TSTP Solution File: NUM521+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM521+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.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 08:45:26 EDT 2022
% Result : Theorem 22.03s 6.20s
% Output : Proof 26.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM521+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jul 7 15:42:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.59 ____ _
% 0.19/0.59 ___ / __ \_____(_)___ ________ __________
% 0.19/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic
% 0.19/0.59 (ePrincess v.1.0)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2015
% 0.19/0.59 (c) Peter Backeman, 2014-2015
% 0.19/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.59 Bug reports to peter@backeman.se
% 0.19/0.59
% 0.19/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.90/1.04 Prover 0: Preprocessing ...
% 3.64/1.52 Prover 0: Constructing countermodel ...
% 20.83/5.96 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 21.10/6.01 Prover 1: Preprocessing ...
% 21.49/6.14 Prover 1: Constructing countermodel ...
% 21.95/6.20 Prover 1: proved (237ms)
% 22.03/6.20 Prover 0: stopped
% 22.03/6.20
% 22.03/6.20 No countermodel exists, formula is valid
% 22.03/6.20 % SZS status Theorem for theBenchmark
% 22.03/6.20
% 22.03/6.20 Generating proof ... found it (size 163)
% 25.46/7.08
% 25.46/7.08 % SZS output start Proof for theBenchmark
% 25.46/7.08 Assumed formulas after preprocessing and simplification:
% 25.46/7.08 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & ~ (v7 = 0) & ~ (v4 = 0) & ~ (v3 = 0) & ~ (sz10 = sz00) & isPrime0(xp) = 0 & doDivides0(xp, v2) = 0 & doDivides0(xp, xm) = v8 & doDivides0(xp, xn) = v7 & sdtlseqdt0(xp, xm) = v4 & sdtlseqdt0(xp, xn) = v3 & sdtlseqdt0(xm, xp) = v6 & sdtlseqdt0(xn, xp) = v5 & sdtasdt0(xn, xm) = v2 & sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) = v0 & aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 & ~ (isPrime0(sz10) = 0) & ~ (isPrime0(sz00) = 0) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | v9 = sz00 | ~ (sdtlseqdt0(v12, v13) = v14) | ~ (sdtasdt0(v9, v11) = v13) | ~ (sdtasdt0(v9, v10) = v12) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (sdtlseqdt0(v19, v20) = v21 & sdtlseqdt0(v10, v11) = v18 & sdtasdt0(v11, v9) = v20 & sdtasdt0(v10, v9) = v19 & aNaturalNumber0(v11) = v17 & aNaturalNumber0(v10) = v16 & aNaturalNumber0(v9) = v15 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | (v21 = 0 & v14 = 0 & ~ (v20 = v19) & ~ (v13 = v12))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = v9 | ~ (sdtlseqdt0(v12, v13) = v14) | ~ (sdtlseqdt0(v9, v10) = 0) | ~ (sdtpldt0(v10, v11) = v13) | ~ (sdtpldt0(v9, v11) = v12) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((sdtlseqdt0(v16, v17) = v18 & sdtpldt0(v11, v10) = v17 & sdtpldt0(v11, v9) = v16 & aNaturalNumber0(v11) = v15 & ( ~ (v15 = 0) | (v18 = 0 & v14 = 0 & ~ (v17 = v16) & ~ (v13 = v12)))) | (aNaturalNumber0(v10) = v16 & aNaturalNumber0(v9) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v9 = sz00 | ~ (sdtsldt0(v13, v9) = v14) | ~ (sdtsldt0(v10, v9) = v11) | ~ (sdtasdt0(v12, v10) = v13) | ? [v15] : ? [v16] : ? [v17] : ((doDivides0(v9, v10) = v17 & aNaturalNumber0(v10) = v16 & aNaturalNumber0(v9) = v15 & ( ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0))) | (sdtasdt0(v12, v11) = v16 & aNaturalNumber0(v12) = v15 & ( ~ (v15 = 0) | v16 = v14)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtasdt0(v9, v11) = v13) | ~ (sdtasdt0(v9, v10) = v12) | ~ (sdtpldt0(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (sdtasdt0(v18, v9) = v20 & sdtasdt0(v11, v9) = v22 & sdtasdt0(v10, v9) = v21 & sdtasdt0(v9, v18) = v19 & sdtpldt0(v21, v22) = v23 & sdtpldt0(v10, v11) = v18 & aNaturalNumber0(v11) = v17 & aNaturalNumber0(v10) = v16 & aNaturalNumber0(v9) = v15 & ( ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | (v23 = v20 & v19 = v14)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (doDivides0(v9, v12) = v13) | ~ (sdtpldt0(v10, v11) = v12) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (doDivides0(v9, v11) = v18 & doDivides0(v9, v10) = v17 & aNaturalNumber0(v11) = v16 & aNaturalNumber0(v10) = v15 & aNaturalNumber0(v9) = v14 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | v9 = sz00 | ~ (sdtasdt0(v9, v11) = v13) | ~ (sdtasdt0(v9, v10) = v12) | ~ (aNaturalNumber0(v9) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (sdtasdt0(v11, v9) = v17 & sdtasdt0(v10, v9) = v16 & aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | ( ~ (v17 = v16) & ~ (v13 = v12))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtpldt0(v9, v11) = v13) | ~ (sdtpldt0(v9, v10) = v12) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (sdtpldt0(v11, v9) = v18 & sdtpldt0(v10, v9) = v17 & aNaturalNumber0(v11) = v16 & aNaturalNumber0(v10) = v15 & aNaturalNumber0(v9) = v14 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ( ~ (v18 = v17) & ~ (v13 = v12))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtasdt0(v12, v11) = v13) | ~ (sdtasdt0(v9, v10) = v12) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (sdtasdt0(v10, v11) = v17 & sdtasdt0(v9, v17) = v18 & aNaturalNumber0(v11) = v16 & aNaturalNumber0(v10) = v15 & aNaturalNumber0(v9) = v14 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | v18 = v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtpldt0(v12, v11) = v13) | ~ (sdtpldt0(v9, v10) = v12) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (sdtpldt0(v10, v11) = v17 & sdtpldt0(v9, v17) = v18 & aNaturalNumber0(v11) = v16 & aNaturalNumber0(v10) = v15 & aNaturalNumber0(v9) = v14 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | v18 = v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | v9 = sz00 | ~ (sdtsldt0(v10, v9) = v11) | ~ (sdtasdt0(v9, v12) = v10) | ? [v13] : ? [v14] : ? [v15] : (( ~ (v13 = 0) & aNaturalNumber0(v12) = v13) | (doDivides0(v9, v10) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (sdtmndt0(v10, v9) = v11) | ~ (sdtpldt0(v9, v12) = v10) | ? [v13] : ? [v14] : ? [v15] : (( ~ (v13 = 0) & aNaturalNumber0(v12) = v13) | (sdtlseqdt0(v9, v10) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | v9 = sz00 | ~ (sdtsldt0(v10, v9) = v11) | ~ (sdtasdt0(v9, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (doDivides0(v9, v10) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (sdtmndt0(v10, v9) = v11) | ~ (sdtpldt0(v9, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (sdtlseqdt0(v9, v10) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v9 = sz00 | ~ (sdtlseqdt0(v10, v11) = v12) | ~ (sdtasdt0(v10, v9) = v11) | ? [v13] : ? [v14] : (aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (doDivides0(v9, v11) = v12) | ~ (doDivides0(v9, v10) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (doDivides0(v10, v11) = v16 & aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (sdtlseqdt0(v9, v11) = v12) | ~ (sdtlseqdt0(v9, v10) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (sdtlseqdt0(v10, v11) = v16 & aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (doDivides0(v9, v10) = v11) | ~ (sdtasdt0(v9, v12) = v10) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & aNaturalNumber0(v12) = v13) | (aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (sdtlseqdt0(v9, v10) = v11) | ~ (sdtpldt0(v9, v12) = v10) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & aNaturalNumber0(v12) = v13) | (aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (sdtsldt0(v12, v11) = v10) | ~ (sdtsldt0(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (doDivides0(v12, v11) = v10) | ~ (doDivides0(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (iLess0(v12, v11) = v10) | ~ (iLess0(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (sdtmndt0(v12, v11) = v10) | ~ (sdtmndt0(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (sdtlseqdt0(v12, v11) = v10) | ~ (sdtlseqdt0(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (sdtasdt0(v12, v11) = v10) | ~ (sdtasdt0(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (sdtpldt0(v12, v11) = v10) | ~ (sdtpldt0(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = sz00 | ~ (sdtsldt0(v10, v9) = v11) | ~ (sdtasdt0(v9, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ((v13 = 0 & aNaturalNumber0(v11) = 0) | (doDivides0(v9, v10) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (doDivides0(v11, v12) = 0) | ~ (sdtasdt0(v9, v10) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (isPrime0(v11) = v16 & doDivides0(v11, v10) = v21 & doDivides0(v11, v9) = v20 & iLess0(v18, v1) = v19 & sdtpldt0(v17, v11) = v18 & sdtpldt0(v9, v10) = v17 & aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v19 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | v21 = 0 | v20 = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (doDivides0(v9, v12) = 0) | ~ (sdtpldt0(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (doDivides0(v9, v11) = v17 & doDivides0(v9, v10) = v16 & aNaturalNumber0(v11) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | v17 = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtmndt0(v10, v9) = v11) | ~ (sdtpldt0(v9, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ((v13 = 0 & aNaturalNumber0(v11) = 0) | (sdtlseqdt0(v9, v10) = v15 & aNaturalNumber0(v10) = v14 & aNaturalNumber0(v9) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = v9 | ~ (iLess0(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (sdtlseqdt0(v9, v10) = v14 & aNaturalNumber0(v10) = v13 & aNaturalNumber0(v9) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (sdtlseqdt0(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (sdtlseqdt0(v10, v9) = v14 & aNaturalNumber0(v10) = v13 & aNaturalNumber0(v9) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | (v14 = 0 & ~ (v10 = v9))))) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (isPrime0(v11) = v10) | ~ (isPrime0(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (aNaturalNumber0(v11) = v10) | ~ (aNaturalNumber0(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v10, v9) = v14 & aNaturalNumber0(v10) = v13 & aNaturalNumber0(v9) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | v14 = v11))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (aNaturalNumber0(v11) = v14 & aNaturalNumber0(v10) = v13 & aNaturalNumber0(v9) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | v14 = 0))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtpldt0(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (sdtpldt0(v10, v9) = v14 & aNaturalNumber0(v10) = v13 & aNaturalNumber0(v9) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | v14 = v11))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtpldt0(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (aNaturalNumber0(v11) = v14 & aNaturalNumber0(v10) = v13 & aNaturalNumber0(v9) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | v14 = 0))) & ! [v9] : ! [v10] : (v10 = v9 | v10 = sz10 | ~ (isPrime0(v9) = 0) | ~ (doDivides0(v10, v9) = 0) | ? [v11] : (( ~ (v11 = 0) & aNaturalNumber0(v10) = v11) | ( ~ (v11 = 0) & aNaturalNumber0(v9) = v11))) & ! [v9] : ! [v10] : (v10 = v9 | ~ (sdtlseqdt0(v9, v10) = 0) | ? [v11] : ? [v12] : ? [v13] : (sdtlseqdt0(v10, v9) = v13 & aNaturalNumber0(v10) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v9] : ! [v10] : (v10 = sz00 | v9 = sz00 | ~ (sdtasdt0(v9, v10) = sz00) | ? [v11] : ? [v12] : (aNaturalNumber0(v10) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v9] : ! [v10] : (v10 = sz00 | ~ (doDivides0(v9, v10) = 0) | ? [v11] : ? [v12] : ? [v13] : (sdtlseqdt0(v9, v10) = v13 & aNaturalNumber0(v10) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) | v13 = 0))) & ! [v9] : ! [v10] : (v10 = sz00 | ~ (sdtpldt0(v9, v10) = sz00) | ? [v11] : ? [v12] : (aNaturalNumber0(v10) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v9] : ! [v10] : (v10 = 0 | v9 = sz10 | v9 = sz00 | ~ (isPrime0(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & ~ (v11 = v9) & ~ (v11 = sz10) & doDivides0(v11, v9) = 0 & aNaturalNumber0(v11) = 0) | ( ~ (v11 = 0) & aNaturalNumber0(v9) = v11))) & ! [v9] : ! [v10] : (v10 = 0 | v9 = sz10 | v9 = sz00 | ~ (sdtlseqdt0(sz10, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & aNaturalNumber0(v9) = v11)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (sdtlseqdt0(v9, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & aNaturalNumber0(v9) = v11)) & ! [v9] : ! [v10] : (v9 = sz00 | ~ (sdtpldt0(v9, v10) = sz00) | ? [v11] : ? [v12] : (aNaturalNumber0(v10) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v9] : ! [v10] : ( ~ (doDivides0(v9, v10) = 0) | ? [v11] : ? [v12] : ? [v13] : ((v13 = v10 & v12 = 0 & sdtasdt0(v9, v11) = v10 & aNaturalNumber0(v11) = 0) | (aNaturalNumber0(v10) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v9] : ! [v10] : ( ~ (sdtlseqdt0(v9, v10) = 0) | ? [v11] : ? [v12] : ? [v13] : ((v13 = v10 & v12 = 0 & sdtpldt0(v9, v11) = v10 & aNaturalNumber0(v11) = 0) | (aNaturalNumber0(v10) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v9] : ! [v10] : ( ~ (sdtasdt0(sz10, v9) = v10) | ? [v11] : ? [v12] : (sdtasdt0(v9, sz10) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v11 = 0) | (v12 = v9 & v10 = v9)))) & ! [v9] : ! [v10] : ( ~ (sdtasdt0(sz00, v9) = v10) | ? [v11] : ? [v12] : (sdtasdt0(v9, sz00) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v11 = 0) | (v12 = sz00 & v10 = sz00)))) & ! [v9] : ! [v10] : ( ~ (sdtpldt0(sz00, v9) = v10) | ? [v11] : ? [v12] : (sdtpldt0(v9, sz00) = v12 & aNaturalNumber0(v9) = v11 & ( ~ (v11 = 0) | (v12 = v9 & v10 = v9)))) & ! [v9] : (v9 = sz10 | v9 = sz00 | ~ (aNaturalNumber0(v9) = 0) | ? [v10] : (isPrime0(v10) = 0 & doDivides0(v10, v9) = 0 & aNaturalNumber0(v10) = 0)) & ( ~ (v6 = 0) | ~ (v5 = 0) | xp = xm | xp = xn))
% 25.91/7.15 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 yields:
% 25.91/7.15 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & ~ (all_0_4_4 = 0) & ~ (all_0_5_5 = 0) & ~ (sz10 = sz00) & isPrime0(xp) = 0 & doDivides0(xp, all_0_6_6) = 0 & doDivides0(xp, xm) = all_0_0_0 & doDivides0(xp, xn) = all_0_1_1 & sdtlseqdt0(xp, xm) = all_0_4_4 & sdtlseqdt0(xp, xn) = all_0_5_5 & sdtlseqdt0(xm, xp) = all_0_2_2 & sdtlseqdt0(xn, xp) = all_0_3_3 & sdtasdt0(xn, xm) = all_0_6_6 & sdtpldt0(all_0_8_8, xp) = all_0_7_7 & sdtpldt0(xn, xm) = all_0_8_8 & aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 & ~ (isPrime0(sz10) = 0) & ~ (isPrime0(sz00) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | v0 = sz00 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (sdtlseqdt0(v10, v11) = v12 & sdtlseqdt0(v1, v2) = v9 & sdtasdt0(v2, v0) = v11 & sdtasdt0(v1, v0) = v10 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v12 = 0 & v5 = 0 & ~ (v11 = v10) & ~ (v4 = v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtlseqdt0(v0, v1) = 0) | ~ (sdtpldt0(v1, v2) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((sdtlseqdt0(v7, v8) = v9 & sdtpldt0(v2, v1) = v8 & sdtpldt0(v2, v0) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0 & ~ (v8 = v7) & ~ (v4 = v3)))) | (aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ((doDivides0(v0, v1) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))) | (sdtasdt0(v3, v2) = v7 & aNaturalNumber0(v3) = v6 & ( ~ (v6 = 0) | v7 = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v9, v0) = v11 & sdtasdt0(v2, v0) = v13 & sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v9) = v10 & sdtpldt0(v12, v13) = v14 & sdtpldt0(v1, v2) = v9 