TSTP Solution File: NUM471+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM471+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n019.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 08:44:50 EDT 2022
% Result : Theorem 5.70s 1.96s
% Output : Proof 10.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM471+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n019.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 : Tue Jul 5 06:42:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.63/0.64 ____ _
% 0.63/0.64 ___ / __ \_____(_)___ ________ __________
% 0.63/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.63/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.63/0.64
% 0.63/0.64 A Theorem Prover for First-Order Logic
% 0.63/0.64 (ePrincess v.1.0)
% 0.63/0.64
% 0.63/0.64 (c) Philipp Rümmer, 2009-2015
% 0.63/0.64 (c) Peter Backeman, 2014-2015
% 0.63/0.64 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.64 Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.64 Bug reports to peter@backeman.se
% 0.63/0.64
% 0.63/0.64 For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.64
% 0.63/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.80/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.82/1.03 Prover 0: Preprocessing ...
% 3.55/1.48 Prover 0: Constructing countermodel ...
% 5.70/1.96 Prover 0: proved (1275ms)
% 5.70/1.96
% 5.70/1.96 No countermodel exists, formula is valid
% 5.70/1.96 % SZS status Theorem for theBenchmark
% 5.70/1.96
% 5.70/1.96 Generating proof ... found it (size 165)
% 9.46/2.85
% 9.46/2.85 % SZS output start Proof for theBenchmark
% 9.46/2.85 Assumed formulas after preprocessing and simplification:
% 9.46/2.85 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (xl = sz00) & ~ (sz10 = sz00) & sdtsldt0(v0, xl) = xq & sdtsldt0(xm, xl) = xp & sdtasdt0(xl, v2) = xm & sdtasdt0(xl, v1) = v0 & sdtasdt0(xl, xq) = v0 & sdtasdt0(xl, xp) = xm & sdtpldt0(xm, xn) = v0 & doDivides0(xl, v0) & doDivides0(xl, xm) & aNaturalNumber0(v2) & aNaturalNumber0(v1) & aNaturalNumber0(xq) & aNaturalNumber0(xp) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & aNaturalNumber0(xl) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ sdtlseqdt0(xp, xq) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v5, v3) = v7) | ~ (sdtasdt0(v4, v3) = v6) | ~ (sdtpldt0(v6, v7) = v8) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (sdtasdt0(v9, v3) = v8 & sdtasdt0(v3, v9) = v10 & sdtasdt0(v3, v5) = v12 & sdtasdt0(v3, v4) = v11 & sdtpldt0(v11, v12) = v10 & sdtpldt0(v4, v5) = v9)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v3, v5) = v7) | ~ (sdtasdt0(v3, v4) = v6) | ~ (sdtpldt0(v6, v7) = v8) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (sdtasdt0(v9, v3) = v10 & sdtasdt0(v5, v3) = v12 & sdtasdt0(v4, v3) = v11 & sdtasdt0(v3, v9) = v8 & sdtpldt0(v11, v12) = v10 & sdtpldt0(v4, v5) = v9)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | v3 = sz00 | ~ (sdtasdt0(v5, v3) = v7) | ~ (sdtasdt0(v4, v3) = v6) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | sdtlseqdt0(v6, v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | v3 = sz00 | ~ (sdtasdt0(v5, v3) = v7) | ~ (sdtasdt0(v4, v3) = v6) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v8] : ? [v9] : ( ~ (v9 = v8) & sdtasdt0(v3, v5) = v9 & sdtasdt0(v3, v4) = v8 & sdtlseqdt0(v8, v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | v3 = sz00 | ~ (sdtasdt0(v5, v3) = v7) | ~ (sdtasdt0(v4, v3) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v8] : ? [v9] : ( ~ (v9 = v8) & sdtasdt0(v3, v5) = v9 & sdtasdt0(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | v3 = sz00 | ~ (sdtasdt0(v5, v3) = v7) | ~ (sdtasdt0(v3, v4) = v6) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v8] : ? [v9] : ( ~ (v9 = v7) & ~ (v8 = v6) & sdtasdt0(v4, v3) = v9 & sdtasdt0(v3, v5) = v8 & sdtlseqdt0(v9, v7) & sdtlseqdt0(v6, v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | v3 = sz00 | ~ (sdtasdt0(v5, v3) = v7) | ~ (sdtasdt0(v3, v4) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v8] : ? [v9] : ( ~ (v9 = v7) & ~ (v8 = v6) & sdtasdt0(v4, v3) = v9 & sdtasdt0(v3, v5) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | v3 = sz00 | ~ (sdtasdt0(v4, v3) = v7) | ~ (sdtasdt0(v3, v5) = v6) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v8] : ? [v9] : ( ~ (v9 = v7) & ~ (v8 = v6) & sdtasdt0(v5, v3) = v9 & sdtasdt0(v3, v4) = v8 & sdtlseqdt0(v8, v6) & sdtlseqdt0(v7, v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | v3 = sz00 | ~ (sdtasdt0(v4, v3) = v7) | ~ (sdtasdt0(v3, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v8] : ? [v9] : ( ~ (v9 = v7) & ~ (v8 = v6) & sdtasdt0(v5, v3) = v9 & sdtasdt0(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | v3 = sz00 | ~ (sdtasdt0(v3, v5) = v7) | ~ (sdtasdt0(v3, v4) = v6) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | sdtlseqdt0(v6, v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | v3 = sz00 | ~ (sdtasdt0(v3, v5) = v7) | ~ (sdtasdt0(v3, v4) = v6) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v8] : ? [v9] : ( ~ (v9 = v8) & sdtasdt0(v5, v3) = v9 & sdtasdt0(v4, v3) = v8 & sdtlseqdt0(v8, v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | v3 = sz00 | ~ (sdtasdt0(v3, v5) = v7) | ~ (sdtasdt0(v3, v4) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v8] : ? [v9] : ( ~ (v9 = v8) & sdtasdt0(v5, v3) = v9 & sdtasdt0(v4, v3) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v5, v3) = v7) | ~ (sdtpldt0(v4, v3) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v8] : ? [v9] : ( ~ (v9 = v8) & sdtpldt0(v3, v5) = v9 & sdtpldt0(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v5, v3) = v7) | ~ (sdtpldt0(v3, v4) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v8] : ? [v9] : ( ~ (v9 = v7) & ~ (v8 = v6) & sdtpldt0(v4, v3) = v9 & sdtpldt0(v3, v5) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v4, v3) = v7) | ~ (sdtpldt0(v3, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v8] : ? [v9] : ( ~ (v9 = v7) & ~ (v8 = v6) & sdtpldt0(v5, v3) = v9 & sdtpldt0(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v3, v5) = v7) | ~ (sdtpldt0(v3, v4) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v8] : ? [v9] : ( ~ (v9 = v8) & sdtpldt0(v5, v3) = v9 & sdtpldt0(v4, v3) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v6, v5) = v7) | ~ (sdtasdt0(v3, v4) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v8] : (sdtasdt0(v4, v5) = v8 & sdtasdt0(v3, v8) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v6, v3) = v7) | ~ (sdtpldt0(v4, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (sdtasdt0(v5, v3) = v12 & sdtasdt0(v4, v3) = v11 & sdtasdt0(v3, v6) = v8 & sdtasdt0(v3, v5) = v10 & sdtasdt0(v3, v4) = v9 & sdtpldt0(v11, v12) = v7 & sdtpldt0(v9, v10) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v4, v5) = v6) | ~ (sdtasdt0(v3, v6) = v7) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v8] : (sdtasdt0(v8, v5) = v7 & sdtasdt0(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v3, v6) = v7) | ~ (sdtpldt0(v4, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (sdtasdt0(v6, v3) = v10 & sdtasdt0(v5, v3) = v12 & sdtasdt0(v4, v3) = v11 & sdtasdt0(v3, v5) = v9 & sdtasdt0(v3, v4) = v8 & sdtpldt0(v11, v12) = v10 & sdtpldt0(v8, v9) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v6, v5) = v7) | ~ (sdtpldt0(v3, v4) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v8] : (sdtpldt0(v4, v5) = v8 & sdtpldt0(v3, v8) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v4, v5) = v6) | ~ (sdtpldt0(v3, v6) = v7) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v8] : (sdtpldt0(v8, v5) = v7 & sdtpldt0(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | v3 = sz00 | ~ (sdtsldt0(v4, v3) = v5) | ~ (sdtasdt0(v3, v6) = v4) | ~ doDivides0(v3, v4) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtmndt0(v4, v3) = v5) | ~ (sdtpldt0(v3, v6) = v4) | ~ sdtlseqdt0(v3, v4) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v4 | v3 = sz00 | ~ (sdtsldt0(v4, v3) = v5) | ~ (sdtasdt0(v3, v5) = v6) | ~ doDivides0(v3, v4) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v4 | ~ (sdtmndt0(v4, v3) = v5) | ~ (sdtpldt0(v3, v5) = v6) | ~ sdtlseqdt0(v3, v4) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | v3 = sz00 | ~ (sdtasdt0(v5, v3) = v6) | ~ (sdtasdt0(v4, v3) = v6) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | v3 = sz00 | ~ (sdtasdt0(v5, v3) = v6) | ~ (sdtasdt0(v4, v3) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | v3 = sz00 | ~ (sdtasdt0(v3, v5) = v6) | ~ (sdtasdt0(v3, v4) = v6) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | v3 = sz00 | ~ (sdtasdt0(v3, v5) = v6) | ~ (sdtasdt0(v3, v4) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (sdtpldt0(v5, v3) = v6) | ~ (sdtpldt0(v4, v3) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (sdtpldt0(v3, v5) = v6) | ~ (sdtpldt0(v3, v4) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (sdtsldt0(v6, v5) = v4) | ~ (sdtsldt0(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (sdtmndt0(v6, v5) = v4) | ~ (sdtmndt0(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (sdtasdt0(v6, v5) = v4) | ~ (sdtasdt0(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (sdtpldt0(v6, v5) = v4) | ~ (sdtpldt0(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (sdtpldt0(v5, v4) = v6) | ~ sdtlseqdt0(v3, v4) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = v8) & ~ (v7 = v6) & sdtpldt0(v5, v3) = v7 & sdtpldt0(v4, v5) = v9 & sdtpldt0(v3, v5) = v8 & sdtlseqdt0(v8, v9) & sdtlseqdt0(v7, v6))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (sdtpldt0(v5, v3) = v6) | ~ sdtlseqdt0(v3, v4) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = v8) & ~ (v7 = v6) & sdtpldt0(v5, v4) = v7 & sdtpldt0(v4, v5) = v9 & sdtpldt0(v3, v5) = v8 & sdtlseqdt0(v8, v9) & sdtlseqdt0(v6, v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (sdtpldt0(v4, v5) = v6) | ~ sdtlseqdt0(v3, v4) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = v6) & ~ (v8 = v7) & sdtpldt0(v5, v4) = v8 & sdtpldt0(v5, v3) = v7 & sdtpldt0(v3, v5) = v9 & sdtlseqdt0(v9, v6) & sdtlseqdt0(v7, v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (sdtpldt0(v3, v5) = v6) | ~ sdtlseqdt0(v3, v4) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = v6) & ~ (v8 = v7) & sdtpldt0(v5, v4) = v8 & sdtpldt0(v5, v3) = v7 & sdtpldt0(v4, v5) = v9 & sdtlseqdt0(v7, v8) & sdtlseqdt0(v6, v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = sz00 | ~ (sdtsldt0(v4, v3) = v5) | ~ (sdtasdt0(v3, v5) = v6) | ~ doDivides0(v3, v4) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | aNaturalNumber0(v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtmndt0(v4, v3) = v5) | ~ (sdtpldt0(v3, v5) = v6) | ~ sdtlseqdt0(v3, v4) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | aNaturalNumber0(v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v4, v5) = v6) | ~ doDivides0(v3, v5) | ~ doDivides0(v3, v4) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | doDivides0(v3, v6)) & ! [v3] : ! [v4] : ! [v5] : (v3 = sz00 | ~ (sdtasdt0(v4, v3) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | sdtlseqdt0(v4, v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v4, v3) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | sdtasdt0(v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v3, v5) = v4) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | doDivides0(v3, v4)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v3, v4) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | sdtasdt0(v4, v3) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v3, v4) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | aNaturalNumber0(v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtpldt0(v4, v3) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | sdtpldt0(v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtpldt0(v3, v5) = v4) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | sdtlseqdt0(v3, v4)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | sdtpldt0(v4, v3) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | aNaturalNumber0(v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ doDivides0(v4, v5) | ~ doDivides0(v3, v4) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | doDivides0(v3, v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ sdtlseqdt0(v4, v5) | ~ sdtlseqdt0(v3, v4) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | sdtlseqdt0(v3, v5)) & ! [v3] : ! [v4] : (v4 = v3 | ~ (sdtasdt0(v3, sz10) = v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : (v4 = v3 | ~ (sdtasdt0(sz10, v3) = v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : (v4 = v3 | ~ (sdtpldt0(v3, sz00) = v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : (v4 = v3 | ~ (sdtpldt0(sz00, v3) = v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : (v4 = v3 | ~ sdtlseqdt0(v4, v3) | ~ sdtlseqdt0(v3, v4) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : (v4 = v3 | ~ sdtlseqdt0(v3, v4) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | iLess0(v3, v4)) & ! [v3] : ! [v4] : (v4 = sz00 | v3 = sz00 | ~ (sdtasdt0(v3, v4) = sz00) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : (v4 = sz00 | ~ (sdtasdt0(v3, sz00) = v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : (v4 = sz00 | ~ (sdtasdt0(sz00, v3) = v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : (v4 = sz00 | ~ (sdtpldt0(v3, v4) = sz00) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : (v3 = sz00 | ~ (sdtpldt0(v3, v4) = sz00) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3)) & ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, sz10) = v4) | ~ aNaturalNumber0(v3) | sdtasdt0(sz10, v3) = v3) & ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, sz00) = v4) | ~ aNaturalNumber0(v3) | sdtasdt0(sz00, v3) = sz00) & ! [v3] : ! [v4] : ( ~ (sdtasdt0(sz10, v3) = v4) | ~ aNaturalNumber0(v3) | sdtasdt0(v3, sz10) = v3) & ! [v3] : ! [v4] : ( ~ (sdtasdt0(sz00, v3) = v4) | ~ aNaturalNumber0(v3) | sdtasdt0(v3, sz00) = sz00) & ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, sz00) = v4) | ~ aNaturalNumber0(v3) | sdtpldt0(sz00, v3) = v3) & ! [v3] : ! [v4] : ( ~ (sdtpldt0(sz00, v3) = v4) | ~ aNaturalNumber0(v3) | sdtpldt0(v3, sz00) = v3) & ! [v3] : ! [v4] : ( ~ doDivides0(v3, v4) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v5] : (sdtasdt0(v3, v5) = v4 & aNaturalNumber0(v5))) & ! [v3] : ! [v4] : ( ~ sdtlseqdt0(v3, v4) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ? [v5] : (sdtpldt0(v3, v5) = v4 & aNaturalNumber0(v5))) & ! [v3] : ! [v4] : ( ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | sdtlseqdt0(v4, v3) | sdtlseqdt0(v3, v4)) & ! [v3] : (v3 = sz10 | v3 = sz00 | ~ aNaturalNumber0(v3) | sdtlseqdt0(sz10, v3)) & ! [v3] : ( ~ aNaturalNumber0(v3) | sdtlseqdt0(v3, v3)) & ! [v3] : ( ~ aNaturalNumber0(v3) | ? [v4] : ( ~ (v4 = xq) & sdtpldt0(xp, v3) = v4)))
% 9.91/2.91 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 9.91/2.91 | (1) ~ (xl = sz00) & ~ (sz10 = sz00) & sdtsldt0(all_0_2_2, xl) = xq & sdtsldt0(xm, xl) = xp & sdtasdt0(xl, all_0_0_0) = xm & sdtasdt0(xl, all_0_1_1) = all_0_2_2 & sdtasdt0(xl, xq) = all_0_2_2 & sdtasdt0(xl, xp) = xm & sdtpldt0(xm, xn) = all_0_2_2 & doDivides0(xl, all_0_2_2) & doDivides0(xl, xm) & aNaturalNumber0(all_0_0_0) & aNaturalNumber0(all_0_1_1) & 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))
