TSTP Solution File: NUM473+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM473+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 08:44:52 EDT 2022
% Result : Theorem 6.03s 1.99s
% Output : Proof 11.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM473+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jul 6 22:44:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.57 ____ _
% 0.19/0.57 ___ / __ \_____(_)___ ________ __________
% 0.19/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.57
% 0.19/0.57 A Theorem Prover for First-Order Logic
% 0.19/0.57 (ePrincess v.1.0)
% 0.19/0.57
% 0.19/0.57 (c) Philipp Rümmer, 2009-2015
% 0.19/0.57 (c) Peter Backeman, 2014-2015
% 0.19/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.57 Bug reports to peter@backeman.se
% 0.19/0.57
% 0.19/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.57
% 0.19/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.70/0.95 Prover 0: Preprocessing ...
% 3.49/1.45 Prover 0: Constructing countermodel ...
% 6.03/1.99 Prover 0: proved (1352ms)
% 6.03/1.99
% 6.03/1.99 No countermodel exists, formula is valid
% 6.03/1.99 % SZS status Theorem for theBenchmark
% 6.03/1.99
% 6.03/1.99 Generating proof ... found it (size 156)
% 10.86/3.10
% 10.86/3.10 % SZS output start Proof for theBenchmark
% 10.86/3.10 Assumed formulas after preprocessing and simplification:
% 10.86/3.10 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (xl = sz00) & ~ (sz10 = sz00) & sdtsldt0(v0, xl) = xq & sdtsldt0(xm, xl) = xp & sdtasdt0(xl, v3) = xm & sdtasdt0(xl, v2) = v0 & sdtasdt0(xl, xq) = v0 & sdtasdt0(xl, xp) = xm & sdtpldt0(xm, v1) = v0 & sdtpldt0(xm, xn) = v0 & doDivides0(xl, v0) & doDivides0(xl, xm) & sdtlseqdt0(xm, v0) & aNaturalNumber0(v3) & aNaturalNumber0(v2) & aNaturalNumber0(v1) & aNaturalNumber0(xq) & aNaturalNumber0(xp) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & aNaturalNumber0(xl) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ sdtlseqdt0(xp, xq) & ! [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, 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] : (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)) & ! [v4] : ( ~ aNaturalNumber0(v4) | ? [v5] : ( ~ (v5 = xq) & sdtpldt0(xp, v4) = v5)))
% 10.86/3.17 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 10.86/3.17 | (1) ~ (xl = sz00) & ~ (sz10 = sz00) & sdtsldt0(all_0_3_3, xl) = xq & sdtsldt0(xm, xl) = xp & sdtasdt0(xl, all_0_0_0) = xm & sdtasdt0(xl, all_0_1_1) = all_0_3_3 & sdtasdt0(xl, xq) = all_0_3_3 & sdtasdt0(xl, xp) = xm & sdtpldt0(xm, all_0_2_2) = all_0_3_3 & sdtpldt0(xm, xn) = all_0_3_3 & doDivides0(xl, all_0_3_3) & doDivides0(xl, xm) & sdtlseqdt0(xm, all_0_3_3) & aNaturalNumber0(all_0_0_0) & aNaturalNumber0(all_0_1_1) & aNaturalNumber0(all_0_2_2) & aNaturalNumber0(xq) & aNaturalNumber0(xp) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & aNaturalNumber0(xl) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ sdtlseqdt0(xp, xq) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtlseqdt0(v6, v4) & sdtlseqdt0(v3, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v3) & sdtlseqdt0(v4, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtlseqdt0(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v0, v2) = v6 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v6, v7) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v1) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v4, v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v0) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v1) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v1, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v0, v2) = v6 & sdtlseqdt0(v6, v3) & sdtlseqdt0(v4, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1)) & ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0) & ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2))) & ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2))) & ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) & ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = xq) & sdtpldt0(xp, v0) = v1))
% 10.86/3.19 |
% 10.86/3.19 | Applying alpha-rule on (1) yields:
% 10.86/3.19 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4))
% 10.86/3.19 | (3) ~ sdtlseqdt0(xp, xq)
% 10.86/3.19 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.86/3.19 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 10.86/3.19 | (6) sdtasdt0(xl, xq) = all_0_3_3
% 10.86/3.19 | (7) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 10.86/3.19 | (8) ! [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))
% 10.86/3.19 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.86/3.19 | (10) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 10.86/3.19 | (11) ! [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))
% 10.86/3.19 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6))
% 10.86/3.19 | (13) sdtsldt0(xm, xl) = xp
% 10.86/3.19 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2)
% 10.86/3.19 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v0, v2) = v6 & sdtpldt0(v0, v1) = v5))
% 10.86/3.19 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.86/3.19 | (17) ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 10.86/3.20 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 10.86/3.20 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 10.86/3.20 | (20) ! [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))
% 11.36/3.20 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 11.36/3.20 | (22) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 11.36/3.20 | (23) aNaturalNumber0(sz10)
% 11.36/3.20 | (24) aNaturalNumber0(xp)
% 11.36/3.20 | (25) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0))
% 11.36/3.20 | (26) ! [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))
% 11.37/3.20 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 11.37/3.20 | (28) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0))
% 11.37/3.20 | (29) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 11.38/3.20 | (30) ! [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))
% 11.38/3.20 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 11.38/3.20 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 11.38/3.20 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v1) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v4, v3)))
% 11.38/3.20 | (34) ! [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))
