TSTP Solution File: NUM498+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM498+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n008.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 08:45:09 EDT 2022
% Result : Theorem 40.45s 12.91s
% Output : Proof 46.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM498+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jul 5 12:23:38 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.60/0.59 ____ _
% 0.60/0.59 ___ / __ \_____(_)___ ________ __________
% 0.60/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.60/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.60/0.59
% 0.60/0.59 A Theorem Prover for First-Order Logic
% 0.60/0.59 (ePrincess v.1.0)
% 0.60/0.59
% 0.60/0.59 (c) Philipp Rümmer, 2009-2015
% 0.60/0.59 (c) Peter Backeman, 2014-2015
% 0.60/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.60/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.60/0.59 Bug reports to peter@backeman.se
% 0.60/0.59
% 0.60/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.60/0.59
% 0.60/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.01/1.03 Prover 0: Preprocessing ...
% 4.07/1.60 Prover 0: Constructing countermodel ...
% 21.14/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 21.63/6.05 Prover 1: Preprocessing ...
% 22.49/6.22 Prover 1: Constructing countermodel ...
% 31.07/8.53 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 31.37/8.61 Prover 2: Preprocessing ...
% 31.97/8.81 Prover 2: Warning: ignoring some quantifiers
% 32.38/8.82 Prover 2: Constructing countermodel ...
% 37.57/11.54 Prover 0: stopped
% 37.74/11.74 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 38.02/11.81 Prover 3: Preprocessing ...
% 38.04/11.88 Prover 3: Constructing countermodel ...
% 40.45/12.90 Prover 3: proved (1159ms)
% 40.45/12.91 Prover 2: stopped
% 40.45/12.91 Prover 1: stopped
% 40.45/12.91
% 40.45/12.91 No countermodel exists, formula is valid
% 40.45/12.91 % SZS status Theorem for theBenchmark
% 40.45/12.91
% 40.45/12.91 Generating proof ... found it (size 107)
% 45.94/14.28
% 45.94/14.28 % SZS output start Proof for theBenchmark
% 45.94/14.28 Assumed formulas after preprocessing and simplification:
% 45.94/14.28 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (xp = xm) & ~ (xp = xn) & ~ (xp = sz10) & ~ (xp = sz00) & ~ (sz10 = sz00) & sdtsldt0(v2, xp) = xk & sdtasdt0(xp, v5) = v2 & sdtasdt0(xp, xk) = v2 & sdtasdt0(xn, xm) = v2 & sdtpldt0(v0, xp) = v1 & sdtpldt0(xm, v3) = xp & sdtpldt0(xn, v4) = xp & sdtpldt0(xn, xm) = v0 & isPrime0(xp) & doDivides0(xp, v2) & sdtlseqdt0(xm, xp) & sdtlseqdt0(xn, xp) & aNaturalNumber0(v5) & aNaturalNumber0(v4) & aNaturalNumber0(v3) & aNaturalNumber0(xk) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ isPrime0(sz10) & ~ isPrime0(sz00) & ~ doDivides0(xp, xm) & ~ doDivides0(xp, xn) & ~ sdtlseqdt0(xp, xm) & ~ sdtlseqdt0(xp, xn) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v6 = sz00 | ~ (sdtsldt0(v10, v6) = v11) | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v9, v7) = v10) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtasdt0(v9, v8) = v11) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v6, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ (sdtpldt0(v9, v10) = v11) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (sdtasdt0(v12, v6) = v13 & sdtasdt0(v8, v6) = v15 & sdtasdt0(v7, v6) = v14 & sdtasdt0(v6, v12) = v11 & sdtpldt0(v14, v15) = v13 & sdtpldt0(v7, v8) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v6, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v9, v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v6, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v11) & sdtasdt0(v8, v6) = v12 & sdtasdt0(v7, v6) = v11 & sdtlseqdt0(v11, v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v6, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v11) & sdtasdt0(v8, v6) = v12 & sdtasdt0(v7, v6) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v6, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v11) & sdtpldt0(v8, v6) = v12 & sdtpldt0(v7, v6) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = sz10 | v8 = sz00 | ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ iLess0(v10, v1) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v8, v7) | doDivides0(v8, v6) | ? [v11] : ? [v12] : ? [v13] : ((v13 = v8 & ~ (v11 = v8) & ~ (v11 = sz10) & sdtasdt0(v11, v12) = v8 & doDivides0(v11, v8) & aNaturalNumber0(v12) & aNaturalNumber0(v11)) | (sdtasdt0(v6, v7) = v11 & ~ doDivides0(v8, v11) & ! [v14] : ( ~ (sdtasdt0(v8, v14) = v11) | ~ aNaturalNumber0(v14))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = sz10 | v8 = sz00 | ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ iLess0(v10, v1) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v8, v7) | ? [v11] : ? [v12] : ? [v13] : ((v13 = v8 & ~ (v11 = v8) & ~ (v11 = sz10) & sdtasdt0(v11, v12) = v8 & doDivides0(v11, v8) & aNaturalNumber0(v12) & aNaturalNumber0(v11)) | (v12 = v6 & sdtasdt0(v8, v11) = v6 & aNaturalNumber0(v11)) | (sdtasdt0(v6, v7) = v11 & ~ doDivides0(v8, v11) & ! [v14] : ( ~ (sdtasdt0(v8, v14) = v11) | ~ aNaturalNumber0(v14))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = sz10 | v8 = sz00 | ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ iLess0(v10, v1) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v8, v6) | ? [v11] : ? [v12] : ? [v13] : ((v13 = v8 & ~ (v11 = v8) & ~ (v11 = sz10) & sdtasdt0(v11, v12) = v8 & doDivides0(v11, v8) & aNaturalNumber0(v12) & aNaturalNumber0(v11)) | (v12 = v7 & sdtasdt0(v8, v11) = v7 & aNaturalNumber0(v11)) | (sdtasdt0(v6, v7) = v11 & ~ doDivides0(v8, v11) & ! [v14] : ( ~ (sdtasdt0(v8, v14) = v11) | ~ aNaturalNumber0(v14))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = sz10 | v8 = sz00 | ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ iLess0(v10, v1) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ? [v13] : ((v13 = v8 & ~ (v11 = v8) & ~ (v11 = sz10) & sdtasdt0(v11, v12) = v8 & doDivides0(v11, v8) & aNaturalNumber0(v12) & aNaturalNumber0(v11)) | (v12 = v7 & sdtasdt0(v8, v11) = v7 & aNaturalNumber0(v11)) | (v12 = v6 & sdtasdt0(v8, v11) = v6 & aNaturalNumber0(v11)) | (sdtasdt0(v6, v7) = v11 & ~ doDivides0(v8, v11) & ! [v14] : ( ~ (sdtasdt0(v8, v14) = v11) | ~ aNaturalNumber0(v14))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v9, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : (sdtasdt0(v7, v8) = v11 & sdtasdt0(v6, v11) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ isPrime0(v8) | ~ iLess0(v10, v1) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v8, v7) | doDivides0(v8, v6) | ? [v11] : (sdtasdt0(v6, v7) = v11 & ~ doDivides0(v8, v11) & ! [v12] : ( ~ (sdtasdt0(v8, v12) = v11) | ~ aNaturalNumber0(v12)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ isPrime0(v8) | ~ iLess0(v10, v1) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v8, v7) | ? [v11] : ? [v12] : ((v12 = v6 & sdtasdt0(v8, v11) = v6 & aNaturalNumber0(v11)) | (sdtasdt0(v6, v7) = v11 & ~ doDivides0(v8, v11) & ! [v13] : ( ~ (sdtasdt0(v8, v13) = v11) | ~ aNaturalNumber0(v13))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ isPrime0(v8) | ~ iLess0(v10, v1) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v8, v6) | ? [v11] : ? [v12] : ((v12 = v7 & sdtasdt0(v8, v11) = v7 & aNaturalNumber0(v11)) | (sdtasdt0(v6, v7) = v11 & ~ doDivides0(v8, v11) & ! [v13] : ( ~ (sdtasdt0(v8, v13) = v11) | ~ aNaturalNumber0(v13))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ isPrime0(v8) | ~ iLess0(v10, v1) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ((v12 = v7 & sdtasdt0(v8, v11) = v7 & aNaturalNumber0(v11)) | (v12 = v6 & sdtasdt0(v8, v11) = v6 & aNaturalNumber0(v11)) | (sdtasdt0(v6, v7) = v11 & ~ doDivides0(v8, v11) & ! [v13] : ( ~ (sdtasdt0(v8, v13) = v11) | ~ aNaturalNumber0(v13))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : (sdtpldt0(v7, v8) = v11 & sdtpldt0(v6, v11) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | v6 = sz00 | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v6, v9) = v7) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (sdtmndt0(v7, v6) = v8) | ~ (sdtpldt0(v6, v9) = v7) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | v6 = sz00 | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v6, v8) = v9) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (sdtmndt0(v7, v6) = v8) | ~ (sdtpldt0(v6, v8) = v9) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v6, v8) = v9) | ~ (sdtasdt0(v6, v7) = v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v6, v8) = v9) | ~ (sdtasdt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (sdtpldt0(v6, v8) = v9) | ~ (sdtpldt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtsldt0(v9, v8) = v7) | ~ (sdtsldt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtmndt0(v9, v8) = v7) | ~ (sdtmndt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtasdt0(v9, v8) = v7) | ~ (sdtasdt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v9, v8) = v7) | ~ (sdtpldt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v6, v8) = v9) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = v9) & ~ (v11 = v10) & sdtpldt0(v8, v7) = v11 & sdtpldt0(v8, v6) = v10 & sdtpldt0(v7, v8) = v12 & sdtlseqdt0(v10, v11) & sdtlseqdt0(v9, v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = sz00 | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v6, v8) = v9) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | aNaturalNumber0(v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtmndt0(v7, v6) = v8) | ~ (sdtpldt0(v6, v8) = v9) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | aNaturalNumber0(v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v7, v8) = v9) | ~ doDivides0(v6, v9) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v7, v8) = v9) | ~ doDivides0(v6, v8) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v6, v9)) & ! [v6] : ! [v7] : ! [v8] : (v6 = sz00 | ~ (sdtasdt0(v7, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v7, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v6, v8) = v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtasdt0(v7, v6) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | aNaturalNumber0(v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v6, v8) = v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtpldt0(v7, v6) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | aNaturalNumber0(v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ doDivides0(v7, v8) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ sdtlseqdt0(v7, v8) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v6, v8)) & ! [v6] : ! [v7] : (v7 = v6 | v7 = sz10 | ~ isPrime0(v6) | ~ doDivides0(v7, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (sdtasdt0(sz10, v6) = v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (sdtpldt0(sz00, v6) = v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ sdtlseqdt0(v7, v6) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | iLess0(v6, v7)) & ! [v6] : ! [v7] : (v7 = sz00 | v6 = sz00 | ~ (sdtasdt0(v6, v7) = sz00) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = sz00 | ~ (sdtasdt0(sz00, v6) = v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = sz00 | ~ (sdtpldt0(v6, v7) = sz00) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = sz00 | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v6, v7)) & ! [v6] : ! [v7] : (v6 = xp | v6 = sz10 | ~ (sdtasdt0(v6, v7) = xp) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v6 = sz00 | ~ (sdtpldt0(v6, v7) = sz00) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ( ~ (sdtasdt0(sz10, v6) = v7) | ~ aNaturalNumber0(v6) | sdtasdt0(v6, sz10) = v6) & ! [v6] : ! [v7] : ( ~ (sdtasdt0(sz00, v6) = v7) | ~ aNaturalNumber0(v6) | sdtasdt0(v6, sz00) = sz00) & ! [v6] : ! [v7] : ( ~ (sdtpldt0(sz00, v6) = v7) | ~ aNaturalNumber0(v6) | sdtpldt0(v6, sz00) = v6) & ! [v6] : ! [v7] : ( ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v8] : (sdtasdt0(v6, v8) = v7 & aNaturalNumber0(v8))) & ! [v6] : ! [v7] : ( ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v8] : (sdtpldt0(v6, v8) = v7 & aNaturalNumber0(v8))) & ! [v6] : ! [v7] : ( ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v7, v6) | sdtlseqdt0(v6, v7)) & ! [v6] : (v6 = xp | v6 = sz10 | ~ doDivides0(v6, xp) | ~ aNaturalNumber0(v6)) & ! [v6] : (v6 = sz10 | v6 = sz00 | ~ aNaturalNumber0(v6) | isPrime0(v6) | ? [v7] : ( ~ (v7 = v6) & ~ (v7 = sz10) & doDivides0(v7, v6) & aNaturalNumber0(v7))) & ! [v6] : (v6 = sz10 | v6 = sz00 | ~ aNaturalNumber0(v6) | sdtlseqdt0(sz10, v6)) & ! [v6] : (v6 = sz10 | v6 = sz00 | ~ aNaturalNumber0(v6) | ? [v7] : (isPrime0(v7) & doDivides0(v7, v6) & aNaturalNumber0(v7))) & ! [v6] : ( ~ (sdtpldt0(xp, v6) = xm) | ~ aNaturalNumber0(v6)) & ! [v6] : ( ~ (sdtpldt0(xp, v6) = xn) | ~ aNaturalNumber0(v6)) & ! [v6] : ( ~ aNaturalNumber0(v6) | sdtlseqdt0(v6, v6)) & ! [v6] : ( ~ aNaturalNumber0(v6) | ? [v7] : ( ~ (v7 = xm) & sdtasdt0(xp, v6) = v7)) & ! [v6] : ( ~ aNaturalNumber0(v6) | ? [v7] : ( ~ (v7 = xn) & sdtasdt0(xp, v6) = v7)) & (xk = sz10 | xk = sz00))
% 46.36/14.37 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 46.36/14.37 | (1) ~ (xp = xm) & ~ (xp = xn) & ~ (xp = sz10) & ~ (xp = sz00) & ~ (sz10 = sz00) & sdtsldt0(all_0_3_3, xp) = xk & sdtasdt0(xp, all_0_0_0) = all_0_3_3 & sdtasdt0(xp, xk) = all_0_3_3 & sdtasdt0(xn, xm) = all_0_3_3 & sdtpldt0(all_0_5_5, xp) = all_0_4_4 & sdtpldt0(xm, all_0_2_2) = xp & sdtpldt0(xn, all_0_1_1) = xp & sdtpldt0(xn, xm) = all_0_5_5 & isPrime0(xp) & doDivides0(xp, all_0_3_3) & sdtlseqdt0(xm, xp) & sdtlseqdt0(xn, xp) & aNaturalNumber0(all_0_0_0) & aNaturalNumber0(all_0_1_1) & aNaturalNumber0(all_0_2_2) & aNaturalNumber0(xk) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ isPrime0(sz10) & ~ isPrime0(sz00) & ~ doDivides0(xp, xm) & ~ doDivides0(xp, xn) & ~ sdtlseqdt0(xp, xm) & ~ sdtlseqdt0(xp, xn) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v3, v2) = v5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtlseqdt0(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) | ? [v5] : (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v6] : ( ~ (sdtasdt0(v2, v6) = v5) | ~ aNaturalNumber0(v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5] : ? [v6] : ((v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ((v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ((v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(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] : (v1 = v0 | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1)) & ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0] : ! [v1] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1) = xp) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0) & ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2))) & ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2))) & ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) & ! [v0] : (v0 = xp | v0 = sz10 | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0)) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1] : ( ~ (v1 = v0) & ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1))) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1))) & ! [v0] : ( ~ (sdtpldt0(xp, v0) = xm) | ~ aNaturalNumber0(v0)) & ! [v0] : ( ~ (sdtpldt0(xp, v0) = xn) | ~ aNaturalNumber0(v0)) & ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = xm) & sdtasdt0(xp, v0) = v1)) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = xn) & sdtasdt0(xp, v0) = v1)) & (xk = sz10 | xk = sz00)
% 46.36/14.39 |
% 46.36/14.39 | Applying alpha-rule on (1) yields:
% 46.36/14.39 | (2) sdtasdt0(xp, all_0_0_0) = all_0_3_3
% 46.36/14.39 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8)))))
% 46.36/14.40 | (4) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 46.36/14.40 | (5) ! [v0] : ! [v1] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1) = xp) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 46.36/14.40 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4))
% 46.36/14.40 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 46.36/14.40 | (8) sdtsldt0(all_0_3_3, xp) = xk
% 46.36/14.40 | (9) sdtpldt0(all_0_5_5, xp) = all_0_4_4
% 46.36/14.40 | (10) ~ (xp = xm)
% 46.36/14.40 | (11) ~ isPrime0(sz10)
% 46.36/14.40 | (12) ~ (xp = sz10)
% 46.36/14.40 | (13) ! [v0] : ( ~ (sdtpldt0(xp, v0) = xm) | ~ aNaturalNumber0(v0))
% 46.36/14.40 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5))
% 46.36/14.40 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 46.36/14.40 | (16) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 46.36/14.40 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3))
% 46.36/14.40 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4))
% 46.36/14.40 | (19) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 46.36/14.40 | (20) ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = xn) & sdtasdt0(xp, v0) = v1))
% 46.36/14.40 | (21) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 46.36/14.40 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6))
% 46.36/14.40 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 46.36/14.40 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v3, v2) = v5)
% 46.36/14.40 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 46.36/14.40 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtlseqdt0(v5, v6)))
% 46.36/14.40 | (27) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 46.36/14.40 | (28) sdtpldt0(xm, all_0_2_2) = xp
% 46.36/14.40 | (29) doDivides0(xp, all_0_3_3)
% 46.36/14.40 | (30) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 46.36/14.40 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 46.36/14.40 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 46.36/14.40 | (33) ! [v0] : ! [v1] : (v1 = sz00 | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 46.36/14.40 | (34) sdtasdt0(xp, xk) = all_0_3_3