% 10.03/2.93 |
% 10.03/2.93 | Applying alpha-rule on (1) yields:
% 10.03/2.93 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 10.03/2.93 | (3) aNaturalNumber0(xm)
% 10.03/2.93 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 10.03/2.93 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5))
% 10.03/2.93 | (6) ! [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)))
% 10.03/2.94 | (7) aNaturalNumber0(xn)
% 10.03/2.94 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.03/2.94 | (9) sdtasdt0(xl, all_0_0_0) = xm
% 10.03/2.94 | (10) aNaturalNumber0(xl)
% 10.03/2.94 | (11) aNaturalNumber0(xq)
% 10.03/2.94 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 10.03/2.94 | (13) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.03/2.94 | (14) ~ sdtlseqdt0(xp, xq)
% 10.03/2.94 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.03/2.94 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5))
% 10.03/2.94 | (17) sdtasdt0(xl, all_0_1_1) = all_0_2_2
% 10.03/2.94 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.03/2.94 | (19) ! [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)))
% 10.03/2.94 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 10.03/2.94 | (21) doDivides0(xl, xm)
% 10.03/2.94 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0))
% 10.03/2.94 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.03/2.94 | (24) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.03/2.94 | (25) ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 10.03/2.94 | (26) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00)
% 10.03/2.94 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.03/2.94 | (28) ! [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))
% 10.03/2.94 | (29) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 10.03/2.94 | (30) ! [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))
% 10.03/2.94 | (31) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.03/2.94 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 10.03/2.94 | (33) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 10.03/2.94 | (34) ~ (sz10 = sz00)
% 10.03/2.94 | (35) sdtasdt0(xl, xp) = xm
% 10.03/2.94 | (36) ! [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)))
% 10.03/2.94 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4))
% 10.03/2.94 | (38) doDivides0(xl, all_0_2_2)
% 10.03/2.94 | (39) aNaturalNumber0(all_0_1_1)
% 10.03/2.94 | (40) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 10.03/2.94 | (41) ! [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))
% 10.03/2.94 | (42) aNaturalNumber0(xp)
% 10.03/2.94 | (43) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 10.03/2.94 | (44) ! [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))
% 10.03/2.95 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.03/2.95 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v1, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v0, v2) = v6 & sdtlseqdt0(v6, v3) & sdtlseqdt0(v4, v5)))
% 10.03/2.95 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5))
% 10.03/2.95 | (48) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.03/2.95 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 10.03/2.95 | (50) ! [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))
% 10.03/2.95 | (51) ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = xq) & sdtpldt0(xp, v0) = v1))
% 10.03/2.95 | (52) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 10.03/2.95 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 10.03/2.95 | (54) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 10.03/2.95 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5))
% 10.03/2.95 | (56) ~ (xl = sz00)
% 10.03/2.95 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.03/2.95 | (58) sdtsldt0(all_0_2_2, xl) = xq
% 10.03/2.95 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6))
% 10.03/2.95 | (60) ! [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)))
% 10.03/2.95 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.03/2.95 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 10.03/2.95 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.03/2.95 | (64) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 10.03/2.95 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2)
% 10.03/2.95 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 10.03/2.95 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 10.03/2.95 | (68) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 10.03/2.95 | (69) ! [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))
% 10.03/2.95 | (70) sdtasdt0(xl, xq) = all_0_2_2
% 10.03/2.95 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3))
% 10.03/2.95 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5))
% 10.03/2.95 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 10.03/2.95 | (74) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 10.03/2.95 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.03/2.95 | (76) sdtpldt0(xm, xn) = all_0_2_2
% 10.03/2.96 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v1) = v5))
% 10.03/2.96 | (78) ! [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)))
% 10.03/2.96 | (79) ! [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))
% 10.03/2.96 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2)
% 10.03/2.96 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.03/2.96 | (82) sdtsldt0(xm, xl) = xp
% 10.03/2.96 | (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))
% 10.03/2.96 | (84) ! [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))
% 10.03/2.96 | (85) ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 10.03/2.96 | (86) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 10.03/2.96 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v3) & sdtlseqdt0(v4, v6)))
% 10.03/2.96 | (88) aNaturalNumber0(sz10)
% 10.03/2.96 | (89) ! [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))
% 10.03/2.96 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 10.03/2.96 | (91) ! [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)))
% 10.03/2.96 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 10.03/2.96 | (93) aNaturalNumber0(sz00)
% 10.03/2.96 | (94) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 10.03/2.96 | (95) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0)
% 10.03/2.96 | (96) ! [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))
% 10.03/2.96 | (97) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0))
% 10.03/2.96 | (98) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0)
% 10.03/2.96 | (99) aNaturalNumber0(all_0_0_0)
% 10.03/2.96 |
% 10.03/2.96 | Instantiating formula (75) 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:
% 10.03/2.96 | (100) all_0_0_0 = xp | xl = sz00
% 10.03/2.96 |
% 10.03/2.96 | Instantiating formula (75) with all_0_2_2, all_0_1_1, xq, xl and discharging atoms sdtasdt0(xl, all_0_1_1) = all_0_2_2, sdtasdt0(xl, xq) = all_0_2_2, aNaturalNumber0(all_0_1_1), aNaturalNumber0(xq), aNaturalNumber0(xl), yields:
% 10.03/2.96 | (101) all_0_1_1 = xq | xl = sz00
% 10.03/2.96 |
% 10.03/2.96 | Instantiating formula (51) with all_0_0_0 and discharging atoms aNaturalNumber0(all_0_0_0), yields:
% 10.03/2.96 | (102) ? [v0] : ( ~ (v0 = xq) & sdtpldt0(xp, all_0_0_0) = v0)
% 10.03/2.96 |