% 11.38/3.20 | (35) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 11.38/3.20 | (36) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00)
% 11.38/3.20 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 11.38/3.20 | (38) sdtsldt0(all_0_3_3, xl) = xq
% 11.38/3.20 | (39) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 11.38/3.20 | (40) sdtasdt0(xl, xp) = xm
% 11.38/3.20 | (41) aNaturalNumber0(all_0_2_2)
% 11.38/3.20 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 11.38/3.20 | (43) doDivides0(xl, xm)
% 11.38/3.20 | (44) aNaturalNumber0(all_0_0_0)
% 11.38/3.20 | (45) aNaturalNumber0(xq)
% 11.38/3.20 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v0) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v1) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v3, v4)))
% 11.38/3.20 | (47) aNaturalNumber0(all_0_1_1)
% 11.38/3.20 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 11.38/3.20 | (49) ! [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))
% 11.38/3.21 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 11.38/3.21 | (51) ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = xq) & sdtpldt0(xp, v0) = v1))
% 11.38/3.21 | (52) ! [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))
% 11.38/3.21 | (53) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 11.38/3.21 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 11.38/3.21 | (55) aNaturalNumber0(xn)
% 11.38/3.21 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2)
% 11.38/3.21 | (57) ! [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))
% 11.38/3.21 | (58) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 11.38/3.21 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 11.38/3.21 | (60) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 11.38/3.21 | (61) aNaturalNumber0(xl)
% 11.38/3.21 | (62) ! [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))
% 11.38/3.21 | (63) ~ (xl = sz00)
% 11.38/3.21 | (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) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v6)))
% 11.38/3.21 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4))
% 11.38/3.21 | (66) sdtpldt0(xm, xn) = all_0_3_3
% 11.38/3.21 | (67) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 11.38/3.21 | (68) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0)
% 11.38/3.21 | (69) sdtasdt0(xl, all_0_1_1) = all_0_3_3
% 11.38/3.21 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4))
% 11.38/3.21 | (71) ! [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)))
% 11.38/3.21 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 11.38/3.21 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6)))
% 11.38/3.21 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5))
% 11.38/3.21 | (75) aNaturalNumber0(sz00)
% 11.38/3.21 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 11.38/3.21 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtlseqdt0(v5, v6)))
% 11.38/3.21 | (78) ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 11.38/3.21 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 11.38/3.21 | (80) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 11.38/3.21 | (81) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0)
% 11.38/3.21 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v6, v7) = v5))
% 11.38/3.21 | (83) ! [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))
% 11.38/3.21 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5))
% 11.38/3.21 | (85) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 11.38/3.22 | (86) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 11.38/3.22 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 11.38/3.22 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 11.38/3.22 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 11.38/3.22 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3))
% 11.38/3.22 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtlseqdt0(v6, v4) & sdtlseqdt0(v3, v5)))
% 11.38/3.22 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 11.38/3.22 | (93) sdtpldt0(xm, all_0_2_2) = all_0_3_3
% 11.38/3.22 | (94) ~ (sz10 = sz00)
% 11.38/3.22 | (95) ! [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))
% 11.38/3.22 | (96) aNaturalNumber0(xm)
% 11.38/3.22 | (97) doDivides0(xl, all_0_3_3)
% 11.38/3.22 | (98) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 11.38/3.22 | (99) ! [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)))
% 11.38/3.22 | (100) sdtasdt0(xl, all_0_0_0) = xm
% 11.38/3.22 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4))
% 11.38/3.22 | (102) sdtlseqdt0(xm, all_0_3_3)
% 11.38/3.22 |
% 11.38/3.22 | Instantiating formula (4) with all_0_3_3, all_0_2_2, xn, xm and discharging atoms sdtpldt0(xm, all_0_2_2) = all_0_3_3, sdtpldt0(xm, xn) = all_0_3_3, aNaturalNumber0(all_0_2_2), aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 11.38/3.22 | (103) all_0_2_2 = xn
% 11.38/3.22 |
% 11.38/3.22 | Instantiating formula (42) with xm, all_0_0_0, xp, xl and discharging atoms sdtasdt0(xl, all_0_0_0) = xm, sdtasdt0(xl, xp) = xm, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 11.38/3.22 | (104) all_0_0_0 = xp | xl = sz00
% 11.38/3.22 |
% 11.38/3.22 | Instantiating formula (42) with all_0_3_3, all_0_1_1, xq, xl and discharging atoms sdtasdt0(xl, all_0_1_1) = all_0_3_3, sdtasdt0(xl, xq) = all_0_3_3, aNaturalNumber0(all_0_1_1), aNaturalNumber0(xq), aNaturalNumber0(xl), yields:
% 11.38/3.22 | (105) all_0_1_1 = xq | xl = sz00
% 11.38/3.22 |
% 11.38/3.22 | From (103) and (93) follows:
% 11.38/3.22 | (66) sdtpldt0(xm, xn) = all_0_3_3
% 11.38/3.22 |
% 11.38/3.22 | From (103) and (41) follows:
% 11.38/3.22 | (55) aNaturalNumber0(xn)
% 11.38/3.22 |
% 11.38/3.22 +-Applying beta-rule and splitting (105), into two cases.
% 11.38/3.22 |-Branch one:
% 11.38/3.22 | (108) xl = sz00
% 11.38/3.22 |
% 11.38/3.22 | Equations (108) can reduce 63 to:
% 11.38/3.22 | (109) $false
% 11.38/3.22 |
% 11.38/3.22 |-The branch is then unsatisfiable
% 11.38/3.22 |-Branch two:
% 11.38/3.22 | (63) ~ (xl = sz00)
% 11.38/3.22 | (111) all_0_1_1 = xq
% 11.38/3.22 |
% 11.38/3.23 | From (111) and (69) follows:
% 11.38/3.23 | (6) sdtasdt0(xl, xq) = all_0_3_3
% 11.38/3.23 |
% 11.38/3.23 | From (111) and (47) follows:
% 11.38/3.23 | (45) aNaturalNumber0(xq)
% 11.38/3.23 |
% 11.38/3.23 +-Applying beta-rule and splitting (104), into two cases.
