TSTP Solution File: NUM496+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM496+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.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 08:45:08 EDT 2022
% Result : Theorem 15.26s 4.22s
% Output : Proof 63.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM496+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jul 5 07:14:37 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.56/0.57 ____ _
% 0.56/0.57 ___ / __ \_____(_)___ ________ __________
% 0.56/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.57
% 0.56/0.57 A Theorem Prover for First-Order Logic
% 0.56/0.57 (ePrincess v.1.0)
% 0.56/0.57
% 0.56/0.57 (c) Philipp Rümmer, 2009-2015
% 0.56/0.57 (c) Peter Backeman, 2014-2015
% 0.56/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.57 Bug reports to peter@backeman.se
% 0.56/0.57
% 0.56/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.57
% 0.56/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.56/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.97/0.98 Prover 0: Preprocessing ...
% 4.07/1.51 Prover 0: Constructing countermodel ...
% 15.26/4.21 Prover 0: proved (3593ms)
% 15.26/4.22
% 15.26/4.22 No countermodel exists, formula is valid
% 15.26/4.22 % SZS status Theorem for theBenchmark
% 15.26/4.22
% 15.26/4.22 Generating proof ... found it (size 505)
% 62.86/34.49
% 62.86/34.49 % SZS output start Proof for theBenchmark
% 62.86/34.49 Assumed formulas after preprocessing and simplification:
% 62.86/34.49 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (xr = xn) & ~ (xp = sz10) & ~ (xp = sz00) & ~ (sz10 = sz00) & sdtmndt0(xn, xp) = xr & sdtasdt0(xr, xm) = v3 & sdtasdt0(xp, v8) = v2 & sdtasdt0(xp, v5) = v3 & sdtasdt0(xp, v4) = xr & sdtasdt0(xn, xm) = v2 & sdtpldt0(v0, xp) = v1 & sdtpldt0(xr, v6) = xn & sdtpldt0(xp, v7) = xn & sdtpldt0(xp, xr) = xn & sdtpldt0(xn, xm) = v0 & isPrime0(xp) & doDivides0(xp, v3) & doDivides0(xp, v2) & doDivides0(xp, xr) & sdtlseqdt0(xr, xn) & sdtlseqdt0(xp, xn) & aNaturalNumber0(v8) & aNaturalNumber0(v7) & aNaturalNumber0(v6) & aNaturalNumber0(v5) & aNaturalNumber0(v4) & aNaturalNumber0(xr) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ isPrime0(sz10) & ~ isPrime0(sz00) & ~ doDivides0(xp, xm) & ~ doDivides0(xp, xn) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v9 = sz00 | ~ (sdtsldt0(v13, v9) = v14) | ~ (sdtsldt0(v10, v9) = v11) | ~ (sdtasdt0(v12, v10) = v13) | ~ doDivides0(v9, v10) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | sdtasdt0(v12, v11) = v14) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtasdt0(v11, v9) = v13) | ~ (sdtasdt0(v10, v9) = v12) | ~ (sdtpldt0(v12, v13) = v14) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (sdtasdt0(v15, v9) = v14 & sdtasdt0(v9, v15) = v16 & sdtasdt0(v9, v11) = v18 & sdtasdt0(v9, v10) = v17 & sdtpldt0(v17, v18) = v16 & sdtpldt0(v10, v11) = v15)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtasdt0(v9, v11) = v13) | ~ (sdtasdt0(v9, v10) = v12) | ~ (sdtpldt0(v12, v13) = v14) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (sdtasdt0(v15, v9) = v16 & sdtasdt0(v11, v9) = v18 & sdtasdt0(v10, v9) = v17 & sdtasdt0(v9, v15) = v14 & sdtpldt0(v17, v18) = v16 & sdtpldt0(v10, v11) = v15)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | v9 = sz00 | ~ (sdtasdt0(v11, v9) = v13) | ~ (sdtasdt0(v10, v9) = v12) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | sdtlseqdt0(v12, v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | v9 = sz00 | ~ (sdtasdt0(v11, v9) = v13) | ~ (sdtasdt0(v10, v9) = v12) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : ? [v15] : ( ~ (v15 = v14) & sdtasdt0(v9, v11) = v15 & sdtasdt0(v9, v10) = v14 & sdtlseqdt0(v14, v15))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | v9 = sz00 | ~ (sdtasdt0(v11, v9) = v13) | ~ (sdtasdt0(v10, v9) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : ? [v15] : ( ~ (v15 = v14) & sdtasdt0(v9, v11) = v15 & sdtasdt0(v9, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | v9 = sz00 | ~ (sdtasdt0(v11, v9) = v13) | ~ (sdtasdt0(v9, v10) = v12) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : ? [v15] : ( ~ (v15 = v13) & ~ (v14 = v12) & sdtasdt0(v10, v9) = v15 & sdtasdt0(v9, v11) = v14 & sdtlseqdt0(v15, v13) & sdtlseqdt0(v12, v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | v9 = sz00 | ~ (sdtasdt0(v11, v9) = v13) | ~ (sdtasdt0(v9, v10) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : ? [v15] : ( ~ (v15 = v13) & ~ (v14 = v12) & sdtasdt0(v10, v9) = v15 & sdtasdt0(v9, v11) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | v9 = sz00 | ~ (sdtasdt0(v10, v9) = v13) | ~ (sdtasdt0(v9, v11) = v12) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : ? [v15] : ( ~ (v15 = v13) & ~ (v14 = v12) & sdtasdt0(v11, v9) = v15 & sdtasdt0(v9, v10) = v14 & sdtlseqdt0(v14, v12) & sdtlseqdt0(v13, v15))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | v9 = sz00 | ~ (sdtasdt0(v10, v9) = v13) | ~ (sdtasdt0(v9, v11) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : ? [v15] : ( ~ (v15 = v13) & ~ (v14 = v12) & sdtasdt0(v11, v9) = v15 & sdtasdt0(v9, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | v9 = sz00 | ~ (sdtasdt0(v9, v11) = v13) | ~ (sdtasdt0(v9, v10) = v12) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | sdtlseqdt0(v12, v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | v9 = sz00 | ~ (sdtasdt0(v9, v11) = v13) | ~ (sdtasdt0(v9, v10) = v12) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : ? [v15] : ( ~ (v15 = v14) & sdtasdt0(v11, v9) = v15 & sdtasdt0(v10, v9) = v14 & sdtlseqdt0(v14, v15))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | v9 = sz00 | ~ (sdtasdt0(v9, v11) = v13) | ~ (sdtasdt0(v9, v10) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : ? [v15] : ( ~ (v15 = v14) & sdtasdt0(v11, v9) = v15 & sdtasdt0(v10, v9) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtpldt0(v11, v9) = v13) | ~ (sdtpldt0(v10, v9) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : ? [v15] : ( ~ (v15 = v14) & sdtpldt0(v9, v11) = v15 & sdtpldt0(v9, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtpldt0(v11, v9) = v13) | ~ (sdtpldt0(v9, v10) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : ? [v15] : ( ~ (v15 = v13) & ~ (v14 = v12) & sdtpldt0(v10, v9) = v15 & sdtpldt0(v9, v11) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtpldt0(v10, v9) = v13) | ~ (sdtpldt0(v9, v11) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : ? [v15] : ( ~ (v15 = v13) & ~ (v14 = v12) & sdtpldt0(v11, v9) = v15 & sdtpldt0(v9, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtpldt0(v9, v11) = v13) | ~ (sdtpldt0(v9, v10) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : ? [v15] : ( ~ (v15 = v14) & sdtpldt0(v11, v9) = v15 & sdtpldt0(v10, v9) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = sz10 | v11 = sz00 | ~ (sdtpldt0(v12, v11) = v13) | ~ (sdtpldt0(v9, v10) = v12) | ~ iLess0(v13, v1) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | doDivides0(v11, v10) | doDivides0(v11, v9) | ? [v14] : ? [v15] : ? [v16] : ((v16 = v11 & ~ (v14 = v11) & ~ (v14 = sz10) & sdtasdt0(v14, v15) = v11 & doDivides0(v14, v11) & aNaturalNumber0(v15) & aNaturalNumber0(v14)) | (sdtasdt0(v9, v10) = v14 & ~ doDivides0(v11, v14) & ! [v17] : ( ~ (sdtasdt0(v11, v17) = v14) | ~ aNaturalNumber0(v17))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = sz10 | v11 = sz00 | ~ (sdtpldt0(v12, v11) = v13) | ~ (sdtpldt0(v9, v10) = v12) | ~ iLess0(v13, v1) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | doDivides0(v11, v10) | ? [v14] : ? [v15] : ? [v16] : ((v16 = v11 & ~ (v14 = v11) & ~ (v14 = sz10) & sdtasdt0(v14, v15) = v11 & doDivides0(v14, v11) & aNaturalNumber0(v15) & aNaturalNumber0(v14)) | (v15 = v9 & sdtasdt0(v11, v14) = v9 & aNaturalNumber0(v14)) | (sdtasdt0(v9, v10) = v14 & ~ doDivides0(v11, v14) & ! [v17] : ( ~ (sdtasdt0(v11, v17) = v14) | ~ aNaturalNumber0(v17))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = sz10 | v11 = sz00 | ~ (sdtpldt0(v12, v11) = v13) | ~ (sdtpldt0(v9, v10) = v12) | ~ iLess0(v13, v1) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | doDivides0(v11, v9) | ? [v14] : ? [v15] : ? [v16] : ((v16 = v11 & ~ (v14 = v11) & ~ (v14 = sz10) & sdtasdt0(v14, v15) = v11 & doDivides0(v14, v11) & aNaturalNumber0(v15) & aNaturalNumber0(v14)) | (v15 = v10 & sdtasdt0(v11, v14) = v10 & aNaturalNumber0(v14)) | (sdtasdt0(v9, v10) = v14 & ~ doDivides0(v11, v14) & ! [v17] : ( ~ (sdtasdt0(v11, v17) = v14) | ~ aNaturalNumber0(v17))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = sz10 | v11 = sz00 | ~ (sdtpldt0(v12, v11) = v13) | ~ (sdtpldt0(v9, v10) = v12) | ~ iLess0(v13, v1) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : ? [v15] : ? [v16] : ((v16 = v11 & ~ (v14 = v11) & ~ (v14 = sz10) & sdtasdt0(v14, v15) = v11 & doDivides0(v14, v11) & aNaturalNumber0(v15) & aNaturalNumber0(v14)) | (v15 = v10 & sdtasdt0(v11, v14) = v10 & aNaturalNumber0(v14)) | (v15 = v9 & sdtasdt0(v11, v14) = v9 & aNaturalNumber0(v14)) | (sdtasdt0(v9, v10) = v14 & ~ doDivides0(v11, v14) & ! [v17] : ( ~ (sdtasdt0(v11, v17) = v14) | ~ aNaturalNumber0(v17))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = sz00 | ~ (sdtsldt0(v10, v9) = v11) | ~ (sdtasdt0(v12, v11) = v13) | ~ doDivides0(v9, v10) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : (sdtsldt0(v14, v9) = v13 & sdtasdt0(v12, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtasdt0(v12, v11) = v13) | ~ (sdtasdt0(v9, v10) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : (sdtasdt0(v10, v11) = v14 & sdtasdt0(v9, v14) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtasdt0(v12, v9) = v13) | ~ (sdtpldt0(v10, v11) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (sdtasdt0(v11, v9) = v18 & sdtasdt0(v10, v9) = v17 & sdtasdt0(v9, v12) = v14 & sdtasdt0(v9, v11) = v16 & sdtasdt0(v9, v10) = v15 & sdtpldt0(v17, v18) = v13 & sdtpldt0(v15, v16) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtasdt0(v10, v11) = v12) | ~ (sdtasdt0(v9, v12) = v13) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : (sdtasdt0(v14, v11) = v13 & sdtasdt0(v9, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtasdt0(v9, v12) = v13) | ~ (sdtpldt0(v10, v11) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (sdtasdt0(v12, v9) = v16 & sdtasdt0(v11, v9) = v18 & sdtasdt0(v10, v9) = v17 & sdtasdt0(v9, v11) = v15 & sdtasdt0(v9, v10) = v14 & sdtpldt0(v17, v18) = v16 & sdtpldt0(v14, v15) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtpldt0(v12, v11) = v13) | ~ (sdtpldt0(v9, v10) = v12) | ~ isPrime0(v11) | ~ iLess0(v13, v1) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | doDivides0(v11, v10) | doDivides0(v11, v9) | ? [v14] : (sdtasdt0(v9, v10) = v14 & ~ doDivides0(v11, v14) & ! [v15] : ( ~ (sdtasdt0(v11, v15) = v14) | ~ aNaturalNumber0(v15)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtpldt0(v12, v11) = v13) | ~ (sdtpldt0(v9, v10) = v12) | ~ isPrime0(v11) | ~ iLess0(v13, v1) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | doDivides0(v11, v10) | ? [v14] : ? [v15] : ((v15 = v9 & sdtasdt0(v11, v14) = v9 & aNaturalNumber0(v14)) | (sdtasdt0(v9, v10) = v14 & ~ doDivides0(v11, v14) & ! [v16] : ( ~ (sdtasdt0(v11, v16) = v14) | ~ aNaturalNumber0(v16))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtpldt0(v12, v11) = v13) | ~ (sdtpldt0(v9, v10) = v12) | ~ isPrime0(v11) | ~ iLess0(v13, v1) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | doDivides0(v11, v9) | ? [v14] : ? [v15] : ((v15 = v10 & sdtasdt0(v11, v14) = v10 & aNaturalNumber0(v14)) | (sdtasdt0(v9, v10) = v14 & ~ doDivides0(v11, v14) & ! [v16] : ( ~ (sdtasdt0(v11, v16) = v14) | ~ aNaturalNumber0(v16))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtpldt0(v12, v11) = v13) | ~ (sdtpldt0(v9, v10) = v12) | ~ isPrime0(v11) | ~ iLess0(v13, v1) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : ? [v15] : ((v15 = v10 & sdtasdt0(v11, v14) = v10 & aNaturalNumber0(v14)) | (v15 = v9 & sdtasdt0(v11, v14) = v9 & aNaturalNumber0(v14)) | (sdtasdt0(v9, v10) = v14 & ~ doDivides0(v11, v14) & ! [v16] : ( ~ (sdtasdt0(v11, v16) = v14) | ~ aNaturalNumber0(v16))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtpldt0(v12, v11) = v13) | ~ (sdtpldt0(v9, v10) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : (sdtpldt0(v10, v11) = v14 & sdtpldt0(v9, v14) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtpldt0(v10, v11) = v12) | ~ (sdtpldt0(v9, v12) = v13) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v14] : (sdtpldt0(v14, v11) = v13 & sdtpldt0(v9, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | v9 = sz00 | ~ (sdtsldt0(v10, v9) = v11) | ~ (sdtasdt0(v9, v12) = v10) | ~ doDivides0(v9, v10) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (sdtmndt0(v10, v9) = v11) | ~ (sdtpldt0(v9, v12) = v10) | ~ sdtlseqdt0(v9, v10) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | v9 = sz00 | ~ (sdtsldt0(v10, v9) = v11) | ~ (sdtasdt0(v9, v11) = v12) | ~ doDivides0(v9, v10) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (sdtmndt0(v10, v9) = v11) | ~ (sdtpldt0(v9, v11) = v12) | ~ sdtlseqdt0(v9, v10) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | v9 = sz00 | ~ (sdtasdt0(v11, v9) = v12) | ~ (sdtasdt0(v10, v9) = v12) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | v9 = sz00 | ~ (sdtasdt0(v11, v9) = v12) | ~ (sdtasdt0(v10, v9) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | v9 = sz00 | ~ (sdtasdt0(v9, v11) = v12) | ~ (sdtasdt0(v9, v10) = v12) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | v9 = sz00 | ~ (sdtasdt0(v9, v11) = v12) | ~ (sdtasdt0(v9, v10) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (sdtpldt0(v11, v9) = v12) | ~ (sdtpldt0(v10, v9) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (sdtpldt0(v9, v11) = v12) | ~ (sdtpldt0(v9, v10) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (sdtsldt0(v12, v11) = v10) | ~ (sdtsldt0(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (sdtmndt0(v12, v11) = v10) | ~ (sdtmndt0(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] : (v10 = v9 | ~ (sdtpldt0(v11, v10) = v12) | ~ sdtlseqdt0(v9, v10) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v13] : ? [v14] : ? [v15] : ( ~ (v15 = v14) & ~ (v13 = v12) & sdtpldt0(v11, v9) = v13 & sdtpldt0(v10, v11) = v15 & sdtpldt0(v9, v11) = v14 & sdtlseqdt0(v14, v15) & sdtlseqdt0(v13, v12))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (sdtpldt0(v11, v9) = v12) | ~ sdtlseqdt0(v9, v10) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v13] : ? [v14] : ? [v15] : ( ~ (v15 = v14) & ~ (v13 = v12) & sdtpldt0(v11, v10) = v13 & sdtpldt0(v10, v11) = v15 & sdtpldt0(v9, v11) = v14 & sdtlseqdt0(v14, v15) & sdtlseqdt0(v12, v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (sdtpldt0(v10, v11) = v12) | ~ sdtlseqdt0(v9, v10) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v13] : ? [v14] : ? [v15] : ( ~ (v15 = v12) & ~ (v14 = v13) & sdtpldt0(v11, v10) = v14 & sdtpldt0(v11, v9) = v13 & sdtpldt0(v9, v11) = v15 & sdtlseqdt0(v15, v12) & sdtlseqdt0(v13, v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (sdtpldt0(v9, v11) = v12) | ~ sdtlseqdt0(v9, v10) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v13] : ? [v14] : ? [v15] : ( ~ (v15 = v12) & ~ (v14 = v13) & sdtpldt0(v11, v10) = v14 & sdtpldt0(v11, v9) = v13 & sdtpldt0(v10, v11) = v15 & sdtlseqdt0(v13, v14) & sdtlseqdt0(v12, v15))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = sz00 | ~ (sdtsldt0(v10, v9) = v11) | ~ (sdtasdt0(v9, v11) = v12) | ~ doDivides0(v9, v10) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | aNaturalNumber0(v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtmndt0(v10, v9) = v11) | ~ (sdtpldt0(v9, v11) = v12) | ~ sdtlseqdt0(v9, v10) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | aNaturalNumber0(v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtpldt0(v10, v11) = v12) | ~ doDivides0(v9, v12) | ~ doDivides0(v9, v10) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | doDivides0(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtpldt0(v10, v11) = v12) | ~ doDivides0(v9, v11) | ~ doDivides0(v9, v10) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | doDivides0(v9, v12)) & ! [v9] : ! [v10] : ! [v11] : (v9 = sz00 | ~ (sdtasdt0(v10, v9) = v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | sdtlseqdt0(v10, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v10, v9) = v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | sdtasdt0(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v9, v11) = v10) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | doDivides0(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v9, v10) = v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | sdtasdt0(v10, v9) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v9, v10) = v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | aNaturalNumber0(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtpldt0(v10, v9) = v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | sdtpldt0(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtpldt0(v9, v11) = v10) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | sdtlseqdt0(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtpldt0(v9, v10) = v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | sdtpldt0(v10, v9) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtpldt0(v9, v10) = v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | aNaturalNumber0(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ doDivides0(v10, v11) | ~ doDivides0(v9, v10) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | doDivides0(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ sdtlseqdt0(v10, v11) | ~ sdtlseqdt0(v9, v10) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | sdtlseqdt0(v9, v11)) & ! [v9] : ! [v10] : (v10 = v9 | v10 = sz10 | ~ isPrime0(v9) | ~ doDivides0(v10, v9) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (sdtasdt0(v9, sz10) = v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (sdtasdt0(sz10, v9) = v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (sdtpldt0(v9, sz00) = v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (sdtpldt0(sz00, v9) = v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : (v10 = v9 | ~ sdtlseqdt0(v10, v9) | ~ sdtlseqdt0(v9, v10) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : (v10 = v9 | ~ sdtlseqdt0(v9, v10) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | iLess0(v9, v10)) & ! [v9] : ! [v10] : (v10 = sz00 | v9 = sz00 | ~ (sdtasdt0(v9, v10) = sz00) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : (v10 = sz00 | ~ (sdtasdt0(v9, sz00) = v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : (v10 = sz00 | ~ (sdtasdt0(sz00, v9) = v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : (v10 = sz00 | ~ (sdtpldt0(v9, v10) = sz00) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : (v10 = sz00 | ~ doDivides0(v9, v10) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | sdtlseqdt0(v9, v10)) & ! [v9] : ! [v10] : (v9 = xp | v9 = sz10 | ~ (sdtasdt0(v9, v10) = xp) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : (v9 = sz00 | ~ (sdtpldt0(v9, v10) = sz00) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9)) & ! [v9] : ! [v10] : ( ~ (sdtasdt0(v9, sz10) = v10) | ~ aNaturalNumber0(v9) | sdtasdt0(sz10, v9) = v9) & ! [v9] : ! [v10] : ( ~ (sdtasdt0(v9, sz00) = v10) | ~ aNaturalNumber0(v9) | sdtasdt0(sz00, v9) = sz00) & ! [v9] : ! [v10] : ( ~ (sdtasdt0(sz10, v9) = v10) | ~ aNaturalNumber0(v9) | sdtasdt0(v9, sz10) = v9) & ! [v9] : ! [v10] : ( ~ (sdtasdt0(sz00, v9) = v10) | ~ aNaturalNumber0(v9) | sdtasdt0(v9, sz00) = sz00) & ! [v9] : ! [v10] : ( ~ (sdtpldt0(v9, sz00) = v10) | ~ aNaturalNumber0(v9) | sdtpldt0(sz00, v9) = v9) & ! [v9] : ! [v10] : ( ~ (sdtpldt0(sz00, v9) = v10) | ~ aNaturalNumber0(v9) | sdtpldt0(v9, sz00) = v9) & ! [v9] : ! [v10] : ( ~ doDivides0(v9, v10) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v11] : (sdtasdt0(v9, v11) = v10 & aNaturalNumber0(v11))) & ! [v9] : ! [v10] : ( ~ sdtlseqdt0(v9, v10) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | ? [v11] : (sdtpldt0(v9, v11) = v10 & aNaturalNumber0(v11))) & ! [v9] : ! [v10] : ( ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v9) | sdtlseqdt0(v10, v9) | sdtlseqdt0(v9, v10)) & ! [v9] : (v9 = xp | v9 = sz10 | ~ doDivides0(v9, xp) | ~ aNaturalNumber0(v9)) & ! [v9] : (v9 = sz10 | v9 = sz00 | ~ aNaturalNumber0(v9) | isPrime0(v9) | ? [v10] : ( ~ (v10 = v9) & ~ (v10 = sz10) & doDivides0(v10, v9) & aNaturalNumber0(v10))) & ! [v9] : (v9 = sz10 | v9 = sz00 | ~ aNaturalNumber0(v9) | sdtlseqdt0(sz10, v9)) & ! [v9] : (v9 = sz10 | v9 = sz00 | ~ aNaturalNumber0(v9) | ? [v10] : (isPrime0(v10) & doDivides0(v10, v9) & aNaturalNumber0(v10))) & ! [v9] : ( ~ aNaturalNumber0(v9) | sdtlseqdt0(v9, v9)) & ! [v9] : ( ~ aNaturalNumber0(v9) | ? [v10] : ( ~ (v10 = xm) & sdtasdt0(xp, v9) = v10)) & ! [v9] : ( ~ aNaturalNumber0(v9) | ? [v10] : ( ~ (v10 = xn) & sdtasdt0(xp, v9) = v10)))
% 63.18/34.58 | 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:
% 63.18/34.58 | (1) ~ (xr = xn) & ~ (xp = sz10) & ~ (xp = sz00) & ~ (sz10 = sz00) & sdtmndt0(xn, xp) = xr & sdtasdt0(xr, xm) = all_0_5_5 & sdtasdt0(xp, all_0_0_0) = all_0_6_6 & sdtasdt0(xp, all_0_3_3) = all_0_5_5 & sdtasdt0(xp, all_0_4_4) = xr & sdtasdt0(xn, xm) = all_0_6_6 & sdtpldt0(all_0_8_8, xp) = all_0_7_7 & sdtpldt0(xr, all_0_2_2) = xn & sdtpldt0(xp, all_0_1_1) = xn & sdtpldt0(xp, xr) = xn & sdtpldt0(xn, xm) = all_0_8_8 & isPrime0(xp) & doDivides0(xp, all_0_5_5) & doDivides0(xp, all_0_6_6) & doDivides0(xp, xr) & sdtlseqdt0(xr, xn) & sdtlseqdt0(xp, xn) & aNaturalNumber0(all_0_0_0) & aNaturalNumber0(all_0_1_1) & aNaturalNumber0(all_0_2_2) & aNaturalNumber0(all_0_3_3) & aNaturalNumber0(all_0_4_4) & aNaturalNumber0(xr) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ isPrime0(sz10) & ~ isPrime0(sz00) & ~ doDivides0(xp, xm) & ~ doDivides0(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(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [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(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtlseqdt0(v6, v4) & sdtlseqdt0(v3, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v3) & sdtlseqdt0(v4, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5)) & ! [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(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v0, v2) = v6 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v1) = 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_7_7) | ~ 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_7_7) | ~ 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_7_7) | ~ 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_7_7) | ~ 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] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v2) = v4) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtsldt0(v5, v0) = v4 & sdtasdt0(v3, v1) = v5)) & ! [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] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v6, v7) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_7_7) | ~ 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_7_7) | ~ 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_7_7) | ~ 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_7_7) | ~ 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] : ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5)) & ! [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(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ 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(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = 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(v2, v1) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v4, v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v0) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v1) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v1, 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(v0, v2) = v6 & sdtlseqdt0(v6, v3) & sdtlseqdt0(v4, v5))) & ! [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(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, 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(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = 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(v0, sz10) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = 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(v0, sz00) = 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(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00) & ! [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(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0) & ! [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] : ( ~ 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))
% 63.18/34.61 |
% 63.18/34.61 | Applying alpha-rule on (1) yields:
% 63.18/34.61 | (2) doDivides0(xp, xr)
% 63.18/34.61 | (3) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 63.18/34.61 | (4) ! [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)
% 63.18/34.61 | (5) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1] : ( ~ (v1 = v0) & ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 63.18/34.61 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5))
% 63.18/34.61 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v1) = v5))
% 63.18/34.61 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5))
% 63.18/34.61 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 63.18/34.61 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2)
% 63.18/34.61 | (11) aNaturalNumber0(all_0_2_2)
% 63.18/34.61 | (12) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0)
% 63.18/34.61 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 63.18/34.61 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_7_7) | ~ 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)))))
% 63.18/34.61 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_7_7) | ~ 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)))))
% 63.18/34.61 | (16) ! [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)))
% 63.18/34.61 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v1, 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(v0, v2) = v6 & sdtlseqdt0(v6, v3) & sdtlseqdt0(v4, v5)))
% 63.18/34.61 | (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))
% 63.18/34.61 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_7_7) | ~ 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)))))
% 63.18/34.61 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 63.18/34.61 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0))
% 63.18/34.61 | (22) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 63.18/34.61 | (23) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 63.18/34.61 | (24) aNaturalNumber0(all_0_3_3)
% 63.18/34.61 | (25) doDivides0(xp, all_0_6_6)
% 63.18/34.61 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 63.18/34.61 | (27) sdtpldt0(xn, xm) = all_0_8_8
% 63.18/34.61 | (28) ! [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))
% 63.18/34.61 | (29) sdtlseqdt0(xp, xn)
% 63.18/34.61 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2)
% 63.18/34.61 | (31) ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 63.18/34.62 | (32) ~ (xp = sz10)
% 63.18/34.62 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_7_7) | ~ 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)))))
% 63.18/34.62 | (34) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 63.18/34.62 | (35) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 63.18/34.62 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 63.18/34.62 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtlseqdt0(v6, v4) & sdtlseqdt0(v3, v5)))
% 63.18/34.62 | (38) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 63.18/34.62 | (39) ! [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))
% 63.18/34.62 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 63.18/34.62 | (41) ~ (xp = sz00)
% 63.18/34.62 | (42) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 63.18/34.62 | (43) sdtlseqdt0(xr, xn)
% 63.18/34.62 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 63.18/34.62 | (45) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0)
% 63.18/34.62 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 63.18/34.62 | (47) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0))
% 63.18/34.62 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v1) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v4, v3)))
% 63.18/34.62 | (49) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 63.18/34.62 | (50) ~ isPrime0(sz00)
% 63.18/34.62 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 63.18/34.62 | (52) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 63.18/34.62 | (53) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 63.18/34.62 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_7_7) | ~ 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)))))
% 63.18/34.62 | (55) doDivides0(xp, all_0_5_5)
% 63.18/34.62 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 63.18/34.62 | (57) ! [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))
% 63.18/34.62 | (58) ! [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))
% 63.18/34.62 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_7_7) | ~ 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)))))
% 63.18/34.62 | (60) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 63.18/34.62 | (61) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 63.18/34.62 | (62) ! [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))
% 63.18/34.63 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6))
% 63.18/34.63 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 63.18/34.63 | (65) sdtpldt0(xr, all_0_2_2) = xn
% 63.18/34.63 | (66) aNaturalNumber0(xp)
% 63.18/34.63 | (67) sdtasdt0(xn, xm) = all_0_6_6
% 63.18/34.63 | (68) ! [v0] : ! [v1] : (v1 = sz00 | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 63.18/34.63 | (69) ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = xn) & sdtasdt0(xp, v0) = v1))
% 63.18/34.63 | (70) aNaturalNumber0(all_0_4_4)
% 63.18/34.63 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_7_7) | ~ 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))))
% 63.18/34.63 | (72) sdtasdt0(xp, all_0_3_3) = all_0_5_5
% 63.18/34.63 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 63.18/34.63 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 63.18/34.63 | (75) ! [v0] : (v0 = xp | v0 = sz10 | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0))
% 63.18/34.63 | (76) ! [v0] : ! [v1] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1) = xp) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 63.18/34.63 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v0) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v1) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v3, v4)))
% 63.18/34.63 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 63.18/34.63 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 63.18/34.63 | (80) aNaturalNumber0(sz00)
% 63.18/34.63 | (81) sdtasdt0(xr, xm) = all_0_5_5
% 63.18/34.63 | (82) sdtmndt0(xn, xp) = xr
% 63.18/34.63 | (83) ! [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))
% 63.18/34.63 | (84) sdtasdt0(xp, all_0_4_4) = xr
% 63.18/34.63 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v3) & sdtlseqdt0(v4, v6)))
% 63.18/34.63 | (86) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 63.18/34.63 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5))
% 63.18/34.63 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4))
% 63.18/34.63 | (89) ~ doDivides0(xp, xm)
% 63.18/34.63 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5))
% 63.18/34.63 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 63.18/34.63 | (92) aNaturalNumber0(xr)
% 63.18/34.63 | (93) aNaturalNumber0(xn)
% 63.18/34.63 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v6, v7) = v5))
% 63.18/34.63 | (95) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00)
% 63.18/34.63 | (96) ~ (sz10 = sz00)
% 63.18/34.63 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_7_7) | ~ 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)))))
% 63.18/34.64 | (98) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 63.18/34.64 | (99) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 63.18/34.64 | (100) isPrime0(xp)
% 63.18/34.64 | (101) ! [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)))
% 63.18/34.64 | (102) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 63.65/34.64 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5))
% 63.65/34.64 | (104) sdtpldt0(xp, all_0_1_1) = xn
% 63.65/34.64 | (105) ~ isPrime0(sz10)
% 63.65/34.64 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5))
% 63.65/34.64 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 63.65/34.64 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v2) = v4) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtsldt0(v5, v0) = v4 & sdtasdt0(v3, v1) = v5))
% 63.65/34.64 | (109) aNaturalNumber0(sz10)
% 63.65/34.64 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3))
% 63.65/34.64 | (111) aNaturalNumber0(all_0_0_0)
% 63.65/34.64 | (112) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 63.65/34.64 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 63.65/34.64 | (114) ! [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))
% 63.65/34.64 | (115) ~ (xr = xn)
% 63.65/34.64 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 63.65/34.64 | (117) ~ doDivides0(xp, xn)
% 63.65/34.64 | (118) sdtpldt0(xp, xr) = xn
% 63.65/34.64 | (119) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 63.65/34.64 | (120) ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 63.65/34.64 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 63.65/34.64 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v0, v2) = v6 & sdtpldt0(v0, v1) = v5))
% 63.65/34.64 | (123) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 63.65/34.64 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4))
% 63.65/34.64 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v6)))
% 63.65/34.64 | (126) sdtpldt0(all_0_8_8, xp) = all_0_7_7
% 63.65/34.64 | (127) aNaturalNumber0(all_0_1_1)
% 63.65/34.64 | (128) aNaturalNumber0(xm)
% 63.65/34.64 | (129) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 63.65/34.64 | (130) sdtasdt0(xp, all_0_0_0) = all_0_6_6
% 63.65/34.64 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 63.65/34.64 | (132) ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = xm) & sdtasdt0(xp, v0) = v1))
% 63.65/34.64 |
% 63.65/34.64 | Instantiating formula (73) with all_0_1_1, xr, xn, xp and discharging atoms sdtmndt0(xn, xp) = xr, sdtpldt0(xp, all_0_1_1) = xn, sdtlseqdt0(xp, xn), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 63.65/34.65 | (133) all_0_1_1 = xr
% 63.65/34.65 |
% 63.65/34.65 | From (133) and (104) follows:
% 63.65/34.65 | (118) sdtpldt0(xp, xr) = xn
% 63.65/34.65 |
% 63.65/34.65 | From (133) and (127) follows:
% 63.65/34.65 | (92) aNaturalNumber0(xr)
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (99) with all_0_2_2 and discharging atoms aNaturalNumber0(all_0_2_2), yields:
% 63.65/34.65 | (136) all_0_2_2 = sz10 | all_0_2_2 = sz00 | ? [v0] : (isPrime0(v0) & doDivides0(v0, all_0_2_2) & aNaturalNumber0(v0))
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (69) with all_0_2_2 and discharging atoms aNaturalNumber0(all_0_2_2), yields:
% 63.65/34.65 | (137) ? [v0] : ( ~ (v0 = xn) & sdtasdt0(xp, all_0_2_2) = v0)
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (132) with all_0_4_4 and discharging atoms aNaturalNumber0(all_0_4_4), yields:
