TSTP Solution File: NUM468+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM468+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 08:44:48 EDT 2022
% Result : Theorem 4.58s 1.70s
% Output : Proof 7.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM468+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jul 6 08:17:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.61/0.60 ____ _
% 0.61/0.60 ___ / __ \_____(_)___ ________ __________
% 0.61/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.61/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.61/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.61/0.60
% 0.61/0.60 A Theorem Prover for First-Order Logic
% 0.61/0.60 (ePrincess v.1.0)
% 0.61/0.60
% 0.61/0.60 (c) Philipp Rümmer, 2009-2015
% 0.61/0.60 (c) Peter Backeman, 2014-2015
% 0.61/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.61/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.61/0.60 Bug reports to peter@backeman.se
% 0.61/0.60
% 0.61/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.61/0.60
% 0.61/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.63/1.01 Prover 0: Preprocessing ...
% 3.57/1.47 Prover 0: Constructing countermodel ...
% 4.58/1.70 Prover 0: proved (1048ms)
% 4.58/1.70
% 4.58/1.70 No countermodel exists, formula is valid
% 4.58/1.70 % SZS status Theorem for theBenchmark
% 4.58/1.70
% 4.58/1.70 Generating proof ... found it (size 90)
% 7.36/2.33
% 7.36/2.33 % SZS output start Proof for theBenchmark
% 7.36/2.33 Assumed formulas after preprocessing and simplification:
% 7.36/2.33 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v4 = v2) & ~ (xl = sz00) & ~ (sz10 = sz00) & sdtsldt0(xn, xl) = v1 & sdtsldt0(xm, xl) = v0 & sdtasdt0(xl, v6) = xm & sdtasdt0(xl, v5) = xn & sdtasdt0(xl, v3) = v4 & sdtasdt0(xl, v1) = xn & sdtasdt0(xl, v0) = xm & sdtpldt0(v0, v1) = v3 & sdtpldt0(xm, xn) = v2 & doDivides0(xl, xn) & doDivides0(xl, xm) & aNaturalNumber0(v6) & aNaturalNumber0(v5) & aNaturalNumber0(v1) & aNaturalNumber0(v0) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & aNaturalNumber0(xl) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtasdt0(v9, v7) = v11) | ~ (sdtasdt0(v8, v7) = v10) | ~ (sdtpldt0(v10, v11) = v12) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (sdtasdt0(v13, v7) = v12 & sdtasdt0(v7, v13) = v14 & sdtasdt0(v7, v9) = v16 & sdtasdt0(v7, v8) = v15 & sdtpldt0(v15, v16) = v14 & sdtpldt0(v8, v9) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtasdt0(v7, v9) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ~ (sdtpldt0(v10, v11) = v12) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (sdtasdt0(v13, v7) = v14 & sdtasdt0(v9, v7) = v16 & sdtasdt0(v8, v7) = v15 & sdtasdt0(v7, v13) = v12 & sdtpldt0(v15, v16) = v14 & sdtpldt0(v8, v9) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v9, v7) = v11) | ~ (sdtasdt0(v8, v7) = v10) | ~ sdtlseqdt0(v8, v9) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtlseqdt0(v10, v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v9, v7) = v11) | ~ (sdtasdt0(v8, v7) = v10) | ~ sdtlseqdt0(v8, v9) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v12) & sdtasdt0(v7, v9) = v13 & sdtasdt0(v7, v8) = v12 & sdtlseqdt0(v12, v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v9, v7) = v11) | ~ (sdtasdt0(v8, v7) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v12) & sdtasdt0(v7, v9) = v13 & sdtasdt0(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v9, v7) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ~ sdtlseqdt0(v8, v9) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v11) & ~ (v12 = v10) & sdtasdt0(v8, v7) = v13 & sdtasdt0(v7, v9) = v12 & sdtlseqdt0(v13, v11) & sdtlseqdt0(v10, v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v9, v7) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v11) & ~ (v12 = v10) & sdtasdt0(v8, v7) = v13 & sdtasdt0(v7, v9) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v8, v7) = v11) | ~ (sdtasdt0(v7, v9) = v10) | ~ sdtlseqdt0(v8, v9) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v11) & ~ (v12 = v10) & sdtasdt0(v9, v7) = v13 & sdtasdt0(v7, v8) = v12 & sdtlseqdt0(v12, v10) & sdtlseqdt0(v11, v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v8, v7) = v11) | ~ (sdtasdt0(v7, v9) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v11) & ~ (v12 = v10) & sdtasdt0(v9, v7) = v13 & sdtasdt0(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v7, v9) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ~ sdtlseqdt0(v8, v9) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtlseqdt0(v10, v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v7, v9) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ~ sdtlseqdt0(v8, v9) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v12) & sdtasdt0(v9, v7) = v13 & sdtasdt0(v8, v7) = v12 & sdtlseqdt0(v12, v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v7, v9) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v12) & sdtasdt0(v9, v7) = v13 & sdtasdt0(v8, v7) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (sdtpldt0(v9, v7) = v11) | ~ (sdtpldt0(v8, v7) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v12) & sdtpldt0(v7, v9) = v13 & sdtpldt0(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (sdtpldt0(v9, v7) = v11) | ~ (sdtpldt0(v7, v8) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v11) & ~ (v12 = v10) & sdtpldt0(v8, v7) = v13 & sdtpldt0(v7, v9) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (sdtpldt0(v8, v7) = v11) | ~ (sdtpldt0(v7, v9) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v11) & ~ (v12 = v10) & sdtpldt0(v9, v7) = v13 & sdtpldt0(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (sdtpldt0(v7, v9) = v11) | ~ (sdtpldt0(v7, v8) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ( ~ (v13 = v12) & sdtpldt0(v9, v7) = v13 & sdtpldt0(v8, v7) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v10, v9) = v11) | ~ (sdtasdt0(v7, v8) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : (sdtasdt0(v8, v9) = v12 & sdtasdt0(v7, v12) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v10, v7) = v11) | ~ (sdtpldt0(v8, v9) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (sdtasdt0(v9, v7) = v16 & sdtasdt0(v8, v7) = v15 & sdtasdt0(v7, v10) = v12 & sdtasdt0(v7, v9) = v14 & sdtasdt0(v7, v8) = v13 & sdtpldt0(v15, v16) = v11 & sdtpldt0(v13, v14) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v8, v9) = v10) | ~ (sdtasdt0(v7, v10) = v11) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : (sdtasdt0(v12, v9) = v11 & sdtasdt0(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtasdt0(v7, v10) = v11) | ~ (sdtpldt0(v8, v9) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (sdtasdt0(v10, v7) = v14 & sdtasdt0(v9, v7) = v16 & sdtasdt0(v8, v7) = v15 & sdtasdt0(v7, v9) = v13 & sdtasdt0(v7, v8) = v12 & sdtpldt0(v15, v16) = v14 & sdtpldt0(v12, v13) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtpldt0(v10, v9) = v11) | ~ (sdtpldt0(v7, v8) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : (sdtpldt0(v8, v9) = v12 & sdtpldt0(v7, v12) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (sdtpldt0(v8, v9) = v10) | ~ (sdtpldt0(v7, v10) = v11) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v12] : (sdtpldt0(v12, v9) = v11 & sdtpldt0(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | v7 = sz00 | ~ (sdtsldt0(v8, v7) = v9) | ~ (sdtasdt0(v7, v10) = v8) | ~ doDivides0(v7, v8) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (sdtmndt0(v8, v7) = v9) | ~ (sdtpldt0(v7, v10) = v8) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v10) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | v7 = sz00 | ~ (sdtsldt0(v8, v7) = v9) | ~ (sdtasdt0(v7, v9) = v10) | ~ doDivides0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (sdtmndt0(v8, v7) = v9) | ~ (sdtpldt0(v7, v9) = v10) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v9, v7) = v10) | ~ (sdtasdt0(v8, v7) = v10) | ~ sdtlseqdt0(v8, v9) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v9, v7) = v10) | ~ (sdtasdt0(v8, v7) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v7, v9) = v10) | ~ (sdtasdt0(v7, v8) = v10) | ~ sdtlseqdt0(v8, v9) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | v7 = sz00 | ~ (sdtasdt0(v7, v9) = v10) | ~ (sdtasdt0(v7, v8) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (sdtpldt0(v9, v7) = v10) | ~ (sdtpldt0(v8, v7) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (sdtpldt0(v7, v9) = v10) | ~ (sdtpldt0(v7, v8) = v10) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtsldt0(v10, v9) = v8) | ~ (sdtsldt0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtmndt0(v10, v9) = v8) | ~ (sdtmndt0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtasdt0(v10, v9) = v8) | ~ (sdtasdt0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v10, v9) = v8) | ~ (sdtpldt0(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v9, v8) = v10) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v11] : ? [v12] : ? [v13] : ( ~ (v13 = v12) & ~ (v11 = v10) & sdtpldt0(v9, v7) = v11 & sdtpldt0(v8, v9) = v13 & sdtpldt0(v7, v9) = v12 & sdtlseqdt0(v12, v13) & sdtlseqdt0(v11, v10))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v9, v7) = v10) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v11] : ? [v12] : ? [v13] : ( ~ (v13 = v12) & ~ (v11 = v10) & sdtpldt0(v9, v8) = v11 & sdtpldt0(v8, v9) = v13 & sdtpldt0(v7, v9) = v12 & sdtlseqdt0(v12, v13) & sdtlseqdt0(v10, v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v8, v9) = v10) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v11] : ? [v12] : ? [v13] : ( ~ (v13 = v10) & ~ (v12 = v11) & sdtpldt0(v9, v8) = v12 & sdtpldt0(v9, v7) = v11 & sdtpldt0(v7, v9) = v13 & sdtlseqdt0(v13, v10) & sdtlseqdt0(v11, v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (sdtpldt0(v7, v9) = v10) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v11] : ? [v12] : ? [v13] : ( ~ (v13 = v10) & ~ (v12 = v11) & sdtpldt0(v9, v8) = v12 & sdtpldt0(v9, v7) = v11 & sdtpldt0(v8, v9) = v13 & sdtlseqdt0(v11, v12) & sdtlseqdt0(v10, v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = sz00 | ~ (sdtsldt0(v8, v7) = v9) | ~ (sdtasdt0(v7, v9) = v10) | ~ doDivides0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | aNaturalNumber0(v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtmndt0(v8, v7) = v9) | ~ (sdtpldt0(v7, v9) = v10) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | aNaturalNumber0(v9)) & ! [v7] : ! [v8] : ! [v9] : (v7 = sz00 | ~ (sdtasdt0(v8, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtlseqdt0(v8, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v8, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtasdt0(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v7, v9) = v8) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | doDivides0(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v7, v8) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtasdt0(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v7, v8) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | aNaturalNumber0(v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v8, v7) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtpldt0(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v7, v9) = v8) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtlseqdt0(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v7, v8) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtpldt0(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v7, v8) = v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | aNaturalNumber0(v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ doDivides0(v8, v9) | ~ doDivides0(v7, v8) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | doDivides0(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ sdtlseqdt0(v8, v9) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v9) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtlseqdt0(v7, v9)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (sdtasdt0(v7, sz10) = v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (sdtasdt0(sz10, v7) = v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (sdtpldt0(v7, sz00) = v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (sdtpldt0(sz00, v7) = v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v8 = v7 | ~ sdtlseqdt0(v8, v7) | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v8 = v7 | ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | iLess0(v7, v8)) & ! [v7] : ! [v8] : (v8 = sz00 | v7 = sz00 | ~ (sdtasdt0(v7, v8) = sz00) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v8 = sz00 | ~ (sdtasdt0(v7, sz00) = v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v8 = sz00 | ~ (sdtasdt0(sz00, v7) = v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v8 = sz00 | ~ (sdtpldt0(v7, v8) = sz00) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : (v7 = sz00 | ~ (sdtpldt0(v7, v8) = sz00) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7)) & ! [v7] : ! [v8] : ( ~ (sdtasdt0(v7, sz10) = v8) | ~ aNaturalNumber0(v7) | sdtasdt0(sz10, v7) = v7) & ! [v7] : ! [v8] : ( ~ (sdtasdt0(v7, sz00) = v8) | ~ aNaturalNumber0(v7) | sdtasdt0(sz00, v7) = sz00) & ! [v7] : ! [v8] : ( ~ (sdtasdt0(sz10, v7) = v8) | ~ aNaturalNumber0(v7) | sdtasdt0(v7, sz10) = v7) & ! [v7] : ! [v8] : ( ~ (sdtasdt0(sz00, v7) = v8) | ~ aNaturalNumber0(v7) | sdtasdt0(v7, sz00) = sz00) & ! [v7] : ! [v8] : ( ~ (sdtpldt0(v7, sz00) = v8) | ~ aNaturalNumber0(v7) | sdtpldt0(sz00, v7) = v7) & ! [v7] : ! [v8] : ( ~ (sdtpldt0(sz00, v7) = v8) | ~ aNaturalNumber0(v7) | sdtpldt0(v7, sz00) = v7) & ! [v7] : ! [v8] : ( ~ doDivides0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v9] : (sdtasdt0(v7, v9) = v8 & aNaturalNumber0(v9))) & ! [v7] : ! [v8] : ( ~ sdtlseqdt0(v7, v8) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | ? [v9] : (sdtpldt0(v7, v9) = v8 & aNaturalNumber0(v9))) & ! [v7] : ! [v8] : ( ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v7) | sdtlseqdt0(v8, v7) | sdtlseqdt0(v7, v8)) & ! [v7] : (v7 = sz10 | v7 = sz00 | ~ aNaturalNumber0(v7) | sdtlseqdt0(sz10, v7)) & ! [v7] : ( ~ aNaturalNumber0(v7) | sdtlseqdt0(v7, v7)))
% 7.36/2.39 | 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 yields:
% 7.36/2.39 | (1) ~ (all_0_2_2 = all_0_4_4) & ~ (xl = sz00) & ~ (sz10 = sz00) & sdtsldt0(xn, xl) = all_0_5_5 & sdtsldt0(xm, xl) = all_0_6_6 & 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_5_5) = xn & sdtasdt0(xl, all_0_6_6) = xm & sdtpldt0(all_0_6_6, all_0_5_5) = 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(all_0_5_5) & aNaturalNumber0(all_0_6_6) & 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] : (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))
% 7.80/2.41 |
% 7.80/2.41 | Applying alpha-rule on (1) yields:
% 7.80/2.41 | (2) ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 7.80/2.42 | (3) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 7.80/2.42 | (4) sdtpldt0(all_0_6_6, all_0_5_5) = all_0_3_3
