TSTP Solution File: NUM478+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM478+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n018.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 08:44:55 EDT 2022
% Result : Theorem 5.52s 1.97s
% Output : Proof 9.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM478+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n018.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 : Fri Jul 8 00:26:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.65/0.64 ____ _
% 0.65/0.64 ___ / __ \_____(_)___ ________ __________
% 0.65/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.65/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.65/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.65/0.64
% 0.65/0.64 A Theorem Prover for First-Order Logic
% 0.65/0.64 (ePrincess v.1.0)
% 0.65/0.64
% 0.65/0.64 (c) Philipp Rümmer, 2009-2015
% 0.65/0.64 (c) Peter Backeman, 2014-2015
% 0.65/0.64 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.65/0.64 Free software under GNU Lesser General Public License (LGPL).
% 0.65/0.64 Bug reports to peter@backeman.se
% 0.65/0.64
% 0.65/0.64 For more information, visit http://user.uu.se/~petba168/breu/
% 0.65/0.64
% 0.65/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.92/1.07 Prover 0: Preprocessing ...
% 3.45/1.49 Prover 0: Constructing countermodel ...
% 5.52/1.96 Prover 0: proved (1271ms)
% 5.52/1.97
% 5.52/1.97 No countermodel exists, formula is valid
% 5.52/1.97 % SZS status Theorem for theBenchmark
% 5.52/1.97
% 5.52/1.97 Generating proof ... found it (size 55)
% 8.67/2.75
% 8.67/2.75 % SZS output start Proof for theBenchmark
% 8.67/2.75 Assumed formulas after preprocessing and simplification:
% 8.67/2.75 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v1) & ~ (xl = sz00) & ~ (sz10 = sz00) & sdtsldt0(v2, xl) = v3 & sdtsldt0(xm, xl) = v0 & sdtasdt0(xn, v0) = v1 & sdtasdt0(xn, xm) = v2 & doDivides0(xl, xm) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & aNaturalNumber0(xl) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v6, v4) = v8) | ~ (sdtasdt0(v5, v4) = v7) | ~ (sdtpldt0(v7, v8) = v9) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (sdtasdt0(v10, v4) = v9 & sdtasdt0(v4, v10) = v11 & sdtasdt0(v4, v6) = v13 & sdtasdt0(v4, v5) = v12 & sdtpldt0(v12, v13) = v11 & sdtpldt0(v5, v6) = v10)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v4, v6) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ (sdtpldt0(v7, v8) = v9) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (sdtasdt0(v10, v4) = v11 & sdtasdt0(v6, v4) = v13 & sdtasdt0(v5, v4) = v12 & sdtasdt0(v4, v10) = v9 & sdtpldt0(v12, v13) = v11 & sdtpldt0(v5, v6) = v10)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v8) | ~ (sdtasdt0(v5, v4) = v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v7, v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v8) | ~ (sdtasdt0(v5, v4) = v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtasdt0(v4, v6) = v10 & sdtasdt0(v4, v5) = v9 & sdtlseqdt0(v9, v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v8) | ~ (sdtasdt0(v5, v4) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtasdt0(v4, v6) = v10 & sdtasdt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtasdt0(v5, v4) = v10 & sdtasdt0(v4, v6) = v9 & sdtlseqdt0(v10, v8) & sdtlseqdt0(v7, v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtasdt0(v5, v4) = v10 & sdtasdt0(v4, v6) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v5, v4) = v8) | ~ (sdtasdt0(v4, v6) = v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtasdt0(v6, v4) = v10 & sdtasdt0(v4, v5) = v9 & sdtlseqdt0(v9, v7) & sdtlseqdt0(v8, v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v5, v4) = v8) | ~ (sdtasdt0(v4, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtasdt0(v6, v4) = v10 & sdtasdt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v4, v6) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v7, v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v4, v6) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtasdt0(v6, v4) = v10 & sdtasdt0(v5, v4) = v9 & sdtlseqdt0(v9, v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v4, v6) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtasdt0(v6, v4) = v10 & sdtasdt0(v5, v4) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v6, v4) = v8) | ~ (sdtpldt0(v5, v4) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtpldt0(v4, v6) = v10 & sdtpldt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v6, v4) = v8) | ~ (sdtpldt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtpldt0(v5, v4) = v10 & sdtpldt0(v4, v6) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v5, v4) = v8) | ~ (sdtpldt0(v4, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtpldt0(v6, v4) = v10 & sdtpldt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v4, v6) = v8) | ~ (sdtpldt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtpldt0(v6, v4) = v10 & sdtpldt0(v5, v4) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v7, v6) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : (sdtasdt0(v5, v6) = v9 & sdtasdt0(v4, v9) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v7, v4) = v8) | ~ (sdtpldt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (sdtasdt0(v6, v4) = v13 & sdtasdt0(v5, v4) = v12 & sdtasdt0(v4, v7) = v9 & sdtasdt0(v4, v6) = v11 & sdtasdt0(v4, v5) = v10 & sdtpldt0(v12, v13) = v8 & sdtpldt0(v10, v11) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v5, v6) = v7) | ~ (sdtasdt0(v4, v7) = v8) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : (sdtasdt0(v9, v6) = v8 & sdtasdt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v4, v7) = v8) | ~ (sdtpldt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (sdtasdt0(v7, v4) = v11 & sdtasdt0(v6, v4) = v13 & sdtasdt0(v5, v4) = v12 & sdtasdt0(v4, v6) = v10 & sdtasdt0(v4, v5) = v9 & sdtpldt0(v12, v13) = v11 & sdtpldt0(v9, v10) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v7, v6) = v8) | ~ (sdtpldt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : (sdtpldt0(v5, v6) = v9 & sdtpldt0(v4, v9) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ (sdtpldt0(v4, v7) = v8) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : (sdtpldt0(v9, v6) = v8 & sdtpldt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | v4 = sz00 | ~ (sdtsldt0(v5, v4) = v6) | ~ (sdtasdt0(v4, v7) = v5) | ~ doDivides0(v4, v5) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (sdtmndt0(v5, v4) = v6) | ~ (sdtpldt0(v4, v7) = v5) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | v4 = sz00 | ~ (sdtsldt0(v5, v4) = v6) | ~ (sdtasdt0(v4, v6) = v7) | ~ doDivides0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (sdtmndt0(v5, v4) = v6) | ~ (sdtpldt0(v4, v6) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v7) | ~ (sdtasdt0(v5, v4) = v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v7) | ~ (sdtasdt0(v5, v4) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v4, v6) = v7) | ~ (sdtasdt0(v4, v5) = v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v4, v6) = v7) | ~ (sdtasdt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (sdtpldt0(v6, v4) = v7) | ~ (sdtpldt0(v5, v4) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (sdtpldt0(v4, v6) = v7) | ~ (sdtpldt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtsldt0(v7, v6) = v5) | ~ (sdtsldt0(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtmndt0(v7, v6) = v5) | ~ (sdtmndt0(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtasdt0(v7, v6) = v5) | ~ (sdtasdt0(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v7, v6) = v5) | ~ (sdtpldt0(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v6, v5) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = v9) & ~ (v8 = v7) & sdtpldt0(v6, v4) = v8 & sdtpldt0(v5, v6) = v10 & sdtpldt0(v4, v6) = v9 & sdtlseqdt0(v9, v10) & sdtlseqdt0(v8, v7))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v6, v4) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = v9) & ~ (v8 = v7) & sdtpldt0(v6, v5) = v8 & sdtpldt0(v5, v6) = v10 & sdtpldt0(v4, v6) = v9 & sdtlseqdt0(v9, v10) & sdtlseqdt0(v7, v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v5, v6) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = v7) & ~ (v9 = v8) & sdtpldt0(v6, v5) = v9 & sdtpldt0(v6, v4) = v8 & sdtpldt0(v4, v6) = v10 & sdtlseqdt0(v10, v7) & sdtlseqdt0(v8, v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v4, v6) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = v7) & ~ (v9 = v8) & sdtpldt0(v6, v5) = v9 & sdtpldt0(v6, v4) = v8 & sdtpldt0(v5, v6) = v10 & sdtlseqdt0(v8, v9) & sdtlseqdt0(v7, v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v4 = sz00 | ~ (sdtsldt0(v5, v4) = v6) | ~ (sdtasdt0(v4, v6) = v7) | ~ doDivides0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | aNaturalNumber0(v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtmndt0(v5, v4) = v6) | ~ (sdtpldt0(v4, v6) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | aNaturalNumber0(v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ doDivides0(v4, v7) | ~ doDivides0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | doDivides0(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ doDivides0(v4, v6) | ~ doDivides0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | doDivides0(v4, v7)) & ! [v4] : ! [v5] : ! [v6] : (v4 = sz00 | ~ (sdtasdt0(v5, v4) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v5, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, v4) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtasdt0(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v4, v6) = v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | doDivides0(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v4, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtasdt0(v5, v4) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v4, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | aNaturalNumber0(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v5, v4) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtpldt0(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v4, v6) = v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v4, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtpldt0(v5, v4) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v4, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | aNaturalNumber0(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ doDivides0(v5, v6) | ~ doDivides0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | doDivides0(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ sdtlseqdt0(v5, v6) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v4, v6)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtasdt0(v4, sz10) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtasdt0(sz10, v4) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtpldt0(v4, sz00) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtpldt0(sz00, v4) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ sdtlseqdt0(v5, v4) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | iLess0(v4, v5)) & ! [v4] : ! [v5] : (v5 = sz00 | v4 = sz00 | ~ (sdtasdt0(v4, v5) = sz00) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = sz00 | ~ (sdtasdt0(v4, sz00) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = sz00 | ~ (sdtasdt0(sz00, v4) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = sz00 | ~ (sdtpldt0(v4, v5) = sz00) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = sz00 | ~ doDivides0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v4, v5)) & ! [v4] : ! [v5] : (v4 = sz00 | ~ (sdtpldt0(v4, v5) = sz00) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ( ~ (sdtasdt0(v4, sz10) = v5) | ~ aNaturalNumber0(v4) | sdtasdt0(sz10, v4) = v4) & ! [v4] : ! [v5] : ( ~ (sdtasdt0(v4, sz00) = v5) | ~ aNaturalNumber0(v4) | sdtasdt0(sz00, v4) = sz00) & ! [v4] : ! [v5] : ( ~ (sdtasdt0(sz10, v4) = v5) | ~ aNaturalNumber0(v4) | sdtasdt0(v4, sz10) = v4) & ! [v4] : ! [v5] : ( ~ (sdtasdt0(sz00, v4) = v5) | ~ aNaturalNumber0(v4) | sdtasdt0(v4, sz00) = sz00) & ! [v4] : ! [v5] : ( ~ (sdtpldt0(v4, sz00) = v5) | ~ aNaturalNumber0(v4) | sdtpldt0(sz00, v4) = v4) & ! [v4] : ! [v5] : ( ~ (sdtpldt0(sz00, v4) = v5) | ~ aNaturalNumber0(v4) | sdtpldt0(v4, sz00) = v4) & ! [v4] : ! [v5] : ( ~ doDivides0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v6] : (sdtasdt0(v4, v6) = v5 & aNaturalNumber0(v6))) & ! [v4] : ! [v5] : ( ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v6] : (sdtpldt0(v4, v6) = v5 & aNaturalNumber0(v6))) & ! [v4] : ! [v5] : ( ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v5, v4) | sdtlseqdt0(v4, v5)) & ! [v4] : (v4 = sz10 | v4 = sz00 | ~ aNaturalNumber0(v4) | sdtlseqdt0(sz10, v4)) & ! [v4] : ( ~ aNaturalNumber0(v4) | sdtlseqdt0(v4, v4)))
% 9.09/2.81 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 9.09/2.81 | (1) ~ (all_0_0_0 = all_0_2_2) & ~ (xl = sz00) & ~ (sz10 = sz00) & sdtsldt0(all_0_1_1, xl) = all_0_0_0 & sdtsldt0(xm, xl) = all_0_3_3 & sdtasdt0(xn, all_0_3_3) = all_0_2_2 & sdtasdt0(xn, xm) = all_0_1_1 & 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))
% 9.38/2.83 |
% 9.38/2.83 | Applying alpha-rule on (1) yields:
% 9.38/2.83 | (2) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00)
% 9.38/2.83 | (3) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 9.38/2.83 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 9.38/2.83 | (5) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0)
% 9.38/2.83 | (6) ! [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)))
% 9.38/2.83 | (7) ! [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))