% 11.38/3.23 |-Branch one:
% 11.38/3.23 | (108) xl = sz00
% 11.38/3.23 |
% 11.38/3.23 | Equations (108) can reduce 63 to:
% 11.38/3.23 | (109) $false
% 11.38/3.23 |
% 11.38/3.23 |-The branch is then unsatisfiable
% 11.38/3.23 |-Branch two:
% 11.38/3.23 | (63) ~ (xl = sz00)
% 11.38/3.23 | (117) all_0_0_0 = xp
% 11.38/3.23 |
% 11.38/3.23 | From (117) and (100) follows:
% 11.38/3.23 | (40) sdtasdt0(xl, xp) = xm
% 11.38/3.23 |
% 11.38/3.23 | From (117) and (44) follows:
% 11.38/3.23 | (24) aNaturalNumber0(xp)
% 11.38/3.23 |
% 11.38/3.23 | Instantiating formula (51) with xq and discharging atoms aNaturalNumber0(xq), yields:
% 11.38/3.23 | (120) ? [v0] : ( ~ (v0 = xq) & sdtpldt0(xp, xq) = v0)
% 11.38/3.23 |
% 11.38/3.23 | Instantiating formula (10) with xp, xq and discharging atoms aNaturalNumber0(xq), aNaturalNumber0(xp), ~ sdtlseqdt0(xp, xq), yields:
% 11.38/3.23 | (121) sdtlseqdt0(xq, xp)
% 11.38/3.23 |
% 11.38/3.23 | Instantiating formula (51) with xp and discharging atoms aNaturalNumber0(xp), yields:
% 11.38/3.23 | (122) ? [v0] : ( ~ (v0 = xq) & sdtpldt0(xp, xp) = v0)
% 11.38/3.23 |
% 11.38/3.23 | Instantiating formula (51) with xn and discharging atoms aNaturalNumber0(xn), yields:
% 11.38/3.23 | (123) ? [v0] : ( ~ (v0 = xq) & sdtpldt0(xp, xn) = v0)
% 11.38/3.23 |
% 11.38/3.23 | Instantiating formula (14) with all_0_3_3, xm, xn and discharging atoms sdtpldt0(xm, xn) = all_0_3_3, aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 11.38/3.23 | (124) sdtpldt0(xn, xm) = all_0_3_3
% 11.38/3.23 |
% 11.38/3.23 | Instantiating formula (51) with xm and discharging atoms aNaturalNumber0(xm), yields:
% 11.38/3.23 | (125) ? [v0] : ( ~ (v0 = xq) & sdtpldt0(xp, xm) = v0)
% 11.38/3.23 |
% 11.38/3.23 | Instantiating formula (74) with all_0_3_3, xm, xq, xp, xl and discharging atoms sdtasdt0(xl, xq) = all_0_3_3, sdtasdt0(xl, xp) = xm, aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 11.38/3.23 | (126) xq = xp | xl = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xq, xl) = v1 & sdtasdt0(xp, xl) = v0)
% 11.38/3.23 |
% 11.38/3.23 | Instantiating formula (56) with all_0_3_3, xl, xq and discharging atoms sdtasdt0(xl, xq) = all_0_3_3, aNaturalNumber0(xq), aNaturalNumber0(xl), yields:
% 11.38/3.23 | (127) sdtasdt0(xq, xl) = all_0_3_3
% 11.38/3.23 |
% 11.38/3.23 | Instantiating formula (16) with all_0_3_3, xq, xl and discharging atoms sdtasdt0(xl, xq) = all_0_3_3, aNaturalNumber0(xq), aNaturalNumber0(xl), yields:
% 11.38/3.23 | (128) aNaturalNumber0(all_0_3_3)
% 11.38/3.23 |
% 11.38/3.23 | Instantiating formula (74) with xm, all_0_3_3, xp, xq, xl and discharging atoms sdtasdt0(xl, xq) = all_0_3_3, sdtasdt0(xl, xp) = xm, aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 11.38/3.23 | (129) xq = xp | xl = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xq, xl) = v0 & sdtasdt0(xp, xl) = v1)
% 11.38/3.23 |
% 11.38/3.23 | Instantiating formula (56) with xm, xl, xp and discharging atoms sdtasdt0(xl, xp) = xm, aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 11.38/3.23 | (130) sdtasdt0(xp, xl) = xm
% 11.38/3.23 |
% 11.38/3.23 | Instantiating formula (17) with xm, xl and discharging atoms doDivides0(xl, xm), aNaturalNumber0(xm), aNaturalNumber0(xl), yields:
% 11.38/3.23 | (131) ? [v0] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0))
% 11.38/3.23 |
% 11.38/3.23 | Instantiating formula (51) with xl and discharging atoms aNaturalNumber0(xl), yields:
% 11.38/3.23 | (132) ? [v0] : ( ~ (v0 = xq) & sdtpldt0(xp, xl) = v0)
% 11.38/3.23 |
% 11.38/3.23 | Instantiating formula (51) with sz10 and discharging atoms aNaturalNumber0(sz10), yields:
% 11.38/3.23 | (133) ? [v0] : ( ~ (v0 = xq) & sdtpldt0(xp, sz10) = v0)
% 11.38/3.23 |
% 11.38/3.23 | Instantiating formula (51) with sz00 and discharging atoms aNaturalNumber0(sz00), yields:
% 11.38/3.23 | (134) ? [v0] : ( ~ (v0 = xq) & sdtpldt0(xp, sz00) = v0)
% 11.38/3.23 |
% 11.38/3.23 | Instantiating (123) with all_21_0_4 yields:
% 11.38/3.23 | (135) ~ (all_21_0_4 = xq) & sdtpldt0(xp, xn) = all_21_0_4
% 11.38/3.23 |
% 11.38/3.23 | Applying alpha-rule on (135) yields:
% 11.38/3.23 | (136) ~ (all_21_0_4 = xq)
% 11.38/3.23 | (137) sdtpldt0(xp, xn) = all_21_0_4
% 11.38/3.23 |
% 11.38/3.23 | Instantiating (134) with all_23_0_5 yields:
% 11.38/3.23 | (138) ~ (all_23_0_5 = xq) & sdtpldt0(xp, sz00) = all_23_0_5
% 11.38/3.23 |
% 11.38/3.23 | Applying alpha-rule on (138) yields:
% 11.38/3.23 | (139) ~ (all_23_0_5 = xq)
% 11.38/3.23 | (140) sdtpldt0(xp, sz00) = all_23_0_5
% 11.38/3.23 |
% 11.38/3.23 | Instantiating (133) with all_25_0_6 yields:
% 11.38/3.23 | (141) ~ (all_25_0_6 = xq) & sdtpldt0(xp, sz10) = all_25_0_6
% 11.38/3.23 |
% 11.38/3.23 | Applying alpha-rule on (141) yields:
% 11.38/3.23 | (142) ~ (all_25_0_6 = xq)
% 11.38/3.23 | (143) sdtpldt0(xp, sz10) = all_25_0_6
% 11.38/3.23 |
% 11.38/3.23 | Instantiating (125) with all_27_0_7 yields:
% 11.38/3.23 | (144) ~ (all_27_0_7 = xq) & sdtpldt0(xp, xm) = all_27_0_7
% 11.38/3.23 |
% 11.38/3.23 | Applying alpha-rule on (144) yields:
% 11.38/3.23 | (145) ~ (all_27_0_7 = xq)
% 11.38/3.23 | (146) sdtpldt0(xp, xm) = all_27_0_7
% 11.38/3.23 |
% 11.38/3.23 | Instantiating (120) with all_29_0_8 yields:
% 11.38/3.23 | (147) ~ (all_29_0_8 = xq) & sdtpldt0(xp, xq) = all_29_0_8
% 11.38/3.23 |
% 11.38/3.23 | Applying alpha-rule on (147) yields:
% 11.38/3.23 | (148) ~ (all_29_0_8 = xq)
% 11.38/3.23 | (149) sdtpldt0(xp, xq) = all_29_0_8
% 11.38/3.23 |
% 11.38/3.23 | Instantiating (132) with all_31_0_9 yields:
% 11.38/3.23 | (150) ~ (all_31_0_9 = xq) & sdtpldt0(xp, xl) = all_31_0_9
% 11.38/3.23 |
% 11.38/3.23 | Applying alpha-rule on (150) yields:
% 11.38/3.23 | (151) ~ (all_31_0_9 = xq)
% 11.38/3.23 | (152) sdtpldt0(xp, xl) = all_31_0_9
% 11.38/3.23 |
% 11.38/3.23 | Instantiating (122) with all_33_0_10 yields:
% 11.38/3.23 | (153) ~ (all_33_0_10 = xq) & sdtpldt0(xp, xp) = all_33_0_10
% 11.38/3.23 |
% 11.38/3.23 | Applying alpha-rule on (153) yields:
% 11.38/3.23 | (154) ~ (all_33_0_10 = xq)
% 11.38/3.23 | (155) sdtpldt0(xp, xp) = all_33_0_10
% 11.38/3.23 |
% 11.38/3.23 | Instantiating (131) with all_35_0_11 yields:
% 11.38/3.23 | (156) sdtasdt0(xl, all_35_0_11) = xm & aNaturalNumber0(all_35_0_11)
% 11.38/3.23 |
% 11.38/3.23 | Applying alpha-rule on (156) yields:
% 11.38/3.23 | (157) sdtasdt0(xl, all_35_0_11) = xm
% 11.38/3.23 | (158) aNaturalNumber0(all_35_0_11)
% 11.38/3.23 |
% 11.38/3.23 | Instantiating formula (19) with all_23_0_5, xp and discharging atoms sdtpldt0(xp, sz00) = all_23_0_5, aNaturalNumber0(xp), yields:
% 11.38/3.23 | (159) all_23_0_5 = xp
% 11.38/3.23 |
% 11.38/3.23 | Instantiating formula (42) with xm, xp, all_35_0_11, xl and discharging atoms sdtasdt0(xl, all_35_0_11) = xm, sdtasdt0(xl, xp) = xm, aNaturalNumber0(all_35_0_11), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 11.38/3.23 | (160) all_35_0_11 = xp | xl = sz00
% 11.38/3.23 |
% 11.38/3.24 | Equations (159) can reduce 139 to:
% 11.38/3.24 | (161) ~ (xq = xp)
% 11.38/3.24 |
% 11.38/3.24 | Simplifying 161 yields:
% 11.38/3.24 | (162) ~ (xq = xp)
% 11.38/3.24 |
% 11.38/3.24 | From (159) and (140) follows:
% 11.38/3.24 | (163) sdtpldt0(xp, sz00) = xp
% 11.38/3.24 |
% 11.38/3.24 +-Applying beta-rule and splitting (129), into two cases.
% 11.38/3.24 |-Branch one:
% 11.38/3.24 | (108) xl = sz00
% 11.38/3.24 |
% 11.38/3.24 | Equations (108) can reduce 63 to:
% 11.38/3.24 | (109) $false
% 11.38/3.24 |
% 11.38/3.24 |-The branch is then unsatisfiable
% 11.38/3.24 |-Branch two:
% 11.38/3.24 | (63) ~ (xl = sz00)
% 11.38/3.24 | (167) xq = xp | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xq, xl) = v0 & sdtasdt0(xp, xl) = v1)
% 11.38/3.24 |
% 11.38/3.24 +-Applying beta-rule and splitting (126), into two cases.
% 11.38/3.24 |-Branch one:
% 11.38/3.24 | (108) xl = sz00
% 11.38/3.24 |
% 11.38/3.24 | Equations (108) can reduce 63 to:
% 11.38/3.24 | (109) $false
% 11.38/3.24 |
% 11.38/3.24 |-The branch is then unsatisfiable
% 11.38/3.24 |-Branch two:
% 11.38/3.24 | (63) ~ (xl = sz00)
% 11.38/3.24 | (171) xq = xp | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xq, xl) = v1 & sdtasdt0(xp, xl) = v0)
% 11.38/3.24 |
% 11.38/3.24 +-Applying beta-rule and splitting (167), into two cases.
% 11.38/3.24 |-Branch one:
% 11.38/3.24 | (172) xq = xp
% 11.38/3.24 |
% 11.38/3.24 | Equations (172) can reduce 162 to:
% 11.38/3.24 | (109) $false
% 11.38/3.24 |
% 11.38/3.24 |-The branch is then unsatisfiable
% 11.38/3.24 |-Branch two:
% 11.38/3.24 | (162) ~ (xq = xp)
% 11.38/3.24 | (175) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xq, xl) = v0 & sdtasdt0(xp, xl) = v1)
% 11.38/3.24 |
% 11.38/3.24 | Instantiating (175) with all_53_0_12, all_53_1_13 yields:
% 11.38/3.24 | (176) ~ (all_53_0_12 = all_53_1_13) & sdtasdt0(xq, xl) = all_53_1_13 & sdtasdt0(xp, xl) = all_53_0_12
% 11.38/3.24 |
% 11.38/3.24 | Applying alpha-rule on (176) yields:
% 11.38/3.24 | (177) ~ (all_53_0_12 = all_53_1_13)
% 11.38/3.24 | (178) sdtasdt0(xq, xl) = all_53_1_13
% 11.38/3.24 | (179) sdtasdt0(xp, xl) = all_53_0_12
% 11.38/3.24 |
% 11.38/3.24 +-Applying beta-rule and splitting (160), into two cases.