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v14 = v11 & v10 = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (doDivides0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (doDivides0(v0, v2) = v9 & doDivides0(v0, v1) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v8 = v7) & ~ (v4 = v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtpldt0(v2, v0) = v9 & sdtpldt0(v1, v0) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v9 = v8) & ~ (v4 = v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtpldt0(v1, v2) = v8 & sdtpldt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v0 = sz00 | ~ (sdtlseqdt0(v1, v2) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ? [v4] : ? [v5] : (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (doDivides0(v0, v2) = v3) | ~ (doDivides0(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (doDivides0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (sdtlseqdt0(v0, v2) = v3) | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (sdtlseqdt0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (doDivides0(v0, v1) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (doDivides0(v2, v3) = 0) | ~ (sdtasdt0(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (isPrime0(v2) = v7 & doDivides0(v2, v1) = v12 & doDivides0(v2, v0) = v11 & iLess0(v9, all_0_7_7) = v10 & sdtpldt0(v8, v2) = v9 & sdtpldt0(v0, v1) = v8 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v10 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v12 = 0 | v11 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (doDivides0(v0, v3) = 0) | ~ (sdtpldt0(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (doDivides0(v0, v2) = v8 & doDivides0(v0, v1) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (iLess0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtlseqdt0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtlseqdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v5 = 0 & ~ (v1 = v0))))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ (isPrime0(v0) = 0) | ~ (doDivides0(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (sdtlseqdt0(v1, v0) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (doDivides0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (sdtlseqdt0(v0, v1) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0))) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (isPrime0(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & ~ (v2 = v0) & ~ (v2 = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)) & ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (doDivides0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ! [v0] : ! [v1] : ( ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00)))) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0)) & ( ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | xp = xm | xp = xn)
% 25.91/7.17 |
% 25.91/7.17 | Applying alpha-rule on (1) yields:
% 25.91/7.17 | (2) sdtlseqdt0(xp, xm) = all_0_4_4
% 25.91/7.17 | (3) ! [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)))
% 25.91/7.17 | (4) doDivides0(xp, xn) = all_0_1_1
% 25.91/7.17 | (5) sdtpldt0(xn, xm) = all_0_8_8
% 25.91/7.17 | (6) ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | xp = xm | xp = xn
% 25.91/7.17 | (7) ~ (all_0_1_1 = 0)
% 25.91/7.17 | (8) ~ (all_0_0_0 = 0)
% 25.91/7.17 | (9) aNaturalNumber0(xp) = 0
% 25.91/7.17 | (10) sdtpldt0(all_0_8_8, xp) = all_0_7_7
% 25.91/7.17 | (11) ! [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)))))
% 25.91/7.17 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0))
% 25.91/7.17 | (13) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 25.91/7.17 | (14) aNaturalNumber0(xn) = 0
% 25.91/7.17 | (15) ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 25.91/7.17 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0))
% 25.91/7.17 | (17) ! [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)))))
% 25.91/7.18 | (18) isPrime0(xp) = 0
% 25.91/7.18 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0))
% 25.91/7.18 | (20) ~ (all_0_5_5 = 0)
% 25.91/7.18 | (21) ! [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)))))
% 25.91/7.18 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 25.91/7.18 | (23) ! [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)))))
% 25.91/7.18 | (24) sdtlseqdt0(xp, xn) = all_0_5_5
% 25.91/7.18 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 25.91/7.18 | (26) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00))))
% 25.91/7.18 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 25.91/7.18 | (28) ! [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))))
% 25.91/7.18 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (doDivides0(v2, v3) = 0) | ~ (sdtasdt0(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (isPrime0(v2) = v7 & doDivides0(v2, v1) = v12 & doDivides0(v2, v0) = v11 & iLess0(v9, all_0_7_7) = v10 & sdtpldt0(v8, v2) = v9 & sdtpldt0(v0, v1) = v8 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v10 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v12 = 0 | v11 = 0)))
% 25.91/7.18 | (30) ! [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))))
% 25.91/7.18 | (31) ! [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)))))
% 25.91/7.18 | (32) sdtlseqdt0(xm, xp) = all_0_2_2
% 25.91/7.18 | (33) ! [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)))
% 25.91/7.18 | (34) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 25.91/7.18 | (35) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0))
% 25.91/7.18 | (36) aNaturalNumber0(xm) = 0
% 25.91/7.18 | (37) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 25.91/7.18 | (38) ! [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)))))
% 25.91/7.18 | (39) doDivides0(xp, all_0_6_6) = 0
% 25.91/7.18 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (doDivides0(v0, v3) = 0) | ~ (sdtpldt0(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (doDivides0(v0, v2) = v8 & doDivides0(v0, v1) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v8 = 0)))
% 25.91/7.18 | (41) ! [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)))))
% 25.91/7.18 | (42) ~ (isPrime0(sz00) = 0)
% 25.91/7.18 | (43) sdtasdt0(xn, xm) = all_0_6_6
% 25.91/7.18 | (44) ! [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)))))
% 25.91/7.19 | (45) ! [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)))))
% 25.91/7.19 | (46) sdtlseqdt0(xn, xp) = all_0_3_3
% 25.91/7.19 | (47) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 25.91/7.19 | (48) ! [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)))
% 25.91/7.19 | (49) ! [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)))
% 25.91/7.19 | (50) ! [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))))
% 25.91/7.19 | (51) ! [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)))
% 25.91/7.19 | (52) ! [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))))
% 25.91/7.19 | (53) ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 25.91/7.19 | (54) aNaturalNumber0(sz10) = 0
% 25.91/7.19 | (55) ! [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)))))
% 25.91/7.19 | (56) ! [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))))
% 25.91/7.19 | (57) ~ (isPrime0(sz10) = 0)
% 25.91/7.19 | (58) ! [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))))
% 25.91/7.19 | (59) ~ (sz10 = sz00)
% 25.91/7.19 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 25.91/7.19 | (61) ! [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)))))
% 25.91/7.19 | (62) ! [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))))
% 25.91/7.19 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0))
% 25.91/7.19 | (64) ! [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))))
% 25.91/7.19 | (65) aNaturalNumber0(sz00) = 0