% 63.65/34.65 | (138) ? [v0] : ( ~ (v0 = xm) & sdtasdt0(xp, all_0_4_4) = v0)
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (132) with xr and discharging atoms aNaturalNumber0(xr), yields:
% 63.65/34.65 | (139) ? [v0] : ( ~ (v0 = xm) & sdtasdt0(xp, xr) = v0)
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (69) with xr and discharging atoms aNaturalNumber0(xr), yields:
% 63.65/34.65 | (140) ? [v0] : ( ~ (v0 = xn) & sdtasdt0(xp, xr) = v0)
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (10) with xr, xp, all_0_4_4 and discharging atoms sdtasdt0(xp, all_0_4_4) = xr, aNaturalNumber0(all_0_4_4), aNaturalNumber0(xp), yields:
% 63.65/34.65 | (141) sdtasdt0(all_0_4_4, xp) = xr
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (30) with xn, xp, xr and discharging atoms sdtpldt0(xp, xr) = xn, aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 63.65/34.65 | (142) sdtpldt0(xr, xp) = xn
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (31) with xr, xp and discharging atoms doDivides0(xp, xr), aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 63.65/34.65 | (143) ? [v0] : (sdtasdt0(xp, v0) = xr & aNaturalNumber0(v0))
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (102) with xp and discharging atoms aNaturalNumber0(xp), yields:
% 63.65/34.65 | (144) xp = sz10 | xp = sz00 | sdtlseqdt0(sz10, xp)
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (99) with xp and discharging atoms aNaturalNumber0(xp), yields:
% 63.65/34.65 | (145) xp = sz10 | xp = sz00 | ? [v0] : (isPrime0(v0) & doDivides0(v0, xp) & aNaturalNumber0(v0))
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (132) with xp and discharging atoms aNaturalNumber0(xp), yields:
% 63.65/34.65 | (146) ? [v0] : ( ~ (v0 = xm) & sdtasdt0(xp, xp) = v0)
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (69) with xp and discharging atoms aNaturalNumber0(xp), yields:
% 63.65/34.65 | (147) ? [v0] : ( ~ (v0 = xn) & sdtasdt0(xp, xp) = v0)
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (94) with all_0_6_6, xn, all_0_2_2, xr, xm and discharging atoms sdtasdt0(xn, xm) = all_0_6_6, sdtpldt0(xr, all_0_2_2) = xn, aNaturalNumber0(all_0_2_2), aNaturalNumber0(xr), aNaturalNumber0(xm), yields:
% 63.65/34.65 | (148) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_2_2, xm) = v4 & sdtasdt0(xr, xm) = v3 & sdtasdt0(xm, all_0_2_2) = v2 & sdtasdt0(xm, xr) = v1 & sdtasdt0(xm, xn) = v0 & sdtpldt0(v3, v4) = all_0_6_6 & sdtpldt0(v1, v2) = v0)
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (94) with all_0_6_6, xn, xr, xp, xm and discharging atoms sdtasdt0(xn, xm) = all_0_6_6, sdtpldt0(xp, xr) = xn, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 63.65/34.65 | (149) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(xr, xm) = v4 & sdtasdt0(xp, xm) = v3 & sdtasdt0(xm, xr) = v2 & sdtasdt0(xm, xp) = v1 & sdtasdt0(xm, xn) = v0 & sdtpldt0(v3, v4) = all_0_6_6 & sdtpldt0(v1, v2) = v0)
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (18) with all_0_8_8, xn, xm, all_0_2_2, xr and discharging atoms sdtpldt0(xr, all_0_2_2) = xn, sdtpldt0(xn, xm) = all_0_8_8, aNaturalNumber0(all_0_2_2), aNaturalNumber0(xr), aNaturalNumber0(xm), yields:
% 63.65/34.65 | (150) ? [v0] : (sdtpldt0(all_0_2_2, xm) = v0 & sdtpldt0(xr, v0) = all_0_8_8)
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (18) with all_0_8_8, xn, xm, xr, xp and discharging atoms sdtpldt0(xp, xr) = xn, sdtpldt0(xn, xm) = all_0_8_8, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 63.65/34.65 | (151) ? [v0] : (sdtpldt0(xr, xm) = v0 & sdtpldt0(xp, v0) = all_0_8_8)
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (132) with xm and discharging atoms aNaturalNumber0(xm), yields:
% 63.65/34.65 | (152) ? [v0] : ( ~ (v0 = xm) & sdtasdt0(xp, xm) = v0)
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (69) with xm and discharging atoms aNaturalNumber0(xm), yields:
% 63.65/34.65 | (153) ? [v0] : ( ~ (v0 = xn) & sdtasdt0(xp, xm) = v0)
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (125) with all_0_6_6, all_0_5_5, xn, xr, xm and discharging atoms sdtasdt0(xr, xm) = all_0_5_5, sdtasdt0(xn, xm) = all_0_6_6, sdtlseqdt0(xr, xn), aNaturalNumber0(xr), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 63.65/34.65 | (154) xr = xn | xm = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xm, xr) = v0 & sdtasdt0(xm, xn) = v1 & sdtlseqdt0(v0, v1))
% 63.65/34.65 |
% 63.65/34.65 | Instantiating formula (103) with all_0_6_6, all_0_5_5, xn, xr, xm and discharging atoms sdtasdt0(xr, xm) = all_0_5_5, sdtasdt0(xn, xm) = all_0_6_6, aNaturalNumber0(xr), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 63.65/34.66 | (155) xr = xn | xm = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xm, xr) = v0 & sdtasdt0(xm, xn) = v1)
% 63.65/34.66 |
% 63.65/34.66 | Instantiating formula (10) with all_0_6_6, xn, xm and discharging atoms sdtasdt0(xn, xm) = all_0_6_6, aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 63.65/34.66 | (156) sdtasdt0(xm, xn) = all_0_6_6
% 63.65/34.66 |
% 63.65/34.66 | Instantiating formula (18) 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, aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 63.65/34.66 | (157) ? [v0] : (sdtpldt0(xm, xp) = v0 & sdtpldt0(xn, v0) = all_0_7_7)
% 63.65/34.66 |
% 63.65/34.66 | Instantiating formula (101) with xn, all_0_2_2, xn, xr and discharging atoms sdtpldt0(xr, all_0_2_2) = xn, sdtlseqdt0(xr, xn), aNaturalNumber0(all_0_2_2), aNaturalNumber0(xr), aNaturalNumber0(xn), yields:
% 63.65/34.66 | (158) xr = xn | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xn) & ~ (v1 = v0) & sdtpldt0(all_0_2_2, xr) = v0 & sdtpldt0(all_0_2_2, xn) = v1 & sdtpldt0(xn, all_0_2_2) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xn, v2))
% 63.65/34.66 |
% 63.65/34.66 | Instantiating formula (77) with xn, xp, xn, xr and discharging atoms sdtpldt0(xp, xr) = xn, sdtlseqdt0(xr, xn), aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 63.65/34.66 | (159) xr = xn | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = xn) & sdtpldt0(xr, xp) = v1 & sdtpldt0(xp, xn) = v0 & sdtpldt0(xn, xp) = v2 & sdtlseqdt0(v1, v2) & sdtlseqdt0(xn, v0))
% 63.65/34.66 |
% 63.65/34.66 | Instantiating formula (101) with xn, xr, xn, xp and discharging atoms sdtpldt0(xp, xr) = xn, sdtlseqdt0(xp, xn), aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 63.65/34.66 | (160) xp = xn | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xn) & ~ (v1 = v0) & sdtpldt0(xr, xp) = v0 & sdtpldt0(xr, xn) = v1 & sdtpldt0(xn, xr) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xn, v2))
% 63.65/34.66 |
% 63.65/34.66 | Instantiating formula (17) with all_0_8_8, xm, xn, xr and discharging atoms sdtpldt0(xn, xm) = all_0_8_8, sdtlseqdt0(xr, xn), aNaturalNumber0(xr), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 63.65/34.66 | (161) xr = xn | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_8_8) & ~ (v1 = v0) & sdtpldt0(xr, xm) = v2 & sdtpldt0(xm, xr) = v0 & sdtpldt0(xm, xn) = v1 & sdtlseqdt0(v2, all_0_8_8) & sdtlseqdt0(v0, v1))
% 63.65/34.66 |
% 63.65/34.66 | Instantiating formula (17) with all_0_8_8, xm, xn, xp and discharging atoms sdtpldt0(xn, xm) = all_0_8_8, sdtlseqdt0(xp, xn), aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 63.65/34.66 | (162) xp = xn | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_8_8) & ~ (v1 = v0) & sdtpldt0(xp, xm) = v2 & sdtpldt0(xm, xp) = v0 & sdtpldt0(xm, xn) = v1 & sdtlseqdt0(v2, all_0_8_8) & sdtlseqdt0(v0, v1))
% 63.65/34.66 |
% 63.65/34.66 | Instantiating formula (30) with all_0_8_8, xn, xm and discharging atoms sdtpldt0(xn, xm) = all_0_8_8, aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 63.65/34.66 | (163) sdtpldt0(xm, xn) = all_0_8_8
% 63.65/34.66 |
% 63.65/34.66 | Instantiating formula (3) with xn, xr and discharging atoms sdtlseqdt0(xr, xn), aNaturalNumber0(xr), aNaturalNumber0(xn), yields:
% 63.65/34.66 | (164) ? [v0] : (sdtpldt0(xr, v0) = xn & aNaturalNumber0(v0))
% 63.65/34.66 |
% 63.65/34.66 | Instantiating formula (3) with xn, xp and discharging atoms sdtlseqdt0(xp, xn), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 63.65/34.66 | (165) ? [v0] : (sdtpldt0(xp, v0) = xn & aNaturalNumber0(v0))
% 63.65/34.66 |
% 63.65/34.66 | Instantiating formula (132) with xn and discharging atoms aNaturalNumber0(xn), yields:
% 63.65/34.66 | (166) ? [v0] : ( ~ (v0 = xm) & sdtasdt0(xp, xn) = v0)
% 63.65/34.66 |
% 63.65/34.66 | Instantiating formula (69) with xn and discharging atoms aNaturalNumber0(xn), yields:
% 63.65/34.66 | (167) ? [v0] : ( ~ (v0 = xn) & sdtasdt0(xp, xn) = v0)
% 63.65/34.66 |
% 63.65/34.66 | Instantiating formula (132) with sz10 and discharging atoms aNaturalNumber0(sz10), yields:
% 63.65/34.66 | (168) ? [v0] : ( ~ (v0 = xm) & sdtasdt0(xp, sz10) = v0)
% 63.65/34.66 |
% 63.65/34.66 | Instantiating formula (69) with sz10 and discharging atoms aNaturalNumber0(sz10), yields:
% 63.65/34.66 | (169) ? [v0] : ( ~ (v0 = xn) & sdtasdt0(xp, sz10) = v0)
% 63.65/34.66 |
% 63.65/34.66 | Instantiating formula (132) with sz00 and discharging atoms aNaturalNumber0(sz00), yields:
% 63.65/34.66 | (170) ? [v0] : ( ~ (v0 = xm) & sdtasdt0(xp, sz00) = v0)
% 63.65/34.66 |
% 63.65/34.66 | Instantiating formula (69) with sz00 and discharging atoms aNaturalNumber0(sz00), yields:
% 63.65/34.66 | (171) ? [v0] : ( ~ (v0 = xn) & sdtasdt0(xp, sz00) = v0)
% 63.65/34.66 |
% 63.65/34.66 | Instantiating (137) with all_13_0_9 yields:
% 63.65/34.66 | (172) ~ (all_13_0_9 = xn) & sdtasdt0(xp, all_0_2_2) = all_13_0_9
% 63.65/34.66 |
% 63.65/34.66 | Applying alpha-rule on (172) yields:
% 63.65/34.66 | (173) ~ (all_13_0_9 = xn)
% 63.65/34.66 | (174) sdtasdt0(xp, all_0_2_2) = all_13_0_9
% 63.65/34.66 |
% 63.65/34.66 | Instantiating (143) with all_17_0_11 yields:
% 63.65/34.66 | (175) sdtasdt0(xp, all_17_0_11) = xr & aNaturalNumber0(all_17_0_11)
% 63.65/34.66 |
% 63.65/34.66 | Applying alpha-rule on (175) yields:
% 63.65/34.66 | (176) sdtasdt0(xp, all_17_0_11) = xr
% 63.65/34.66 | (177) aNaturalNumber0(all_17_0_11)
% 63.65/34.66 |
% 63.65/34.66 | Instantiating (140) with all_23_0_14 yields:
% 63.65/34.66 | (178) ~ (all_23_0_14 = xn) & sdtasdt0(xp, xr) = all_23_0_14
% 63.65/34.66 |
% 63.65/34.66 | Applying alpha-rule on (178) yields:
% 63.65/34.66 | (179) ~ (all_23_0_14 = xn)
% 63.65/34.66 | (180) sdtasdt0(xp, xr) = all_23_0_14
% 63.65/34.66 |
% 63.65/34.66 | Instantiating (139) with all_25_0_15 yields:
% 63.65/34.66 | (181) ~ (all_25_0_15 = xm) & sdtasdt0(xp, xr) = all_25_0_15
% 63.65/34.66 |
% 63.65/34.66 | Applying alpha-rule on (181) yields:
% 63.65/34.66 | (182) ~ (all_25_0_15 = xm)
% 63.65/34.66 | (183) sdtasdt0(xp, xr) = all_25_0_15
% 63.65/34.66 |
% 63.65/34.66 | Instantiating (138) with all_27_0_16 yields:
% 63.65/34.66 | (184) ~ (all_27_0_16 = xm) & sdtasdt0(xp, all_0_4_4) = all_27_0_16
% 63.65/34.66 |
% 63.65/34.66 | Applying alpha-rule on (184) yields:
% 63.65/34.66 | (185) ~ (all_27_0_16 = xm)
% 63.65/34.66 | (186) sdtasdt0(xp, all_0_4_4) = all_27_0_16
% 63.65/34.66 |
% 63.65/34.66 | Instantiating (168) with all_33_0_19 yields:
% 63.65/34.66 | (187) ~ (all_33_0_19 = xm) & sdtasdt0(xp, sz10) = all_33_0_19
% 63.65/34.66 |
% 63.65/34.66 | Applying alpha-rule on (187) yields:
% 63.65/34.66 | (188) ~ (all_33_0_19 = xm)
% 63.65/34.66 | (189) sdtasdt0(xp, sz10) = all_33_0_19
% 63.65/34.66 |
% 63.65/34.66 | Instantiating (165) with all_35_0_20 yields:
% 63.65/34.66 | (190) sdtpldt0(xp, all_35_0_20) = xn & aNaturalNumber0(all_35_0_20)
% 63.65/34.66 |
% 63.65/34.66 | Applying alpha-rule on (190) yields:
% 63.65/34.66 | (191) sdtpldt0(xp, all_35_0_20) = xn
% 63.65/34.66 | (192) aNaturalNumber0(all_35_0_20)
% 63.65/34.66 |
% 63.65/34.66 | Instantiating (169) with all_37_0_21 yields:
% 63.65/34.66 | (193) ~ (all_37_0_21 = xn) & sdtasdt0(xp, sz10) = all_37_0_21
% 63.65/34.66 |
% 63.65/34.66 | Applying alpha-rule on (193) yields:
% 63.65/34.66 | (194) ~ (all_37_0_21 = xn)
% 63.65/34.66 | (195) sdtasdt0(xp, sz10) = all_37_0_21
% 63.65/34.66 |
% 63.65/34.66 | Instantiating (167) with all_39_0_22 yields:
% 63.65/34.66 | (196) ~ (all_39_0_22 = xn) & sdtasdt0(xp, xn) = all_39_0_22
% 63.65/34.66 |
% 63.65/34.67 | Applying alpha-rule on (196) yields:
% 63.65/34.67 | (197) ~ (all_39_0_22 = xn)
% 63.65/34.67 | (198) sdtasdt0(xp, xn) = all_39_0_22
% 63.65/34.67 |
% 63.65/34.67 | Instantiating (171) with all_41_0_23 yields:
% 63.65/34.67 | (199) ~ (all_41_0_23 = xn) & sdtasdt0(xp, sz00) = all_41_0_23
% 63.65/34.67 |
% 63.65/34.67 | Applying alpha-rule on (199) yields:
% 63.65/34.67 | (200) ~ (all_41_0_23 = xn)
% 63.65/34.67 | (201) sdtasdt0(xp, sz00) = all_41_0_23
% 63.65/34.67 |
% 63.65/34.67 | Instantiating (170) with all_43_0_24 yields:
% 63.65/34.67 | (202) ~ (all_43_0_24 = xm) & sdtasdt0(xp, sz00) = all_43_0_24
% 63.65/34.67 |
% 63.65/34.67 | Applying alpha-rule on (202) yields:
% 63.65/34.67 | (203) ~ (all_43_0_24 = xm)
% 63.65/34.67 | (204) sdtasdt0(xp, sz00) = all_43_0_24
% 63.65/34.67 |
% 63.65/34.67 | Instantiating (157) with all_45_0_25 yields:
% 63.65/34.67 | (205) sdtpldt0(xm, xp) = all_45_0_25 & sdtpldt0(xn, all_45_0_25) = all_0_7_7
% 63.65/34.67 |
% 63.65/34.67 | Applying alpha-rule on (205) yields:
% 63.65/34.67 | (206) sdtpldt0(xm, xp) = all_45_0_25
% 63.65/34.67 | (207) sdtpldt0(xn, all_45_0_25) = all_0_7_7
% 63.65/34.67 |
% 63.65/34.67 | Instantiating (166) with all_47_0_26 yields:
% 63.65/34.67 | (208) ~ (all_47_0_26 = xm) & sdtasdt0(xp, xn) = all_47_0_26
% 63.65/34.67 |
% 63.65/34.67 | Applying alpha-rule on (208) yields:
% 63.65/34.67 | (209) ~ (all_47_0_26 = xm)
% 63.65/34.67 | (210) sdtasdt0(xp, xn) = all_47_0_26
% 63.65/34.67 |
% 63.65/34.67 | Instantiating (148) with all_49_0_27, all_49_1_28, all_49_2_29, all_49_3_30, all_49_4_31 yields:
% 63.65/34.67 | (211) sdtasdt0(all_0_2_2, xm) = all_49_0_27 & sdtasdt0(xr, xm) = all_49_1_28 & sdtasdt0(xm, all_0_2_2) = all_49_2_29 & sdtasdt0(xm, xr) = all_49_3_30 & sdtasdt0(xm, xn) = all_49_4_31 & sdtpldt0(all_49_1_28, all_49_0_27) = all_0_6_6 & sdtpldt0(all_49_3_30, all_49_2_29) = all_49_4_31
% 63.65/34.67 |
% 63.65/34.67 | Applying alpha-rule on (211) yields:
% 63.65/34.67 | (212) sdtasdt0(all_0_2_2, xm) = all_49_0_27
% 63.65/34.67 | (213) sdtpldt0(all_49_1_28, all_49_0_27) = all_0_6_6
% 63.65/34.67 | (214) sdtasdt0(xm, xn) = all_49_4_31
% 63.65/34.67 | (215) sdtasdt0(xr, xm) = all_49_1_28
% 63.65/34.67 | (216) sdtasdt0(xm, xr) = all_49_3_30
% 63.65/34.67 | (217) sdtpldt0(all_49_3_30, all_49_2_29) = all_49_4_31
% 63.65/34.67 | (218) sdtasdt0(xm, all_0_2_2) = all_49_2_29
% 63.65/34.67 |
% 63.65/34.67 | Instantiating (153) with all_51_0_32 yields:
% 63.65/34.67 | (219) ~ (all_51_0_32 = xn) & sdtasdt0(xp, xm) = all_51_0_32
% 63.65/34.67 |
% 63.65/34.67 | Applying alpha-rule on (219) yields:
% 63.65/34.67 | (220) ~ (all_51_0_32 = xn)
% 63.65/34.67 | (221) sdtasdt0(xp, xm) = all_51_0_32
% 63.65/34.67 |
% 63.65/34.67 | Instantiating (147) with all_53_0_33 yields:
% 63.65/34.67 | (222) ~ (all_53_0_33 = xn) & sdtasdt0(xp, xp) = all_53_0_33
% 63.65/34.67 |
% 63.65/34.67 | Applying alpha-rule on (222) yields:
% 63.65/34.67 | (223) ~ (all_53_0_33 = xn)
% 63.65/34.67 | (224) sdtasdt0(xp, xp) = all_53_0_33
% 63.65/34.67 |
% 63.65/34.67 | Instantiating (146) with all_55_0_34 yields:
% 63.65/34.67 | (225) ~ (all_55_0_34 = xm) & sdtasdt0(xp, xp) = all_55_0_34
% 63.65/34.67 |
% 63.65/34.67 | Applying alpha-rule on (225) yields:
% 63.65/34.67 | (226) ~ (all_55_0_34 = xm)
% 63.65/34.67 | (227) sdtasdt0(xp, xp) = all_55_0_34
% 63.65/34.67 |
% 63.65/34.67 | Instantiating (152) with all_57_0_35 yields:
% 63.65/34.67 | (228) ~ (all_57_0_35 = xm) & sdtasdt0(xp, xm) = all_57_0_35
% 63.65/34.67 |
% 63.65/34.67 | Applying alpha-rule on (228) yields:
% 63.65/34.67 | (229) ~ (all_57_0_35 = xm)
% 63.65/34.67 | (230) sdtasdt0(xp, xm) = all_57_0_35
% 63.65/34.67 |
% 63.65/34.67 | Instantiating (151) with all_59_0_36 yields:
% 63.65/34.67 | (231) sdtpldt0(xr, xm) = all_59_0_36 & sdtpldt0(xp, all_59_0_36) = all_0_8_8
% 63.65/34.67 |
% 63.65/34.67 | Applying alpha-rule on (231) yields:
% 63.65/34.67 | (232) sdtpldt0(xr, xm) = all_59_0_36
% 63.65/34.67 | (233) sdtpldt0(xp, all_59_0_36) = all_0_8_8
% 63.65/34.67 |
% 63.65/34.67 | Instantiating (150) with all_61_0_37 yields:
% 63.65/34.67 | (234) sdtpldt0(all_0_2_2, xm) = all_61_0_37 & sdtpldt0(xr, all_61_0_37) = all_0_8_8
% 63.65/34.67 |
% 63.65/34.67 | Applying alpha-rule on (234) yields:
% 63.65/34.67 | (235) sdtpldt0(all_0_2_2, xm) = all_61_0_37
% 63.65/34.67 | (236) sdtpldt0(xr, all_61_0_37) = all_0_8_8
% 63.65/34.67 |
% 63.65/34.67 | Instantiating (164) with all_65_0_39 yields:
% 63.65/34.67 | (237) sdtpldt0(xr, all_65_0_39) = xn & aNaturalNumber0(all_65_0_39)
% 63.65/34.67 |
% 63.65/34.67 | Applying alpha-rule on (237) yields:
% 63.65/34.67 | (238) sdtpldt0(xr, all_65_0_39) = xn
% 63.65/34.67 | (239) aNaturalNumber0(all_65_0_39)
% 63.65/34.67 |
% 63.65/34.67 | Instantiating (149) with all_67_0_40, all_67_1_41, all_67_2_42, all_67_3_43, all_67_4_44 yields:
% 63.65/34.67 | (240) sdtasdt0(xr, xm) = all_67_0_40 & sdtasdt0(xp, xm) = all_67_1_41 & sdtasdt0(xm, xr) = all_67_2_42 & sdtasdt0(xm, xp) = all_67_3_43 & sdtasdt0(xm, xn) = all_67_4_44 & sdtpldt0(all_67_1_41, all_67_0_40) = all_0_6_6 & sdtpldt0(all_67_3_43, all_67_2_42) = all_67_4_44
% 63.65/34.67 |
% 63.65/34.67 | Applying alpha-rule on (240) yields:
% 63.65/34.67 | (241) sdtasdt0(xm, xr) = all_67_2_42
% 63.65/34.67 | (242) sdtasdt0(xr, xm) = all_67_0_40
% 63.65/34.67 | (243) sdtasdt0(xm, xp) = all_67_3_43
% 63.65/34.67 | (244) sdtasdt0(xm, xn) = all_67_4_44
% 63.65/34.67 | (245) sdtasdt0(xp, xm) = all_67_1_41
% 63.65/34.67 | (246) sdtpldt0(all_67_3_43, all_67_2_42) = all_67_4_44
% 63.65/34.67 | (247) sdtpldt0(all_67_1_41, all_67_0_40) = all_0_6_6
% 63.65/34.67 |
% 63.65/34.67 +-Applying beta-rule and splitting (158), into two cases.
