0(xp) = all_18_1_22
% 38.05/11.33 | (135) ~ (all_18_1_22 = 0) | ~ (all_18_2_23 = 0) | all_18_0_21 = 0
% 38.05/11.33 |
% 38.05/11.33 | Instantiating (106) with all_20_0_24, all_20_1_25, all_20_2_26 yields:
% 38.05/11.33 | (136) sdtpldt0(xp, all_0_7_7) = all_20_0_24 & aNaturalNumber0(all_0_7_7) = all_20_2_26 & aNaturalNumber0(xp) = all_20_1_25 & ( ~ (all_20_1_25 = 0) | ~ (all_20_2_26 = 0) | all_20_0_24 = all_0_6_6)
% 38.05/11.33 |
% 38.05/11.33 | Applying alpha-rule on (136) yields:
% 38.05/11.33 | (137) sdtpldt0(xp, all_0_7_7) = all_20_0_24
% 38.05/11.33 | (138) aNaturalNumber0(all_0_7_7) = all_20_2_26
% 38.05/11.33 | (139) aNaturalNumber0(xp) = all_20_1_25
% 38.05/11.33 | (140) ~ (all_20_1_25 = 0) | ~ (all_20_2_26 = 0) | all_20_0_24 = all_0_6_6
% 38.05/11.33 |
% 38.05/11.33 | Instantiating (110) with all_22_0_27, all_22_1_28, all_22_2_29 yields:
% 38.05/11.33 | (141) sdtpldt0(xm, xn) = all_22_0_27 & aNaturalNumber0(xm) = all_22_1_28 & aNaturalNumber0(xn) = all_22_2_29 & ( ~ (all_22_1_28 = 0) | ~ (all_22_2_29 = 0) | all_22_0_27 = all_0_7_7)
% 38.05/11.33 |
% 38.05/11.33 | Applying alpha-rule on (141) yields:
% 38.05/11.33 | (142) sdtpldt0(xm, xn) = all_22_0_27
% 38.05/11.33 | (143) aNaturalNumber0(xm) = all_22_1_28
% 38.05/11.33 | (144) aNaturalNumber0(xn) = all_22_2_29
% 38.05/11.33 | (145) ~ (all_22_1_28 = 0) | ~ (all_22_2_29 = 0) | all_22_0_27 = all_0_7_7
% 38.05/11.33 |
% 38.05/11.33 | Instantiating (105) with all_24_0_30, all_24_1_31, all_24_2_32 yields:
% 38.05/11.33 | (146) aNaturalNumber0(all_0_2_2) = all_24_0_30 & aNaturalNumber0(all_0_7_7) = all_24_2_32 & aNaturalNumber0(xr) = all_24_1_31 & ( ~ (all_24_1_31 = 0) | ~ (all_24_2_32 = 0) | all_24_0_30 = 0)
% 38.05/11.33 |
% 38.05/11.33 | Applying alpha-rule on (146) yields:
% 38.05/11.33 | (147) aNaturalNumber0(all_0_2_2) = all_24_0_30
% 38.05/11.33 | (148) aNaturalNumber0(all_0_7_7) = all_24_2_32
% 38.05/11.33 | (149) aNaturalNumber0(xr) = all_24_1_31
% 38.05/11.33 | (150) ~ (all_24_1_31 = 0) | ~ (all_24_2_32 = 0) | all_24_0_30 = 0
% 38.05/11.33 |
% 38.05/11.33 | Instantiating (103) with all_26_0_33, all_26_1_34, all_26_2_35 yields:
% 38.05/11.33 | (151) aNaturalNumber0(all_0_5_5) = all_26_0_33 & aNaturalNumber0(xm) = all_26_1_34 & aNaturalNumber0(xn) = all_26_2_35 & ( ~ (all_26_1_34 = 0) | ~ (all_26_2_35 = 0) | all_26_0_33 = 0)
% 38.05/11.33 |
% 38.05/11.33 | Applying alpha-rule on (151) yields:
% 38.05/11.33 | (152) aNaturalNumber0(all_0_5_5) = all_26_0_33
% 38.05/11.33 | (153) aNaturalNumber0(xm) = all_26_1_34
% 38.05/11.33 | (154) aNaturalNumber0(xn) = all_26_2_35
% 38.05/11.33 | (155) ~ (all_26_1_34 = 0) | ~ (all_26_2_35 = 0) | all_26_0_33 = 0
% 38.05/11.33 |
% 38.05/11.33 | Instantiating (101) with all_28_0_36, all_28_1_37, all_28_2_38, all_28_3_39, all_28_4_40, all_28_5_41, all_28_6_42, all_28_7_43, all_28_8_44 yields:
% 38.05/11.33 | (156) isPrime0(xp) = all_28_5_41 & doDivides0(xp, xm) = all_28_0_36 & doDivides0(xp, xn) = all_28_1_37 & iLess0(all_28_3_39, all_0_6_6) = all_28_2_38 & sdtpldt0(all_28_4_40, xp) = all_28_3_39 & sdtpldt0(xn, xm) = all_28_4_40 & aNaturalNumber0(xp) = all_28_6_42 & aNaturalNumber0(xm) = all_28_7_43 & aNaturalNumber0(xn) = all_28_8_44 & ( ~ (all_28_2_38 = 0) | ~ (all_28_5_41 = 0) | ~ (all_28_6_42 = 0) | ~ (all_28_7_43 = 0) | ~ (all_28_8_44 = 0) | all_28_0_36 = 0 | all_28_1_37 = 0)
% 38.05/11.33 |
% 38.05/11.33 | Applying alpha-rule on (156) yields:
% 38.05/11.33 | (157) ~ (all_28_2_38 = 0) | ~ (all_28_5_41 = 0) | ~ (all_28_6_42 = 0) | ~ (all_28_7_43 = 0) | ~ (all_28_8_44 = 0) | all_28_0_36 = 0 | all_28_1_37 = 0
% 38.05/11.33 | (158) aNaturalNumber0(xm) = all_28_7_43
% 38.05/11.33 | (159) aNaturalNumber0(xn) = all_28_8_44
% 38.05/11.33 | (160) sdtpldt0(xn, xm) = all_28_4_40
% 38.05/11.33 | (161) aNaturalNumber0(xp) = all_28_6_42
% 38.05/11.33 | (162) iLess0(all_28_3_39, all_0_6_6) = all_28_2_38
% 38.05/11.33 | (163) doDivides0(xp, xm) = all_28_0_36
% 38.05/11.33 | (164) doDivides0(xp, xn) = all_28_1_37
% 38.05/11.33 | (165) isPrime0(xp) = all_28_5_41
% 38.05/11.33 | (166) sdtpldt0(all_28_4_40, xp) = all_28_3_39
% 38.05/11.33 |
% 38.05/11.33 | Instantiating (100) with all_31_0_48, all_31_1_49, all_31_2_50, all_31_3_51, all_31_4_52, all_31_5_53, all_31_6_54, all_31_7_55, all_31_8_56 yields:
% 38.05/11.33 | (167) isPrime0(xr) = all_31_5_53 & doDivides0(xr, xm) = all_31_0_48 & doDivides0(xr, xn) = all_31_1_49 & iLess0(all_31_3_51, all_0_6_6) = all_31_2_50 & sdtpldt0(all_31_4_52, xr) = all_31_3_51 & sdtpldt0(xn, xm) = all_31_4_52 & aNaturalNumber0(xr) = all_31_6_54 & aNaturalNumber0(xm) = all_31_7_55 & aNaturalNumber0(xn) = all_31_8_56 & ( ~ (all_31_2_50 = 0) | ~ (all_31_5_53 = 0) | ~ (all_31_6_54 = 0) | ~ (all_31_7_55 = 0) | ~ (all_31_8_56 = 0) | all_31_0_48 = 0 | all_31_1_49 = 0)
% 38.05/11.33 |
% 38.05/11.33 | Applying alpha-rule on (167) yields:
% 38.05/11.33 | (168) ~ (all_31_2_50 = 0) | ~ (all_31_5_53 = 0) | ~ (all_31_6_54 = 0) | ~ (all_31_7_55 = 0) | ~ (all_31_8_56 = 0) | all_31_0_48 = 0 | all_31_1_49 = 0
% 38.05/11.33 | (169) isPrime0(xr) = all_31_5_53
% 38.05/11.34 | (170) aNaturalNumber0(xr) = all_31_6_54
% 38.05/11.34 | (171) aNaturalNumber0(xm) = all_31_7_55
% 38.05/11.34 | (172) sdtpldt0(xn, xm) = all_31_4_52
% 38.05/11.34 | (173) sdtpldt0(all_31_4_52, xr) = all_31_3_51
% 38.05/11.34 | (174) doDivides0(xr, xn) = all_31_1_49
% 38.05/11.34 | (175) doDivides0(xr, xm) = all_31_0_48
% 38.05/11.34 | (176) aNaturalNumber0(xn) = all_31_8_56
% 38.05/11.34 | (177) iLess0(all_31_3_51, all_0_6_6) = all_31_2_50
% 38.05/11.34 |
% 38.05/11.34 | Instantiating (102) with all_34_0_60, all_34_1_61, all_34_2_62 yields:
% 38.05/11.34 | (178) sdtasdt0(xm, xn) = all_34_0_60 & aNaturalNumber0(xm) = all_34_1_61 & aNaturalNumber0(xn) = all_34_2_62 & ( ~ (all_34_1_61 = 0) | ~ (all_34_2_62 = 0) | all_34_0_60 = all_0_5_5)
% 38.05/11.34 |
% 38.05/11.34 | Applying alpha-rule on (178) yields:
% 38.05/11.34 | (179) sdtasdt0(xm, xn) = all_34_0_60
% 38.05/11.34 | (180) aNaturalNumber0(xm) = all_34_1_61
% 38.05/11.34 | (181) aNaturalNumber0(xn) = all_34_2_62
% 38.05/11.34 | (182) ~ (all_34_1_61 = 0) | ~ (all_34_2_62 = 0) | all_34_0_60 = all_0_5_5
% 38.05/11.34 |
% 38.05/11.34 | Instantiating (104) with all_36_0_63, all_36_1_64, all_36_2_65 yields:
% 38.05/11.34 | (183) sdtpldt0(xr, all_0_7_7) = all_36_0_63 & aNaturalNumber0(all_0_7_7) = all_36_2_65 & aNaturalNumber0(xr) = all_36_1_64 & ( ~ (all_36_1_64 = 0) | ~ (all_36_2_65 = 0) | all_36_0_63 = all_0_2_2)
% 38.05/11.34 |
% 38.05/11.34 | Applying alpha-rule on (183) yields:
% 38.05/11.34 | (184) sdtpldt0(xr, all_0_7_7) = all_36_0_63
% 38.05/11.34 | (185) aNaturalNumber0(all_0_7_7) = all_36_2_65
% 38.05/11.34 | (186) aNaturalNumber0(xr) = all_36_1_64
% 38.05/11.34 | (187) ~ (all_36_1_64 = 0) | ~ (all_36_2_65 = 0) | all_36_0_63 = all_0_2_2
% 38.05/11.34 |
% 38.05/11.34 | Instantiating (98) with all_42_0_78, all_42_1_79, all_42_2_80 yields:
% 38.05/11.34 | (188) (all_42_0_78 = all_0_6_6 & all_42_1_79 = 0 & sdtpldt0(all_0_2_2, all_42_2_80) = all_0_6_6 & aNaturalNumber0(all_42_2_80) = 0) | (aNaturalNumber0(all_0_2_2) = all_42_2_80 & aNaturalNumber0(all_0_6_6) = all_42_1_79 & ( ~ (all_42_1_79 = 0) | ~ (all_42_2_80 = 0)))
% 38.05/11.34 |
% 38.05/11.34 +-Applying beta-rule and splitting (99), into two cases.
