TSTP Solution File: NUM469+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM469+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n013.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 08:44:49 EDT 2022
% Result : Theorem 8.99s 2.77s
% Output : Proof 15.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM469+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n013.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 04:17:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.58 ____ _
% 0.19/0.58 ___ / __ \_____(_)___ ________ __________
% 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic
% 0.19/0.59 (ePrincess v.1.0)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2015
% 0.19/0.59 (c) Peter Backeman, 2014-2015
% 0.19/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.59 Bug reports to peter@backeman.se
% 0.19/0.59
% 0.19/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.83/1.02 Prover 0: Preprocessing ...
% 3.62/1.51 Prover 0: Constructing countermodel ...
% 8.99/2.76 Prover 0: proved (2095ms)
% 8.99/2.77
% 8.99/2.77 No countermodel exists, formula is valid
% 8.99/2.77 % SZS status Theorem for theBenchmark
% 8.99/2.77
% 8.99/2.77 Generating proof ... found it (size 138)
% 14.94/4.18
% 14.94/4.18 % SZS output start Proof for theBenchmark
% 14.94/4.18 Assumed formulas after preprocessing and simplification:
% 14.94/4.18 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (sz10 = sz00) & sdtsldt0(xn, xl) = v2 & sdtsldt0(xm, xl) = v0 & sdtasdt0(xl, v8) = xm & sdtasdt0(xl, v7) = xn & sdtasdt0(xl, v5) = v6 & sdtasdt0(xl, v2) = v3 & sdtasdt0(xl, v0) = v1 & sdtpldt0(v0, v2) = v5 & sdtpldt0(xm, xn) = v4 & doDivides0(xl, xn) & doDivides0(xl, xm) & aNaturalNumber0(v8) & aNaturalNumber0(v7) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & aNaturalNumber0(xl) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ doDivides0(xl, v4) & ! [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] : ( ~ (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) | ~ 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] : (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 | ~ (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] : (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 = sz10 | v9 = sz00 | ~ aNaturalNumber0(v9) | sdtlseqdt0(sz10, v9)) & ! [v9] : ( ~ aNaturalNumber0(v9) | sdtlseqdt0(v9, v9)) & ! [v9] : ( ~ aNaturalNumber0(v9) | ? [v10] : ( ~ (v10 = v4) & sdtasdt0(xl, v9) = v10)) & (xl = sz00 | (v6 = v4 & v3 = xn & v1 = xm & aNaturalNumber0(v2) & aNaturalNumber0(v0))))
% 15.28/4.26 | 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:
% 15.28/4.26 | (1) ~ (sz10 = sz00) & sdtsldt0(xn, xl) = all_0_6_6 & sdtsldt0(xm, xl) = all_0_8_8 & sdtasdt0(xl, all_0_0_0) = xm & sdtasdt0(xl, all_0_1_1) = xn & sdtasdt0(xl, all_0_3_3) = all_0_2_2 & sdtasdt0(xl, all_0_6_6) = all_0_5_5 & sdtasdt0(xl, all_0_8_8) = all_0_7_7 & sdtpldt0(all_0_8_8, all_0_6_6) = all_0_3_3 & sdtpldt0(xm, xn) = all_0_4_4 & doDivides0(xl, xn) & doDivides0(xl, xm) & aNaturalNumber0(all_0_0_0) & aNaturalNumber0(all_0_1_1) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & aNaturalNumber0(xl) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ doDivides0(xl, all_0_4_4) & ! [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] : (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)) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_4_4) & sdtasdt0(xl, v0) = v1)) & (xl = sz00 | (all_0_2_2 = all_0_4_4 & all_0_5_5 = xn & all_0_7_7 = xm & aNaturalNumber0(all_0_6_6) & aNaturalNumber0(all_0_8_8)))
% 15.63/4.28 |
% 15.63/4.28 | Applying alpha-rule on (1) yields:
% 15.63/4.28 | (2) ! [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))
% 15.63/4.28 | (3) ! [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))
% 15.63/4.28 | (4) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 15.63/4.29 | (5) ! [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))
% 15.63/4.29 | (6) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 15.63/4.29 | (7) ! [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))
% 15.63/4.29 | (8) sdtsldt0(xm, xl) = all_0_8_8
% 15.63/4.29 | (9) ! [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)))
% 15.63/4.29 | (10) ! [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)))
% 15.63/4.29 | (11) ! [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))
% 15.63/4.29 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 15.63/4.29 | (13) ! [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))
% 15.63/4.29 | (14) xl = sz00 | (all_0_2_2 = all_0_4_4 & all_0_5_5 = xn & all_0_7_7 = xm & aNaturalNumber0(all_0_6_6) & aNaturalNumber0(all_0_8_8))
% 15.63/4.29 | (15) ! [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))
% 15.63/4.29 | (16) ! [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))
% 15.63/4.29 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 15.63/4.29 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2)
% 15.63/4.29 | (19) ! [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))
% 15.63/4.29 | (20) sdtasdt0(xl, all_0_0_0) = xm
% 15.63/4.29 | (21) ! [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))
% 15.63/4.29 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 15.63/4.29 | (23) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 15.63/4.29 | (24) aNaturalNumber0(xn)