% 10.03/2.96 | Instantiating formula (51) with all_0_1_1 and discharging atoms aNaturalNumber0(all_0_1_1), yields:
% 10.03/2.96 | (103) ? [v0] : ( ~ (v0 = xq) & sdtpldt0(xp, all_0_1_1) = v0)
% 10.03/2.96 |
% 10.03/2.96 | Instantiating formula (51) with xq and discharging atoms aNaturalNumber0(xq), yields:
% 10.03/2.96 | (104) ? [v0] : ( ~ (v0 = xq) & sdtpldt0(xp, xq) = v0)
% 10.03/2.96 |
% 10.03/2.96 | Instantiating formula (68) with xp, xq and discharging atoms aNaturalNumber0(xq), aNaturalNumber0(xp), ~ sdtlseqdt0(xp, xq), yields:
% 10.03/2.96 | (105) sdtlseqdt0(xq, xp)
% 10.03/2.96 |
% 10.03/2.96 | Instantiating formula (51) with xp and discharging atoms aNaturalNumber0(xp), yields:
% 10.03/2.96 | (106) ? [v0] : ( ~ (v0 = xq) & sdtpldt0(xp, xp) = v0)
% 10.03/2.96 |
% 10.03/2.96 | Instantiating formula (51) with xn and discharging atoms aNaturalNumber0(xn), yields:
% 10.03/2.96 | (107) ? [v0] : ( ~ (v0 = xq) & sdtpldt0(xp, xn) = v0)
% 10.03/2.96 |
% 10.03/2.96 | Instantiating formula (51) with xm and discharging atoms aNaturalNumber0(xm), yields:
% 10.03/2.96 | (108) ? [v0] : ( ~ (v0 = xq) & sdtpldt0(xp, xm) = v0)
% 10.03/2.96 |
% 10.03/2.96 | Instantiating formula (89) with xm, all_0_2_2, all_0_0_0, all_0_1_1, xl and discharging atoms sdtasdt0(xl, all_0_0_0) = xm, sdtasdt0(xl, all_0_1_1) = all_0_2_2, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 10.03/2.96 | (109) all_0_0_0 = all_0_1_1 | xl = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(all_0_0_0, xl) = v1 & sdtasdt0(all_0_1_1, xl) = v0)
% 10.03/2.96 |
% 10.03/2.96 | Instantiating formula (80) with xm, xl, all_0_0_0 and discharging atoms sdtasdt0(xl, all_0_0_0) = xm, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), yields:
% 10.03/2.96 | (110) sdtasdt0(all_0_0_0, xl) = xm
% 10.03/2.96 |
% 10.03/2.96 | Instantiating formula (89) with all_0_2_2, all_0_2_2, all_0_1_1, xq, xl and discharging atoms sdtasdt0(xl, all_0_1_1) = all_0_2_2, sdtasdt0(xl, xq) = all_0_2_2, aNaturalNumber0(all_0_1_1), aNaturalNumber0(xq), aNaturalNumber0(xl), yields:
% 10.03/2.96 | (111) all_0_1_1 = xq | xl = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(all_0_1_1, xl) = v1 & sdtasdt0(xq, xl) = v0)
% 10.03/2.96 |
% 10.03/2.96 | Instantiating formula (89) with all_0_2_2, xm, all_0_1_1, xp, xl and discharging atoms sdtasdt0(xl, all_0_1_1) = all_0_2_2, sdtasdt0(xl, xp) = xm, aNaturalNumber0(all_0_1_1), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 10.03/2.96 | (112) all_0_1_1 = xp | xl = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(all_0_1_1, xl) = v1 & sdtasdt0(xp, xl) = v0)
% 10.03/2.96 |
% 10.03/2.96 | Instantiating formula (80) with all_0_2_2, xl, all_0_1_1 and discharging atoms sdtasdt0(xl, all_0_1_1) = all_0_2_2, aNaturalNumber0(all_0_1_1), aNaturalNumber0(xl), yields:
% 10.03/2.96 | (113) sdtasdt0(all_0_1_1, xl) = all_0_2_2
% 10.03/2.96 |
% 10.03/2.96 | Instantiating formula (15) with all_0_2_2, xq, xl and discharging atoms sdtasdt0(xl, xq) = all_0_2_2, aNaturalNumber0(xq), aNaturalNumber0(xl), yields:
% 10.03/2.96 | (114) aNaturalNumber0(all_0_2_2)
% 10.03/2.96 |
% 10.03/2.96 | Instantiating formula (89) with xm, all_0_2_2, xp, all_0_1_1, xl and discharging atoms sdtasdt0(xl, all_0_1_1) = all_0_2_2, sdtasdt0(xl, xp) = xm, aNaturalNumber0(all_0_1_1), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 10.03/2.97 | (115) all_0_1_1 = xp | xl = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(all_0_1_1, xl) = v0 & sdtasdt0(xp, xl) = v1)
% 10.03/2.97 |
% 10.03/2.97 | Instantiating formula (85) with xm, xl and discharging atoms doDivides0(xl, xm), aNaturalNumber0(xm), aNaturalNumber0(xl), yields:
% 10.03/2.97 | (116) ? [v0] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0))
% 10.03/2.97 |
% 10.03/2.97 | Instantiating formula (51) with xl and discharging atoms aNaturalNumber0(xl), yields:
% 10.03/2.97 | (117) ? [v0] : ( ~ (v0 = xq) & sdtpldt0(xp, xl) = v0)
% 10.03/2.97 |
% 10.03/2.97 | Instantiating formula (51) with sz10 and discharging atoms aNaturalNumber0(sz10), yields:
% 10.03/2.97 | (118) ? [v0] : ( ~ (v0 = xq) & sdtpldt0(xp, sz10) = v0)
% 10.03/2.97 |
% 10.03/2.97 | Instantiating formula (51) with sz00 and discharging atoms aNaturalNumber0(sz00), yields:
% 10.03/2.97 | (119) ? [v0] : ( ~ (v0 = xq) & sdtpldt0(xp, sz00) = v0)
% 10.03/2.97 |
% 10.03/2.97 | Instantiating (104) with all_9_0_3 yields:
% 10.03/2.97 | (120) ~ (all_9_0_3 = xq) & sdtpldt0(xp, xq) = all_9_0_3
% 10.03/2.97 |
% 10.03/2.97 | Applying alpha-rule on (120) yields:
% 10.03/2.97 | (121) ~ (all_9_0_3 = xq)
% 10.03/2.97 | (122) sdtpldt0(xp, xq) = all_9_0_3
% 10.03/2.97 |
% 10.03/2.97 | Instantiating (103) with all_11_0_4 yields:
% 10.03/2.97 | (123) ~ (all_11_0_4 = xq) & sdtpldt0(xp, all_0_1_1) = all_11_0_4
% 10.03/2.97 |
% 10.03/2.97 | Applying alpha-rule on (123) yields:
% 10.03/2.97 | (124) ~ (all_11_0_4 = xq)
% 10.03/2.97 | (125) sdtpldt0(xp, all_0_1_1) = all_11_0_4
% 10.03/2.97 |
% 10.03/2.97 | Instantiating (116) with all_13_0_5 yields:
% 10.03/2.97 | (126) sdtasdt0(xl, all_13_0_5) = xm & aNaturalNumber0(all_13_0_5)
% 10.03/2.97 |
% 10.03/2.97 | Applying alpha-rule on (126) yields:
% 10.03/2.97 | (127) sdtasdt0(xl, all_13_0_5) = xm
% 10.03/2.97 | (128) aNaturalNumber0(all_13_0_5)
% 10.03/2.97 |
% 10.03/2.97 | Instantiating (117) with all_15_0_6 yields:
% 10.03/2.97 | (129) ~ (all_15_0_6 = xq) & sdtpldt0(xp, xl) = all_15_0_6
% 10.03/2.97 |
% 10.03/2.97 | Applying alpha-rule on (129) yields:
% 10.03/2.97 | (130) ~ (all_15_0_6 = xq)
% 10.03/2.97 | (131) sdtpldt0(xp, xl) = all_15_0_6
% 10.03/2.97 |
% 10.03/2.97 | Instantiating (102) with all_17_0_7 yields:
% 10.03/2.97 | (132) ~ (all_17_0_7 = xq) & sdtpldt0(xp, all_0_0_0) = all_17_0_7
% 10.03/2.97 |
% 10.03/2.97 | Applying alpha-rule on (132) yields:
% 10.03/2.97 | (133) ~ (all_17_0_7 = xq)
% 10.03/2.97 | (134) sdtpldt0(xp, all_0_0_0) = all_17_0_7
% 10.03/2.97 |
% 10.03/2.97 | Instantiating (107) with all_19_0_8 yields:
% 10.03/2.97 | (135) ~ (all_19_0_8 = xq) & sdtpldt0(xp, xn) = all_19_0_8
% 10.03/2.97 |
% 10.03/2.97 | Applying alpha-rule on (135) yields:
% 10.03/2.97 | (136) ~ (all_19_0_8 = xq)
% 10.03/2.97 | (137) sdtpldt0(xp, xn) = all_19_0_8
% 10.03/2.97 |
% 10.03/2.97 | Instantiating (108) with all_21_0_9 yields:
% 10.03/2.97 | (138) ~ (all_21_0_9 = xq) & sdtpldt0(xp, xm) = all_21_0_9
% 10.03/2.97 |
% 10.03/2.97 | Applying alpha-rule on (138) yields:
% 10.03/2.97 | (139) ~ (all_21_0_9 = xq)
% 10.03/2.97 | (140) sdtpldt0(xp, xm) = all_21_0_9
% 10.03/2.97 |
% 10.03/2.97 | Instantiating (106) with all_23_0_10 yields:
% 10.03/2.97 | (141) ~ (all_23_0_10 = xq) & sdtpldt0(xp, xp) = all_23_0_10
% 10.03/2.97 |
% 10.03/2.97 | Applying alpha-rule on (141) yields:
% 10.03/2.97 | (142) ~ (all_23_0_10 = xq)
% 10.03/2.97 | (143) sdtpldt0(xp, xp) = all_23_0_10
% 10.03/2.97 |
% 10.03/2.97 | Instantiating (119) with all_25_0_11 yields:
% 10.03/2.97 | (144) ~ (all_25_0_11 = xq) & sdtpldt0(xp, sz00) = all_25_0_11
% 10.03/2.97 |
% 10.03/2.97 | Applying alpha-rule on (144) yields:
% 10.03/2.97 | (145) ~ (all_25_0_11 = xq)
% 10.03/2.97 | (146) sdtpldt0(xp, sz00) = all_25_0_11
% 10.03/2.97 |
% 10.03/2.97 | Instantiating (118) with all_27_0_12 yields:
% 10.03/2.97 | (147) ~ (all_27_0_12 = xq) & sdtpldt0(xp, sz10) = all_27_0_12
% 10.03/2.97 |
% 10.03/2.97 | Applying alpha-rule on (147) yields:
% 10.03/2.97 | (148) ~ (all_27_0_12 = xq)
% 10.03/2.97 | (149) sdtpldt0(xp, sz10) = all_27_0_12
% 10.03/2.97 |
% 10.03/2.97 +-Applying beta-rule and splitting (111), into two cases.