% 38.05/11.34 |-Branch one:
% 38.05/11.34 | (189) xk = xp
% 38.05/11.34 |
% 38.05/11.34 | Equations (189) can reduce 26 to:
% 38.05/11.34 | (190) $false
% 38.05/11.34 |
% 38.05/11.34 |-The branch is then unsatisfiable
% 38.05/11.34 |-Branch two:
% 38.05/11.34 | (26) ~ (xk = xp)
% 38.05/11.34 | (192) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, xk) = v2 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 38.05/11.34 |
% 38.05/11.34 | Instantiating (192) with all_48_0_84, all_48_1_85, all_48_2_86 yields:
% 38.05/11.34 | (193) sdtlseqdt0(xp, xk) = all_48_0_84 & aNaturalNumber0(xk) = all_48_2_86 & aNaturalNumber0(xp) = all_48_1_85 & ( ~ (all_48_0_84 = 0) | ~ (all_48_1_85 = 0) | ~ (all_48_2_86 = 0))
% 38.05/11.34 |
% 38.05/11.34 | Applying alpha-rule on (193) yields:
% 38.05/11.34 | (194) sdtlseqdt0(xp, xk) = all_48_0_84
% 38.05/11.34 | (195) aNaturalNumber0(xk) = all_48_2_86
% 38.05/11.34 | (196) aNaturalNumber0(xp) = all_48_1_85
% 38.05/11.34 | (197) ~ (all_48_0_84 = 0) | ~ (all_48_1_85 = 0) | ~ (all_48_2_86 = 0)
% 38.05/11.34 |
% 38.05/11.34 +-Applying beta-rule and splitting (94), into two cases.
% 38.05/11.34 |-Branch one:
% 38.05/11.34 | (198) all_0_0_0 = 0
% 38.05/11.34 |
% 38.05/11.34 | Equations (198) can reduce 78 to:
% 38.05/11.34 | (190) $false
% 38.05/11.34 |
% 38.05/11.34 |-The branch is then unsatisfiable
% 38.05/11.34 |-Branch two:
% 38.05/11.34 | (78) ~ (all_0_0_0 = 0)
% 38.05/11.34 | (201) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(xk, xm) = v3 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 38.05/11.34 |
% 38.05/11.34 | Instantiating (201) with all_53_0_87, all_53_1_88, all_53_2_89, all_53_3_90 yields:
% 38.05/11.34 | (202) doDivides0(xk, xm) = all_53_0_87 & aNaturalNumber0(xr) = all_53_3_90 & aNaturalNumber0(xk) = all_53_2_89 & aNaturalNumber0(xm) = all_53_1_88 & ( ~ (all_53_0_87 = 0) | ~ (all_53_1_88 = 0) | ~ (all_53_2_89 = 0) | ~ (all_53_3_90 = 0))
% 38.05/11.34 |
% 38.05/11.34 | Applying alpha-rule on (202) yields:
% 38.05/11.34 | (203) aNaturalNumber0(xm) = all_53_1_88
% 38.05/11.34 | (204) doDivides0(xk, xm) = all_53_0_87
% 38.05/11.34 | (205) ~ (all_53_0_87 = 0) | ~ (all_53_1_88 = 0) | ~ (all_53_2_89 = 0) | ~ (all_53_3_90 = 0)
% 38.05/11.34 | (206) aNaturalNumber0(xk) = all_53_2_89
% 38.05/11.34 | (207) aNaturalNumber0(xr) = all_53_3_90
% 38.05/11.34 |
% 38.05/11.34 +-Applying beta-rule and splitting (95), into two cases.
% 38.05/11.34 |-Branch one:
% 38.05/11.34 | (208) all_0_1_1 = 0
% 38.05/11.34 |
% 38.05/11.34 | Equations (208) can reduce 19 to:
% 38.05/11.34 | (190) $false
% 38.05/11.34 |
% 38.05/11.34 |-The branch is then unsatisfiable
% 38.05/11.34 |-Branch two:
% 38.05/11.34 | (19) ~ (all_0_1_1 = 0)
% 38.05/11.34 | (211) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_5_5, xn) = v3 & aNaturalNumber0(all_0_5_5) = v1 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 38.05/11.34 |
% 38.05/11.34 | Instantiating (211) with all_58_0_91, all_58_1_92, all_58_2_93, all_58_3_94 yields:
% 38.05/11.34 | (212) doDivides0(all_0_5_5, xn) = all_58_0_91 & aNaturalNumber0(all_0_5_5) = all_58_2_93 & aNaturalNumber0(xr) = all_58_3_94 & aNaturalNumber0(xn) = all_58_1_92 & ( ~ (all_58_0_91 = 0) | ~ (all_58_1_92 = 0) | ~ (all_58_2_93 = 0) | ~ (all_58_3_94 = 0))
% 38.05/11.34 |
% 38.05/11.34 | Applying alpha-rule on (212) yields:
% 38.05/11.34 | (213) aNaturalNumber0(xn) = all_58_1_92
% 38.05/11.34 | (214) ~ (all_58_0_91 = 0) | ~ (all_58_1_92 = 0) | ~ (all_58_2_93 = 0) | ~ (all_58_3_94 = 0)
% 38.05/11.35 | (215) doDivides0(all_0_5_5, xn) = all_58_0_91
% 38.05/11.35 | (216) aNaturalNumber0(xr) = all_58_3_94
% 38.05/11.35 | (217) aNaturalNumber0(all_0_5_5) = all_58_2_93
% 38.05/11.35 |
% 38.05/11.35 +-Applying beta-rule and splitting (96), into two cases.
% 38.05/11.35 |-Branch one:
% 38.05/11.35 | (208) all_0_1_1 = 0
% 38.05/11.35 |
% 38.05/11.35 | Equations (208) can reduce 19 to:
% 38.05/11.35 | (190) $false
% 38.05/11.35 |
% 38.05/11.35 |-The branch is then unsatisfiable
% 38.05/11.35 |-Branch two:
% 38.05/11.35 | (19) ~ (all_0_1_1 = 0)
% 38.05/11.35 | (221) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(xk, xn) = v3 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 38.05/11.35 |
% 38.05/11.35 | Instantiating (221) with all_63_0_95, all_63_1_96, all_63_2_97, all_63_3_98 yields:
% 38.05/11.35 | (222) doDivides0(xk, xn) = all_63_0_95 & aNaturalNumber0(xr) = all_63_3_98 & aNaturalNumber0(xk) = all_63_2_97 & aNaturalNumber0(xn) = all_63_1_96 & ( ~ (all_63_0_95 = 0) | ~ (all_63_1_96 = 0) | ~ (all_63_2_97 = 0) | ~ (all_63_3_98 = 0))
% 38.05/11.35 |
% 38.05/11.35 | Applying alpha-rule on (222) yields:
% 38.05/11.35 | (223) aNaturalNumber0(xk) = all_63_2_97
% 38.05/11.35 | (224) aNaturalNumber0(xn) = all_63_1_96
% 38.05/11.35 | (225) ~ (all_63_0_95 = 0) | ~ (all_63_1_96 = 0) | ~ (all_63_2_97 = 0) | ~ (all_63_3_98 = 0)
% 38.05/11.35 | (226) aNaturalNumber0(xr) = all_63_3_98
% 38.05/11.35 | (227) doDivides0(xk, xn) = all_63_0_95
% 38.05/11.35 |
% 38.05/11.35 +-Applying beta-rule and splitting (97), into two cases.
