TSTP Solution File: NUM474+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM474+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n014.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 08:44:52 EDT 2022
% Result : Theorem 5.99s 2.06s
% Output : Proof 12.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM474+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 5 07:49:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.57 ____ _
% 0.18/0.57 ___ / __ \_____(_)___ ________ __________
% 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.57
% 0.18/0.57 A Theorem Prover for First-Order Logic
% 0.18/0.57 (ePrincess v.1.0)
% 0.18/0.57
% 0.18/0.57 (c) Philipp Rümmer, 2009-2015
% 0.18/0.57 (c) Peter Backeman, 2014-2015
% 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.57 Bug reports to peter@backeman.se
% 0.18/0.57
% 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.57
% 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.78/1.00 Prover 0: Preprocessing ...
% 3.43/1.46 Prover 0: Constructing countermodel ...
% 5.99/2.06 Prover 0: proved (1403ms)
% 5.99/2.06
% 5.99/2.06 No countermodel exists, formula is valid
% 5.99/2.06 % SZS status Theorem for theBenchmark
% 5.99/2.06
% 5.99/2.06 Generating proof ... found it (size 176)
% 12.05/3.48
% 12.05/3.48 % SZS output start Proof for theBenchmark
% 12.05/3.48 Assumed formulas after preprocessing and simplification:
% 12.05/3.48 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = v3) & ~ (xl = sz00) & ~ (sz10 = sz00) & sdtsldt0(v0, xl) = xq & sdtsldt0(xm, xl) = xp & sdtmndt0(xq, xp) = xr & sdtasdt0(xl, xr) = v2 & sdtasdt0(xl, xp) = v1 & sdtpldt0(v1, v2) = v3 & sdtpldt0(v1, xn) = v4 & sdtpldt0(xm, xn) = v0 & doDivides0(xl, v0) & doDivides0(xl, xm) & sdtlseqdt0(xp, xq) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & aNaturalNumber0(xl) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v7, v5) = v9) | ~ (sdtasdt0(v6, v5) = v8) | ~ (sdtpldt0(v8, v9) = v10) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v11, v5) = v10 & sdtasdt0(v5, v11) = v12 & sdtasdt0(v5, v7) = v14 & sdtasdt0(v5, v6) = v13 & sdtpldt0(v13, v14) = v12 & sdtpldt0(v6, v7) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v5, v7) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ (sdtpldt0(v8, v9) = v10) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v11, v5) = v12 & sdtasdt0(v7, v5) = v14 & sdtasdt0(v6, v5) = v13 & sdtasdt0(v5, v11) = v10 & sdtpldt0(v13, v14) = v12 & sdtpldt0(v6, v7) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v9) | ~ (sdtasdt0(v6, v5) = v8) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtlseqdt0(v8, v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v9) | ~ (sdtasdt0(v6, v5) = v8) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtasdt0(v5, v7) = v11 & sdtasdt0(v5, v6) = v10 & sdtlseqdt0(v10, v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v9) | ~ (sdtasdt0(v6, v5) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtasdt0(v5, v7) = v11 & sdtasdt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtasdt0(v6, v5) = v11 & sdtasdt0(v5, v7) = v10 & sdtlseqdt0(v11, v9) & sdtlseqdt0(v8, v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtasdt0(v6, v5) = v11 & sdtasdt0(v5, v7) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v6, v5) = v9) | ~ (sdtasdt0(v5, v7) = v8) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtasdt0(v7, v5) = v11 & sdtasdt0(v5, v6) = v10 & sdtlseqdt0(v10, v8) & sdtlseqdt0(v9, v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v6, v5) = v9) | ~ (sdtasdt0(v5, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtasdt0(v7, v5) = v11 & sdtasdt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v5, v7) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtlseqdt0(v8, v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v5, v7) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtasdt0(v7, v5) = v11 & sdtasdt0(v6, v5) = v10 & sdtlseqdt0(v10, v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v5, v7) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtasdt0(v7, v5) = v11 & sdtasdt0(v6, v5) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v7, v5) = v9) | ~ (sdtpldt0(v6, v5) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtpldt0(v5, v7) = v11 & sdtpldt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v7, v5) = v9) | ~ (sdtpldt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtpldt0(v6, v5) = v11 & sdtpldt0(v5, v7) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v6, v5) = v9) | ~ (sdtpldt0(v5, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtpldt0(v7, v5) = v11 & sdtpldt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v5, v7) = v9) | ~ (sdtpldt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtpldt0(v7, v5) = v11 & sdtpldt0(v6, v5) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v8, v7) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : (sdtasdt0(v6, v7) = v10 & sdtasdt0(v5, v10) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v8, v5) = v9) | ~ (sdtpldt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v7, v5) = v14 & sdtasdt0(v6, v5) = v13 & sdtasdt0(v5, v8) = v10 & sdtasdt0(v5, v7) = v12 & sdtasdt0(v5, v6) = v11 & sdtpldt0(v13, v14) = v9 & sdtpldt0(v11, v12) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v6, v7) = v8) | ~ (sdtasdt0(v5, v8) = v9) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : (sdtasdt0(v10, v7) = v9 & sdtasdt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v5, v8) = v9) | ~ (sdtpldt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v8, v5) = v12 & sdtasdt0(v7, v5) = v14 & sdtasdt0(v6, v5) = v13 & sdtasdt0(v5, v7) = v11 & sdtasdt0(v5, v6) = v10 & sdtpldt0(v13, v14) = v12 & sdtpldt0(v10, v11) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v8, v7) = v9) | ~ (sdtpldt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : (sdtpldt0(v6, v7) = v10 & sdtpldt0(v5, v10) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v6, v7) = v8) | ~ (sdtpldt0(v5, v8) = v9) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : (sdtpldt0(v10, v7) = v9 & sdtpldt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | v5 = sz00 | ~ (sdtsldt0(v6, v5) = v7) | ~ (sdtasdt0(v5, v8) = v6) | ~ doDivides0(v5, v6) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ (sdtmndt0(v6, v5) = v7) | ~ (sdtpldt0(v5, v8) = v6) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v6 | v5 = sz00 | ~ (sdtsldt0(v6, v5) = v7) | ~ (sdtasdt0(v5, v7) = v8) | ~ doDivides0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v6 | ~ (sdtmndt0(v6, v5) = v7) | ~ (sdtpldt0(v5, v7) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v8) | ~ (sdtasdt0(v6, v5) = v8) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v8) | ~ (sdtasdt0(v6, v5) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v5, v7) = v8) | ~ (sdtasdt0(v5, v6) = v8) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v5, v7) = v8) | ~ (sdtasdt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (sdtpldt0(v7, v5) = v8) | ~ (sdtpldt0(v6, v5) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (sdtpldt0(v5, v7) = v8) | ~ (sdtpldt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtsldt0(v8, v7) = v6) | ~ (sdtsldt0(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtmndt0(v8, v7) = v6) | ~ (sdtmndt0(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtasdt0(v8, v7) = v6) | ~ (sdtasdt0(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v8, v7) = v6) | ~ (sdtpldt0(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v7, v6) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = v10) & ~ (v9 = v8) & sdtpldt0(v7, v5) = v9 & sdtpldt0(v6, v7) = v11 & sdtpldt0(v5, v7) = v10 & sdtlseqdt0(v10, v11) & sdtlseqdt0(v9, v8))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v7, v5) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = v10) & ~ (v9 = v8) & sdtpldt0(v7, v6) = v9 & sdtpldt0(v6, v7) = v11 & sdtpldt0(v5, v7) = v10 & sdtlseqdt0(v10, v11) & sdtlseqdt0(v8, v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v6, v7) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = v8) & ~ (v10 = v9) & sdtpldt0(v7, v6) = v10 & sdtpldt0(v7, v5) = v9 & sdtpldt0(v5, v7) = v11 & sdtlseqdt0(v11, v8) & sdtlseqdt0(v9, v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v5, v7) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = v8) & ~ (v10 = v9) & sdtpldt0(v7, v6) = v10 & sdtpldt0(v7, v5) = v9 & sdtpldt0(v6, v7) = v11 & sdtlseqdt0(v9, v10) & sdtlseqdt0(v8, v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = sz00 | ~ (sdtsldt0(v6, v5) = v7) | ~ (sdtasdt0(v5, v7) = v8) | ~ doDivides0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | aNaturalNumber0(v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtmndt0(v6, v5) = v7) | ~ (sdtpldt0(v5, v7) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | aNaturalNumber0(v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v6, v7) = v8) | ~ doDivides0(v5, v7) | ~ doDivides0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | doDivides0(v5, v8)) & ! [v5] : ! [v6] : ! [v7] : (v5 = sz00 | ~ (sdtasdt0(v6, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtlseqdt0(v6, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v6, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtasdt0(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v5, v7) = v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | doDivides0(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtasdt0(v6, v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | aNaturalNumber0(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v6, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtpldt0(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v7) = v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtlseqdt0(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtpldt0(v6, v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | aNaturalNumber0(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ doDivides0(v6, v7) | ~ doDivides0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | doDivides0(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ sdtlseqdt0(v6, v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtlseqdt0(v5, v7)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtasdt0(v5, sz10) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtasdt0(sz10, v5) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtpldt0(v5, sz00) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtpldt0(sz00, v5) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ sdtlseqdt0(v6, v5) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | iLess0(v5, v6)) & ! [v5] : ! [v6] : (v6 = sz00 | v5 = sz00 | ~ (sdtasdt0(v5, v6) = sz00) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = sz00 | ~ (sdtasdt0(v5, sz00) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = sz00 | ~ (sdtasdt0(sz00, v5) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = sz00 | ~ (sdtpldt0(v5, v6) = sz00) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v5 = sz00 | ~ (sdtpldt0(v5, v6) = sz00) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, sz10) = v6) | ~ aNaturalNumber0(v5) | sdtasdt0(sz10, v5) = v5) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, sz00) = v6) | ~ aNaturalNumber0(v5) | sdtasdt0(sz00, v5) = sz00) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(sz10, v5) = v6) | ~ aNaturalNumber0(v5) | sdtasdt0(v5, sz10) = v5) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(sz00, v5) = v6) | ~ aNaturalNumber0(v5) | sdtasdt0(v5, sz00) = sz00) & ! [v5] : ! [v6] : ( ~ (sdtpldt0(v5, sz00) = v6) | ~ aNaturalNumber0(v5) | sdtpldt0(sz00, v5) = v5) & ! [v5] : ! [v6] : ( ~ (sdtpldt0(sz00, v5) = v6) | ~ aNaturalNumber0(v5) | sdtpldt0(v5, sz00) = v5) & ! [v5] : ! [v6] : ( ~ doDivides0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v7] : (sdtasdt0(v5, v7) = v6 & aNaturalNumber0(v7))) & ! [v5] : ! [v6] : ( ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v7] : (sdtpldt0(v5, v7) = v6 & aNaturalNumber0(v7))) & ! [v5] : ! [v6] : ( ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtlseqdt0(v6, v5) | sdtlseqdt0(v5, v6)) & ! [v5] : (v5 = sz10 | v5 = sz00 | ~ aNaturalNumber0(v5) | sdtlseqdt0(sz10, v5)) & ! [v5] : ( ~ aNaturalNumber0(v5) | sdtlseqdt0(v5, v5)))