% 11.38/3.24 |-Branch one:
% 11.38/3.24 | (108) xl = sz00
% 11.38/3.24 |
% 11.38/3.24 | Equations (108) can reduce 63 to:
% 11.38/3.24 | (109) $false
% 11.38/3.24 |
% 11.38/3.24 |-The branch is then unsatisfiable
% 11.38/3.24 |-Branch two:
% 11.38/3.24 | (63) ~ (xl = sz00)
% 11.38/3.24 | (183) all_35_0_11 = xp
% 11.38/3.24 |
% 11.38/3.24 | From (183) and (157) follows:
% 11.38/3.24 | (40) sdtasdt0(xl, xp) = xm
% 11.38/3.24 |
% 11.38/3.24 | From (183) and (158) follows:
% 11.38/3.24 | (24) aNaturalNumber0(xp)
% 11.38/3.24 |
% 11.38/3.24 | Instantiating formula (54) with xq, xl, all_53_1_13, all_0_3_3 and discharging atoms sdtasdt0(xq, xl) = all_53_1_13, sdtasdt0(xq, xl) = all_0_3_3, yields:
% 11.38/3.24 | (186) all_53_1_13 = all_0_3_3
% 11.38/3.24 |
% 11.38/3.24 | Instantiating formula (54) with xp, xl, all_53_0_12, xm and discharging atoms sdtasdt0(xp, xl) = all_53_0_12, sdtasdt0(xp, xl) = xm, yields:
% 11.38/3.24 | (187) all_53_0_12 = xm
% 11.38/3.24 |
% 11.38/3.24 | Equations (187,186) can reduce 177 to:
% 11.38/3.24 | (188) ~ (all_0_3_3 = xm)
% 11.38/3.24 |
% 11.38/3.24 | Simplifying 188 yields:
% 11.38/3.24 | (189) ~ (all_0_3_3 = xm)
% 11.38/3.24 |
% 11.38/3.24 | From (186) and (178) follows:
% 11.38/3.24 | (127) sdtasdt0(xq, xl) = all_0_3_3
% 11.38/3.24 |
% 11.38/3.24 | From (187) and (179) follows:
% 11.38/3.24 | (130) sdtasdt0(xp, xl) = xm
% 11.38/3.24 |
% 11.38/3.24 | Instantiating formula (20) with all_33_0_10, all_29_0_8, xq, xp, xp and discharging atoms sdtpldt0(xp, xq) = all_29_0_8, sdtpldt0(xp, xp) = all_33_0_10, aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 11.38/3.24 | (192) xq = xp | ? [v0] : ? [v1] : ( ~ (v1 = all_33_0_10) & ~ (v0 = all_29_0_8) & sdtpldt0(xq, xp) = v1 & sdtpldt0(xp, xp) = v0)
% 11.38/3.24 |
% 11.38/3.24 | Instantiating formula (95) with all_29_0_8, all_33_0_10, xq, xp, xp and discharging atoms sdtpldt0(xp, xq) = all_29_0_8, sdtpldt0(xp, xp) = all_33_0_10, aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 11.38/3.24 | (193) xq = xp | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xq, xp) = v1 & sdtpldt0(xp, xp) = v0)
% 11.38/3.24 |
% 11.38/3.24 | Instantiating formula (95) with all_33_0_10, all_29_0_8, xp, xq, xp and discharging atoms sdtpldt0(xp, xq) = all_29_0_8, sdtpldt0(xp, xp) = all_33_0_10, aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 11.38/3.24 | (194) xq = xp | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xq, xp) = v0 & sdtpldt0(xp, xp) = v1)
% 11.38/3.24 |
% 11.38/3.24 | Instantiating formula (95) with xp, all_31_0_9, sz00, xl, xp and discharging atoms sdtpldt0(xp, xl) = all_31_0_9, sdtpldt0(xp, sz00) = xp, aNaturalNumber0(xp), aNaturalNumber0(xl), aNaturalNumber0(sz00), yields:
% 11.38/3.24 | (195) xl = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xl, xp) = v0 & sdtpldt0(sz00, xp) = v1)
% 11.38/3.24 |
% 11.38/3.24 | Instantiating formula (77) with xm, all_0_3_3, xp, xq, xl and discharging atoms sdtasdt0(xl, xq) = all_0_3_3, sdtasdt0(xl, xp) = xm, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 11.38/3.24 | (196) xq = xp | xl = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xq, xl) = v0 & sdtasdt0(xp, xl) = v1 & sdtlseqdt0(v0, v1))
% 11.38/3.24 |
% 11.38/3.24 | Instantiating formula (52) with xm, all_0_3_3, xp, xq, xl and discharging atoms sdtasdt0(xq, xl) = all_0_3_3, sdtasdt0(xp, xl) = xm, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 11.38/3.24 | (197) xq = xp | xl = sz00 | sdtlseqdt0(all_0_3_3, xm)
% 11.38/3.24 |
% 11.38/3.24 | Instantiating formula (46) with all_29_0_8, xp, xp, xq and discharging atoms sdtpldt0(xp, xq) = all_29_0_8, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 11.38/3.24 | (198) xq = xp | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = all_29_0_8) & sdtpldt0(xq, xp) = v1 & sdtpldt0(xp, xp) = v2 & sdtpldt0(xp, xp) = v0 & sdtlseqdt0(v1, v2) & sdtlseqdt0(all_29_0_8, v0))
% 11.38/3.24 |
% 11.38/3.24 | Instantiating formula (99) with all_29_0_8, xq, xp, xq and discharging atoms sdtpldt0(xp, xq) = all_29_0_8, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 11.38/3.24 | (199) xq = xp | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_29_0_8) & ~ (v1 = v0) & sdtpldt0(xq, xq) = v2 & sdtpldt0(xq, xq) = v0 & sdtpldt0(xq, xp) = v1 & sdtlseqdt0(v2, all_29_0_8) & sdtlseqdt0(v0, v1))
% 11.38/3.24 |
% 11.38/3.24 | Instantiating formula (33) with all_33_0_10, xp, xp, xq and discharging atoms sdtpldt0(xp, xp) = all_33_0_10, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 11.38/3.24 | (200) xq = xp | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = all_33_0_10) & sdtpldt0(xq, xp) = v1 & sdtpldt0(xp, xq) = v0 & sdtpldt0(xp, xp) = v2 & sdtlseqdt0(v1, v2) & sdtlseqdt0(v0, all_33_0_10))
% 11.38/3.24 |
% 11.38/3.24 | Instantiating formula (99) with all_33_0_10, xp, xp, xq and discharging atoms sdtpldt0(xp, xp) = all_33_0_10, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 11.38/3.24 | (201) xq = xp | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_33_0_10) & ~ (v1 = v0) & sdtpldt0(xq, xp) = v2 & sdtpldt0(xp, xq) = v0 & sdtpldt0(xp, xp) = v1 & sdtlseqdt0(v2, all_33_0_10) & sdtlseqdt0(v0, v1))
% 11.38/3.24 |
% 11.38/3.24 | Instantiating formula (99) with all_21_0_4, xn, xp, xq and discharging atoms sdtpldt0(xp, xn) = all_21_0_4, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 11.38/3.24 | (202) xq = xp | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_21_0_4) & ~ (v1 = v0) & sdtpldt0(xq, xn) = v2 & sdtpldt0(xn, xq) = v0 & sdtpldt0(xn, xp) = v1 & sdtlseqdt0(v2, all_21_0_4) & sdtlseqdt0(v0, v1))