% 38.05/11.35 |-Branch one:
% 38.05/11.35 | (228) all_0_2_2 = all_0_6_6
% 38.05/11.35 |
% 38.05/11.35 | Equations (228) can reduce 75 to:
% 38.05/11.35 | (190) $false
% 38.05/11.35 |
% 38.05/11.35 |-The branch is then unsatisfiable
% 38.05/11.35 |-Branch two:
% 38.05/11.35 | (75) ~ (all_0_2_2 = all_0_6_6)
% 38.05/11.35 | (231) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_0_6_6, all_0_2_2) = v2 & aNaturalNumber0(all_0_2_2) = v0 & aNaturalNumber0(all_0_6_6) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 38.05/11.35 |
% 38.05/11.35 | Instantiating (231) with all_68_0_99, all_68_1_100, all_68_2_101 yields:
% 38.05/11.35 | (232) sdtlseqdt0(all_0_6_6, all_0_2_2) = all_68_0_99 & aNaturalNumber0(all_0_2_2) = all_68_2_101 & aNaturalNumber0(all_0_6_6) = all_68_1_100 & ( ~ (all_68_0_99 = 0) | ~ (all_68_1_100 = 0) | ~ (all_68_2_101 = 0))
% 38.05/11.35 |
% 38.05/11.35 | Applying alpha-rule on (232) yields:
% 38.05/11.35 | (233) sdtlseqdt0(all_0_6_6, all_0_2_2) = all_68_0_99
% 38.05/11.35 | (234) aNaturalNumber0(all_0_2_2) = all_68_2_101
% 38.05/11.35 | (235) aNaturalNumber0(all_0_6_6) = all_68_1_100
% 38.05/11.35 | (236) ~ (all_68_0_99 = 0) | ~ (all_68_1_100 = 0) | ~ (all_68_2_101 = 0)
% 38.05/11.35 |
% 38.05/11.35 +-Applying beta-rule and splitting (92), into two cases.
% 38.05/11.35 |-Branch one:
% 38.05/11.35 | (237) xk = sz00
% 38.05/11.35 |
% 38.05/11.35 | Equations (237) can reduce 15 to:
% 38.05/11.35 | (190) $false
% 38.05/11.35 |
% 38.05/11.35 |-The branch is then unsatisfiable
% 38.05/11.35 |-Branch two:
% 38.05/11.35 | (15) ~ (xk = sz00)
% 38.05/11.35 | (240) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xr, xk) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 38.05/11.35 |
% 38.05/11.35 | Instantiating (240) with all_73_0_102, all_73_1_103, all_73_2_104 yields:
% 38.05/11.35 | (241) sdtlseqdt0(xr, xk) = all_73_0_102 & aNaturalNumber0(xr) = all_73_2_104 & aNaturalNumber0(xk) = all_73_1_103 & ( ~ (all_73_1_103 = 0) | ~ (all_73_2_104 = 0) | all_73_0_102 = 0)
% 38.05/11.35 |
% 38.05/11.35 | Applying alpha-rule on (241) yields:
% 38.05/11.35 | (242) sdtlseqdt0(xr, xk) = all_73_0_102
% 38.05/11.35 | (243) aNaturalNumber0(xr) = all_73_2_104
% 38.05/11.35 | (244) aNaturalNumber0(xk) = all_73_1_103
% 38.05/11.35 | (245) ~ (all_73_1_103 = 0) | ~ (all_73_2_104 = 0) | all_73_0_102 = 0
% 38.05/11.35 |
% 38.05/11.35 +-Applying beta-rule and splitting (93), into two cases.
% 38.05/11.35 |-Branch one:
% 38.05/11.35 | (198) all_0_0_0 = 0
% 38.05/11.35 |
% 38.05/11.35 | Equations (198) can reduce 78 to:
% 38.05/11.35 | (190) $false
% 38.05/11.35 |
% 38.05/11.35 |-The branch is then unsatisfiable
% 38.05/11.35 |-Branch two:
% 38.05/11.35 | (78) ~ (all_0_0_0 = 0)
% 38.05/11.35 | (249) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_5_5, xm) = v3 & aNaturalNumber0(all_0_5_5) = v1 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 38.44/11.35 |
% 38.44/11.35 | Instantiating (249) with all_78_0_105, all_78_1_106, all_78_2_107, all_78_3_108 yields:
% 38.44/11.35 | (250) doDivides0(all_0_5_5, xm) = all_78_0_105 & aNaturalNumber0(all_0_5_5) = all_78_2_107 & aNaturalNumber0(xr) = all_78_3_108 & aNaturalNumber0(xm) = all_78_1_106 & ( ~ (all_78_0_105 = 0) | ~ (all_78_1_106 = 0) | ~ (all_78_2_107 = 0) | ~ (all_78_3_108 = 0))
% 38.44/11.35 |
% 38.44/11.35 | Applying alpha-rule on (250) yields:
% 38.44/11.35 | (251) aNaturalNumber0(all_0_5_5) = all_78_2_107
% 38.44/11.35 | (252) aNaturalNumber0(xr) = all_78_3_108
% 38.44/11.35 | (253) doDivides0(all_0_5_5, xm) = all_78_0_105
% 38.44/11.35 | (254) ~ (all_78_0_105 = 0) | ~ (all_78_1_106 = 0) | ~ (all_78_2_107 = 0) | ~ (all_78_3_108 = 0)
% 38.44/11.35 | (255) aNaturalNumber0(xm) = all_78_1_106
% 38.44/11.35 |
% 38.44/11.35 | Instantiating formula (52) with xr, all_31_5_53, 0 and discharging atoms isPrime0(xr) = all_31_5_53, isPrime0(xr) = 0, yields:
% 38.44/11.35 | (256) all_31_5_53 = 0
% 38.44/11.35 |
% 38.44/11.35 | Instantiating formula (37) with xr, xm, all_31_0_48, all_0_0_0 and discharging atoms doDivides0(xr, xm) = all_31_0_48, doDivides0(xr, xm) = all_0_0_0, yields:
% 38.44/11.35 | (257) all_31_0_48 = all_0_0_0
% 38.44/11.35 |
% 38.44/11.35 | Instantiating formula (37) with xr, xn, all_31_1_49, all_0_1_1 and discharging atoms doDivides0(xr, xn) = all_31_1_49, doDivides0(xr, xn) = all_0_1_1, yields:
% 38.44/11.35 | (258) all_31_1_49 = all_0_1_1
% 38.44/11.35 |
% 38.44/11.35 | Instantiating formula (68) with all_0_7_7, xr, all_31_3_51, all_0_2_2 and discharging atoms sdtpldt0(all_0_7_7, xr) = all_0_2_2, yields:
% 38.44/11.35 | (259) all_31_3_51 = all_0_2_2 | ~ (sdtpldt0(all_0_7_7, xr) = all_31_3_51)
% 38.44/11.35 |
% 38.44/11.35 | Instantiating formula (68) with xn, xm, all_31_4_52, all_0_7_7 and discharging atoms sdtpldt0(xn, xm) = all_31_4_52, sdtpldt0(xn, xm) = all_0_7_7, yields:
% 38.44/11.35 | (260) all_31_4_52 = all_0_7_7
% 38.44/11.35 |
% 38.44/11.35 | Instantiating formula (68) with xn, xm, all_28_4_40, all_31_4_52 and discharging atoms sdtpldt0(xn, xm) = all_31_4_52, sdtpldt0(xn, xm) = all_28_4_40, yields:
% 38.44/11.35 | (261) all_31_4_52 = all_28_4_40
% 38.44/11.35 |
% 38.44/11.35 | Instantiating formula (24) with all_0_2_2, all_24_0_30, all_68_2_101 and discharging atoms aNaturalNumber0(all_0_2_2) = all_68_2_101, aNaturalNumber0(all_0_2_2) = all_24_0_30, yields:
% 38.44/11.35 | (262) all_68_2_101 = all_24_0_30
% 38.44/11.35 |
% 38.44/11.35 | Instantiating formula (24) with all_0_6_6, all_18_0_21, all_68_1_100 and discharging atoms aNaturalNumber0(all_0_6_6) = all_68_1_100, aNaturalNumber0(all_0_6_6) = all_18_0_21, yields:
% 38.44/11.35 | (263) all_68_1_100 = all_18_0_21
% 38.44/11.35 |
% 38.44/11.35 | Instantiating formula (24) with all_0_7_7, all_24_2_32, all_36_2_65 and discharging atoms aNaturalNumber0(all_0_7_7) = all_36_2_65, aNaturalNumber0(all_0_7_7) = all_24_2_32, yields:
% 38.44/11.35 | (264) all_36_2_65 = all_24_2_32
% 38.44/11.35 |
% 38.44/11.35 | Instantiating formula (24) with all_0_7_7, all_20_2_26, all_36_2_65 and discharging atoms aNaturalNumber0(all_0_7_7) = all_36_2_65, aNaturalNumber0(all_0_7_7) = all_20_2_26, yields:
% 38.44/11.35 | (265) all_36_2_65 = all_20_2_26
% 38.44/11.35 |
% 38.44/11.35 | Instantiating formula (24) with all_0_7_7, all_18_2_23, all_36_2_65 and discharging atoms aNaturalNumber0(all_0_7_7) = all_36_2_65, aNaturalNumber0(all_0_7_7) = all_18_2_23, yields:
% 38.44/11.35 | (266) all_36_2_65 = all_18_2_23
% 38.44/11.35 |
% 38.44/11.35 | Instantiating formula (24) with all_0_7_7, all_12_0_8, all_24_2_32 and discharging atoms aNaturalNumber0(all_0_7_7) = all_24_2_32, aNaturalNumber0(all_0_7_7) = all_12_0_8, yields:
% 38.44/11.35 | (267) all_24_2_32 = all_12_0_8
% 38.44/11.35 |
% 38.44/11.35 | Instantiating formula (24) with xr, all_73_2_104, 0 and discharging atoms aNaturalNumber0(xr) = all_73_2_104, aNaturalNumber0(xr) = 0, yields:
% 38.44/11.35 | (268) all_73_2_104 = 0
% 38.44/11.35 |
% 38.44/11.35 | Instantiating formula (24) with xr, all_63_3_98, all_78_3_108 and discharging atoms aNaturalNumber0(xr) = all_78_3_108, aNaturalNumber0(xr) = all_63_3_98, yields:
% 38.44/11.35 | (269) all_78_3_108 = all_63_3_98
% 38.44/11.35 |
% 38.44/11.35 | Instantiating formula (24) with xr, all_58_3_94, all_63_3_98 and discharging atoms aNaturalNumber0(xr) = all_63_3_98, aNaturalNumber0(xr) = all_58_3_94, yields:
% 38.44/11.35 | (270) all_63_3_98 = all_58_3_94
% 38.44/11.35 |
% 38.44/11.35 | Instantiating formula (24) with xr, all_53_3_90, all_73_2_104 and discharging atoms aNaturalNumber0(xr) = all_73_2_104, aNaturalNumber0(xr) = all_53_3_90, yields:
% 38.44/11.35 | (271) all_73_2_104 = all_53_3_90
% 38.44/11.35 |
% 38.44/11.35 | Instantiating formula (24) with xr, all_36_1_64, all_58_3_94 and discharging atoms aNaturalNumber0(xr) = all_58_3_94, aNaturalNumber0(xr) = all_36_1_64, yields:
% 38.44/11.35 | (272) all_58_3_94 = all_36_1_64
% 38.44/11.35 |
% 38.44/11.35 | Instantiating formula (24) with xr, all_31_6_54, all_53_3_90 and discharging atoms aNaturalNumber0(xr) = all_53_3_90, aNaturalNumber0(xr) = all_31_6_54, yields:
% 38.44/11.35 | (273) all_53_3_90 = all_31_6_54
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xr, all_24_1_31, all_53_3_90 and discharging atoms aNaturalNumber0(xr) = all_53_3_90, aNaturalNumber0(xr) = all_24_1_31, yields:
% 38.44/11.36 | (274) all_53_3_90 = all_24_1_31
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xr, all_24_1_31, all_36_1_64 and discharging atoms aNaturalNumber0(xr) = all_36_1_64, aNaturalNumber0(xr) = all_24_1_31, yields:
% 38.44/11.36 | (275) all_36_1_64 = all_24_1_31
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xr, all_16_2_18, all_78_3_108 and discharging atoms aNaturalNumber0(xr) = all_78_3_108, aNaturalNumber0(xr) = all_16_2_18, yields:
% 38.44/11.36 | (276) all_78_3_108 = all_16_2_18
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xp, all_28_6_42, all_48_1_85 and discharging atoms aNaturalNumber0(xp) = all_48_1_85, aNaturalNumber0(xp) = all_28_6_42, yields:
% 38.44/11.36 | (277) all_48_1_85 = all_28_6_42
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xp, all_20_1_25, all_28_6_42 and discharging atoms aNaturalNumber0(xp) = all_28_6_42, aNaturalNumber0(xp) = all_20_1_25, yields:
% 38.44/11.36 | (278) all_28_6_42 = all_20_1_25
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xp, all_18_1_22, 0 and discharging atoms aNaturalNumber0(xp) = all_18_1_22, aNaturalNumber0(xp) = 0, yields:
% 38.44/11.36 | (279) all_18_1_22 = 0
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xp, all_18_1_22, all_20_1_25 and discharging atoms aNaturalNumber0(xp) = all_20_1_25, aNaturalNumber0(xp) = all_18_1_22, yields:
% 38.44/11.36 | (280) all_20_1_25 = all_18_1_22
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xp, all_14_2_13, all_48_1_85 and discharging atoms aNaturalNumber0(xp) = all_48_1_85, aNaturalNumber0(xp) = all_14_2_13, yields:
% 38.44/11.36 | (281) all_48_1_85 = all_14_2_13
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xm, all_34_1_61, all_53_1_88 and discharging atoms aNaturalNumber0(xm) = all_53_1_88, aNaturalNumber0(xm) = all_34_1_61, yields:
% 38.44/11.36 | (282) all_53_1_88 = all_34_1_61
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xm, all_31_7_55, all_78_1_106 and discharging atoms aNaturalNumber0(xm) = all_78_1_106, aNaturalNumber0(xm) = all_31_7_55, yields:
% 38.44/11.36 | (283) all_78_1_106 = all_31_7_55
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xm, all_28_7_43, all_78_1_106 and discharging atoms aNaturalNumber0(xm) = all_78_1_106, aNaturalNumber0(xm) = all_28_7_43, yields:
% 38.44/11.36 | (284) all_78_1_106 = all_28_7_43
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xm, all_28_7_43, all_53_1_88 and discharging atoms aNaturalNumber0(xm) = all_53_1_88, aNaturalNumber0(xm) = all_28_7_43, yields:
% 38.44/11.36 | (285) all_53_1_88 = all_28_7_43
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xm, all_26_1_34, all_53_1_88 and discharging atoms aNaturalNumber0(xm) = all_53_1_88, aNaturalNumber0(xm) = all_26_1_34, yields:
% 38.44/11.36 | (286) all_53_1_88 = all_26_1_34
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xm, all_22_1_28, all_78_1_106 and discharging atoms aNaturalNumber0(xm) = all_78_1_106, aNaturalNumber0(xm) = all_22_1_28, yields:
% 38.44/11.36 | (287) all_78_1_106 = all_22_1_28
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xm, all_16_3_19, 0 and discharging atoms aNaturalNumber0(xm) = all_16_3_19, aNaturalNumber0(xm) = 0, yields:
% 38.44/11.36 | (288) all_16_3_19 = 0
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xm, all_16_3_19, all_53_1_88 and discharging atoms aNaturalNumber0(xm) = all_53_1_88, aNaturalNumber0(xm) = all_16_3_19, yields:
% 38.44/11.36 | (289) all_53_1_88 = all_16_3_19
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xm, all_14_3_14, all_34_1_61 and discharging atoms aNaturalNumber0(xm) = all_34_1_61, aNaturalNumber0(xm) = all_14_3_14, yields:
% 38.44/11.36 | (290) all_34_1_61 = all_14_3_14
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xm, all_12_1_9, all_53_1_88 and discharging atoms aNaturalNumber0(xm) = all_53_1_88, aNaturalNumber0(xm) = all_12_1_9, yields:
% 38.44/11.36 | (291) all_53_1_88 = all_12_1_9
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xn, all_58_1_92, all_63_1_96 and discharging atoms aNaturalNumber0(xn) = all_63_1_96, aNaturalNumber0(xn) = all_58_1_92, yields:
% 38.44/11.36 | (292) all_63_1_96 = all_58_1_92
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xn, all_31_8_56, all_34_2_62 and discharging atoms aNaturalNumber0(xn) = all_34_2_62, aNaturalNumber0(xn) = all_31_8_56, yields:
% 38.44/11.36 | (293) all_34_2_62 = all_31_8_56
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xn, all_28_8_44, all_58_1_92 and discharging atoms aNaturalNumber0(xn) = all_58_1_92, aNaturalNumber0(xn) = all_28_8_44, yields:
% 38.44/11.36 | (294) all_58_1_92 = all_28_8_44
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xn, all_28_8_44, all_31_8_56 and discharging atoms aNaturalNumber0(xn) = all_31_8_56, aNaturalNumber0(xn) = all_28_8_44, yields:
% 38.44/11.36 | (295) all_31_8_56 = all_28_8_44
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xn, all_26_2_35, all_34_2_62 and discharging atoms aNaturalNumber0(xn) = all_34_2_62, aNaturalNumber0(xn) = all_26_2_35, yields:
% 38.44/11.36 | (296) all_34_2_62 = all_26_2_35
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xn, all_22_2_29, all_31_8_56 and discharging atoms aNaturalNumber0(xn) = all_31_8_56, aNaturalNumber0(xn) = all_22_2_29, yields:
% 38.44/11.36 | (297) all_31_8_56 = all_22_2_29
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xn, all_16_4_20, 0 and discharging atoms aNaturalNumber0(xn) = all_16_4_20, aNaturalNumber0(xn) = 0, yields:
% 38.44/11.36 | (298) all_16_4_20 = 0
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xn, all_16_4_20, all_22_2_29 and discharging atoms aNaturalNumber0(xn) = all_22_2_29, aNaturalNumber0(xn) = all_16_4_20, yields:
% 38.44/11.36 | (299) all_22_2_29 = all_16_4_20
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xn, all_14_4_15, all_63_1_96 and discharging atoms aNaturalNumber0(xn) = all_63_1_96, aNaturalNumber0(xn) = all_14_4_15, yields:
% 38.44/11.36 | (300) all_63_1_96 = all_14_4_15
% 38.44/11.36 |
% 38.44/11.36 | Instantiating formula (24) with xn, all_12_2_10, all_16_4_20 and discharging atoms aNaturalNumber0(xn) = all_16_4_20, aNaturalNumber0(xn) = all_12_2_10, yields:
% 38.44/11.36 | (301) all_16_4_20 = all_12_2_10
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (284,283) yields a new equation:
% 38.44/11.36 | (302) all_31_7_55 = all_28_7_43
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (287,283) yields a new equation:
% 38.44/11.36 | (303) all_31_7_55 = all_22_1_28
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (269,276) yields a new equation:
% 38.44/11.36 | (304) all_63_3_98 = all_16_2_18
% 38.44/11.36 |
% 38.44/11.36 | Simplifying 304 yields:
% 38.44/11.36 | (305) all_63_3_98 = all_16_2_18
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (271,268) yields a new equation:
% 38.44/11.36 | (306) all_53_3_90 = 0
% 38.44/11.36 |
% 38.44/11.36 | Simplifying 306 yields:
% 38.44/11.36 | (307) all_53_3_90 = 0
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (292,300) yields a new equation:
% 38.44/11.36 | (308) all_58_1_92 = all_14_4_15
% 38.44/11.36 |
% 38.44/11.36 | Simplifying 308 yields:
% 38.44/11.36 | (309) all_58_1_92 = all_14_4_15
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (270,305) yields a new equation:
% 38.44/11.36 | (310) all_58_3_94 = all_16_2_18
% 38.44/11.36 |
% 38.44/11.36 | Simplifying 310 yields:
% 38.44/11.36 | (311) all_58_3_94 = all_16_2_18
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (294,309) yields a new equation:
% 38.44/11.36 | (312) all_28_8_44 = all_14_4_15
% 38.44/11.36 |
% 38.44/11.36 | Simplifying 312 yields:
% 38.44/11.36 | (313) all_28_8_44 = all_14_4_15
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (272,311) yields a new equation:
% 38.44/11.36 | (314) all_36_1_64 = all_16_2_18
% 38.44/11.36 |
% 38.44/11.36 | Simplifying 314 yields:
% 38.44/11.36 | (315) all_36_1_64 = all_16_2_18
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (285,286) yields a new equation:
% 38.44/11.36 | (316) all_28_7_43 = all_26_1_34
% 38.44/11.36 |
% 38.44/11.36 | Simplifying 316 yields:
% 38.44/11.36 | (317) all_28_7_43 = all_26_1_34
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (291,286) yields a new equation:
% 38.44/11.36 | (318) all_26_1_34 = all_12_1_9
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (289,286) yields a new equation:
% 38.44/11.36 | (319) all_26_1_34 = all_16_3_19
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (282,286) yields a new equation:
% 38.44/11.36 | (320) all_34_1_61 = all_26_1_34
% 38.44/11.36 |
% 38.44/11.36 | Simplifying 320 yields:
% 38.44/11.36 | (321) all_34_1_61 = all_26_1_34
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (274,273) yields a new equation:
% 38.44/11.36 | (322) all_31_6_54 = all_24_1_31
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (307,273) yields a new equation:
% 38.44/11.36 | (323) all_31_6_54 = 0
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (277,281) yields a new equation:
% 38.44/11.36 | (324) all_28_6_42 = all_14_2_13
% 38.44/11.36 |
% 38.44/11.36 | Simplifying 324 yields:
% 38.44/11.36 | (325) all_28_6_42 = all_14_2_13
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (275,315) yields a new equation:
% 38.44/11.36 | (326) all_24_1_31 = all_16_2_18
% 38.44/11.36 |
% 38.44/11.36 | Simplifying 326 yields:
% 38.44/11.36 | (327) all_24_1_31 = all_16_2_18
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (264,265) yields a new equation:
% 38.44/11.36 | (328) all_24_2_32 = all_20_2_26
% 38.44/11.36 |
% 38.44/11.36 | Simplifying 328 yields:
% 38.44/11.36 | (329) all_24_2_32 = all_20_2_26
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (266,265) yields a new equation:
% 38.44/11.36 | (330) all_20_2_26 = all_18_2_23
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (321,290) yields a new equation:
% 38.44/11.36 | (331) all_26_1_34 = all_14_3_14
% 38.44/11.36 |
% 38.44/11.36 | Simplifying 331 yields:
% 38.44/11.36 | (332) all_26_1_34 = all_14_3_14
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (293,296) yields a new equation:
% 38.44/11.36 | (333) all_31_8_56 = all_26_2_35
% 38.44/11.36 |
% 38.44/11.36 | Simplifying 333 yields:
% 38.44/11.36 | (334) all_31_8_56 = all_26_2_35
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (260,261) yields a new equation:
% 38.44/11.36 | (335) all_28_4_40 = all_0_7_7
% 38.44/11.36 |
% 38.44/11.36 | Combining equations (322,323) yields a new equation:
% 38.44/11.36 | (336) all_24_1_31 = 0
% 38.44/11.36 |
% 38.44/11.36 | Simplifying 336 yields:
% 38.44/11.36 | (337) all_24_1_31 = 0
% 38.44/11.36 |
% 38.44/11.37 | Combining equations (302,303) yields a new equation:
% 38.44/11.37 | (338) all_28_7_43 = all_22_1_28
% 38.44/11.37 |
% 38.44/11.37 | Simplifying 338 yields:
% 38.44/11.37 | (339) all_28_7_43 = all_22_1_28
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (295,334) yields a new equation:
% 38.44/11.37 | (340) all_28_8_44 = all_26_2_35
% 38.44/11.37 |
% 38.44/11.37 | Simplifying 340 yields:
% 38.44/11.37 | (341) all_28_8_44 = all_26_2_35
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (297,334) yields a new equation:
% 38.44/11.37 | (342) all_26_2_35 = all_22_2_29
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (278,325) yields a new equation:
% 38.44/11.37 | (343) all_20_1_25 = all_14_2_13
% 38.44/11.37 |
% 38.44/11.37 | Simplifying 343 yields:
% 38.44/11.37 | (344) all_20_1_25 = all_14_2_13
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (317,339) yields a new equation:
% 38.44/11.37 | (345) all_26_1_34 = all_22_1_28
% 38.44/11.37 |
% 38.44/11.37 | Simplifying 345 yields:
% 38.44/11.37 | (346) all_26_1_34 = all_22_1_28
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (341,313) yields a new equation:
% 38.44/11.37 | (347) all_26_2_35 = all_14_4_15
% 38.44/11.37 |
% 38.44/11.37 | Simplifying 347 yields:
% 38.44/11.37 | (348) all_26_2_35 = all_14_4_15
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (319,346) yields a new equation:
% 38.44/11.37 | (349) all_22_1_28 = all_16_3_19
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (318,346) yields a new equation:
% 38.44/11.37 | (350) all_22_1_28 = all_12_1_9
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (332,346) yields a new equation:
% 38.44/11.37 | (351) all_22_1_28 = all_14_3_14
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (342,348) yields a new equation:
% 38.44/11.37 | (352) all_22_2_29 = all_14_4_15
% 38.44/11.37 |
% 38.44/11.37 | Simplifying 352 yields:
% 38.44/11.37 | (353) all_22_2_29 = all_14_4_15
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (327,337) yields a new equation:
% 38.44/11.37 | (354) all_16_2_18 = 0
% 38.44/11.37 |
% 38.44/11.37 | Simplifying 354 yields:
% 38.44/11.37 | (355) all_16_2_18 = 0
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (329,267) yields a new equation:
% 38.44/11.37 | (356) all_20_2_26 = all_12_0_8
% 38.44/11.37 |
% 38.44/11.37 | Simplifying 356 yields:
% 38.44/11.37 | (357) all_20_2_26 = all_12_0_8
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (349,351) yields a new equation:
% 38.44/11.37 | (358) all_16_3_19 = all_14_3_14
% 38.44/11.37 |
% 38.44/11.37 | Simplifying 358 yields:
% 38.44/11.37 | (359) all_16_3_19 = all_14_3_14
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (350,351) yields a new equation:
% 38.44/11.37 | (360) all_14_3_14 = all_12_1_9
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (299,353) yields a new equation:
% 38.44/11.37 | (361) all_16_4_20 = all_14_4_15
% 38.44/11.37 |
% 38.44/11.37 | Simplifying 361 yields:
% 38.44/11.37 | (362) all_16_4_20 = all_14_4_15
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (280,344) yields a new equation:
% 38.44/11.37 | (363) all_18_1_22 = all_14_2_13
% 38.44/11.37 |
% 38.44/11.37 | Simplifying 363 yields:
% 38.44/11.37 | (364) all_18_1_22 = all_14_2_13
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (330,357) yields a new equation:
% 38.44/11.37 | (365) all_18_2_23 = all_12_0_8
% 38.44/11.37 |
% 38.44/11.37 | Simplifying 365 yields:
% 38.44/11.37 | (366) all_18_2_23 = all_12_0_8
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (279,364) yields a new equation:
% 38.44/11.37 | (367) all_14_2_13 = 0
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (359,288) yields a new equation:
% 38.44/11.37 | (368) all_14_3_14 = 0
% 38.44/11.37 |
% 38.44/11.37 | Simplifying 368 yields:
% 38.44/11.37 | (369) all_14_3_14 = 0
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (301,362) yields a new equation:
% 38.44/11.37 | (370) all_14_4_15 = all_12_2_10
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (298,362) yields a new equation:
% 38.44/11.37 | (371) all_14_4_15 = 0
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (360,369) yields a new equation:
% 38.44/11.37 | (372) all_12_1_9 = 0
% 38.44/11.37 |
% 38.44/11.37 | Simplifying 372 yields:
% 38.44/11.37 | (373) all_12_1_9 = 0
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (370,371) yields a new equation:
% 38.44/11.37 | (374) all_12_2_10 = 0
% 38.44/11.37 |
% 38.44/11.37 | Simplifying 374 yields:
% 38.44/11.37 | (375) all_12_2_10 = 0
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (371,362) yields a new equation:
% 38.44/11.37 | (298) all_16_4_20 = 0
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (367,364) yields a new equation:
% 38.44/11.37 | (279) all_18_1_22 = 0
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (369,351) yields a new equation:
% 38.44/11.37 | (378) all_22_1_28 = 0
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (371,348) yields a new equation:
% 38.44/11.37 | (379) all_26_2_35 = 0
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (379,334) yields a new equation:
% 38.44/11.37 | (380) all_31_8_56 = 0
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (378,303) yields a new equation:
% 38.44/11.37 | (381) all_31_7_55 = 0
% 38.44/11.37 |
% 38.44/11.37 | Combining equations (335,261) yields a new equation:
% 38.44/11.37 | (260) all_31_4_52 = all_0_7_7
% 38.44/11.37 |
% 38.44/11.37 | From (260) and (173) follows:
% 38.44/11.37 | (383) sdtpldt0(all_0_7_7, xr) = all_31_3_51
% 38.44/11.37 |
% 38.44/11.37 | From (262) and (234) follows:
% 38.44/11.37 | (147) aNaturalNumber0(all_0_2_2) = all_24_0_30
% 38.44/11.37 |
% 38.44/11.37 | From (263) and (235) follows:
% 38.44/11.37 | (132) aNaturalNumber0(all_0_6_6) = all_18_0_21
% 38.44/11.37 |
% 38.44/11.37 +-Applying beta-rule and splitting (127), into two cases.