% 12.46/3.55 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 12.46/3.55 | (1) ~ (all_0_0_0 = all_0_1_1) & ~ (xl = sz00) & ~ (sz10 = sz00) & sdtsldt0(all_0_4_4, xl) = xq & sdtsldt0(xm, xl) = xp & sdtmndt0(xq, xp) = xr & sdtasdt0(xl, xr) = all_0_2_2 & sdtasdt0(xl, xp) = all_0_3_3 & sdtpldt0(all_0_3_3, all_0_2_2) = all_0_1_1 & sdtpldt0(all_0_3_3, xn) = all_0_0_0 & sdtpldt0(xm, xn) = all_0_4_4 & doDivides0(xl, all_0_4_4) & doDivides0(xl, xm) & sdtlseqdt0(xp, xq) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & aNaturalNumber0(xl) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ! [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] : ( ~ (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) | ~ 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, 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 | ~ (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] : (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 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) & ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 12.46/3.57 |
% 12.46/3.57 | Applying alpha-rule on (1) yields:
% 12.46/3.57 | (2) ! [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))
% 12.46/3.57 | (3) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 12.46/3.57 | (4) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0)
% 12.46/3.57 | (5) ! [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))
% 12.46/3.57 | (6) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 12.46/3.57 | (7) ~ (sz10 = sz00)
% 12.46/3.57 | (8) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 12.46/3.57 | (9) sdtsldt0(all_0_4_4, xl) = xq
% 12.46/3.57 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 12.46/3.57 | (11) ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 12.46/3.57 | (12) aNaturalNumber0(xn)
% 12.46/3.57 | (13) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 12.46/3.57 | (14) ! [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)))
% 12.46/3.58 | (15) ! [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))
% 12.46/3.58 | (16) doDivides0(xl, xm)
% 12.46/3.58 | (17) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0))
% 12.46/3.58 | (18) sdtsldt0(xm, xl) = xp
% 12.46/3.58 | (19) ! [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))
% 12.46/3.58 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 12.46/3.58 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3))
% 12.46/3.58 | (22) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 12.46/3.58 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 12.46/3.58 | (24) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 12.46/3.58 | (25) ! [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)))
% 12.46/3.58 | (26) ! [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))
% 12.46/3.58 | (27) ! [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)))
% 12.46/3.58 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 12.46/3.58 | (29) ! [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))
% 12.46/3.58 | (30) ~ (all_0_0_0 = all_0_1_1)
% 12.46/3.58 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 12.46/3.58 | (32) sdtmndt0(xq, xp) = xr
% 12.46/3.58 | (33) sdtpldt0(xm, xn) = all_0_4_4
% 12.46/3.58 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 12.46/3.58 | (35) ! [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))
% 12.46/3.58 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 12.46/3.58 | (37) ~ (xl = sz00)
% 12.46/3.58 | (38) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 12.46/3.58 | (39) ! [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)))
% 12.46/3.58 | (40) ! [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))
% 12.46/3.58 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 12.46/3.58 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 12.46/3.58 | (43) aNaturalNumber0(sz00)
% 12.46/3.58 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 12.46/3.58 | (45) ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 12.46/3.59 | (46) ! [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))
% 12.46/3.59 | (47) ! [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))
% 12.46/3.59 | (48) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 12.46/3.59 | (49) sdtpldt0(all_0_3_3, all_0_2_2) = all_0_1_1
% 12.46/3.59 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2)
% 12.46/3.59 | (51) sdtpldt0(all_0_3_3, xn) = all_0_0_0
% 12.46/3.59 | (52) ! [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))
% 12.46/3.59 | (53) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 12.46/3.59 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2)
% 12.46/3.59 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 12.46/3.59 | (56) ! [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))
% 12.46/3.59 | (57) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 12.46/3.59 | (58) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00)
% 12.88/3.59 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 12.88/3.59 | (60) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 12.88/3.59 | (61) ! [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)))
% 12.88/3.59 | (62) ! [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)))
% 12.88/3.59 | (63) doDivides0(xl, all_0_4_4)
% 12.88/3.59 | (64) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 12.88/3.59 | (65) ! [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)))
% 12.88/3.59 | (66) ! [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))
% 12.88/3.59 | (67) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 12.88/3.59 | (68) ! [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))
% 12.88/3.59 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 12.88/3.59 | (70) aNaturalNumber0(xl)
% 12.88/3.59 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 12.88/3.59 | (72) sdtasdt0(xl, xp) = all_0_3_3
% 12.88/3.59 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 12.88/3.59 | (74) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 12.88/3.59 | (75) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 12.88/3.59 | (76) ! [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)))
% 12.88/3.59 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 12.88/3.59 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 12.88/3.59 | (79) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 12.88/3.59 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 12.88/3.59 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 12.88/3.59 | (82) ! [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))
% 12.88/3.59 | (83) sdtasdt0(xl, xr) = all_0_2_2
% 12.88/3.59 | (84) ! [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))
% 12.88/3.59 | (85) ! [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))
% 12.88/3.59 | (86) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0)
% 12.88/3.60 | (87) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 12.88/3.60 | (88) ! [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))
% 12.88/3.60 | (89) sdtlseqdt0(xp, xq)
% 12.88/3.60 | (90) aNaturalNumber0(sz10)
% 12.88/3.60 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 12.88/3.60 | (92) ! [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))
% 12.88/3.60 | (93) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0))
% 12.88/3.60 | (94) aNaturalNumber0(xm)
% 12.88/3.60 | (95) ! [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))
% 12.88/3.60 | (96) ! [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))
% 12.88/3.60 |
% 12.88/3.60 | Instantiating formula (81) with all_0_3_3, xp, xm, xl and discharging atoms sdtsldt0(xm, xl) = xp, sdtasdt0(xl, xp) = all_0_3_3, doDivides0(xl, xm), aNaturalNumber0(xm), aNaturalNumber0(xl), yields:
% 12.88/3.60 | (97) all_0_3_3 = xm | xl = sz00
% 12.88/3.60 |
% 12.88/3.60 | Instantiating formula (28) with all_0_4_4, xn, xm and discharging atoms sdtpldt0(xm, xn) = all_0_4_4, aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 12.88/3.60 | (98) aNaturalNumber0(all_0_4_4)
% 12.88/3.60 |
% 12.88/3.60 | Instantiating formula (23) with all_0_3_3, xp, xm, xl and discharging atoms sdtsldt0(xm, xl) = xp, sdtasdt0(xl, xp) = all_0_3_3, doDivides0(xl, xm), aNaturalNumber0(xm), aNaturalNumber0(xl), yields:
% 12.88/3.60 | (99) xl = sz00 | aNaturalNumber0(xp)
% 12.88/3.60 |
% 12.88/3.60 | Instantiating formula (45) with xm, xl and discharging atoms doDivides0(xl, xm), aNaturalNumber0(xm), aNaturalNumber0(xl), yields:
% 12.88/3.60 | (100) ? [v0] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0))
% 12.88/3.60 |
% 12.88/3.60 | Instantiating formula (67) with xl, xl and discharging atoms aNaturalNumber0(xl), yields:
% 12.88/3.60 | (101) sdtlseqdt0(xl, xl)
% 12.88/3.60 |
% 12.88/3.60 | Instantiating (100) with all_9_0_5 yields:
% 12.88/3.60 | (102) sdtasdt0(xl, all_9_0_5) = xm & aNaturalNumber0(all_9_0_5)
% 12.88/3.60 |
% 12.88/3.60 | Applying alpha-rule on (102) yields:
% 12.88/3.60 | (103) sdtasdt0(xl, all_9_0_5) = xm
% 12.88/3.60 | (104) aNaturalNumber0(all_9_0_5)
% 12.88/3.60 |
% 12.88/3.60 +-Applying beta-rule and splitting (99), into two cases.