% 9.38/2.83 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 9.38/2.83 | (9) ! [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))
% 9.38/2.83 | (10) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 9.38/2.83 | (11) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 9.38/2.83 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 9.38/2.83 | (13) ! [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))
% 9.38/2.83 | (14) ! [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)))
% 9.38/2.83 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 9.38/2.83 | (16) ! [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)))
% 9.38/2.83 | (17) aNaturalNumber0(sz10)
% 9.38/2.83 | (18) ! [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))
% 9.38/2.84 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 9.38/2.84 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 9.38/2.84 | (21) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 9.38/2.84 | (22) ! [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))
% 9.38/2.84 | (23) aNaturalNumber0(xl)
% 9.38/2.84 | (24) ! [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))
% 9.38/2.84 | (25) ! [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))
% 9.38/2.84 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 9.38/2.84 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2)
% 9.38/2.84 | (28) ! [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))
% 9.38/2.84 | (29) ! [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))
% 9.38/2.84 | (30) sdtsldt0(xm, xl) = all_0_3_3
% 9.38/2.84 | (31) ! [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))
% 9.38/2.84 | (32) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 9.38/2.84 | (33) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 9.38/2.84 | (34) ! [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)))
% 9.38/2.84 | (35) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 9.38/2.84 | (36) ! [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))
% 9.38/2.84 | (37) ~ (all_0_0_0 = all_0_2_2)
% 9.38/2.84 | (38) ! [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))
% 9.38/2.84 | (39) ~ (xl = sz00)
% 9.38/2.84 | (40) ! [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))
% 9.38/2.84 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 9.38/2.84 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 9.38/2.84 | (43) sdtasdt0(xn, xm) = all_0_1_1
% 9.38/2.84 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 9.38/2.84 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 9.38/2.84 | (46) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0)
% 9.38/2.84 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 9.38/2.84 | (48) ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 9.38/2.84 | (49) ! [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))
% 9.38/2.84 | (50) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 9.38/2.84 | (51) aNaturalNumber0(xm)
% 9.38/2.84 | (52) ! [v0] : ! [v1] : (v1 = sz00 | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 9.38/2.84 | (53) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 9.38/2.84 | (54) ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 9.38/2.84 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2)
% 9.38/2.84 | (56) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0))
% 9.38/2.84 | (57) ! [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))
% 9.38/2.84 | (58) ! [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))
% 9.38/2.84 | (59) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 9.38/2.84 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 9.38/2.84 | (61) sdtsldt0(all_0_1_1, xl) = all_0_0_0
% 9.38/2.84 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 9.38/2.84 | (63) ! [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))
% 9.38/2.84 | (64) ! [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))
% 9.38/2.84 | (65) ! [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)))
% 9.38/2.84 | (66) aNaturalNumber0(sz00)
% 9.38/2.84 | (67) aNaturalNumber0(xn)
% 9.38/2.84 | (68) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 9.38/2.84 | (69) ! [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))
% 9.38/2.84 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 9.38/2.84 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 9.38/2.84 | (72) ~ (sz10 = sz00)
% 9.38/2.84 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3))