% 7.80/2.42 | (5) ! [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))
% 7.80/2.42 | (6) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 7.80/2.42 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 7.80/2.42 | (8) ! [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)))
% 7.80/2.42 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 7.80/2.42 | (10) ~ (xl = sz00)
% 7.80/2.42 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2)
% 7.80/2.42 | (12) sdtasdt0(xl, all_0_1_1) = xn
% 7.80/2.42 | (13) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 7.80/2.42 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 7.80/2.42 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2)
% 7.80/2.42 | (16) aNaturalNumber0(all_0_0_0)
% 7.80/2.42 | (17) sdtasdt0(xl, all_0_6_6) = xm
% 7.80/2.42 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 7.80/2.42 | (19) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 7.80/2.42 | (20) aNaturalNumber0(sz00)
% 7.80/2.42 | (21) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 7.80/2.42 | (22) ! [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)))
% 7.80/2.42 | (23) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 7.80/2.42 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 7.80/2.42 | (25) sdtasdt0(xl, all_0_0_0) = xm
% 7.80/2.42 | (26) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 7.80/2.42 | (27) ! [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)))
% 7.80/2.42 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 7.80/2.42 | (29) doDivides0(xl, xm)
% 7.80/2.42 | (30) aNaturalNumber0(sz10)
% 7.80/2.42 | (31) ! [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)))
% 7.80/2.42 | (32) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 7.80/2.42 | (33) ! [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))
% 7.80/2.42 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 7.80/2.42 | (35) ! [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))
% 7.80/2.42 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 7.80/2.42 | (37) aNaturalNumber0(all_0_5_5)
% 7.80/2.42 | (38) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 7.80/2.42 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 7.80/2.43 | (40) ! [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))
% 7.80/2.43 | (41) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0))
% 7.80/2.43 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 7.80/2.43 | (43) ! [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))
% 7.80/2.43 | (44) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 7.80/2.43 | (45) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0))
% 7.80/2.43 | (46) sdtasdt0(xl, all_0_5_5) = xn
% 7.80/2.43 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 7.80/2.43 | (48) aNaturalNumber0(all_0_6_6)
% 7.80/2.43 | (49) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 7.80/2.43 | (50) ! [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))
% 7.80/2.43 | (51) ! [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))
% 7.80/2.43 | (52) ! [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))
% 7.80/2.43 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 7.80/2.43 | (54) ! [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)))
% 7.80/2.43 | (55) ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 7.80/2.43 | (56) aNaturalNumber0(xm)
% 7.80/2.43 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 7.80/2.43 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 7.80/2.43 | (59) ! [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))
% 7.80/2.43 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 7.80/2.43 | (61) ~ (all_0_2_2 = all_0_4_4)
% 7.80/2.43 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 7.80/2.43 | (63) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 7.80/2.43 | (64) ~ (sz10 = sz00)
% 7.80/2.43 | (65) ! [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))
% 7.80/2.44 | (66) sdtasdt0(xl, all_0_3_3) = all_0_2_2
% 7.80/2.44 | (67) ! [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))
% 7.80/2.44 | (68) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 7.80/2.44 | (69) sdtsldt0(xm, xl) = all_0_6_6
% 7.80/2.44 | (70) ! [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))
% 7.80/2.44 | (71) ! [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))
% 7.80/2.44 | (72) ! [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))
% 7.80/2.44 | (73) aNaturalNumber0(xn)
% 7.80/2.44 | (74) sdtsldt0(xn, xl) = all_0_5_5
% 7.80/2.44 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 7.80/2.44 | (76) ! [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))
% 7.80/2.44 | (77) aNaturalNumber0(all_0_1_1)
% 7.80/2.44 | (78) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 7.80/2.44 | (79) ! [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))