% 46.36/14.40 | (35) aNaturalNumber0(all_0_0_0)
% 46.36/14.40 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 46.36/14.40 | (37) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 46.36/14.40 | (38) aNaturalNumber0(xk)
% 46.36/14.40 | (39) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0))
% 46.36/14.40 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 46.36/14.40 | (41) sdtpldt0(xn, xm) = all_0_5_5
% 46.36/14.40 | (42) ~ doDivides0(xp, xn)
% 46.36/14.40 | (43) aNaturalNumber0(sz10)
% 46.36/14.40 | (44) ~ sdtlseqdt0(xp, xm)
% 46.36/14.40 | (45) sdtlseqdt0(xm, xp)
% 46.36/14.40 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5))
% 46.36/14.40 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 46.36/14.40 | (48) aNaturalNumber0(sz00)
% 46.36/14.40 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 46.36/14.40 | (50) ~ (sz10 = sz00)
% 46.36/14.40 | (51) sdtasdt0(xn, xm) = all_0_3_3
% 46.36/14.40 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 46.36/14.40 | (53) ~ (xp = sz00)
% 46.36/14.40 | (54) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 46.36/14.40 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 46.36/14.40 | (56) ~ isPrime0(sz00)
% 46.36/14.40 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8)))))
% 46.36/14.40 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 46.36/14.40 | (59) ~ sdtlseqdt0(xp, xn)
% 46.36/14.40 | (60) sdtlseqdt0(xn, xp)
% 46.36/14.40 | (61) ! [v0] : ( ~ (sdtpldt0(xp, v0) = xn) | ~ aNaturalNumber0(v0))
% 46.36/14.40 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 46.36/14.40 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 46.36/14.40 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 46.36/14.40 | (65) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 46.36/14.41 | (66) ~ (xp = xn)
% 46.36/14.41 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8)))))
% 46.87/14.41 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 46.87/14.41 | (69) ~ doDivides0(xp, xm)
% 46.87/14.41 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 46.87/14.41 | (71) ! [v0] : (v0 = xp | v0 = sz10 | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0))
% 46.87/14.41 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 46.87/14.41 | (73) aNaturalNumber0(xm)
% 46.87/14.41 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8)))))
% 46.87/14.41 | (75) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 46.87/14.41 | (76) ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 46.87/14.41 | (77) ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 46.87/14.41 | (78) sdtpldt0(xn, all_0_1_1) = xp
% 46.87/14.41 | (79) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1] : ( ~ (v1 = v0) & ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 46.87/14.41 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 46.87/14.41 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 46.87/14.41 | (82) aNaturalNumber0(xp)
% 46.87/14.41 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ((v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7)))))
% 46.87/14.41 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 46.87/14.41 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5] : ? [v6] : ((v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7)))))
% 46.87/14.41 | (86) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 46.87/14.41 | (87) xk = sz10 | xk = sz00
% 46.87/14.41 | (88) aNaturalNumber0(all_0_1_1)
% 46.87/14.41 | (89) isPrime0(xp)
% 46.87/14.41 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6)))
% 46.87/14.41 | (91) aNaturalNumber0(all_0_2_2)
% 46.87/14.41 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) | ? [v5] : (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v6] : ( ~ (sdtasdt0(v2, v6) = v5) | ~ aNaturalNumber0(v6))))
% 46.87/14.42 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_4_4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ((v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7)))))
% 46.87/14.42 | (94) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 46.87/14.42 | (95) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 46.87/14.42 | (96) aNaturalNumber0(xn)
% 46.87/14.42 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 46.87/14.42 | (98) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 46.87/14.42 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4))
% 46.87/14.42 | (100) ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = xm) & sdtasdt0(xp, v0) = v1))
% 46.87/14.42 | (101) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 46.87/14.42 |
% 46.87/14.42 | Instantiating formula (31) with all_0_3_3, all_0_0_0, xk, xp and discharging atoms sdtasdt0(xp, all_0_0_0) = all_0_3_3, sdtasdt0(xp, xk) = all_0_3_3, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xk), aNaturalNumber0(xp), yields:
% 46.87/14.42 | (102) all_0_0_0 = xk | xp = sz00
% 46.87/14.42 |
% 46.87/14.42 | Instantiating formula (39) with all_0_3_3, xm and discharging atoms aNaturalNumber0(xm), yields:
% 46.87/14.42 | (103) all_0_3_3 = xm | ~ (sdtasdt0(sz10, xm) = all_0_3_3)
% 46.87/14.42 |
% 46.87/14.42 | Instantiating formula (4) with xm, xn and discharging atoms aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 46.87/14.42 | (104) xm = sz00 | xn = sz00 | ~ (sdtasdt0(xn, xm) = sz00)
% 46.87/14.42 |
% 46.87/14.42 | Instantiating formula (5) with xm, xn and discharging atoms aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 46.87/14.42 | (105) xp = xn | xn = sz10 | ~ (sdtasdt0(xn, xm) = xp)
% 46.87/14.42 |
% 46.87/14.42 | Using (29) and (69) yields:
% 46.87/14.42 | (106) ~ (all_0_3_3 = xm)
% 46.87/14.42 |
% 46.87/14.42 +-Applying beta-rule and splitting (103), into two cases.