% 9.38/2.85 | (74) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 9.38/2.85 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 9.38/2.85 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 9.38/2.85 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 9.38/2.85 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 9.38/2.85 | (79) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 9.38/2.85 | (80) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 9.38/2.85 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 9.38/2.85 | (82) ! [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))
% 9.38/2.85 | (83) ! [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))
% 9.38/2.85 | (84) ! [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)))
% 9.38/2.85 | (85) sdtasdt0(xn, all_0_3_3) = all_0_2_2
% 9.38/2.85 | (86) ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 9.38/2.85 | (87) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0))
% 9.38/2.85 | (88) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 9.38/2.85 | (89) ! [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)))
% 9.38/2.85 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 9.38/2.85 | (91) ! [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)))
% 9.38/2.85 | (92) doDivides0(xl, xm)
% 9.38/2.85 |
% 9.38/2.85 | Instantiating formula (50) with xn, xn and discharging atoms aNaturalNumber0(xn), yields:
% 9.38/2.85 | (93) sdtlseqdt0(xn, xn)
% 9.38/2.85 |
% 9.38/2.85 | Instantiating formula (55) with all_0_1_1, xn, xm and discharging atoms sdtasdt0(xn, xm) = all_0_1_1, aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 9.38/2.85 | (94) sdtasdt0(xm, xn) = all_0_1_1
% 9.38/2.85 |
% 9.38/2.85 | Instantiating formula (76) with all_0_1_1, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_1_1, aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 9.38/2.85 | (95) aNaturalNumber0(all_0_1_1)
% 9.38/2.85 |
% 9.38/2.85 | Instantiating formula (54) with xm, xl and discharging atoms doDivides0(xl, xm), aNaturalNumber0(xm), aNaturalNumber0(xl), yields:
% 9.38/2.85 | (96) ? [v0] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0))
% 9.38/2.85 |
% 9.38/2.85 | Instantiating (96) with all_9_0_4 yields:
% 9.38/2.85 | (97) sdtasdt0(xl, all_9_0_4) = xm & aNaturalNumber0(all_9_0_4)
% 9.38/2.85 |
% 9.38/2.85 | Applying alpha-rule on (97) yields:
% 9.38/2.85 | (98) sdtasdt0(xl, all_9_0_4) = xm
% 9.38/2.85 | (99) aNaturalNumber0(all_9_0_4)
% 9.38/2.85 |
% 9.38/2.85 | Instantiating formula (25) with all_9_0_4, all_0_3_3, xm, xl and discharging atoms sdtsldt0(xm, xl) = all_0_3_3, sdtasdt0(xl, all_9_0_4) = xm, doDivides0(xl, xm), aNaturalNumber0(all_9_0_4), aNaturalNumber0(xm), aNaturalNumber0(xl), yields:
% 9.38/2.85 | (100) all_9_0_4 = all_0_3_3 | xl = sz00
% 9.38/2.85 |
% 9.38/2.85 | Instantiating formula (79) with xn, xn and discharging atoms sdtlseqdt0(xn, xn), aNaturalNumber0(xn), yields:
% 9.38/2.85 | (101) ? [v0] : (sdtpldt0(xn, v0) = xn & aNaturalNumber0(v0))
% 9.38/2.85 |
% 9.38/2.85 | Instantiating formula (18) with all_0_1_1, xm, xn, all_9_0_4, xl and discharging atoms sdtasdt0(xm, xn) = all_0_1_1, sdtasdt0(xl, all_9_0_4) = xm, aNaturalNumber0(all_9_0_4), aNaturalNumber0(xn), aNaturalNumber0(xl), yields:
% 9.38/2.85 | (102) ? [v0] : (sdtasdt0(all_9_0_4, xn) = v0 & sdtasdt0(xl, v0) = all_0_1_1)
% 9.38/2.85 |
% 9.38/2.85 | Instantiating formula (55) with xm, xl, all_9_0_4 and discharging atoms sdtasdt0(xl, all_9_0_4) = xm, aNaturalNumber0(all_9_0_4), aNaturalNumber0(xl), yields:
% 9.38/2.85 | (103) sdtasdt0(all_9_0_4, xl) = xm
% 9.38/2.85 |
% 9.38/2.85 | Instantiating formula (90) with xn, all_0_1_1, xm and discharging atoms sdtasdt0(xm, xn) = all_0_1_1, aNaturalNumber0(all_0_1_1), aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 9.38/2.85 | (104) doDivides0(xm, all_0_1_1)
% 9.38/2.85 |
% 9.38/2.85 | Instantiating (102) with all_19_0_6 yields:
% 9.38/2.85 | (105) sdtasdt0(all_9_0_4, xn) = all_19_0_6 & sdtasdt0(xl, all_19_0_6) = all_0_1_1
% 9.38/2.85 |
% 9.38/2.85 | Applying alpha-rule on (105) yields:
% 9.38/2.85 | (106) sdtasdt0(all_9_0_4, xn) = all_19_0_6
% 9.38/2.85 | (107) sdtasdt0(xl, all_19_0_6) = all_0_1_1
% 9.38/2.85 |
% 9.38/2.85 | Instantiating (101) with all_29_0_11 yields:
% 9.38/2.85 | (108) sdtpldt0(xn, all_29_0_11) = xn & aNaturalNumber0(all_29_0_11)
% 9.38/2.85 |
% 9.38/2.85 | Applying alpha-rule on (108) yields:
% 9.38/2.85 | (109) sdtpldt0(xn, all_29_0_11) = xn
% 9.38/2.85 | (110) aNaturalNumber0(all_29_0_11)
% 9.38/2.85 |
% 9.38/2.85 +-Applying beta-rule and splitting (100), into two cases.
