TSTP Solution File: NUM480+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM480+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.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 08:44:56 EDT 2022
% Result : Theorem 6.11s 2.00s
% Output : Proof 11.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : NUM480+1 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.11 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.32 % Computer : n024.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Thu Jul 7 09:08:59 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.18/0.56 ____ _
% 0.18/0.56 ___ / __ \_____(_)___ ________ __________
% 0.18/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.56
% 0.18/0.56 A Theorem Prover for First-Order Logic
% 0.18/0.56 (ePrincess v.1.0)
% 0.18/0.56
% 0.18/0.56 (c) Philipp Rümmer, 2009-2015
% 0.18/0.56 (c) Peter Backeman, 2014-2015
% 0.18/0.56 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.56 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.56 Bug reports to peter@backeman.se
% 0.18/0.56
% 0.18/0.56 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.56
% 0.18/0.56 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.77/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.74/0.99 Prover 0: Preprocessing ...
% 3.48/1.43 Prover 0: Constructing countermodel ...
% 6.11/2.00 Prover 0: proved (1378ms)
% 6.11/2.00
% 6.11/2.00 No countermodel exists, formula is valid
% 6.11/2.00 % SZS status Theorem for theBenchmark
% 6.11/2.00
% 6.11/2.00 Generating proof ... found it (size 86)
% 10.51/2.99
% 10.51/2.99 % SZS output start Proof for theBenchmark
% 10.51/2.99 Assumed formulas after preprocessing and simplification:
% 10.51/3.00 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v4) & ~ (xl = sz00) & ~ (sz10 = sz00) & sdtsldt0(v3, xl) = v4 & sdtsldt0(xm, xl) = v1 & sdtasdt0(v0, v1) = v2 & sdtasdt0(xn, v1) = v5 & sdtasdt0(xn, xm) = v3 & sdtasdt0(xl, v4) = v2 & sdtasdt0(xl, xn) = v0 & doDivides0(xl, xm) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & aNaturalNumber0(xl) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v8, v6) = v10) | ~ (sdtasdt0(v7, v6) = v9) | ~ (sdtpldt0(v9, v10) = v11) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (sdtasdt0(v12, v6) = v11 & sdtasdt0(v6, v12) = v13 & sdtasdt0(v6, v8) = v15 & sdtasdt0(v6, v7) = v14 & sdtpldt0(v14, v15) = v13 & sdtpldt0(v7, v8) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v6, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ (sdtpldt0(v9, v10) = v11) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (sdtasdt0(v12, v6) = v13 & sdtasdt0(v8, v6) = v15 & sdtasdt0(v7, v6) = v14 & sdtasdt0(v6, v12) = v11 & sdtpldt0(v14, v15) = v13 & sdtpldt0(v7, v8) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v8, v6) = v10) | ~ (sdtasdt0(v7, v6) = v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v9, v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v8, v6) = v10) | ~ (sdtasdt0(v7, v6) = v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v11) & sdtasdt0(v6, v8) = v12 & sdtasdt0(v6, v7) = v11 & sdtlseqdt0(v11, v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v8, v6) = v10) | ~ (sdtasdt0(v7, v6) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v11) & sdtasdt0(v6, v8) = v12 & sdtasdt0(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v8, v6) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v10) & ~ (v11 = v9) & sdtasdt0(v7, v6) = v12 & sdtasdt0(v6, v8) = v11 & sdtlseqdt0(v12, v10) & sdtlseqdt0(v9, v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v8, v6) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v10) & ~ (v11 = v9) & sdtasdt0(v7, v6) = v12 & sdtasdt0(v6, v8) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v7, v6) = v10) | ~ (sdtasdt0(v6, v8) = v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v10) & ~ (v11 = v9) & sdtasdt0(v8, v6) = v12 & sdtasdt0(v6, v7) = v11 & sdtlseqdt0(v11, v9) & sdtlseqdt0(v10, v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v7, v6) = v10) | ~ (sdtasdt0(v6, v8) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v10) & ~ (v11 = v9) & sdtasdt0(v8, v6) = v12 & sdtasdt0(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v6, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v9, v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v6, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v11) & sdtasdt0(v8, v6) = v12 & sdtasdt0(v7, v6) = v11 & sdtlseqdt0(v11, v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v6, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v11) & sdtasdt0(v8, v6) = v12 & sdtasdt0(v7, v6) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v8, v6) = v10) | ~ (sdtpldt0(v7, v6) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v11) & sdtpldt0(v6, v8) = v12 & sdtpldt0(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v8, v6) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v10) & ~ (v11 = v9) & sdtpldt0(v7, v6) = v12 & sdtpldt0(v6, v8) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v7, v6) = v10) | ~ (sdtpldt0(v6, v8) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v10) & ~ (v11 = v9) & sdtpldt0(v8, v6) = v12 & sdtpldt0(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v6, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ( ~ (v12 = v11) & sdtpldt0(v8, v6) = v12 & sdtpldt0(v7, v6) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v9, v8) = v10) | ~ (sdtasdt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : (sdtasdt0(v7, v8) = v11 & sdtasdt0(v6, v11) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v9, v6) = v10) | ~ (sdtpldt0(v7, v8) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (sdtasdt0(v8, v6) = v15 & sdtasdt0(v7, v6) = v14 & sdtasdt0(v6, v9) = v11 & sdtasdt0(v6, v8) = v13 & sdtasdt0(v6, v7) = v12 & sdtpldt0(v14, v15) = v10 & sdtpldt0(v12, v13) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v7, v8) = v9) | ~ (sdtasdt0(v6, v9) = v10) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : (sdtasdt0(v11, v8) = v10 & sdtasdt0(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v6, v9) = v10) | ~ (sdtpldt0(v7, v8) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (sdtasdt0(v9, v6) = v13 & sdtasdt0(v8, v6) = v15 & sdtasdt0(v7, v6) = v14 & sdtasdt0(v6, v8) = v12 & sdtasdt0(v6, v7) = v11 & sdtpldt0(v14, v15) = v13 & sdtpldt0(v11, v12) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt0(v9, v8) = v10) | ~ (sdtpldt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : (sdtpldt0(v7, v8) = v11 & sdtpldt0(v6, v11) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt0(v7, v8) = v9) | ~ (sdtpldt0(v6, v9) = v10) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v11] : (sdtpldt0(v11, v8) = v10 & sdtpldt0(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | v6 = sz00 | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v6, v9) = v7) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (sdtmndt0(v7, v6) = v8) | ~ (sdtpldt0(v6, v9) = v7) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | v6 = sz00 | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v6, v8) = v9) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (sdtmndt0(v7, v6) = v8) | ~ (sdtpldt0(v6, v8) = v9) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v8, v6) = v9) | ~ (sdtasdt0(v7, v6) = v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v8, v6) = v9) | ~ (sdtasdt0(v7, v6) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v6, v8) = v9) | ~ (sdtasdt0(v6, v7) = v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | v6 = sz00 | ~ (sdtasdt0(v6, v8) = v9) | ~ (sdtasdt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (sdtpldt0(v8, v6) = v9) | ~ (sdtpldt0(v7, v6) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (sdtpldt0(v6, v8) = v9) | ~ (sdtpldt0(v6, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtsldt0(v9, v8) = v7) | ~ (sdtsldt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtmndt0(v9, v8) = v7) | ~ (sdtmndt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtasdt0(v9, v8) = v7) | ~ (sdtasdt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v9, v8) = v7) | ~ (sdtpldt0(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v8, v7) = v9) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = v11) & ~ (v10 = v9) & sdtpldt0(v8, v6) = v10 & sdtpldt0(v7, v8) = v12 & sdtpldt0(v6, v8) = v11 & sdtlseqdt0(v11, v12) & sdtlseqdt0(v10, v9))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v8, v6) = v9) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = v11) & ~ (v10 = v9) & sdtpldt0(v8, v7) = v10 & sdtpldt0(v7, v8) = v12 & sdtpldt0(v6, v8) = v11 & sdtlseqdt0(v11, v12) & sdtlseqdt0(v9, v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v7, v8) = v9) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = v9) & ~ (v11 = v10) & sdtpldt0(v8, v7) = v11 & sdtpldt0(v8, v6) = v10 & sdtpldt0(v6, v8) = v12 & sdtlseqdt0(v12, v9) & sdtlseqdt0(v10, v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v6, v8) = v9) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = v9) & ~ (v11 = v10) & sdtpldt0(v8, v7) = v11 & sdtpldt0(v8, v6) = v10 & sdtpldt0(v7, v8) = v12 & sdtlseqdt0(v10, v11) & sdtlseqdt0(v9, v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = sz00 | ~ (sdtsldt0(v7, v6) = v8) | ~ (sdtasdt0(v6, v8) = v9) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | aNaturalNumber0(v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtmndt0(v7, v6) = v8) | ~ (sdtpldt0(v6, v8) = v9) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | aNaturalNumber0(v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v7, v8) = v9) | ~ doDivides0(v6, v9) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v7, v8) = v9) | ~ doDivides0(v6, v8) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v6, v9)) & ! [v6] : ! [v7] : ! [v8] : (v6 = sz00 | ~ (sdtasdt0(v7, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v7, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v7, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtasdt0(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v6, v8) = v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtasdt0(v7, v6) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | aNaturalNumber0(v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v7, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtpldt0(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v6, v8) = v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtpldt0(v7, v6) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | aNaturalNumber0(v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ doDivides0(v7, v8) | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | doDivides0(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ sdtlseqdt0(v7, v8) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v6, v8)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (sdtasdt0(v6, sz10) = v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (sdtasdt0(sz10, v6) = v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (sdtpldt0(v6, sz00) = v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (sdtpldt0(sz00, v6) = v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ sdtlseqdt0(v7, v6) | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | iLess0(v6, v7)) & ! [v6] : ! [v7] : (v7 = sz00 | v6 = sz00 | ~ (sdtasdt0(v6, v7) = sz00) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = sz00 | ~ (sdtasdt0(v6, sz00) = v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = sz00 | ~ (sdtasdt0(sz00, v6) = v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = sz00 | ~ (sdtpldt0(v6, v7) = sz00) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : (v7 = sz00 | ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v6, v7)) & ! [v6] : ! [v7] : (v6 = sz00 | ~ (sdtpldt0(v6, v7) = sz00) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6)) & ! [v6] : ! [v7] : ( ~ (sdtasdt0(v6, sz10) = v7) | ~ aNaturalNumber0(v6) | sdtasdt0(sz10, v6) = v6) & ! [v6] : ! [v7] : ( ~ (sdtasdt0(v6, sz00) = v7) | ~ aNaturalNumber0(v6) | sdtasdt0(sz00, v6) = sz00) & ! [v6] : ! [v7] : ( ~ (sdtasdt0(sz10, v6) = v7) | ~ aNaturalNumber0(v6) | sdtasdt0(v6, sz10) = v6) & ! [v6] : ! [v7] : ( ~ (sdtasdt0(sz00, v6) = v7) | ~ aNaturalNumber0(v6) | sdtasdt0(v6, sz00) = sz00) & ! [v6] : ! [v7] : ( ~ (sdtpldt0(v6, sz00) = v7) | ~ aNaturalNumber0(v6) | sdtpldt0(sz00, v6) = v6) & ! [v6] : ! [v7] : ( ~ (sdtpldt0(sz00, v6) = v7) | ~ aNaturalNumber0(v6) | sdtpldt0(v6, sz00) = v6) & ! [v6] : ! [v7] : ( ~ doDivides0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v8] : (sdtasdt0(v6, v8) = v7 & aNaturalNumber0(v8))) & ! [v6] : ! [v7] : ( ~ sdtlseqdt0(v6, v7) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ? [v8] : (sdtpldt0(v6, v8) = v7 & aNaturalNumber0(v8))) & ! [v6] : ! [v7] : ( ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | sdtlseqdt0(v7, v6) | sdtlseqdt0(v6, v7)) & ! [v6] : (v6 = sz10 | v6 = sz00 | ~ aNaturalNumber0(v6) | sdtlseqdt0(sz10, v6)) & ! [v6] : ( ~ aNaturalNumber0(v6) | sdtlseqdt0(v6, v6)))
% 10.61/3.06 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 10.61/3.06 | (1) ~ (all_0_0_0 = all_0_1_1) & ~ (xl = sz00) & ~ (sz10 = sz00) & sdtsldt0(all_0_2_2, xl) = all_0_1_1 & sdtsldt0(xm, xl) = all_0_4_4 & sdtasdt0(all_0_5_5, all_0_4_4) = all_0_3_3 & sdtasdt0(xn, all_0_4_4) = all_0_0_0 & sdtasdt0(xn, xm) = all_0_2_2 & sdtasdt0(xl, all_0_1_1) = all_0_3_3 & sdtasdt0(xl, xn) = all_0_5_5 & doDivides0(xl, xm) & 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, v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1)) & ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0] : ! [v1] : (v0 = 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))
% 10.61/3.09 |
% 10.61/3.09 | Applying alpha-rule on (1) yields:
% 10.61/3.09 | (2) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 10.61/3.09 | (3) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 10.61/3.09 | (4) ! [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)))
% 10.61/3.09 | (5) aNaturalNumber0(sz10)
% 10.61/3.09 | (6) ! [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))
% 10.61/3.09 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.61/3.09 | (8) aNaturalNumber0(xl)
% 10.61/3.09 | (9) ! [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))