% 46.87/14.42 |-Branch one:
% 46.87/14.42 | (107) ~ (sdtasdt0(sz10, xm) = all_0_3_3)
% 46.87/14.42 |
% 46.87/14.42 +-Applying beta-rule and splitting (102), into two cases.
% 46.87/14.42 |-Branch one:
% 46.87/14.42 | (108) xp = sz00
% 46.87/14.42 |
% 46.87/14.42 | Equations (108) can reduce 53 to:
% 46.87/14.42 | (109) $false
% 46.87/14.42 |
% 46.87/14.42 |-The branch is then unsatisfiable
% 46.87/14.42 |-Branch two:
% 46.87/14.42 | (53) ~ (xp = sz00)
% 46.87/14.42 | (111) all_0_0_0 = xk
% 46.87/14.42 |
% 46.87/14.42 | From (111) and (2) follows:
% 46.87/14.42 | (34) sdtasdt0(xp, xk) = all_0_3_3
% 46.87/14.42 |
% 46.87/14.42 | From (111) and (35) follows:
% 46.87/14.42 | (38) aNaturalNumber0(xk)
% 46.87/14.42 |
% 46.87/14.42 | Using (51) and (107) yields:
% 46.87/14.42 | (114) ~ (xn = sz10)
% 46.87/14.42 |
% 46.87/14.42 +-Applying beta-rule and splitting (105), into two cases.
% 46.87/14.42 |-Branch one:
% 46.87/14.42 | (115) ~ (sdtasdt0(xn, xm) = xp)
% 46.87/14.42 |
% 46.87/14.42 | Using (51) and (115) yields:
% 46.87/14.42 | (116) ~ (all_0_3_3 = xp)
% 46.87/14.42 |
% 46.87/14.42 | Instantiating formula (36) with all_0_3_3, xk, xp and discharging atoms sdtasdt0(xp, xk) = all_0_3_3, aNaturalNumber0(xk), aNaturalNumber0(xp), yields:
% 46.87/14.42 | (117) sdtasdt0(xk, xp) = all_0_3_3
% 46.87/14.42 |
% 46.87/14.42 | Instantiating formula (76) with all_0_3_3, xp and discharging atoms doDivides0(xp, all_0_3_3), aNaturalNumber0(xp), yields:
% 46.87/14.42 | (118) ~ aNaturalNumber0(all_0_3_3) | ? [v0] : (sdtasdt0(xp, v0) = all_0_3_3 & aNaturalNumber0(v0))
% 46.87/14.42 |
% 46.87/14.42 | Instantiating formula (65) with xp and discharging atoms aNaturalNumber0(xp), yields:
% 46.87/14.42 | (119) xp = sz10 | xp = sz00 | ? [v0] : (isPrime0(v0) & doDivides0(v0, xp) & aNaturalNumber0(v0))
% 46.87/14.43 |
% 46.87/14.43 | Instantiating formula (52) with all_0_3_3, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_3_3, aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 46.87/14.43 | (120) aNaturalNumber0(all_0_3_3)
% 46.87/14.43 |
% 46.87/14.43 | Instantiating formula (70) with xm, all_0_3_3, xn and discharging atoms sdtasdt0(xn, xm) = all_0_3_3, aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 46.87/14.43 | (121) ~ aNaturalNumber0(all_0_3_3) | doDivides0(xn, all_0_3_3)
% 46.87/14.43 |
% 46.87/14.43 | Instantiating formula (65) with xn and discharging atoms aNaturalNumber0(xn), yields:
% 46.87/14.43 | (122) xn = sz10 | xn = sz00 | ? [v0] : (isPrime0(v0) & doDivides0(v0, xn) & aNaturalNumber0(v0))
% 46.87/14.43 |
% 46.87/14.43 | Instantiating formula (36) with all_0_3_3, sz10, xp and discharging atoms aNaturalNumber0(xp), aNaturalNumber0(sz10), yields:
% 46.87/14.43 | (123) ~ (sdtasdt0(xp, sz10) = all_0_3_3) | sdtasdt0(sz10, xp) = all_0_3_3
% 46.87/14.43 |
% 46.87/14.43 | Instantiating formula (100) with sz00 and discharging atoms aNaturalNumber0(sz00), yields:
% 46.87/14.43 | (124) ? [v0] : ( ~ (v0 = xm) & sdtasdt0(xp, sz00) = v0)
% 46.87/14.43 |
% 46.87/14.43 | Instantiating formula (20) with sz00 and discharging atoms aNaturalNumber0(sz00), yields:
% 46.87/14.43 | (125) ? [v0] : ( ~ (v0 = xn) & sdtasdt0(xp, sz00) = v0)
% 46.87/14.43 |
% 46.87/14.43 | Instantiating (125) with all_53_0_16 yields:
% 46.87/14.43 | (126) ~ (all_53_0_16 = xn) & sdtasdt0(xp, sz00) = all_53_0_16
% 46.87/14.43 |
% 46.87/14.43 | Applying alpha-rule on (126) yields:
% 46.87/14.43 | (127) ~ (all_53_0_16 = xn)
% 46.87/14.43 | (128) sdtasdt0(xp, sz00) = all_53_0_16
% 46.87/14.43 |
% 46.87/14.43 | Instantiating (124) with all_55_0_17 yields:
% 46.87/14.43 | (129) ~ (all_55_0_17 = xm) & sdtasdt0(xp, sz00) = all_55_0_17
% 46.87/14.43 |
% 46.87/14.43 | Applying alpha-rule on (129) yields:
% 46.87/14.43 | (130) ~ (all_55_0_17 = xm)
% 46.87/14.43 | (131) sdtasdt0(xp, sz00) = all_55_0_17
% 46.87/14.43 |
% 46.87/14.43 +-Applying beta-rule and splitting (119), into two cases.