% 15.63/4.29 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 15.63/4.29 | (26) ~ (sz10 = sz00)
% 15.63/4.29 | (27) ! [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))
% 15.63/4.30 | (28) doDivides0(xl, xm)
% 15.63/4.30 | (29) aNaturalNumber0(all_0_1_1)
% 15.63/4.30 | (30) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0))
% 15.63/4.30 | (31) ! [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))
% 15.63/4.30 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 15.63/4.30 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 15.63/4.30 | (34) sdtasdt0(xl, all_0_8_8) = all_0_7_7
% 15.63/4.30 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 15.63/4.30 | (36) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 15.63/4.30 | (37) aNaturalNumber0(sz10)
% 15.63/4.30 | (38) doDivides0(xl, xn)
% 15.63/4.30 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 15.63/4.30 | (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) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtlseqdt0(v5, v6)))
% 15.63/4.30 | (41) ! [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)))
% 15.63/4.30 | (42) ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_4_4) & sdtasdt0(xl, v0) = v1))
% 15.63/4.30 | (43) ! [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)))
% 15.63/4.30 | (44) ! [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))
% 15.63/4.30 | (45) ! [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))
% 15.63/4.30 | (46) aNaturalNumber0(sz00)
% 15.63/4.30 | (47) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 15.63/4.30 | (48) aNaturalNumber0(all_0_0_0)
% 15.63/4.30 | (49) ! [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))
% 15.63/4.30 | (50) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 15.63/4.30 | (51) ! [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)))
% 15.63/4.30 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 15.63/4.30 | (53) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 15.63/4.30 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 15.63/4.30 | (55) sdtsldt0(xn, xl) = all_0_6_6
% 15.63/4.30 | (56) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00)
% 15.63/4.31 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 15.63/4.31 | (58) aNaturalNumber0(xm)
% 15.63/4.31 | (59) ! [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)))
% 15.63/4.31 | (60) ! [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))
% 15.63/4.31 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 15.63/4.31 | (62) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 15.63/4.31 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 15.63/4.31 | (64) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 15.63/4.31 | (65) ! [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)))
% 15.63/4.31 | (66) sdtpldt0(xm, xn) = all_0_4_4
% 15.63/4.31 | (67) ! [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))
% 15.63/4.31 | (68) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 15.63/4.31 | (69) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0))
% 15.63/4.31 | (70) ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 15.63/4.31 | (71) aNaturalNumber0(xl)
% 15.63/4.31 | (72) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 15.63/4.31 | (73) ! [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))
% 15.63/4.31 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 15.63/4.31 | (75) sdtasdt0(xl, all_0_6_6) = all_0_5_5
% 15.63/4.31 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 15.63/4.31 | (77) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 15.63/4.31 | (78) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 15.63/4.31 | (79) ! [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))
% 15.63/4.31 | (80) ! [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))
% 15.63/4.31 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 15.63/4.31 | (82) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 15.63/4.31 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 15.63/4.31 | (84) ~ doDivides0(xl, all_0_4_4)
% 15.63/4.31 | (85) ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 15.63/4.32 | (86) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0)
% 15.63/4.32 | (87) sdtasdt0(xl, all_0_3_3) = all_0_2_2
% 15.63/4.32 | (88) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 15.63/4.32 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2)
% 15.63/4.32 | (90) ! [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))
% 15.63/4.32 | (91) sdtasdt0(xl, all_0_1_1) = xn
% 15.63/4.32 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 15.63/4.32 | (93) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 15.63/4.32 | (94) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 15.63/4.32 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 15.63/4.32 | (96) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 15.63/4.32 | (97) sdtpldt0(all_0_8_8, all_0_6_6) = all_0_3_3
% 15.63/4.32 | (98) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0)
% 15.63/4.32 |
% 15.63/4.32 | Instantiating formula (42) with all_0_0_0 and discharging atoms aNaturalNumber0(all_0_0_0), yields:
% 15.63/4.32 | (99) ? [v0] : ( ~ (v0 = all_0_4_4) & sdtasdt0(xl, all_0_0_0) = v0)
% 15.63/4.32 |