% 10.61/3.09 | (10) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 10.61/3.09 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.61/3.09 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 10.61/3.09 | (13) ! [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))
% 10.61/3.09 | (14) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 10.61/3.09 | (15) ! [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)))
% 10.61/3.09 | (16) doDivides0(xl, xm)
% 10.61/3.09 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.61/3.09 | (18) ! [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))
% 10.61/3.09 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 10.61/3.09 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.61/3.10 | (21) ! [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))
% 10.61/3.10 | (22) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0)
% 10.61/3.10 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 10.61/3.10 | (24) ! [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))
% 10.61/3.10 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 10.61/3.10 | (26) ! [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))
% 10.61/3.10 | (27) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00)
% 10.61/3.10 | (28) ! [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))
% 10.61/3.10 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.61/3.10 | (30) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 10.61/3.10 | (31) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 10.61/3.10 | (32) ! [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))
% 10.61/3.10 | (33) ! [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))
% 10.61/3.10 | (34) ! [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))
% 10.61/3.10 | (35) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0))
% 10.61/3.10 | (36) ! [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))
% 10.61/3.10 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 10.61/3.10 | (38) ! [v0] : ! [v1] : (v1 = sz00 | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 10.61/3.10 | (39) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 10.61/3.10 | (40) ! [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))
% 10.61/3.10 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.61/3.10 | (42) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.61/3.10 | (43) ! [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))
% 10.61/3.10 | (44) ! [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)))
% 11.09/3.11 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 11.09/3.11 | (46) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 11.09/3.11 | (47) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 11.09/3.11 | (48) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0))
% 11.09/3.11 | (49) ~ (all_0_0_0 = all_0_1_1)
% 11.09/3.11 | (50) ! [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)))
% 11.09/3.11 | (51) sdtsldt0(all_0_2_2, xl) = all_0_1_1
% 11.09/3.11 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 11.09/3.11 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 11.09/3.11 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2)
% 11.09/3.11 | (55) ! [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))
% 11.09/3.11 | (56) ! [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))
% 11.09/3.11 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2)
% 11.09/3.11 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 11.09/3.11 | (59) sdtasdt0(xn, all_0_4_4) = all_0_0_0
% 11.09/3.11 | (60) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 11.09/3.11 | (61) ~ (xl = sz00)
% 11.09/3.11 | (62) ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 11.09/3.11 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 11.09/3.11 | (64) ! [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)))
% 11.09/3.11 | (65) aNaturalNumber0(xm)
% 11.09/3.11 | (66) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 11.09/3.11 | (67) ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 11.09/3.11 | (68) sdtasdt0(xl, all_0_1_1) = all_0_3_3
% 11.09/3.11 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 11.09/3.11 | (70) ! [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))
% 11.09/3.11 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 11.09/3.11 | (72) aNaturalNumber0(xn)
% 11.09/3.11 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 11.09/3.11 | (74) sdtasdt0(all_0_5_5, all_0_4_4) = all_0_3_3
% 11.09/3.12 | (75) aNaturalNumber0(sz00)
% 11.09/3.12 | (76) ! [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))
% 11.09/3.12 | (77) sdtasdt0(xn, xm) = all_0_2_2
% 11.09/3.12 | (78) ~ (sz10 = sz00)
