TSTP Solution File: NUM462+2 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM462+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.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 08:44:44 EDT 2022
% Result : Theorem 8.56s 2.67s
% Output : Proof 19.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM462+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jul 7 17:43:14 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.57/0.60 ____ _
% 0.57/0.60 ___ / __ \_____(_)___ ________ __________
% 0.57/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.60
% 0.57/0.60 A Theorem Prover for First-Order Logic
% 0.57/0.60 (ePrincess v.1.0)
% 0.57/0.60
% 0.57/0.60 (c) Philipp Rümmer, 2009-2015
% 0.57/0.60 (c) Peter Backeman, 2014-2015
% 0.57/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.60 Bug reports to peter@backeman.se
% 0.57/0.60
% 0.57/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.60
% 0.57/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.85/1.02 Prover 0: Preprocessing ...
% 3.59/1.49 Prover 0: Constructing countermodel ...
% 8.56/2.67 Prover 0: proved (2015ms)
% 8.56/2.67
% 8.56/2.67 No countermodel exists, formula is valid
% 8.56/2.67 % SZS status Theorem for theBenchmark
% 8.56/2.67
% 8.56/2.67 Generating proof ... found it (size 166)
% 18.56/5.07
% 18.56/5.07 % SZS output start Proof for theBenchmark
% 18.56/5.07 Assumed formulas after preprocessing and simplification:
% 18.56/5.07 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (xn = xl) & ~ (xm = sz00) & ~ (sz10 = sz00) & sdtasdt0(xn, xm) = v3 & sdtasdt0(xl, xm) = v2 & sdtasdt0(xm, xn) = v1 & sdtasdt0(xm, xl) = v0 & sdtpldt0(xl, v4) = xn & sdtlseqdt0(xl, xn) & aNaturalNumber0(v4) & aNaturalNumber0(xn) & aNaturalNumber0(xl) & aNaturalNumber0(xm) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v7, v5) = v9) | ~ (sdtasdt0(v6, v5) = v8) | ~ (sdtpldt0(v8, v9) = v10) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v11, v5) = v10 & sdtasdt0(v5, v11) = v12 & sdtasdt0(v5, v7) = v14 & sdtasdt0(v5, v6) = v13 & sdtpldt0(v13, v14) = v12 & sdtpldt0(v6, v7) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v5, v7) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ (sdtpldt0(v8, v9) = v10) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v11, v5) = v12 & sdtasdt0(v7, v5) = v14 & sdtasdt0(v6, v5) = v13 & sdtasdt0(v5, v11) = v10 & sdtpldt0(v13, v14) = v12 & sdtpldt0(v6, v7) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v9) | ~ (sdtasdt0(v6, v5) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtasdt0(v5, v7) = v11 & sdtasdt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtasdt0(v6, v5) = v11 & sdtasdt0(v5, v7) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v6, v5) = v9) | ~ (sdtasdt0(v5, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtasdt0(v7, v5) = v11 & sdtasdt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v5, v7) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtasdt0(v7, v5) = v11 & sdtasdt0(v6, v5) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v7, v5) = v9) | ~ (sdtpldt0(v6, v5) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtpldt0(v5, v7) = v11 & sdtpldt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v7, v5) = v9) | ~ (sdtpldt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtpldt0(v6, v5) = v11 & sdtpldt0(v5, v7) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v6, v5) = v9) | ~ (sdtpldt0(v5, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtpldt0(v7, v5) = v11 & sdtpldt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v5, v7) = v9) | ~ (sdtpldt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtpldt0(v7, v5) = v11 & sdtpldt0(v6, v5) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v8, v7) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : (sdtasdt0(v6, v7) = v10 & sdtasdt0(v5, v10) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v8, v5) = v9) | ~ (sdtpldt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v7, v5) = v14 & sdtasdt0(v6, v5) = v13 & sdtasdt0(v5, v8) = v10 & sdtasdt0(v5, v7) = v12 & sdtasdt0(v5, v6) = v11 & sdtpldt0(v13, v14) = v9 & sdtpldt0(v11, v12) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v6, v7) = v8) | ~ (sdtasdt0(v5, v8) = v9) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : (sdtasdt0(v10, v7) = v9 & sdtasdt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v5, v8) = v9) | ~ (sdtpldt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v8, v5) = v12 & sdtasdt0(v7, v5) = v14 & sdtasdt0(v6, v5) = v13 & sdtasdt0(v5, v7) = v11 & sdtasdt0(v5, v6) = v10 & sdtpldt0(v13, v14) = v12 & sdtpldt0(v10, v11) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v8, v7) = v9) | ~ (sdtpldt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : (sdtpldt0(v6, v7) = v10 & sdtpldt0(v5, v10) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v6, v7) = v8) | ~ (sdtpldt0(v5, v8) = v9) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : (sdtpldt0(v10, v7) = v9 & sdtpldt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ (sdtmndt0(v6, v5) = v7) | ~ (sdtpldt0(v5, v8) = v6) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v6 | ~ (sdtmndt0(v6, v5) = v7) | ~ (sdtpldt0(v5, v7) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v8) | ~ (sdtasdt0(v6, v5) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v5, v7) = v8) | ~ (sdtasdt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (sdtpldt0(v7, v5) = v8) | ~ (sdtpldt0(v6, v5) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (sdtpldt0(v5, v7) = v8) | ~ (sdtpldt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtmndt0(v8, v7) = v6) | ~ (sdtmndt0(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtasdt0(v8, v7) = v6) | ~ (sdtasdt0(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v8, v7) = v6) | ~ (sdtpldt0(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v7, v6) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = v10) & ~ (v9 = v8) & sdtpldt0(v7, v5) = v9 & sdtpldt0(v6, v7) = v11 & sdtpldt0(v5, v7) = v10 & sdtlseqdt0(v10, v11) & sdtlseqdt0(v9, v8))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v7, v5) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = v10) & ~ (v9 = v8) & sdtpldt0(v7, v6) = v9 & sdtpldt0(v6, v7) = v11 & sdtpldt0(v5, v7) = v10 & sdtlseqdt0(v10, v11) & sdtlseqdt0(v8, v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v6, v7) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = v8) & ~ (v10 = v9) & sdtpldt0(v7, v6) = v10 & sdtpldt0(v7, v5) = v9 & sdtpldt0(v5, v7) = v11 & sdtlseqdt0(v11, v8) & sdtlseqdt0(v9, v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v5, v7) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = v8) & ~ (v10 = v9) & sdtpldt0(v7, v6) = v10 & sdtpldt0(v7, v5) = v9 & sdtpldt0(v6, v7) = v11 & sdtlseqdt0(v9, v10) & sdtlseqdt0(v8, v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtmndt0(v6, v5) = v7) | ~ (sdtpldt0(v5, v7) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | aNaturalNumber0(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v6, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtasdt0(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtasdt0(v6, v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | aNaturalNumber0(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v6, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtpldt0(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v7) = v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtlseqdt0(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtpldt0(v6, v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | aNaturalNumber0(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ sdtlseqdt0(v6, v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtlseqdt0(v5, v7)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtasdt0(v5, sz10) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtasdt0(sz10, v5) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtpldt0(v5, sz00) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtpldt0(sz00, v5) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ sdtlseqdt0(v6, v5) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = sz00 | v5 = sz00 | ~ (sdtasdt0(v5, v6) = sz00) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = sz00 | ~ (sdtasdt0(v5, sz00) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = sz00 | ~ (sdtasdt0(sz00, v5) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = sz00 | ~ (sdtpldt0(v5, v6) = sz00) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v5 = sz00 | ~ (sdtpldt0(v5, v6) = sz00) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, sz10) = v6) | ~ aNaturalNumber0(v5) | sdtasdt0(sz10, v5) = v5) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, sz00) = v6) | ~ aNaturalNumber0(v5) | sdtasdt0(sz00, v5) = sz00) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(sz10, v5) = v6) | ~ aNaturalNumber0(v5) | sdtasdt0(v5, sz10) = v5) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(sz00, v5) = v6) | ~ aNaturalNumber0(v5) | sdtasdt0(v5, sz00) = sz00) & ! [v5] : ! [v6] : ( ~ (sdtpldt0(v5, sz00) = v6) | ~ aNaturalNumber0(v5) | sdtpldt0(sz00, v5) = v5) & ! [v5] : ! [v6] : ( ~ (sdtpldt0(sz00, v5) = v6) | ~ aNaturalNumber0(v5) | sdtpldt0(v5, sz00) = v5) & ! [v5] : ! [v6] : ( ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v7] : (sdtpldt0(v5, v7) = v6 & aNaturalNumber0(v7))) & ! [v5] : ! [v6] : ( ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtlseqdt0(v6, v5) | sdtlseqdt0(v5, v6)) & ! [v5] : ( ~ aNaturalNumber0(v5) | sdtlseqdt0(v5, v5)) & (v3 = v2 | v1 = v0 | ( ~ sdtlseqdt0(v2, v3) & ! [v5] : ( ~ aNaturalNumber0(v5) | ? [v6] : ( ~ (v6 = v3) & sdtpldt0(v2, v5) = v6))) | ( ~ sdtlseqdt0(v0, v1) & ! [v5] : ( ~ aNaturalNumber0(v5) | ? [v6] : ( ~ (v6 = v1) & sdtpldt0(v0, v5) = v6)))))
% 18.86/5.15 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 18.86/5.15 | (1) ~ (xn = xl) & ~ (xm = sz00) & ~ (sz10 = sz00) & sdtasdt0(xn, xm) = all_0_1_1 & sdtasdt0(xl, xm) = all_0_2_2 & sdtasdt0(xm, xn) = all_0_3_3 & sdtasdt0(xm, xl) = all_0_4_4 & sdtpldt0(xl, all_0_0_0) = xn & sdtlseqdt0(xl, xn) & aNaturalNumber0(all_0_0_0) & aNaturalNumber0(xn) & aNaturalNumber0(xl) & aNaturalNumber0(xm) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ 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) | ~ 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) | ~ 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) | ~ 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 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ 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) | ~ 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 | ~ (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] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2) & ! [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] : ( ~ 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 = 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] : ( ~ 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] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) & (all_0_1_1 = all_0_2_2 | all_0_3_3 = all_0_4_4 | ( ~ sdtlseqdt0(all_0_2_2, all_0_1_1) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_1_1) & sdtpldt0(all_0_2_2, v0) = v1))) | ( ~ sdtlseqdt0(all_0_4_4, all_0_3_3) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_3_3) & sdtpldt0(all_0_4_4, v0) = v1))))
% 18.86/5.17 |
% 18.86/5.17 | Applying alpha-rule on (1) yields:
% 18.86/5.17 | (2) ! [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))
% 18.86/5.17 | (3) ! [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))
% 18.86/5.17 | (4) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 18.86/5.17 | (5) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 18.86/5.17 | (6) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 18.86/5.17 | (7) ! [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))
% 18.86/5.17 | (8) ! [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))