% 63.65/34.67 |-Branch one:
% 63.65/34.67 | (248) xr = xn
% 63.65/34.67 |
% 63.65/34.67 | Equations (248) can reduce 115 to:
% 63.65/34.67 | (249) $false
% 63.65/34.67 |
% 63.65/34.67 |-The branch is then unsatisfiable
% 63.65/34.67 |-Branch two:
% 63.65/34.67 | (115) ~ (xr = xn)
% 63.65/34.67 | (251) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xn) & ~ (v1 = v0) & sdtpldt0(all_0_2_2, xr) = v0 & sdtpldt0(all_0_2_2, xn) = v1 & sdtpldt0(xn, all_0_2_2) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xn, v2))
% 63.65/34.67 |
% 63.65/34.67 | Instantiating (251) with all_76_0_45, all_76_1_46, all_76_2_47 yields:
% 63.65/34.67 | (252) ~ (all_76_0_45 = xn) & ~ (all_76_1_46 = all_76_2_47) & sdtpldt0(all_0_2_2, xr) = all_76_2_47 & sdtpldt0(all_0_2_2, xn) = all_76_1_46 & sdtpldt0(xn, all_0_2_2) = all_76_0_45 & sdtlseqdt0(all_76_2_47, all_76_1_46) & sdtlseqdt0(xn, all_76_0_45)
% 63.65/34.67 |
% 63.65/34.67 | Applying alpha-rule on (252) yields:
% 63.65/34.67 | (253) sdtlseqdt0(xn, all_76_0_45)
% 63.65/34.67 | (254) sdtpldt0(all_0_2_2, xr) = all_76_2_47
% 63.65/34.67 | (255) sdtpldt0(all_0_2_2, xn) = all_76_1_46
% 63.65/34.67 | (256) ~ (all_76_0_45 = xn)
% 63.65/34.67 | (257) sdtlseqdt0(all_76_2_47, all_76_1_46)
% 63.65/34.67 | (258) ~ (all_76_1_46 = all_76_2_47)
% 63.65/34.67 | (259) sdtpldt0(xn, all_0_2_2) = all_76_0_45
% 63.65/34.67 |
% 63.65/34.67 +-Applying beta-rule and splitting (159), into two cases.
% 63.65/34.67 |-Branch one:
% 63.65/34.67 | (248) xr = xn
% 63.65/34.67 |
% 63.65/34.67 | Equations (248) can reduce 115 to:
% 63.65/34.67 | (249) $false
% 63.65/34.67 |
% 63.65/34.67 |-The branch is then unsatisfiable
% 63.65/34.67 |-Branch two:
% 63.65/34.67 | (115) ~ (xr = xn)
% 63.65/34.67 | (263) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = xn) & sdtpldt0(xr, xp) = v1 & sdtpldt0(xp, xn) = v0 & sdtpldt0(xn, xp) = v2 & sdtlseqdt0(v1, v2) & sdtlseqdt0(xn, v0))
% 63.65/34.67 |
% 63.65/34.67 | Instantiating (263) with all_81_0_48, all_81_1_49, all_81_2_50 yields:
% 63.65/34.67 | (264) ~ (all_81_0_48 = all_81_1_49) & ~ (all_81_2_50 = xn) & sdtpldt0(xr, xp) = all_81_1_49 & sdtpldt0(xp, xn) = all_81_2_50 & sdtpldt0(xn, xp) = all_81_0_48 & sdtlseqdt0(all_81_1_49, all_81_0_48) & sdtlseqdt0(xn, all_81_2_50)
% 63.65/34.67 |
% 63.65/34.67 | Applying alpha-rule on (264) yields:
% 63.65/34.67 | (265) sdtlseqdt0(xn, all_81_2_50)
% 63.65/34.67 | (266) sdtlseqdt0(all_81_1_49, all_81_0_48)
% 63.65/34.67 | (267) ~ (all_81_2_50 = xn)
% 63.65/34.67 | (268) sdtpldt0(xr, xp) = all_81_1_49
% 63.65/34.67 | (269) sdtpldt0(xn, xp) = all_81_0_48
% 63.65/34.67 | (270) ~ (all_81_0_48 = all_81_1_49)
% 63.65/34.67 | (271) sdtpldt0(xp, xn) = all_81_2_50
% 63.65/34.67 |
% 63.65/34.67 +-Applying beta-rule and splitting (144), into two cases.
% 63.65/34.67 |-Branch one:
% 63.65/34.67 | (272) sdtlseqdt0(sz10, xp)
% 63.65/34.67 |
% 63.65/34.67 +-Applying beta-rule and splitting (161), into two cases.
% 63.65/34.67 |-Branch one:
% 63.65/34.67 | (248) xr = xn
% 63.65/34.67 |
% 63.65/34.67 | Equations (248) can reduce 115 to:
% 63.65/34.67 | (249) $false
% 63.65/34.67 |
% 63.65/34.67 |-The branch is then unsatisfiable
% 63.65/34.67 |-Branch two:
% 63.65/34.67 | (115) ~ (xr = xn)
% 63.65/34.67 | (276) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_8_8) & ~ (v1 = v0) & sdtpldt0(xr, xm) = v2 & sdtpldt0(xm, xr) = v0 & sdtpldt0(xm, xn) = v1 & sdtlseqdt0(v2, all_0_8_8) & sdtlseqdt0(v0, v1))
% 63.65/34.67 |
% 63.65/34.67 | Instantiating (276) with all_91_0_51, all_91_1_52, all_91_2_53 yields:
% 63.65/34.67 | (277) ~ (all_91_0_51 = all_0_8_8) & ~ (all_91_1_52 = all_91_2_53) & sdtpldt0(xr, xm) = all_91_0_51 & sdtpldt0(xm, xr) = all_91_2_53 & sdtpldt0(xm, xn) = all_91_1_52 & sdtlseqdt0(all_91_0_51, all_0_8_8) & sdtlseqdt0(all_91_2_53, all_91_1_52)
% 63.65/34.68 |
% 63.65/34.68 | Applying alpha-rule on (277) yields:
% 63.65/34.68 | (278) sdtpldt0(xr, xm) = all_91_0_51
% 63.65/34.68 | (279) sdtlseqdt0(all_91_2_53, all_91_1_52)
% 63.65/34.68 | (280) sdtlseqdt0(all_91_0_51, all_0_8_8)
% 63.65/34.68 | (281) ~ (all_91_0_51 = all_0_8_8)
% 63.65/34.68 | (282) sdtpldt0(xm, xn) = all_91_1_52
% 63.65/34.68 | (283) sdtpldt0(xm, xr) = all_91_2_53
% 63.65/34.68 | (284) ~ (all_91_1_52 = all_91_2_53)
% 63.65/34.68 |
% 63.65/34.68 +-Applying beta-rule and splitting (145), into two cases.
% 63.65/34.68 |-Branch one:
% 63.65/34.68 | (285) xp = sz00
% 63.65/34.68 |
% 63.65/34.68 | Equations (285) can reduce 41 to:
% 63.65/34.68 | (249) $false
% 63.65/34.68 |
% 63.65/34.68 |-The branch is then unsatisfiable
% 63.65/34.68 |-Branch two:
% 63.65/34.68 | (41) ~ (xp = sz00)
% 63.65/34.68 | (288) xp = sz10 | ? [v0] : (isPrime0(v0) & doDivides0(v0, xp) & aNaturalNumber0(v0))
% 63.65/34.68 |
% 63.65/34.68 +-Applying beta-rule and splitting (288), into two cases.
% 63.65/34.68 |-Branch one:
% 63.65/34.68 | (289) xp = sz10
% 63.65/34.68 |
% 63.65/34.68 | Equations (289) can reduce 32 to:
% 63.65/34.68 | (249) $false
% 63.65/34.68 |
% 63.65/34.68 |-The branch is then unsatisfiable
% 63.65/34.68 |-Branch two:
% 63.65/34.68 | (32) ~ (xp = sz10)
% 63.65/34.68 | (292) ? [v0] : (isPrime0(v0) & doDivides0(v0, xp) & aNaturalNumber0(v0))
% 63.65/34.68 |
% 63.65/34.68 | Instantiating formula (36) with xp, all_0_4_4, all_27_0_16, xr and discharging atoms sdtasdt0(xp, all_0_4_4) = all_27_0_16, sdtasdt0(xp, all_0_4_4) = xr, yields:
% 63.65/34.68 | (293) all_27_0_16 = xr
% 63.65/34.68 |
% 63.65/34.68 | Instantiating formula (36) with xp, xr, all_23_0_14, all_25_0_15 and discharging atoms sdtasdt0(xp, xr) = all_25_0_15, sdtasdt0(xp, xr) = all_23_0_14, yields:
% 63.65/34.68 | (294) all_25_0_15 = all_23_0_14
% 63.65/34.68 |
% 63.65/34.68 | Instantiating formula (36) with xp, xp, all_53_0_33, all_55_0_34 and discharging atoms sdtasdt0(xp, xp) = all_55_0_34, sdtasdt0(xp, xp) = all_53_0_33, yields:
% 63.65/34.68 | (295) all_55_0_34 = all_53_0_33
% 63.65/34.68 |
% 63.65/34.68 | Instantiating formula (36) with xp, xm, all_57_0_35, all_67_1_41 and discharging atoms sdtasdt0(xp, xm) = all_67_1_41, sdtasdt0(xp, xm) = all_57_0_35, yields:
% 63.65/34.68 | (296) all_67_1_41 = all_57_0_35
% 63.65/34.68 |
% 63.65/34.68 | Instantiating formula (36) with xp, xm, all_51_0_32, all_67_1_41 and discharging atoms sdtasdt0(xp, xm) = all_67_1_41, sdtasdt0(xp, xm) = all_51_0_32, yields:
% 63.65/34.68 | (297) all_67_1_41 = all_51_0_32
% 63.65/34.68 |
% 63.65/34.68 | Instantiating formula (36) with xp, xn, all_39_0_22, all_47_0_26 and discharging atoms sdtasdt0(xp, xn) = all_47_0_26, sdtasdt0(xp, xn) = all_39_0_22, yields:
% 63.65/34.68 | (298) all_47_0_26 = all_39_0_22
% 63.65/34.68 |
% 63.65/34.68 | Instantiating formula (47) with all_37_0_21, xp and discharging atoms sdtasdt0(xp, sz10) = all_37_0_21, aNaturalNumber0(xp), yields:
% 63.65/34.68 | (299) all_37_0_21 = xp
% 63.65/34.68 |
% 63.65/34.68 | Instantiating formula (36) with xp, sz10, all_33_0_19, all_37_0_21 and discharging atoms sdtasdt0(xp, sz10) = all_37_0_21, sdtasdt0(xp, sz10) = all_33_0_19, yields:
% 63.65/34.68 | (300) all_37_0_21 = all_33_0_19
% 63.65/34.68 |
% 63.65/34.68 | Instantiating formula (35) with all_43_0_24, xp and discharging atoms sdtasdt0(xp, sz00) = all_43_0_24, aNaturalNumber0(xp), yields:
% 63.65/34.68 | (301) all_43_0_24 = sz00
% 63.65/34.68 |
% 63.65/34.68 | Instantiating formula (36) with xp, sz00, all_41_0_23, all_43_0_24 and discharging atoms sdtasdt0(xp, sz00) = all_43_0_24, sdtasdt0(xp, sz00) = all_41_0_23, yields:
% 63.65/34.68 | (302) all_43_0_24 = all_41_0_23
% 63.65/34.68 |
% 63.65/34.68 | Instantiating formula (36) with xm, xn, all_49_4_31, all_67_4_44 and discharging atoms sdtasdt0(xm, xn) = all_67_4_44, sdtasdt0(xm, xn) = all_49_4_31, yields:
% 63.65/34.68 | (303) all_67_4_44 = all_49_4_31
% 63.65/34.68 |
% 63.65/34.68 | Instantiating formula (36) with xm, xn, all_0_6_6, all_67_4_44 and discharging atoms sdtasdt0(xm, xn) = all_67_4_44, sdtasdt0(xm, xn) = all_0_6_6, yields:
% 63.65/34.68 | (304) all_67_4_44 = all_0_6_6
% 63.65/34.68 |
% 63.65/34.68 | Instantiating formula (121) with xr, xp, xn, all_81_1_49 and discharging atoms sdtpldt0(xr, xp) = all_81_1_49, sdtpldt0(xr, xp) = xn, yields:
% 63.65/34.68 | (305) all_81_1_49 = xn
% 63.65/34.68 |
% 63.65/34.68 | Instantiating formula (121) with xr, xm, all_59_0_36, all_91_0_51 and discharging atoms sdtpldt0(xr, xm) = all_91_0_51, sdtpldt0(xr, xm) = all_59_0_36, yields:
% 63.65/34.68 | (306) all_91_0_51 = all_59_0_36
% 63.65/34.68 |
% 63.65/34.68 | Instantiating formula (121) with xm, xn, all_0_8_8, all_91_1_52 and discharging atoms sdtpldt0(xm, xn) = all_91_1_52, sdtpldt0(xm, xn) = all_0_8_8, yields:
% 63.65/34.68 | (307) all_91_1_52 = all_0_8_8
% 63.65/34.68 |
% 63.65/34.68 | Instantiating formula (79) with xn, all_0_2_2, all_65_0_39, xr and discharging atoms sdtpldt0(xr, all_65_0_39) = xn, sdtpldt0(xr, all_0_2_2) = xn, aNaturalNumber0(all_65_0_39), aNaturalNumber0(all_0_2_2), aNaturalNumber0(xr), yields:
% 63.65/34.68 | (308) all_65_0_39 = all_0_2_2
% 63.65/34.68 |
% 63.65/34.68 | Instantiating formula (79) with xn, all_65_0_39, xp, xr and discharging atoms sdtpldt0(xr, all_65_0_39) = xn, sdtpldt0(xr, xp) = xn, aNaturalNumber0(all_65_0_39), aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 63.65/34.68 | (309) all_65_0_39 = xp
% 63.65/34.68 |
% 63.65/34.68 | Instantiating formula (79) with xn, xr, all_35_0_20, xp and discharging atoms sdtpldt0(xp, all_35_0_20) = xn, sdtpldt0(xp, xr) = xn, aNaturalNumber0(all_35_0_20), aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 63.65/34.68 | (310) all_35_0_20 = xr
% 63.65/34.68 |
% 63.65/34.68 | Instantiating formula (113) with xr, all_0_4_4, all_17_0_11, xp and discharging atoms sdtasdt0(xp, all_17_0_11) = xr, sdtasdt0(xp, all_0_4_4) = xr, aNaturalNumber0(all_17_0_11), aNaturalNumber0(all_0_4_4), aNaturalNumber0(xp), yields:
% 63.65/34.68 | (311) all_17_0_11 = all_0_4_4 | xp = sz00
% 63.65/34.68 |
% 63.65/34.68 | Combining equations (297,296) yields a new equation:
% 63.65/34.68 | (312) all_57_0_35 = all_51_0_32
% 63.65/34.68 |
% 63.65/34.68 | Combining equations (304,303) yields a new equation:
% 63.65/34.68 | (313) all_49_4_31 = all_0_6_6
% 63.65/34.68 |
% 63.65/34.68 | Combining equations (308,309) yields a new equation:
% 63.65/34.68 | (314) all_0_2_2 = xp
% 63.65/34.68 |
% 63.65/34.68 | Simplifying 314 yields:
% 63.65/34.68 | (315) all_0_2_2 = xp
% 63.65/34.68 |
% 63.65/34.68 | Combining equations (301,302) yields a new equation:
% 63.65/34.68 | (316) all_41_0_23 = sz00
% 63.65/34.68 |
% 63.65/34.68 | Combining equations (299,300) yields a new equation:
% 63.65/34.68 | (317) all_33_0_19 = xp
% 63.65/34.68 |
% 63.65/34.68 | Combining equations (317,300) yields a new equation:
% 63.65/34.68 | (299) all_37_0_21 = xp
% 63.65/34.68 |
% 63.65/34.68 | Combining equations (316,302) yields a new equation:
% 63.65/34.68 | (301) all_43_0_24 = sz00
% 63.65/34.68 |
% 63.65/34.68 | Equations (301) can reduce 203 to:
% 63.65/34.68 | (320) ~ (xm = sz00)
% 63.65/34.68 |
% 63.65/34.68 | Simplifying 320 yields:
% 63.65/34.68 | (321) ~ (xm = sz00)
% 63.65/34.68 |
% 63.65/34.68 | Equations (316) can reduce 200 to:
% 63.65/34.68 | (322) ~ (xn = sz00)
% 63.65/34.68 |
% 63.65/34.68 | Simplifying 322 yields:
% 63.65/34.68 | (323) ~ (xn = sz00)
% 63.65/34.68 |
% 63.65/34.68 | Equations (299) can reduce 194 to:
% 63.65/34.68 | (324) ~ (xp = xn)
% 63.65/34.68 |
% 63.65/34.68 | Equations (317) can reduce 188 to:
% 63.65/34.68 | (325) ~ (xp = xm)
% 63.65/34.68 |
% 63.65/34.68 | Equations (293) can reduce 185 to:
% 63.65/34.68 | (326) ~ (xr = xm)
% 63.65/34.68 |
% 63.65/34.68 | From (315) and (212) follows:
% 63.65/34.68 | (327) sdtasdt0(xp, xm) = all_49_0_27
% 63.65/34.68 |
% 63.65/34.68 | From (315) and (174) follows:
% 63.65/34.68 | (328) sdtasdt0(xp, xp) = all_13_0_9
% 63.65/34.68 |
% 63.65/34.68 | From (294) and (183) follows:
% 63.65/34.68 | (180) sdtasdt0(xp, xr) = all_23_0_14
% 63.65/34.68 |
% 63.65/34.68 | From (295) and (227) follows:
% 63.65/34.68 | (224) sdtasdt0(xp, xp) = all_53_0_33
% 63.65/34.68 |
% 63.65/34.68 | From (312) and (230) follows:
% 63.65/34.68 | (221) sdtasdt0(xp, xm) = all_51_0_32
% 63.65/34.68 |
% 63.65/34.68 | From (298) and (210) follows:
% 63.65/34.68 | (198) sdtasdt0(xp, xn) = all_39_0_22
% 63.65/34.68 |
% 63.65/34.68 | From (317) and (189) follows:
% 63.65/34.68 | (333) sdtasdt0(xp, sz10) = xp
% 63.65/34.68 |
% 63.65/34.68 | From (316) and (201) follows:
% 63.65/34.68 | (334) sdtasdt0(xp, sz00) = sz00
% 63.65/34.68 |
% 63.65/34.68 | From (315) and (218) follows:
% 63.65/34.68 | (335) sdtasdt0(xm, xp) = all_49_2_29
% 63.65/34.68 |
% 63.65/34.68 | From (313) and (214) follows:
% 63.65/34.68 | (156) sdtasdt0(xm, xn) = all_0_6_6
% 63.65/34.68 |
% 63.65/34.68 | From (315) and (235) follows:
% 63.65/34.68 | (337) sdtpldt0(xp, xm) = all_61_0_37
% 63.65/34.68 |
% 63.65/34.68 | From (315) and (255) follows:
% 63.65/34.68 | (338) sdtpldt0(xp, xn) = all_76_1_46
% 63.65/34.68 |
% 63.65/34.68 | From (305) and (268) follows:
% 63.65/34.68 | (142) sdtpldt0(xr, xp) = xn
% 63.65/34.68 |
% 63.65/34.68 | From (306) and (278) follows:
% 63.65/34.68 | (232) sdtpldt0(xr, xm) = all_59_0_36
% 63.65/34.68 |
% 63.65/34.68 | From (310) and (191) follows:
% 63.65/34.68 | (118) sdtpldt0(xp, xr) = xn
% 63.65/34.68 |
% 63.65/34.68 | From (307) and (282) follows:
% 63.65/34.68 | (163) sdtpldt0(xm, xn) = all_0_8_8
% 63.65/34.68 |
% 63.65/34.68 | From (315) and (259) follows:
% 63.65/34.68 | (343) sdtpldt0(xn, xp) = all_76_0_45
% 63.65/34.68 |
% 63.65/34.68 | From (310) and (192) follows:
% 63.65/34.68 | (92) aNaturalNumber0(xr)
% 63.65/34.68 |
% 63.65/34.68 | From (315) and (11) follows:
% 63.65/34.68 | (66) aNaturalNumber0(xp)
% 63.65/34.68 |
% 63.65/34.68 +-Applying beta-rule and splitting (155), into two cases.
% 63.65/34.68 |-Branch one:
% 63.65/34.68 | (346) xm = sz00
% 63.65/34.68 |
% 63.65/34.68 | Equations (346) can reduce 321 to:
% 63.65/34.68 | (249) $false
% 63.65/34.68 |
% 63.65/34.68 |-The branch is then unsatisfiable
% 63.65/34.68 |-Branch two:
% 63.65/34.68 | (321) ~ (xm = sz00)
% 63.65/34.68 | (349) xr = xn | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xm, xr) = v0 & sdtasdt0(xm, xn) = v1)
% 63.65/34.68 |
% 63.65/34.68 +-Applying beta-rule and splitting (349), into two cases.