% 12.88/3.60 |-Branch one:
% 12.88/3.60 | (105) aNaturalNumber0(xp)
% 12.88/3.60 |
% 12.88/3.60 +-Applying beta-rule and splitting (97), into two cases.
% 12.88/3.60 |-Branch one:
% 12.88/3.60 | (106) xl = sz00
% 12.88/3.60 |
% 12.88/3.60 | Equations (106) can reduce 37 to:
% 12.88/3.60 | (107) $false
% 12.88/3.60 |
% 12.88/3.60 |-The branch is then unsatisfiable
% 12.88/3.60 |-Branch two:
% 12.88/3.60 | (37) ~ (xl = sz00)
% 12.88/3.60 | (109) all_0_3_3 = xm
% 12.88/3.60 |
% 12.88/3.60 | From (109) and (72) follows:
% 12.88/3.60 | (110) sdtasdt0(xl, xp) = xm
% 12.88/3.60 |
% 12.88/3.60 | From (109) and (49) follows:
% 12.88/3.60 | (111) sdtpldt0(xm, all_0_2_2) = all_0_1_1
% 12.88/3.60 |
% 12.88/3.60 | From (109) and (51) follows:
% 12.88/3.60 | (112) sdtpldt0(xm, xn) = all_0_0_0
% 12.88/3.60 |
% 12.88/3.60 | Instantiating formula (91) with xm, xn, all_0_0_0, all_0_4_4 and discharging atoms sdtpldt0(xm, xn) = all_0_0_0, sdtpldt0(xm, xn) = all_0_4_4, yields:
% 12.88/3.60 | (113) all_0_0_0 = all_0_4_4
% 12.88/3.60 |
% 12.88/3.60 | Instantiating formula (10) with xm, all_9_0_5, xp, xl and discharging atoms sdtasdt0(xl, all_9_0_5) = xm, sdtasdt0(xl, xp) = xm, aNaturalNumber0(all_9_0_5), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 12.88/3.60 | (114) all_9_0_5 = xp | xl = sz00
% 12.88/3.60 |
% 12.88/3.60 | Equations (113) can reduce 30 to:
% 12.88/3.60 | (115) ~ (all_0_1_1 = all_0_4_4)
% 12.88/3.60 |
% 12.88/3.60 | Simplifying 115 yields:
% 12.88/3.60 | (116) ~ (all_0_1_1 = all_0_4_4)
% 12.88/3.60 |
% 12.88/3.60 +-Applying beta-rule and splitting (114), into two cases.
% 12.88/3.60 |-Branch one:
% 12.88/3.60 | (106) xl = sz00
% 12.88/3.60 |
% 12.88/3.60 | Equations (106) can reduce 37 to:
% 12.88/3.60 | (107) $false
% 12.88/3.60 |
% 12.88/3.60 |-The branch is then unsatisfiable
% 12.88/3.60 |-Branch two:
% 12.88/3.60 | (37) ~ (xl = sz00)
% 12.88/3.60 | (120) all_9_0_5 = xp
% 12.88/3.60 |
% 12.88/3.60 | From (120) and (103) follows:
% 12.88/3.60 | (110) sdtasdt0(xl, xp) = xm
% 12.88/3.60 |
% 12.88/3.60 | From (120) and (104) follows:
% 12.88/3.60 | (105) aNaturalNumber0(xp)
% 12.88/3.60 |
% 12.88/3.60 | Instantiating formula (6) with xl, xl and discharging atoms sdtlseqdt0(xl, xl), aNaturalNumber0(xl), yields:
% 12.88/3.60 | (123) ? [v0] : (sdtpldt0(xl, v0) = xl & aNaturalNumber0(v0))
% 12.88/3.60 |
% 12.88/3.60 | Instantiating formula (45) with all_0_4_4, xl and discharging atoms doDivides0(xl, all_0_4_4), aNaturalNumber0(all_0_4_4), aNaturalNumber0(xl), yields:
% 12.88/3.60 | (124) ? [v0] : (sdtasdt0(xl, v0) = all_0_4_4 & aNaturalNumber0(v0))
% 12.88/3.60 |
% 12.88/3.60 | Instantiating formula (50) with xm, xl, xp and discharging atoms sdtasdt0(xl, xp) = xm, aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 12.88/3.60 | (125) sdtasdt0(xp, xl) = xm
% 12.88/3.60 |
% 12.88/3.60 | Instantiating formula (67) with xp, xp and discharging atoms aNaturalNumber0(xp), yields:
% 12.88/3.60 | (126) sdtlseqdt0(xp, xp)
% 12.88/3.60 |
% 12.88/3.60 | Instantiating (124) with all_33_0_6 yields:
% 12.88/3.60 | (127) sdtasdt0(xl, all_33_0_6) = all_0_4_4 & aNaturalNumber0(all_33_0_6)
% 12.88/3.61 |
% 12.88/3.61 | Applying alpha-rule on (127) yields:
% 12.88/3.61 | (128) sdtasdt0(xl, all_33_0_6) = all_0_4_4
% 12.88/3.61 | (129) aNaturalNumber0(all_33_0_6)
% 12.88/3.61 |
% 12.88/3.61 | Instantiating (123) with all_41_0_10 yields:
% 12.88/3.61 | (130) sdtpldt0(xl, all_41_0_10) = xl & aNaturalNumber0(all_41_0_10)
% 12.88/3.61 |
% 12.88/3.61 | Applying alpha-rule on (130) yields:
% 12.88/3.61 | (131) sdtpldt0(xl, all_41_0_10) = xl
% 12.88/3.61 | (132) aNaturalNumber0(all_41_0_10)
% 12.88/3.61 |
% 12.88/3.61 | Instantiating formula (19) with all_33_0_6, xq, all_0_4_4, xl and discharging atoms sdtsldt0(all_0_4_4, xl) = xq, sdtasdt0(xl, all_33_0_6) = all_0_4_4, doDivides0(xl, all_0_4_4), aNaturalNumber0(all_33_0_6), aNaturalNumber0(all_0_4_4), aNaturalNumber0(xl), yields:
% 12.88/3.61 | (133) all_33_0_6 = xq | xl = sz00
% 12.88/3.61 |
% 12.88/3.61 +-Applying beta-rule and splitting (133), into two cases.