% 10.03/2.97 |-Branch one:
% 10.03/2.97 | (150) xl = sz00
% 10.03/2.97 |
% 10.03/2.97 | Equations (150) can reduce 56 to:
% 10.03/2.97 | (151) $false
% 10.03/2.97 |
% 10.03/2.97 |-The branch is then unsatisfiable
% 10.03/2.97 |-Branch two:
% 10.03/2.97 | (56) ~ (xl = sz00)
% 10.03/2.97 | (153) all_0_1_1 = xq | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(all_0_1_1, xl) = v1 & sdtasdt0(xq, xl) = v0)
% 10.03/2.97 |
% 10.03/2.97 +-Applying beta-rule and splitting (153), into two cases.
% 10.03/2.97 |-Branch one:
% 10.03/2.97 | (154) all_0_1_1 = xq
% 10.03/2.97 |
% 10.03/2.97 | From (154) and (113) follows:
% 10.03/2.97 | (155) sdtasdt0(xq, xl) = all_0_2_2
% 10.03/2.97 |
% 10.03/2.97 | From (154) and (17) follows:
% 10.03/2.97 | (70) sdtasdt0(xl, xq) = all_0_2_2
% 10.03/2.97 |
% 10.03/2.97 | From (154) and (125) follows:
% 10.03/2.97 | (157) sdtpldt0(xp, xq) = all_11_0_4
% 10.03/2.97 |
% 10.03/2.97 | From (154) and (39) follows:
% 10.03/2.97 | (11) aNaturalNumber0(xq)
% 10.03/2.97 |
% 10.03/2.97 +-Applying beta-rule and splitting (100), into two cases.
% 10.03/2.97 |-Branch one:
% 10.03/2.97 | (150) xl = sz00
% 10.03/2.97 |
% 10.03/2.97 | Equations (150) can reduce 56 to:
% 10.03/2.97 | (151) $false
% 10.03/2.97 |
% 10.03/2.97 |-The branch is then unsatisfiable
% 10.03/2.97 |-Branch two:
% 10.03/2.97 | (56) ~ (xl = sz00)
% 10.03/2.97 | (162) all_0_0_0 = xp
% 10.03/2.97 |
% 10.03/2.97 | From (162) and (110) follows:
% 10.03/2.97 | (163) sdtasdt0(xp, xl) = xm
% 10.03/2.97 |
% 10.03/2.97 | From (162) and (9) follows:
% 10.03/2.97 | (35) sdtasdt0(xl, xp) = xm
% 10.03/2.97 |
% 10.03/2.97 | From (162) and (134) follows:
% 10.03/2.97 | (165) sdtpldt0(xp, xp) = all_17_0_7
% 10.03/2.97 |
% 10.03/2.97 | From (162) and (99) follows:
% 10.03/2.97 | (42) aNaturalNumber0(xp)
% 10.03/2.97 |
% 10.03/2.97 | Instantiating formula (73) with xp, xq, all_9_0_3, all_11_0_4 and discharging atoms sdtpldt0(xp, xq) = all_11_0_4, sdtpldt0(xp, xq) = all_9_0_3, yields:
% 10.03/2.97 | (167) all_11_0_4 = all_9_0_3
% 10.03/2.97 |
% 10.03/2.97 | Instantiating formula (73) with xp, xp, all_17_0_7, all_23_0_10 and discharging atoms sdtpldt0(xp, xp) = all_23_0_10, sdtpldt0(xp, xp) = all_17_0_7, yields:
% 10.03/2.97 | (168) all_23_0_10 = all_17_0_7
% 10.03/2.97 |
% 10.03/2.97 | Instantiating formula (54) with all_25_0_11, xp and discharging atoms sdtpldt0(xp, sz00) = all_25_0_11, aNaturalNumber0(xp), yields:
% 10.03/2.97 | (169) all_25_0_11 = xp
% 10.03/2.97 |
% 10.03/2.97 | Instantiating formula (75) with xm, xp, all_13_0_5, xl and discharging atoms sdtasdt0(xl, all_13_0_5) = xm, sdtasdt0(xl, xp) = xm, aNaturalNumber0(all_13_0_5), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 10.03/2.97 | (170) all_13_0_5 = xp | xl = sz00
% 10.03/2.97 |
% 10.03/2.97 | Equations (169) can reduce 145 to:
% 10.03/2.97 | (171) ~ (xq = xp)
% 10.03/2.97 |
% 10.03/2.97 | Simplifying 171 yields:
% 10.03/2.97 | (172) ~ (xq = xp)
% 10.03/2.97 |
% 10.03/2.97 | From (167) and (157) follows:
% 10.03/2.97 | (122) sdtpldt0(xp, xq) = all_9_0_3
% 10.03/2.97 |
% 10.03/2.97 | From (168) and (143) follows:
% 10.03/2.97 | (165) sdtpldt0(xp, xp) = all_17_0_7
% 10.03/2.97 |
% 10.03/2.97 | From (169) and (146) follows:
% 10.03/2.97 | (175) sdtpldt0(xp, sz00) = xp
% 10.03/2.97 |
% 10.03/2.97 +-Applying beta-rule and splitting (112), into two cases.
% 10.03/2.97 |-Branch one:
% 10.03/2.97 | (150) xl = sz00
% 10.03/2.97 |
% 10.03/2.97 | Equations (150) can reduce 56 to:
% 10.03/2.97 | (151) $false
% 10.03/2.97 |
% 10.03/2.97 |-The branch is then unsatisfiable
% 10.03/2.97 |-Branch two:
% 10.03/2.97 | (56) ~ (xl = sz00)
% 10.03/2.97 | (179) all_0_1_1 = xp | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(all_0_1_1, xl) = v1 & sdtasdt0(xp, xl) = v0)
% 10.03/2.97 |
% 10.03/2.97 +-Applying beta-rule and splitting (115), into two cases.
% 10.03/2.97 |-Branch one:
% 10.03/2.97 | (150) xl = sz00
% 10.03/2.97 |
% 10.03/2.97 | Equations (150) can reduce 56 to:
% 10.03/2.97 | (151) $false
% 10.03/2.97 |
% 10.03/2.97 |-The branch is then unsatisfiable
% 10.03/2.97 |-Branch two:
% 10.03/2.97 | (56) ~ (xl = sz00)
% 10.03/2.97 | (183) all_0_1_1 = xp | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(all_0_1_1, xl) = v0 & sdtasdt0(xp, xl) = v1)
% 10.03/2.97 |
% 10.03/2.97 +-Applying beta-rule and splitting (109), into two cases.
% 10.03/2.97 |-Branch one:
% 10.03/2.97 | (150) xl = sz00
% 10.03/2.97 |
% 10.03/2.97 | Equations (150) can reduce 56 to:
% 10.03/2.97 | (151) $false
% 10.03/2.97 |
% 10.03/2.97 |-The branch is then unsatisfiable
% 10.03/2.97 |-Branch two:
% 10.03/2.97 | (56) ~ (xl = sz00)
% 10.03/2.97 | (187) all_0_0_0 = all_0_1_1 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(all_0_0_0, xl) = v1 & sdtasdt0(all_0_1_1, xl) = v0)
% 10.03/2.97 |
% 10.03/2.97 +-Applying beta-rule and splitting (187), into two cases.