% 63.65/34.68 |-Branch one:
% 63.65/34.68 | (248) xr = xn
% 63.65/34.68 |
% 63.65/34.68 | Equations (248) can reduce 115 to:
% 63.65/34.68 | (249) $false
% 63.65/34.68 |
% 63.65/34.68 |-The branch is then unsatisfiable
% 63.65/34.68 |-Branch two:
% 63.65/34.68 | (115) ~ (xr = xn)
% 63.65/34.68 | (353) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xm, xr) = v0 & sdtasdt0(xm, xn) = v1)
% 63.65/34.69 |
% 63.65/34.69 | Instantiating (353) with all_122_0_55, all_122_1_56 yields:
% 63.65/34.69 | (354) ~ (all_122_0_55 = all_122_1_56) & sdtasdt0(xm, xr) = all_122_1_56 & sdtasdt0(xm, xn) = all_122_0_55
% 63.65/34.69 |
% 63.65/34.69 | Applying alpha-rule on (354) yields:
% 63.65/34.69 | (355) ~ (all_122_0_55 = all_122_1_56)
% 63.65/34.69 | (356) sdtasdt0(xm, xr) = all_122_1_56
% 63.65/34.69 | (357) sdtasdt0(xm, xn) = all_122_0_55
% 63.65/34.69 |
% 63.65/34.69 +-Applying beta-rule and splitting (154), into two cases.
% 63.65/34.69 |-Branch one:
% 63.65/34.69 | (346) xm = sz00
% 63.65/34.69 |
% 63.65/34.69 | Equations (346) can reduce 321 to:
% 63.65/34.69 | (249) $false
% 63.65/34.69 |
% 63.65/34.69 |-The branch is then unsatisfiable
% 63.65/34.69 |-Branch two:
% 63.65/34.69 | (321) ~ (xm = sz00)
% 63.65/34.69 | (361) xr = xn | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xm, xr) = v0 & sdtasdt0(xm, xn) = v1 & sdtlseqdt0(v0, v1))
% 63.65/34.69 |
% 63.65/34.69 +-Applying beta-rule and splitting (160), into two cases.
% 63.65/34.69 |-Branch one:
% 63.65/34.69 | (362) xp = xn
% 63.65/34.69 |
% 63.65/34.69 | Equations (362) can reduce 324 to:
% 63.65/34.69 | (249) $false
% 63.65/34.69 |
% 63.65/34.69 |-The branch is then unsatisfiable
% 63.65/34.69 |-Branch two:
% 63.65/34.69 | (324) ~ (xp = xn)
% 63.65/34.69 | (365) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xn) & ~ (v1 = v0) & sdtpldt0(xr, xp) = v0 & sdtpldt0(xr, xn) = v1 & sdtpldt0(xn, xr) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xn, v2))
% 63.65/34.69 |
% 63.65/34.69 | Instantiating (365) with all_131_0_57, all_131_1_58, all_131_2_59 yields:
% 63.65/34.69 | (366) ~ (all_131_0_57 = xn) & ~ (all_131_1_58 = all_131_2_59) & sdtpldt0(xr, xp) = all_131_2_59 & sdtpldt0(xr, xn) = all_131_1_58 & sdtpldt0(xn, xr) = all_131_0_57 & sdtlseqdt0(all_131_2_59, all_131_1_58) & sdtlseqdt0(xn, all_131_0_57)
% 63.65/34.69 |
% 63.65/34.69 | Applying alpha-rule on (366) yields:
% 63.65/34.69 | (367) ~ (all_131_1_58 = all_131_2_59)
% 63.65/34.69 | (368) sdtpldt0(xr, xn) = all_131_1_58
% 63.65/34.69 | (369) sdtpldt0(xn, xr) = all_131_0_57
% 63.65/34.69 | (370) sdtlseqdt0(xn, all_131_0_57)
% 63.65/34.69 | (371) ~ (all_131_0_57 = xn)
% 63.65/34.69 | (372) sdtpldt0(xr, xp) = all_131_2_59
% 63.65/34.69 | (373) sdtlseqdt0(all_131_2_59, all_131_1_58)
% 63.65/34.69 |
% 63.65/34.69 +-Applying beta-rule and splitting (361), into two cases.
% 63.65/34.69 |-Branch one:
% 63.65/34.69 | (248) xr = xn
% 63.65/34.69 |
% 63.65/34.69 | Equations (248) can reduce 115 to:
% 63.65/34.69 | (249) $false
% 63.65/34.69 |
% 63.65/34.69 |-The branch is then unsatisfiable
% 63.65/34.69 |-Branch two:
% 63.65/34.69 | (115) ~ (xr = xn)
% 63.65/34.69 | (377) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xm, xr) = v0 & sdtasdt0(xm, xn) = v1 & sdtlseqdt0(v0, v1))
% 63.65/34.69 |
% 63.65/34.69 | Instantiating (377) with all_137_0_60, all_137_1_61 yields:
% 63.65/34.69 | (378) ~ (all_137_0_60 = all_137_1_61) & sdtasdt0(xm, xr) = all_137_1_61 & sdtasdt0(xm, xn) = all_137_0_60 & sdtlseqdt0(all_137_1_61, all_137_0_60)
% 63.65/34.69 |
% 63.65/34.69 | Applying alpha-rule on (378) yields:
% 63.65/34.69 | (379) ~ (all_137_0_60 = all_137_1_61)
% 63.65/34.69 | (380) sdtasdt0(xm, xr) = all_137_1_61
% 63.65/34.69 | (381) sdtasdt0(xm, xn) = all_137_0_60
% 63.65/34.69 | (382) sdtlseqdt0(all_137_1_61, all_137_0_60)
% 63.65/34.69 |
% 63.65/34.69 +-Applying beta-rule and splitting (311), into two cases.
% 63.65/34.69 |-Branch one:
% 63.65/34.69 | (285) xp = sz00
% 63.65/34.69 |
% 63.65/34.69 | Equations (285) can reduce 41 to:
% 63.65/34.69 | (249) $false
% 63.65/34.69 |
% 63.65/34.69 |-The branch is then unsatisfiable
% 63.65/34.69 |-Branch two:
% 63.65/34.69 | (41) ~ (xp = sz00)
% 63.65/34.69 | (386) all_17_0_11 = all_0_4_4
% 63.65/34.69 |
% 63.65/34.69 | From (386) and (176) follows:
% 63.90/34.69 | (84) sdtasdt0(xp, all_0_4_4) = xr
% 63.90/34.69 |
% 63.90/34.69 | From (386) and (177) follows:
% 63.90/34.69 | (70) aNaturalNumber0(all_0_4_4)
% 63.90/34.69 |
% 63.90/34.69 +-Applying beta-rule and splitting (136), into two cases.
% 63.90/34.69 |-Branch one:
% 63.90/34.69 | (389) all_0_2_2 = sz00
% 63.90/34.69 |
% 63.90/34.69 | Combining equations (389,315) yields a new equation:
% 63.90/34.69 | (285) xp = sz00
% 63.90/34.69 |
% 63.90/34.69 | Equations (285) can reduce 41 to:
% 63.90/34.69 | (249) $false
% 63.90/34.69 |
% 63.90/34.69 |-The branch is then unsatisfiable
% 63.90/34.69 |-Branch two:
% 63.90/34.69 | (392) ~ (all_0_2_2 = sz00)
% 63.90/34.69 | (393) all_0_2_2 = sz10 | ? [v0] : (isPrime0(v0) & doDivides0(v0, all_0_2_2) & aNaturalNumber0(v0))
% 63.90/34.69 |
% 63.90/34.69 | Equations (315) can reduce 392 to:
% 63.90/34.69 | (41) ~ (xp = sz00)
% 63.90/34.69 |
% 63.90/34.69 +-Applying beta-rule and splitting (162), into two cases.
% 63.90/34.69 |-Branch one:
% 63.90/34.69 | (362) xp = xn
% 63.90/34.69 |
% 63.90/34.69 | Equations (362) can reduce 324 to:
% 63.90/34.69 | (249) $false
% 63.90/34.69 |
% 63.90/34.69 |-The branch is then unsatisfiable
% 63.90/34.69 |-Branch two:
% 63.90/34.69 | (324) ~ (xp = xn)
% 63.90/34.69 | (398) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_8_8) & ~ (v1 = v0) & sdtpldt0(xp, xm) = v2 & sdtpldt0(xm, xp) = v0 & sdtpldt0(xm, xn) = v1 & sdtlseqdt0(v2, all_0_8_8) & sdtlseqdt0(v0, v1))
% 63.90/34.69 |
% 63.90/34.69 | Instantiating (398) with all_158_0_62, all_158_1_63, all_158_2_64 yields:
% 63.90/34.69 | (399) ~ (all_158_0_62 = all_0_8_8) & ~ (all_158_1_63 = all_158_2_64) & sdtpldt0(xp, xm) = all_158_0_62 & sdtpldt0(xm, xp) = all_158_2_64 & sdtpldt0(xm, xn) = all_158_1_63 & sdtlseqdt0(all_158_0_62, all_0_8_8) & sdtlseqdt0(all_158_2_64, all_158_1_63)
% 63.90/34.69 |
% 63.90/34.69 | Applying alpha-rule on (399) yields:
% 63.90/34.69 | (400) sdtlseqdt0(all_158_2_64, all_158_1_63)
% 63.90/34.69 | (401) ~ (all_158_1_63 = all_158_2_64)
% 63.90/34.69 | (402) sdtpldt0(xm, xn) = all_158_1_63
% 63.90/34.69 | (403) sdtpldt0(xp, xm) = all_158_0_62
% 63.90/34.69 | (404) ~ (all_158_0_62 = all_0_8_8)
% 63.90/34.69 | (405) sdtpldt0(xm, xp) = all_158_2_64
% 63.90/34.69 | (406) sdtlseqdt0(all_158_0_62, all_0_8_8)
% 63.90/34.69 |
% 63.90/34.69 +-Applying beta-rule and splitting (393), into two cases.
% 63.90/34.69 |-Branch one:
% 63.90/34.69 | (407) all_0_2_2 = sz10
% 63.90/34.69 |
% 63.90/34.69 | Combining equations (407,315) yields a new equation:
% 63.90/34.69 | (289) xp = sz10
% 63.90/34.69 |
% 63.90/34.69 | Equations (289) can reduce 32 to:
% 63.90/34.69 | (249) $false
% 63.90/34.69 |
% 63.90/34.69 |-The branch is then unsatisfiable
% 63.90/34.69 |-Branch two:
% 63.90/34.69 | (410) ~ (all_0_2_2 = sz10)
% 63.90/34.69 | (411) ? [v0] : (isPrime0(v0) & doDivides0(v0, all_0_2_2) & aNaturalNumber0(v0))
% 63.90/34.69 |
% 63.90/34.69 | Equations (315) can reduce 410 to:
% 63.90/34.69 | (32) ~ (xp = sz10)
% 63.90/34.69 |
% 63.90/34.69 | Instantiating formula (36) with xp, xp, all_13_0_9, all_53_0_33 and discharging atoms sdtasdt0(xp, xp) = all_53_0_33, sdtasdt0(xp, xp) = all_13_0_9, yields:
% 63.90/34.69 | (413) all_53_0_33 = all_13_0_9
% 63.90/34.69 |
% 63.90/34.69 | Instantiating formula (36) with xp, xm, all_49_0_27, all_51_0_32 and discharging atoms sdtasdt0(xp, xm) = all_51_0_32, sdtasdt0(xp, xm) = all_49_0_27, yields:
% 63.90/34.69 | (414) all_51_0_32 = all_49_0_27
% 63.90/34.69 |
% 63.90/34.69 | Instantiating formula (36) with xm, xp, all_49_2_29, all_67_3_43 and discharging atoms sdtasdt0(xm, xp) = all_67_3_43, sdtasdt0(xm, xp) = all_49_2_29, yields:
% 63.90/34.69 | (415) all_67_3_43 = all_49_2_29
% 63.90/34.69 |
% 63.90/34.69 | Instantiating formula (36) with xm, xn, all_137_0_60, all_0_6_6 and discharging atoms sdtasdt0(xm, xn) = all_137_0_60, sdtasdt0(xm, xn) = all_0_6_6, yields:
% 63.90/34.69 | (416) all_137_0_60 = all_0_6_6
% 63.90/34.69 |
% 63.90/34.69 | Instantiating formula (36) with xm, xn, all_122_0_55, all_137_0_60 and discharging atoms sdtasdt0(xm, xn) = all_137_0_60, sdtasdt0(xm, xn) = all_122_0_55, yields:
% 63.90/34.69 | (417) all_137_0_60 = all_122_0_55
% 63.90/34.69 |
% 63.90/34.69 | Instantiating formula (121) with xr, xp, all_131_2_59, xn and discharging atoms sdtpldt0(xr, xp) = all_131_2_59, sdtpldt0(xr, xp) = xn, yields:
% 63.90/34.69 | (418) all_131_2_59 = xn
% 63.90/34.69 |
% 63.90/34.69 | Instantiating formula (121) with xp, xm, all_61_0_37, all_158_0_62 and discharging atoms sdtpldt0(xp, xm) = all_158_0_62, sdtpldt0(xp, xm) = all_61_0_37, yields:
% 63.90/34.69 | (419) all_158_0_62 = all_61_0_37
% 63.90/34.69 |
% 63.90/34.69 | Instantiating formula (121) with xp, xn, all_76_1_46, all_81_2_50 and discharging atoms sdtpldt0(xp, xn) = all_81_2_50, sdtpldt0(xp, xn) = all_76_1_46, yields:
% 63.90/34.69 | (420) all_81_2_50 = all_76_1_46
% 63.90/34.69 |
% 63.90/34.69 | Instantiating formula (121) with xm, xp, all_158_2_64, all_45_0_25 and discharging atoms sdtpldt0(xm, xp) = all_158_2_64, sdtpldt0(xm, xp) = all_45_0_25, yields:
% 63.90/34.69 | (421) all_158_2_64 = all_45_0_25
% 63.90/34.69 |
% 63.90/34.69 | Instantiating formula (121) with xm, xn, all_158_1_63, all_0_8_8 and discharging atoms sdtpldt0(xm, xn) = all_158_1_63, sdtpldt0(xm, xn) = all_0_8_8, yields:
% 63.90/34.69 | (422) all_158_1_63 = all_0_8_8
% 63.90/34.69 |
% 63.90/34.69 | Instantiating formula (121) with xn, xp, all_76_0_45, all_81_0_48 and discharging atoms sdtpldt0(xn, xp) = all_81_0_48, sdtpldt0(xn, xp) = all_76_0_45, yields:
% 63.90/34.69 | (423) all_81_0_48 = all_76_0_45
% 63.90/34.69 |
% 63.90/34.69 | Combining equations (416,417) yields a new equation:
% 63.90/34.69 | (424) all_122_0_55 = all_0_6_6
% 63.90/34.69 |
% 63.90/34.69 | From (413) and (224) follows:
% 63.90/34.69 | (328) sdtasdt0(xp, xp) = all_13_0_9
% 63.90/34.69 |
% 63.90/34.69 | From (414) and (221) follows:
% 63.90/34.69 | (327) sdtasdt0(xp, xm) = all_49_0_27
% 63.90/34.69 |
% 63.90/34.69 | From (415) and (243) follows:
% 63.90/34.69 | (335) sdtasdt0(xm, xp) = all_49_2_29
% 63.90/34.69 |
% 63.90/34.69 | From (424) and (357) follows:
% 63.90/34.69 | (156) sdtasdt0(xm, xn) = all_0_6_6
% 63.90/34.69 |
% 63.90/34.69 | From (418) and (372) follows:
% 63.90/34.69 | (142) sdtpldt0(xr, xp) = xn
% 63.90/34.69 |
% 63.90/34.69 | From (419) and (403) follows:
% 63.90/34.69 | (337) sdtpldt0(xp, xm) = all_61_0_37
% 63.90/34.69 |
% 63.90/34.69 | From (420) and (271) follows:
% 63.90/34.69 | (338) sdtpldt0(xp, xn) = all_76_1_46
% 63.90/34.69 |
% 63.90/34.69 | From (421) and (405) follows:
% 63.90/34.69 | (206) sdtpldt0(xm, xp) = all_45_0_25
% 63.90/34.69 |
% 63.90/34.69 | From (422) and (402) follows:
% 63.90/34.69 | (163) sdtpldt0(xm, xn) = all_0_8_8
% 63.90/34.69 |
% 63.90/34.69 | From (423) and (269) follows:
% 63.90/34.69 | (343) sdtpldt0(xn, xp) = all_76_0_45
% 63.90/34.69 |
% 63.90/34.69 | Instantiating formula (62) with all_23_0_14, all_49_0_27, xr, xm, xp and discharging atoms sdtasdt0(xp, xr) = all_23_0_14, sdtasdt0(xp, xm) = all_49_0_27, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 63.90/34.69 | (435) xr = xm | xp = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xr, xp) = v1 & sdtasdt0(xm, xp) = v0)
% 63.90/34.69 |
% 63.90/34.69 | Instantiating formula (62) with all_49_0_27, all_23_0_14, xm, xr, xp and discharging atoms sdtasdt0(xp, xr) = all_23_0_14, sdtasdt0(xp, xm) = all_49_0_27, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 63.90/34.69 | (436) xr = xm | xp = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xr, xp) = v0 & sdtasdt0(xm, xp) = v1)
% 63.90/34.69 |
% 63.90/34.69 | Instantiating formula (62) with all_49_0_27, all_13_0_9, xm, xp, xp and discharging atoms sdtasdt0(xp, xp) = all_13_0_9, sdtasdt0(xp, xm) = all_49_0_27, aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 63.90/34.70 | (437) xp = xm | xp = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v0 & sdtasdt0(xm, xp) = v1)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (106) with all_13_0_9, all_49_0_27, xp, xm, xp and discharging atoms sdtasdt0(xp, xp) = all_13_0_9, sdtasdt0(xp, xm) = all_49_0_27, aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 63.90/34.70 | (438) xp = xm | xp = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = all_13_0_9) & ~ (v0 = all_49_0_27) & sdtasdt0(xp, xp) = v0 & sdtasdt0(xm, xp) = v1)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (106) with all_39_0_22, all_0_6_6, xp, xm, xn and discharging atoms sdtasdt0(xp, xn) = all_39_0_22, sdtasdt0(xn, xm) = all_0_6_6, aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 63.90/34.70 | (439) xp = xm | xn = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = all_39_0_22) & ~ (v0 = all_0_6_6) & sdtasdt0(xm, xn) = v1 & sdtasdt0(xn, xp) = v0)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (16) with all_39_0_22, all_23_0_14, xn, xr, xp and discharging atoms sdtasdt0(xp, xr) = all_23_0_14, sdtasdt0(xp, xn) = all_39_0_22, sdtlseqdt0(xr, xn), aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 63.90/34.70 | (440) xr = xn | xp = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xr, xp) = v0 & sdtasdt0(xn, xp) = v1 & sdtlseqdt0(v0, v1))
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (62) with all_39_0_22, all_23_0_14, xn, xr, xp and discharging atoms sdtasdt0(xp, xr) = all_23_0_14, sdtasdt0(xp, xn) = all_39_0_22, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 63.90/34.70 | (441) xr = xn | xp = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xr, xp) = v0 & sdtasdt0(xn, xp) = v1)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (16) with all_39_0_22, all_13_0_9, xn, xp, xp and discharging atoms sdtasdt0(xp, xp) = all_13_0_9, sdtasdt0(xp, xn) = all_39_0_22, sdtlseqdt0(xp, xn), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 63.90/34.70 | (442) xp = xn | xp = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v0 & sdtasdt0(xn, xp) = v1 & sdtlseqdt0(v0, v1))
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (62) with all_13_0_9, all_39_0_22, xp, xn, xp and discharging atoms sdtasdt0(xp, xp) = all_13_0_9, sdtasdt0(xp, xn) = all_39_0_22, aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 63.90/34.70 | (443) xp = xn | xp = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v1 & sdtasdt0(xn, xp) = v0)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (62) with all_39_0_22, all_13_0_9, xn, xp, xp and discharging atoms sdtasdt0(xp, xp) = all_13_0_9, sdtasdt0(xp, xn) = all_39_0_22, aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 63.90/34.70 | (444) xp = xn | xp = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v0 & sdtasdt0(xn, xp) = v1)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (57) with xn, xr, xp, all_0_4_4, sz10, xp and discharging atoms sdtasdt0(xp, all_0_4_4) = xr, sdtasdt0(xp, sz10) = xp, sdtpldt0(xp, xr) = xn, aNaturalNumber0(all_0_4_4), aNaturalNumber0(xp), aNaturalNumber0(sz10), yields:
% 63.90/34.70 | (445) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v0, xp) = v1 & sdtasdt0(all_0_4_4, xp) = v3 & sdtasdt0(xp, v0) = xn & sdtasdt0(sz10, xp) = v2 & sdtpldt0(v2, v3) = v1 & sdtpldt0(sz10, all_0_4_4) = v0)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (62) with all_13_0_9, xp, xp, sz10, xp and discharging atoms sdtasdt0(xp, xp) = all_13_0_9, sdtasdt0(xp, sz10) = xp, aNaturalNumber0(xp), aNaturalNumber0(sz10), yields:
% 63.90/34.70 | (446) xp = sz10 | xp = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v1 & sdtasdt0(sz10, xp) = v0)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (62) with xp, all_13_0_9, sz10, xp, xp and discharging atoms sdtasdt0(xp, xp) = all_13_0_9, sdtasdt0(xp, sz10) = xp, aNaturalNumber0(xp), aNaturalNumber0(sz10), yields:
% 63.90/34.70 | (447) xp = sz10 | xp = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v0 & sdtasdt0(sz10, xp) = v1)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (106) with all_13_0_9, xp, xp, sz10, xp and discharging atoms sdtasdt0(xp, xp) = all_13_0_9, sdtasdt0(xp, sz10) = xp, aNaturalNumber0(xp), aNaturalNumber0(sz10), yields:
% 63.90/34.70 | (448) xp = sz10 | xp = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = all_13_0_9) & ~ (v0 = xp) & sdtasdt0(xp, xp) = v0 & sdtasdt0(sz10, xp) = v1)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (20) with sz10, xp, xp and discharging atoms sdtasdt0(xp, sz10) = xp, aNaturalNumber0(xp), aNaturalNumber0(sz10), yields:
% 63.90/34.70 | (449) doDivides0(xp, xp)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (45) with xp, xp and discharging atoms sdtasdt0(xp, sz10) = xp, aNaturalNumber0(xp), yields:
% 63.90/34.70 | (450) sdtasdt0(sz10, xp) = xp
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (62) with sz00, all_13_0_9, sz00, xp, xp and discharging atoms sdtasdt0(xp, xp) = all_13_0_9, sdtasdt0(xp, sz00) = sz00, aNaturalNumber0(xp), aNaturalNumber0(sz00), yields:
% 63.90/34.70 | (451) xp = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v0 & sdtasdt0(sz00, xp) = v1)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (106) with all_13_0_9, sz00, xp, sz00, xp and discharging atoms sdtasdt0(xp, xp) = all_13_0_9, sdtasdt0(xp, sz00) = sz00, aNaturalNumber0(xp), aNaturalNumber0(sz00), yields:
% 63.90/34.70 | (452) xp = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = all_13_0_9) & ~ (v0 = sz00) & sdtasdt0(xp, xp) = v0 & sdtasdt0(sz00, xp) = v1)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (62) with all_49_0_27, sz00, xm, sz00, xp and discharging atoms sdtasdt0(xp, xm) = all_49_0_27, sdtasdt0(xp, sz00) = sz00, aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(sz00), yields:
% 63.90/34.70 | (453) xp = sz00 | xm = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xm, xp) = v1 & sdtasdt0(sz00, xp) = v0)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (62) with sz00, all_49_0_27, sz00, xm, xp and discharging atoms sdtasdt0(xp, xm) = all_49_0_27, sdtasdt0(xp, sz00) = sz00, aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(sz00), yields:
% 63.90/34.70 | (454) xp = sz00 | xm = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xm, xp) = v0 & sdtasdt0(sz00, xp) = v1)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (62) with sz00, all_39_0_22, sz00, xn, xp and discharging atoms sdtasdt0(xp, xn) = all_39_0_22, sdtasdt0(xp, sz00) = sz00, aNaturalNumber0(xp), aNaturalNumber0(xn), aNaturalNumber0(sz00), yields:
% 63.90/34.70 | (455) xp = sz00 | xn = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xn, xp) = v0 & sdtasdt0(sz00, xp) = v1)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (62) with xp, sz00, sz10, sz00, xp and discharging atoms sdtasdt0(xp, sz10) = xp, sdtasdt0(xp, sz00) = sz00, aNaturalNumber0(xp), aNaturalNumber0(sz10), aNaturalNumber0(sz00), yields:
% 63.90/34.70 | (456) xp = sz00 | sz10 = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(sz10, xp) = v1 & sdtasdt0(sz00, xp) = v0)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (6) with all_49_2_29, all_23_0_14, xr, xm, xp and discharging atoms sdtasdt0(xp, xr) = all_23_0_14, sdtasdt0(xm, xp) = all_49_2_29, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 63.90/34.70 | (457) xr = xm | xp = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = all_49_2_29) & ~ (v0 = all_23_0_14) & sdtasdt0(xr, xp) = v1 & sdtasdt0(xp, xm) = v0)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (103) with all_49_2_29, all_13_0_9, xm, xp, xp and discharging atoms sdtasdt0(xp, xp) = all_13_0_9, sdtasdt0(xm, xp) = all_49_2_29, aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 63.90/34.70 | (458) xp = xm | xp = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v0 & sdtasdt0(xp, xm) = v1)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (6) with all_49_2_29, all_13_0_9, xp, xm, xp and discharging atoms sdtasdt0(xp, xp) = all_13_0_9, sdtasdt0(xm, xp) = all_49_2_29, aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 63.90/34.70 | (459) xp = xm | xp = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = all_49_2_29) & ~ (v0 = all_13_0_9) & sdtasdt0(xp, xp) = v1 & sdtasdt0(xp, xm) = v0)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (106) with all_49_2_29, sz00, xm, sz00, xp and discharging atoms sdtasdt0(xp, sz00) = sz00, sdtasdt0(xm, xp) = all_49_2_29, aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(sz00), yields:
% 63.90/34.70 | (460) xp = sz00 | xm = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = all_49_2_29) & ~ (v0 = sz00) & sdtasdt0(xp, xm) = v0 & sdtasdt0(sz00, xp) = v1)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (103) with all_0_6_6, all_39_0_22, xm, xp, xn and discharging atoms sdtasdt0(xp, xn) = all_39_0_22, sdtasdt0(xm, xn) = all_0_6_6, aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 63.90/34.70 | (461) xp = xm | xn = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xn, xp) = v0 & sdtasdt0(xn, xm) = v1)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (57) with xn, xp, xr, sz10, all_0_4_4, xp and discharging atoms sdtasdt0(xp, all_0_4_4) = xr, sdtasdt0(xp, sz10) = xp, sdtpldt0(xr, xp) = xn, aNaturalNumber0(all_0_4_4), aNaturalNumber0(xp), aNaturalNumber0(sz10), yields:
% 63.90/34.70 | (462) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v0, xp) = v1 & sdtasdt0(all_0_4_4, xp) = v2 & sdtasdt0(xp, v0) = xn & sdtasdt0(sz10, xp) = v3 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_0_4_4, sz10) = v0)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (87) with xn, all_59_0_36, xp, xm, xr and discharging atoms sdtpldt0(xr, xm) = all_59_0_36, sdtpldt0(xp, xr) = xn, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 63.90/34.70 | (463) xp = xm | ? [v0] : ? [v1] : ( ~ (v1 = xn) & ~ (v0 = all_59_0_36) & sdtpldt0(xr, xp) = v0 & sdtpldt0(xm, xr) = v1)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (83) with xn, all_59_0_36, xp, xm, xr and discharging atoms sdtpldt0(xr, xp) = xn, sdtpldt0(xr, xm) = all_59_0_36, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 63.90/34.70 | (464) xp = xm | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xp, xr) = v1 & sdtpldt0(xm, xr) = v0)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (83) with all_61_0_37, xn, xm, xr, xp and discharging atoms sdtpldt0(xp, xr) = xn, sdtpldt0(xp, xm) = all_61_0_37, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 63.90/34.70 | (465) xr = xm | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xr, xp) = v0 & sdtpldt0(xm, xp) = v1)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (87) with xn, all_61_0_37, xr, xm, xp and discharging atoms sdtpldt0(xr, xp) = xn, sdtpldt0(xp, xm) = all_61_0_37, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 63.90/34.70 | (466) xr = xm | ? [v0] : ? [v1] : ( ~ (v1 = xn) & ~ (v0 = all_61_0_37) & sdtpldt0(xp, xr) = v0 & sdtpldt0(xm, xp) = v1)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (87) with all_76_1_46, all_0_8_8, xp, xm, xn and discharging atoms sdtpldt0(xp, xn) = all_76_1_46, sdtpldt0(xn, xm) = all_0_8_8, aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 63.90/34.70 | (467) xp = xm | ? [v0] : ? [v1] : ( ~ (v1 = all_76_1_46) & ~ (v0 = all_0_8_8) & sdtpldt0(xm, xn) = v1 & sdtpldt0(xn, xp) = v0)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (8) with all_76_1_46, xn, xp, xr, xp and discharging atoms sdtpldt0(xr, xp) = xn, sdtpldt0(xp, xn) = all_76_1_46, aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 63.90/34.70 | (468) ? [v0] : (sdtpldt0(v0, xp) = all_76_1_46 & sdtpldt0(xp, xr) = v0)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (122) with all_91_2_53, xn, xm, xp, xr and discharging atoms sdtpldt0(xp, xr) = xn, sdtpldt0(xm, xr) = all_91_2_53, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 63.90/34.70 | (469) xp = xm | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xr, xp) = v0 & sdtpldt0(xr, xm) = v1)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (7) with all_91_2_53, xn, xp, xm, xr and discharging atoms sdtpldt0(xr, xp) = xn, sdtpldt0(xm, xr) = all_91_2_53, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 63.90/34.70 | (470) xp = xm | ? [v0] : ? [v1] : ( ~ (v1 = all_91_2_53) & ~ (v0 = xn) & sdtpldt0(xr, xm) = v0 & sdtpldt0(xp, xr) = v1)
% 63.90/34.70 |
% 63.90/34.70 | Instantiating formula (7) with all_45_0_25, xn, xr, xm, xp and discharging atoms sdtpldt0(xp, xr) = xn, sdtpldt0(xm, xp) = all_45_0_25, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 63.90/34.71 | (471) xr = xm | ? [v0] : ? [v1] : ( ~ (v1 = all_45_0_25) & ~ (v0 = xn) & sdtpldt0(xr, xp) = v1 & sdtpldt0(xp, xm) = v0)
% 63.90/34.71 |
% 63.90/34.71 | Instantiating formula (122) with all_45_0_25, xn, xm, xr, xp and discharging atoms sdtpldt0(xr, xp) = xn, sdtpldt0(xm, xp) = all_45_0_25, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 63.90/34.71 | (472) xr = xm | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xp, xr) = v0 & sdtpldt0(xp, xm) = v1)
% 63.90/34.71 |
% 63.90/34.71 | Instantiating formula (122) with all_131_1_58, all_0_8_8, xr, xm, xn and discharging atoms sdtpldt0(xr, xn) = all_131_1_58, sdtpldt0(xm, xn) = all_0_8_8, aNaturalNumber0(xr), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 63.90/34.71 | (473) xr = xm | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xn, xr) = v1 & sdtpldt0(xn, xm) = v0)
% 63.90/34.71 |
% 63.90/34.71 | Instantiating formula (122) with all_0_8_8, all_131_1_58, xm, xr, xn and discharging atoms sdtpldt0(xr, xn) = all_131_1_58, sdtpldt0(xm, xn) = all_0_8_8, aNaturalNumber0(xr), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 63.90/34.71 | (474) xr = xm | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xn, xr) = v0 & sdtpldt0(xn, xm) = v1)
% 63.90/34.71 |
% 63.90/34.71 | Instantiating formula (122) with all_0_8_8, all_76_1_46, xm, xp, xn and discharging atoms sdtpldt0(xp, xn) = all_76_1_46, sdtpldt0(xm, xn) = all_0_8_8, aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 63.90/34.71 | (475) xp = xm | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xn, xp) = v0 & sdtpldt0(xn, xm) = v1)
% 63.90/34.71 |
% 63.90/34.71 | Instantiating formula (83) with all_0_8_8, all_131_0_57, xm, xr, xn and discharging atoms sdtpldt0(xn, xr) = all_131_0_57, sdtpldt0(xn, xm) = all_0_8_8, aNaturalNumber0(xr), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 63.90/34.71 | (476) xr = xm | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xr, xn) = v0 & sdtpldt0(xm, xn) = v1)
% 63.90/34.71 |
% 63.90/34.71 | Instantiating formula (18) with all_131_0_57, xn, xr, xp, xr and discharging atoms sdtpldt0(xr, xp) = xn, sdtpldt0(xn, xr) = all_131_0_57, aNaturalNumber0(xr), aNaturalNumber0(xp), yields:
% 63.90/34.71 | (477) ? [v0] : (sdtpldt0(xr, v0) = all_131_0_57 & sdtpldt0(xp, xr) = v0)
% 63.90/34.71 |
% 63.90/34.71 | Instantiating formula (7) with all_0_8_8, all_131_0_57, xr, xm, xn and discharging atoms sdtpldt0(xm, xn) = all_0_8_8, sdtpldt0(xn, xr) = all_131_0_57, aNaturalNumber0(xr), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 63.90/34.71 | (478) xr = xm | ? [v0] : ? [v1] : ( ~ (v1 = all_0_8_8) & ~ (v0 = all_131_0_57) & sdtpldt0(xr, xn) = v1 & sdtpldt0(xn, xm) = v0)
% 63.90/34.71 |
% 63.90/34.71 | Instantiating formula (83) with all_76_0_45, all_0_8_8, xp, xm, xn and discharging atoms sdtpldt0(xn, xp) = all_76_0_45, sdtpldt0(xn, xm) = all_0_8_8, aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 63.90/34.71 | (479) xp = xm | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xp, xn) = v1 & sdtpldt0(xm, xn) = v0)
% 63.90/34.71 |
% 63.90/34.71 | Instantiating formula (83) with all_0_8_8, all_76_0_45, xm, xp, xn and discharging atoms sdtpldt0(xn, xp) = all_76_0_45, sdtpldt0(xn, xm) = all_0_8_8, aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 63.90/34.71 | (480) xp = xm | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xp, xn) = v0 & sdtpldt0(xm, xn) = v1)
% 63.90/34.71 |
% 63.90/34.71 | Instantiating formula (7) with all_0_8_8, all_76_0_45, xp, xm, xn and discharging atoms sdtpldt0(xm, xn) = all_0_8_8, sdtpldt0(xn, xp) = all_76_0_45, aNaturalNumber0(xp), aNaturalNumber0(xm), aNaturalNumber0(xn), yields:
% 63.90/34.71 | (481) xp = xm | ? [v0] : ? [v1] : ( ~ (v1 = all_0_8_8) & ~ (v0 = all_76_0_45) & sdtpldt0(xp, xn) = v1 & sdtpldt0(xn, xm) = v0)
% 63.90/34.71 |
% 63.90/34.71 | Instantiating formula (37) with all_13_0_9, xp, xp, sz10, xp and discharging atoms sdtasdt0(xp, xp) = all_13_0_9, sdtasdt0(xp, sz10) = xp, sdtlseqdt0(sz10, xp), aNaturalNumber0(xp), aNaturalNumber0(sz10), yields:
% 63.90/34.71 | (482) xp = sz10 | xp = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = all_13_0_9) & ~ (v0 = xp) & sdtasdt0(xp, xp) = v0 & sdtasdt0(sz10, xp) = v1 & sdtlseqdt0(v1, all_13_0_9) & sdtlseqdt0(xp, v0))
% 63.90/34.71 |
% 63.90/34.71 | Instantiating formula (16) with all_13_0_9, xp, xp, sz10, xp and discharging atoms sdtasdt0(xp, xp) = all_13_0_9, sdtasdt0(xp, sz10) = xp, sdtlseqdt0(sz10, xp), aNaturalNumber0(xp), aNaturalNumber0(sz10), yields:
% 63.90/34.71 | (483) xp = sz10 | xp = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v1 & sdtasdt0(sz10, xp) = v0 & sdtlseqdt0(v0, v1))
% 63.90/34.71 |
% 63.90/34.71 | Instantiating formula (17) with xn, xr, xp, sz10 and discharging atoms sdtpldt0(xp, xr) = xn, sdtlseqdt0(sz10, xp), aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(sz10), yields:
% 63.90/34.71 | (484) xp = sz10 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xn) & ~ (v1 = v0) & sdtpldt0(xr, xp) = v1 & sdtpldt0(xr, sz10) = v0 & sdtpldt0(sz10, xr) = v2 & sdtlseqdt0(v2, xn) & sdtlseqdt0(v0, v1))
% 63.90/34.71 |
% 63.90/34.71 | Instantiating formula (48) with xn, xr, xp, sz10 and discharging atoms sdtpldt0(xr, xp) = xn, sdtlseqdt0(sz10, xp), aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(sz10), yields:
% 63.90/34.71 | (485) xp = sz10 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = xn) & sdtpldt0(xr, sz10) = v0 & sdtpldt0(xp, xr) = v2 & sdtpldt0(sz10, xr) = v1 & sdtlseqdt0(v1, v2) & sdtlseqdt0(v0, xn))
% 63.90/34.71 |
% 63.90/34.71 | Instantiating formula (48) with all_76_0_45, xn, xp, sz10 and discharging atoms sdtpldt0(xn, xp) = all_76_0_45, sdtlseqdt0(sz10, xp), aNaturalNumber0(xp), aNaturalNumber0(xn), aNaturalNumber0(sz10), yields:
% 63.90/34.71 | (486) xp = sz10 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = all_76_0_45) & sdtpldt0(xp, xn) = v2 & sdtpldt0(xn, sz10) = v0 & sdtpldt0(sz10, xn) = v1 & sdtlseqdt0(v1, v2) & sdtlseqdt0(v0, all_76_0_45))
% 63.90/34.71 |
% 63.90/34.71 | Instantiating (468) with all_218_0_91 yields:
% 63.90/34.71 | (487) sdtpldt0(all_218_0_91, xp) = all_76_1_46 & sdtpldt0(xp, xr) = all_218_0_91
% 63.90/34.71 |
% 63.90/34.71 | Applying alpha-rule on (487) yields:
% 63.90/34.71 | (488) sdtpldt0(all_218_0_91, xp) = all_76_1_46
% 63.90/34.71 | (489) sdtpldt0(xp, xr) = all_218_0_91
% 63.90/34.71 |
% 63.90/34.71 | Instantiating (445) with all_236_0_100, all_236_1_101, all_236_2_102, all_236_3_103 yields:
% 63.90/34.71 | (490) sdtasdt0(all_236_3_103, xp) = all_236_2_102 & sdtasdt0(all_0_4_4, xp) = all_236_0_100 & sdtasdt0(xp, all_236_3_103) = xn & sdtasdt0(sz10, xp) = all_236_1_101 & sdtpldt0(all_236_1_101, all_236_0_100) = all_236_2_102 & sdtpldt0(sz10, all_0_4_4) = all_236_3_103
% 63.90/34.71 |
% 63.90/34.71 | Applying alpha-rule on (490) yields:
% 63.90/34.71 | (491) sdtpldt0(sz10, all_0_4_4) = all_236_3_103
% 63.90/34.71 | (492) sdtpldt0(all_236_1_101, all_236_0_100) = all_236_2_102
% 63.90/34.71 | (493) sdtasdt0(all_0_4_4, xp) = all_236_0_100
% 63.90/34.71 | (494) sdtasdt0(sz10, xp) = all_236_1_101
% 63.90/34.71 | (495) sdtasdt0(all_236_3_103, xp) = all_236_2_102
% 63.90/34.71 | (496) sdtasdt0(xp, all_236_3_103) = xn
% 63.90/34.71 |
% 63.90/34.71 | Instantiating (477) with all_274_0_131 yields:
% 63.90/34.71 | (497) sdtpldt0(xr, all_274_0_131) = all_131_0_57 & sdtpldt0(xp, xr) = all_274_0_131
% 63.90/34.71 |
% 63.90/34.71 | Applying alpha-rule on (497) yields:
% 63.90/34.71 | (498) sdtpldt0(xr, all_274_0_131) = all_131_0_57
% 63.90/34.71 | (499) sdtpldt0(xp, xr) = all_274_0_131
% 63.90/34.71 |
% 63.90/34.71 | Instantiating (462) with all_304_0_149, all_304_1_150, all_304_2_151, all_304_3_152 yields:
% 63.90/34.71 | (500) sdtasdt0(all_304_3_152, xp) = all_304_2_151 & sdtasdt0(all_0_4_4, xp) = all_304_1_150 & sdtasdt0(xp, all_304_3_152) = xn & sdtasdt0(sz10, xp) = all_304_0_149 & sdtpldt0(all_304_1_150, all_304_0_149) = all_304_2_151 & sdtpldt0(all_0_4_4, sz10) = all_304_3_152
% 63.90/34.71 |
% 63.90/34.71 | Applying alpha-rule on (500) yields:
% 63.90/34.71 | (501) sdtasdt0(sz10, xp) = all_304_0_149
% 63.90/34.71 | (502) sdtasdt0(all_304_3_152, xp) = all_304_2_151
% 63.90/34.71 | (503) sdtasdt0(xp, all_304_3_152) = xn
% 63.90/34.71 | (504) sdtpldt0(all_0_4_4, sz10) = all_304_3_152
% 63.90/34.71 | (505) sdtasdt0(all_0_4_4, xp) = all_304_1_150
% 63.90/34.71 | (506) sdtpldt0(all_304_1_150, all_304_0_149) = all_304_2_151
% 63.90/34.71 |
% 63.90/34.71 +-Applying beta-rule and splitting (473), into two cases.