% 9.38/2.85 |-Branch one:
% 9.38/2.85 | (111) xl = sz00
% 9.38/2.85 |
% 9.38/2.85 | Equations (111) can reduce 39 to:
% 9.38/2.85 | (112) $false
% 9.38/2.85 |
% 9.38/2.85 |-The branch is then unsatisfiable
% 9.38/2.85 |-Branch two:
% 9.38/2.85 | (39) ~ (xl = sz00)
% 9.38/2.85 | (114) all_9_0_4 = all_0_3_3
% 9.38/2.85 |
% 9.38/2.85 | From (114) and (106) follows:
% 9.38/2.85 | (115) sdtasdt0(all_0_3_3, xn) = all_19_0_6
% 9.38/2.85 |
% 9.38/2.85 | From (114) and (103) follows:
% 9.38/2.85 | (116) sdtasdt0(all_0_3_3, xl) = xm
% 9.38/2.85 |
% 9.38/2.85 | From (114) and (99) follows:
% 9.38/2.85 | (117) aNaturalNumber0(all_0_3_3)
% 9.38/2.85 |
% 9.38/2.85 | Instantiating formula (86) with all_0_1_1, xm, xl and discharging atoms doDivides0(xm, all_0_1_1), doDivides0(xl, xm), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xm), aNaturalNumber0(xl), yields:
% 9.38/2.85 | (118) doDivides0(xl, all_0_1_1)
% 9.38/2.85 |
% 9.38/2.85 | Instantiating formula (83) with all_0_2_2, xn, all_29_0_11, xn, all_0_3_3 and discharging atoms sdtasdt0(xn, all_0_3_3) = all_0_2_2, sdtpldt0(xn, all_29_0_11) = xn, aNaturalNumber0(all_29_0_11), aNaturalNumber0(all_0_3_3), aNaturalNumber0(xn), yields:
% 9.38/2.85 | (119) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_29_0_11, all_0_3_3) = v4 & sdtasdt0(all_0_3_3, all_29_0_11) = v2 & sdtasdt0(all_0_3_3, xn) = v1 & sdtasdt0(all_0_3_3, xn) = v0 & sdtasdt0(xn, all_0_3_3) = v3 & sdtpldt0(v3, v4) = all_0_2_2 & sdtpldt0(v1, v2) = v0)
% 9.38/2.85 |
% 9.38/2.85 | Instantiating formula (58) with all_19_0_6, xn, all_29_0_11, xn, all_0_3_3 and discharging atoms sdtasdt0(all_0_3_3, xn) = all_19_0_6, sdtpldt0(xn, all_29_0_11) = xn, aNaturalNumber0(all_29_0_11), aNaturalNumber0(all_0_3_3), aNaturalNumber0(xn), yields:
% 9.38/2.86 | (120) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_29_0_11, all_0_3_3) = v4 & sdtasdt0(all_0_3_3, all_29_0_11) = v1 & sdtasdt0(all_0_3_3, xn) = v0 & sdtasdt0(xn, all_0_3_3) = v3 & sdtasdt0(xn, all_0_3_3) = v2 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_19_0_6)
% 9.38/2.86 |
% 9.38/2.86 | Instantiating formula (55) with all_19_0_6, all_0_3_3, xn and discharging atoms sdtasdt0(all_0_3_3, xn) = all_19_0_6, aNaturalNumber0(all_0_3_3), aNaturalNumber0(xn), yields:
% 9.38/2.86 | (121) sdtasdt0(xn, all_0_3_3) = all_19_0_6
% 9.38/2.86 |
% 9.38/2.86 | Instantiating formula (76) with all_19_0_6, xn, all_0_3_3 and discharging atoms sdtasdt0(all_0_3_3, xn) = all_19_0_6, aNaturalNumber0(all_0_3_3), aNaturalNumber0(xn), yields:
% 9.38/2.86 | (122) aNaturalNumber0(all_19_0_6)
% 9.38/2.86 |
% 9.38/2.86 | Instantiating formula (13) with all_0_1_1, xm, xl, all_0_3_3, xn and discharging atoms sdtasdt0(all_0_3_3, xl) = xm, sdtasdt0(xn, xm) = all_0_1_1, aNaturalNumber0(all_0_3_3), aNaturalNumber0(xn), aNaturalNumber0(xl), yields:
% 9.38/2.86 | (123) ? [v0] : (sdtasdt0(v0, xl) = all_0_1_1 & sdtasdt0(xn, all_0_3_3) = v0)
% 9.38/2.86 |
% 9.38/2.86 | Instantiating (123) with all_49_0_18 yields:
% 9.38/2.86 | (124) sdtasdt0(all_49_0_18, xl) = all_0_1_1 & sdtasdt0(xn, all_0_3_3) = all_49_0_18
% 9.38/2.86 |
% 9.38/2.86 | Applying alpha-rule on (124) yields:
% 9.38/2.86 | (125) sdtasdt0(all_49_0_18, xl) = all_0_1_1
% 9.38/2.86 | (126) sdtasdt0(xn, all_0_3_3) = all_49_0_18
% 9.38/2.86 |
% 9.38/2.86 | Instantiating (119) with all_53_0_24, all_53_1_25, all_53_2_26, all_53_3_27, all_53_4_28 yields:
% 9.38/2.86 | (127) sdtasdt0(all_29_0_11, all_0_3_3) = all_53_0_24 & sdtasdt0(all_0_3_3, all_29_0_11) = all_53_2_26 & sdtasdt0(all_0_3_3, xn) = all_53_3_27 & sdtasdt0(all_0_3_3, xn) = all_53_4_28 & sdtasdt0(xn, all_0_3_3) = all_53_1_25 & sdtpldt0(all_53_1_25, all_53_0_24) = all_0_2_2 & sdtpldt0(all_53_3_27, all_53_2_26) = all_53_4_28
% 9.38/2.86 |
% 9.38/2.86 | Applying alpha-rule on (127) yields:
% 9.38/2.86 | (128) sdtpldt0(all_53_3_27, all_53_2_26) = all_53_4_28
% 9.38/2.86 | (129) sdtasdt0(xn, all_0_3_3) = all_53_1_25
% 9.38/2.86 | (130) sdtasdt0(all_29_0_11, all_0_3_3) = all_53_0_24
% 9.38/2.86 | (131) sdtasdt0(all_0_3_3, xn) = all_53_3_27
% 9.38/2.86 | (132) sdtasdt0(all_0_3_3, xn) = all_53_4_28
% 9.38/2.86 | (133) sdtpldt0(all_53_1_25, all_53_0_24) = all_0_2_2
% 9.38/2.86 | (134) sdtasdt0(all_0_3_3, all_29_0_11) = all_53_2_26
% 9.38/2.86 |
% 9.38/2.86 | Instantiating (120) with all_67_0_47, all_67_1_48, all_67_2_49, all_67_3_50, all_67_4_51 yields:
% 9.38/2.86 | (135) sdtasdt0(all_29_0_11, all_0_3_3) = all_67_0_47 & sdtasdt0(all_0_3_3, all_29_0_11) = all_67_3_50 & sdtasdt0(all_0_3_3, xn) = all_67_4_51 & sdtasdt0(xn, all_0_3_3) = all_67_1_48 & sdtasdt0(xn, all_0_3_3) = all_67_2_49 & sdtpldt0(all_67_1_48, all_67_0_47) = all_67_2_49 & sdtpldt0(all_67_4_51, all_67_3_50) = all_19_0_6
% 9.38/2.86 |
% 9.38/2.86 | Applying alpha-rule on (135) yields:
% 9.38/2.86 | (136) sdtpldt0(all_67_4_51, all_67_3_50) = all_19_0_6
% 9.38/2.86 | (137) sdtasdt0(all_0_3_3, xn) = all_67_4_51
% 9.38/2.86 | (138) sdtasdt0(all_29_0_11, all_0_3_3) = all_67_0_47
% 9.38/2.86 | (139) sdtasdt0(all_0_3_3, all_29_0_11) = all_67_3_50
% 9.38/2.86 | (140) sdtpldt0(all_67_1_48, all_67_0_47) = all_67_2_49
% 9.38/2.86 | (141) sdtasdt0(xn, all_0_3_3) = all_67_1_48
% 9.38/2.86 | (142) sdtasdt0(xn, all_0_3_3) = all_67_2_49
% 9.38/2.86 |
% 9.38/2.86 | Instantiating formula (71) with xn, all_0_3_3, all_67_2_49, all_67_1_48 and discharging atoms sdtasdt0(xn, all_0_3_3) = all_67_1_48, sdtasdt0(xn, all_0_3_3) = all_67_2_49, yields:
% 9.38/2.86 | (143) all_67_1_48 = all_67_2_49
% 9.38/2.86 |
% 9.38/2.86 | Instantiating formula (71) with xn, all_0_3_3, all_53_1_25, all_0_2_2 and discharging atoms sdtasdt0(xn, all_0_3_3) = all_53_1_25, sdtasdt0(xn, all_0_3_3) = all_0_2_2, yields:
% 9.38/2.86 | (144) all_53_1_25 = all_0_2_2