% 18.86/5.18 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 18.86/5.18 | (10) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 18.86/5.18 | (11) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 18.86/5.18 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 18.86/5.18 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 18.86/5.18 | (14) ~ (xn = xl)
% 18.86/5.18 | (15) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 18.86/5.18 | (16) ~ (sz10 = sz00)
% 18.86/5.18 | (17) aNaturalNumber0(all_0_0_0)
% 18.86/5.18 | (18) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 18.86/5.18 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 18.86/5.18 | (20) ! [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))
% 18.86/5.18 | (21) sdtpldt0(xl, all_0_0_0) = xn
% 18.86/5.18 | (22) aNaturalNumber0(xn)
% 18.86/5.18 | (23) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 18.86/5.18 | (24) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0))
% 18.86/5.18 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 18.86/5.18 | (26) aNaturalNumber0(xm)
% 18.86/5.18 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 18.86/5.18 | (28) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 18.86/5.18 | (29) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 18.86/5.18 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 18.86/5.18 | (31) sdtasdt0(xm, xl) = all_0_4_4
% 18.86/5.18 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 18.86/5.18 | (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)))
% 18.86/5.18 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 18.86/5.18 | (35) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0)
% 18.86/5.18 | (36) ! [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))
% 18.86/5.18 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 18.86/5.18 | (38) ! [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))
% 18.86/5.19 | (39) ! [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))
% 18.86/5.19 | (40) ! [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)))
% 18.86/5.19 | (41) ! [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))
% 18.86/5.19 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 18.86/5.19 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2)
% 18.86/5.19 | (44) ! [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)))
% 18.86/5.19 | (45) ~ (xm = sz00)
% 18.86/5.19 | (46) ! [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)))
% 18.86/5.19 | (47) ! [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))
% 18.86/5.19 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 18.86/5.19 | (49) ! [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))
% 18.86/5.19 | (50) sdtasdt0(xl, xm) = all_0_2_2
% 18.86/5.19 | (51) sdtasdt0(xm, xn) = all_0_3_3
% 18.86/5.19 | (52) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00)
% 18.86/5.19 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 18.86/5.19 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 18.86/5.19 | (55) ! [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))
% 18.86/5.19 | (56) ! [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))
% 18.86/5.19 | (57) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0))
% 18.86/5.19 | (58) ! [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))
% 18.86/5.19 | (59) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0))
% 18.86/5.20 | (60) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 18.86/5.20 | (61) ! [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))
% 18.86/5.20 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 18.86/5.20 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2)
% 18.86/5.20 | (64) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0)
% 18.86/5.20 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 18.86/5.20 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 18.86/5.20 | (67) ! [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))
% 18.86/5.20 | (68) sdtlseqdt0(xl, xn)