% 12.88/3.61 |-Branch one:
% 12.88/3.61 | (106) xl = sz00
% 12.88/3.61 |
% 12.88/3.61 | Equations (106) can reduce 37 to:
% 12.88/3.61 | (107) $false
% 12.88/3.61 |
% 12.88/3.61 |-The branch is then unsatisfiable
% 12.88/3.61 |-Branch two:
% 12.88/3.61 | (37) ~ (xl = sz00)
% 12.88/3.61 | (137) all_33_0_6 = xq
% 12.88/3.61 |
% 12.88/3.61 | From (137) and (128) follows:
% 12.88/3.61 | (138) sdtasdt0(xl, xq) = all_0_4_4
% 12.88/3.61 |
% 12.88/3.61 | From (137) and (129) follows:
% 12.88/3.61 | (139) aNaturalNumber0(xq)
% 12.88/3.61 |
% 12.88/3.61 | Instantiating formula (6) with xp, xp and discharging atoms sdtlseqdt0(xp, xp), aNaturalNumber0(xp), yields:
% 12.88/3.61 | (140) ? [v0] : (sdtpldt0(xp, v0) = xp & aNaturalNumber0(v0))
% 12.88/3.61 |
% 12.88/3.61 | Instantiating formula (29) with xm, xl, all_41_0_10, xl, xp and discharging atoms sdtasdt0(xl, xp) = xm, sdtpldt0(xl, all_41_0_10) = xl, aNaturalNumber0(all_41_0_10), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 12.88/3.61 | (141) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_41_0_10, xp) = v4 & sdtasdt0(xp, all_41_0_10) = v2 & sdtasdt0(xp, xl) = v1 & sdtasdt0(xp, xl) = v0 & sdtasdt0(xl, xp) = v3 & sdtpldt0(v3, v4) = xm & sdtpldt0(v1, v2) = v0)
% 12.88/3.61 |
% 12.88/3.61 | Instantiating formula (26) with xm, xl, all_41_0_10, xl, xp and discharging atoms sdtasdt0(xp, xl) = xm, sdtpldt0(xl, all_41_0_10) = xl, aNaturalNumber0(all_41_0_10), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 12.88/3.61 | (142) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_41_0_10, xp) = v4 & sdtasdt0(xp, all_41_0_10) = v1 & sdtasdt0(xp, xl) = v0 & sdtasdt0(xl, xp) = v3 & sdtasdt0(xl, xp) = v2 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = xm)
% 12.88/3.61 |
% 12.88/3.61 | Instantiating formula (54) with xl, xl, all_41_0_10 and discharging atoms sdtpldt0(xl, all_41_0_10) = xl, aNaturalNumber0(all_41_0_10), aNaturalNumber0(xl), yields:
% 12.88/3.61 | (143) sdtpldt0(all_41_0_10, xl) = xl
% 12.88/3.61 |
% 12.88/3.61 | Instantiating formula (29) with all_0_4_4, xl, all_41_0_10, xl, xq and discharging atoms sdtasdt0(xl, xq) = all_0_4_4, sdtpldt0(xl, all_41_0_10) = xl, aNaturalNumber0(all_41_0_10), aNaturalNumber0(xq), aNaturalNumber0(xl), yields:
% 12.88/3.61 | (144) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_41_0_10, xq) = v4 & sdtasdt0(xq, all_41_0_10) = v2 & sdtasdt0(xq, xl) = v1 & sdtasdt0(xq, xl) = v0 & sdtasdt0(xl, xq) = v3 & sdtpldt0(v3, v4) = all_0_4_4 & sdtpldt0(v1, v2) = v0)
% 12.88/3.61 |
% 12.88/3.61 | Instantiating formula (50) with all_0_4_4, xl, xq and discharging atoms sdtasdt0(xl, xq) = all_0_4_4, aNaturalNumber0(xq), aNaturalNumber0(xl), yields:
% 12.88/3.61 | (145) sdtasdt0(xq, xl) = all_0_4_4
% 12.88/3.61 |
% 12.88/3.61 | Instantiating formula (6) with xq, xp and discharging atoms sdtlseqdt0(xp, xq), aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 12.88/3.61 | (146) ? [v0] : (sdtpldt0(xp, v0) = xq & aNaturalNumber0(v0))
% 12.88/3.61 |
% 12.88/3.61 | Instantiating (146) with all_59_0_12 yields:
% 12.88/3.61 | (147) sdtpldt0(xp, all_59_0_12) = xq & aNaturalNumber0(all_59_0_12)
% 12.88/3.61 |
% 12.88/3.61 | Applying alpha-rule on (147) yields:
% 12.88/3.61 | (148) sdtpldt0(xp, all_59_0_12) = xq
% 12.88/3.61 | (149) aNaturalNumber0(all_59_0_12)
% 12.88/3.61 |
% 12.88/3.61 | Instantiating (142) with all_71_0_18, all_71_1_19, all_71_2_20, all_71_3_21, all_71_4_22 yields:
% 12.88/3.61 | (150) sdtasdt0(all_41_0_10, xp) = all_71_0_18 & sdtasdt0(xp, all_41_0_10) = all_71_3_21 & sdtasdt0(xp, xl) = all_71_4_22 & sdtasdt0(xl, xp) = all_71_1_19 & sdtasdt0(xl, xp) = all_71_2_20 & sdtpldt0(all_71_1_19, all_71_0_18) = all_71_2_20 & sdtpldt0(all_71_4_22, all_71_3_21) = xm
% 12.88/3.61 |
% 12.88/3.61 | Applying alpha-rule on (150) yields:
% 12.88/3.61 | (151) sdtasdt0(xp, all_41_0_10) = all_71_3_21
% 12.88/3.61 | (152) sdtasdt0(xl, xp) = all_71_2_20
% 12.88/3.61 | (153) sdtasdt0(xp, xl) = all_71_4_22
% 12.88/3.61 | (154) sdtasdt0(xl, xp) = all_71_1_19
% 12.88/3.61 | (155) sdtpldt0(all_71_4_22, all_71_3_21) = xm
% 12.88/3.61 | (156) sdtasdt0(all_41_0_10, xp) = all_71_0_18
% 12.88/3.61 | (157) sdtpldt0(all_71_1_19, all_71_0_18) = all_71_2_20
% 12.88/3.61 |
% 12.88/3.61 | Instantiating (141) with all_73_0_23, all_73_1_24, all_73_2_25, all_73_3_26, all_73_4_27 yields:
% 12.88/3.61 | (158) sdtasdt0(all_41_0_10, xp) = all_73_0_23 & sdtasdt0(xp, all_41_0_10) = all_73_2_25 & sdtasdt0(xp, xl) = all_73_3_26 & sdtasdt0(xp, xl) = all_73_4_27 & sdtasdt0(xl, xp) = all_73_1_24 & sdtpldt0(all_73_1_24, all_73_0_23) = xm & sdtpldt0(all_73_3_26, all_73_2_25) = all_73_4_27
% 12.88/3.61 |
% 12.88/3.61 | Applying alpha-rule on (158) yields:
% 12.88/3.61 | (159) sdtasdt0(xl, xp) = all_73_1_24
% 12.88/3.61 | (160) sdtasdt0(xp, xl) = all_73_4_27
% 12.88/3.61 | (161) sdtasdt0(all_41_0_10, xp) = all_73_0_23
% 12.88/3.61 | (162) sdtpldt0(all_73_1_24, all_73_0_23) = xm
% 12.88/3.61 | (163) sdtasdt0(xp, xl) = all_73_3_26
% 12.88/3.61 | (164) sdtasdt0(xp, all_41_0_10) = all_73_2_25
% 12.88/3.61 | (165) sdtpldt0(all_73_3_26, all_73_2_25) = all_73_4_27
% 12.88/3.61 |
% 12.88/3.61 | Instantiating (140) with all_75_0_28 yields:
% 12.88/3.61 | (166) sdtpldt0(xp, all_75_0_28) = xp & aNaturalNumber0(all_75_0_28)
% 12.88/3.61 |
% 12.88/3.61 | Applying alpha-rule on (166) yields:
% 12.88/3.61 | (167) sdtpldt0(xp, all_75_0_28) = xp
% 12.88/3.61 | (168) aNaturalNumber0(all_75_0_28)
% 12.88/3.61 |
% 12.88/3.61 | Instantiating (144) with all_79_0_30, all_79_1_31, all_79_2_32, all_79_3_33, all_79_4_34 yields:
% 12.88/3.61 | (169) sdtasdt0(all_41_0_10, xq) = all_79_0_30 & sdtasdt0(xq, all_41_0_10) = all_79_2_32 & sdtasdt0(xq, xl) = all_79_3_33 & sdtasdt0(xq, xl) = all_79_4_34 & sdtasdt0(xl, xq) = all_79_1_31 & sdtpldt0(all_79_1_31, all_79_0_30) = all_0_4_4 & sdtpldt0(all_79_3_33, all_79_2_32) = all_79_4_34
% 12.88/3.61 |
% 12.88/3.61 | Applying alpha-rule on (169) yields:
% 12.88/3.61 | (170) sdtpldt0(all_79_3_33, all_79_2_32) = all_79_4_34
% 12.88/3.61 | (171) sdtasdt0(xl, xq) = all_79_1_31
% 12.88/3.61 | (172) sdtasdt0(all_41_0_10, xq) = all_79_0_30
% 12.88/3.61 | (173) sdtasdt0(xq, xl) = all_79_4_34
% 12.88/3.61 | (174) sdtasdt0(xq, xl) = all_79_3_33
% 12.88/3.61 | (175) sdtpldt0(all_79_1_31, all_79_0_30) = all_0_4_4
% 12.88/3.61 | (176) sdtasdt0(xq, all_41_0_10) = all_79_2_32
% 12.88/3.61 |
% 12.88/3.61 | Instantiating formula (42) with xq, xl, all_79_4_34, all_79_3_33 and discharging atoms sdtasdt0(xq, xl) = all_79_3_33, sdtasdt0(xq, xl) = all_79_4_34, yields:
% 12.88/3.61 | (177) all_79_3_33 = all_79_4_34
% 12.88/3.61 |
% 12.88/3.61 | Instantiating formula (42) with xq, xl, all_0_4_4, all_79_3_33 and discharging atoms sdtasdt0(xq, xl) = all_79_3_33, sdtasdt0(xq, xl) = all_0_4_4, yields:
% 12.88/3.61 | (178) all_79_3_33 = all_0_4_4
% 12.88/3.61 |