% 38.44/11.37 |-Branch one:
% 38.44/11.37 | (386) ~ (all_16_2_18 = 0)
% 38.44/11.37 |
% 38.44/11.37 | Equations (355) can reduce 386 to:
% 38.44/11.37 | (190) $false
% 38.44/11.37 |
% 38.44/11.37 |-The branch is then unsatisfiable
% 38.44/11.37 |-Branch two:
% 38.44/11.37 | (355) all_16_2_18 = 0
% 38.44/11.37 | (389) ~ (all_16_3_19 = 0) | ~ (all_16_4_20 = 0) | all_16_0_16 = all_0_2_2
% 38.44/11.37 |
% 38.44/11.37 +-Applying beta-rule and splitting (168), into two cases.
% 38.44/11.37 |-Branch one:
% 38.44/11.37 | (390) ~ (all_31_2_50 = 0)
% 38.44/11.37 |
% 38.44/11.37 +-Applying beta-rule and splitting (389), into two cases.
% 38.44/11.37 |-Branch one:
% 38.44/11.37 | (391) ~ (all_16_3_19 = 0)
% 38.44/11.37 |
% 38.44/11.37 | Equations (288) can reduce 391 to:
% 38.44/11.37 | (190) $false
% 38.44/11.37 |
% 38.44/11.37 |-The branch is then unsatisfiable
% 38.44/11.37 |-Branch two:
% 38.44/11.37 | (288) all_16_3_19 = 0
% 38.44/11.37 | (394) ~ (all_16_4_20 = 0) | all_16_0_16 = all_0_2_2
% 38.44/11.37 |
% 38.44/11.37 +-Applying beta-rule and splitting (394), into two cases.
% 38.44/11.37 |-Branch one:
% 38.44/11.37 | (395) ~ (all_16_4_20 = 0)
% 38.44/11.37 |
% 38.44/11.37 | Equations (298) can reduce 395 to:
% 38.44/11.37 | (190) $false
% 38.44/11.37 |
% 38.44/11.37 |-The branch is then unsatisfiable
% 38.44/11.37 |-Branch two:
% 38.44/11.37 | (298) all_16_4_20 = 0
% 38.44/11.37 | (398) all_16_0_16 = all_0_2_2
% 38.44/11.37 |
% 38.44/11.37 | From (398) and (126) follows:
% 38.44/11.37 | (399) sdtpldt0(xn, all_16_1_17) = all_0_2_2
% 38.44/11.37 |
% 38.44/11.37 +-Applying beta-rule and splitting (119), into two cases.
% 38.44/11.37 |-Branch one:
% 38.44/11.37 | (400) ~ (all_14_2_13 = 0)
% 38.44/11.37 |
% 38.44/11.37 | Equations (367) can reduce 400 to:
% 38.44/11.37 | (190) $false
% 38.44/11.37 |
% 38.44/11.37 |-The branch is then unsatisfiable
% 38.44/11.37 |-Branch two:
% 38.44/11.37 | (367) all_14_2_13 = 0
% 38.44/11.37 | (403) ~ (all_14_3_14 = 0) | ~ (all_14_4_15 = 0) | all_14_0_11 = all_0_6_6
% 38.44/11.37 |
% 38.44/11.37 +-Applying beta-rule and splitting (403), into two cases.
% 38.44/11.37 |-Branch one:
% 38.44/11.37 | (404) ~ (all_14_3_14 = 0)
% 38.44/11.37 |
% 38.44/11.37 | Equations (369) can reduce 404 to:
% 38.44/11.37 | (190) $false
% 38.44/11.37 |
% 38.44/11.37 |-The branch is then unsatisfiable
% 38.44/11.37 |-Branch two:
% 38.44/11.37 | (369) all_14_3_14 = 0
% 38.44/11.37 | (407) ~ (all_14_4_15 = 0) | all_14_0_11 = all_0_6_6
% 38.44/11.37 |
% 38.44/11.37 +-Applying beta-rule and splitting (407), into two cases.
% 38.44/11.37 |-Branch one:
% 38.44/11.37 | (408) ~ (all_14_4_15 = 0)
% 38.44/11.37 |
% 38.44/11.37 | Equations (371) can reduce 408 to:
% 38.44/11.37 | (190) $false
% 38.44/11.37 |
% 38.44/11.37 |-The branch is then unsatisfiable
% 38.44/11.37 |-Branch two:
% 38.44/11.37 | (371) all_14_4_15 = 0
% 38.44/11.37 | (411) all_14_0_11 = all_0_6_6
% 38.44/11.37 |
% 38.44/11.37 | From (411) and (123) follows:
% 38.44/11.37 | (412) sdtpldt0(xn, all_14_1_12) = all_0_6_6
% 38.44/11.37 |
% 38.44/11.37 +-Applying beta-rule and splitting (116), into two cases.
% 38.44/11.37 |-Branch one:
% 38.44/11.37 | (413) ~ (all_12_1_9 = 0)
% 38.44/11.37 |
% 38.44/11.37 | Equations (373) can reduce 413 to:
% 38.44/11.37 | (190) $false
% 38.44/11.37 |
% 38.44/11.37 |-The branch is then unsatisfiable
% 38.44/11.37 |-Branch two:
% 38.44/11.37 | (373) all_12_1_9 = 0
% 38.44/11.37 | (416) ~ (all_12_2_10 = 0) | all_12_0_8 = 0
% 38.44/11.37 |
% 38.44/11.37 +-Applying beta-rule and splitting (416), into two cases.
% 38.44/11.37 |-Branch one:
% 38.44/11.37 | (417) ~ (all_12_2_10 = 0)
% 38.44/11.37 |
% 38.44/11.37 | Equations (375) can reduce 417 to:
% 38.44/11.37 | (190) $false
% 38.44/11.37 |
% 38.44/11.37 |-The branch is then unsatisfiable
% 38.44/11.37 |-Branch two:
% 38.44/11.37 | (375) all_12_2_10 = 0
% 38.44/11.37 | (420) all_12_0_8 = 0
% 38.44/11.37 |
% 38.44/11.38 | Combining equations (420,366) yields a new equation:
% 38.44/11.38 | (421) all_18_2_23 = 0
% 38.44/11.38 |
% 38.44/11.38 | Combining equations (420,267) yields a new equation:
% 38.44/11.38 | (422) all_24_2_32 = 0
% 38.44/11.38 |
% 38.44/11.38 +-Applying beta-rule and splitting (135), into two cases.
% 38.44/11.38 |-Branch one:
% 38.44/11.38 | (423) ~ (all_18_1_22 = 0)
% 38.44/11.38 |
% 38.44/11.38 | Equations (279) can reduce 423 to:
% 38.44/11.38 | (190) $false
% 38.44/11.38 |
% 38.44/11.38 |-The branch is then unsatisfiable
% 38.44/11.38 |-Branch two:
% 38.44/11.38 | (279) all_18_1_22 = 0
% 38.44/11.38 | (426) ~ (all_18_2_23 = 0) | all_18_0_21 = 0
% 38.44/11.38 |
% 38.44/11.38 +-Applying beta-rule and splitting (426), into two cases.
% 38.44/11.38 |-Branch one:
% 38.44/11.38 | (427) ~ (all_18_2_23 = 0)
% 38.44/11.38 |
% 38.44/11.38 | Equations (421) can reduce 427 to:
% 38.44/11.38 | (190) $false
% 38.44/11.38 |
% 38.44/11.38 |-The branch is then unsatisfiable
% 38.44/11.38 |-Branch two:
% 38.44/11.38 | (421) all_18_2_23 = 0
% 38.44/11.38 | (430) all_18_0_21 = 0
% 38.44/11.38 |
% 38.44/11.38 | From (430) and (132) follows:
% 38.44/11.38 | (431) aNaturalNumber0(all_0_6_6) = 0
% 38.44/11.38 |
% 38.44/11.38 +-Applying beta-rule and splitting (150), into two cases.
% 38.44/11.38 |-Branch one:
% 38.44/11.38 | (432) ~ (all_24_1_31 = 0)
% 38.44/11.38 |
% 38.44/11.38 | Equations (337) can reduce 432 to:
% 38.44/11.38 | (190) $false
% 38.44/11.38 |
% 38.44/11.38 |-The branch is then unsatisfiable
% 38.44/11.38 |-Branch two:
% 38.44/11.38 | (337) all_24_1_31 = 0
% 38.44/11.38 | (435) ~ (all_24_2_32 = 0) | all_24_0_30 = 0
% 38.44/11.38 |
% 38.44/11.38 +-Applying beta-rule and splitting (435), into two cases.
% 38.44/11.38 |-Branch one:
% 38.44/11.38 | (436) ~ (all_24_2_32 = 0)
% 38.44/11.38 |
% 38.44/11.38 | Equations (422) can reduce 436 to:
% 38.44/11.38 | (190) $false
% 38.44/11.38 |
% 38.44/11.38 |-The branch is then unsatisfiable
% 38.44/11.38 |-Branch two:
% 38.44/11.38 | (422) all_24_2_32 = 0
% 38.44/11.38 | (439) all_24_0_30 = 0
% 38.44/11.38 |
% 38.44/11.38 | From (439) and (147) follows:
% 38.44/11.38 | (440) aNaturalNumber0(all_0_2_2) = 0
% 38.44/11.38 |
% 38.44/11.38 +-Applying beta-rule and splitting (188), into two cases.
% 38.44/11.38 |-Branch one:
% 38.44/11.38 | (441) all_42_0_78 = all_0_6_6 & all_42_1_79 = 0 & sdtpldt0(all_0_2_2, all_42_2_80) = all_0_6_6 & aNaturalNumber0(all_42_2_80) = 0
% 38.44/11.38 |
% 38.44/11.38 | Applying alpha-rule on (441) yields:
% 38.44/11.38 | (442) all_42_0_78 = all_0_6_6
% 38.44/11.38 | (443) all_42_1_79 = 0
% 38.44/11.38 | (444) sdtpldt0(all_0_2_2, all_42_2_80) = all_0_6_6
% 38.44/11.38 | (445) aNaturalNumber0(all_42_2_80) = 0
% 38.44/11.38 |
% 38.44/11.38 +-Applying beta-rule and splitting (259), into two cases.