% 46.87/14.43 |-Branch one:
% 46.87/14.43 | (108) xp = sz00
% 46.87/14.43 |
% 46.87/14.43 | Equations (108) can reduce 53 to:
% 46.87/14.43 | (109) $false
% 46.87/14.43 |
% 46.87/14.43 |-The branch is then unsatisfiable
% 46.87/14.43 |-Branch two:
% 46.87/14.43 | (53) ~ (xp = sz00)
% 46.87/14.43 | (135) xp = sz10 | ? [v0] : (isPrime0(v0) & doDivides0(v0, xp) & aNaturalNumber0(v0))
% 46.87/14.43 |
% 46.87/14.43 +-Applying beta-rule and splitting (135), into two cases.
% 46.87/14.43 |-Branch one:
% 46.87/14.43 | (136) xp = sz10
% 46.87/14.43 |
% 46.87/14.43 | Equations (136) can reduce 12 to:
% 46.87/14.43 | (109) $false
% 46.87/14.43 |
% 46.87/14.43 |-The branch is then unsatisfiable
% 46.87/14.43 |-Branch two:
% 46.87/14.43 | (12) ~ (xp = sz10)
% 46.87/14.43 | (139) ? [v0] : (isPrime0(v0) & doDivides0(v0, xp) & aNaturalNumber0(v0))
% 46.87/14.43 |
% 46.87/14.43 | Instantiating (139) with all_85_0_23 yields:
% 46.87/14.43 | (140) isPrime0(all_85_0_23) & doDivides0(all_85_0_23, xp) & aNaturalNumber0(all_85_0_23)
% 46.87/14.43 |
% 46.87/14.43 | Applying alpha-rule on (140) yields:
% 46.87/14.43 | (141) isPrime0(all_85_0_23)
% 46.87/14.43 | (142) doDivides0(all_85_0_23, xp)
% 46.87/14.43 | (143) aNaturalNumber0(all_85_0_23)
% 46.87/14.43 |
% 46.87/14.43 +-Applying beta-rule and splitting (118), into two cases.
% 46.87/14.43 |-Branch one:
% 46.87/14.43 | (144) ~ aNaturalNumber0(all_0_3_3)
% 46.87/14.43 |
% 46.87/14.43 | Using (120) and (144) yields:
% 46.87/14.43 | (145) $false
% 46.87/14.43 |
% 46.87/14.43 |-The branch is then unsatisfiable
% 46.87/14.43 |-Branch two:
% 46.87/14.43 | (120) aNaturalNumber0(all_0_3_3)
% 46.87/14.43 | (147) ? [v0] : (sdtasdt0(xp, v0) = all_0_3_3 & aNaturalNumber0(v0))
% 46.87/14.43 |
% 46.87/14.43 | Instantiating (147) with all_103_0_27 yields:
% 46.87/14.43 | (148) sdtasdt0(xp, all_103_0_27) = all_0_3_3 & aNaturalNumber0(all_103_0_27)
% 46.87/14.43 |
% 46.87/14.43 | Applying alpha-rule on (148) yields:
% 46.87/14.43 | (149) sdtasdt0(xp, all_103_0_27) = all_0_3_3
% 46.87/14.43 | (150) aNaturalNumber0(all_103_0_27)
% 46.87/14.43 |
% 46.87/14.43 +-Applying beta-rule and splitting (121), into two cases.
% 46.87/14.43 |-Branch one:
% 46.87/14.43 | (144) ~ aNaturalNumber0(all_0_3_3)
% 46.87/14.43 |
% 46.87/14.43 | Using (120) and (144) yields:
% 46.87/14.43 | (145) $false
% 46.87/14.43 |
% 46.87/14.43 |-The branch is then unsatisfiable
% 46.87/14.43 |-Branch two:
% 46.87/14.43 | (120) aNaturalNumber0(all_0_3_3)
% 46.87/14.43 | (154) doDivides0(xn, all_0_3_3)
% 46.87/14.43 |
% 46.87/14.43 | Instantiating formula (39) with all_0_3_3, xp and discharging atoms aNaturalNumber0(xp), yields:
% 46.87/14.43 | (155) all_0_3_3 = xp | ~ (sdtasdt0(sz10, xp) = all_0_3_3)
% 46.87/14.43 |
% 46.87/14.43 | Instantiating formula (30) with all_0_3_3, xp and discharging atoms aNaturalNumber0(xp), yields:
% 46.87/14.43 | (156) all_0_3_3 = sz00 | ~ (sdtasdt0(sz00, xp) = all_0_3_3)
% 46.87/14.43 |
% 46.87/14.43 | Instantiating formula (81) with xp, sz00, all_55_0_17, all_0_3_3 and discharging atoms sdtasdt0(xp, sz00) = all_55_0_17, yields:
% 46.87/14.43 | (157) all_55_0_17 = all_0_3_3 | ~ (sdtasdt0(xp, sz00) = all_0_3_3)
% 46.87/14.43 |
% 46.87/14.43 | Instantiating formula (81) with xp, sz00, all_53_0_16, all_55_0_17 and discharging atoms sdtasdt0(xp, sz00) = all_55_0_17, sdtasdt0(xp, sz00) = all_53_0_16, yields:
% 46.87/14.43 | (158) all_55_0_17 = all_53_0_16
% 46.87/14.43 |
% 46.87/14.43 | Using (141) and (11) yields:
% 46.87/14.43 | (159) ~ (all_85_0_23 = sz10)
% 46.87/14.43 |
% 46.87/14.43 | Using (141) and (56) yields:
% 46.87/14.43 | (160) ~ (all_85_0_23 = sz00)
% 46.87/14.43 |
% 46.87/14.43 | Instantiating formula (71) with all_85_0_23 and discharging atoms doDivides0(all_85_0_23, xp), aNaturalNumber0(all_85_0_23), yields:
% 46.87/14.43 | (161) all_85_0_23 = xp | all_85_0_23 = sz10
% 46.87/14.43 |
% 46.87/14.43 | Instantiating formula (49) with all_103_0_27, xk, all_0_3_3, xp and discharging atoms sdtsldt0(all_0_3_3, xp) = xk, sdtasdt0(xp, all_103_0_27) = all_0_3_3, doDivides0(xp, all_0_3_3), aNaturalNumber0(all_103_0_27), aNaturalNumber0(all_0_3_3), aNaturalNumber0(xp), yields:
% 46.87/14.43 | (162) all_103_0_27 = xk | xp = sz00
% 46.87/14.43 |
% 46.87/14.43 | Equations (158) can reduce 130 to:
% 46.87/14.43 | (163) ~ (all_53_0_16 = xm)
% 46.87/14.43 |
% 46.87/14.43 +-Applying beta-rule and splitting (161), into two cases.