% 12.88/3.61 | Instantiating formula (42) with xp, xl, all_73_4_27, xm and discharging atoms sdtasdt0(xp, xl) = all_73_4_27, sdtasdt0(xp, xl) = xm, yields:
% 12.88/3.61 | (179) all_73_4_27 = xm
% 12.88/3.61 |
% 12.88/3.61 | Instantiating formula (42) with xp, xl, all_73_4_27, all_73_3_26 and discharging atoms sdtasdt0(xp, xl) = all_73_3_26, sdtasdt0(xp, xl) = all_73_4_27, yields:
% 12.88/3.61 | (180) all_73_3_26 = all_73_4_27
% 12.88/3.61 |
% 12.88/3.61 | Instantiating formula (42) with xp, xl, all_71_4_22, all_73_3_26 and discharging atoms sdtasdt0(xp, xl) = all_73_3_26, sdtasdt0(xp, xl) = all_71_4_22, yields:
% 12.88/3.61 | (181) all_73_3_26 = all_71_4_22
% 12.88/3.61 |
% 12.88/3.61 | Instantiating formula (42) with xl, xq, all_79_1_31, all_0_4_4 and discharging atoms sdtasdt0(xl, xq) = all_79_1_31, sdtasdt0(xl, xq) = all_0_4_4, yields:
% 12.88/3.61 | (182) all_79_1_31 = all_0_4_4
% 12.88/3.61 |
% 12.88/3.61 | Instantiating formula (42) with xl, xp, all_73_1_24, xm and discharging atoms sdtasdt0(xl, xp) = all_73_1_24, sdtasdt0(xl, xp) = xm, yields:
% 12.88/3.61 | (183) all_73_1_24 = xm
% 12.88/3.61 |
% 12.88/3.61 | Instantiating formula (42) with xl, xp, all_71_1_19, all_73_1_24 and discharging atoms sdtasdt0(xl, xp) = all_73_1_24, sdtasdt0(xl, xp) = all_71_1_19, yields:
% 12.88/3.61 | (184) all_73_1_24 = all_71_1_19
% 12.88/3.61 |
% 12.88/3.61 | Instantiating formula (42) with xl, xp, all_71_2_20, all_73_1_24 and discharging atoms sdtasdt0(xl, xp) = all_73_1_24, sdtasdt0(xl, xp) = all_71_2_20, yields:
% 12.88/3.61 | (185) all_73_1_24 = all_71_2_20
% 12.88/3.61 |
% 12.88/3.61 | Instantiating formula (80) with all_59_0_12, xr, xq, xp and discharging atoms sdtmndt0(xq, xp) = xr, sdtpldt0(xp, all_59_0_12) = xq, sdtlseqdt0(xp, xq), aNaturalNumber0(all_59_0_12), aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 12.88/3.61 | (186) all_59_0_12 = xr
% 12.88/3.61 |
% 12.88/3.61 | Combining equations (178,177) yields a new equation:
% 12.88/3.61 | (187) all_79_4_34 = all_0_4_4
% 12.88/3.61 |
% 12.88/3.61 | Combining equations (185,184) yields a new equation:
% 12.88/3.61 | (188) all_71_1_19 = all_71_2_20
% 12.88/3.61 |
% 12.88/3.61 | Combining equations (183,184) yields a new equation:
% 12.88/3.61 | (189) all_71_1_19 = xm
% 12.88/3.61 |
% 12.88/3.61 | Combining equations (180,181) yields a new equation:
% 12.88/3.61 | (190) all_73_4_27 = all_71_4_22
% 12.88/3.61 |
% 12.88/3.61 | Simplifying 190 yields:
% 12.88/3.61 | (191) all_73_4_27 = all_71_4_22
% 12.88/3.61 |
% 12.88/3.61 | Combining equations (191,179) yields a new equation:
% 12.88/3.61 | (192) all_71_4_22 = xm
% 12.88/3.61 |
% 12.88/3.61 | Simplifying 192 yields:
% 12.88/3.61 | (193) all_71_4_22 = xm
% 12.88/3.61 |
% 12.88/3.61 | Combining equations (189,188) yields a new equation:
% 12.88/3.61 | (194) all_71_2_20 = xm
% 12.88/3.61 |
% 12.88/3.61 | From (187) and (173) follows:
% 12.88/3.61 | (145) sdtasdt0(xq, xl) = all_0_4_4
% 12.88/3.61 |
% 12.88/3.61 | From (193) and (153) follows:
% 12.88/3.61 | (125) sdtasdt0(xp, xl) = xm
% 12.88/3.61 |
% 12.88/3.61 | From (182) and (171) follows:
% 12.88/3.61 | (138) sdtasdt0(xl, xq) = all_0_4_4
% 12.88/3.61 |
% 12.88/3.61 | From (194) and (152) follows:
% 12.88/3.61 | (110) sdtasdt0(xl, xp) = xm
% 12.88/3.61 |
% 12.88/3.61 | From (186) and (148) follows:
% 12.88/3.62 | (199) sdtpldt0(xp, xr) = xq
% 12.88/3.62 |
% 12.88/3.62 | From (186) and (149) follows:
% 12.88/3.62 | (200) aNaturalNumber0(xr)
% 12.88/3.62 |
% 12.88/3.62 | Instantiating formula (26) with xm, xl, xl, all_41_0_10, xp and discharging atoms sdtasdt0(xp, xl) = xm, sdtpldt0(all_41_0_10, xl) = xl, aNaturalNumber0(all_41_0_10), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 12.88/3.62 | (201) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_41_0_10, xp) = v3 & sdtasdt0(xp, all_41_0_10) = v0 & sdtasdt0(xp, xl) = v1 & sdtasdt0(xl, xp) = v4 & sdtasdt0(xl, xp) = v2 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = xm)
% 12.88/3.62 |
% 12.88/3.62 | Instantiating formula (29) with xm, xl, xl, all_41_0_10, xp and discharging atoms sdtasdt0(xl, xp) = xm, sdtpldt0(all_41_0_10, xl) = xl, aNaturalNumber0(all_41_0_10), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 12.88/3.62 | (202) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_41_0_10, xp) = v3 & sdtasdt0(xp, all_41_0_10) = v1 & sdtasdt0(xp, xl) = v2 & sdtasdt0(xp, xl) = v0 & sdtasdt0(xl, xp) = v4 & sdtpldt0(v3, v4) = xm & sdtpldt0(v1, v2) = v0)
% 12.88/3.62 |
% 12.88/3.62 | Instantiating formula (29) with xm, xp, all_75_0_28, xp, xl and discharging atoms sdtasdt0(xp, xl) = xm, sdtpldt0(xp, all_75_0_28) = xp, aNaturalNumber0(all_75_0_28), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 12.88/3.62 | (203) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_75_0_28, xl) = v4 & sdtasdt0(xp, xl) = v3 & sdtasdt0(xl, all_75_0_28) = v2 & sdtasdt0(xl, xp) = v1 & sdtasdt0(xl, xp) = v0 & sdtpldt0(v3, v4) = xm & sdtpldt0(v1, v2) = v0)
% 12.88/3.62 |
% 12.88/3.62 | Instantiating formula (26) with xm, xp, all_75_0_28, xp, xl and discharging atoms sdtasdt0(xl, xp) = xm, sdtpldt0(xp, all_75_0_28) = xp, aNaturalNumber0(all_75_0_28), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 12.88/3.62 | (204) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_75_0_28, xl) = v4 & sdtasdt0(xp, xl) = v3 & sdtasdt0(xp, xl) = v2 & sdtasdt0(xl, all_75_0_28) = v1 & sdtasdt0(xl, xp) = v0 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = xm)
% 12.88/3.62 |
% 12.88/3.62 | Instantiating formula (92) with all_0_1_1, all_0_2_2, xm, xr, xp, xl and discharging atoms sdtasdt0(xl, xr) = all_0_2_2, sdtasdt0(xl, xp) = xm, sdtpldt0(xm, all_0_2_2) = all_0_1_1, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 12.88/3.62 | (205) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(xr, xl) = v3 & sdtasdt0(xp, xl) = v2 & sdtasdt0(xl, v0) = all_0_1_1 & sdtpldt0(v2, v3) = v1 & sdtpldt0(xp, xr) = v0)
% 12.88/3.62 |
% 12.88/3.62 | Instantiating formula (29) with all_0_2_2, xl, all_41_0_10, xl, xr and discharging atoms sdtasdt0(xl, xr) = all_0_2_2, sdtpldt0(xl, all_41_0_10) = xl, aNaturalNumber0(all_41_0_10), aNaturalNumber0(xr), aNaturalNumber0(xl), yields:
% 12.88/3.62 | (206) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_41_0_10, xr) = v4 & sdtasdt0(xr, all_41_0_10) = v2 & sdtasdt0(xr, xl) = v1 & sdtasdt0(xr, xl) = v0 & sdtasdt0(xl, xr) = v3 & sdtpldt0(v3, v4) = all_0_2_2 & sdtpldt0(v1, v2) = v0)
% 12.88/3.62 |
% 12.88/3.62 | Instantiating formula (29) with all_0_2_2, xl, xl, all_41_0_10, xr and discharging atoms sdtasdt0(xl, xr) = all_0_2_2, sdtpldt0(all_41_0_10, xl) = xl, aNaturalNumber0(all_41_0_10), aNaturalNumber0(xr), aNaturalNumber0(xl), yields:
% 12.88/3.62 | (207) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_41_0_10, xr) = v3 & sdtasdt0(xr, all_41_0_10) = v1 & sdtasdt0(xr, xl) = v2 & sdtasdt0(xr, xl) = v0 & sdtasdt0(xl, xr) = v4 & sdtpldt0(v3, v4) = all_0_2_2 & sdtpldt0(v1, v2) = v0)