% 63.90/34.71 |-Branch one:
% 63.90/34.71 | (507) xr = xm
% 63.90/34.71 |
% 63.90/34.71 | Equations (507) can reduce 326 to:
% 63.90/34.71 | (249) $false
% 63.90/34.71 |
% 63.90/34.71 |-The branch is then unsatisfiable
% 63.90/34.71 |-Branch two:
% 63.90/34.71 | (326) ~ (xr = xm)
% 63.90/34.71 | (510) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xn, xr) = v1 & sdtpldt0(xn, xm) = v0)
% 63.90/34.71 |
% 63.90/34.71 +-Applying beta-rule and splitting (479), into two cases.
% 63.90/34.71 |-Branch one:
% 63.90/34.71 | (511) xp = xm
% 63.90/34.71 |
% 63.90/34.71 | Equations (511) can reduce 325 to:
% 63.90/34.71 | (249) $false
% 63.90/34.71 |
% 63.90/34.71 |-The branch is then unsatisfiable
% 63.90/34.71 |-Branch two:
% 63.90/34.71 | (325) ~ (xp = xm)
% 63.90/34.71 | (514) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xp, xn) = v1 & sdtpldt0(xm, xn) = v0)
% 63.90/34.71 |
% 63.90/34.71 +-Applying beta-rule and splitting (446), into two cases.
% 63.90/34.71 |-Branch one:
% 63.90/34.71 | (285) xp = sz00
% 63.90/34.71 |
% 63.90/34.71 | Equations (285) can reduce 41 to:
% 63.90/34.71 | (249) $false
% 63.90/34.71 |
% 63.90/34.71 |-The branch is then unsatisfiable
% 63.90/34.71 |-Branch two:
% 63.90/34.71 | (41) ~ (xp = sz00)
% 63.90/34.71 | (518) xp = sz10 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v1 & sdtasdt0(sz10, xp) = v0)
% 63.90/34.71 |
% 63.90/34.71 +-Applying beta-rule and splitting (518), into two cases.
% 63.90/34.71 |-Branch one:
% 63.90/34.71 | (289) xp = sz10
% 63.90/34.71 |
% 63.90/34.71 | Equations (289) can reduce 32 to:
% 63.90/34.71 | (249) $false
% 63.90/34.71 |
% 63.90/34.71 |-The branch is then unsatisfiable
% 63.90/34.71 |-Branch two:
% 63.90/34.71 | (32) ~ (xp = sz10)
% 63.90/34.71 | (522) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v1 & sdtasdt0(sz10, xp) = v0)
% 63.90/34.71 |
% 63.90/34.71 +-Applying beta-rule and splitting (483), into two cases.
% 63.90/34.71 |-Branch one:
% 63.90/34.71 | (285) xp = sz00
% 63.90/34.71 |
% 63.90/34.71 | Equations (285) can reduce 41 to:
% 63.90/34.71 | (249) $false
% 63.90/34.71 |
% 63.90/34.71 |-The branch is then unsatisfiable
% 63.90/34.71 |-Branch two:
% 63.90/34.71 | (41) ~ (xp = sz00)
% 63.90/34.71 | (526) xp = sz10 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v1 & sdtasdt0(sz10, xp) = v0 & sdtlseqdt0(v0, v1))
% 63.90/34.71 |
% 63.90/34.71 +-Applying beta-rule and splitting (482), into two cases.
% 63.90/34.71 |-Branch one:
% 63.90/34.71 | (285) xp = sz00
% 63.90/34.71 |
% 63.90/34.71 | Equations (285) can reduce 41 to:
% 63.90/34.71 | (249) $false
% 63.90/34.71 |
% 63.90/34.71 |-The branch is then unsatisfiable
% 63.90/34.71 |-Branch two:
% 63.90/34.71 | (41) ~ (xp = sz00)
% 63.90/34.71 | (530) xp = sz10 | ? [v0] : ? [v1] : ( ~ (v1 = all_13_0_9) & ~ (v0 = xp) & sdtasdt0(xp, xp) = v0 & sdtasdt0(sz10, xp) = v1 & sdtlseqdt0(v1, all_13_0_9) & sdtlseqdt0(xp, v0))
% 63.90/34.71 |
% 63.90/34.71 +-Applying beta-rule and splitting (439), into two cases.
% 63.90/34.71 |-Branch one:
% 63.90/34.71 | (531) xn = sz00
% 63.90/34.71 |
% 63.90/34.71 | Equations (531) can reduce 323 to:
% 63.90/34.71 | (249) $false
% 63.90/34.71 |
% 63.90/34.71 |-The branch is then unsatisfiable
% 63.90/34.71 |-Branch two:
% 63.90/34.71 | (323) ~ (xn = sz00)
% 63.90/34.71 | (534) xp = xm | ? [v0] : ? [v1] : ( ~ (v1 = all_39_0_22) & ~ (v0 = all_0_6_6) & sdtasdt0(xm, xn) = v1 & sdtasdt0(xn, xp) = v0)
% 63.90/34.71 |
% 63.90/34.71 +-Applying beta-rule and splitting (530), into two cases.
% 63.90/34.71 |-Branch one:
% 63.90/34.71 | (289) xp = sz10
% 63.90/34.71 |
% 63.90/34.71 | Equations (289) can reduce 32 to:
% 63.90/34.71 | (249) $false
% 63.90/34.71 |
% 63.90/34.71 |-The branch is then unsatisfiable
% 63.90/34.71 |-Branch two:
% 63.90/34.71 | (32) ~ (xp = sz10)
% 63.90/34.71 | (538) ? [v0] : ? [v1] : ( ~ (v1 = all_13_0_9) & ~ (v0 = xp) & sdtasdt0(xp, xp) = v0 & sdtasdt0(sz10, xp) = v1 & sdtlseqdt0(v1, all_13_0_9) & sdtlseqdt0(xp, v0))
% 63.90/34.71 |
% 63.90/34.71 +-Applying beta-rule and splitting (534), into two cases.
% 63.90/34.71 |-Branch one:
% 63.90/34.71 | (511) xp = xm
% 63.90/34.71 |
% 63.90/34.71 | Equations (511) can reduce 325 to:
% 63.90/34.71 | (249) $false
% 63.90/34.71 |
% 63.90/34.71 |-The branch is then unsatisfiable
% 63.90/34.71 |-Branch two:
% 63.90/34.72 | (325) ~ (xp = xm)
% 63.90/34.72 | (542) ? [v0] : ? [v1] : ( ~ (v1 = all_39_0_22) & ~ (v0 = all_0_6_6) & sdtasdt0(xm, xn) = v1 & sdtasdt0(xn, xp) = v0)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (476), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (507) xr = xm
% 63.90/34.72 |
% 63.90/34.72 | Equations (507) can reduce 326 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (326) ~ (xr = xm)
% 63.90/34.72 | (546) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xr, xn) = v0 & sdtpldt0(xm, xn) = v1)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (484), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (289) xp = sz10
% 63.90/34.72 |
% 63.90/34.72 | Equations (289) can reduce 32 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (32) ~ (xp = sz10)
% 63.90/34.72 | (550) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xn) & ~ (v1 = v0) & sdtpldt0(xr, xp) = v1 & sdtpldt0(xr, sz10) = v0 & sdtpldt0(sz10, xr) = v2 & sdtlseqdt0(v2, xn) & sdtlseqdt0(v0, v1))
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (469), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (511) xp = xm
% 63.90/34.72 |
% 63.90/34.72 | Equations (511) can reduce 325 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (325) ~ (xp = xm)
% 63.90/34.72 | (554) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xr, xp) = v0 & sdtpldt0(xr, xm) = v1)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (526), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (289) xp = sz10
% 63.90/34.72 |
% 63.90/34.72 | Equations (289) can reduce 32 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (32) ~ (xp = sz10)
% 63.90/34.72 | (558) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v1 & sdtasdt0(sz10, xp) = v0 & sdtlseqdt0(v0, v1))
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (475), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (511) xp = xm
% 63.90/34.72 |
% 63.90/34.72 | Equations (511) can reduce 325 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (325) ~ (xp = xm)
% 63.90/34.72 | (562) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xn, xp) = v0 & sdtpldt0(xn, xm) = v1)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (470), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (511) xp = xm
% 63.90/34.72 |
% 63.90/34.72 | Equations (511) can reduce 325 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (325) ~ (xp = xm)
% 63.90/34.72 | (566) ? [v0] : ? [v1] : ( ~ (v1 = all_91_2_53) & ~ (v0 = xn) & sdtpldt0(xr, xm) = v0 & sdtpldt0(xp, xr) = v1)
% 63.90/34.72 |
% 63.90/34.72 | Instantiating (566) with all_420_0_191, all_420_1_192 yields:
% 63.90/34.72 | (567) ~ (all_420_0_191 = all_91_2_53) & ~ (all_420_1_192 = xn) & sdtpldt0(xr, xm) = all_420_1_192 & sdtpldt0(xp, xr) = all_420_0_191
% 63.90/34.72 |
% 63.90/34.72 | Applying alpha-rule on (567) yields:
% 63.90/34.72 | (568) ~ (all_420_0_191 = all_91_2_53)
% 63.90/34.72 | (569) ~ (all_420_1_192 = xn)
% 63.90/34.72 | (570) sdtpldt0(xr, xm) = all_420_1_192
% 63.90/34.72 | (571) sdtpldt0(xp, xr) = all_420_0_191
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (474), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (507) xr = xm
% 63.90/34.72 |
% 63.90/34.72 | Equations (507) can reduce 326 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (326) ~ (xr = xm)
% 63.90/34.72 | (575) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xn, xr) = v0 & sdtpldt0(xn, xm) = v1)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (486), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (289) xp = sz10
% 63.90/34.72 |
% 63.90/34.72 | Equations (289) can reduce 32 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (32) ~ (xp = sz10)
% 63.90/34.72 | (579) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = all_76_0_45) & sdtpldt0(xp, xn) = v2 & sdtpldt0(xn, sz10) = v0 & sdtpldt0(sz10, xn) = v1 & sdtlseqdt0(v1, v2) & sdtlseqdt0(v0, all_76_0_45))
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (436), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (285) xp = sz00
% 63.90/34.72 |
% 63.90/34.72 | Equations (285) can reduce 41 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (41) ~ (xp = sz00)
% 63.90/34.72 | (583) xr = xm | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xr, xp) = v0 & sdtasdt0(xm, xp) = v1)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (583), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (507) xr = xm
% 63.90/34.72 |
% 63.90/34.72 | Equations (507) can reduce 326 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (326) ~ (xr = xm)
% 63.90/34.72 | (587) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xr, xp) = v0 & sdtasdt0(xm, xp) = v1)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (438), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (285) xp = sz00
% 63.90/34.72 |
% 63.90/34.72 | Equations (285) can reduce 41 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (41) ~ (xp = sz00)
% 63.90/34.72 | (591) xp = xm | ? [v0] : ? [v1] : ( ~ (v1 = all_13_0_9) & ~ (v0 = all_49_0_27) & sdtasdt0(xp, xp) = v0 & sdtasdt0(xm, xp) = v1)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (437), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (285) xp = sz00
% 63.90/34.72 |
% 63.90/34.72 | Equations (285) can reduce 41 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (41) ~ (xp = sz00)
% 63.90/34.72 | (595) xp = xm | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v0 & sdtasdt0(xm, xp) = v1)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (591), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (511) xp = xm
% 63.90/34.72 |
% 63.90/34.72 | Equations (511) can reduce 325 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (325) ~ (xp = xm)
% 63.90/34.72 | (599) ? [v0] : ? [v1] : ( ~ (v1 = all_13_0_9) & ~ (v0 = all_49_0_27) & sdtasdt0(xp, xp) = v0 & sdtasdt0(xm, xp) = v1)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (452), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (285) xp = sz00
% 63.90/34.72 |
% 63.90/34.72 | Equations (285) can reduce 41 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (41) ~ (xp = sz00)
% 63.90/34.72 | (603) ? [v0] : ? [v1] : ( ~ (v1 = all_13_0_9) & ~ (v0 = sz00) & sdtasdt0(xp, xp) = v0 & sdtasdt0(sz00, xp) = v1)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (595), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (511) xp = xm
% 63.90/34.72 |
% 63.90/34.72 | Equations (511) can reduce 325 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (325) ~ (xp = xm)
% 63.90/34.72 | (607) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v0 & sdtasdt0(xm, xp) = v1)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (448), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (285) xp = sz00
% 63.90/34.72 |
% 63.90/34.72 | Equations (285) can reduce 41 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (41) ~ (xp = sz00)
% 63.90/34.72 | (611) xp = sz10 | ? [v0] : ? [v1] : ( ~ (v1 = all_13_0_9) & ~ (v0 = xp) & sdtasdt0(xp, xp) = v0 & sdtasdt0(sz10, xp) = v1)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (451), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (285) xp = sz00
% 63.90/34.72 |
% 63.90/34.72 | Equations (285) can reduce 41 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (41) ~ (xp = sz00)
% 63.90/34.72 | (615) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v0 & sdtasdt0(sz00, xp) = v1)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (611), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (289) xp = sz10
% 63.90/34.72 |
% 63.90/34.72 | Equations (289) can reduce 32 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (32) ~ (xp = sz10)
% 63.90/34.72 | (619) ? [v0] : ? [v1] : ( ~ (v1 = all_13_0_9) & ~ (v0 = xp) & sdtasdt0(xp, xp) = v0 & sdtasdt0(sz10, xp) = v1)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (447), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (285) xp = sz00
% 63.90/34.72 |
% 63.90/34.72 | Equations (285) can reduce 41 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (41) ~ (xp = sz00)
% 63.90/34.72 | (623) xp = sz10 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v0 & sdtasdt0(sz10, xp) = v1)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (441), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (285) xp = sz00
% 63.90/34.72 |
% 63.90/34.72 | Equations (285) can reduce 41 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (41) ~ (xp = sz00)
% 63.90/34.72 | (627) xr = xn | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xr, xp) = v0 & sdtasdt0(xn, xp) = v1)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (623), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (289) xp = sz10
% 63.90/34.72 |
% 63.90/34.72 | Equations (289) can reduce 32 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (32) ~ (xp = sz10)
% 63.90/34.72 | (631) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v0 & sdtasdt0(sz10, xp) = v1)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (442), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (285) xp = sz00
% 63.90/34.72 |
% 63.90/34.72 | Equations (285) can reduce 41 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (41) ~ (xp = sz00)
% 63.90/34.72 | (635) xp = xn | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v0 & sdtasdt0(xn, xp) = v1 & sdtlseqdt0(v0, v1))
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (444), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (285) xp = sz00
% 63.90/34.72 |
% 63.90/34.72 | Equations (285) can reduce 41 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (41) ~ (xp = sz00)
% 63.90/34.72 | (639) xp = xn | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v0 & sdtasdt0(xn, xp) = v1)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (440), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (285) xp = sz00
% 63.90/34.72 |
% 63.90/34.72 | Equations (285) can reduce 41 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (41) ~ (xp = sz00)
% 63.90/34.72 | (643) xr = xn | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xr, xp) = v0 & sdtasdt0(xn, xp) = v1 & sdtlseqdt0(v0, v1))
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (478), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.72 | (507) xr = xm
% 63.90/34.72 |
% 63.90/34.72 | Equations (507) can reduce 326 to:
% 63.90/34.72 | (249) $false
% 63.90/34.72 |
% 63.90/34.72 |-The branch is then unsatisfiable
% 63.90/34.72 |-Branch two:
% 63.90/34.72 | (326) ~ (xr = xm)
% 63.90/34.72 | (647) ? [v0] : ? [v1] : ( ~ (v1 = all_0_8_8) & ~ (v0 = all_131_0_57) & sdtpldt0(xr, xn) = v1 & sdtpldt0(xn, xm) = v0)
% 63.90/34.72 |
% 63.90/34.72 +-Applying beta-rule and splitting (471), into two cases.