% 15.63/4.32 | Instantiating formula (42) with all_0_1_1 and discharging atoms aNaturalNumber0(all_0_1_1), yields:
% 15.63/4.32 | (100) ? [v0] : ( ~ (v0 = all_0_4_4) & sdtasdt0(xl, all_0_1_1) = v0)
% 15.63/4.32 |
% 15.63/4.32 | Instantiating formula (42) with xn and discharging atoms aNaturalNumber0(xn), yields:
% 15.63/4.32 | (101) ? [v0] : ( ~ (v0 = all_0_4_4) & sdtasdt0(xl, xn) = v0)
% 15.63/4.32 |
% 15.63/4.32 | Instantiating formula (18) with all_0_4_4, xm, xn and discharging atoms sdtpldt0(xm, xn) = all_0_4_4, aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 15.63/4.32 | (102) sdtpldt0(xn, xm) = all_0_4_4
% 15.63/4.32 |
% 15.63/4.32 | Instantiating formula (61) with all_0_4_4, xn, xm and discharging atoms sdtpldt0(xm, xn) = all_0_4_4, aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 15.63/4.32 | (103) aNaturalNumber0(all_0_4_4)
% 15.63/4.32 |
% 15.63/4.32 | Instantiating formula (89) with xm, xl, all_0_0_0 and discharging atoms sdtasdt0(xl, all_0_0_0) = xm, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), yields:
% 15.63/4.32 | (104) sdtasdt0(all_0_0_0, xl) = xm
% 15.63/4.32 |
% 15.63/4.32 | Instantiating formula (3) with all_0_4_4, xn, xm, all_0_1_1, all_0_0_0, xl and discharging atoms sdtasdt0(xl, all_0_0_0) = xm, sdtasdt0(xl, all_0_1_1) = xn, sdtpldt0(xm, xn) = all_0_4_4, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 15.63/4.32 | (105) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_0_0_0, xl) = v2 & sdtasdt0(all_0_1_1, xl) = v3 & sdtasdt0(xl, v0) = all_0_4_4 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_0_0_0, all_0_1_1) = v0)
% 15.63/4.32 |
% 15.63/4.32 | Instantiating formula (89) with xn, xl, all_0_1_1 and discharging atoms sdtasdt0(xl, all_0_1_1) = xn, aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 15.63/4.32 | (106) sdtasdt0(all_0_1_1, xl) = xn
% 15.63/4.32 |
% 15.63/4.33 | Instantiating formula (70) with xn, xl and discharging atoms doDivides0(xl, xn), aNaturalNumber0(xn), aNaturalNumber0(xl), yields:
% 15.63/4.33 | (107) ? [v0] : (sdtasdt0(xl, v0) = xn & aNaturalNumber0(v0))
% 15.63/4.33 |
% 15.63/4.33 | Instantiating formula (70) with xm, xl and discharging atoms doDivides0(xl, xm), aNaturalNumber0(xm), aNaturalNumber0(xl), yields:
% 15.63/4.33 | (108) ? [v0] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0))
% 15.63/4.33 |
% 15.63/4.33 | Instantiating formula (42) with sz10 and discharging atoms aNaturalNumber0(sz10), yields:
% 15.63/4.33 | (109) ? [v0] : ( ~ (v0 = all_0_4_4) & sdtasdt0(xl, sz10) = v0)
% 15.63/4.33 |
% 15.63/4.33 | Instantiating (108) with all_9_0_9 yields:
% 15.63/4.33 | (110) sdtasdt0(xl, all_9_0_9) = xm & aNaturalNumber0(all_9_0_9)
% 15.63/4.33 |
% 15.63/4.33 | Applying alpha-rule on (110) yields:
% 15.63/4.33 | (111) sdtasdt0(xl, all_9_0_9) = xm
% 15.63/4.33 | (112) aNaturalNumber0(all_9_0_9)
% 15.63/4.33 |
% 15.63/4.33 | Instantiating (99) with all_13_0_11 yields:
% 15.63/4.33 | (113) ~ (all_13_0_11 = all_0_4_4) & sdtasdt0(xl, all_0_0_0) = all_13_0_11
% 15.63/4.33 |
% 15.63/4.33 | Applying alpha-rule on (113) yields:
% 15.63/4.33 | (114) ~ (all_13_0_11 = all_0_4_4)
% 15.63/4.33 | (115) sdtasdt0(xl, all_0_0_0) = all_13_0_11
% 15.63/4.33 |
% 15.63/4.33 | Instantiating (100) with all_15_0_12 yields:
% 15.63/4.33 | (116) ~ (all_15_0_12 = all_0_4_4) & sdtasdt0(xl, all_0_1_1) = all_15_0_12
% 15.63/4.33 |
% 15.63/4.33 | Applying alpha-rule on (116) yields:
% 15.63/4.33 | (117) ~ (all_15_0_12 = all_0_4_4)
% 15.63/4.33 | (118) sdtasdt0(xl, all_0_1_1) = all_15_0_12
% 15.63/4.33 |
% 15.63/4.33 | Instantiating (109) with all_17_0_13 yields:
% 15.63/4.33 | (119) ~ (all_17_0_13 = all_0_4_4) & sdtasdt0(xl, sz10) = all_17_0_13
% 15.63/4.33 |
% 15.63/4.33 | Applying alpha-rule on (119) yields:
% 15.63/4.33 | (120) ~ (all_17_0_13 = all_0_4_4)
% 15.63/4.33 | (121) sdtasdt0(xl, sz10) = all_17_0_13
% 15.63/4.33 |
% 15.63/4.33 | Instantiating (101) with all_19_0_14 yields:
% 15.63/4.33 | (122) ~ (all_19_0_14 = all_0_4_4) & sdtasdt0(xl, xn) = all_19_0_14
% 15.63/4.33 |
% 15.63/4.33 | Applying alpha-rule on (122) yields:
% 15.63/4.33 | (123) ~ (all_19_0_14 = all_0_4_4)
% 15.63/4.33 | (124) sdtasdt0(xl, xn) = all_19_0_14
% 15.63/4.33 |
% 15.63/4.33 | Instantiating (107) with all_21_0_15 yields:
% 15.63/4.33 | (125) sdtasdt0(xl, all_21_0_15) = xn & aNaturalNumber0(all_21_0_15)
% 15.63/4.33 |
% 15.63/4.33 | Applying alpha-rule on (125) yields:
% 15.63/4.33 | (126) sdtasdt0(xl, all_21_0_15) = xn
% 15.63/4.33 | (127) aNaturalNumber0(all_21_0_15)
% 15.63/4.33 |
% 15.63/4.33 | Instantiating (105) with all_27_0_18, all_27_1_19, all_27_2_20, all_27_3_21 yields:
% 15.63/4.33 | (128) sdtasdt0(all_27_3_21, xl) = all_27_2_20 & sdtasdt0(all_0_0_0, xl) = all_27_1_19 & sdtasdt0(all_0_1_1, xl) = all_27_0_18 & sdtasdt0(xl, all_27_3_21) = all_0_4_4 & sdtpldt0(all_27_1_19, all_27_0_18) = all_27_2_20 & sdtpldt0(all_0_0_0, all_0_1_1) = all_27_3_21
% 15.63/4.33 |
% 15.63/4.33 | Applying alpha-rule on (128) yields:
% 15.63/4.33 | (129) sdtasdt0(all_0_0_0, xl) = all_27_1_19
% 15.63/4.33 | (130) sdtpldt0(all_0_0_0, all_0_1_1) = all_27_3_21
% 15.63/4.33 | (131) sdtasdt0(all_0_1_1, xl) = all_27_0_18
% 15.63/4.33 | (132) sdtpldt0(all_27_1_19, all_27_0_18) = all_27_2_20
% 15.63/4.33 | (133) sdtasdt0(all_27_3_21, xl) = all_27_2_20