% 12.88/3.62 |
% 12.88/3.62 | Instantiating formula (50) with all_0_2_2, xl, xr and discharging atoms sdtasdt0(xl, xr) = all_0_2_2, aNaturalNumber0(xr), aNaturalNumber0(xl), yields:
% 12.88/3.62 | (208) sdtasdt0(xr, xl) = all_0_2_2
% 12.88/3.62 |
% 12.88/3.62 | Instantiating formula (26) with all_0_4_4, xq, xr, xp, xl and discharging atoms sdtasdt0(xl, xq) = all_0_4_4, sdtpldt0(xp, xr) = xq, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 12.88/3.62 | (209) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(xr, xl) = v4 & sdtasdt0(xq, xl) = v2 & sdtasdt0(xp, xl) = v3 & sdtasdt0(xl, xr) = v1 & sdtasdt0(xl, xp) = v0 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_0_4_4)
% 12.88/3.62 |
% 12.88/3.62 | Instantiating formula (29) with all_0_4_4, xq, xr, xp, xl and discharging atoms sdtasdt0(xq, xl) = all_0_4_4, sdtpldt0(xp, xr) = xq, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 12.88/3.62 | (210) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(xr, xl) = v4 & sdtasdt0(xp, xl) = v3 & sdtasdt0(xl, xr) = v2 & sdtasdt0(xl, xq) = v0 & sdtasdt0(xl, xp) = v1 & sdtpldt0(v3, v4) = all_0_4_4 & sdtpldt0(v1, v2) = v0)
% 12.88/3.62 |
% 12.88/3.62 | Instantiating (202) with all_123_0_53, all_123_1_54, all_123_2_55, all_123_3_56, all_123_4_57 yields:
% 12.88/3.62 | (211) sdtasdt0(all_41_0_10, xp) = all_123_1_54 & sdtasdt0(xp, all_41_0_10) = all_123_3_56 & sdtasdt0(xp, xl) = all_123_2_55 & sdtasdt0(xp, xl) = all_123_4_57 & sdtasdt0(xl, xp) = all_123_0_53 & sdtpldt0(all_123_1_54, all_123_0_53) = xm & sdtpldt0(all_123_3_56, all_123_2_55) = all_123_4_57
% 12.88/3.62 |
% 12.88/3.62 | Applying alpha-rule on (211) yields:
% 12.88/3.62 | (212) sdtpldt0(all_123_3_56, all_123_2_55) = all_123_4_57
% 12.88/3.62 | (213) sdtasdt0(xp, xl) = all_123_4_57
% 12.88/3.62 | (214) sdtpldt0(all_123_1_54, all_123_0_53) = xm
% 12.88/3.62 | (215) sdtasdt0(all_41_0_10, xp) = all_123_1_54
% 12.88/3.62 | (216) sdtasdt0(xp, xl) = all_123_2_55
% 12.88/3.62 | (217) sdtasdt0(xp, all_41_0_10) = all_123_3_56
% 12.88/3.62 | (218) sdtasdt0(xl, xp) = all_123_0_53
% 12.88/3.62 |
% 12.88/3.62 | Instantiating (209) with all_131_0_69, all_131_1_70, all_131_2_71, all_131_3_72, all_131_4_73 yields:
% 12.88/3.62 | (219) sdtasdt0(xr, xl) = all_131_0_69 & sdtasdt0(xq, xl) = all_131_2_71 & sdtasdt0(xp, xl) = all_131_1_70 & sdtasdt0(xl, xr) = all_131_3_72 & sdtasdt0(xl, xp) = all_131_4_73 & sdtpldt0(all_131_1_70, all_131_0_69) = all_131_2_71 & sdtpldt0(all_131_4_73, all_131_3_72) = all_0_4_4
% 12.88/3.62 |
% 12.88/3.62 | Applying alpha-rule on (219) yields:
% 12.88/3.62 | (220) sdtpldt0(all_131_4_73, all_131_3_72) = all_0_4_4
% 12.88/3.62 | (221) sdtasdt0(xp, xl) = all_131_1_70
% 12.88/3.62 | (222) sdtpldt0(all_131_1_70, all_131_0_69) = all_131_2_71
% 12.88/3.62 | (223) sdtasdt0(xl, xp) = all_131_4_73
% 12.88/3.62 | (224) sdtasdt0(xq, xl) = all_131_2_71
% 12.88/3.62 | (225) sdtasdt0(xl, xr) = all_131_3_72
% 12.88/3.62 | (226) sdtasdt0(xr, xl) = all_131_0_69
% 12.88/3.62 |
% 12.88/3.62 | Instantiating (204) with all_135_0_79, all_135_1_80, all_135_2_81, all_135_3_82, all_135_4_83 yields:
% 12.88/3.62 | (227) sdtasdt0(all_75_0_28, xl) = all_135_0_79 & sdtasdt0(xp, xl) = all_135_1_80 & sdtasdt0(xp, xl) = all_135_2_81 & sdtasdt0(xl, all_75_0_28) = all_135_3_82 & sdtasdt0(xl, xp) = all_135_4_83 & sdtpldt0(all_135_1_80, all_135_0_79) = all_135_2_81 & sdtpldt0(all_135_4_83, all_135_3_82) = xm
% 12.88/3.62 |
% 12.88/3.62 | Applying alpha-rule on (227) yields:
% 12.88/3.62 | (228) sdtasdt0(all_75_0_28, xl) = all_135_0_79
% 12.88/3.62 | (229) sdtpldt0(all_135_4_83, all_135_3_82) = xm
% 12.88/3.62 | (230) sdtasdt0(xp, xl) = all_135_2_81
% 12.88/3.62 | (231) sdtasdt0(xl, xp) = all_135_4_83
% 12.88/3.62 | (232) sdtasdt0(xp, xl) = all_135_1_80
% 12.88/3.62 | (233) sdtpldt0(all_135_1_80, all_135_0_79) = all_135_2_81
% 12.88/3.62 | (234) sdtasdt0(xl, all_75_0_28) = all_135_3_82
% 12.88/3.62 |
% 12.88/3.62 | Instantiating (203) with all_141_0_90, all_141_1_91, all_141_2_92, all_141_3_93, all_141_4_94 yields:
% 12.88/3.62 | (235) sdtasdt0(all_75_0_28, xl) = all_141_0_90 & sdtasdt0(xp, xl) = all_141_1_91 & sdtasdt0(xl, all_75_0_28) = all_141_2_92 & sdtasdt0(xl, xp) = all_141_3_93 & sdtasdt0(xl, xp) = all_141_4_94 & sdtpldt0(all_141_1_91, all_141_0_90) = xm & sdtpldt0(all_141_3_93, all_141_2_92) = all_141_4_94
% 12.88/3.62 |
% 12.88/3.62 | Applying alpha-rule on (235) yields:
% 12.88/3.62 | (236) sdtasdt0(xp, xl) = all_141_1_91
% 12.88/3.62 | (237) sdtasdt0(xl, xp) = all_141_4_94
% 12.88/3.62 | (238) sdtasdt0(all_75_0_28, xl) = all_141_0_90
% 12.88/3.62 | (239) sdtpldt0(all_141_3_93, all_141_2_92) = all_141_4_94
% 12.88/3.62 | (240) sdtasdt0(xl, xp) = all_141_3_93
% 12.88/3.62 | (241) sdtpldt0(all_141_1_91, all_141_0_90) = xm
% 12.88/3.62 | (242) sdtasdt0(xl, all_75_0_28) = all_141_2_92
% 12.88/3.62 |
% 12.88/3.62 | Instantiating (210) with all_149_0_98, all_149_1_99, all_149_2_100, all_149_3_101, all_149_4_102 yields:
% 12.88/3.62 | (243) sdtasdt0(xr, xl) = all_149_0_98 & sdtasdt0(xp, xl) = all_149_1_99 & sdtasdt0(xl, xr) = all_149_2_100 & sdtasdt0(xl, xq) = all_149_4_102 & sdtasdt0(xl, xp) = all_149_3_101 & sdtpldt0(all_149_1_99, all_149_0_98) = all_0_4_4 & sdtpldt0(all_149_3_101, all_149_2_100) = all_149_4_102
% 12.88/3.62 |
% 12.88/3.62 | Applying alpha-rule on (243) yields:
% 12.88/3.62 | (244) sdtasdt0(xr, xl) = all_149_0_98
% 12.88/3.62 | (245) sdtasdt0(xp, xl) = all_149_1_99
% 12.88/3.62 | (246) sdtasdt0(xl, xr) = all_149_2_100
% 12.88/3.62 | (247) sdtasdt0(xl, xq) = all_149_4_102
% 12.88/3.62 | (248) sdtasdt0(xl, xp) = all_149_3_101
% 12.88/3.62 | (249) sdtpldt0(all_149_1_99, all_149_0_98) = all_0_4_4
% 12.88/3.62 | (250) sdtpldt0(all_149_3_101, all_149_2_100) = all_149_4_102
% 12.88/3.62 |
% 12.88/3.62 | Instantiating (201) with all_151_0_103, all_151_1_104, all_151_2_105, all_151_3_106, all_151_4_107 yields:
% 12.88/3.62 | (251) sdtasdt0(all_41_0_10, xp) = all_151_1_104 & sdtasdt0(xp, all_41_0_10) = all_151_4_107 & sdtasdt0(xp, xl) = all_151_3_106 & sdtasdt0(xl, xp) = all_151_0_103 & sdtasdt0(xl, xp) = all_151_2_105 & sdtpldt0(all_151_1_104, all_151_0_103) = all_151_2_105 & sdtpldt0(all_151_4_107, all_151_3_106) = xm
% 12.88/3.62 |
% 12.88/3.62 | Applying alpha-rule on (251) yields:
% 12.88/3.62 | (252) sdtpldt0(all_151_1_104, all_151_0_103) = all_151_2_105
% 12.88/3.62 | (253) sdtasdt0(xp, all_41_0_10) = all_151_4_107
% 12.88/3.62 | (254) sdtpldt0(all_151_4_107, all_151_3_106) = xm
% 12.88/3.62 | (255) sdtasdt0(xl, xp) = all_151_2_105
% 12.88/3.62 | (256) sdtasdt0(xp, xl) = all_151_3_106
% 12.88/3.62 | (257) sdtasdt0(xl, xp) = all_151_0_103
% 12.88/3.62 | (258) sdtasdt0(all_41_0_10, xp) = all_151_1_104
% 12.88/3.62 |
% 12.88/3.62 | Instantiating (207) with all_159_0_111, all_159_1_112, all_159_2_113, all_159_3_114, all_159_4_115 yields:
% 12.88/3.62 | (259) sdtasdt0(all_41_0_10, xr) = all_159_1_112 & sdtasdt0(xr, all_41_0_10) = all_159_3_114 & sdtasdt0(xr, xl) = all_159_2_113 & sdtasdt0(xr, xl) = all_159_4_115 & sdtasdt0(xl, xr) = all_159_0_111 & sdtpldt0(all_159_1_112, all_159_0_111) = all_0_2_2 & sdtpldt0(all_159_3_114, all_159_2_113) = all_159_4_115
% 12.88/3.62 |
% 12.88/3.62 | Applying alpha-rule on (259) yields:
% 12.88/3.62 | (260) sdtasdt0(xr, all_41_0_10) = all_159_3_114
% 12.88/3.62 | (261) sdtpldt0(all_159_3_114, all_159_2_113) = all_159_4_115
% 12.88/3.63 | (262) sdtpldt0(all_159_1_112, all_159_0_111) = all_0_2_2
% 12.88/3.63 | (263) sdtasdt0(xl, xr) = all_159_0_111
% 12.88/3.63 | (264) sdtasdt0(xr, xl) = all_159_4_115
% 12.88/3.63 | (265) sdtasdt0(xr, xl) = all_159_2_113
% 12.88/3.63 | (266) sdtasdt0(all_41_0_10, xr) = all_159_1_112
% 12.88/3.63 |
% 12.88/3.63 | Instantiating (206) with all_161_0_116, all_161_1_117, all_161_2_118, all_161_3_119, all_161_4_120 yields:
% 12.88/3.63 | (267) sdtasdt0(all_41_0_10, xr) = all_161_0_116 & sdtasdt0(xr, all_41_0_10) = all_161_2_118 & sdtasdt0(xr, xl) = all_161_3_119 & sdtasdt0(xr, xl) = all_161_4_120 & sdtasdt0(xl, xr) = all_161_1_117 & sdtpldt0(all_161_1_117, all_161_0_116) = all_0_2_2 & sdtpldt0(all_161_3_119, all_161_2_118) = all_161_4_120
% 12.88/3.63 |
% 12.88/3.63 | Applying alpha-rule on (267) yields:
% 12.88/3.63 | (268) sdtasdt0(xr, all_41_0_10) = all_161_2_118
% 12.88/3.63 | (269) sdtasdt0(xr, xl) = all_161_4_120
% 12.88/3.63 | (270) sdtpldt0(all_161_1_117, all_161_0_116) = all_0_2_2
% 12.88/3.63 | (271) sdtasdt0(all_41_0_10, xr) = all_161_0_116
% 12.88/3.63 | (272) sdtasdt0(xr, xl) = all_161_3_119
% 12.88/3.63 | (273) sdtpldt0(all_161_3_119, all_161_2_118) = all_161_4_120
% 12.88/3.63 | (274) sdtasdt0(xl, xr) = all_161_1_117
% 12.88/3.63 |
% 12.88/3.63 | Instantiating (205) with all_163_0_121, all_163_1_122, all_163_2_123, all_163_3_124 yields:
% 12.88/3.63 | (275) sdtasdt0(all_163_3_124, xl) = all_163_2_123 & sdtasdt0(xr, xl) = all_163_0_121 & sdtasdt0(xp, xl) = all_163_1_122 & sdtasdt0(xl, all_163_3_124) = all_0_1_1 & sdtpldt0(all_163_1_122, all_163_0_121) = all_163_2_123 & sdtpldt0(xp, xr) = all_163_3_124
% 12.88/3.63 |
% 12.88/3.63 | Applying alpha-rule on (275) yields:
% 12.88/3.63 | (276) sdtasdt0(xp, xl) = all_163_1_122
% 12.88/3.63 | (277) sdtpldt0(all_163_1_122, all_163_0_121) = all_163_2_123
% 12.88/3.63 | (278) sdtasdt0(xr, xl) = all_163_0_121
% 12.88/3.63 | (279) sdtpldt0(xp, xr) = all_163_3_124
% 12.88/3.63 | (280) sdtasdt0(xl, all_163_3_124) = all_0_1_1
% 12.88/3.63 | (281) sdtasdt0(all_163_3_124, xl) = all_163_2_123
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xr, xl, all_161_3_119, all_163_0_121 and discharging atoms sdtasdt0(xr, xl) = all_163_0_121, sdtasdt0(xr, xl) = all_161_3_119, yields:
% 12.88/3.63 | (282) all_163_0_121 = all_161_3_119
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xr, xl, all_0_2_2, all_163_0_121 and discharging atoms sdtasdt0(xr, xl) = all_163_0_121, sdtasdt0(xr, xl) = all_0_2_2, yields:
% 12.88/3.63 | (283) all_163_0_121 = all_0_2_2
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xp, xl, all_151_3_106, xm and discharging atoms sdtasdt0(xp, xl) = all_151_3_106, sdtasdt0(xp, xl) = xm, yields:
% 12.88/3.63 | (284) all_151_3_106 = xm
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xp, xl, all_149_1_99, all_163_1_122 and discharging atoms sdtasdt0(xp, xl) = all_163_1_122, sdtasdt0(xp, xl) = all_149_1_99, yields:
% 12.88/3.63 | (285) all_163_1_122 = all_149_1_99
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xp, xl, all_141_1_91, all_151_3_106 and discharging atoms sdtasdt0(xp, xl) = all_151_3_106, sdtasdt0(xp, xl) = all_141_1_91, yields:
% 12.88/3.63 | (286) all_151_3_106 = all_141_1_91
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xp, xl, all_135_1_80, all_149_1_99 and discharging atoms sdtasdt0(xp, xl) = all_149_1_99, sdtasdt0(xp, xl) = all_135_1_80, yields:
% 12.88/3.63 | (287) all_149_1_99 = all_135_1_80
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xp, xl, all_135_2_81, all_135_1_80 and discharging atoms sdtasdt0(xp, xl) = all_135_1_80, sdtasdt0(xp, xl) = all_135_2_81, yields:
% 12.88/3.63 | (288) all_135_1_80 = all_135_2_81
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xp, xl, all_131_1_70, all_151_3_106 and discharging atoms sdtasdt0(xp, xl) = all_151_3_106, sdtasdt0(xp, xl) = all_131_1_70, yields:
% 12.88/3.63 | (289) all_151_3_106 = all_131_1_70
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xp, xl, all_131_1_70, all_135_2_81 and discharging atoms sdtasdt0(xp, xl) = all_135_2_81, sdtasdt0(xp, xl) = all_131_1_70, yields:
% 12.88/3.63 | (290) all_135_2_81 = all_131_1_70
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xp, xl, all_123_2_55, all_163_1_122 and discharging atoms sdtasdt0(xp, xl) = all_163_1_122, sdtasdt0(xp, xl) = all_123_2_55, yields:
% 12.88/3.63 | (291) all_163_1_122 = all_123_2_55
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xl, xr, all_161_1_117, all_0_2_2 and discharging atoms sdtasdt0(xl, xr) = all_161_1_117, sdtasdt0(xl, xr) = all_0_2_2, yields:
% 12.88/3.63 | (292) all_161_1_117 = all_0_2_2
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xl, xr, all_159_0_111, all_161_1_117 and discharging atoms sdtasdt0(xl, xr) = all_161_1_117, sdtasdt0(xl, xr) = all_159_0_111, yields:
% 12.88/3.63 | (293) all_161_1_117 = all_159_0_111
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xl, xr, all_149_2_100, all_161_1_117 and discharging atoms sdtasdt0(xl, xr) = all_161_1_117, sdtasdt0(xl, xr) = all_149_2_100, yields:
% 12.88/3.63 | (294) all_161_1_117 = all_149_2_100
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xl, xr, all_131_3_72, all_149_2_100 and discharging atoms sdtasdt0(xl, xr) = all_149_2_100, sdtasdt0(xl, xr) = all_131_3_72, yields:
% 12.88/3.63 | (295) all_149_2_100 = all_131_3_72
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xl, xp, all_151_2_105, all_151_0_103 and discharging atoms sdtasdt0(xl, xp) = all_151_0_103, sdtasdt0(xl, xp) = all_151_2_105, yields:
% 12.88/3.63 | (296) all_151_0_103 = all_151_2_105
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xl, xp, all_149_3_101, xm and discharging atoms sdtasdt0(xl, xp) = all_149_3_101, sdtasdt0(xl, xp) = xm, yields:
% 12.88/3.63 | (297) all_149_3_101 = xm
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xl, xp, all_141_3_93, all_151_0_103 and discharging atoms sdtasdt0(xl, xp) = all_151_0_103, sdtasdt0(xl, xp) = all_141_3_93, yields:
% 12.88/3.63 | (298) all_151_0_103 = all_141_3_93
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xl, xp, all_141_4_94, all_141_3_93 and discharging atoms sdtasdt0(xl, xp) = all_141_3_93, sdtasdt0(xl, xp) = all_141_4_94, yields:
% 12.88/3.63 | (299) all_141_3_93 = all_141_4_94