% 63.90/34.72 |-Branch one:
% 63.90/34.73 | (507) xr = xm
% 63.90/34.73 |
% 63.90/34.73 | Equations (507) can reduce 326 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (326) ~ (xr = xm)
% 63.90/34.73 | (651) ? [v0] : ? [v1] : ( ~ (v1 = all_45_0_25) & ~ (v0 = xn) & sdtpldt0(xr, xp) = v1 & sdtpldt0(xp, xm) = v0)
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (460), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (285) xp = sz00
% 63.90/34.73 |
% 63.90/34.73 | Equations (285) can reduce 41 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (41) ~ (xp = sz00)
% 63.90/34.73 | (655) xm = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = all_49_2_29) & ~ (v0 = sz00) & sdtasdt0(xp, xm) = v0 & sdtasdt0(sz00, xp) = v1)
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (435), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (285) xp = sz00
% 63.90/34.73 |
% 63.90/34.73 | Equations (285) can reduce 41 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (41) ~ (xp = sz00)
% 63.90/34.73 | (659) xr = xm | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xr, xp) = v1 & sdtasdt0(xm, xp) = v0)
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (443), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (285) xp = sz00
% 63.90/34.73 |
% 63.90/34.73 | Equations (285) can reduce 41 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (41) ~ (xp = sz00)
% 63.90/34.73 | (663) xp = xn | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v1 & sdtasdt0(xn, xp) = v0)
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (659), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (507) xr = xm
% 63.90/34.73 |
% 63.90/34.73 | Equations (507) can reduce 326 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (326) ~ (xr = xm)
% 63.90/34.73 | (667) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xr, xp) = v1 & sdtasdt0(xm, xp) = v0)
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (485), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (289) xp = sz10
% 63.90/34.73 |
% 63.90/34.73 | Equations (289) can reduce 32 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (32) ~ (xp = sz10)
% 63.90/34.73 | (671) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = xn) & sdtpldt0(xr, sz10) = v0 & sdtpldt0(xp, xr) = v2 & sdtpldt0(sz10, xr) = v1 & sdtlseqdt0(v1, v2) & sdtlseqdt0(v0, xn))
% 63.90/34.73 |
% 63.90/34.73 | Instantiating (671) with all_720_0_257, all_720_1_258, all_720_2_259 yields:
% 63.90/34.73 | (672) ~ (all_720_0_257 = all_720_1_258) & ~ (all_720_2_259 = xn) & sdtpldt0(xr, sz10) = all_720_2_259 & sdtpldt0(xp, xr) = all_720_0_257 & sdtpldt0(sz10, xr) = all_720_1_258 & sdtlseqdt0(all_720_1_258, all_720_0_257) & sdtlseqdt0(all_720_2_259, xn)
% 63.90/34.73 |
% 63.90/34.73 | Applying alpha-rule on (672) yields:
% 63.90/34.73 | (673) sdtpldt0(xp, xr) = all_720_0_257
% 63.90/34.73 | (674) ~ (all_720_2_259 = xn)
% 63.90/34.73 | (675) sdtlseqdt0(all_720_1_258, all_720_0_257)
% 63.90/34.73 | (676) sdtpldt0(xr, sz10) = all_720_2_259
% 63.90/34.73 | (677) sdtlseqdt0(all_720_2_259, xn)
% 63.90/34.73 | (678) sdtpldt0(sz10, xr) = all_720_1_258
% 63.90/34.73 | (679) ~ (all_720_0_257 = all_720_1_258)
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (463), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (511) xp = xm
% 63.90/34.73 |
% 63.90/34.73 | Equations (511) can reduce 325 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (325) ~ (xp = xm)
% 63.90/34.73 | (683) ? [v0] : ? [v1] : ( ~ (v1 = xn) & ~ (v0 = all_59_0_36) & sdtpldt0(xr, xp) = v0 & sdtpldt0(xm, xr) = v1)
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (461), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (531) xn = sz00
% 63.90/34.73 |
% 63.90/34.73 | Equations (531) can reduce 323 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (323) ~ (xn = sz00)
% 63.90/34.73 | (687) xp = xm | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xn, xp) = v0 & sdtasdt0(xn, xm) = v1)
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (687), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (511) xp = xm
% 63.90/34.73 |
% 63.90/34.73 | Equations (511) can reduce 325 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (325) ~ (xp = xm)
% 63.90/34.73 | (691) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xn, xp) = v0 & sdtasdt0(xn, xm) = v1)
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (466), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (507) xr = xm
% 63.90/34.73 |
% 63.90/34.73 | Equations (507) can reduce 326 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (326) ~ (xr = xm)
% 63.90/34.73 | (695) ? [v0] : ? [v1] : ( ~ (v1 = xn) & ~ (v0 = all_61_0_37) & sdtpldt0(xp, xr) = v0 & sdtpldt0(xm, xp) = v1)
% 63.90/34.73 |
% 63.90/34.73 | Instantiating (695) with all_773_0_278, all_773_1_279 yields:
% 63.90/34.73 | (696) ~ (all_773_0_278 = xn) & ~ (all_773_1_279 = all_61_0_37) & sdtpldt0(xp, xr) = all_773_1_279 & sdtpldt0(xm, xp) = all_773_0_278
% 63.90/34.73 |
% 63.90/34.73 | Applying alpha-rule on (696) yields:
% 63.90/34.73 | (697) ~ (all_773_0_278 = xn)
% 63.90/34.73 | (698) ~ (all_773_1_279 = all_61_0_37)
% 63.90/34.73 | (699) sdtpldt0(xp, xr) = all_773_1_279
% 63.90/34.73 | (700) sdtpldt0(xm, xp) = all_773_0_278
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (453), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (285) xp = sz00
% 63.90/34.73 |
% 63.90/34.73 | Equations (285) can reduce 41 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (41) ~ (xp = sz00)
% 63.90/34.73 | (704) xm = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xm, xp) = v1 & sdtasdt0(sz00, xp) = v0)
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (465), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (507) xr = xm
% 63.90/34.73 |
% 63.90/34.73 | Equations (507) can reduce 326 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (326) ~ (xr = xm)
% 63.90/34.73 | (708) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xr, xp) = v0 & sdtpldt0(xm, xp) = v1)
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (481), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (511) xp = xm
% 63.90/34.73 |
% 63.90/34.73 | Equations (511) can reduce 325 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (325) ~ (xp = xm)
% 63.90/34.73 | (712) ? [v0] : ? [v1] : ( ~ (v1 = all_0_8_8) & ~ (v0 = all_76_0_45) & sdtpldt0(xp, xn) = v1 & sdtpldt0(xn, xm) = v0)
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (480), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (511) xp = xm
% 63.90/34.73 |
% 63.90/34.73 | Equations (511) can reduce 325 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (325) ~ (xp = xm)
% 63.90/34.73 | (716) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xp, xn) = v0 & sdtpldt0(xm, xn) = v1)
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (472), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (507) xr = xm
% 63.90/34.73 |
% 63.90/34.73 | Equations (507) can reduce 326 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (326) ~ (xr = xm)
% 63.90/34.73 | (720) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xp, xr) = v0 & sdtpldt0(xp, xm) = v1)
% 63.90/34.73 |
% 63.90/34.73 | Instantiating (720) with all_833_0_295, all_833_1_296 yields:
% 63.90/34.73 | (721) ~ (all_833_0_295 = all_833_1_296) & sdtpldt0(xp, xr) = all_833_1_296 & sdtpldt0(xp, xm) = all_833_0_295
% 63.90/34.73 |
% 63.90/34.73 | Applying alpha-rule on (721) yields:
% 63.90/34.73 | (722) ~ (all_833_0_295 = all_833_1_296)
% 63.90/34.73 | (723) sdtpldt0(xp, xr) = all_833_1_296
% 63.90/34.73 | (724) sdtpldt0(xp, xm) = all_833_0_295
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (467), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (511) xp = xm
% 63.90/34.73 |
% 63.90/34.73 | Equations (511) can reduce 325 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (325) ~ (xp = xm)
% 63.90/34.73 | (728) ? [v0] : ? [v1] : ( ~ (v1 = all_76_1_46) & ~ (v0 = all_0_8_8) & sdtpldt0(xm, xn) = v1 & sdtpldt0(xn, xp) = v0)
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (458), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (285) xp = sz00
% 63.90/34.73 |
% 63.90/34.73 | Equations (285) can reduce 41 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (41) ~ (xp = sz00)
% 63.90/34.73 | (732) xp = xm | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v0 & sdtasdt0(xp, xm) = v1)
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (457), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (285) xp = sz00
% 63.90/34.73 |
% 63.90/34.73 | Equations (285) can reduce 41 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (41) ~ (xp = sz00)
% 63.90/34.73 | (736) xr = xm | ? [v0] : ? [v1] : ( ~ (v1 = all_49_2_29) & ~ (v0 = all_23_0_14) & sdtasdt0(xr, xp) = v1 & sdtasdt0(xp, xm) = v0)
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (732), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (511) xp = xm
% 63.90/34.73 |
% 63.90/34.73 | Equations (511) can reduce 325 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (325) ~ (xp = xm)
% 63.90/34.73 | (740) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xp, xp) = v0 & sdtasdt0(xp, xm) = v1)
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (456), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (285) xp = sz00
% 63.90/34.73 |
% 63.90/34.73 | Equations (285) can reduce 41 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (41) ~ (xp = sz00)
% 63.90/34.73 | (744) sz10 = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(sz10, xp) = v1 & sdtasdt0(sz00, xp) = v0)
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (455), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (285) xp = sz00
% 63.90/34.73 |
% 63.90/34.73 | Equations (285) can reduce 41 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.73 |-The branch is then unsatisfiable
% 63.90/34.73 |-Branch two:
% 63.90/34.73 | (41) ~ (xp = sz00)
% 63.90/34.73 | (748) xn = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xn, xp) = v0 & sdtasdt0(sz00, xp) = v1)
% 63.90/34.73 |
% 63.90/34.73 +-Applying beta-rule and splitting (454), into two cases.
% 63.90/34.73 |-Branch one:
% 63.90/34.73 | (285) xp = sz00
% 63.90/34.73 |
% 63.90/34.73 | Equations (285) can reduce 41 to:
% 63.90/34.73 | (249) $false
% 63.90/34.73 |
% 63.90/34.74 |-The branch is then unsatisfiable
% 63.90/34.74 |-Branch two:
% 63.90/34.74 | (41) ~ (xp = sz00)
% 63.90/34.74 | (752) xm = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xm, xp) = v0 & sdtasdt0(sz00, xp) = v1)
% 63.90/34.74 |
% 63.90/34.74 +-Applying beta-rule and splitting (459), into two cases.
% 63.90/34.74 |-Branch one:
% 63.90/34.74 | (285) xp = sz00
% 63.90/34.74 |
% 63.90/34.74 | Equations (285) can reduce 41 to:
% 63.90/34.74 | (249) $false
% 63.90/34.74 |
% 63.90/34.74 |-The branch is then unsatisfiable
% 63.90/34.74 |-Branch two:
% 63.90/34.74 | (41) ~ (xp = sz00)
% 63.90/34.74 | (756) xp = xm | ? [v0] : ? [v1] : ( ~ (v1 = all_49_2_29) & ~ (v0 = all_13_0_9) & sdtasdt0(xp, xp) = v1 & sdtasdt0(xp, xm) = v0)
% 63.90/34.74 |
% 63.90/34.74 +-Applying beta-rule and splitting (756), into two cases.
% 63.90/34.74 |-Branch one:
% 63.90/34.74 | (511) xp = xm
% 63.90/34.74 |
% 63.90/34.74 | Equations (511) can reduce 325 to:
% 63.90/34.74 | (249) $false
% 63.90/34.74 |
% 63.90/34.74 |-The branch is then unsatisfiable
% 63.90/34.74 |-Branch two:
% 63.90/34.74 | (325) ~ (xp = xm)
% 63.90/34.74 | (760) ? [v0] : ? [v1] : ( ~ (v1 = all_49_2_29) & ~ (v0 = all_13_0_9) & sdtasdt0(xp, xp) = v1 & sdtasdt0(xp, xm) = v0)
% 63.90/34.74 |
% 63.90/34.74 +-Applying beta-rule and splitting (464), into two cases.
% 63.90/34.74 |-Branch one:
% 63.90/34.74 | (511) xp = xm
% 63.90/34.74 |
% 63.90/34.74 | Equations (511) can reduce 325 to:
% 63.90/34.74 | (249) $false
% 63.90/34.74 |
% 63.90/34.74 |-The branch is then unsatisfiable
% 63.90/34.74 |-Branch two:
% 63.90/34.74 | (325) ~ (xp = xm)
% 63.90/34.74 | (764) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xp, xr) = v1 & sdtpldt0(xm, xr) = v0)
% 63.90/34.74 |
% 63.90/34.74 | Instantiating (764) with all_943_0_323, all_943_1_324 yields:
% 63.90/34.74 | (765) ~ (all_943_0_323 = all_943_1_324) & sdtpldt0(xp, xr) = all_943_0_323 & sdtpldt0(xm, xr) = all_943_1_324
% 63.90/34.74 |
% 63.90/34.74 | Applying alpha-rule on (765) yields:
% 63.90/34.74 | (766) ~ (all_943_0_323 = all_943_1_324)
% 63.90/34.74 | (767) sdtpldt0(xp, xr) = all_943_0_323
% 63.90/34.74 | (768) sdtpldt0(xm, xr) = all_943_1_324
% 63.90/34.74 |
% 63.90/34.74 | Instantiating formula (36) with all_0_4_4, xp, all_304_1_150, xr and discharging atoms sdtasdt0(all_0_4_4, xp) = all_304_1_150, sdtasdt0(all_0_4_4, xp) = xr, yields:
% 63.90/34.74 | (769) all_304_1_150 = xr
% 63.90/34.74 |
% 63.90/34.74 | Instantiating formula (36) with all_0_4_4, xp, all_236_0_100, all_304_1_150 and discharging atoms sdtasdt0(all_0_4_4, xp) = all_304_1_150, sdtasdt0(all_0_4_4, xp) = all_236_0_100, yields:
% 63.90/34.74 | (770) all_304_1_150 = all_236_0_100
% 63.90/34.74 |
% 63.90/34.74 | Instantiating formula (36) with sz10, xp, xp, all_236_1_101 and discharging atoms sdtasdt0(sz10, xp) = all_236_1_101, sdtasdt0(sz10, xp) = xp, yields:
% 63.90/34.74 | (771) all_236_1_101 = xp
% 63.90/34.74 |
% 63.90/34.74 | Instantiating formula (121) with xp, xr, all_833_1_296, all_943_0_323 and discharging atoms sdtpldt0(xp, xr) = all_943_0_323, sdtpldt0(xp, xr) = all_833_1_296, yields:
% 63.90/34.74 | (772) all_943_0_323 = all_833_1_296
% 63.90/34.74 |
% 63.90/34.74 | Instantiating formula (121) with xp, xr, all_773_1_279, xn and discharging atoms sdtpldt0(xp, xr) = all_773_1_279, sdtpldt0(xp, xr) = xn, yields:
% 63.90/34.74 | (773) all_773_1_279 = xn
% 63.90/34.74 |
% 63.90/34.74 | Instantiating formula (121) with xp, xr, all_720_0_257, all_773_1_279 and discharging atoms sdtpldt0(xp, xr) = all_773_1_279, sdtpldt0(xp, xr) = all_720_0_257, yields:
% 63.90/34.74 | (774) all_773_1_279 = all_720_0_257
% 63.90/34.74 |
% 63.90/34.74 | Instantiating formula (121) with xp, xr, all_420_0_191, all_833_1_296 and discharging atoms sdtpldt0(xp, xr) = all_833_1_296, sdtpldt0(xp, xr) = all_420_0_191, yields:
% 63.90/34.74 | (775) all_833_1_296 = all_420_0_191
% 63.90/34.74 |
% 63.90/34.74 | Instantiating formula (121) with xp, xr, all_420_0_191, all_720_0_257 and discharging atoms sdtpldt0(xp, xr) = all_720_0_257, sdtpldt0(xp, xr) = all_420_0_191, yields:
% 63.90/34.74 | (776) all_720_0_257 = all_420_0_191
% 63.90/34.74 |
% 63.90/34.74 | Instantiating formula (121) with xp, xr, all_274_0_131, all_720_0_257 and discharging atoms sdtpldt0(xp, xr) = all_720_0_257, sdtpldt0(xp, xr) = all_274_0_131, yields:
% 63.90/34.74 | (777) all_720_0_257 = all_274_0_131
% 63.90/34.74 |
% 63.90/34.74 | Instantiating formula (121) with xp, xr, all_218_0_91, all_943_0_323 and discharging atoms sdtpldt0(xp, xr) = all_943_0_323, sdtpldt0(xp, xr) = all_218_0_91, yields:
% 63.90/34.74 | (778) all_943_0_323 = all_218_0_91
% 63.90/34.74 |
% 63.90/34.74 | Combining equations (772,778) yields a new equation:
% 63.90/34.74 | (779) all_833_1_296 = all_218_0_91
% 63.90/34.74 |
% 63.90/34.74 | Simplifying 779 yields:
% 63.90/34.74 | (780) all_833_1_296 = all_218_0_91
% 63.90/34.74 |
% 63.90/34.74 | Combining equations (775,780) yields a new equation:
% 63.90/34.74 | (781) all_420_0_191 = all_218_0_91
% 63.90/34.74 |
% 63.90/34.74 | Simplifying 781 yields:
% 63.90/34.74 | (782) all_420_0_191 = all_218_0_91
% 63.90/34.74 |
% 63.90/34.74 | Combining equations (774,773) yields a new equation:
% 63.90/34.74 | (783) all_720_0_257 = xn
% 63.90/34.74 |
% 63.90/34.74 | Simplifying 783 yields:
% 63.90/34.74 | (784) all_720_0_257 = xn
% 63.90/34.74 |
% 63.90/34.74 | Combining equations (776,777) yields a new equation:
% 63.90/34.74 | (785) all_420_0_191 = all_274_0_131
% 63.90/34.74 |
% 63.90/34.74 | Simplifying 785 yields:
% 63.90/34.74 | (786) all_420_0_191 = all_274_0_131
% 63.90/34.74 |
% 63.90/34.74 | Combining equations (784,777) yields a new equation:
% 63.90/34.74 | (787) all_274_0_131 = xn
% 63.90/34.74 |
% 63.90/34.74 | Combining equations (786,782) yields a new equation:
% 63.90/34.74 | (788) all_274_0_131 = all_218_0_91
% 63.90/34.74 |
% 63.90/34.74 | Simplifying 788 yields:
% 63.90/34.74 | (789) all_274_0_131 = all_218_0_91
% 63.90/34.74 |
% 63.90/34.74 | Combining equations (770,769) yields a new equation:
% 63.90/34.74 | (790) all_236_0_100 = xr
% 63.90/34.74 |
% 63.90/34.74 | Simplifying 790 yields:
% 63.90/34.74 | (791) all_236_0_100 = xr
% 63.90/34.74 |
% 63.90/34.74 | Combining equations (787,789) yields a new equation:
% 63.90/34.74 | (792) all_218_0_91 = xn
% 63.90/34.74 |
% 63.90/34.74 | From (771)(791) and (492) follows:
% 63.90/34.74 | (793) sdtpldt0(xp, xr) = all_236_2_102
% 63.90/34.74 |
% 63.90/34.74 | From (792) and (489) follows:
% 63.90/34.74 | (118) sdtpldt0(xp, xr) = xn
% 63.90/34.74 |
% 63.90/34.74 | Instantiating formula (121) with xp, xr, all_236_2_102, xn and discharging atoms sdtpldt0(xp, xr) = all_236_2_102, sdtpldt0(xp, xr) = xn, yields:
% 63.90/34.74 | (795) all_236_2_102 = xn
% 63.90/34.74 |
% 63.90/34.74 | From (795) and (793) follows:
% 63.90/34.74 | (118) sdtpldt0(xp, xr) = xn
% 63.90/34.74 |
% 63.90/34.74 | Instantiating formula (110) with xn, xr, xp, xp and discharging atoms sdtpldt0(xp, xr) = xn, doDivides0(xp, xr), doDivides0(xp, xp), aNaturalNumber0(xr), aNaturalNumber0(xp), ~ doDivides0(xp, xn), yields:
% 63.90/34.74 | (797) $false
% 63.90/34.74 |
% 63.90/34.74 |-The branch is then unsatisfiable
% 63.90/34.75 |-Branch two:
% 63.90/34.75 | (798) ~ sdtlseqdt0(sz10, xp)
% 63.90/34.75 | (799) xp = sz10 | xp = sz00
% 63.90/34.75 |
% 63.90/34.75 +-Applying beta-rule and splitting (799), into two cases.
% 63.90/34.75 |-Branch one:
% 63.90/34.75 | (285) xp = sz00
% 63.90/34.75 |
% 63.90/34.75 | Equations (285) can reduce 41 to:
% 63.90/34.75 | (249) $false
% 63.90/34.75 |
% 63.90/34.75 |-The branch is then unsatisfiable
% 63.90/34.75 |-Branch two:
% 63.90/34.75 | (41) ~ (xp = sz00)
% 63.90/34.75 | (289) xp = sz10
% 63.90/34.75 |
% 63.90/34.75 | Equations (289) can reduce 32 to:
% 63.90/34.75 | (249) $false
% 63.90/34.75 |
% 63.90/34.75 |-The branch is then unsatisfiable
% 63.90/34.75 % SZS output end Proof for theBenchmark
% 63.90/34.75
% 63.90/34.75 34165ms
%------------------------------------------------------------------------------