% 10.03/2.97 |-Branch one:
% 10.03/2.97 | (188) all_0_0_0 = all_0_1_1
% 10.03/2.97 |
% 10.03/2.97 | Combining equations (188,162) yields a new equation:
% 10.03/2.97 | (189) all_0_1_1 = xp
% 10.03/2.97 |
% 10.03/2.97 | Simplifying 189 yields:
% 10.03/2.97 | (190) all_0_1_1 = xp
% 10.03/2.97 |
% 10.03/2.97 | Combining equations (190,154) yields a new equation:
% 10.03/2.98 | (191) xq = xp
% 10.03/2.98 |
% 10.03/2.98 | Equations (191) can reduce 172 to:
% 10.03/2.98 | (151) $false
% 10.03/2.98 |
% 10.03/2.98 |-The branch is then unsatisfiable
% 10.03/2.98 |-Branch two:
% 10.03/2.98 | (193) ~ (all_0_0_0 = all_0_1_1)
% 10.03/2.98 | (194) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(all_0_0_0, xl) = v1 & sdtasdt0(all_0_1_1, xl) = v0)
% 10.03/2.98 |
% 10.03/2.98 | Instantiating (194) with all_61_0_13, all_61_1_14 yields:
% 10.03/2.98 | (195) ~ (all_61_0_13 = all_61_1_14) & sdtasdt0(all_0_0_0, xl) = all_61_0_13 & sdtasdt0(all_0_1_1, xl) = all_61_1_14
% 10.03/2.98 |
% 10.03/2.98 | Applying alpha-rule on (195) yields:
% 10.03/2.98 | (196) ~ (all_61_0_13 = all_61_1_14)
% 10.03/2.98 | (197) sdtasdt0(all_0_0_0, xl) = all_61_0_13
% 10.03/2.98 | (198) sdtasdt0(all_0_1_1, xl) = all_61_1_14
% 10.03/2.98 |
% 10.03/2.98 | Equations (162,154) can reduce 193 to:
% 10.03/2.98 | (171) ~ (xq = xp)
% 10.03/2.98 |
% 10.03/2.98 | Simplifying 171 yields:
% 10.03/2.98 | (172) ~ (xq = xp)
% 10.03/2.98 |
% 10.03/2.98 | From (162) and (197) follows:
% 10.03/2.98 | (201) sdtasdt0(xp, xl) = all_61_0_13
% 10.03/2.98 |
% 10.03/2.98 | From (154) and (198) follows:
% 10.03/2.98 | (202) sdtasdt0(xq, xl) = all_61_1_14
% 10.03/2.98 |
% 10.03/2.98 +-Applying beta-rule and splitting (170), into two cases.
% 10.03/2.98 |-Branch one:
% 10.03/2.98 | (150) xl = sz00
% 10.03/2.98 |
% 10.03/2.98 | Equations (150) can reduce 56 to:
% 10.03/2.98 | (151) $false
% 10.03/2.98 |
% 10.03/2.98 |-The branch is then unsatisfiable
% 10.03/2.98 |-Branch two:
% 10.03/2.98 | (56) ~ (xl = sz00)
% 10.03/2.98 | (206) all_13_0_5 = xp
% 10.03/2.98 |
% 10.03/2.98 | From (206) and (127) follows:
% 10.03/2.98 | (35) sdtasdt0(xl, xp) = xm
% 10.03/2.98 |
% 10.03/2.98 | From (206) and (128) follows:
% 10.03/2.98 | (42) aNaturalNumber0(xp)
% 10.03/2.98 |
% 10.03/2.98 | Instantiating formula (62) with xq, xl, all_61_1_14, all_0_2_2 and discharging atoms sdtasdt0(xq, xl) = all_61_1_14, sdtasdt0(xq, xl) = all_0_2_2, yields:
% 10.03/2.98 | (209) all_61_1_14 = all_0_2_2
% 10.03/2.98 |
% 10.03/2.98 | Instantiating formula (62) with xp, xl, all_61_0_13, xm and discharging atoms sdtasdt0(xp, xl) = all_61_0_13, sdtasdt0(xp, xl) = xm, yields:
% 10.03/2.98 | (210) all_61_0_13 = xm
% 10.03/2.98 |
% 10.03/2.98 | Equations (210,209) can reduce 196 to:
% 10.03/2.98 | (211) ~ (all_0_2_2 = xm)
% 10.03/2.98 |
% 10.03/2.98 | Simplifying 211 yields:
% 10.03/2.98 | (212) ~ (all_0_2_2 = xm)
% 10.03/2.98 |
% 10.03/2.98 | From (209) and (202) follows:
% 10.03/2.98 | (155) sdtasdt0(xq, xl) = all_0_2_2
% 10.03/2.98 |
% 10.03/2.98 | From (210) and (201) follows:
% 10.03/2.98 | (163) sdtasdt0(xp, xl) = xm
% 10.03/2.98 |
% 10.03/2.98 | Instantiating formula (77) with all_17_0_7, all_9_0_3, xq, xp, xp and discharging atoms sdtpldt0(xp, xq) = all_9_0_3, sdtpldt0(xp, xp) = all_17_0_7, aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 10.03/2.98 | (215) xq = xp | ? [v0] : ? [v1] : ( ~ (v1 = all_17_0_7) & ~ (v0 = all_9_0_3) & sdtpldt0(xq, xp) = v1 & sdtpldt0(xp, xp) = v0)
% 10.03/2.98 |
% 10.03/2.98 | Instantiating formula (16) with all_17_0_7, all_9_0_3, xp, xq, xp and discharging atoms sdtpldt0(xp, xq) = all_9_0_3, sdtpldt0(xp, xp) = all_17_0_7, aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 10.03/2.98 | (216) xq = xp | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xq, xp) = v0 & sdtpldt0(xp, xp) = v1)
% 10.03/2.98 |
% 10.03/2.98 | Instantiating formula (16) with xp, all_15_0_6, sz00, xl, xp and discharging atoms sdtpldt0(xp, xl) = all_15_0_6, sdtpldt0(xp, sz00) = xp, aNaturalNumber0(xp), aNaturalNumber0(xl), aNaturalNumber0(sz00), yields:
% 10.03/2.98 | (217) xl = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xl, xp) = v0 & sdtpldt0(sz00, xp) = v1)
% 10.03/2.98 |
% 10.03/2.98 | Instantiating formula (87) with all_0_2_2, xm, xp, xq, xl and discharging atoms sdtasdt0(xq, xl) = all_0_2_2, sdtasdt0(xl, xp) = xm, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 10.03/2.98 | (218) xq = xp | xl = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = all_0_2_2) & ~ (v0 = xm) & sdtasdt0(xp, xl) = v1 & sdtasdt0(xl, xq) = v0 & sdtlseqdt0(v0, xm) & sdtlseqdt0(all_0_2_2, v1))
% 10.03/2.98 |
% 10.03/2.98 | Instantiating formula (36) with xm, all_0_2_2, xp, xq, xl and discharging atoms sdtasdt0(xp, xl) = xm, sdtasdt0(xl, xq) = all_0_2_2, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 10.03/2.98 | (219) xq = xp | xl = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = xm) & ~ (v0 = all_0_2_2) & sdtasdt0(xq, xl) = v1 & sdtasdt0(xl, xp) = v0 & sdtlseqdt0(v1, xm) & sdtlseqdt0(all_0_2_2, v0))
% 10.03/2.98 |
% 10.03/2.98 | Instantiating formula (37) with xm, all_0_2_2, xp, xq, xl and discharging atoms sdtasdt0(xq, xl) = all_0_2_2, sdtasdt0(xp, xl) = xm, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 10.03/2.98 | (220) xq = xp | xl = sz00 | sdtlseqdt0(all_0_2_2, xm)
% 10.03/2.98 |
% 10.03/2.98 | Instantiating formula (19) with all_17_0_7, xp, xp, xq and discharging atoms sdtpldt0(xp, xp) = all_17_0_7, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 10.03/2.98 | (221) xq = xp | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = all_17_0_7) & sdtpldt0(xq, xp) = v1 & sdtpldt0(xp, xq) = v0 & sdtpldt0(xp, xp) = v2 & sdtlseqdt0(v1, v2) & sdtlseqdt0(v0, all_17_0_7))
% 10.03/2.98 |
% 10.03/2.98 | Instantiating formula (46) with all_17_0_7, xp, xp, xq and discharging atoms sdtpldt0(xp, xp) = all_17_0_7, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), yields:
% 10.03/2.98 | (222) xq = xp | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_17_0_7) & ~ (v1 = v0) & sdtpldt0(xq, xp) = v2 & sdtpldt0(xp, xq) = v0 & sdtpldt0(xp, xp) = v1 & sdtlseqdt0(v2, all_17_0_7) & sdtlseqdt0(v0, v1))