% 25.91/7.19 | (66) ! [v0] : ! [v1] : (v1 = sz00 | ~ (doDivides0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (sdtlseqdt0(v0, v1) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0)))
% 25.91/7.19 | (67) ! [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)))))
% 25.91/7.19 | (68) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 25.91/7.19 | (69) ~ (all_0_4_4 = 0)
% 25.91/7.19 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0))
% 25.91/7.19 | (71) ! [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)))
% 25.91/7.19 | (72) ! [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))))
% 25.91/7.20 | (73) ! [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))))
% 25.91/7.20 | (74) ! [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)))))
% 25.91/7.20 | (75) doDivides0(xp, xm) = all_0_0_0
% 25.91/7.20 | (76) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ (isPrime0(v0) = 0) | ~ (doDivides0(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 25.91/7.20 | (77) ! [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)))
% 25.91/7.20 |
% 25.91/7.20 | Instantiating formula (52) with all_0_0_0, xm, all_0_6_6, xp and discharging atoms doDivides0(xp, all_0_6_6) = 0, doDivides0(xp, xm) = all_0_0_0, yields:
% 25.91/7.20 | (78) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_6_6, xm) = v3 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 25.91/7.20 |
% 25.91/7.20 | Instantiating formula (52) with all_0_1_1, xn, all_0_6_6, xp and discharging atoms doDivides0(xp, all_0_6_6) = 0, doDivides0(xp, xn) = all_0_1_1, yields:
% 25.91/7.20 | (79) all_0_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_6_6, xn) = v3 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 25.91/7.20 |
% 25.91/7.21 | Instantiating formula (53) with all_0_4_4, xm yields:
% 25.91/7.21 | (80) all_0_4_4 = 0 | ~ (sdtlseqdt0(xm, xm) = all_0_4_4) | ? [v0] : ( ~ (v0 = 0) & aNaturalNumber0(xm) = v0)
% 25.91/7.21 |
% 25.91/7.21 | Instantiating formula (23) with all_0_4_4, xm, xp and discharging atoms sdtlseqdt0(xp, xm) = all_0_4_4, yields:
% 25.91/7.21 | (81) all_0_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xm, xp) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xp = xm))))
% 25.91/7.21 |
% 25.91/7.21 | Instantiating formula (23) with all_0_5_5, xn, xp and discharging atoms sdtlseqdt0(xp, xn) = all_0_5_5, yields:
% 25.91/7.21 | (82) all_0_5_5 = 0 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xn, xp) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xp = xn))))
% 25.91/7.21 |
% 25.91/7.21 | Instantiating formula (23) with all_0_2_2, xp, xm and discharging atoms sdtlseqdt0(xm, xp) = all_0_2_2, yields:
% 25.91/7.21 | (83) all_0_2_2 = 0 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, xm) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xp = xm))))
% 25.91/7.21 |
% 25.91/7.21 | Instantiating formula (23) with all_0_3_3, xp, xn and discharging atoms sdtlseqdt0(xn, xp) = all_0_3_3, yields:
% 25.91/7.21 | (84) all_0_3_3 = 0 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, xn) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xp = xn))))
% 25.91/7.21 |
% 25.91/7.21 | Instantiating formula (29) with all_0_6_6, xp, xm, xn and discharging atoms doDivides0(xp, all_0_6_6) = 0, sdtasdt0(xn, xm) = all_0_6_6, yields:
% 25.91/7.21 | (85) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (isPrime0(xp) = v3 & doDivides0(xp, xm) = v8 & doDivides0(xp, xn) = v7 & iLess0(v5, all_0_7_7) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xn, xm) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v6 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 25.91/7.21 |
% 25.91/7.21 | Instantiating formula (71) with all_0_6_6, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_6_6, yields:
% 25.91/7.21 | (86) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_6_6))
% 25.91/7.21 |
% 25.91/7.21 | Instantiating formula (33) with all_0_6_6, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_6_6, yields:
% 25.91/7.21 | (87) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_6_6) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 25.91/7.21 |
% 25.91/7.21 | Instantiating formula (51) with all_0_7_7, xp, all_0_8_8 and discharging atoms sdtpldt0(all_0_8_8, xp) = all_0_7_7, yields:
% 25.91/7.21 | (88) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, all_0_8_8) = v2 & aNaturalNumber0(all_0_8_8) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_7_7))
% 25.91/7.21 |
% 25.91/7.21 | Instantiating formula (49) with all_0_7_7, xp, all_0_8_8 and discharging atoms sdtpldt0(all_0_8_8, xp) = all_0_7_7, yields:
% 25.91/7.21 | (89) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_7_7) = v2 & aNaturalNumber0(all_0_8_8) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 25.91/7.21 |
% 25.91/7.21 | Instantiating formula (48) with all_0_7_7, all_0_8_8, xp, xm, xn and discharging atoms sdtpldt0(all_0_8_8, xp) = all_0_7_7, sdtpldt0(xn, xm) = all_0_8_8, yields:
% 25.91/7.21 | (90) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xm, xp) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_7_7))
% 25.91/7.21 |
% 25.91/7.21 | Instantiating formula (51) with all_0_8_8, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_8_8, yields:
% 25.91/7.21 | (91) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_8_8))
% 25.91/7.21 |
% 25.91/7.21 | Instantiating formula (49) with all_0_8_8, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_8_8, yields:
% 25.91/7.21 | (92) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_8_8) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 25.91/7.21 |
% 25.91/7.21 | Instantiating (92) with all_12_0_9, all_12_1_10, all_12_2_11 yields:
% 25.91/7.21 | (93) aNaturalNumber0(all_0_8_8) = all_12_0_9 & aNaturalNumber0(xm) = all_12_1_10 & aNaturalNumber0(xn) = all_12_2_11 & ( ~ (all_12_1_10 = 0) | ~ (all_12_2_11 = 0) | all_12_0_9 = 0)
% 25.91/7.21 |
% 25.91/7.21 | Applying alpha-rule on (93) yields:
% 25.91/7.21 | (94) aNaturalNumber0(all_0_8_8) = all_12_0_9
% 25.91/7.21 | (95) aNaturalNumber0(xm) = all_12_1_10
% 25.91/7.21 | (96) aNaturalNumber0(xn) = all_12_2_11
% 25.91/7.21 | (97) ~ (all_12_1_10 = 0) | ~ (all_12_2_11 = 0) | all_12_0_9 = 0
% 25.91/7.21 |
% 25.91/7.21 | Instantiating (90) with all_14_0_12, all_14_1_13, all_14_2_14, all_14_3_15, all_14_4_16 yields:
% 25.91/7.21 | (98) sdtpldt0(xm, xp) = all_14_1_13 & sdtpldt0(xn, all_14_1_13) = all_14_0_12 & aNaturalNumber0(xp) = all_14_2_14 & aNaturalNumber0(xm) = all_14_3_15 & aNaturalNumber0(xn) = all_14_4_16 & ( ~ (all_14_2_14 = 0) | ~ (all_14_3_15 = 0) | ~ (all_14_4_16 = 0) | all_14_0_12 = all_0_7_7)
% 25.91/7.21 |
% 25.91/7.21 | Applying alpha-rule on (98) yields:
% 25.91/7.21 | (99) aNaturalNumber0(xn) = all_14_4_16
% 25.91/7.21 | (100) ~ (all_14_2_14 = 0) | ~ (all_14_3_15 = 0) | ~ (all_14_4_16 = 0) | all_14_0_12 = all_0_7_7
% 25.91/7.21 | (101) sdtpldt0(xn, all_14_1_13) = all_14_0_12
% 25.91/7.21 | (102) aNaturalNumber0(xm) = all_14_3_15
% 25.91/7.21 | (103) sdtpldt0(xm, xp) = all_14_1_13
% 25.91/7.21 | (104) aNaturalNumber0(xp) = all_14_2_14
% 25.91/7.21 |
% 25.91/7.21 | Instantiating (89) with all_16_0_17, all_16_1_18, all_16_2_19 yields:
% 25.91/7.21 | (105) aNaturalNumber0(all_0_7_7) = all_16_0_17 & aNaturalNumber0(all_0_8_8) = all_16_2_19 & aNaturalNumber0(xp) = all_16_1_18 & ( ~ (all_16_1_18 = 0) | ~ (all_16_2_19 = 0) | all_16_0_17 = 0)
% 25.91/7.21 |
% 25.91/7.21 | Applying alpha-rule on (105) yields:
% 25.91/7.21 | (106) aNaturalNumber0(all_0_7_7) = all_16_0_17
% 25.91/7.21 | (107) aNaturalNumber0(all_0_8_8) = all_16_2_19
% 25.91/7.21 | (108) aNaturalNumber0(xp) = all_16_1_18
% 25.91/7.21 | (109) ~ (all_16_1_18 = 0) | ~ (all_16_2_19 = 0) | all_16_0_17 = 0