% 9.38/2.86 |
% 9.38/2.86 | Instantiating formula (71) with xn, all_0_3_3, all_53_1_25, all_67_2_49 and discharging atoms sdtasdt0(xn, all_0_3_3) = all_67_2_49, sdtasdt0(xn, all_0_3_3) = all_53_1_25, yields:
% 9.38/2.86 | (145) all_67_2_49 = all_53_1_25
% 9.38/2.86 |
% 9.38/2.86 | Instantiating formula (71) with xn, all_0_3_3, all_49_0_18, all_67_1_48 and discharging atoms sdtasdt0(xn, all_0_3_3) = all_67_1_48, sdtasdt0(xn, all_0_3_3) = all_49_0_18, yields:
% 9.38/2.86 | (146) all_67_1_48 = all_49_0_18
% 9.38/2.86 |
% 9.38/2.86 | Instantiating formula (71) with xn, all_0_3_3, all_19_0_6, all_53_1_25 and discharging atoms sdtasdt0(xn, all_0_3_3) = all_53_1_25, sdtasdt0(xn, all_0_3_3) = all_19_0_6, yields:
% 9.38/2.86 | (147) all_53_1_25 = all_19_0_6
% 9.38/2.86 |
% 9.38/2.86 | Instantiating formula (25) with all_19_0_6, all_0_0_0, all_0_1_1, xl and discharging atoms sdtsldt0(all_0_1_1, xl) = all_0_0_0, sdtasdt0(xl, all_19_0_6) = all_0_1_1, doDivides0(xl, all_0_1_1), aNaturalNumber0(all_19_0_6), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 9.38/2.86 | (148) all_19_0_6 = all_0_0_0 | xl = sz00
% 9.38/2.86 |
% 9.63/2.86 | Combining equations (143,146) yields a new equation:
% 9.63/2.86 | (149) all_67_2_49 = all_49_0_18
% 9.63/2.86 |
% 9.63/2.86 | Simplifying 149 yields:
% 9.63/2.86 | (150) all_67_2_49 = all_49_0_18
% 9.63/2.86 |
% 9.63/2.86 | Combining equations (145,150) yields a new equation:
% 9.63/2.86 | (151) all_53_1_25 = all_49_0_18
% 9.63/2.86 |
% 9.63/2.86 | Simplifying 151 yields:
% 9.63/2.86 | (152) all_53_1_25 = all_49_0_18
% 9.63/2.86 |
% 9.63/2.86 | Combining equations (144,152) yields a new equation:
% 9.63/2.86 | (153) all_49_0_18 = all_0_2_2
% 9.63/2.86 |
% 9.63/2.86 | Combining equations (147,152) yields a new equation:
% 9.63/2.86 | (154) all_49_0_18 = all_19_0_6
% 9.63/2.86 |
% 9.63/2.86 | Combining equations (154,153) yields a new equation:
% 9.63/2.86 | (155) all_19_0_6 = all_0_2_2
% 9.63/2.86 |
% 9.63/2.86 | Simplifying 155 yields:
% 9.63/2.86 | (156) all_19_0_6 = all_0_2_2
% 9.63/2.86 |
% 9.63/2.86 +-Applying beta-rule and splitting (148), into two cases.
% 9.63/2.86 |-Branch one:
% 9.63/2.86 | (111) xl = sz00
% 9.63/2.86 |
% 9.63/2.86 | Equations (111) can reduce 39 to:
% 9.63/2.86 | (112) $false
% 9.63/2.86 |
% 9.63/2.86 |-The branch is then unsatisfiable
% 9.63/2.86 |-Branch two:
% 9.63/2.86 | (39) ~ (xl = sz00)
% 9.63/2.86 | (160) all_19_0_6 = all_0_0_0
% 9.63/2.86 |
% 9.63/2.86 | Combining equations (156,160) yields a new equation:
% 9.63/2.86 | (161) all_0_0_0 = all_0_2_2
% 9.63/2.86 |
% 9.63/2.86 | Equations (161) can reduce 37 to:
% 9.63/2.86 | (112) $false
% 9.63/2.86 |
% 9.63/2.86 |-The branch is then unsatisfiable
% 9.63/2.86 % SZS output end Proof for theBenchmark
% 9.63/2.86
% 9.63/2.86 2209ms
%------------------------------------------------------------------------------