% 11.09/3.12 | (79) ! [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)))
% 11.09/3.12 | (80) ! [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)))
% 11.09/3.12 | (81) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0)
% 11.09/3.12 | (82) ! [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))
% 11.09/3.12 | (83) sdtsldt0(xm, xl) = all_0_4_4
% 11.09/3.12 | (84) ! [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))
% 11.09/3.12 | (85) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 11.09/3.12 | (86) sdtasdt0(xl, xn) = all_0_5_5
% 11.09/3.12 | (87) ! [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)))
% 11.09/3.12 | (88) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 11.09/3.12 | (89) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 11.09/3.12 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 11.09/3.12 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 11.09/3.12 | (92) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 11.09/3.12 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3))
% 11.09/3.12 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 11.09/3.12 | (95) ! [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))
% 11.09/3.12 |
% 11.09/3.12 | Instantiating formula (31) with xn, xn and discharging atoms aNaturalNumber0(xn), yields:
% 11.09/3.12 | (96) sdtlseqdt0(xn, xn)
% 11.09/3.12 |
% 11.09/3.12 | Instantiating formula (54) with all_0_2_2, xn, xm and discharging atoms sdtasdt0(xn, xm) = all_0_2_2, aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 11.09/3.13 | (97) sdtasdt0(xm, xn) = all_0_2_2
% 11.09/3.13 |
% 11.09/3.13 | Instantiating formula (88) with all_0_2_2, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_2_2, aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 11.09/3.13 | (98) aNaturalNumber0(all_0_2_2)
% 11.09/3.13 |
% 11.09/3.13 | Instantiating formula (54) with all_0_5_5, xl, xn and discharging atoms sdtasdt0(xl, xn) = all_0_5_5, aNaturalNumber0(xn), aNaturalNumber0(xl), yields:
% 11.09/3.13 | (99) sdtasdt0(xn, xl) = all_0_5_5
% 11.09/3.13 |
% 11.09/3.13 | Instantiating formula (88) with all_0_5_5, xn, xl and discharging atoms sdtasdt0(xl, xn) = all_0_5_5, aNaturalNumber0(xn), aNaturalNumber0(xl), yields:
% 11.09/3.13 | (100) aNaturalNumber0(all_0_5_5)
% 11.09/3.13 |
% 11.09/3.13 | Instantiating formula (67) with xm, xl and discharging atoms doDivides0(xl, xm), aNaturalNumber0(xm), aNaturalNumber0(xl), yields:
% 11.09/3.13 | (101) ? [v0] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0))
% 11.09/3.13 |
% 11.09/3.13 | Instantiating (101) with all_9_0_6 yields:
% 11.09/3.13 | (102) sdtasdt0(xl, all_9_0_6) = xm & aNaturalNumber0(all_9_0_6)
% 11.09/3.13 |
% 11.09/3.13 | Applying alpha-rule on (102) yields:
% 11.09/3.13 | (103) sdtasdt0(xl, all_9_0_6) = xm
% 11.09/3.13 | (104) aNaturalNumber0(all_9_0_6)
% 11.09/3.13 |
% 11.09/3.13 | Instantiating formula (70) with all_9_0_6, all_0_4_4, xm, xl and discharging atoms sdtsldt0(xm, xl) = all_0_4_4, sdtasdt0(xl, all_9_0_6) = xm, doDivides0(xl, xm), aNaturalNumber0(all_9_0_6), aNaturalNumber0(xm), aNaturalNumber0(xl), yields:
% 11.09/3.13 | (105) all_9_0_6 = all_0_4_4 | xl = sz00
% 11.09/3.13 |
% 11.09/3.13 | Instantiating formula (3) with xn, xn and discharging atoms sdtlseqdt0(xn, xn), aNaturalNumber0(xn), yields:
% 11.09/3.13 | (106) ? [v0] : (sdtpldt0(xn, v0) = xn & aNaturalNumber0(v0))
% 11.09/3.13 |
% 11.09/3.13 | Instantiating formula (33) with all_0_2_2, xm, xn, all_9_0_6, xl and discharging atoms sdtasdt0(xm, xn) = all_0_2_2, sdtasdt0(xl, all_9_0_6) = xm, aNaturalNumber0(all_9_0_6), aNaturalNumber0(xn), aNaturalNumber0(xl), yields:
% 11.09/3.13 | (107) ? [v0] : (sdtasdt0(all_9_0_6, xn) = v0 & sdtasdt0(xl, v0) = all_0_2_2)
% 11.09/3.13 |
% 11.09/3.13 | Instantiating formula (21) with all_0_2_2, xm, all_9_0_6, xl, xn and discharging atoms sdtasdt0(xn, xm) = all_0_2_2, sdtasdt0(xl, all_9_0_6) = xm, aNaturalNumber0(all_9_0_6), aNaturalNumber0(xn), aNaturalNumber0(xl), yields:
% 11.09/3.13 | (108) ? [v0] : (sdtasdt0(v0, all_9_0_6) = all_0_2_2 & sdtasdt0(xn, xl) = v0)
% 11.09/3.13 |
% 11.09/3.13 | Instantiating formula (54) with xm, xl, all_9_0_6 and discharging atoms sdtasdt0(xl, all_9_0_6) = xm, aNaturalNumber0(all_9_0_6), aNaturalNumber0(xl), yields:
% 11.09/3.13 | (109) sdtasdt0(all_9_0_6, xl) = xm
% 11.09/3.13 |
% 11.09/3.13 | Instantiating formula (25) with xn, all_0_2_2, xm and discharging atoms sdtasdt0(xm, xn) = all_0_2_2, aNaturalNumber0(all_0_2_2), aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 11.09/3.13 | (110) doDivides0(xm, all_0_2_2)
% 11.09/3.13 |
% 11.09/3.13 | Instantiating formula (25) with xn, all_0_5_5, xl and discharging atoms sdtasdt0(xl, xn) = all_0_5_5, aNaturalNumber0(all_0_5_5), aNaturalNumber0(xn), aNaturalNumber0(xl), yields:
% 11.09/3.13 | (111) doDivides0(xl, all_0_5_5)
% 11.09/3.13 |
% 11.09/3.13 | Instantiating (108) with all_17_0_7 yields:
% 11.09/3.13 | (112) sdtasdt0(all_17_0_7, all_9_0_6) = all_0_2_2 & sdtasdt0(xn, xl) = all_17_0_7
% 11.09/3.13 |
% 11.09/3.13 | Applying alpha-rule on (112) yields:
% 11.09/3.13 | (113) sdtasdt0(all_17_0_7, all_9_0_6) = all_0_2_2
% 11.09/3.13 | (114) sdtasdt0(xn, xl) = all_17_0_7
% 11.09/3.13 |
% 11.09/3.13 | Instantiating (106) with all_19_0_8 yields:
% 11.09/3.13 | (115) sdtpldt0(xn, all_19_0_8) = xn & aNaturalNumber0(all_19_0_8)
% 11.09/3.13 |
% 11.09/3.13 | Applying alpha-rule on (115) yields:
% 11.09/3.13 | (116) sdtpldt0(xn, all_19_0_8) = xn
% 11.09/3.13 | (117) aNaturalNumber0(all_19_0_8)
% 11.09/3.13 |
% 11.09/3.13 | Instantiating (107) with all_21_0_9 yields:
% 11.09/3.13 | (118) sdtasdt0(all_9_0_6, xn) = all_21_0_9 & sdtasdt0(xl, all_21_0_9) = all_0_2_2
% 11.09/3.13 |
% 11.09/3.13 | Applying alpha-rule on (118) yields:
% 11.09/3.13 | (119) sdtasdt0(all_9_0_6, xn) = all_21_0_9
% 11.09/3.13 | (120) sdtasdt0(xl, all_21_0_9) = all_0_2_2
% 11.09/3.13 |
% 11.09/3.13 +-Applying beta-rule and splitting (105), into two cases.
% 11.09/3.13 |-Branch one:
% 11.09/3.13 | (121) xl = sz00
% 11.09/3.13 |
% 11.09/3.13 | Equations (121) can reduce 61 to:
% 11.09/3.13 | (122) $false
% 11.09/3.13 |
% 11.09/3.13 |-The branch is then unsatisfiable
% 11.09/3.13 |-Branch two:
% 11.09/3.13 | (61) ~ (xl = sz00)
% 11.09/3.13 | (124) all_9_0_6 = all_0_4_4
% 11.09/3.13 |
% 11.09/3.13 | From (124) and (113) follows:
% 11.09/3.13 | (125) sdtasdt0(all_17_0_7, all_0_4_4) = all_0_2_2
% 11.09/3.13 |
% 11.09/3.13 | From (124) and (119) follows:
% 11.09/3.13 | (126) sdtasdt0(all_0_4_4, xn) = all_21_0_9
% 11.09/3.13 |
% 11.09/3.13 | From (124) and (109) follows:
% 11.09/3.13 | (127) sdtasdt0(all_0_4_4, xl) = xm
% 11.09/3.13 |
% 11.09/3.13 | From (124) and (104) follows:
% 11.09/3.13 | (128) aNaturalNumber0(all_0_4_4)
% 11.09/3.13 |
% 11.09/3.13 | Instantiating formula (58) with xn, xl, all_17_0_7, all_0_5_5 and discharging atoms sdtasdt0(xn, xl) = all_17_0_7, sdtasdt0(xn, xl) = all_0_5_5, yields:
% 11.09/3.13 | (129) all_17_0_7 = all_0_5_5
% 11.09/3.13 |
% 11.09/3.13 | From (129) and (125) follows:
% 11.09/3.14 | (130) sdtasdt0(all_0_5_5, all_0_4_4) = all_0_2_2
% 11.09/3.14 |
% 11.09/3.14 | Instantiating formula (58) with all_0_5_5, all_0_4_4, all_0_2_2, all_0_3_3 and discharging atoms sdtasdt0(all_0_5_5, all_0_4_4) = all_0_2_2, sdtasdt0(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 11.09/3.14 | (131) all_0_2_2 = all_0_3_3
% 11.09/3.14 |
% 11.09/3.14 | From (131) and (51) follows:
% 11.09/3.14 | (132) sdtsldt0(all_0_3_3, xl) = all_0_1_1
% 11.09/3.14 |
% 11.09/3.14 | From (131) and (130) follows:
% 11.09/3.14 | (74) sdtasdt0(all_0_5_5, all_0_4_4) = all_0_3_3
% 11.09/3.14 |
% 11.09/3.14 | From (131) and (77) follows:
% 11.09/3.14 | (134) sdtasdt0(xn, xm) = all_0_3_3
% 11.09/3.14 |
% 11.09/3.14 | From (131) and (120) follows:
% 11.09/3.14 | (135) sdtasdt0(xl, all_21_0_9) = all_0_3_3
% 11.09/3.14 |
% 11.09/3.14 | From (131) and (110) follows:
% 11.09/3.14 | (136) doDivides0(xm, all_0_3_3)
% 11.09/3.14 |
% 11.09/3.14 | From (131) and (98) follows:
% 11.09/3.14 | (137) aNaturalNumber0(all_0_3_3)
% 11.09/3.14 |
% 11.09/3.14 | Instantiating formula (67) with all_0_5_5, xl and discharging atoms doDivides0(xl, all_0_5_5), aNaturalNumber0(all_0_5_5), aNaturalNumber0(xl), yields:
% 11.09/3.14 | (138) ? [v0] : (sdtasdt0(xl, v0) = all_0_5_5 & aNaturalNumber0(v0))
% 11.09/3.14 |
% 11.09/3.14 | Instantiating formula (63) with all_0_3_3, xm, xl and discharging atoms doDivides0(xm, all_0_3_3), doDivides0(xl, xm), aNaturalNumber0(all_0_3_3), aNaturalNumber0(xm), aNaturalNumber0(xl), yields:
% 11.09/3.14 | (139) doDivides0(xl, all_0_3_3)
% 11.09/3.14 |
% 11.09/3.14 | Instantiating formula (33) with all_0_3_3, all_0_5_5, all_0_4_4, xn, xl and discharging atoms sdtasdt0(all_0_5_5, all_0_4_4) = all_0_3_3, sdtasdt0(xl, xn) = all_0_5_5, aNaturalNumber0(all_0_4_4), aNaturalNumber0(xn), aNaturalNumber0(xl), yields:
% 11.09/3.14 | (140) ? [v0] : (sdtasdt0(xn, all_0_4_4) = v0 & sdtasdt0(xl, v0) = all_0_3_3)
% 11.09/3.14 |
% 11.09/3.14 | Instantiating formula (84) with all_0_0_0, xn, all_19_0_8, xn, all_0_4_4 and discharging atoms sdtasdt0(xn, all_0_4_4) = all_0_0_0, sdtpldt0(xn, all_19_0_8) = xn, aNaturalNumber0(all_19_0_8), aNaturalNumber0(all_0_4_4), aNaturalNumber0(xn), yields:
% 11.09/3.14 | (141) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_19_0_8, all_0_4_4) = v4 & sdtasdt0(all_0_4_4, all_19_0_8) = v2 & sdtasdt0(all_0_4_4, xn) = v1 & sdtasdt0(all_0_4_4, xn) = v0 & sdtasdt0(xn, all_0_4_4) = v3 & sdtpldt0(v3, v4) = all_0_0_0 & sdtpldt0(v1, v2) = v0)