% 25.91/7.21 |
% 25.91/7.21 | Instantiating (88) with all_18_0_20, all_18_1_21, all_18_2_22 yields:
% 25.91/7.21 | (110) sdtpldt0(xp, all_0_8_8) = all_18_0_20 & aNaturalNumber0(all_0_8_8) = all_18_2_22 & aNaturalNumber0(xp) = all_18_1_21 & ( ~ (all_18_1_21 = 0) | ~ (all_18_2_22 = 0) | all_18_0_20 = all_0_7_7)
% 25.91/7.21 |
% 25.91/7.21 | Applying alpha-rule on (110) yields:
% 25.91/7.21 | (111) sdtpldt0(xp, all_0_8_8) = all_18_0_20
% 25.91/7.21 | (112) aNaturalNumber0(all_0_8_8) = all_18_2_22
% 25.91/7.21 | (113) aNaturalNumber0(xp) = all_18_1_21
% 25.91/7.21 | (114) ~ (all_18_1_21 = 0) | ~ (all_18_2_22 = 0) | all_18_0_20 = all_0_7_7
% 25.91/7.21 |
% 25.91/7.21 | Instantiating (91) with all_20_0_23, all_20_1_24, all_20_2_25 yields:
% 25.91/7.21 | (115) sdtpldt0(xm, xn) = all_20_0_23 & aNaturalNumber0(xm) = all_20_1_24 & aNaturalNumber0(xn) = all_20_2_25 & ( ~ (all_20_1_24 = 0) | ~ (all_20_2_25 = 0) | all_20_0_23 = all_0_8_8)
% 25.91/7.21 |
% 25.91/7.21 | Applying alpha-rule on (115) yields:
% 25.91/7.21 | (116) sdtpldt0(xm, xn) = all_20_0_23
% 25.91/7.21 | (117) aNaturalNumber0(xm) = all_20_1_24
% 25.91/7.21 | (118) aNaturalNumber0(xn) = all_20_2_25
% 25.91/7.21 | (119) ~ (all_20_1_24 = 0) | ~ (all_20_2_25 = 0) | all_20_0_23 = all_0_8_8
% 25.91/7.21 |
% 25.91/7.21 | Instantiating (87) with all_22_0_26, all_22_1_27, all_22_2_28 yields:
% 25.91/7.21 | (120) aNaturalNumber0(all_0_6_6) = all_22_0_26 & aNaturalNumber0(xm) = all_22_1_27 & aNaturalNumber0(xn) = all_22_2_28 & ( ~ (all_22_1_27 = 0) | ~ (all_22_2_28 = 0) | all_22_0_26 = 0)
% 25.91/7.21 |
% 25.91/7.21 | Applying alpha-rule on (120) yields:
% 25.91/7.21 | (121) aNaturalNumber0(all_0_6_6) = all_22_0_26
% 25.91/7.21 | (122) aNaturalNumber0(xm) = all_22_1_27
% 25.91/7.21 | (123) aNaturalNumber0(xn) = all_22_2_28
% 25.91/7.21 | (124) ~ (all_22_1_27 = 0) | ~ (all_22_2_28 = 0) | all_22_0_26 = 0
% 25.91/7.21 |
% 25.91/7.21 | Instantiating (86) with all_24_0_29, all_24_1_30, all_24_2_31 yields:
% 25.91/7.21 | (125) sdtasdt0(xm, xn) = all_24_0_29 & aNaturalNumber0(xm) = all_24_1_30 & aNaturalNumber0(xn) = all_24_2_31 & ( ~ (all_24_1_30 = 0) | ~ (all_24_2_31 = 0) | all_24_0_29 = all_0_6_6)
% 25.91/7.21 |
% 25.91/7.21 | Applying alpha-rule on (125) yields:
% 25.91/7.21 | (126) sdtasdt0(xm, xn) = all_24_0_29
% 25.91/7.21 | (127) aNaturalNumber0(xm) = all_24_1_30
% 25.91/7.21 | (128) aNaturalNumber0(xn) = all_24_2_31
% 25.91/7.21 | (129) ~ (all_24_1_30 = 0) | ~ (all_24_2_31 = 0) | all_24_0_29 = all_0_6_6
% 25.91/7.21 |
% 25.91/7.21 | Instantiating (85) with all_26_0_32, all_26_1_33, all_26_2_34, all_26_3_35, all_26_4_36, all_26_5_37, all_26_6_38, all_26_7_39, all_26_8_40 yields:
% 25.91/7.21 | (130) isPrime0(xp) = all_26_5_37 & doDivides0(xp, xm) = all_26_0_32 & doDivides0(xp, xn) = all_26_1_33 & iLess0(all_26_3_35, all_0_7_7) = all_26_2_34 & sdtpldt0(all_26_4_36, xp) = all_26_3_35 & sdtpldt0(xn, xm) = all_26_4_36 & aNaturalNumber0(xp) = all_26_6_38 & aNaturalNumber0(xm) = all_26_7_39 & aNaturalNumber0(xn) = all_26_8_40 & ( ~ (all_26_2_34 = 0) | ~ (all_26_5_37 = 0) | ~ (all_26_6_38 = 0) | ~ (all_26_7_39 = 0) | ~ (all_26_8_40 = 0) | all_26_0_32 = 0 | all_26_1_33 = 0)
% 25.91/7.21 |
% 25.91/7.21 | Applying alpha-rule on (130) yields:
% 25.91/7.21 | (131) iLess0(all_26_3_35, all_0_7_7) = all_26_2_34
% 25.91/7.21 | (132) aNaturalNumber0(xp) = all_26_6_38
% 25.91/7.21 | (133) doDivides0(xp, xn) = all_26_1_33
% 25.91/7.21 | (134) doDivides0(xp, xm) = all_26_0_32
% 25.91/7.21 | (135) aNaturalNumber0(xn) = all_26_8_40
% 25.91/7.21 | (136) sdtpldt0(all_26_4_36, xp) = all_26_3_35
% 25.91/7.21 | (137) aNaturalNumber0(xm) = all_26_7_39
% 25.91/7.21 | (138) ~ (all_26_2_34 = 0) | ~ (all_26_5_37 = 0) | ~ (all_26_6_38 = 0) | ~ (all_26_7_39 = 0) | ~ (all_26_8_40 = 0) | all_26_0_32 = 0 | all_26_1_33 = 0
% 25.91/7.21 | (139) sdtpldt0(xn, xm) = all_26_4_36
% 25.91/7.21 | (140) isPrime0(xp) = all_26_5_37
% 25.91/7.21 |
% 25.91/7.21 +-Applying beta-rule and splitting (78), into two cases.
% 25.91/7.21 |-Branch one:
% 25.91/7.21 | (141) all_0_0_0 = 0
% 25.91/7.21 |
% 25.91/7.21 | Equations (141) can reduce 8 to:
% 25.91/7.21 | (142) $false
% 25.91/7.21 |
% 25.91/7.21 |-The branch is then unsatisfiable
% 25.91/7.21 |-Branch two:
% 25.91/7.21 | (8) ~ (all_0_0_0 = 0)
% 25.91/7.21 | (144) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_6_6, xm) = v3 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 25.91/7.21 |
% 25.91/7.21 | Instantiating (144) with all_33_0_44, all_33_1_45, all_33_2_46, all_33_3_47 yields:
% 25.91/7.21 | (145) doDivides0(all_0_6_6, xm) = all_33_0_44 & aNaturalNumber0(all_0_6_6) = all_33_2_46 & aNaturalNumber0(xp) = all_33_3_47 & aNaturalNumber0(xm) = all_33_1_45 & ( ~ (all_33_0_44 = 0) | ~ (all_33_1_45 = 0) | ~ (all_33_2_46 = 0) | ~ (all_33_3_47 = 0))
% 25.91/7.21 |
% 25.91/7.21 | Applying alpha-rule on (145) yields:
% 25.91/7.21 | (146) ~ (all_33_0_44 = 0) | ~ (all_33_1_45 = 0) | ~ (all_33_2_46 = 0) | ~ (all_33_3_47 = 0)
% 25.91/7.21 | (147) doDivides0(all_0_6_6, xm) = all_33_0_44
% 25.91/7.21 | (148) aNaturalNumber0(all_0_6_6) = all_33_2_46
% 25.91/7.21 | (149) aNaturalNumber0(xm) = all_33_1_45
% 25.91/7.21 | (150) aNaturalNumber0(xp) = all_33_3_47
% 25.91/7.21 |
% 25.91/7.21 +-Applying beta-rule and splitting (79), into two cases.
% 25.91/7.21 |-Branch one:
% 25.91/7.21 | (151) all_0_1_1 = 0
% 25.91/7.21 |
% 25.91/7.21 | Equations (151) can reduce 7 to:
% 25.91/7.21 | (142) $false
% 25.91/7.21 |
% 25.91/7.21 |-The branch is then unsatisfiable
% 25.91/7.21 |-Branch two:
% 25.91/7.21 | (7) ~ (all_0_1_1 = 0)
% 25.91/7.21 | (154) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_6_6, xn) = v3 & aNaturalNumber0(all_0_6_6) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 25.91/7.21 |
% 25.91/7.21 | Instantiating (154) with all_38_0_48, all_38_1_49, all_38_2_50, all_38_3_51 yields:
% 25.91/7.21 | (155) doDivides0(all_0_6_6, xn) = all_38_0_48 & aNaturalNumber0(all_0_6_6) = all_38_2_50 & aNaturalNumber0(xp) = all_38_3_51 & aNaturalNumber0(xn) = all_38_1_49 & ( ~ (all_38_0_48 = 0) | ~ (all_38_1_49 = 0) | ~ (all_38_2_50 = 0) | ~ (all_38_3_51 = 0))
% 25.91/7.21 |
% 25.91/7.21 | Applying alpha-rule on (155) yields:
% 25.91/7.21 | (156) ~ (all_38_0_48 = 0) | ~ (all_38_1_49 = 0) | ~ (all_38_2_50 = 0) | ~ (all_38_3_51 = 0)
% 25.91/7.21 | (157) doDivides0(all_0_6_6, xn) = all_38_0_48
% 25.91/7.21 | (158) aNaturalNumber0(all_0_6_6) = all_38_2_50
% 25.91/7.21 | (159) aNaturalNumber0(xn) = all_38_1_49
% 25.91/7.21 | (160) aNaturalNumber0(xp) = all_38_3_51
% 25.91/7.21 |
% 25.91/7.21 | Instantiating formula (19) with xp, all_33_3_47, all_38_3_51 and discharging atoms aNaturalNumber0(xp) = all_38_3_51, aNaturalNumber0(xp) = all_33_3_47, yields:
% 25.91/7.21 | (161) all_38_3_51 = all_33_3_47
% 25.91/7.21 |
% 25.91/7.21 | Instantiating formula (19) with xp, all_26_6_38, all_33_3_47 and discharging atoms aNaturalNumber0(xp) = all_33_3_47, aNaturalNumber0(xp) = all_26_6_38, yields:
% 25.91/7.22 | (162) all_33_3_47 = all_26_6_38
% 25.91/7.22 |
% 25.91/7.22 | Instantiating formula (19) with xp, all_18_1_21, all_26_6_38 and discharging atoms aNaturalNumber0(xp) = all_26_6_38, aNaturalNumber0(xp) = all_18_1_21, yields:
% 25.91/7.22 | (163) all_26_6_38 = all_18_1_21
% 25.91/7.22 |
% 25.91/7.22 | Instantiating formula (19) with xp, all_16_1_18, 0 and discharging atoms aNaturalNumber0(xp) = all_16_1_18, aNaturalNumber0(xp) = 0, yields:
% 25.91/7.22 | (164) all_16_1_18 = 0
% 25.91/7.22 |
% 25.91/7.22 | Instantiating formula (19) with xp, all_16_1_18, all_18_1_21 and discharging atoms aNaturalNumber0(xp) = all_18_1_21, aNaturalNumber0(xp) = all_16_1_18, yields:
% 25.91/7.22 | (165) all_18_1_21 = all_16_1_18
% 25.91/7.22 |
% 26.47/7.22 | Instantiating formula (19) with xp, all_14_2_14, all_38_3_51 and discharging atoms aNaturalNumber0(xp) = all_38_3_51, aNaturalNumber0(xp) = all_14_2_14, yields:
% 26.47/7.22 | (166) all_38_3_51 = all_14_2_14
% 26.47/7.22 |
% 26.47/7.22 | Instantiating formula (19) with xm, all_26_7_39, 0 and discharging atoms aNaturalNumber0(xm) = all_26_7_39, aNaturalNumber0(xm) = 0, yields:
% 26.47/7.22 | (167) all_26_7_39 = 0
% 26.47/7.22 |
% 26.47/7.22 | Instantiating formula (19) with xm, all_26_7_39, all_33_1_45 and discharging atoms aNaturalNumber0(xm) = all_33_1_45, aNaturalNumber0(xm) = all_26_7_39, yields:
% 26.47/7.22 | (168) all_33_1_45 = all_26_7_39
% 26.47/7.22 |
% 26.47/7.22 | Instantiating formula (19) with xm, all_24_1_30, all_33_1_45 and discharging atoms aNaturalNumber0(xm) = all_33_1_45, aNaturalNumber0(xm) = all_24_1_30, yields:
% 26.47/7.22 | (169) all_33_1_45 = all_24_1_30
% 26.47/7.22 |
% 26.47/7.22 | Instantiating formula (19) with xm, all_20_1_24, all_33_1_45 and discharging atoms aNaturalNumber0(xm) = all_33_1_45, aNaturalNumber0(xm) = all_20_1_24, yields:
% 26.47/7.22 | (170) all_33_1_45 = all_20_1_24
% 26.47/7.22 |
% 26.47/7.22 | Instantiating formula (19) with xm, all_14_3_15, all_22_1_27 and discharging atoms aNaturalNumber0(xm) = all_22_1_27, aNaturalNumber0(xm) = all_14_3_15, yields:
% 26.47/7.22 | (171) all_22_1_27 = all_14_3_15
% 26.47/7.22 |
% 26.47/7.22 | Instantiating formula (19) with xm, all_14_3_15, all_20_1_24 and discharging atoms aNaturalNumber0(xm) = all_20_1_24, aNaturalNumber0(xm) = all_14_3_15, yields:
% 26.47/7.22 | (172) all_20_1_24 = all_14_3_15
% 26.47/7.22 |
% 26.47/7.22 | Instantiating formula (19) with xm, all_12_1_10, all_22_1_27 and discharging atoms aNaturalNumber0(xm) = all_22_1_27, aNaturalNumber0(xm) = all_12_1_10, yields:
% 26.47/7.22 | (173) all_22_1_27 = all_12_1_10
% 26.47/7.22 |
% 26.47/7.22 | Instantiating formula (19) with xn, all_24_2_31, 0 and discharging atoms aNaturalNumber0(xn) = all_24_2_31, aNaturalNumber0(xn) = 0, yields:
% 26.47/7.22 | (174) all_24_2_31 = 0
% 26.47/7.22 |
% 26.47/7.22 | Instantiating formula (19) with xn, all_22_2_28, all_24_2_31 and discharging atoms aNaturalNumber0(xn) = all_24_2_31, aNaturalNumber0(xn) = all_22_2_28, yields:
% 26.47/7.22 | (175) all_24_2_31 = all_22_2_28
% 26.47/7.22 |
% 26.47/7.22 | Instantiating formula (19) with xn, all_20_2_25, all_38_1_49 and discharging atoms aNaturalNumber0(xn) = all_38_1_49, aNaturalNumber0(xn) = all_20_2_25, yields:
% 26.47/7.22 | (176) all_38_1_49 = all_20_2_25
% 26.47/7.22 |
% 26.47/7.22 | Instantiating formula (19) with xn, all_20_2_25, all_26_8_40 and discharging atoms aNaturalNumber0(xn) = all_26_8_40, aNaturalNumber0(xn) = all_20_2_25, yields:
% 26.47/7.22 | (177) all_26_8_40 = all_20_2_25
% 26.47/7.22 |
% 26.47/7.22 | Instantiating formula (19) with xn, all_20_2_25, all_22_2_28 and discharging atoms aNaturalNumber0(xn) = all_22_2_28, aNaturalNumber0(xn) = all_20_2_25, yields:
% 26.47/7.22 | (178) all_22_2_28 = all_20_2_25
% 26.47/7.22 |
% 26.47/7.22 | Instantiating formula (19) with xn, all_14_4_16, all_26_8_40 and discharging atoms aNaturalNumber0(xn) = all_26_8_40, aNaturalNumber0(xn) = all_14_4_16, yields:
% 26.47/7.22 | (179) all_26_8_40 = all_14_4_16
% 26.47/7.22 |
% 26.47/7.22 | Instantiating formula (19) with xn, all_12_2_11, all_38_1_49 and discharging atoms aNaturalNumber0(xn) = all_38_1_49, aNaturalNumber0(xn) = all_12_2_11, yields:
% 26.47/7.22 | (180) all_38_1_49 = all_12_2_11
% 26.47/7.22 |
% 26.47/7.22 | Combining equations (176,180) yields a new equation:
% 26.47/7.22 | (181) all_20_2_25 = all_12_2_11
% 26.47/7.22 |
% 26.47/7.22 | Simplifying 181 yields:
% 26.47/7.22 | (182) all_20_2_25 = all_12_2_11
% 26.47/7.22 |
% 26.47/7.22 | Combining equations (161,166) yields a new equation:
% 26.47/7.22 | (183) all_33_3_47 = all_14_2_14
% 26.47/7.22 |
% 26.47/7.22 | Simplifying 183 yields:
% 26.47/7.22 | (184) all_33_3_47 = all_14_2_14
% 26.47/7.22 |
% 26.47/7.22 | Combining equations (168,169) yields a new equation:
% 26.47/7.22 | (185) all_26_7_39 = all_24_1_30
% 26.47/7.22 |
% 26.47/7.22 | Simplifying 185 yields:
% 26.47/7.22 | (186) all_26_7_39 = all_24_1_30
% 26.47/7.22 |
% 26.47/7.22 | Combining equations (170,169) yields a new equation:
% 26.47/7.22 | (187) all_24_1_30 = all_20_1_24
% 26.47/7.22 |
% 26.47/7.22 | Combining equations (162,184) yields a new equation:
% 26.47/7.22 | (188) all_26_6_38 = all_14_2_14
% 26.47/7.22 |
% 26.47/7.22 | Simplifying 188 yields:
% 26.47/7.22 | (189) all_26_6_38 = all_14_2_14
% 26.47/7.22 |
% 26.47/7.22 | Combining equations (163,189) yields a new equation:
% 26.47/7.22 | (190) all_18_1_21 = all_14_2_14
% 26.47/7.22 |
% 26.47/7.22 | Simplifying 190 yields:
% 26.47/7.22 | (191) all_18_1_21 = all_14_2_14
% 26.47/7.22 |
% 26.47/7.22 | Combining equations (186,167) yields a new equation:
% 26.47/7.22 | (192) all_24_1_30 = 0
% 26.47/7.22 |
% 26.47/7.22 | Simplifying 192 yields:
% 26.47/7.22 | (193) all_24_1_30 = 0
% 26.47/7.22 |
% 26.47/7.22 | Combining equations (177,179) yields a new equation:
% 26.47/7.22 | (194) all_20_2_25 = all_14_4_16
% 26.47/7.22 |
% 26.47/7.22 | Simplifying 194 yields:
% 26.47/7.22 | (195) all_20_2_25 = all_14_4_16
% 26.47/7.22 |
% 26.47/7.22 | Combining equations (187,193) yields a new equation:
% 26.47/7.22 | (196) all_20_1_24 = 0
% 26.47/7.22 |
% 26.47/7.22 | Simplifying 196 yields:
% 26.47/7.22 | (197) all_20_1_24 = 0
% 26.47/7.22 |
% 26.47/7.22 | Combining equations (175,174) yields a new equation:
% 26.47/7.22 | (198) all_22_2_28 = 0
% 26.47/7.22 |
% 26.47/7.22 | Simplifying 198 yields:
% 26.47/7.22 | (199) all_22_2_28 = 0
% 26.47/7.22 |
% 26.47/7.22 | Combining equations (171,173) yields a new equation:
% 26.47/7.22 | (200) all_14_3_15 = all_12_1_10
% 26.47/7.22 |
% 26.47/7.22 | Simplifying 200 yields:
% 26.47/7.22 | (201) all_14_3_15 = all_12_1_10
% 26.47/7.22 |
% 26.47/7.22 | Combining equations (178,199) yields a new equation:
% 26.47/7.22 | (202) all_20_2_25 = 0
% 26.47/7.22 |
% 26.47/7.22 | Simplifying 202 yields:
% 26.47/7.22 | (203) all_20_2_25 = 0
% 26.47/7.22 |
% 26.47/7.22 | Combining equations (172,197) yields a new equation:
% 26.47/7.22 | (204) all_14_3_15 = 0
% 26.47/7.22 |
% 26.47/7.22 | Simplifying 204 yields:
% 26.47/7.22 | (205) all_14_3_15 = 0
% 26.47/7.22 |
% 26.47/7.22 | Combining equations (182,195) yields a new equation:
% 26.47/7.22 | (206) all_14_4_16 = all_12_2_11
% 26.47/7.22 |
% 26.47/7.22 | Combining equations (203,195) yields a new equation:
% 26.47/7.22 | (207) all_14_4_16 = 0
% 26.47/7.22 |
% 26.47/7.22 | Combining equations (165,191) yields a new equation:
% 26.47/7.22 | (208) all_16_1_18 = all_14_2_14
% 26.47/7.22 |
% 26.47/7.22 | Simplifying 208 yields:
% 26.47/7.22 | (209) all_16_1_18 = all_14_2_14
% 26.47/7.22 |
% 26.47/7.22 | Combining equations (164,209) yields a new equation:
% 26.47/7.22 | (210) all_14_2_14 = 0
% 26.47/7.22 |
% 26.47/7.22 | Combining equations (201,205) yields a new equation:
% 26.47/7.22 | (211) all_12_1_10 = 0
% 26.47/7.22 |
% 26.47/7.22 | Simplifying 211 yields:
% 26.47/7.22 | (212) all_12_1_10 = 0
% 26.47/7.22 |
% 26.47/7.22 | Combining equations (207,206) yields a new equation:
% 26.47/7.22 | (213) all_12_2_11 = 0
% 26.47/7.22 |
% 26.47/7.22 | From (210) and (104) follows:
% 26.47/7.22 | (9) aNaturalNumber0(xp) = 0
% 26.47/7.22 |
% 26.47/7.22 | From (212) and (95) follows:
% 26.47/7.22 | (36) aNaturalNumber0(xm) = 0
% 26.47/7.22 |
% 26.47/7.22 | From (213) and (96) follows:
% 26.47/7.22 | (14) aNaturalNumber0(xn) = 0
% 26.47/7.22 |
% 26.47/7.22 +-Applying beta-rule and splitting (82), into two cases.