% 38.44/11.38 |-Branch one:
% 38.44/11.38 | (446) ~ (sdtpldt0(all_0_7_7, xr) = all_31_3_51)
% 38.44/11.38 |
% 38.44/11.38 | Using (383) and (446) yields:
% 38.44/11.38 | (447) $false
% 38.44/11.38 |
% 38.44/11.38 |-The branch is then unsatisfiable
% 38.44/11.38 |-Branch two:
% 38.44/11.38 | (383) sdtpldt0(all_0_7_7, xr) = all_31_3_51
% 38.44/11.38 | (449) all_31_3_51 = all_0_2_2
% 38.44/11.38 |
% 38.44/11.38 | From (449) and (177) follows:
% 38.44/11.38 | (450) iLess0(all_0_2_2, all_0_6_6) = all_31_2_50
% 38.44/11.38 |
% 38.44/11.38 | Instantiating formula (86) with all_31_2_50, all_0_6_6, all_0_2_2 and discharging atoms iLess0(all_0_2_2, all_0_6_6) = all_31_2_50, yields:
% 38.44/11.38 | (451) all_31_2_50 = 0 | all_0_2_2 = all_0_6_6 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_0_2_2, all_0_6_6) = v2 & aNaturalNumber0(all_0_2_2) = v0 & aNaturalNumber0(all_0_6_6) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 38.44/11.38 |
% 38.44/11.38 | Instantiating formula (27) with all_0_6_6, all_42_2_80, all_0_2_2 and discharging atoms sdtpldt0(all_0_2_2, all_42_2_80) = all_0_6_6, yields:
% 38.44/11.38 | (452) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_42_2_80, all_0_2_2) = v2 & aNaturalNumber0(all_42_2_80) = v1 & aNaturalNumber0(all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_6_6))
% 38.44/11.38 |
% 38.44/11.38 | Instantiating formula (41) with all_0_2_2, all_16_1_17, xn and discharging atoms sdtpldt0(xn, all_16_1_17) = all_0_2_2, yields:
% 38.44/11.38 | (453) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_16_1_17) = v1 & aNaturalNumber0(all_0_2_2) = v2 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 38.44/11.38 |
% 38.44/11.38 | Instantiating formula (41) with all_0_6_6, all_14_1_12, xn and discharging atoms sdtpldt0(xn, all_14_1_12) = all_0_6_6, yields:
% 38.44/11.38 | (454) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_14_1_12) = v1 & aNaturalNumber0(all_0_6_6) = v2 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 38.44/11.38 |
% 38.44/11.38 | Instantiating (454) with all_266_0_111, all_266_1_112, all_266_2_113 yields:
% 38.44/11.38 | (455) aNaturalNumber0(all_14_1_12) = all_266_1_112 & aNaturalNumber0(all_0_6_6) = all_266_0_111 & aNaturalNumber0(xn) = all_266_2_113 & ( ~ (all_266_1_112 = 0) | ~ (all_266_2_113 = 0) | all_266_0_111 = 0)
% 38.44/11.38 |
% 38.44/11.38 | Applying alpha-rule on (455) yields:
% 38.44/11.38 | (456) aNaturalNumber0(all_14_1_12) = all_266_1_112
% 38.44/11.38 | (457) aNaturalNumber0(all_0_6_6) = all_266_0_111
% 38.44/11.38 | (458) aNaturalNumber0(xn) = all_266_2_113
% 38.44/11.38 | (459) ~ (all_266_1_112 = 0) | ~ (all_266_2_113 = 0) | all_266_0_111 = 0
% 38.44/11.38 |
% 38.44/11.38 | Instantiating (452) with all_272_0_120, all_272_1_121, all_272_2_122 yields:
% 38.44/11.38 | (460) sdtpldt0(all_42_2_80, all_0_2_2) = all_272_0_120 & aNaturalNumber0(all_42_2_80) = all_272_1_121 & aNaturalNumber0(all_0_2_2) = all_272_2_122 & ( ~ (all_272_1_121 = 0) | ~ (all_272_2_122 = 0) | all_272_0_120 = all_0_6_6)
% 38.44/11.38 |
% 38.44/11.38 | Applying alpha-rule on (460) yields:
% 38.44/11.38 | (461) sdtpldt0(all_42_2_80, all_0_2_2) = all_272_0_120
% 38.44/11.38 | (462) aNaturalNumber0(all_42_2_80) = all_272_1_121
% 38.44/11.38 | (463) aNaturalNumber0(all_0_2_2) = all_272_2_122
% 38.44/11.38 | (464) ~ (all_272_1_121 = 0) | ~ (all_272_2_122 = 0) | all_272_0_120 = all_0_6_6
% 38.44/11.38 |
% 38.44/11.38 | Instantiating (453) with all_296_0_184, all_296_1_185, all_296_2_186 yields:
% 38.44/11.38 | (465) aNaturalNumber0(all_16_1_17) = all_296_1_185 & aNaturalNumber0(all_0_2_2) = all_296_0_184 & aNaturalNumber0(xn) = all_296_2_186 & ( ~ (all_296_1_185 = 0) | ~ (all_296_2_186 = 0) | all_296_0_184 = 0)
% 38.44/11.38 |
% 38.44/11.38 | Applying alpha-rule on (465) yields:
% 38.44/11.38 | (466) aNaturalNumber0(all_16_1_17) = all_296_1_185
% 38.44/11.38 | (467) aNaturalNumber0(all_0_2_2) = all_296_0_184
% 38.44/11.38 | (468) aNaturalNumber0(xn) = all_296_2_186
% 38.44/11.38 | (469) ~ (all_296_1_185 = 0) | ~ (all_296_2_186 = 0) | all_296_0_184 = 0
% 38.44/11.38 |
% 38.44/11.38 | Instantiating formula (24) with all_0_2_2, all_296_0_184, 0 and discharging atoms aNaturalNumber0(all_0_2_2) = all_296_0_184, aNaturalNumber0(all_0_2_2) = 0, yields:
% 38.44/11.38 | (470) all_296_0_184 = 0
% 38.44/11.38 |
% 38.44/11.38 | Instantiating formula (24) with all_0_2_2, all_272_2_122, all_296_0_184 and discharging atoms aNaturalNumber0(all_0_2_2) = all_296_0_184, aNaturalNumber0(all_0_2_2) = all_272_2_122, yields:
% 38.44/11.38 | (471) all_296_0_184 = all_272_2_122
% 38.44/11.38 |
% 38.44/11.38 | Instantiating formula (24) with all_0_6_6, all_266_0_111, 0 and discharging atoms aNaturalNumber0(all_0_6_6) = all_266_0_111, aNaturalNumber0(all_0_6_6) = 0, yields:
% 38.44/11.38 | (472) all_266_0_111 = 0
% 38.44/11.38 |
% 38.44/11.38 | Combining equations (470,471) yields a new equation:
% 38.44/11.38 | (473) all_272_2_122 = 0
% 38.44/11.38 |
% 38.44/11.38 | From (473) and (463) follows:
% 38.44/11.38 | (440) aNaturalNumber0(all_0_2_2) = 0
% 38.44/11.38 |
% 38.44/11.38 | From (472) and (457) follows:
% 38.44/11.38 | (431) aNaturalNumber0(all_0_6_6) = 0
% 38.44/11.38 |
% 38.44/11.38 +-Applying beta-rule and splitting (451), into two cases.
% 38.44/11.38 |-Branch one:
% 38.44/11.38 | (476) all_31_2_50 = 0
% 38.44/11.38 |
% 38.44/11.38 | Equations (476) can reduce 390 to:
% 38.44/11.38 | (190) $false
% 38.44/11.38 |
% 38.44/11.38 |-The branch is then unsatisfiable
% 38.44/11.38 |-Branch two:
% 38.44/11.38 | (390) ~ (all_31_2_50 = 0)
% 38.44/11.38 | (479) all_0_2_2 = all_0_6_6 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_0_2_2, all_0_6_6) = v2 & aNaturalNumber0(all_0_2_2) = v0 & aNaturalNumber0(all_0_6_6) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 38.44/11.38 |
% 38.44/11.38 +-Applying beta-rule and splitting (479), into two cases.