% 7.80/2.44 | (80) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 7.80/2.44 | (81) ! [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)))
% 7.80/2.44 | (82) doDivides0(xl, xn)
% 7.80/2.44 | (83) ! [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))
% 7.80/2.44 | (84) sdtpldt0(xm, xn) = all_0_4_4
% 7.80/2.44 | (85) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00)
% 7.80/2.44 | (86) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 7.80/2.44 | (87) ! [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)))
% 7.80/2.44 | (88) ! [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)))
% 7.80/2.44 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 7.80/2.44 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 7.80/2.44 | (91) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0)
% 7.80/2.44 | (92) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 7.80/2.44 | (93) ! [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))
% 7.80/2.44 | (94) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0)
% 7.80/2.44 | (95) aNaturalNumber0(xl)
% 7.80/2.44 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 7.80/2.44 | (97) ! [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))
% 7.80/2.44 | (98) ! [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))
% 7.80/2.44 | (99) ! [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))
% 7.80/2.44 |
% 7.80/2.44 | Instantiating formula (39) with xm, all_0_0_0, all_0_6_6, xl and discharging atoms sdtasdt0(xl, all_0_0_0) = xm, sdtasdt0(xl, all_0_6_6) = xm, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_6_6), aNaturalNumber0(xl), yields:
% 7.80/2.44 | (100) all_0_0_0 = all_0_6_6 | xl = sz00
% 7.80/2.44 |
% 7.80/2.44 | Instantiating formula (39) with xn, all_0_1_1, all_0_5_5, xl and discharging atoms sdtasdt0(xl, all_0_1_1) = xn, sdtasdt0(xl, all_0_5_5) = xn, aNaturalNumber0(all_0_1_1), aNaturalNumber0(all_0_5_5), aNaturalNumber0(xl), yields:
% 7.80/2.45 | (101) all_0_1_1 = all_0_5_5 | xl = sz00
% 7.80/2.45 |
% 7.80/2.45 | Instantiating formula (11) 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:
% 7.80/2.45 | (102) sdtasdt0(all_0_0_0, xl) = xm
% 7.80/2.45 |
% 7.80/2.45 | Instantiating formula (65) 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:
% 7.80/2.45 | (103) ? [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)
% 7.80/2.45 |
% 7.80/2.45 | Instantiating formula (65) with all_0_4_4, xn, xm, all_0_1_1, all_0_6_6, xl and discharging atoms sdtasdt0(xl, all_0_1_1) = xn, sdtasdt0(xl, all_0_6_6) = xm, sdtpldt0(xm, xn) = all_0_4_4, aNaturalNumber0(all_0_1_1), aNaturalNumber0(all_0_6_6), aNaturalNumber0(xl), yields:
% 7.80/2.45 | (104) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_0_1_1, xl) = v3 & sdtasdt0(all_0_6_6, xl) = v2 & sdtasdt0(xl, v0) = all_0_4_4 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_0_6_6, all_0_1_1) = v0)
% 7.80/2.45 |
% 7.80/2.45 | Instantiating formula (11) 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:
% 7.80/2.45 | (105) sdtasdt0(all_0_1_1, xl) = xn
% 7.80/2.45 |
% 7.80/2.45 | Instantiating formula (33) with all_0_2_2, all_0_3_3, all_0_5_5, all_0_6_6, xl and discharging atoms sdtasdt0(xl, all_0_3_3) = all_0_2_2, sdtpldt0(all_0_6_6, all_0_5_5) = all_0_3_3, aNaturalNumber0(all_0_5_5), aNaturalNumber0(all_0_6_6), aNaturalNumber0(xl), yields:
% 7.80/2.45 | (106) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_3_3, xl) = v2 & sdtasdt0(all_0_5_5, xl) = v4 & sdtasdt0(all_0_6_6, xl) = v3 & sdtasdt0(xl, all_0_5_5) = v1 & sdtasdt0(xl, all_0_6_6) = v0 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_0_2_2)
% 7.80/2.45 |
% 7.80/2.45 | Instantiating formula (65) with all_0_4_4, xn, xm, all_0_5_5, all_0_0_0, xl and discharging atoms sdtasdt0(xl, all_0_0_0) = xm, sdtasdt0(xl, all_0_5_5) = xn, sdtpldt0(xm, xn) = all_0_4_4, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_5_5), aNaturalNumber0(xl), yields:
% 7.80/2.45 | (107) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_0_0_0, xl) = v2 & sdtasdt0(all_0_5_5, xl) = v3 & sdtasdt0(xl, v0) = all_0_4_4 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_0_0_0, all_0_5_5) = v0)
% 7.80/2.45 |
% 7.80/2.45 | Instantiating formula (65) with all_0_4_4, xn, xm, all_0_5_5, all_0_6_6, xl and discharging atoms sdtasdt0(xl, all_0_5_5) = xn, sdtasdt0(xl, all_0_6_6) = xm, sdtpldt0(xm, xn) = all_0_4_4, aNaturalNumber0(all_0_5_5), aNaturalNumber0(all_0_6_6), aNaturalNumber0(xl), yields:
% 7.80/2.45 | (108) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v0, xl) = v1 & sdtasdt0(all_0_5_5, xl) = v3 & sdtasdt0(all_0_6_6, xl) = v2 & sdtasdt0(xl, v0) = all_0_4_4 & sdtpldt0(v2, v3) = v1 & sdtpldt0(all_0_6_6, all_0_5_5) = v0)
% 7.80/2.45 |
% 7.80/2.45 | Instantiating (106) with all_11_0_8, all_11_1_9, all_11_2_10, all_11_3_11, all_11_4_12 yields:
% 7.80/2.45 | (109) sdtasdt0(all_0_3_3, xl) = all_11_2_10 & sdtasdt0(all_0_5_5, xl) = all_11_0_8 & sdtasdt0(all_0_6_6, xl) = all_11_1_9 & sdtasdt0(xl, all_0_5_5) = all_11_3_11 & sdtasdt0(xl, all_0_6_6) = all_11_4_12 & sdtpldt0(all_11_1_9, all_11_0_8) = all_11_2_10 & sdtpldt0(all_11_4_12, all_11_3_11) = all_0_2_2
% 7.80/2.45 |
% 7.80/2.45 | Applying alpha-rule on (109) yields:
% 7.80/2.45 | (110) sdtasdt0(xl, all_0_6_6) = all_11_4_12
% 7.80/2.45 | (111) sdtasdt0(all_0_6_6, xl) = all_11_1_9
% 7.80/2.45 | (112) sdtasdt0(all_0_5_5, xl) = all_11_0_8
% 7.80/2.45 | (113) sdtasdt0(all_0_3_3, xl) = all_11_2_10
% 7.80/2.45 | (114) sdtasdt0(xl, all_0_5_5) = all_11_3_11
% 7.80/2.45 | (115) sdtpldt0(all_11_4_12, all_11_3_11) = all_0_2_2
% 7.80/2.45 | (116) sdtpldt0(all_11_1_9, all_11_0_8) = all_11_2_10
% 7.80/2.45 |
% 7.80/2.45 | Instantiating (107) with all_15_0_14, all_15_1_15, all_15_2_16, all_15_3_17 yields:
% 7.80/2.45 | (117) sdtasdt0(all_15_3_17, xl) = all_15_2_16 & sdtasdt0(all_0_0_0, xl) = all_15_1_15 & sdtasdt0(all_0_5_5, xl) = all_15_0_14 & sdtasdt0(xl, all_15_3_17) = all_0_4_4 & sdtpldt0(all_15_1_15, all_15_0_14) = all_15_2_16 & sdtpldt0(all_0_0_0, all_0_5_5) = all_15_3_17
% 7.80/2.45 |
% 7.80/2.45 | Applying alpha-rule on (117) yields:
% 7.80/2.45 | (118) sdtasdt0(all_0_5_5, xl) = all_15_0_14
% 7.80/2.45 | (119) sdtasdt0(all_0_0_0, xl) = all_15_1_15
% 7.80/2.45 | (120) sdtasdt0(xl, all_15_3_17) = all_0_4_4
% 7.80/2.45 | (121) sdtpldt0(all_0_0_0, all_0_5_5) = all_15_3_17
% 7.80/2.45 | (122) sdtasdt0(all_15_3_17, xl) = all_15_2_16
% 7.80/2.45 | (123) sdtpldt0(all_15_1_15, all_15_0_14) = all_15_2_16
% 7.80/2.45 |
% 7.80/2.45 | Instantiating (103) with all_17_0_18, all_17_1_19, all_17_2_20, all_17_3_21 yields:
% 7.80/2.45 | (124) sdtasdt0(all_17_3_21, xl) = all_17_2_20 & sdtasdt0(all_0_0_0, xl) = all_17_1_19 & sdtasdt0(all_0_1_1, xl) = all_17_0_18 & sdtasdt0(xl, all_17_3_21) = all_0_4_4 & sdtpldt0(all_17_1_19, all_17_0_18) = all_17_2_20 & sdtpldt0(all_0_0_0, all_0_1_1) = all_17_3_21
% 7.80/2.45 |
% 7.80/2.45 | Applying alpha-rule on (124) yields:
% 7.80/2.45 | (125) sdtasdt0(all_17_3_21, xl) = all_17_2_20
% 7.80/2.45 | (126) sdtasdt0(all_0_0_0, xl) = all_17_1_19
% 7.80/2.45 | (127) sdtasdt0(xl, all_17_3_21) = all_0_4_4
% 7.80/2.45 | (128) sdtasdt0(all_0_1_1, xl) = all_17_0_18
% 7.80/2.45 | (129) sdtpldt0(all_17_1_19, all_17_0_18) = all_17_2_20
% 7.80/2.45 | (130) sdtpldt0(all_0_0_0, all_0_1_1) = all_17_3_21
% 7.80/2.45 |
% 7.80/2.45 | Instantiating (104) with all_19_0_22, all_19_1_23, all_19_2_24, all_19_3_25 yields:
% 7.80/2.45 | (131) sdtasdt0(all_19_3_25, xl) = all_19_2_24 & sdtasdt0(all_0_1_1, xl) = all_19_0_22 & sdtasdt0(all_0_6_6, xl) = all_19_1_23 & sdtasdt0(xl, all_19_3_25) = all_0_4_4 & sdtpldt0(all_19_1_23, all_19_0_22) = all_19_2_24 & sdtpldt0(all_0_6_6, all_0_1_1) = all_19_3_25
% 7.80/2.45 |
% 7.80/2.45 | Applying alpha-rule on (131) yields:
% 7.80/2.45 | (132) sdtpldt0(all_0_6_6, all_0_1_1) = all_19_3_25
% 7.80/2.45 | (133) sdtasdt0(xl, all_19_3_25) = all_0_4_4
% 7.80/2.45 | (134) sdtasdt0(all_0_6_6, xl) = all_19_1_23
% 7.80/2.45 | (135) sdtpldt0(all_19_1_23, all_19_0_22) = all_19_2_24
% 7.80/2.45 | (136) sdtasdt0(all_19_3_25, xl) = all_19_2_24
% 7.80/2.45 | (137) sdtasdt0(all_0_1_1, xl) = all_19_0_22
% 7.80/2.45 |
% 7.80/2.45 | Instantiating (108) with all_21_0_26, all_21_1_27, all_21_2_28, all_21_3_29 yields:
% 7.80/2.45 | (138) sdtasdt0(all_21_3_29, xl) = all_21_2_28 & sdtasdt0(all_0_5_5, xl) = all_21_0_26 & sdtasdt0(all_0_6_6, xl) = all_21_1_27 & sdtasdt0(xl, all_21_3_29) = all_0_4_4 & sdtpldt0(all_21_1_27, all_21_0_26) = all_21_2_28 & sdtpldt0(all_0_6_6, all_0_5_5) = all_21_3_29
% 7.80/2.45 |
% 7.80/2.45 | Applying alpha-rule on (138) yields:
% 7.80/2.45 | (139) sdtasdt0(all_0_6_6, xl) = all_21_1_27
% 7.80/2.45 | (140) sdtasdt0(all_21_3_29, xl) = all_21_2_28
% 7.80/2.45 | (141) sdtpldt0(all_21_1_27, all_21_0_26) = all_21_2_28
% 7.80/2.45 | (142) sdtasdt0(all_0_5_5, xl) = all_21_0_26
% 7.80/2.45 | (143) sdtasdt0(xl, all_21_3_29) = all_0_4_4
% 7.80/2.45 | (144) sdtpldt0(all_0_6_6, all_0_5_5) = all_21_3_29
% 7.80/2.45 |
% 7.80/2.45 +-Applying beta-rule and splitting (100), into two cases.
% 7.80/2.45 |-Branch one:
% 7.80/2.45 | (145) xl = sz00
% 7.80/2.45 |
% 7.80/2.45 | Equations (145) can reduce 10 to:
% 7.80/2.45 | (146) $false
% 7.80/2.45 |
% 7.80/2.45 |-The branch is then unsatisfiable
% 7.80/2.45 |-Branch two:
% 7.80/2.45 | (10) ~ (xl = sz00)
% 7.80/2.45 | (148) all_0_0_0 = all_0_6_6
% 7.80/2.45 |
% 7.80/2.45 | From (148) and (126) follows:
% 7.80/2.45 | (149) sdtasdt0(all_0_6_6, xl) = all_17_1_19
% 7.80/2.45 |
% 7.80/2.45 | From (148) and (119) follows:
% 7.80/2.45 | (150) sdtasdt0(all_0_6_6, xl) = all_15_1_15
% 7.80/2.45 |
% 7.80/2.45 | From (148) and (102) follows:
% 7.80/2.46 | (151) sdtasdt0(all_0_6_6, xl) = xm
% 7.80/2.46 |
% 7.80/2.46 | From (148) and (25) follows:
% 7.80/2.46 | (17) sdtasdt0(xl, all_0_6_6) = xm
% 7.80/2.46 |
% 7.80/2.46 +-Applying beta-rule and splitting (101), into two cases.