% 10.03/2.98 |
% 10.03/2.98 | Instantiating formula (46) with all_19_0_8, xn, xp, xq and discharging atoms sdtpldt0(xp, xn) = all_19_0_8, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xn), yields:
% 10.03/2.98 | (223) xq = xp | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_19_0_8) & ~ (v1 = v0) & sdtpldt0(xq, xn) = v2 & sdtpldt0(xn, xq) = v0 & sdtpldt0(xn, xp) = v1 & sdtlseqdt0(v2, all_19_0_8) & sdtlseqdt0(v0, v1))
% 10.03/2.98 |
% 10.03/2.98 | Instantiating formula (46) with all_21_0_9, xm, xp, xq and discharging atoms sdtpldt0(xp, xm) = all_21_0_9, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xm), yields:
% 10.03/2.98 | (224) xq = xp | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_21_0_9) & ~ (v1 = v0) & sdtpldt0(xq, xm) = v2 & sdtpldt0(xm, xq) = v0 & sdtpldt0(xm, xp) = v1 & sdtlseqdt0(v2, all_21_0_9) & sdtlseqdt0(v0, v1))
% 10.03/2.98 |
% 10.03/2.98 | Instantiating formula (46) with all_15_0_6, xl, xp, xq and discharging atoms sdtpldt0(xp, xl) = all_15_0_6, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 10.03/2.98 | (225) xq = xp | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_15_0_6) & ~ (v1 = v0) & sdtpldt0(xq, xl) = v2 & sdtpldt0(xl, xq) = v0 & sdtpldt0(xl, xp) = v1 & sdtlseqdt0(v2, all_15_0_6) & sdtlseqdt0(v0, v1))
% 10.03/2.98 |
% 10.03/2.98 | Instantiating formula (46) with all_27_0_12, sz10, xp, xq and discharging atoms sdtpldt0(xp, sz10) = all_27_0_12, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(sz10), yields:
% 10.03/2.98 | (226) xq = xp | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_27_0_12) & ~ (v1 = v0) & sdtpldt0(xq, sz10) = v2 & sdtpldt0(sz10, xq) = v0 & sdtpldt0(sz10, xp) = v1 & sdtlseqdt0(v2, all_27_0_12) & sdtlseqdt0(v0, v1))
% 10.03/2.98 |
% 10.03/2.98 | Instantiating formula (46) with xp, sz00, xp, xq and discharging atoms sdtpldt0(xp, sz00) = xp, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(sz00), yields:
% 10.03/2.98 | (227) 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))
% 10.03/2.98 |
% 10.03/2.98 | Instantiating formula (94) with xn, all_0_2_2, xm and discharging atoms sdtpldt0(xm, xn) = all_0_2_2, aNaturalNumber0(all_0_2_2), aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 10.03/2.98 | (228) sdtlseqdt0(xm, all_0_2_2)
% 10.03/2.98 |
% 10.03/2.98 +-Applying beta-rule and splitting (215), into two cases.
% 10.03/2.98 |-Branch one:
% 10.03/2.98 | (191) xq = xp
% 10.03/2.98 |
% 10.03/2.98 | Equations (191) can reduce 172 to:
% 10.03/2.98 | (151) $false
% 10.03/2.98 |
% 10.03/2.98 |-The branch is then unsatisfiable
% 10.03/2.98 |-Branch two:
% 10.03/2.98 | (172) ~ (xq = xp)
% 10.03/2.98 | (232) ? [v0] : ? [v1] : ( ~ (v1 = all_17_0_7) & ~ (v0 = all_9_0_3) & sdtpldt0(xq, xp) = v1 & sdtpldt0(xp, xp) = v0)
% 10.03/2.98 |
% 10.03/2.98 +-Applying beta-rule and splitting (222), into two cases.
% 10.03/2.98 |-Branch one:
% 10.03/2.98 | (191) xq = xp
% 10.03/2.98 |
% 10.03/2.98 | Equations (191) can reduce 172 to:
% 10.03/2.98 | (151) $false
% 10.03/2.98 |
% 10.03/2.98 |-The branch is then unsatisfiable
% 10.03/2.98 |-Branch two:
% 10.03/2.98 | (172) ~ (xq = xp)
% 10.03/2.98 | (236) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_17_0_7) & ~ (v1 = v0) & sdtpldt0(xq, xp) = v2 & sdtpldt0(xp, xq) = v0 & sdtpldt0(xp, xp) = v1 & sdtlseqdt0(v2, all_17_0_7) & sdtlseqdt0(v0, v1))
% 10.03/2.98 |
% 10.03/2.98 +-Applying beta-rule and splitting (227), into two cases.
% 10.03/2.98 |-Branch one:
% 10.03/2.98 | (191) xq = xp
% 10.03/2.98 |
% 10.03/2.98 | Equations (191) can reduce 172 to:
% 10.03/2.98 | (151) $false
% 10.03/2.98 |
% 10.03/2.98 |-The branch is then unsatisfiable
% 10.03/2.98 |-Branch two:
% 10.03/2.98 | (172) ~ (xq = xp)
% 10.03/2.98 | (240) ? [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))
% 10.03/2.98 |
% 10.03/2.98 +-Applying beta-rule and splitting (223), into two cases.
% 10.03/2.98 |-Branch one:
% 10.03/2.98 | (191) xq = xp
% 10.03/2.98 |
% 10.03/2.98 | Equations (191) can reduce 172 to:
% 10.03/2.98 | (151) $false
% 10.03/2.98 |
% 10.03/2.98 |-The branch is then unsatisfiable
% 10.03/2.98 |-Branch two:
% 10.03/2.98 | (172) ~ (xq = xp)
% 10.03/2.98 | (244) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_19_0_8) & ~ (v1 = v0) & sdtpldt0(xq, xn) = v2 & sdtpldt0(xn, xq) = v0 & sdtpldt0(xn, xp) = v1 & sdtlseqdt0(v2, all_19_0_8) & sdtlseqdt0(v0, v1))
% 10.03/2.99 |
% 10.03/2.99 +-Applying beta-rule and splitting (224), into two cases.
% 10.03/2.99 |-Branch one:
% 10.03/2.99 | (191) xq = xp
% 10.03/2.99 |
% 10.03/2.99 | Equations (191) can reduce 172 to:
% 10.03/2.99 | (151) $false
% 10.03/2.99 |
% 10.03/2.99 |-The branch is then unsatisfiable
% 10.03/2.99 |-Branch two:
% 10.03/2.99 | (172) ~ (xq = xp)
% 10.03/2.99 | (248) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_21_0_9) & ~ (v1 = v0) & sdtpldt0(xq, xm) = v2 & sdtpldt0(xm, xq) = v0 & sdtpldt0(xm, xp) = v1 & sdtlseqdt0(v2, all_21_0_9) & sdtlseqdt0(v0, v1))
% 10.03/2.99 |
% 10.03/2.99 +-Applying beta-rule and splitting (225), into two cases.
% 10.03/2.99 |-Branch one:
% 10.03/2.99 | (191) xq = xp
% 10.03/2.99 |
% 10.03/2.99 | Equations (191) can reduce 172 to:
% 10.03/2.99 | (151) $false
% 10.03/2.99 |
% 10.03/2.99 |-The branch is then unsatisfiable
% 10.03/2.99 |-Branch two:
% 10.03/2.99 | (172) ~ (xq = xp)
% 10.03/2.99 | (252) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_15_0_6) & ~ (v1 = v0) & sdtpldt0(xq, xl) = v2 & sdtpldt0(xl, xq) = v0 & sdtpldt0(xl, xp) = v1 & sdtlseqdt0(v2, all_15_0_6) & sdtlseqdt0(v0, v1))
% 10.03/2.99 |
% 10.03/2.99 +-Applying beta-rule and splitting (216), into two cases.
% 10.03/2.99 |-Branch one:
% 10.03/2.99 | (191) xq = xp
% 10.03/2.99 |
% 10.03/2.99 | Equations (191) can reduce 172 to:
% 10.03/2.99 | (151) $false
% 10.03/2.99 |
% 10.03/2.99 |-The branch is then unsatisfiable
% 10.03/2.99 |-Branch two:
% 10.03/2.99 | (172) ~ (xq = xp)
% 10.03/2.99 | (256) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xq, xp) = v0 & sdtpldt0(xp, xp) = v1)
% 10.03/2.99 |
% 10.03/2.99 +-Applying beta-rule and splitting (226), into two cases.