% 46.87/14.43 |-Branch one:
% 46.87/14.43 | (164) all_85_0_23 = xp
% 46.87/14.43 |
% 46.87/14.43 | Equations (164) can reduce 160 to:
% 46.87/14.43 | (53) ~ (xp = sz00)
% 46.87/14.43 |
% 46.87/14.43 +-Applying beta-rule and splitting (155), into two cases.
% 46.87/14.43 |-Branch one:
% 46.87/14.43 | (166) ~ (sdtasdt0(sz10, xp) = all_0_3_3)
% 46.87/14.43 |
% 46.87/14.43 +-Applying beta-rule and splitting (123), into two cases.
% 46.87/14.43 |-Branch one:
% 46.87/14.43 | (167) ~ (sdtasdt0(xp, sz10) = all_0_3_3)
% 46.87/14.43 |
% 46.87/14.43 +-Applying beta-rule and splitting (162), into two cases.
% 46.87/14.43 |-Branch one:
% 46.87/14.43 | (108) xp = sz00
% 46.87/14.43 |
% 46.87/14.43 | Equations (108) can reduce 53 to:
% 46.87/14.43 | (109) $false
% 46.87/14.43 |
% 46.87/14.43 |-The branch is then unsatisfiable
% 46.87/14.43 |-Branch two:
% 46.87/14.43 | (53) ~ (xp = sz00)
% 46.87/14.43 | (171) all_103_0_27 = xk
% 46.87/14.43 |
% 46.87/14.43 | From (171) and (149) follows:
% 46.87/14.43 | (34) sdtasdt0(xp, xk) = all_0_3_3
% 46.87/14.43 |
% 46.87/14.43 | Using (34) and (167) yields:
% 46.87/14.43 | (173) ~ (xk = sz10)
% 46.87/14.43 |
% 46.87/14.43 +-Applying beta-rule and splitting (87), into two cases.
% 46.87/14.43 |-Branch one:
% 46.87/14.43 | (174) xk = sz00
% 46.87/14.43 |
% 46.87/14.43 | From (174) and (117) follows:
% 46.87/14.43 | (175) sdtasdt0(sz00, xp) = all_0_3_3
% 46.87/14.43 |
% 46.87/14.43 | From (174) and (34) follows:
% 46.87/14.43 | (176) sdtasdt0(xp, sz00) = all_0_3_3
% 46.87/14.43 |
% 46.87/14.43 +-Applying beta-rule and splitting (157), into two cases.
% 46.87/14.43 |-Branch one:
% 46.87/14.43 | (177) ~ (sdtasdt0(xp, sz00) = all_0_3_3)
% 46.87/14.43 |
% 46.87/14.43 | Using (176) and (177) yields:
% 46.87/14.43 | (145) $false
% 46.87/14.43 |
% 46.87/14.43 |-The branch is then unsatisfiable
% 46.87/14.43 |-Branch two:
% 46.87/14.43 | (176) sdtasdt0(xp, sz00) = all_0_3_3
% 46.87/14.43 | (180) all_55_0_17 = all_0_3_3
% 46.87/14.43 |
% 46.87/14.43 | Combining equations (158,180) yields a new equation:
% 46.87/14.43 | (181) all_53_0_16 = all_0_3_3
% 46.87/14.43 |
% 46.87/14.43 | Simplifying 181 yields:
% 46.87/14.43 | (182) all_53_0_16 = all_0_3_3
% 46.87/14.43 |
% 46.87/14.44 | Equations (182) can reduce 163 to:
% 46.87/14.44 | (106) ~ (all_0_3_3 = xm)
% 46.87/14.44 |
% 46.87/14.44 | Equations (182) can reduce 127 to:
% 46.87/14.44 | (184) ~ (all_0_3_3 = xn)
% 46.87/14.44 |
% 46.87/14.44 +-Applying beta-rule and splitting (156), into two cases.
% 46.87/14.44 |-Branch one:
% 46.87/14.44 | (185) ~ (sdtasdt0(sz00, xp) = all_0_3_3)
% 46.87/14.44 |
% 46.87/14.44 | Using (175) and (185) yields:
% 46.87/14.44 | (145) $false
% 46.87/14.44 |
% 46.87/14.44 |-The branch is then unsatisfiable
% 46.87/14.44 |-Branch two:
% 46.87/14.44 | (175) sdtasdt0(sz00, xp) = all_0_3_3
% 46.87/14.44 | (188) all_0_3_3 = sz00
% 46.87/14.44 |
% 46.87/14.44 | Equations (188) can reduce 106 to:
% 46.87/14.44 | (189) ~ (xm = sz00)
% 46.87/14.44 |
% 46.87/14.44 | Simplifying 189 yields:
% 46.87/14.44 | (190) ~ (xm = sz00)
% 46.87/14.44 |
% 46.87/14.44 | Equations (188) can reduce 184 to:
% 46.87/14.44 | (191) ~ (xn = sz00)
% 46.87/14.44 |
% 46.87/14.44 | Simplifying 191 yields:
% 46.87/14.44 | (192) ~ (xn = sz00)
% 46.87/14.44 |
% 46.87/14.44 | From (188) and (51) follows:
% 46.87/14.44 | (193) sdtasdt0(xn, xm) = sz00
% 46.87/14.44 |
% 46.87/14.44 +-Applying beta-rule and splitting (122), into two cases.