% 15.63/4.33 | (134) sdtasdt0(xl, all_27_3_21) = all_0_4_4
% 15.63/4.33 |
% 15.63/4.33 | Instantiating formula (54) with all_0_0_0, xl, xm, all_27_1_19 and discharging atoms sdtasdt0(all_0_0_0, xl) = all_27_1_19, sdtasdt0(all_0_0_0, xl) = xm, yields:
% 15.63/4.33 | (135) all_27_1_19 = xm
% 15.63/4.33 |
% 15.63/4.33 | Instantiating formula (54) with all_0_1_1, xl, xn, all_27_0_18 and discharging atoms sdtasdt0(all_0_1_1, xl) = all_27_0_18, sdtasdt0(all_0_1_1, xl) = xn, yields:
% 15.63/4.33 | (136) all_27_0_18 = xn
% 15.63/4.33 |
% 15.63/4.33 | Instantiating formula (54) with xl, all_0_0_0, all_13_0_11, xm and discharging atoms sdtasdt0(xl, all_0_0_0) = all_13_0_11, sdtasdt0(xl, all_0_0_0) = xm, yields:
% 15.63/4.33 | (137) all_13_0_11 = xm
% 15.63/4.33 |
% 15.63/4.33 | Instantiating formula (54) with xl, all_0_1_1, all_15_0_12, xn and discharging atoms sdtasdt0(xl, all_0_1_1) = all_15_0_12, sdtasdt0(xl, all_0_1_1) = xn, yields:
% 15.63/4.33 | (138) all_15_0_12 = xn
% 15.63/4.33 |
% 15.63/4.33 | Instantiating formula (69) with all_17_0_13, xl and discharging atoms sdtasdt0(xl, sz10) = all_17_0_13, aNaturalNumber0(xl), yields:
% 15.63/4.33 | (139) all_17_0_13 = xl
% 15.63/4.33 |
% 15.63/4.33 | From (135) and (129) follows:
% 15.63/4.33 | (104) sdtasdt0(all_0_0_0, xl) = xm
% 15.63/4.33 |
% 15.63/4.33 | From (136) and (131) follows:
% 15.63/4.33 | (106) sdtasdt0(all_0_1_1, xl) = xn
% 15.63/4.33 |
% 15.63/4.33 | From (137) and (115) follows:
% 15.63/4.33 | (20) sdtasdt0(xl, all_0_0_0) = xm
% 15.63/4.33 |
% 15.63/4.33 | From (138) and (118) follows:
% 15.63/4.33 | (91) sdtasdt0(xl, all_0_1_1) = xn
% 15.63/4.33 |
% 15.63/4.33 | From (139) and (121) follows:
% 15.63/4.33 | (144) sdtasdt0(xl, sz10) = xl
% 15.63/4.33 |
% 15.63/4.33 | From (135)(136) and (132) follows:
% 15.63/4.33 | (145) sdtpldt0(xm, xn) = all_27_2_20
% 15.63/4.33 |
% 15.63/4.33 | Instantiating formula (74) with xm, xn, all_27_2_20, all_0_4_4 and discharging atoms sdtpldt0(xm, xn) = all_27_2_20, sdtpldt0(xm, xn) = all_0_4_4, yields:
% 15.63/4.33 | (146) all_27_2_20 = all_0_4_4
% 15.63/4.33 |
% 15.63/4.33 | From (146) and (145) follows:
% 15.63/4.33 | (66) sdtpldt0(xm, xn) = all_0_4_4
% 15.63/4.33 |
% 15.63/4.33 | Instantiating formula (11) with all_19_0_14, xn, xl, all_0_1_1, xl and discharging atoms sdtasdt0(all_0_1_1, xl) = xn, sdtasdt0(xl, xn) = all_19_0_14, aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 15.63/4.33 | (148) ? [v0] : (sdtasdt0(v0, xl) = all_19_0_14 & sdtasdt0(xl, all_0_1_1) = v0)
% 15.63/4.33 |
% 15.63/4.33 | Instantiating formula (11) with xn, xl, sz10, xl, all_0_1_1 and discharging atoms sdtasdt0(all_0_1_1, xl) = xn, sdtasdt0(xl, sz10) = xl, aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), aNaturalNumber0(sz10), yields:
% 15.63/4.34 | (149) ? [v0] : (sdtasdt0(v0, sz10) = xn & sdtasdt0(all_0_1_1, xl) = v0)
% 15.63/4.34 |
% 15.63/4.34 | Instantiating formula (18) with all_27_3_21, all_0_0_0, all_0_1_1 and discharging atoms sdtpldt0(all_0_0_0, all_0_1_1) = all_27_3_21, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_1_1), yields:
% 15.63/4.34 | (150) sdtpldt0(all_0_1_1, all_0_0_0) = all_27_3_21
% 15.63/4.34 |
% 15.63/4.34 | Instantiating formula (61) with all_27_3_21, all_0_1_1, all_0_0_0 and discharging atoms sdtpldt0(all_0_0_0, all_0_1_1) = all_27_3_21, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_1_1), yields:
% 15.63/4.34 | (151) aNaturalNumber0(all_27_3_21)
% 15.63/4.34 |
% 15.63/4.34 | Instantiating formula (3) with all_0_4_4, xm, xn, all_0_0_0, all_0_1_1, xl and discharging atoms sdtasdt0(xl, all_0_0_0) = xm, sdtasdt0(xl, all_0_1_1) = xn, sdtpldt0(xn, xm) = all_0_4_4, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 15.63/4.34 | (152) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_0_0_0, xl) = v3 & sdtasdt0(all_0_1_1, xl) = v2 & sdtasdt0(xl, v0) = all_0_4_4 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_0_1_1, all_0_0_0) = v0)
% 15.63/4.34 |
% 15.63/4.34 | Instantiating formula (79) with all_0_4_4, xm, xn, all_0_0_0, all_0_1_1, xl and discharging atoms sdtasdt0(all_0_0_0, xl) = xm, sdtasdt0(all_0_1_1, xl) = xn, sdtpldt0(xn, xm) = all_0_4_4, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 15.63/4.34 | (153) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v0, xl) = all_0_4_4 & sdtasdt0(xl, v0) = v1 & sdtasdt0(xl, all_0_0_0) = v3 & sdtasdt0(xl, all_0_1_1) = v2 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_0_1_1, all_0_0_0) = v0)
% 15.63/4.34 |
% 15.63/4.34 | Instantiating formula (3) with all_0_4_4, xm, xn, all_0_0_0, all_21_0_15, xl and discharging atoms sdtasdt0(xl, all_21_0_15) = xn, sdtasdt0(xl, all_0_0_0) = xm, sdtpldt0(xn, xm) = all_0_4_4, aNaturalNumber0(all_21_0_15), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), yields:
% 15.63/4.34 | (154) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_21_0_15, xl) = v2 & sdtasdt0(all_0_0_0, xl) = v3 & sdtasdt0(xl, v0) = all_0_4_4 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_21_0_15, all_0_0_0) = v0)
% 15.63/4.34 |
% 15.63/4.34 | Instantiating formula (3) with all_0_4_4, xn, xm, all_21_0_15, all_0_0_0, xl and discharging atoms sdtasdt0(xl, all_21_0_15) = xn, sdtasdt0(xl, all_0_0_0) = xm, sdtpldt0(xm, xn) = all_0_4_4, aNaturalNumber0(all_21_0_15), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), yields:
% 15.63/4.34 | (155) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_21_0_15, xl) = v3 & sdtasdt0(all_0_0_0, xl) = v2 & sdtasdt0(xl, v0) = all_0_4_4 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_0_0_0, all_21_0_15) = v0)
% 15.63/4.34 |
% 15.63/4.34 | Instantiating formula (89) with xn, xl, all_21_0_15 and discharging atoms sdtasdt0(xl, all_21_0_15) = xn, aNaturalNumber0(all_21_0_15), aNaturalNumber0(xl), yields:
% 15.63/4.34 | (156) sdtasdt0(all_21_0_15, xl) = xn
% 15.63/4.34 |
% 15.63/4.34 | Instantiating formula (3) with all_0_4_4, xn, xm, all_0_1_1, all_9_0_9, xl and discharging atoms sdtasdt0(xl, all_9_0_9) = xm, sdtasdt0(xl, all_0_1_1) = xn, sdtpldt0(xm, xn) = all_0_4_4, aNaturalNumber0(all_9_0_9), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 15.63/4.34 | (157) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_9_0_9, xl) = v2 & sdtasdt0(all_0_1_1, xl) = v3 & sdtasdt0(xl, v0) = all_0_4_4 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_9_0_9, all_0_1_1) = v0)
% 15.63/4.34 |
% 15.63/4.34 | Instantiating formula (3) with all_0_4_4, xn, xm, all_21_0_15, all_9_0_9, xl and discharging atoms sdtasdt0(xl, all_21_0_15) = xn, sdtasdt0(xl, all_9_0_9) = xm, sdtpldt0(xm, xn) = all_0_4_4, aNaturalNumber0(all_21_0_15), aNaturalNumber0(all_9_0_9), aNaturalNumber0(xl), yields:
% 15.63/4.34 | (158) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_21_0_15, xl) = v3 & sdtasdt0(all_9_0_9, xl) = v2 & sdtasdt0(xl, v0) = all_0_4_4 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_9_0_9, all_21_0_15) = v0)
% 15.63/4.34 |
% 15.63/4.34 | Instantiating formula (3) with all_0_4_4, xm, xn, all_9_0_9, all_0_1_1, xl and discharging atoms sdtasdt0(xl, all_9_0_9) = xm, sdtasdt0(xl, all_0_1_1) = xn, sdtpldt0(xn, xm) = all_0_4_4, aNaturalNumber0(all_9_0_9), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 15.63/4.34 | (159) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_9_0_9, xl) = v3 & sdtasdt0(all_0_1_1, xl) = v2 & sdtasdt0(xl, v0) = all_0_4_4 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_0_1_1, all_9_0_9) = v0)
% 15.63/4.34 |
% 15.63/4.34 | Instantiating formula (3) with all_0_4_4, xm, xn, all_9_0_9, all_21_0_15, xl and discharging atoms sdtasdt0(xl, all_21_0_15) = xn, sdtasdt0(xl, all_9_0_9) = xm, sdtpldt0(xn, xm) = all_0_4_4, aNaturalNumber0(all_21_0_15), aNaturalNumber0(all_9_0_9), aNaturalNumber0(xl), yields:
% 15.63/4.34 | (160) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_21_0_15, xl) = v2 & sdtasdt0(all_9_0_9, xl) = v3 & sdtasdt0(xl, v0) = all_0_4_4 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_21_0_15, all_9_0_9) = v0)
% 15.63/4.34 |
% 15.63/4.34 | Instantiating formula (89) with xm, xl, all_9_0_9 and discharging atoms sdtasdt0(xl, all_9_0_9) = xm, aNaturalNumber0(all_9_0_9), aNaturalNumber0(xl), yields:
% 15.63/4.34 | (161) sdtasdt0(all_9_0_9, xl) = xm
% 15.63/4.34 |
% 15.63/4.34 | Instantiating (157) with all_49_0_25, all_49_1_26, all_49_2_27, all_49_3_28 yields:
% 15.63/4.34 | (162) sdtasdt0(all_49_3_28, xl) = all_49_2_27 & sdtasdt0(all_9_0_9, xl) = all_49_1_26 & sdtasdt0(all_0_1_1, xl) = all_49_0_25 & sdtasdt0(xl, all_49_3_28) = all_0_4_4 & sdtpldt0(all_49_1_26, all_49_0_25) = all_49_2_27 & sdtpldt0(all_9_0_9, all_0_1_1) = all_49_3_28
% 15.63/4.34 |
% 15.63/4.34 | Applying alpha-rule on (162) yields:
% 15.63/4.34 | (163) sdtpldt0(all_49_1_26, all_49_0_25) = all_49_2_27
% 15.63/4.34 | (164) sdtasdt0(all_49_3_28, xl) = all_49_2_27
% 15.63/4.34 | (165) sdtasdt0(xl, all_49_3_28) = all_0_4_4
% 15.63/4.34 | (166) sdtasdt0(all_0_1_1, xl) = all_49_0_25
% 15.63/4.34 | (167) sdtasdt0(all_9_0_9, xl) = all_49_1_26
% 15.63/4.34 | (168) sdtpldt0(all_9_0_9, all_0_1_1) = all_49_3_28
% 15.63/4.34 |
% 15.63/4.34 | Instantiating (160) with all_51_0_29, all_51_1_30, all_51_2_31, all_51_3_32 yields:
% 15.63/4.34 | (169) sdtasdt0(all_51_3_32, xl) = all_51_2_31 & sdtasdt0(all_21_0_15, xl) = all_51_1_30 & sdtasdt0(all_9_0_9, xl) = all_51_0_29 & sdtasdt0(xl, all_51_3_32) = all_0_4_4 & sdtpldt0(all_51_1_30, all_51_0_29) = all_51_2_31 & sdtpldt0(all_21_0_15, all_9_0_9) = all_51_3_32
% 15.63/4.34 |
% 15.63/4.34 | Applying alpha-rule on (169) yields:
% 15.63/4.34 | (170) sdtasdt0(all_21_0_15, xl) = all_51_1_30
% 15.63/4.34 | (171) sdtpldt0(all_51_1_30, all_51_0_29) = all_51_2_31
% 15.63/4.34 | (172) sdtpldt0(all_21_0_15, all_9_0_9) = all_51_3_32
% 15.63/4.34 | (173) sdtasdt0(xl, all_51_3_32) = all_0_4_4
% 15.63/4.34 | (174) sdtasdt0(all_9_0_9, xl) = all_51_0_29
% 15.63/4.34 | (175) sdtasdt0(all_51_3_32, xl) = all_51_2_31
% 15.63/4.34 |
% 15.63/4.34 | Instantiating (159) with all_53_0_33, all_53_1_34, all_53_2_35, all_53_3_36 yields:
% 15.63/4.34 | (176) sdtasdt0(all_53_3_36, xl) = all_53_2_35 & sdtasdt0(all_9_0_9, xl) = all_53_0_33 & sdtasdt0(all_0_1_1, xl) = all_53_1_34 & sdtasdt0(xl, all_53_3_36) = all_0_4_4 & sdtpldt0(all_53_1_34, all_53_0_33) = all_53_2_35 & sdtpldt0(all_0_1_1, all_9_0_9) = all_53_3_36
% 15.63/4.34 |
% 15.63/4.34 | Applying alpha-rule on (176) yields:
% 15.63/4.34 | (177) sdtasdt0(xl, all_53_3_36) = all_0_4_4
% 15.63/4.34 | (178) sdtasdt0(all_0_1_1, xl) = all_53_1_34
% 15.63/4.34 | (179) sdtasdt0(all_9_0_9, xl) = all_53_0_33
% 15.63/4.34 | (180) sdtpldt0(all_53_1_34, all_53_0_33) = all_53_2_35