% 11.09/3.14 |
% 11.09/3.14 | Instantiating formula (76) with all_21_0_9, xn, all_19_0_8, xn, all_0_4_4 and discharging atoms sdtasdt0(all_0_4_4, xn) = all_21_0_9, sdtpldt0(xn, all_19_0_8) = xn, aNaturalNumber0(all_19_0_8), aNaturalNumber0(all_0_4_4), aNaturalNumber0(xn), yields:
% 11.09/3.14 | (142) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_19_0_8, all_0_4_4) = v4 & sdtasdt0(all_0_4_4, all_19_0_8) = v1 & sdtasdt0(all_0_4_4, xn) = v0 & sdtasdt0(xn, all_0_4_4) = v3 & sdtasdt0(xn, all_0_4_4) = v2 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_21_0_9)
% 11.09/3.14 |
% 11.09/3.14 | Instantiating formula (54) with all_21_0_9, all_0_4_4, xn and discharging atoms sdtasdt0(all_0_4_4, xn) = all_21_0_9, aNaturalNumber0(all_0_4_4), aNaturalNumber0(xn), yields:
% 11.09/3.14 | (143) sdtasdt0(xn, all_0_4_4) = all_21_0_9
% 11.09/3.14 |
% 11.09/3.14 | Instantiating formula (88) with all_21_0_9, xn, all_0_4_4 and discharging atoms sdtasdt0(all_0_4_4, xn) = all_21_0_9, aNaturalNumber0(all_0_4_4), aNaturalNumber0(xn), yields:
% 11.09/3.14 | (144) aNaturalNumber0(all_21_0_9)
% 11.09/3.14 |
% 11.09/3.14 | Instantiating formula (21) with all_0_3_3, xm, xl, all_0_4_4, xn and discharging atoms sdtasdt0(all_0_4_4, xl) = xm, sdtasdt0(xn, xm) = all_0_3_3, aNaturalNumber0(all_0_4_4), aNaturalNumber0(xn), aNaturalNumber0(xl), yields:
% 11.09/3.14 | (145) ? [v0] : (sdtasdt0(v0, xl) = all_0_3_3 & sdtasdt0(xn, all_0_4_4) = v0)
% 11.09/3.14 |
% 11.09/3.14 | Instantiating (145) with all_59_0_21 yields:
% 11.09/3.14 | (146) sdtasdt0(all_59_0_21, xl) = all_0_3_3 & sdtasdt0(xn, all_0_4_4) = all_59_0_21
% 11.09/3.14 |
% 11.09/3.14 | Applying alpha-rule on (146) yields:
% 11.09/3.14 | (147) sdtasdt0(all_59_0_21, xl) = all_0_3_3
% 11.09/3.14 | (148) sdtasdt0(xn, all_0_4_4) = all_59_0_21
% 11.09/3.14 |
% 11.09/3.14 | Instantiating (142) with all_61_0_22, all_61_1_23, all_61_2_24, all_61_3_25, all_61_4_26 yields:
% 11.09/3.14 | (149) sdtasdt0(all_19_0_8, all_0_4_4) = all_61_0_22 & sdtasdt0(all_0_4_4, all_19_0_8) = all_61_3_25 & sdtasdt0(all_0_4_4, xn) = all_61_4_26 & sdtasdt0(xn, all_0_4_4) = all_61_1_23 & sdtasdt0(xn, all_0_4_4) = all_61_2_24 & sdtpldt0(all_61_1_23, all_61_0_22) = all_61_2_24 & sdtpldt0(all_61_4_26, all_61_3_25) = all_21_0_9
% 11.09/3.14 |
% 11.09/3.14 | Applying alpha-rule on (149) yields:
% 11.09/3.14 | (150) sdtasdt0(all_0_4_4, all_19_0_8) = all_61_3_25
% 11.09/3.14 | (151) sdtasdt0(xn, all_0_4_4) = all_61_1_23
% 11.09/3.14 | (152) sdtpldt0(all_61_1_23, all_61_0_22) = all_61_2_24
% 11.09/3.14 | (153) sdtasdt0(all_19_0_8, all_0_4_4) = all_61_0_22
% 11.09/3.14 | (154) sdtpldt0(all_61_4_26, all_61_3_25) = all_21_0_9
% 11.09/3.14 | (155) sdtasdt0(all_0_4_4, xn) = all_61_4_26
% 11.09/3.14 | (156) sdtasdt0(xn, all_0_4_4) = all_61_2_24
% 11.09/3.14 |
% 11.09/3.14 | Instantiating (141) with all_83_0_61, all_83_1_62, all_83_2_63, all_83_3_64, all_83_4_65 yields:
% 11.09/3.14 | (157) sdtasdt0(all_19_0_8, all_0_4_4) = all_83_0_61 & sdtasdt0(all_0_4_4, all_19_0_8) = all_83_2_63 & sdtasdt0(all_0_4_4, xn) = all_83_3_64 & sdtasdt0(all_0_4_4, xn) = all_83_4_65 & sdtasdt0(xn, all_0_4_4) = all_83_1_62 & sdtpldt0(all_83_1_62, all_83_0_61) = all_0_0_0 & sdtpldt0(all_83_3_64, all_83_2_63) = all_83_4_65
% 11.09/3.14 |
% 11.09/3.14 | Applying alpha-rule on (157) yields:
% 11.09/3.14 | (158) sdtasdt0(all_0_4_4, xn) = all_83_3_64
% 11.09/3.14 | (159) sdtasdt0(all_19_0_8, all_0_4_4) = all_83_0_61
% 11.09/3.14 | (160) sdtpldt0(all_83_1_62, all_83_0_61) = all_0_0_0
% 11.09/3.14 | (161) sdtasdt0(all_0_4_4, xn) = all_83_4_65
% 11.09/3.14 | (162) sdtpldt0(all_83_3_64, all_83_2_63) = all_83_4_65
% 11.09/3.14 | (163) sdtasdt0(xn, all_0_4_4) = all_83_1_62
% 11.09/3.14 | (164) sdtasdt0(all_0_4_4, all_19_0_8) = all_83_2_63
% 11.09/3.14 |
% 11.09/3.14 | Instantiating (138) with all_89_0_72 yields:
% 11.09/3.14 | (165) sdtasdt0(xl, all_89_0_72) = all_0_5_5 & aNaturalNumber0(all_89_0_72)
% 11.09/3.14 |
% 11.09/3.14 | Applying alpha-rule on (165) yields:
% 11.09/3.14 | (166) sdtasdt0(xl, all_89_0_72) = all_0_5_5
% 11.09/3.14 | (167) aNaturalNumber0(all_89_0_72)
% 11.09/3.14 |
% 11.09/3.14 | Instantiating (140) with all_95_0_75 yields:
% 11.09/3.14 | (168) sdtasdt0(xn, all_0_4_4) = all_95_0_75 & sdtasdt0(xl, all_95_0_75) = all_0_3_3
% 11.09/3.14 |
% 11.09/3.14 | Applying alpha-rule on (168) yields:
% 11.09/3.14 | (169) sdtasdt0(xn, all_0_4_4) = all_95_0_75
% 11.09/3.14 | (170) sdtasdt0(xl, all_95_0_75) = all_0_3_3
% 11.09/3.14 |
% 11.09/3.14 | Instantiating formula (58) with xn, all_0_4_4, all_83_1_62, all_95_0_75 and discharging atoms sdtasdt0(xn, all_0_4_4) = all_95_0_75, sdtasdt0(xn, all_0_4_4) = all_83_1_62, yields:
% 11.09/3.14 | (171) all_95_0_75 = all_83_1_62
% 11.09/3.14 |
% 11.09/3.14 | Instantiating formula (58) with xn, all_0_4_4, all_61_1_23, all_0_0_0 and discharging atoms sdtasdt0(xn, all_0_4_4) = all_61_1_23, sdtasdt0(xn, all_0_4_4) = all_0_0_0, yields:
% 11.09/3.14 | (172) all_61_1_23 = all_0_0_0
% 11.09/3.14 |
% 11.09/3.14 | Instantiating formula (58) with xn, all_0_4_4, all_61_1_23, all_83_1_62 and discharging atoms sdtasdt0(xn, all_0_4_4) = all_83_1_62, sdtasdt0(xn, all_0_4_4) = all_61_1_23, yields:
% 11.09/3.15 | (173) all_83_1_62 = all_61_1_23
% 11.09/3.15 |
% 11.09/3.15 | Instantiating formula (58) with xn, all_0_4_4, all_61_2_24, all_95_0_75 and discharging atoms sdtasdt0(xn, all_0_4_4) = all_95_0_75, sdtasdt0(xn, all_0_4_4) = all_61_2_24, yields:
% 11.09/3.15 | (174) all_95_0_75 = all_61_2_24
% 11.09/3.15 |
% 11.09/3.15 | Instantiating formula (58) with xn, all_0_4_4, all_59_0_21, all_83_1_62 and discharging atoms sdtasdt0(xn, all_0_4_4) = all_83_1_62, sdtasdt0(xn, all_0_4_4) = all_59_0_21, yields:
% 11.09/3.15 | (175) all_83_1_62 = all_59_0_21
% 11.09/3.15 |
% 11.09/3.15 | Instantiating formula (58) with xn, all_0_4_4, all_21_0_9, all_83_1_62 and discharging atoms sdtasdt0(xn, all_0_4_4) = all_83_1_62, sdtasdt0(xn, all_0_4_4) = all_21_0_9, yields:
% 11.09/3.15 | (176) all_83_1_62 = all_21_0_9
% 11.09/3.15 |
% 11.09/3.15 | Instantiating formula (91) with all_0_5_5, xn, all_89_0_72, xl and discharging atoms sdtasdt0(xl, all_89_0_72) = all_0_5_5, sdtasdt0(xl, xn) = all_0_5_5, aNaturalNumber0(all_89_0_72), aNaturalNumber0(xn), aNaturalNumber0(xl), yields:
% 11.09/3.15 | (177) all_89_0_72 = xn | xl = sz00
% 11.09/3.15 |
% 11.09/3.15 | Instantiating formula (70) with all_21_0_9, all_0_1_1, all_0_3_3, xl and discharging atoms sdtsldt0(all_0_3_3, xl) = all_0_1_1, sdtasdt0(xl, all_21_0_9) = all_0_3_3, doDivides0(xl, all_0_3_3), aNaturalNumber0(all_21_0_9), aNaturalNumber0(all_0_3_3), aNaturalNumber0(xl), yields:
% 11.09/3.15 | (178) all_21_0_9 = all_0_1_1 | xl = sz00
% 11.09/3.15 |
% 11.09/3.15 | Combining equations (171,174) yields a new equation:
% 11.09/3.15 | (179) all_83_1_62 = all_61_2_24
% 11.09/3.15 |
% 11.09/3.15 | Simplifying 179 yields:
% 11.09/3.15 | (180) all_83_1_62 = all_61_2_24
% 11.09/3.15 |
% 11.09/3.15 | Combining equations (175,180) yields a new equation:
% 11.09/3.15 | (181) all_61_2_24 = all_59_0_21
% 11.09/3.15 |
% 11.09/3.15 | Combining equations (173,180) yields a new equation:
% 11.09/3.15 | (182) all_61_1_23 = all_61_2_24
% 11.09/3.15 |
% 11.09/3.15 | Simplifying 182 yields:
% 11.09/3.15 | (183) all_61_1_23 = all_61_2_24
% 11.09/3.15 |
% 11.09/3.15 | Combining equations (176,180) yields a new equation:
% 11.09/3.15 | (184) all_61_2_24 = all_21_0_9
% 11.09/3.15 |
% 11.09/3.15 | Combining equations (183,172) yields a new equation:
% 11.09/3.15 | (185) all_61_2_24 = all_0_0_0
% 11.09/3.15 |
% 11.09/3.15 | Simplifying 185 yields:
% 11.09/3.15 | (186) all_61_2_24 = all_0_0_0
% 11.09/3.15 |
% 11.09/3.15 | Combining equations (184,181) yields a new equation:
% 11.09/3.15 | (187) all_59_0_21 = all_21_0_9
% 11.09/3.15 |
% 11.09/3.15 | Combining equations (186,181) yields a new equation:
% 11.09/3.15 | (188) all_59_0_21 = all_0_0_0
% 11.09/3.15 |
% 11.09/3.15 | Combining equations (187,188) yields a new equation:
% 11.09/3.15 | (189) all_21_0_9 = all_0_0_0
% 11.09/3.15 |
% 11.09/3.15 | Simplifying 189 yields:
% 11.09/3.15 | (190) all_21_0_9 = all_0_0_0
% 11.09/3.15 |
% 11.09/3.15 +-Applying beta-rule and splitting (177), into two cases.
% 11.09/3.15 |-Branch one:
% 11.09/3.15 | (121) xl = sz00
% 11.09/3.15 |
% 11.09/3.15 | Equations (121) can reduce 61 to:
% 11.09/3.15 | (122) $false
% 11.09/3.15 |
% 11.09/3.15 |-The branch is then unsatisfiable
% 11.09/3.15 |-Branch two:
% 11.09/3.15 | (61) ~ (xl = sz00)
% 11.09/3.15 | (194) all_89_0_72 = xn
% 11.09/3.15 |
% 11.09/3.15 +-Applying beta-rule and splitting (178), into two cases.
% 11.09/3.15 |-Branch one:
% 11.09/3.15 | (121) xl = sz00
% 11.09/3.15 |
% 11.09/3.15 | Equations (121) can reduce 61 to:
% 11.09/3.15 | (122) $false
% 11.09/3.15 |
% 11.09/3.15 |-The branch is then unsatisfiable
% 11.09/3.15 |-Branch two:
% 11.09/3.15 | (61) ~ (xl = sz00)
% 11.09/3.15 | (198) all_21_0_9 = all_0_1_1
% 11.09/3.15 |
% 11.09/3.15 | Combining equations (198,190) yields a new equation:
% 11.09/3.15 | (199) all_0_0_0 = all_0_1_1
% 11.09/3.15 |
% 11.09/3.15 | Equations (199) can reduce 49 to:
% 11.09/3.15 | (122) $false
% 11.09/3.15 |
% 11.09/3.15 |-The branch is then unsatisfiable
% 11.09/3.15 % SZS output end Proof for theBenchmark
% 11.09/3.15
% 11.09/3.15 2577ms
%------------------------------------------------------------------------------