% 7.80/2.46 |-Branch one:
% 7.80/2.46 | (145) xl = sz00
% 7.80/2.46 |
% 7.80/2.46 | Equations (145) can reduce 10 to:
% 7.80/2.46 | (146) $false
% 7.80/2.46 |
% 7.80/2.46 |-The branch is then unsatisfiable
% 7.80/2.46 |-Branch two:
% 7.80/2.46 | (10) ~ (xl = sz00)
% 7.80/2.46 | (156) all_0_1_1 = all_0_5_5
% 7.80/2.46 |
% 7.80/2.46 | From (156) and (137) follows:
% 7.80/2.46 | (157) sdtasdt0(all_0_5_5, xl) = all_19_0_22
% 7.80/2.46 |
% 7.80/2.46 | From (156) and (128) follows:
% 7.80/2.46 | (158) sdtasdt0(all_0_5_5, xl) = all_17_0_18
% 7.80/2.46 |
% 7.80/2.46 | From (156) and (105) follows:
% 7.80/2.46 | (159) sdtasdt0(all_0_5_5, xl) = xn
% 7.80/2.46 |
% 7.80/2.46 | From (156) and (12) follows:
% 7.80/2.46 | (46) sdtasdt0(xl, all_0_5_5) = xn
% 7.80/2.46 |
% 7.80/2.46 | Instantiating formula (28) with all_0_5_5, xl, all_19_0_22, all_21_0_26 and discharging atoms sdtasdt0(all_0_5_5, xl) = all_21_0_26, sdtasdt0(all_0_5_5, xl) = all_19_0_22, yields:
% 7.80/2.46 | (161) all_21_0_26 = all_19_0_22
% 7.80/2.46 |
% 7.80/2.46 | Instantiating formula (28) with all_0_5_5, xl, all_17_0_18, all_19_0_22 and discharging atoms sdtasdt0(all_0_5_5, xl) = all_19_0_22, sdtasdt0(all_0_5_5, xl) = all_17_0_18, yields:
% 7.80/2.46 | (162) all_19_0_22 = all_17_0_18
% 7.80/2.46 |
% 7.80/2.46 | Instantiating formula (28) with all_0_5_5, xl, all_15_0_14, all_19_0_22 and discharging atoms sdtasdt0(all_0_5_5, xl) = all_19_0_22, sdtasdt0(all_0_5_5, xl) = all_15_0_14, yields:
% 7.80/2.46 | (163) all_19_0_22 = all_15_0_14
% 7.80/2.46 |
% 7.80/2.46 | Instantiating formula (28) with all_0_5_5, xl, all_11_0_8, all_21_0_26 and discharging atoms sdtasdt0(all_0_5_5, xl) = all_21_0_26, sdtasdt0(all_0_5_5, xl) = all_11_0_8, yields:
% 7.80/2.46 | (164) all_21_0_26 = all_11_0_8
% 7.80/2.46 |
% 7.80/2.46 | Instantiating formula (28) with all_0_5_5, xl, xn, all_15_0_14 and discharging atoms sdtasdt0(all_0_5_5, xl) = all_15_0_14, sdtasdt0(all_0_5_5, xl) = xn, yields:
% 7.80/2.46 | (165) all_15_0_14 = xn
% 7.80/2.46 |
% 7.80/2.46 | Instantiating formula (28) with all_0_6_6, xl, all_19_1_23, all_21_1_27 and discharging atoms sdtasdt0(all_0_6_6, xl) = all_21_1_27, sdtasdt0(all_0_6_6, xl) = all_19_1_23, yields:
% 7.80/2.46 | (166) all_21_1_27 = all_19_1_23
% 7.80/2.46 |
% 7.80/2.46 | Instantiating formula (28) with all_0_6_6, xl, all_17_1_19, all_19_1_23 and discharging atoms sdtasdt0(all_0_6_6, xl) = all_19_1_23, sdtasdt0(all_0_6_6, xl) = all_17_1_19, yields:
% 7.80/2.46 | (167) all_19_1_23 = all_17_1_19
% 7.80/2.46 |
% 7.80/2.46 | Instantiating formula (28) with all_0_6_6, xl, all_15_1_15, all_17_1_19 and discharging atoms sdtasdt0(all_0_6_6, xl) = all_17_1_19, sdtasdt0(all_0_6_6, xl) = all_15_1_15, yields:
% 7.80/2.46 | (168) all_17_1_19 = all_15_1_15
% 7.80/2.46 |
% 7.80/2.46 | Instantiating formula (28) with all_0_6_6, xl, all_11_1_9, all_15_1_15 and discharging atoms sdtasdt0(all_0_6_6, xl) = all_15_1_15, sdtasdt0(all_0_6_6, xl) = all_11_1_9, yields:
% 7.80/2.46 | (169) all_15_1_15 = all_11_1_9
% 7.80/2.46 |
% 7.80/2.46 | Instantiating formula (28) with all_0_6_6, xl, xm, all_21_1_27 and discharging atoms sdtasdt0(all_0_6_6, xl) = all_21_1_27, sdtasdt0(all_0_6_6, xl) = xm, yields:
% 7.80/2.46 | (170) all_21_1_27 = xm
% 7.80/2.46 |
% 7.80/2.46 | Instantiating formula (28) with xl, all_0_5_5, all_11_3_11, xn and discharging atoms sdtasdt0(xl, all_0_5_5) = all_11_3_11, sdtasdt0(xl, all_0_5_5) = xn, yields:
% 7.80/2.46 | (171) all_11_3_11 = xn
% 7.80/2.46 |
% 7.80/2.46 | Instantiating formula (28) with xl, all_0_6_6, all_11_4_12, xm and discharging atoms sdtasdt0(xl, all_0_6_6) = all_11_4_12, sdtasdt0(xl, all_0_6_6) = xm, yields:
% 7.80/2.46 | (172) all_11_4_12 = xm
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (161,164) yields a new equation:
% 7.80/2.46 | (173) all_19_0_22 = all_11_0_8
% 7.80/2.46 |
% 7.80/2.46 | Simplifying 173 yields:
% 7.80/2.46 | (174) all_19_0_22 = all_11_0_8
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (166,170) yields a new equation:
% 7.80/2.46 | (175) all_19_1_23 = xm
% 7.80/2.46 |
% 7.80/2.46 | Simplifying 175 yields:
% 7.80/2.46 | (176) all_19_1_23 = xm
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (174,162) yields a new equation:
% 7.80/2.46 | (177) all_17_0_18 = all_11_0_8
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (163,162) yields a new equation:
% 7.80/2.46 | (178) all_17_0_18 = all_15_0_14
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (167,176) yields a new equation:
% 7.80/2.46 | (179) all_17_1_19 = xm
% 7.80/2.46 |
% 7.80/2.46 | Simplifying 179 yields:
% 7.80/2.46 | (180) all_17_1_19 = xm
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (178,177) yields a new equation:
% 7.80/2.46 | (181) all_15_0_14 = all_11_0_8