% 15.63/4.34 | (181) sdtasdt0(all_53_3_36, xl) = all_53_2_35
% 15.63/4.34 | (182) sdtpldt0(all_0_1_1, all_9_0_9) = all_53_3_36
% 15.63/4.34 |
% 15.63/4.34 | Instantiating (158) with all_71_0_45, all_71_1_46, all_71_2_47, all_71_3_48 yields:
% 15.63/4.35 | (183) sdtasdt0(all_71_3_48, xl) = all_71_2_47 & sdtasdt0(all_21_0_15, xl) = all_71_0_45 & sdtasdt0(all_9_0_9, xl) = all_71_1_46 & sdtasdt0(xl, all_71_3_48) = all_0_4_4 & sdtpldt0(all_71_1_46, all_71_0_45) = all_71_2_47 & sdtpldt0(all_9_0_9, all_21_0_15) = all_71_3_48
% 15.63/4.35 |
% 15.63/4.35 | Applying alpha-rule on (183) yields:
% 15.63/4.35 | (184) sdtasdt0(xl, all_71_3_48) = all_0_4_4
% 15.63/4.35 | (185) sdtasdt0(all_9_0_9, xl) = all_71_1_46
% 15.63/4.35 | (186) sdtpldt0(all_9_0_9, all_21_0_15) = all_71_3_48
% 15.63/4.35 | (187) sdtasdt0(all_21_0_15, xl) = all_71_0_45
% 15.63/4.35 | (188) sdtasdt0(all_71_3_48, xl) = all_71_2_47
% 15.63/4.35 | (189) sdtpldt0(all_71_1_46, all_71_0_45) = all_71_2_47
% 15.63/4.35 |
% 15.63/4.35 | Instantiating (149) with all_73_0_49 yields:
% 15.63/4.35 | (190) sdtasdt0(all_73_0_49, sz10) = xn & sdtasdt0(all_0_1_1, xl) = all_73_0_49
% 15.63/4.35 |
% 15.63/4.35 | Applying alpha-rule on (190) yields:
% 15.63/4.35 | (191) sdtasdt0(all_73_0_49, sz10) = xn
% 15.63/4.35 | (192) sdtasdt0(all_0_1_1, xl) = all_73_0_49
% 15.63/4.35 |
% 15.63/4.35 | Instantiating (152) with all_85_0_55, all_85_1_56, all_85_2_57, all_85_3_58 yields:
% 15.63/4.35 | (193) sdtasdt0(all_85_3_58, xl) = all_85_2_57 & sdtasdt0(all_0_0_0, xl) = all_85_0_55 & sdtasdt0(all_0_1_1, xl) = all_85_1_56 & sdtasdt0(xl, all_85_3_58) = all_0_4_4 & sdtpldt0(all_85_1_56, all_85_0_55) = all_85_2_57 & sdtpldt0(all_0_1_1, all_0_0_0) = all_85_3_58
% 15.63/4.35 |
% 15.63/4.35 | Applying alpha-rule on (193) yields:
% 15.63/4.35 | (194) sdtasdt0(all_85_3_58, xl) = all_85_2_57
% 15.63/4.35 | (195) sdtpldt0(all_0_1_1, all_0_0_0) = all_85_3_58
% 15.63/4.35 | (196) sdtasdt0(all_0_0_0, xl) = all_85_0_55
% 15.63/4.35 | (197) sdtasdt0(xl, all_85_3_58) = all_0_4_4
% 15.63/4.35 | (198) sdtpldt0(all_85_1_56, all_85_0_55) = all_85_2_57
% 15.63/4.35 | (199) sdtasdt0(all_0_1_1, xl) = all_85_1_56
% 15.63/4.35 |
% 15.63/4.35 | Instantiating (148) with all_97_0_64 yields:
% 15.63/4.35 | (200) sdtasdt0(all_97_0_64, xl) = all_19_0_14 & sdtasdt0(xl, all_0_1_1) = all_97_0_64
% 15.63/4.35 |
% 15.63/4.35 | Applying alpha-rule on (200) yields:
% 15.63/4.35 | (201) sdtasdt0(all_97_0_64, xl) = all_19_0_14
% 15.63/4.35 | (202) sdtasdt0(xl, all_0_1_1) = all_97_0_64
% 15.63/4.35 |
% 15.63/4.35 | Instantiating (155) with all_101_0_66, all_101_1_67, all_101_2_68, all_101_3_69 yields:
% 15.63/4.35 | (203) sdtasdt0(all_101_3_69, xl) = all_101_2_68 & sdtasdt0(all_21_0_15, xl) = all_101_0_66 & sdtasdt0(all_0_0_0, xl) = all_101_1_67 & sdtasdt0(xl, all_101_3_69) = all_0_4_4 & sdtpldt0(all_101_1_67, all_101_0_66) = all_101_2_68 & sdtpldt0(all_0_0_0, all_21_0_15) = all_101_3_69
% 15.63/4.35 |
% 15.63/4.35 | Applying alpha-rule on (203) yields:
% 15.63/4.35 | (204) sdtpldt0(all_0_0_0, all_21_0_15) = all_101_3_69
% 15.63/4.35 | (205) sdtasdt0(xl, all_101_3_69) = all_0_4_4
% 15.63/4.35 | (206) sdtpldt0(all_101_1_67, all_101_0_66) = all_101_2_68
% 15.63/4.35 | (207) sdtasdt0(all_21_0_15, xl) = all_101_0_66
% 15.63/4.35 | (208) sdtasdt0(all_101_3_69, xl) = all_101_2_68
% 15.63/4.35 | (209) sdtasdt0(all_0_0_0, xl) = all_101_1_67
% 15.63/4.35 |
% 15.63/4.35 | Instantiating (154) with all_103_0_70, all_103_1_71, all_103_2_72, all_103_3_73 yields:
% 15.63/4.35 | (210) sdtasdt0(all_103_3_73, xl) = all_103_2_72 & sdtasdt0(all_21_0_15, xl) = all_103_1_71 & sdtasdt0(all_0_0_0, xl) = all_103_0_70 & sdtasdt0(xl, all_103_3_73) = all_0_4_4 & sdtpldt0(all_103_1_71, all_103_0_70) = all_103_2_72 & sdtpldt0(all_21_0_15, all_0_0_0) = all_103_3_73
% 15.63/4.35 |
% 15.63/4.35 | Applying alpha-rule on (210) yields:
% 15.63/4.35 | (211) sdtasdt0(all_0_0_0, xl) = all_103_0_70
% 15.63/4.35 | (212) sdtasdt0(all_103_3_73, xl) = all_103_2_72
% 15.63/4.35 | (213) sdtpldt0(all_103_1_71, all_103_0_70) = all_103_2_72
% 15.63/4.35 | (214) sdtasdt0(xl, all_103_3_73) = all_0_4_4
% 15.63/4.35 | (215) sdtasdt0(all_21_0_15, xl) = all_103_1_71
% 15.63/4.35 | (216) sdtpldt0(all_21_0_15, all_0_0_0) = all_103_3_73
% 15.63/4.35 |
% 15.63/4.35 | Instantiating (153) with all_111_0_77, all_111_1_78, all_111_2_79, all_111_3_80 yields:
% 15.63/4.35 | (217) sdtasdt0(all_111_3_80, xl) = all_0_4_4 & sdtasdt0(xl, all_111_3_80) = all_111_2_79 & sdtasdt0(xl, all_0_0_0) = all_111_0_77 & sdtasdt0(xl, all_0_1_1) = all_111_1_78 & sdtpldt0(all_111_1_78, all_111_0_77) = all_111_2_79 & sdtpldt0(all_0_1_1, all_0_0_0) = all_111_3_80
% 15.63/4.35 |
% 15.63/4.35 | Applying alpha-rule on (217) yields:
% 15.63/4.35 | (218) sdtasdt0(xl, all_0_0_0) = all_111_0_77
% 15.63/4.35 | (219) sdtpldt0(all_111_1_78, all_111_0_77) = all_111_2_79
% 15.63/4.35 | (220) sdtasdt0(xl, all_0_1_1) = all_111_1_78
% 15.63/4.35 | (221) sdtasdt0(all_111_3_80, xl) = all_0_4_4
% 15.63/4.35 | (222) sdtasdt0(xl, all_111_3_80) = all_111_2_79
% 15.63/4.35 | (223) sdtpldt0(all_0_1_1, all_0_0_0) = all_111_3_80
% 15.63/4.35 |
% 15.63/4.35 | Instantiating formula (54) with all_21_0_15, xl, all_101_0_66, all_103_1_71 and discharging atoms sdtasdt0(all_21_0_15, xl) = all_103_1_71, sdtasdt0(all_21_0_15, xl) = all_101_0_66, yields:
% 15.63/4.35 | (224) all_103_1_71 = all_101_0_66
% 15.63/4.35 |
% 15.63/4.35 | Instantiating formula (54) with all_21_0_15, xl, all_71_0_45, all_101_0_66 and discharging atoms sdtasdt0(all_21_0_15, xl) = all_101_0_66, sdtasdt0(all_21_0_15, xl) = all_71_0_45, yields:
% 15.63/4.35 | (225) all_101_0_66 = all_71_0_45
% 15.63/4.35 |
% 15.63/4.35 | Instantiating formula (54) with all_21_0_15, xl, all_51_1_30, all_71_0_45 and discharging atoms sdtasdt0(all_21_0_15, xl) = all_71_0_45, sdtasdt0(all_21_0_15, xl) = all_51_1_30, yields:
% 15.63/4.35 | (226) all_71_0_45 = all_51_1_30
% 15.63/4.35 |
% 15.63/4.35 | Instantiating formula (54) with all_21_0_15, xl, xn, all_103_1_71 and discharging atoms sdtasdt0(all_21_0_15, xl) = all_103_1_71, sdtasdt0(all_21_0_15, xl) = xn, yields:
% 15.63/4.35 | (227) all_103_1_71 = xn
% 15.63/4.35 |
% 15.63/4.35 | Instantiating formula (54) with all_9_0_9, xl, all_53_0_33, all_71_1_46 and discharging atoms sdtasdt0(all_9_0_9, xl) = all_71_1_46, sdtasdt0(all_9_0_9, xl) = all_53_0_33, yields:
% 15.63/4.35 | (228) all_71_1_46 = all_53_0_33
% 15.63/4.35 |
% 15.63/4.35 | Instantiating formula (54) with all_9_0_9, xl, all_51_0_29, all_53_0_33 and discharging atoms sdtasdt0(all_9_0_9, xl) = all_53_0_33, sdtasdt0(all_9_0_9, xl) = all_51_0_29, yields:
% 15.63/4.35 | (229) all_53_0_33 = all_51_0_29
% 15.63/4.35 |
% 15.63/4.35 | Instantiating formula (54) with all_9_0_9, xl, all_49_1_26, all_71_1_46 and discharging atoms sdtasdt0(all_9_0_9, xl) = all_71_1_46, sdtasdt0(all_9_0_9, xl) = all_49_1_26, yields:
% 15.63/4.35 | (230) all_71_1_46 = all_49_1_26
% 15.63/4.35 |
% 15.63/4.35 | Instantiating formula (54) with all_9_0_9, xl, xm, all_51_0_29 and discharging atoms sdtasdt0(all_9_0_9, xl) = all_51_0_29, sdtasdt0(all_9_0_9, xl) = xm, yields:
% 15.63/4.35 | (231) all_51_0_29 = xm
% 15.63/4.35 |
% 15.63/4.35 | Instantiating formula (54) with all_0_0_0, xl, all_103_0_70, xm and discharging atoms sdtasdt0(all_0_0_0, xl) = all_103_0_70, sdtasdt0(all_0_0_0, xl) = xm, yields:
% 15.63/4.35 | (232) all_103_0_70 = xm
% 15.63/4.35 |
% 15.63/4.35 | Instantiating formula (54) with all_0_0_0, xl, all_101_1_67, all_103_0_70 and discharging atoms sdtasdt0(all_0_0_0, xl) = all_103_0_70, sdtasdt0(all_0_0_0, xl) = all_101_1_67, yields:
% 15.63/4.35 | (233) all_103_0_70 = all_101_1_67
% 15.63/4.35 |
% 15.63/4.35 | Instantiating formula (54) with all_0_0_0, xl, all_85_0_55, all_101_1_67 and discharging atoms sdtasdt0(all_0_0_0, xl) = all_101_1_67, sdtasdt0(all_0_0_0, xl) = all_85_0_55, yields:
% 15.63/4.35 | (234) all_101_1_67 = all_85_0_55
% 15.63/4.35 |
% 15.63/4.35 | Instantiating formula (54) with all_0_1_1, xl, all_85_1_56, xn and discharging atoms sdtasdt0(all_0_1_1, xl) = all_85_1_56, sdtasdt0(all_0_1_1, xl) = xn, yields:
% 15.63/4.35 | (235) all_85_1_56 = xn
% 15.63/4.35 |
% 15.63/4.35 | Instantiating formula (54) with all_0_1_1, xl, all_73_0_49, all_85_1_56 and discharging atoms sdtasdt0(all_0_1_1, xl) = all_85_1_56, sdtasdt0(all_0_1_1, xl) = all_73_0_49, yields:
% 15.63/4.35 | (236) all_85_1_56 = all_73_0_49
% 15.63/4.35 |
% 15.63/4.35 | Instantiating formula (54) with all_0_1_1, xl, all_53_1_34, all_85_1_56 and discharging atoms sdtasdt0(all_0_1_1, xl) = all_85_1_56, sdtasdt0(all_0_1_1, xl) = all_53_1_34, yields:
% 15.63/4.35 | (237) all_85_1_56 = all_53_1_34
% 15.63/4.35 |
% 15.63/4.35 | Instantiating formula (54) with xl, all_0_0_0, all_111_0_77, xm and discharging atoms sdtasdt0(xl, all_0_0_0) = all_111_0_77, sdtasdt0(xl, all_0_0_0) = xm, yields:
% 15.63/4.35 | (238) all_111_0_77 = xm
% 15.63/4.35 |
% 15.63/4.35 | Instantiating formula (54) with xl, all_0_1_1, all_111_1_78, xn and discharging atoms sdtasdt0(xl, all_0_1_1) = all_111_1_78, sdtasdt0(xl, all_0_1_1) = xn, yields:
% 15.63/4.35 | (239) all_111_1_78 = xn
% 15.63/4.35 |
% 15.63/4.35 | Instantiating formula (54) with xl, all_0_1_1, all_97_0_64, all_111_1_78 and discharging atoms sdtasdt0(xl, all_0_1_1) = all_111_1_78, sdtasdt0(xl, all_0_1_1) = all_97_0_64, yields:
% 15.63/4.35 | (240) all_111_1_78 = all_97_0_64
% 15.63/4.35 |
% 15.63/4.35 | Instantiating formula (74) with all_0_1_1, all_0_0_0, all_27_3_21, all_111_3_80 and discharging atoms sdtpldt0(all_0_1_1, all_0_0_0) = all_111_3_80, sdtpldt0(all_0_1_1, all_0_0_0) = all_27_3_21, yields:
% 15.63/4.35 | (241) all_111_3_80 = all_27_3_21
% 15.63/4.35 |
% 15.63/4.35 | Combining equations (239,240) yields a new equation:
% 15.63/4.35 | (242) all_97_0_64 = xn
% 15.63/4.35 |
% 15.63/4.35 | Combining equations (233,232) yields a new equation:
% 15.63/4.35 | (243) all_101_1_67 = xm
% 15.63/4.35 |
% 15.63/4.35 | Simplifying 243 yields:
% 15.63/4.35 | (244) all_101_1_67 = xm
% 15.63/4.35 |
% 15.63/4.35 | Combining equations (224,227) yields a new equation:
% 15.63/4.35 | (245) all_101_0_66 = xn
% 15.63/4.36 |
% 15.63/4.36 | Simplifying 245 yields:
% 15.63/4.36 | (246) all_101_0_66 = xn
% 15.63/4.36 |
% 15.63/4.36 | Combining equations (225,246) yields a new equation:
% 15.63/4.36 | (247) all_71_0_45 = xn
% 15.63/4.36 |
% 15.63/4.36 | Simplifying 247 yields:
% 15.63/4.36 | (248) all_71_0_45 = xn
% 15.63/4.36 |
% 15.63/4.36 | Combining equations (234,244) yields a new equation:
% 15.63/4.36 | (249) all_85_0_55 = xm
% 15.63/4.36 |
% 15.63/4.36 | Simplifying 249 yields:
% 15.63/4.36 | (250) all_85_0_55 = xm
% 15.63/4.36 |
% 15.63/4.36 | Combining equations (237,236) yields a new equation:
% 15.63/4.36 | (251) all_73_0_49 = all_53_1_34
% 15.63/4.36 |
% 15.63/4.36 | Combining equations (235,236) yields a new equation:
% 15.63/4.36 | (252) all_73_0_49 = xn
% 15.63/4.36 |
% 15.63/4.36 | Combining equations (251,252) yields a new equation:
% 15.63/4.36 | (253) all_53_1_34 = xn
% 15.63/4.36 |
% 15.63/4.36 | Simplifying 253 yields:
% 15.63/4.36 | (254) all_53_1_34 = xn
% 15.63/4.36 |
% 15.63/4.36 | Combining equations (226,248) yields a new equation:
% 15.63/4.36 | (255) all_51_1_30 = xn
% 15.63/4.36 |
% 15.63/4.36 | Simplifying 255 yields:
% 15.63/4.36 | (256) all_51_1_30 = xn
% 15.63/4.36 |
% 15.63/4.36 | Combining equations (228,230) yields a new equation:
% 15.63/4.36 | (257) all_53_0_33 = all_49_1_26
% 15.63/4.36 |
% 15.63/4.36 | Simplifying 257 yields:
% 15.63/4.36 | (258) all_53_0_33 = all_49_1_26
% 15.63/4.36 |
% 15.63/4.36 | Combining equations (229,258) yields a new equation:
% 15.63/4.36 | (259) all_51_0_29 = all_49_1_26
% 15.63/4.36 |
% 15.63/4.36 | Simplifying 259 yields:
% 15.63/4.36 | (260) all_51_0_29 = all_49_1_26
% 15.63/4.36 |
% 15.63/4.36 | Combining equations (231,260) yields a new equation:
% 15.63/4.36 | (261) all_49_1_26 = xm
% 15.63/4.36 |
% 15.63/4.36 | Combining equations (261,260) yields a new equation:
% 15.63/4.36 | (231) all_51_0_29 = xm
% 15.63/4.36 |
% 15.63/4.36 | Combining equations (261,258) yields a new equation:
% 15.63/4.36 | (263) all_53_0_33 = xm
% 15.63/4.36 |
% 15.63/4.36 | Combining equations (252,236) yields a new equation:
% 15.63/4.36 | (235) all_85_1_56 = xn
% 15.63/4.36 |
% 15.63/4.36 | Combining equations (242,240) yields a new equation:
% 15.63/4.36 | (239) all_111_1_78 = xn
% 15.63/4.36 |
% 15.63/4.36 | From (241) and (222) follows:
% 15.63/4.36 | (266) sdtasdt0(xl, all_27_3_21) = all_111_2_79
% 15.63/4.36 |
% 15.63/4.36 | From (239)(238) and (219) follows:
% 15.63/4.36 | (267) sdtpldt0(xn, xm) = all_111_2_79
% 15.63/4.36 |
% 15.63/4.36 | From (227)(232) and (213) follows:
% 15.63/4.36 | (268) sdtpldt0(xn, xm) = all_103_2_72
% 15.63/4.36 |
% 15.63/4.36 | From (235)(250) and (198) follows:
% 15.63/4.36 | (269) sdtpldt0(xn, xm) = all_85_2_57
% 15.63/4.36 |
% 15.63/4.36 | From (254)(263) and (180) follows:
% 15.63/4.36 | (270) sdtpldt0(xn, xm) = all_53_2_35
% 15.63/4.36 |
% 15.63/4.36 | From (256)(231) and (171) follows:
% 15.63/4.36 | (271) sdtpldt0(xn, xm) = all_51_2_31
% 15.63/4.36 |
% 15.63/4.36 | Instantiating formula (74) with xn, xm, all_103_2_72, all_111_2_79 and discharging atoms sdtpldt0(xn, xm) = all_111_2_79, sdtpldt0(xn, xm) = all_103_2_72, yields:
% 15.63/4.36 | (272) all_111_2_79 = all_103_2_72
% 15.63/4.36 |
% 15.63/4.36 | Instantiating formula (74) with xn, xm, all_85_2_57, all_0_4_4 and discharging atoms sdtpldt0(xn, xm) = all_85_2_57, sdtpldt0(xn, xm) = all_0_4_4, yields:
% 15.63/4.36 | (273) all_85_2_57 = all_0_4_4
% 15.63/4.36 |
% 15.63/4.36 | Instantiating formula (74) with xn, xm, all_53_2_35, all_103_2_72 and discharging atoms sdtpldt0(xn, xm) = all_103_2_72, sdtpldt0(xn, xm) = all_53_2_35, yields:
% 15.63/4.36 | (274) all_103_2_72 = all_53_2_35
% 15.63/4.36 |
% 15.63/4.36 | Instantiating formula (74) with xn, xm, all_53_2_35, all_85_2_57 and discharging atoms sdtpldt0(xn, xm) = all_85_2_57, sdtpldt0(xn, xm) = all_53_2_35, yields:
% 15.63/4.36 | (275) all_85_2_57 = all_53_2_35
% 15.63/4.36 |
% 15.63/4.36 | Instantiating formula (74) with xn, xm, all_51_2_31, all_111_2_79 and discharging atoms sdtpldt0(xn, xm) = all_111_2_79, sdtpldt0(xn, xm) = all_51_2_31, yields:
% 15.63/4.36 | (276) all_111_2_79 = all_51_2_31
% 15.63/4.36 |
% 15.63/4.36 | Combining equations (272,276) yields a new equation:
% 15.63/4.36 | (277) all_103_2_72 = all_51_2_31
% 15.63/4.36 |
% 15.63/4.36 | Simplifying 277 yields:
% 15.63/4.36 | (278) all_103_2_72 = all_51_2_31
% 15.63/4.36 |
% 15.63/4.36 | Combining equations (274,278) yields a new equation:
% 15.63/4.36 | (279) all_53_2_35 = all_51_2_31
% 15.63/4.36 |
% 15.63/4.36 | Simplifying 279 yields:
% 15.63/4.36 | (280) all_53_2_35 = all_51_2_31
% 15.63/4.36 |
% 15.63/4.36 | Combining equations (275,273) yields a new equation:
% 15.63/4.36 | (281) all_53_2_35 = all_0_4_4
% 15.63/4.36 |
% 15.63/4.36 | Simplifying 281 yields:
% 15.63/4.36 | (282) all_53_2_35 = all_0_4_4
% 15.63/4.36 |
% 15.63/4.36 | Combining equations (282,280) yields a new equation:
% 15.63/4.36 | (283) all_51_2_31 = all_0_4_4
% 15.63/4.36 |
% 15.63/4.36 | Combining equations (283,276) yields a new equation:
% 15.63/4.36 | (284) all_111_2_79 = all_0_4_4
% 15.63/4.36 |
% 15.63/4.36 | From (284) and (266) follows:
% 15.63/4.36 | (134) sdtasdt0(xl, all_27_3_21) = all_0_4_4
% 15.63/4.36 |
% 15.63/4.36 | Instantiating formula (94) with all_27_3_21, all_0_4_4, xl and discharging atoms sdtasdt0(xl, all_27_3_21) = all_0_4_4, aNaturalNumber0(all_27_3_21), aNaturalNumber0(all_0_4_4), aNaturalNumber0(xl), ~ doDivides0(xl, all_0_4_4), yields:
% 15.63/4.36 | (286) $false
% 15.63/4.36 |
% 15.63/4.36 |-The branch is then unsatisfiable
% 15.63/4.36 % SZS output end Proof for theBenchmark
% 15.63/4.36
% 15.63/4.36 3751ms
%------------------------------------------------------------------------------