% 11.38/3.24 |
% 11.38/3.24 | Instantiating formula (99) with all_27_0_7, xm, xp, xq and discharging atoms sdtpldt0(xp, xm) = all_27_0_7, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 11.38/3.25 | (203) xq = xp | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_27_0_7) & ~ (v1 = v0) & sdtpldt0(xq, xm) = v2 & sdtpldt0(xm, xq) = v0 & sdtpldt0(xm, xp) = v1 & sdtlseqdt0(v2, all_27_0_7) & sdtlseqdt0(v0, v1))
% 11.38/3.25 |
% 11.38/3.25 | Instantiating formula (99) with all_31_0_9, xl, xp, xq and discharging atoms sdtpldt0(xp, xl) = all_31_0_9, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 11.38/3.25 | (204) xq = xp | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_31_0_9) & ~ (v1 = v0) & sdtpldt0(xq, xl) = v2 & sdtpldt0(xl, xq) = v0 & sdtpldt0(xl, xp) = v1 & sdtlseqdt0(v2, all_31_0_9) & sdtlseqdt0(v0, v1))
% 11.38/3.25 |
% 11.38/3.25 | Instantiating formula (99) with all_25_0_6, sz10, xp, xq and discharging atoms sdtpldt0(xp, sz10) = all_25_0_6, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(sz10), yields:
% 11.38/3.25 | (205) xq = xp | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_25_0_6) & ~ (v1 = v0) & sdtpldt0(xq, sz10) = v2 & sdtpldt0(sz10, xq) = v0 & sdtpldt0(sz10, xp) = v1 & sdtlseqdt0(v2, all_25_0_6) & sdtlseqdt0(v0, v1))
% 11.38/3.25 |
% 11.38/3.25 | Instantiating formula (99) with xp, sz00, xp, xq and discharging atoms sdtpldt0(xp, sz00) = xp, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(sz00), yields:
% 11.38/3.25 | (206) xq = xp | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xp) & ~ (v1 = v0) & sdtpldt0(xq, sz00) = v2 & sdtpldt0(sz00, xq) = v0 & sdtpldt0(sz00, xp) = v1 & sdtlseqdt0(v2, xp) & sdtlseqdt0(v0, v1))
% 11.38/3.25 |
% 11.38/3.25 | Instantiating formula (73) with all_0_3_3, xn, all_0_3_3, xm and discharging atoms sdtpldt0(xm, xn) = all_0_3_3, sdtlseqdt0(xm, all_0_3_3), aNaturalNumber0(all_0_3_3), aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 11.38/3.25 | (207) all_0_3_3 = xm | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_3_3) & ~ (v1 = v0) & sdtpldt0(all_0_3_3, xn) = v2 & sdtpldt0(xn, all_0_3_3) = v1 & sdtpldt0(xn, xm) = v0 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_3_3, v2))
% 11.38/3.25 |
% 11.38/3.25 | Instantiating formula (46) with all_27_0_7, xp, all_0_3_3, xm and discharging atoms sdtpldt0(xp, xm) = all_27_0_7, sdtlseqdt0(xm, all_0_3_3), aNaturalNumber0(all_0_3_3), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 11.38/3.25 | (208) all_0_3_3 = xm | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = all_27_0_7) & sdtpldt0(all_0_3_3, xp) = v2 & sdtpldt0(xp, all_0_3_3) = v0 & sdtpldt0(xm, xp) = v1 & sdtlseqdt0(v1, v2) & sdtlseqdt0(all_27_0_7, v0))
% 11.38/3.25 |
% 11.38/3.25 | Instantiating formula (46) with all_0_3_3, xn, all_0_3_3, xm and discharging atoms sdtpldt0(xn, xm) = all_0_3_3, sdtlseqdt0(xm, all_0_3_3), aNaturalNumber0(all_0_3_3), aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 11.38/3.25 | (209) all_0_3_3 = xm | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = all_0_3_3) & sdtpldt0(all_0_3_3, xn) = v2 & sdtpldt0(xn, all_0_3_3) = v0 & sdtpldt0(xm, xn) = v1 & sdtlseqdt0(v1, v2) & sdtlseqdt0(all_0_3_3, v0))
% 11.38/3.25 |
% 11.38/3.25 +-Applying beta-rule and splitting (195), into two cases.
% 11.38/3.25 |-Branch one:
% 11.38/3.25 | (108) xl = sz00
% 11.38/3.25 |
% 11.38/3.25 | Equations (108) can reduce 63 to:
% 11.38/3.25 | (109) $false
% 11.38/3.25 |
% 11.38/3.25 |-The branch is then unsatisfiable
% 11.38/3.25 |-Branch two:
% 11.38/3.25 | (63) ~ (xl = sz00)
% 11.38/3.25 | (213) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xl, xp) = v0 & sdtpldt0(sz00, xp) = v1)
% 11.38/3.25 |
% 11.38/3.25 +-Applying beta-rule and splitting (206), into two cases.
% 11.38/3.25 |-Branch one:
% 11.38/3.25 | (172) xq = xp
% 11.38/3.25 |
% 11.38/3.25 | Equations (172) can reduce 162 to:
% 11.38/3.25 | (109) $false
% 11.38/3.25 |
% 11.38/3.25 |-The branch is then unsatisfiable
% 11.38/3.25 |-Branch two:
% 11.38/3.25 | (162) ~ (xq = xp)
% 11.38/3.25 | (217) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xp) & ~ (v1 = v0) & sdtpldt0(xq, sz00) = v2 & sdtpldt0(sz00, xq) = v0 & sdtpldt0(sz00, xp) = v1 & sdtlseqdt0(v2, xp) & sdtlseqdt0(v0, v1))
% 11.38/3.25 |
% 11.38/3.25 +-Applying beta-rule and splitting (205), into two cases.
% 11.38/3.25 |-Branch one:
% 11.38/3.25 | (172) xq = xp
% 11.38/3.25 |
% 11.38/3.25 | Equations (172) can reduce 162 to:
% 11.38/3.25 | (109) $false
% 11.38/3.25 |
% 11.38/3.25 |-The branch is then unsatisfiable
% 11.38/3.25 |-Branch two:
% 11.38/3.25 | (162) ~ (xq = xp)
% 11.38/3.25 | (221) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_25_0_6) & ~ (v1 = v0) & sdtpldt0(xq, sz10) = v2 & sdtpldt0(sz10, xq) = v0 & sdtpldt0(sz10, xp) = v1 & sdtlseqdt0(v2, all_25_0_6) & sdtlseqdt0(v0, v1))
% 11.38/3.25 |
% 11.38/3.25 +-Applying beta-rule and splitting (194), into two cases.
% 11.38/3.25 |-Branch one:
% 11.38/3.25 | (172) xq = xp
% 11.38/3.25 |
% 11.38/3.25 | Equations (172) can reduce 162 to:
% 11.38/3.25 | (109) $false
% 11.38/3.25 |
% 11.38/3.25 |-The branch is then unsatisfiable
% 11.38/3.25 |-Branch two:
% 11.38/3.25 | (162) ~ (xq = xp)
% 11.38/3.25 | (225) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xq, xp) = v0 & sdtpldt0(xp, xp) = v1)
% 11.38/3.25 |
% 11.38/3.25 +-Applying beta-rule and splitting (208), into two cases.