% 18.86/5.20 | (69) aNaturalNumber0(sz00)
% 18.86/5.20 | (70) all_0_1_1 = all_0_2_2 | all_0_3_3 = all_0_4_4 | ( ~ sdtlseqdt0(all_0_2_2, all_0_1_1) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_1_1) & sdtpldt0(all_0_2_2, v0) = v1))) | ( ~ sdtlseqdt0(all_0_4_4, all_0_3_3) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_3_3) & sdtpldt0(all_0_4_4, v0) = v1)))
% 18.86/5.20 | (71) aNaturalNumber0(sz10)
% 18.86/5.20 | (72) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 18.86/5.20 | (73) sdtasdt0(xn, xm) = all_0_1_1
% 18.86/5.20 | (74) aNaturalNumber0(xl)
% 18.86/5.20 |
% 18.86/5.20 | Instantiating formula (46) with xn, all_0_0_0, xn, xl and discharging atoms sdtpldt0(xl, all_0_0_0) = xn, sdtlseqdt0(xl, xn), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xn), aNaturalNumber0(xl), yields:
% 18.86/5.20 | (75) xn = xl | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xn) & ~ (v1 = v0) & sdtpldt0(all_0_0_0, xn) = v1 & sdtpldt0(all_0_0_0, xl) = v0 & sdtpldt0(xn, all_0_0_0) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xn, v2))
% 18.86/5.20 |
% 18.86/5.20 | Instantiating formula (63) with xn, xl, all_0_0_0 and discharging atoms sdtpldt0(xl, all_0_0_0) = xn, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), yields:
% 18.86/5.20 | (76) sdtpldt0(all_0_0_0, xl) = xn
% 18.86/5.20 |
% 18.86/5.20 | Instantiating formula (28) with xn, xl and discharging atoms sdtlseqdt0(xl, xn), aNaturalNumber0(xn), aNaturalNumber0(xl), yields:
% 18.86/5.20 | (77) ? [v0] : (sdtpldt0(xl, v0) = xn & aNaturalNumber0(v0))
% 18.86/5.20 |
% 18.86/5.20 | Instantiating formula (55) with all_0_1_1, all_0_4_4, xn, xl, xm and discharging atoms sdtasdt0(xn, xm) = all_0_1_1, sdtasdt0(xm, xl) = all_0_4_4, aNaturalNumber0(xn), aNaturalNumber0(xl), aNaturalNumber0(xm), yields:
% 18.86/5.20 | (78) xn = xl | xm = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = all_0_1_1) & ~ (v0 = all_0_4_4) & sdtasdt0(xl, xm) = v1 & sdtasdt0(xm, xn) = v0)
% 18.86/5.20 |
% 18.86/5.20 | Instantiating formula (2) with all_0_1_1, xn, all_0_0_0, xl, xm and discharging atoms sdtasdt0(xn, xm) = all_0_1_1, sdtpldt0(xl, all_0_0_0) = xn, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), aNaturalNumber0(xm), yields:
% 18.86/5.20 | (79) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_0_0, xm) = v4 & sdtasdt0(xl, xm) = v3 & sdtasdt0(xm, all_0_0_0) = v2 & sdtasdt0(xm, xn) = v0 & sdtasdt0(xm, xl) = v1 & sdtpldt0(v3, v4) = all_0_1_1 & sdtpldt0(v1, v2) = v0)
% 18.86/5.20 |
% 18.86/5.20 | Instantiating formula (43) with all_0_1_1, xn, xm and discharging atoms sdtasdt0(xn, xm) = all_0_1_1, aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 18.86/5.20 | (80) sdtasdt0(xm, xn) = all_0_1_1
% 18.86/5.20 |
% 18.86/5.20 | Instantiating formula (30) with all_0_1_1, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_1_1, aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 18.86/5.20 | (81) aNaturalNumber0(all_0_1_1)
% 18.86/5.20 |
% 18.86/5.20 | Instantiating formula (67) with all_0_2_2, all_0_1_1, xl, xn, xm and discharging atoms sdtasdt0(xn, xm) = all_0_1_1, sdtasdt0(xl, xm) = all_0_2_2, aNaturalNumber0(xn), aNaturalNumber0(xl), aNaturalNumber0(xm), yields:
% 18.86/5.20 | (82) xn = xl | xm = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xm, xn) = v0 & sdtasdt0(xm, xl) = v1)
% 18.86/5.20 |
% 18.86/5.20 | Instantiating formula (7) with all_0_2_2, all_0_3_3, xn, xl, xm and discharging atoms sdtasdt0(xl, xm) = all_0_2_2, sdtasdt0(xm, xn) = all_0_3_3, aNaturalNumber0(xn), aNaturalNumber0(xl), aNaturalNumber0(xm), yields:
% 18.86/5.20 | (83) xn = xl | xm = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = all_0_2_2) & ~ (v0 = all_0_3_3) & sdtasdt0(xn, xm) = v1 & sdtasdt0(xm, xl) = v0)
% 18.86/5.20 |
% 18.86/5.20 | Instantiating formula (43) with all_0_2_2, xl, xm and discharging atoms sdtasdt0(xl, xm) = all_0_2_2, aNaturalNumber0(xl), aNaturalNumber0(xm), yields:
% 18.86/5.20 | (84) sdtasdt0(xm, xl) = all_0_2_2