% 7.80/2.46 |
% 7.80/2.46 | Simplifying 181 yields:
% 7.80/2.46 | (182) all_15_0_14 = all_11_0_8
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (168,180) yields a new equation:
% 7.80/2.46 | (183) all_15_1_15 = xm
% 7.80/2.46 |
% 7.80/2.46 | Simplifying 183 yields:
% 7.80/2.46 | (184) all_15_1_15 = xm
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (165,182) yields a new equation:
% 7.80/2.46 | (185) all_11_0_8 = xn
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (169,184) yields a new equation:
% 7.80/2.46 | (186) all_11_1_9 = xm
% 7.80/2.46 |
% 7.80/2.46 | Simplifying 186 yields:
% 7.80/2.46 | (187) all_11_1_9 = xm
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (185,182) yields a new equation:
% 7.80/2.46 | (165) all_15_0_14 = xn
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (185,177) yields a new equation:
% 7.80/2.46 | (189) all_17_0_18 = xn
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (189,162) yields a new equation:
% 7.80/2.46 | (190) all_19_0_22 = xn
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (185,164) yields a new equation:
% 7.80/2.46 | (191) all_21_0_26 = xn
% 7.80/2.46 |
% 7.80/2.46 | From (170)(191) and (141) follows:
% 7.80/2.46 | (192) sdtpldt0(xm, xn) = all_21_2_28
% 7.80/2.46 |
% 7.80/2.46 | From (176)(190) and (135) follows:
% 7.80/2.46 | (193) sdtpldt0(xm, xn) = all_19_2_24
% 7.80/2.46 |
% 7.80/2.46 | From (180)(189) and (129) follows:
% 7.80/2.46 | (194) sdtpldt0(xm, xn) = all_17_2_20
% 7.80/2.46 |
% 7.80/2.46 | From (184)(165) and (123) follows:
% 7.80/2.46 | (195) sdtpldt0(xm, xn) = all_15_2_16
% 7.80/2.46 |
% 7.80/2.46 | From (187)(185) and (116) follows:
% 7.80/2.46 | (196) sdtpldt0(xm, xn) = all_11_2_10
% 7.80/2.46 |
% 7.80/2.46 | From (172)(171) and (115) follows:
% 7.80/2.46 | (197) sdtpldt0(xm, xn) = all_0_2_2
% 7.80/2.46 |
% 7.80/2.46 | Instantiating formula (14) with xm, xn, all_19_2_24, all_21_2_28 and discharging atoms sdtpldt0(xm, xn) = all_21_2_28, sdtpldt0(xm, xn) = all_19_2_24, yields:
% 7.80/2.46 | (198) all_21_2_28 = all_19_2_24
% 7.80/2.46 |
% 7.80/2.46 | Instantiating formula (14) with xm, xn, all_17_2_20, all_19_2_24 and discharging atoms sdtpldt0(xm, xn) = all_19_2_24, sdtpldt0(xm, xn) = all_17_2_20, yields:
% 7.80/2.46 | (199) all_19_2_24 = all_17_2_20
% 7.80/2.46 |
% 7.80/2.46 | Instantiating formula (14) with xm, xn, all_15_2_16, all_21_2_28 and discharging atoms sdtpldt0(xm, xn) = all_21_2_28, sdtpldt0(xm, xn) = all_15_2_16, yields:
% 7.80/2.46 | (200) all_21_2_28 = all_15_2_16
% 7.80/2.46 |
% 7.80/2.46 | Instantiating formula (14) with xm, xn, all_11_2_10, all_0_4_4 and discharging atoms sdtpldt0(xm, xn) = all_11_2_10, sdtpldt0(xm, xn) = all_0_4_4, yields:
% 7.80/2.46 | (201) all_11_2_10 = all_0_4_4
% 7.80/2.46 |
% 7.80/2.46 | Instantiating formula (14) with xm, xn, all_11_2_10, all_21_2_28 and discharging atoms sdtpldt0(xm, xn) = all_21_2_28, sdtpldt0(xm, xn) = all_11_2_10, yields:
% 7.80/2.46 | (202) all_21_2_28 = all_11_2_10
% 7.80/2.46 |
% 7.80/2.46 | Instantiating formula (14) with xm, xn, all_0_2_2, all_19_2_24 and discharging atoms sdtpldt0(xm, xn) = all_19_2_24, sdtpldt0(xm, xn) = all_0_2_2, yields:
% 7.80/2.46 | (203) all_19_2_24 = all_0_2_2
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (198,200) yields a new equation:
% 7.80/2.46 | (204) all_19_2_24 = all_15_2_16
% 7.80/2.46 |
% 7.80/2.46 | Simplifying 204 yields:
% 7.80/2.46 | (205) all_19_2_24 = all_15_2_16
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (202,200) yields a new equation:
% 7.80/2.46 | (206) all_15_2_16 = all_11_2_10
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (203,199) yields a new equation:
% 7.80/2.46 | (207) all_17_2_20 = all_0_2_2
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (205,199) yields a new equation:
% 7.80/2.46 | (208) all_17_2_20 = all_15_2_16
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (208,207) yields a new equation:
% 7.80/2.46 | (209) all_15_2_16 = all_0_2_2
% 7.80/2.46 |
% 7.80/2.46 | Simplifying 209 yields:
% 7.80/2.46 | (210) all_15_2_16 = all_0_2_2
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (206,210) yields a new equation:
% 7.80/2.46 | (211) all_11_2_10 = all_0_2_2
% 7.80/2.46 |
% 7.80/2.46 | Simplifying 211 yields:
% 7.80/2.46 | (212) all_11_2_10 = all_0_2_2
% 7.80/2.46 |
% 7.80/2.46 | Combining equations (201,212) yields a new equation:
% 7.80/2.46 | (213) all_0_2_2 = all_0_4_4
% 7.80/2.46 |
% 7.80/2.46 | Equations (213) can reduce 61 to:
% 7.80/2.46 | (146) $false
% 7.80/2.46 |
% 7.80/2.46 |-The branch is then unsatisfiable
% 7.80/2.46 % SZS output end Proof for theBenchmark
% 7.80/2.46
% 7.80/2.46 1851ms
%------------------------------------------------------------------------------