% 11.38/3.25 |-Branch one:
% 11.38/3.25 | (226) all_0_3_3 = xm
% 11.38/3.25 |
% 11.38/3.25 | Equations (226) can reduce 189 to:
% 11.38/3.25 | (109) $false
% 11.38/3.25 |
% 11.38/3.25 |-The branch is then unsatisfiable
% 11.38/3.25 |-Branch two:
% 11.38/3.25 | (189) ~ (all_0_3_3 = xm)
% 11.38/3.25 | (229) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = all_27_0_7) & sdtpldt0(all_0_3_3, xp) = v2 & sdtpldt0(xp, all_0_3_3) = v0 & sdtpldt0(xm, xp) = v1 & sdtlseqdt0(v1, v2) & sdtlseqdt0(all_27_0_7, v0))
% 11.38/3.25 |
% 11.38/3.25 +-Applying beta-rule and splitting (209), into two cases.
% 11.38/3.25 |-Branch one:
% 11.38/3.25 | (226) all_0_3_3 = xm
% 11.38/3.25 |
% 11.38/3.25 | Equations (226) can reduce 189 to:
% 11.38/3.25 | (109) $false
% 11.38/3.25 |
% 11.38/3.25 |-The branch is then unsatisfiable
% 11.38/3.25 |-Branch two:
% 11.38/3.25 | (189) ~ (all_0_3_3 = xm)
% 11.38/3.25 | (233) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = all_0_3_3) & sdtpldt0(all_0_3_3, xn) = v2 & sdtpldt0(xn, all_0_3_3) = v0 & sdtpldt0(xm, xn) = v1 & sdtlseqdt0(v1, v2) & sdtlseqdt0(all_0_3_3, v0))
% 11.38/3.25 |
% 11.38/3.25 +-Applying beta-rule and splitting (197), into two cases.
% 11.38/3.25 |-Branch one:
% 11.38/3.25 | (234) sdtlseqdt0(all_0_3_3, xm)
% 11.38/3.25 |
% 11.38/3.25 +-Applying beta-rule and splitting (207), into two cases.
% 11.38/3.25 |-Branch one:
% 11.38/3.25 | (226) all_0_3_3 = xm
% 11.38/3.25 |
% 11.38/3.25 | Equations (226) can reduce 189 to:
% 11.38/3.25 | (109) $false
% 11.38/3.25 |
% 11.38/3.25 |-The branch is then unsatisfiable
% 11.38/3.25 |-Branch two:
% 11.38/3.25 | (189) ~ (all_0_3_3 = xm)
% 11.38/3.25 | (238) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_3_3) & ~ (v1 = v0) & sdtpldt0(all_0_3_3, xn) = v2 & sdtpldt0(xn, all_0_3_3) = v1 & sdtpldt0(xn, xm) = v0 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_3_3, v2))
% 11.38/3.25 |
% 11.38/3.25 | Instantiating formula (86) with all_0_3_3, xm and discharging atoms sdtlseqdt0(all_0_3_3, xm), sdtlseqdt0(xm, all_0_3_3), aNaturalNumber0(all_0_3_3), aNaturalNumber0(xm), yields:
% 11.38/3.25 | (226) all_0_3_3 = xm
% 11.38/3.25 |
% 11.38/3.25 | Equations (226) can reduce 189 to:
% 11.38/3.25 | (109) $false
% 11.38/3.25 |
% 11.38/3.25 |-The branch is then unsatisfiable
% 11.38/3.25 |-Branch two:
% 11.38/3.25 | (241) ~ sdtlseqdt0(all_0_3_3, xm)
% 11.38/3.25 | (242) xq = xp | xl = sz00
% 11.38/3.25 |
% 11.38/3.25 +-Applying beta-rule and splitting (200), into two cases.
% 11.38/3.25 |-Branch one:
% 11.38/3.25 | (172) xq = xp
% 11.38/3.25 |
% 11.38/3.25 | Equations (172) can reduce 162 to:
% 11.38/3.25 | (109) $false
% 11.38/3.25 |
% 11.38/3.25 |-The branch is then unsatisfiable
% 11.38/3.25 |-Branch two:
% 11.38/3.25 | (162) ~ (xq = xp)
% 11.38/3.25 | (246) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = all_33_0_10) & sdtpldt0(xq, xp) = v1 & sdtpldt0(xp, xq) = v0 & sdtpldt0(xp, xp) = v2 & sdtlseqdt0(v1, v2) & sdtlseqdt0(v0, all_33_0_10))
% 11.38/3.25 |
% 11.38/3.25 +-Applying beta-rule and splitting (196), into two cases.
% 11.38/3.25 |-Branch one:
% 11.38/3.25 | (108) xl = sz00
% 11.38/3.25 |
% 11.38/3.25 | Equations (108) can reduce 63 to:
% 11.38/3.25 | (109) $false
% 11.38/3.25 |
% 11.38/3.25 |-The branch is then unsatisfiable
% 11.38/3.25 |-Branch two:
% 11.38/3.25 | (63) ~ (xl = sz00)
% 11.38/3.25 | (250) xq = xp | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xq, xl) = v0 & sdtasdt0(xp, xl) = v1 & sdtlseqdt0(v0, v1))
% 11.38/3.25 |
% 11.38/3.25 +-Applying beta-rule and splitting (199), into two cases.
% 11.38/3.25 |-Branch one:
% 11.38/3.25 | (172) xq = xp
% 11.38/3.25 |
% 11.38/3.25 | Equations (172) can reduce 162 to:
% 11.38/3.25 | (109) $false
% 11.38/3.25 |
% 11.38/3.25 |-The branch is then unsatisfiable
% 11.38/3.25 |-Branch two:
% 11.38/3.25 | (162) ~ (xq = xp)
% 11.38/3.25 | (254) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_29_0_8) & ~ (v1 = v0) & sdtpldt0(xq, xq) = v2 & sdtpldt0(xq, xq) = v0 & sdtpldt0(xq, xp) = v1 & sdtlseqdt0(v2, all_29_0_8) & sdtlseqdt0(v0, v1))
% 11.38/3.25 |
% 11.38/3.25 +-Applying beta-rule and splitting (201), into two cases.
% 11.38/3.25 |-Branch one:
% 11.38/3.25 | (172) xq = xp
% 11.38/3.25 |
% 11.38/3.25 | Equations (172) can reduce 162 to:
% 11.38/3.25 | (109) $false
% 11.38/3.25 |
% 11.38/3.25 |-The branch is then unsatisfiable
% 11.38/3.25 |-Branch two:
% 11.38/3.25 | (162) ~ (xq = xp)
% 11.38/3.25 | (258) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_33_0_10) & ~ (v1 = v0) & sdtpldt0(xq, xp) = v2 & sdtpldt0(xp, xq) = v0 & sdtpldt0(xp, xp) = v1 & sdtlseqdt0(v2, all_33_0_10) & sdtlseqdt0(v0, v1))
% 11.38/3.25 |
% 11.38/3.25 +-Applying beta-rule and splitting (202), into two cases.