% 10.03/2.99 |-Branch one:
% 10.03/2.99 | (191) xq = xp
% 10.03/2.99 |
% 10.03/2.99 | Equations (191) can reduce 172 to:
% 10.03/2.99 | (151) $false
% 10.03/2.99 |
% 10.03/2.99 |-The branch is then unsatisfiable
% 10.03/2.99 |-Branch two:
% 10.03/2.99 | (172) ~ (xq = xp)
% 10.03/2.99 | (260) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_27_0_12) & ~ (v1 = v0) & sdtpldt0(xq, sz10) = v2 & sdtpldt0(sz10, xq) = v0 & sdtpldt0(sz10, xp) = v1 & sdtlseqdt0(v2, all_27_0_12) & sdtlseqdt0(v0, v1))
% 10.03/2.99 |
% 10.03/2.99 +-Applying beta-rule and splitting (217), into two cases.
% 10.03/2.99 |-Branch one:
% 10.03/2.99 | (150) xl = sz00
% 10.03/2.99 |
% 10.03/2.99 | Equations (150) can reduce 56 to:
% 10.03/2.99 | (151) $false
% 10.03/2.99 |
% 10.03/2.99 |-The branch is then unsatisfiable
% 10.03/2.99 |-Branch two:
% 10.03/2.99 | (56) ~ (xl = sz00)
% 10.03/2.99 | (264) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xl, xp) = v0 & sdtpldt0(sz00, xp) = v1)
% 10.03/2.99 |
% 10.03/2.99 +-Applying beta-rule and splitting (220), into two cases.
% 10.03/2.99 |-Branch one:
% 10.03/2.99 | (265) sdtlseqdt0(all_0_2_2, xm)
% 10.03/2.99 |
% 10.03/2.99 | Instantiating formula (24) with all_0_2_2, xm and discharging atoms sdtlseqdt0(all_0_2_2, xm), sdtlseqdt0(xm, all_0_2_2), aNaturalNumber0(all_0_2_2), aNaturalNumber0(xm), yields:
% 10.03/2.99 | (266) all_0_2_2 = xm
% 10.03/2.99 |
% 10.03/2.99 | Equations (266) can reduce 212 to:
% 10.03/2.99 | (151) $false
% 10.03/2.99 |
% 10.03/2.99 |-The branch is then unsatisfiable
% 10.03/2.99 |-Branch two:
% 10.03/2.99 | (268) ~ sdtlseqdt0(all_0_2_2, xm)
% 10.03/2.99 | (269) xq = xp | xl = sz00
% 10.03/2.99 |
% 10.03/2.99 +-Applying beta-rule and splitting (219), into two cases.
% 10.03/2.99 |-Branch one:
% 10.03/2.99 | (150) xl = sz00
% 10.03/2.99 |
% 10.03/2.99 | Equations (150) can reduce 56 to:
% 10.03/2.99 | (151) $false
% 10.03/2.99 |
% 10.03/2.99 |-The branch is then unsatisfiable
% 10.03/2.99 |-Branch two:
% 10.03/2.99 | (56) ~ (xl = sz00)
% 10.03/2.99 | (273) xq = xp | ? [v0] : ? [v1] : ( ~ (v1 = xm) & ~ (v0 = all_0_2_2) & sdtasdt0(xq, xl) = v1 & sdtasdt0(xl, xp) = v0 & sdtlseqdt0(v1, xm) & sdtlseqdt0(all_0_2_2, v0))
% 10.03/2.99 |
% 10.03/2.99 +-Applying beta-rule and splitting (218), into two cases.
% 10.03/2.99 |-Branch one:
% 10.03/2.99 | (150) xl = sz00
% 10.03/2.99 |
% 10.03/2.99 | Equations (150) can reduce 56 to:
% 10.03/2.99 | (151) $false
% 10.03/2.99 |
% 10.03/2.99 |-The branch is then unsatisfiable
% 10.03/2.99 |-Branch two:
% 10.03/2.99 | (56) ~ (xl = sz00)
% 10.03/2.99 | (277) xq = xp | ? [v0] : ? [v1] : ( ~ (v1 = all_0_2_2) & ~ (v0 = xm) & sdtasdt0(xp, xl) = v1 & sdtasdt0(xl, xq) = v0 & sdtlseqdt0(v0, xm) & sdtlseqdt0(all_0_2_2, v1))
% 10.03/2.99 |
% 10.03/2.99 +-Applying beta-rule and splitting (277), into two cases.
% 10.03/2.99 |-Branch one:
% 10.03/2.99 | (191) xq = xp
% 10.03/2.99 |
% 10.03/2.99 | Equations (191) can reduce 172 to:
% 10.03/2.99 | (151) $false
% 10.03/2.99 |
% 10.03/2.99 |-The branch is then unsatisfiable
% 10.03/2.99 |-Branch two:
% 10.03/2.99 | (172) ~ (xq = xp)
% 10.03/2.99 | (281) ? [v0] : ? [v1] : ( ~ (v1 = all_0_2_2) & ~ (v0 = xm) & sdtasdt0(xp, xl) = v1 & sdtasdt0(xl, xq) = v0 & sdtlseqdt0(v0, xm) & sdtlseqdt0(all_0_2_2, v1))
% 10.03/2.99 |
% 10.03/2.99 +-Applying beta-rule and splitting (221), into two cases.
% 10.03/2.99 |-Branch one:
% 10.03/2.99 | (191) xq = xp
% 10.03/2.99 |
% 10.03/2.99 | Equations (191) can reduce 172 to:
% 10.03/2.99 | (151) $false
% 10.03/2.99 |
% 10.03/2.99 |-The branch is then unsatisfiable
% 10.03/2.99 |-Branch two:
% 10.03/2.99 | (172) ~ (xq = xp)
% 10.03/2.99 | (285) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & ~ (v0 = all_17_0_7) & sdtpldt0(xq, xp) = v1 & sdtpldt0(xp, xq) = v0 & sdtpldt0(xp, xp) = v2 & sdtlseqdt0(v1, v2) & sdtlseqdt0(v0, all_17_0_7))
% 10.03/2.99 |
% 10.03/2.99 +-Applying beta-rule and splitting (269), into two cases.
% 10.03/2.99 |-Branch one:
% 10.03/2.99 | (150) xl = sz00
% 10.03/2.99 |
% 10.03/2.99 | Equations (150) can reduce 56 to:
% 10.03/2.99 | (151) $false
% 10.03/2.99 |
% 10.03/2.99 |-The branch is then unsatisfiable
% 10.03/2.99 |-Branch two:
% 10.03/2.99 | (56) ~ (xl = sz00)
% 10.03/2.99 | (191) xq = xp
% 10.03/2.99 |
% 10.03/2.99 | Equations (191) can reduce 172 to:
% 10.03/2.99 | (151) $false
% 10.03/2.99 |
% 10.03/2.99 |-The branch is then unsatisfiable
% 10.03/2.99 |-Branch two:
% 10.03/2.99 | (291) ~ (all_0_1_1 = xq)
% 10.03/2.99 | (292) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(all_0_1_1, xl) = v1 & sdtasdt0(xq, xl) = v0)
% 10.03/2.99 |
% 10.03/2.99 +-Applying beta-rule and splitting (101), into two cases.
% 10.03/2.99 |-Branch one:
% 10.03/2.99 | (150) xl = sz00
% 10.03/2.99 |
% 10.03/2.99 | Equations (150) can reduce 56 to:
% 10.03/2.99 | (151) $false
% 10.03/2.99 |
% 10.03/2.99 |-The branch is then unsatisfiable
% 10.03/2.99 |-Branch two:
% 10.03/2.99 | (56) ~ (xl = sz00)
% 10.03/2.99 | (154) all_0_1_1 = xq
% 10.03/2.99 |
% 10.03/2.99 | Equations (154) can reduce 291 to:
% 10.03/2.99 | (151) $false
% 10.03/2.99 |
% 10.03/2.99 |-The branch is then unsatisfiable
% 10.03/2.99 % SZS output end Proof for theBenchmark
% 10.03/2.99
% 10.03/2.99 2343ms
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