% 26.47/7.22 |-Branch one:
% 26.47/7.22 | (217) all_0_5_5 = 0
% 26.47/7.22 |
% 26.47/7.22 | Equations (217) can reduce 20 to:
% 26.47/7.22 | (142) $false
% 26.47/7.22 |
% 26.47/7.22 |-The branch is then unsatisfiable
% 26.47/7.22 |-Branch two:
% 26.47/7.22 | (20) ~ (all_0_5_5 = 0)
% 26.47/7.22 | (220) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xn, xp) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xp = xn))))
% 26.47/7.22 |
% 26.47/7.22 | Instantiating (220) with all_57_0_53, all_57_1_54, all_57_2_55 yields:
% 26.47/7.22 | (221) sdtlseqdt0(xn, xp) = all_57_0_53 & aNaturalNumber0(xp) = all_57_2_55 & aNaturalNumber0(xn) = all_57_1_54 & ( ~ (all_57_1_54 = 0) | ~ (all_57_2_55 = 0) | (all_57_0_53 = 0 & ~ (xp = xn)))
% 26.47/7.22 |
% 26.47/7.22 | Applying alpha-rule on (221) yields:
% 26.47/7.22 | (222) sdtlseqdt0(xn, xp) = all_57_0_53
% 26.47/7.22 | (223) aNaturalNumber0(xp) = all_57_2_55
% 26.47/7.22 | (224) aNaturalNumber0(xn) = all_57_1_54
% 26.47/7.22 | (225) ~ (all_57_1_54 = 0) | ~ (all_57_2_55 = 0) | (all_57_0_53 = 0 & ~ (xp = xn))
% 26.47/7.22 |
% 26.47/7.22 +-Applying beta-rule and splitting (80), into two cases.
% 26.47/7.22 |-Branch one:
% 26.47/7.22 | (226) ~ (sdtlseqdt0(xm, xm) = all_0_4_4)
% 26.47/7.23 |
% 26.47/7.23 | Instantiating formula (16) with xn, xp, all_57_0_53, all_0_3_3 and discharging atoms sdtlseqdt0(xn, xp) = all_57_0_53, sdtlseqdt0(xn, xp) = all_0_3_3, yields:
% 26.47/7.23 | (227) all_57_0_53 = all_0_3_3
% 26.47/7.23 |
% 26.47/7.23 | Instantiating formula (19) with xp, all_57_2_55, 0 and discharging atoms aNaturalNumber0(xp) = all_57_2_55, aNaturalNumber0(xp) = 0, yields:
% 26.47/7.23 | (228) all_57_2_55 = 0
% 26.47/7.23 |
% 26.47/7.23 | Instantiating formula (19) with xn, all_57_1_54, 0 and discharging atoms aNaturalNumber0(xn) = all_57_1_54, aNaturalNumber0(xn) = 0, yields:
% 26.47/7.23 | (229) all_57_1_54 = 0
% 26.47/7.23 |
% 26.47/7.23 | Using (2) and (226) yields:
% 26.47/7.23 | (230) ~ (xp = xm)
% 26.47/7.23 |
% 26.47/7.23 | From (228) and (223) follows:
% 26.47/7.23 | (9) aNaturalNumber0(xp) = 0
% 26.47/7.23 |
% 26.47/7.23 +-Applying beta-rule and splitting (83), into two cases.
% 26.47/7.23 |-Branch one:
% 26.47/7.23 | (232) all_0_2_2 = 0
% 26.47/7.23 |
% 26.47/7.23 +-Applying beta-rule and splitting (225), into two cases.
% 26.47/7.23 |-Branch one:
% 26.47/7.23 | (233) ~ (all_57_1_54 = 0)
% 26.47/7.23 |
% 26.47/7.23 | Equations (229) can reduce 233 to:
% 26.47/7.23 | (142) $false
% 26.47/7.23 |
% 26.47/7.23 |-The branch is then unsatisfiable
% 26.47/7.23 |-Branch two:
% 26.47/7.23 | (229) all_57_1_54 = 0
% 26.47/7.23 | (236) ~ (all_57_2_55 = 0) | (all_57_0_53 = 0 & ~ (xp = xn))
% 26.47/7.23 |
% 26.47/7.23 +-Applying beta-rule and splitting (84), into two cases.
% 26.47/7.23 |-Branch one:
% 26.47/7.23 | (237) all_0_3_3 = 0
% 26.47/7.23 |
% 26.47/7.23 +-Applying beta-rule and splitting (236), into two cases.
% 26.47/7.23 |-Branch one:
% 26.47/7.23 | (238) ~ (all_57_2_55 = 0)
% 26.47/7.23 |
% 26.47/7.23 | Equations (228) can reduce 238 to:
% 26.47/7.23 | (142) $false
% 26.47/7.23 |
% 26.47/7.23 |-The branch is then unsatisfiable
% 26.47/7.23 |-Branch two:
% 26.47/7.23 | (228) all_57_2_55 = 0
% 26.47/7.23 | (241) all_57_0_53 = 0 & ~ (xp = xn)
% 26.47/7.23 |
% 26.47/7.23 | Applying alpha-rule on (241) yields:
% 26.47/7.23 | (242) all_57_0_53 = 0
% 26.47/7.23 | (243) ~ (xp = xn)
% 26.47/7.23 |
% 26.47/7.23 +-Applying beta-rule and splitting (6), into two cases.
% 26.47/7.23 |-Branch one:
% 26.47/7.23 | (244) ~ (all_0_2_2 = 0)
% 26.47/7.23 |
% 26.47/7.23 | Equations (232) can reduce 244 to:
% 26.47/7.23 | (142) $false
% 26.47/7.23 |
% 26.47/7.23 |-The branch is then unsatisfiable
% 26.47/7.23 |-Branch two:
% 26.47/7.23 | (232) all_0_2_2 = 0
% 26.47/7.23 | (247) ~ (all_0_3_3 = 0) | xp = xm | xp = xn
% 26.47/7.23 |
% 26.47/7.23 +-Applying beta-rule and splitting (247), into two cases.
% 26.47/7.23 |-Branch one:
% 26.47/7.23 | (248) ~ (all_0_3_3 = 0)
% 26.47/7.23 |
% 26.47/7.23 | Equations (237) can reduce 248 to:
% 26.47/7.23 | (142) $false
% 26.47/7.23 |
% 26.47/7.23 |-The branch is then unsatisfiable
% 26.47/7.23 |-Branch two:
% 26.47/7.23 | (237) all_0_3_3 = 0
% 26.47/7.23 | (251) xp = xm | xp = xn
% 26.47/7.23 |
% 26.47/7.23 +-Applying beta-rule and splitting (251), into two cases.