% 11.38/3.25 |-Branch one:
% 11.38/3.25 | (172) xq = xp
% 11.38/3.25 |
% 11.38/3.25 | Equations (172) can reduce 162 to:
% 11.38/3.25 | (109) $false
% 11.38/3.25 |
% 11.38/3.25 |-The branch is then unsatisfiable
% 11.38/3.25 |-Branch two:
% 11.38/3.25 | (162) ~ (xq = xp)
% 11.38/3.25 | (262) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_21_0_4) & ~ (v1 = v0) & sdtpldt0(xq, xn) = v2 & sdtpldt0(xn, xq) = v0 & sdtpldt0(xn, xp) = v1 & sdtlseqdt0(v2, all_21_0_4) & sdtlseqdt0(v0, v1))
% 11.38/3.26 |
% 11.38/3.26 +-Applying beta-rule and splitting (204), into two cases.
% 11.38/3.26 |-Branch one:
% 11.38/3.26 | (172) xq = xp
% 11.38/3.26 |
% 11.38/3.26 | Equations (172) can reduce 162 to:
% 11.38/3.26 | (109) $false
% 11.38/3.26 |
% 11.38/3.26 |-The branch is then unsatisfiable
% 11.38/3.26 |-Branch two:
% 11.38/3.26 | (162) ~ (xq = xp)
% 11.38/3.26 | (266) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_31_0_9) & ~ (v1 = v0) & sdtpldt0(xq, xl) = v2 & sdtpldt0(xl, xq) = v0 & sdtpldt0(xl, xp) = v1 & sdtlseqdt0(v2, all_31_0_9) & sdtlseqdt0(v0, v1))
% 11.38/3.26 |
% 11.38/3.26 +-Applying beta-rule and splitting (192), into two cases.
% 11.38/3.26 |-Branch one:
% 11.38/3.26 | (172) xq = xp
% 11.38/3.26 |
% 11.38/3.26 | Equations (172) can reduce 162 to:
% 11.38/3.26 | (109) $false
% 11.38/3.26 |
% 11.38/3.26 |-The branch is then unsatisfiable
% 11.38/3.26 |-Branch two:
% 11.38/3.26 | (162) ~ (xq = xp)
% 11.38/3.26 | (270) ? [v0] : ? [v1] : ( ~ (v1 = all_33_0_10) & ~ (v0 = all_29_0_8) & sdtpldt0(xq, xp) = v1 & sdtpldt0(xp, xp) = v0)
% 11.38/3.26 |
% 11.38/3.26 +-Applying beta-rule and splitting (203), into two cases.
% 11.38/3.26 |-Branch one:
% 11.38/3.26 | (172) xq = xp
% 11.38/3.26 |
% 11.38/3.26 | Equations (172) can reduce 162 to:
% 11.38/3.26 | (109) $false
% 11.38/3.26 |
% 11.38/3.26 |-The branch is then unsatisfiable
% 11.38/3.26 |-Branch two:
% 11.38/3.26 | (162) ~ (xq = xp)
% 11.38/3.26 | (274) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_27_0_7) & ~ (v1 = v0) & sdtpldt0(xq, xm) = v2 & sdtpldt0(xm, xq) = v0 & sdtpldt0(xm, xp) = v1 & sdtlseqdt0(v2, all_27_0_7) & sdtlseqdt0(v0, v1))
% 11.38/3.26 |
% 11.38/3.26 +-Applying beta-rule and splitting (193), into two cases.
% 11.38/3.26 |-Branch one:
% 11.38/3.26 | (172) xq = xp
% 11.38/3.26 |
% 11.38/3.26 | Equations (172) can reduce 162 to:
% 11.38/3.26 | (109) $false
% 11.38/3.26 |
% 11.38/3.26 |-The branch is then unsatisfiable
% 11.38/3.26 |-Branch two:
% 11.38/3.26 | (162) ~ (xq = xp)
% 11.38/3.26 | (278) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xq, xp) = v1 & sdtpldt0(xp, xp) = v0)
% 11.38/3.26 |
% 11.38/3.26 +-Applying beta-rule and splitting (250), into two cases.
% 11.38/3.26 |-Branch one:
% 11.38/3.26 | (172) xq = xp
% 11.38/3.26 |
% 11.38/3.26 | Equations (172) can reduce 162 to:
% 11.38/3.26 | (109) $false
% 11.38/3.26 |
% 11.38/3.26 |-The branch is then unsatisfiable
% 11.38/3.26 |-Branch two:
% 11.38/3.26 | (162) ~ (xq = xp)
% 11.38/3.26 | (282) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xq, xl) = v0 & sdtasdt0(xp, xl) = v1 & sdtlseqdt0(v0, v1))
% 11.38/3.26 |
% 11.38/3.26 +-Applying beta-rule and splitting (198), into two cases.
% 11.38/3.26 |-Branch one:
% 11.38/3.26 | (172) xq = xp
% 11.38/3.26 |
% 11.38/3.26 | Equations (172) can reduce 162 to:
% 11.38/3.26 | (109) $false
% 11.38/3.26 |
% 11.38/3.26 |-The branch is then unsatisfiable
% 11.38/3.26 |-Branch two:
% 11.38/3.26 | (162) ~ (xq = xp)
% 11.38/3.26 | (286) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = all_29_0_8) & sdtpldt0(xq, xp) = v1 & sdtpldt0(xp, xp) = v2 & sdtpldt0(xp, xp) = v0 & sdtlseqdt0(v1, v2) & sdtlseqdt0(all_29_0_8, v0))
% 11.38/3.26 |
% 11.38/3.26 +-Applying beta-rule and splitting (242), into two cases.
% 11.38/3.26 |-Branch one:
% 11.38/3.26 | (108) xl = sz00
% 11.38/3.26 |
% 11.38/3.26 | Equations (108) can reduce 63 to:
% 11.38/3.26 | (109) $false
% 11.38/3.26 |
% 11.38/3.26 |-The branch is then unsatisfiable
% 11.38/3.26 |-Branch two:
% 11.38/3.26 | (63) ~ (xl = sz00)
% 11.38/3.26 | (172) xq = xp
% 11.38/3.26 |
% 11.38/3.26 | Equations (172) can reduce 162 to:
% 11.38/3.26 | (109) $false
% 11.38/3.26 |
% 11.38/3.26 |-The branch is then unsatisfiable
% 11.38/3.26 % SZS output end Proof for theBenchmark
% 11.38/3.26
% 11.38/3.26 2678ms
%------------------------------------------------------------------------------