% 38.44/11.38 |-Branch one:
% 38.44/11.38 | (228) all_0_2_2 = all_0_6_6
% 38.44/11.38 |
% 38.44/11.38 | Equations (228) can reduce 75 to:
% 38.44/11.38 | (190) $false
% 38.44/11.38 |
% 38.44/11.38 |-The branch is then unsatisfiable
% 38.44/11.38 |-Branch two:
% 38.44/11.38 | (75) ~ (all_0_2_2 = all_0_6_6)
% 38.44/11.38 | (483) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_0_2_2, all_0_6_6) = v2 & aNaturalNumber0(all_0_2_2) = v0 & aNaturalNumber0(all_0_6_6) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 38.44/11.38 |
% 38.44/11.38 | Instantiating (483) with all_480_0_259, all_480_1_260, all_480_2_261 yields:
% 38.44/11.38 | (484) sdtlseqdt0(all_0_2_2, all_0_6_6) = all_480_0_259 & aNaturalNumber0(all_0_2_2) = all_480_2_261 & aNaturalNumber0(all_0_6_6) = all_480_1_260 & ( ~ (all_480_0_259 = 0) | ~ (all_480_1_260 = 0) | ~ (all_480_2_261 = 0))
% 38.44/11.38 |
% 38.44/11.38 | Applying alpha-rule on (484) yields:
% 38.44/11.38 | (485) sdtlseqdt0(all_0_2_2, all_0_6_6) = all_480_0_259
% 38.44/11.38 | (486) aNaturalNumber0(all_0_2_2) = all_480_2_261
% 38.44/11.38 | (487) aNaturalNumber0(all_0_6_6) = all_480_1_260
% 38.44/11.38 | (488) ~ (all_480_0_259 = 0) | ~ (all_480_1_260 = 0) | ~ (all_480_2_261 = 0)
% 38.44/11.38 |
% 38.44/11.38 | Instantiating formula (44) with all_0_2_2, all_0_6_6, all_480_0_259, 0 and discharging atoms sdtlseqdt0(all_0_2_2, all_0_6_6) = all_480_0_259, sdtlseqdt0(all_0_2_2, all_0_6_6) = 0, yields:
% 38.44/11.39 | (489) all_480_0_259 = 0
% 38.44/11.39 |
% 38.44/11.39 | Instantiating formula (24) with all_0_2_2, all_480_2_261, 0 and discharging atoms aNaturalNumber0(all_0_2_2) = all_480_2_261, aNaturalNumber0(all_0_2_2) = 0, yields:
% 38.44/11.39 | (490) all_480_2_261 = 0
% 38.44/11.39 |
% 38.44/11.39 | Instantiating formula (24) with all_0_6_6, all_480_1_260, 0 and discharging atoms aNaturalNumber0(all_0_6_6) = all_480_1_260, aNaturalNumber0(all_0_6_6) = 0, yields:
% 38.44/11.39 | (491) all_480_1_260 = 0
% 38.44/11.39 |
% 38.44/11.39 +-Applying beta-rule and splitting (488), into two cases.
% 38.44/11.39 |-Branch one:
% 38.44/11.39 | (492) ~ (all_480_0_259 = 0)
% 38.44/11.39 |
% 38.44/11.39 | Equations (489) can reduce 492 to:
% 38.44/11.39 | (190) $false
% 38.44/11.39 |
% 38.44/11.39 |-The branch is then unsatisfiable
% 38.44/11.39 |-Branch two:
% 38.44/11.39 | (489) all_480_0_259 = 0
% 38.44/11.39 | (495) ~ (all_480_1_260 = 0) | ~ (all_480_2_261 = 0)
% 38.44/11.39 |
% 38.44/11.39 +-Applying beta-rule and splitting (495), into two cases.
% 38.44/11.39 |-Branch one:
% 38.44/11.39 | (496) ~ (all_480_1_260 = 0)
% 38.44/11.39 |
% 38.44/11.39 | Equations (491) can reduce 496 to:
% 38.44/11.39 | (190) $false
% 38.44/11.39 |
% 38.44/11.39 |-The branch is then unsatisfiable
% 38.44/11.39 |-Branch two:
% 38.44/11.39 | (491) all_480_1_260 = 0
% 38.44/11.39 | (499) ~ (all_480_2_261 = 0)
% 38.44/11.39 |
% 38.44/11.39 | Equations (490) can reduce 499 to:
% 38.44/11.39 | (190) $false
% 38.44/11.39 |
% 38.44/11.39 |-The branch is then unsatisfiable
% 38.44/11.39 |-Branch two:
% 38.44/11.39 | (501) aNaturalNumber0(all_0_2_2) = all_42_2_80 & aNaturalNumber0(all_0_6_6) = all_42_1_79 & ( ~ (all_42_1_79 = 0) | ~ (all_42_2_80 = 0))
% 38.44/11.39 |
% 38.44/11.39 | Applying alpha-rule on (501) yields:
% 38.44/11.39 | (502) aNaturalNumber0(all_0_2_2) = all_42_2_80
% 38.44/11.39 | (503) aNaturalNumber0(all_0_6_6) = all_42_1_79
% 38.44/11.39 | (504) ~ (all_42_1_79 = 0) | ~ (all_42_2_80 = 0)
% 38.44/11.39 |
% 38.44/11.39 | Instantiating formula (24) with all_0_2_2, all_42_2_80, 0 and discharging atoms aNaturalNumber0(all_0_2_2) = all_42_2_80, aNaturalNumber0(all_0_2_2) = 0, yields:
% 38.44/11.39 | (505) all_42_2_80 = 0
% 38.44/11.39 |
% 38.44/11.39 | Instantiating formula (24) with all_0_6_6, all_42_1_79, 0 and discharging atoms aNaturalNumber0(all_0_6_6) = all_42_1_79, aNaturalNumber0(all_0_6_6) = 0, yields:
% 38.44/11.39 | (443) all_42_1_79 = 0
% 38.44/11.39 |
% 38.44/11.39 +-Applying beta-rule and splitting (504), into two cases.
% 38.44/11.39 |-Branch one:
% 38.44/11.39 | (507) ~ (all_42_1_79 = 0)
% 38.44/11.39 |
% 38.44/11.39 | Equations (443) can reduce 507 to:
% 38.44/11.39 | (190) $false
% 38.44/11.39 |
% 38.44/11.39 |-The branch is then unsatisfiable
% 38.44/11.39 |-Branch two:
% 38.44/11.39 | (443) all_42_1_79 = 0
% 38.44/11.39 | (510) ~ (all_42_2_80 = 0)
% 38.44/11.39 |
% 38.44/11.39 | Equations (505) can reduce 510 to:
% 38.44/11.39 | (190) $false
% 38.44/11.39 |
% 38.44/11.39 |-The branch is then unsatisfiable
% 38.44/11.39 |-Branch two:
% 38.44/11.39 | (476) all_31_2_50 = 0
% 38.44/11.39 | (513) ~ (all_31_5_53 = 0) | ~ (all_31_6_54 = 0) | ~ (all_31_7_55 = 0) | ~ (all_31_8_56 = 0) | all_31_0_48 = 0 | all_31_1_49 = 0
% 38.44/11.39 |
% 38.44/11.39 +-Applying beta-rule and splitting (513), into two cases.
% 38.44/11.39 |-Branch one:
% 38.44/11.39 | (514) ~ (all_31_5_53 = 0)
% 38.44/11.39 |
% 38.44/11.39 | Equations (256) can reduce 514 to:
% 38.44/11.39 | (190) $false
% 38.44/11.39 |
% 38.44/11.39 |-The branch is then unsatisfiable
% 38.44/11.39 |-Branch two:
% 38.44/11.39 | (256) all_31_5_53 = 0
% 38.44/11.39 | (517) ~ (all_31_6_54 = 0) | ~ (all_31_7_55 = 0) | ~ (all_31_8_56 = 0) | all_31_0_48 = 0 | all_31_1_49 = 0
% 38.44/11.39 |
% 38.44/11.39 +-Applying beta-rule and splitting (517), into two cases.
% 38.44/11.39 |-Branch one:
% 38.44/11.39 | (518) ~ (all_31_6_54 = 0)
% 38.44/11.39 |
% 38.44/11.39 | Equations (323) can reduce 518 to:
% 38.44/11.39 | (190) $false
% 38.44/11.39 |
% 38.44/11.39 |-The branch is then unsatisfiable
% 38.44/11.39 |-Branch two:
% 38.44/11.39 | (323) all_31_6_54 = 0
% 38.44/11.39 | (521) ~ (all_31_7_55 = 0) | ~ (all_31_8_56 = 0) | all_31_0_48 = 0 | all_31_1_49 = 0
% 38.44/11.39 |
% 38.44/11.39 +-Applying beta-rule and splitting (521), into two cases.
% 38.44/11.39 |-Branch one:
% 38.44/11.39 | (522) ~ (all_31_7_55 = 0)
% 38.44/11.39 |
% 38.44/11.39 | Equations (381) can reduce 522 to:
% 38.44/11.39 | (190) $false
% 38.44/11.39 |
% 38.44/11.39 |-The branch is then unsatisfiable
% 38.44/11.39 |-Branch two:
% 38.44/11.39 | (381) all_31_7_55 = 0
% 38.64/11.39 | (525) ~ (all_31_8_56 = 0) | all_31_0_48 = 0 | all_31_1_49 = 0
% 38.64/11.39 |
% 38.64/11.39 +-Applying beta-rule and splitting (525), into two cases.
% 38.64/11.39 |-Branch one:
% 38.64/11.39 | (526) ~ (all_31_8_56 = 0)
% 38.64/11.39 |
% 38.64/11.39 | Equations (380) can reduce 526 to:
% 38.64/11.39 | (190) $false
% 38.64/11.39 |
% 38.64/11.39 |-The branch is then unsatisfiable
% 38.64/11.39 |-Branch two:
% 38.64/11.39 | (380) all_31_8_56 = 0
% 38.64/11.39 | (529) all_31_0_48 = 0 | all_31_1_49 = 0
% 38.64/11.39 |
% 38.64/11.39 +-Applying beta-rule and splitting (529), into two cases.
% 38.64/11.39 |-Branch one:
% 38.64/11.39 | (530) all_31_0_48 = 0
% 38.64/11.39 |
% 38.64/11.39 | Combining equations (530,257) yields a new equation:
% 38.64/11.39 | (198) all_0_0_0 = 0
% 38.64/11.39 |
% 38.64/11.39 | Equations (198) can reduce 78 to:
% 38.64/11.39 | (190) $false
% 38.64/11.39 |
% 38.64/11.39 |-The branch is then unsatisfiable
% 38.64/11.39 |-Branch two:
% 38.64/11.39 | (533) ~ (all_31_0_48 = 0)
% 38.64/11.39 | (534) all_31_1_49 = 0
% 38.64/11.39 |
% 38.64/11.39 | Combining equations (534,258) yields a new equation:
% 38.64/11.39 | (208) all_0_1_1 = 0
% 38.64/11.39 |
% 38.64/11.39 | Equations (208) can reduce 19 to:
% 38.64/11.39 | (190) $false
% 38.64/11.39 |
% 38.64/11.39 |-The branch is then unsatisfiable
% 38.64/11.39 % SZS output end Proof for theBenchmark
% 38.64/11.39
% 38.64/11.39 10750ms
%------------------------------------------------------------------------------