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xl, xp, all_135_4_83, all_149_3_101 and discharging atoms sdtasdt0(xl, xp) = all_149_3_101, sdtasdt0(xl, xp) = all_135_4_83, yields:
% 12.88/3.63 | (300) all_149_3_101 = all_135_4_83
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xl, xp, all_135_4_83, all_141_4_94 and discharging atoms sdtasdt0(xl, xp) = all_141_4_94, sdtasdt0(xl, xp) = all_135_4_83, yields:
% 12.88/3.63 | (301) all_141_4_94 = all_135_4_83
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xl, xp, all_131_4_73, all_151_0_103 and discharging atoms sdtasdt0(xl, xp) = all_151_0_103, sdtasdt0(xl, xp) = all_131_4_73, yields:
% 12.88/3.63 | (302) all_151_0_103 = all_131_4_73
% 12.88/3.63 |
% 12.88/3.63 | Instantiating formula (42) with xl, xp, all_123_0_53, all_141_4_94 and discharging atoms sdtasdt0(xl, xp) = all_141_4_94, sdtasdt0(xl, xp) = all_123_0_53, yields:
% 12.88/3.63 | (303) all_141_4_94 = all_123_0_53
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (283,282) yields a new equation:
% 12.88/3.63 | (304) all_161_3_119 = all_0_2_2
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (285,291) yields a new equation:
% 12.88/3.63 | (305) all_149_1_99 = all_123_2_55
% 12.88/3.63 |
% 12.88/3.63 | Simplifying 305 yields:
% 12.88/3.63 | (306) all_149_1_99 = all_123_2_55
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (292,293) yields a new equation:
% 12.88/3.63 | (307) all_159_0_111 = all_0_2_2
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (294,293) yields a new equation:
% 12.88/3.63 | (308) all_159_0_111 = all_149_2_100
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (308,307) yields a new equation:
% 12.88/3.63 | (309) all_149_2_100 = all_0_2_2
% 12.88/3.63 |
% 12.88/3.63 | Simplifying 309 yields:
% 12.88/3.63 | (310) all_149_2_100 = all_0_2_2
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (302,296) yields a new equation:
% 12.88/3.63 | (311) all_151_2_105 = all_131_4_73
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (298,296) yields a new equation:
% 12.88/3.63 | (312) all_151_2_105 = all_141_3_93
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (312,311) yields a new equation:
% 12.88/3.63 | (313) all_141_3_93 = all_131_4_73
% 12.88/3.63 |
% 12.88/3.63 | Simplifying 313 yields:
% 12.88/3.63 | (314) all_141_3_93 = all_131_4_73
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (289,286) yields a new equation:
% 12.88/3.63 | (315) all_141_1_91 = all_131_1_70
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (284,286) yields a new equation:
% 12.88/3.63 | (316) all_141_1_91 = xm
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (287,306) yields a new equation:
% 12.88/3.63 | (317) all_135_1_80 = all_123_2_55
% 12.88/3.63 |
% 12.88/3.63 | Simplifying 317 yields:
% 12.88/3.63 | (318) all_135_1_80 = all_123_2_55
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (295,310) yields a new equation:
% 12.88/3.63 | (319) all_131_3_72 = all_0_2_2
% 12.88/3.63 |
% 12.88/3.63 | Simplifying 319 yields:
% 12.88/3.63 | (320) all_131_3_72 = all_0_2_2
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (300,297) yields a new equation:
% 12.88/3.63 | (321) all_135_4_83 = xm
% 12.88/3.63 |
% 12.88/3.63 | Simplifying 321 yields:
% 12.88/3.63 | (322) all_135_4_83 = xm
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (315,316) yields a new equation:
% 12.88/3.63 | (323) all_131_1_70 = xm
% 12.88/3.63 |
% 12.88/3.63 | Simplifying 323 yields:
% 12.88/3.63 | (324) all_131_1_70 = xm
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (299,314) yields a new equation:
% 12.88/3.63 | (325) all_141_4_94 = all_131_4_73
% 12.88/3.63 |
% 12.88/3.63 | Simplifying 325 yields:
% 12.88/3.63 | (326) all_141_4_94 = all_131_4_73
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (303,326) yields a new equation:
% 12.88/3.63 | (327) all_131_4_73 = all_123_0_53
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (301,326) yields a new equation:
% 12.88/3.63 | (328) all_135_4_83 = all_131_4_73
% 12.88/3.63 |
% 12.88/3.63 | Simplifying 328 yields:
% 12.88/3.63 | (329) all_135_4_83 = all_131_4_73
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (288,318) yields a new equation:
% 12.88/3.63 | (330) all_135_2_81 = all_123_2_55
% 12.88/3.63 |
% 12.88/3.63 | Simplifying 330 yields:
% 12.88/3.63 | (331) all_135_2_81 = all_123_2_55
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (290,331) yields a new equation:
% 12.88/3.63 | (332) all_131_1_70 = all_123_2_55
% 12.88/3.63 |
% 12.88/3.63 | Simplifying 332 yields:
% 12.88/3.63 | (333) all_131_1_70 = all_123_2_55
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (329,322) yields a new equation:
% 12.88/3.63 | (334) all_131_4_73 = xm
% 12.88/3.63 |
% 12.88/3.63 | Simplifying 334 yields:
% 12.88/3.63 | (335) all_131_4_73 = xm
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (324,333) yields a new equation:
% 12.88/3.63 | (336) all_123_2_55 = xm
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (335,327) yields a new equation:
% 12.88/3.63 | (337) all_123_0_53 = xm
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (337,327) yields a new equation:
% 12.88/3.63 | (335) all_131_4_73 = xm
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (336,291) yields a new equation:
% 12.88/3.63 | (339) all_163_1_122 = xm
% 12.88/3.63 |
% 12.88/3.63 | Combining equations (304,282) yields a new equation:
% 12.88/3.63 | (283) all_163_0_121 = all_0_2_2
% 12.88/3.63 |
% 12.88/3.63 | From (339)(283) and (277) follows:
% 12.88/3.63 | (341) sdtpldt0(xm, all_0_2_2) = all_163_2_123
% 12.88/3.64 |
% 12.88/3.64 | From (335)(320) and (220) follows:
% 12.88/3.64 | (342) sdtpldt0(xm, all_0_2_2) = all_0_4_4
% 12.88/3.64 |
% 12.88/3.64 | Instantiating formula (91) with xm, all_0_2_2, all_163_2_123, all_0_1_1 and discharging atoms sdtpldt0(xm, all_0_2_2) = all_163_2_123, sdtpldt0(xm, all_0_2_2) = all_0_1_1, yields:
% 12.88/3.64 | (343) all_163_2_123 = all_0_1_1
% 12.88/3.64 |
% 12.88/3.64 | Instantiating formula (91) with xm, all_0_2_2, all_0_4_4, all_163_2_123 and discharging atoms sdtpldt0(xm, all_0_2_2) = all_163_2_123, sdtpldt0(xm, all_0_2_2) = all_0_4_4, yields:
% 12.88/3.64 | (344) all_163_2_123 = all_0_4_4
% 12.88/3.64 |
% 12.88/3.64 | Combining equations (344,343) yields a new equation:
% 12.88/3.64 | (345) all_0_1_1 = all_0_4_4
% 12.88/3.64 |
% 12.88/3.64 | Equations (345) can reduce 116 to:
% 12.88/3.64 | (107) $false
% 12.88/3.64 |
% 12.88/3.64 |-The branch is then unsatisfiable
% 12.88/3.64 |-Branch two:
% 12.88/3.64 | (347) ~ aNaturalNumber0(xp)
% 12.88/3.64 | (106) xl = sz00
% 12.88/3.64 |
% 12.88/3.64 | Equations (106) can reduce 37 to:
% 12.88/3.64 | (107) $false
% 12.88/3.64 |
% 12.88/3.64 |-The branch is then unsatisfiable
% 12.88/3.64 % SZS output end Proof for theBenchmark
% 12.88/3.64
% 12.88/3.64 3043ms
%------------------------------------------------------------------------------