% 46.87/14.44 |-Branch one:
% 46.87/14.44 | (194) xn = sz00
% 46.87/14.44 |
% 46.87/14.44 | Equations (194) can reduce 192 to:
% 46.87/14.44 | (109) $false
% 46.87/14.44 |
% 46.87/14.44 |-The branch is then unsatisfiable
% 46.87/14.44 |-Branch two:
% 46.87/14.44 | (192) ~ (xn = sz00)
% 46.87/14.44 | (197) xn = sz10 | ? [v0] : (isPrime0(v0) & doDivides0(v0, xn) & aNaturalNumber0(v0))
% 46.87/14.44 |
% 46.87/14.44 +-Applying beta-rule and splitting (104), into two cases.
% 46.87/14.44 |-Branch one:
% 46.87/14.44 | (198) ~ (sdtasdt0(xn, xm) = sz00)
% 46.87/14.44 |
% 46.87/14.44 | Using (193) and (198) yields:
% 46.87/14.44 | (145) $false
% 46.87/14.44 |
% 46.87/14.44 |-The branch is then unsatisfiable
% 46.87/14.44 |-Branch two:
% 46.87/14.44 | (193) sdtasdt0(xn, xm) = sz00
% 46.87/14.44 | (201) xm = sz00 | xn = sz00
% 46.87/14.44 |
% 46.87/14.44 +-Applying beta-rule and splitting (201), into two cases.
% 46.87/14.44 |-Branch one:
% 46.87/14.44 | (202) xm = sz00
% 46.87/14.44 |
% 46.87/14.44 | Equations (202) can reduce 190 to:
% 46.87/14.44 | (109) $false
% 46.87/14.44 |
% 46.87/14.44 |-The branch is then unsatisfiable
% 46.87/14.44 |-Branch two:
% 46.87/14.44 | (190) ~ (xm = sz00)
% 46.87/14.44 | (194) xn = sz00
% 46.87/14.44 |
% 46.87/14.44 | Equations (194) can reduce 192 to:
% 46.87/14.44 | (109) $false
% 46.87/14.44 |
% 46.87/14.44 |-The branch is then unsatisfiable
% 46.87/14.44 |-Branch two:
% 46.87/14.44 | (207) ~ (xk = sz00)
% 46.87/14.44 | (208) xk = sz10
% 46.87/14.44 |
% 46.87/14.44 | Equations (208) can reduce 173 to:
% 46.87/14.44 | (109) $false
% 46.87/14.44 |
% 46.87/14.44 |-The branch is then unsatisfiable
% 46.87/14.44 |-Branch two:
% 46.87/14.44 | (210) sdtasdt0(xp, sz10) = all_0_3_3
% 46.87/14.44 | (211) sdtasdt0(sz10, xp) = all_0_3_3
% 46.87/14.44 |
% 46.87/14.44 | Using (211) and (166) yields:
% 46.87/14.44 | (145) $false
% 46.87/14.44 |
% 46.87/14.44 |-The branch is then unsatisfiable
% 46.87/14.44 |-Branch two:
% 46.87/14.44 | (211) sdtasdt0(sz10, xp) = all_0_3_3
% 46.87/14.44 | (214) all_0_3_3 = xp
% 46.87/14.44 |
% 46.87/14.44 | Equations (214) can reduce 116 to:
% 46.87/14.44 | (109) $false
% 46.87/14.44 |
% 46.87/14.44 |-The branch is then unsatisfiable
% 46.87/14.44 |-Branch two:
% 46.87/14.44 | (216) ~ (all_85_0_23 = xp)
% 46.87/14.44 | (217) all_85_0_23 = sz10
% 46.87/14.44 |
% 46.87/14.44 | Equations (217) can reduce 159 to:
% 46.87/14.44 | (109) $false
% 46.87/14.44 |
% 46.87/14.44 |-The branch is then unsatisfiable
% 46.87/14.44 |-Branch two:
% 46.87/14.44 | (219) sdtasdt0(xn, xm) = xp
% 46.87/14.44 | (220) xp = xn | xn = sz10
% 46.87/14.44 |
% 46.87/14.44 +-Applying beta-rule and splitting (220), into two cases.
% 46.87/14.44 |-Branch one:
% 46.87/14.44 | (221) xp = xn
% 46.87/14.44 |
% 46.87/14.44 | Equations (221) can reduce 66 to:
% 46.87/14.44 | (109) $false
% 46.87/14.44 |
% 46.87/14.44 |-The branch is then unsatisfiable
% 46.87/14.44 |-Branch two:
% 46.87/14.44 | (66) ~ (xp = xn)
% 46.87/14.44 | (224) xn = sz10
% 46.87/14.44 |
% 46.87/14.44 | Equations (224) can reduce 114 to:
% 46.87/14.44 | (109) $false
% 46.87/14.44 |
% 46.87/14.44 |-The branch is then unsatisfiable
% 46.87/14.44 |-Branch two:
% 46.87/14.44 | (226) sdtasdt0(sz10, xm) = all_0_3_3
% 46.87/14.44 | (227) all_0_3_3 = xm
% 46.87/14.44 |
% 46.87/14.44 | Equations (227) can reduce 106 to:
% 46.87/14.44 | (109) $false
% 46.87/14.44 |
% 46.87/14.44 |-The branch is then unsatisfiable
% 46.87/14.44 % SZS output end Proof for theBenchmark
% 46.87/14.44
% 46.87/14.44 13838ms
%------------------------------------------------------------------------------