% 26.47/7.23 |-Branch one:
% 26.47/7.23 | (252) xp = xm
% 26.47/7.23 |
% 26.47/7.23 | Equations (252) can reduce 230 to:
% 26.47/7.23 | (142) $false
% 26.47/7.23 |
% 26.47/7.23 |-The branch is then unsatisfiable
% 26.47/7.23 |-Branch two:
% 26.47/7.23 | (230) ~ (xp = xm)
% 26.47/7.23 | (255) xp = xn
% 26.47/7.23 |
% 26.47/7.23 | Equations (255) can reduce 243 to:
% 26.47/7.23 | (142) $false
% 26.47/7.23 |
% 26.47/7.23 |-The branch is then unsatisfiable
% 26.47/7.23 |-Branch two:
% 26.47/7.23 | (248) ~ (all_0_3_3 = 0)
% 26.47/7.23 | (258) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, xn) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xp = xn))))
% 26.47/7.23 |
% 26.47/7.23 +-Applying beta-rule and splitting (236), into two cases.
% 26.47/7.23 |-Branch one:
% 26.47/7.23 | (238) ~ (all_57_2_55 = 0)
% 26.47/7.23 |
% 26.47/7.23 | Equations (228) can reduce 238 to:
% 26.47/7.23 | (142) $false
% 26.47/7.23 |
% 26.47/7.23 |-The branch is then unsatisfiable
% 26.47/7.23 |-Branch two:
% 26.47/7.23 | (228) all_57_2_55 = 0
% 26.47/7.23 | (241) all_57_0_53 = 0 & ~ (xp = xn)
% 26.47/7.23 |
% 26.47/7.23 | Applying alpha-rule on (241) yields:
% 26.47/7.23 | (242) all_57_0_53 = 0
% 26.47/7.23 | (243) ~ (xp = xn)
% 26.47/7.23 |
% 26.47/7.23 | Combining equations (242,227) yields a new equation:
% 26.47/7.23 | (237) all_0_3_3 = 0
% 26.47/7.23 |
% 26.47/7.23 | Equations (237) can reduce 248 to:
% 26.47/7.23 | (142) $false
% 26.47/7.23 |
% 26.47/7.23 |-The branch is then unsatisfiable
% 26.47/7.23 |-Branch two:
% 26.47/7.23 | (244) ~ (all_0_2_2 = 0)
% 26.47/7.23 | (268) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xp, xm) = v2 & aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xp = xm))))
% 26.47/7.23 |
% 26.47/7.23 | Instantiating (268) with all_151_0_65, all_151_1_66, all_151_2_67 yields:
% 26.47/7.23 | (269) sdtlseqdt0(xp, xm) = all_151_0_65 & aNaturalNumber0(xp) = all_151_1_66 & aNaturalNumber0(xm) = all_151_2_67 & ( ~ (all_151_1_66 = 0) | ~ (all_151_2_67 = 0) | (all_151_0_65 = 0 & ~ (xp = xm)))
% 26.47/7.23 |
% 26.47/7.23 | Applying alpha-rule on (269) yields:
% 26.47/7.23 | (270) sdtlseqdt0(xp, xm) = all_151_0_65
% 26.47/7.23 | (271) aNaturalNumber0(xp) = all_151_1_66
% 26.47/7.23 | (272) aNaturalNumber0(xm) = all_151_2_67
% 26.47/7.23 | (273) ~ (all_151_1_66 = 0) | ~ (all_151_2_67 = 0) | (all_151_0_65 = 0 & ~ (xp = xm))
% 26.47/7.23 |
% 26.47/7.23 | Instantiating formula (16) with xp, xm, all_151_0_65, all_0_4_4 and discharging atoms sdtlseqdt0(xp, xm) = all_151_0_65, sdtlseqdt0(xp, xm) = all_0_4_4, yields:
% 26.47/7.23 | (274) all_151_0_65 = all_0_4_4
% 26.47/7.23 |
% 26.47/7.23 | Instantiating formula (19) with xp, all_151_1_66, 0 and discharging atoms aNaturalNumber0(xp) = all_151_1_66, aNaturalNumber0(xp) = 0, yields:
% 26.47/7.23 | (275) all_151_1_66 = 0
% 26.47/7.23 |
% 26.47/7.23 | Instantiating formula (19) with xm, all_151_2_67, 0 and discharging atoms aNaturalNumber0(xm) = all_151_2_67, aNaturalNumber0(xm) = 0, yields:
% 26.47/7.23 | (276) all_151_2_67 = 0
% 26.47/7.23 |
% 26.47/7.23 +-Applying beta-rule and splitting (81), into two cases.
% 26.47/7.23 |-Branch one:
% 26.47/7.23 | (277) all_0_4_4 = 0
% 26.47/7.23 |
% 26.47/7.23 | Equations (277) can reduce 69 to:
% 26.47/7.23 | (142) $false
% 26.47/7.23 |
% 26.47/7.23 |-The branch is then unsatisfiable
% 26.47/7.23 |-Branch two:
% 26.47/7.23 | (69) ~ (all_0_4_4 = 0)
% 26.47/7.23 | (280) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xm, xp) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xp = xm))))
% 26.47/7.23 |
% 26.47/7.23 +-Applying beta-rule and splitting (273), into two cases.
% 26.47/7.23 |-Branch one:
% 26.47/7.23 | (281) ~ (all_151_1_66 = 0)
% 26.47/7.23 |
% 26.47/7.23 | Equations (275) can reduce 281 to:
% 26.47/7.23 | (142) $false
% 26.47/7.23 |
% 26.47/7.23 |-The branch is then unsatisfiable
% 26.47/7.23 |-Branch two:
% 26.47/7.23 | (275) all_151_1_66 = 0
% 26.47/7.23 | (284) ~ (all_151_2_67 = 0) | (all_151_0_65 = 0 & ~ (xp = xm))
% 26.47/7.23 |
% 26.47/7.23 +-Applying beta-rule and splitting (284), into two cases.
% 26.47/7.23 |-Branch one:
% 26.47/7.23 | (285) ~ (all_151_2_67 = 0)
% 26.47/7.23 |
% 26.47/7.23 | Equations (276) can reduce 285 to:
% 26.47/7.23 | (142) $false
% 26.47/7.23 |
% 26.47/7.23 |-The branch is then unsatisfiable
% 26.47/7.23 |-Branch two:
% 26.47/7.23 | (276) all_151_2_67 = 0
% 26.47/7.23 | (288) all_151_0_65 = 0 & ~ (xp = xm)
% 26.47/7.23 |
% 26.47/7.23 | Applying alpha-rule on (288) yields:
% 26.47/7.23 | (289) all_151_0_65 = 0
% 26.47/7.23 | (230) ~ (xp = xm)
% 26.47/7.23 |
% 26.47/7.23 | Combining equations (289,274) yields a new equation:
% 26.47/7.23 | (277) all_0_4_4 = 0
% 26.47/7.23 |
% 26.47/7.23 | Equations (277) can reduce 69 to:
% 26.47/7.23 | (142) $false
% 26.47/7.23 |
% 26.47/7.23 |-The branch is then unsatisfiable
% 26.47/7.23 |-Branch two:
% 26.47/7.23 | (293) sdtlseqdt0(xm, xm) = all_0_4_4
% 26.47/7.23 | (294) all_0_4_4 = 0 | ? [v0] : ( ~ (v0 = 0) & aNaturalNumber0(xm) = v0)
% 26.47/7.23 |
% 26.47/7.23 +-Applying beta-rule and splitting (294), into two cases.
% 26.47/7.23 |-Branch one:
% 26.47/7.23 | (277) all_0_4_4 = 0
% 26.47/7.23 |
% 26.47/7.23 | Equations (277) can reduce 69 to:
% 26.47/7.23 | (142) $false
% 26.47/7.23 |
% 26.47/7.23 |-The branch is then unsatisfiable
% 26.47/7.23 |-Branch two:
% 26.47/7.23 | (69) ~ (all_0_4_4 = 0)
% 26.47/7.23 | (298) ? [v0] : ( ~ (v0 = 0) & aNaturalNumber0(xm) = v0)
% 26.47/7.23 |
% 26.47/7.23 | Instantiating (298) with all_75_0_74 yields:
% 26.47/7.23 | (299) ~ (all_75_0_74 = 0) & aNaturalNumber0(xm) = all_75_0_74
% 26.47/7.23 |
% 26.47/7.23 | Applying alpha-rule on (299) yields:
% 26.47/7.23 | (300) ~ (all_75_0_74 = 0)
% 26.47/7.23 | (301) aNaturalNumber0(xm) = all_75_0_74
% 26.47/7.23 |
% 26.47/7.23 | Instantiating formula (19) with xm, all_75_0_74, 0 and discharging atoms aNaturalNumber0(xm) = all_75_0_74, aNaturalNumber0(xm) = 0, yields:
% 26.47/7.23 | (302) all_75_0_74 = 0
% 26.47/7.23 |
% 26.47/7.23 | Equations (302) can reduce 300 to:
% 26.47/7.23 | (142) $false
% 26.47/7.23 |
% 26.47/7.23 |-The branch is then unsatisfiable
% 26.47/7.23 % SZS output end Proof for theBenchmark
% 26.47/7.23
% 26.47/7.23 6625ms
%------------------------------------------------------------------------------