% 18.86/5.20 |
% 18.86/5.20 | Instantiating formula (30) with all_0_2_2, xm, xl and discharging atoms sdtasdt0(xl, xm) = all_0_2_2, aNaturalNumber0(xl), aNaturalNumber0(xm), yields:
% 18.86/5.20 | (85) aNaturalNumber0(all_0_2_2)
% 18.86/5.21 |
% 18.86/5.21 | Instantiating formula (38) with all_0_3_3, all_0_4_4, xn, xl, xm and discharging atoms sdtasdt0(xm, xn) = all_0_3_3, sdtasdt0(xm, xl) = all_0_4_4, aNaturalNumber0(xn), aNaturalNumber0(xl), aNaturalNumber0(xm), yields:
% 18.86/5.21 | (86) xn = xl | xm = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xn, xm) = v1 & sdtasdt0(xl, xm) = v0)
% 18.86/5.21 |
% 18.86/5.21 | Instantiating formula (56) with all_0_3_3, xn, all_0_0_0, xl, xm and discharging atoms sdtasdt0(xm, xn) = all_0_3_3, sdtpldt0(xl, all_0_0_0) = xn, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), aNaturalNumber0(xm), yields:
% 18.86/5.21 | (87) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_0_0, xm) = v4 & sdtasdt0(xn, xm) = v2 & sdtasdt0(xl, xm) = v3 & sdtasdt0(xm, all_0_0_0) = v1 & sdtasdt0(xm, xl) = v0 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_0_3_3)
% 18.86/5.21 |
% 18.86/5.21 | Instantiating formula (43) with all_0_3_3, xm, xn and discharging atoms sdtasdt0(xm, xn) = all_0_3_3, aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 18.86/5.21 | (88) sdtasdt0(xn, xm) = all_0_3_3
% 18.86/5.21 |
% 18.86/5.21 | Instantiating formula (38) with all_0_4_4, all_0_3_3, xl, xn, xm and discharging atoms sdtasdt0(xm, xn) = all_0_3_3, sdtasdt0(xm, xl) = all_0_4_4, aNaturalNumber0(xn), aNaturalNumber0(xl), aNaturalNumber0(xm), yields:
% 18.86/5.21 | (89) xn = xl | xm = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xn, xm) = v0 & sdtasdt0(xl, xm) = v1)
% 18.86/5.21 |
% 18.86/5.21 | Instantiating (87) with all_9_0_5, all_9_1_6, all_9_2_7, all_9_3_8, all_9_4_9 yields:
% 18.86/5.21 | (90) sdtasdt0(all_0_0_0, xm) = all_9_0_5 & sdtasdt0(xn, xm) = all_9_2_7 & sdtasdt0(xl, xm) = all_9_1_6 & sdtasdt0(xm, all_0_0_0) = all_9_3_8 & sdtasdt0(xm, xl) = all_9_4_9 & sdtpldt0(all_9_1_6, all_9_0_5) = all_9_2_7 & sdtpldt0(all_9_4_9, all_9_3_8) = all_0_3_3
% 18.86/5.21 |
% 18.86/5.21 | Applying alpha-rule on (90) yields:
% 18.86/5.21 | (91) sdtpldt0(all_9_4_9, all_9_3_8) = all_0_3_3
% 18.86/5.21 | (92) sdtasdt0(xl, xm) = all_9_1_6
% 18.86/5.21 | (93) sdtasdt0(xm, all_0_0_0) = all_9_3_8
% 18.86/5.21 | (94) sdtpldt0(all_9_1_6, all_9_0_5) = all_9_2_7
% 18.86/5.21 | (95) sdtasdt0(xm, xl) = all_9_4_9
% 18.86/5.21 | (96) sdtasdt0(xn, xm) = all_9_2_7
% 18.86/5.21 | (97) sdtasdt0(all_0_0_0, xm) = all_9_0_5
% 18.86/5.21 |
% 18.86/5.21 | Instantiating (79) with all_11_0_10, all_11_1_11, all_11_2_12, all_11_3_13, all_11_4_14 yields:
% 18.86/5.21 | (98) sdtasdt0(all_0_0_0, xm) = all_11_0_10 & sdtasdt0(xl, xm) = all_11_1_11 & sdtasdt0(xm, all_0_0_0) = all_11_2_12 & sdtasdt0(xm, xn) = all_11_4_14 & sdtasdt0(xm, xl) = all_11_3_13 & sdtpldt0(all_11_1_11, all_11_0_10) = all_0_1_1 & sdtpldt0(all_11_3_13, all_11_2_12) = all_11_4_14
% 18.86/5.21 |
% 18.86/5.21 | Applying alpha-rule on (98) yields:
% 18.86/5.21 | (99) sdtpldt0(all_11_3_13, all_11_2_12) = all_11_4_14
% 18.86/5.21 | (100) sdtasdt0(xl, xm) = all_11_1_11
% 18.86/5.21 | (101) sdtasdt0(xm, all_0_0_0) = all_11_2_12
% 18.86/5.21 | (102) sdtasdt0(all_0_0_0, xm) = all_11_0_10
% 18.86/5.21 | (103) sdtasdt0(xm, xn) = all_11_4_14
% 18.86/5.21 | (104) sdtasdt0(xm, xl) = all_11_3_13
% 18.86/5.21 | (105) sdtpldt0(all_11_1_11, all_11_0_10) = all_0_1_1
% 18.86/5.21 |
% 18.86/5.21 | Instantiating (77) with all_13_0_15 yields:
% 18.86/5.21 | (106) sdtpldt0(xl, all_13_0_15) = xn & aNaturalNumber0(all_13_0_15)
% 18.86/5.21 |
% 18.86/5.21 | Applying alpha-rule on (106) yields:
% 18.86/5.21 | (107) sdtpldt0(xl, all_13_0_15) = xn
% 18.86/5.21 | (108) aNaturalNumber0(all_13_0_15)
% 18.86/5.21 |
% 18.86/5.21 +-Applying beta-rule and splitting (83), into two cases.
% 18.86/5.21 |-Branch one:
% 18.86/5.21 | (109) xm = sz00
% 18.86/5.21 |
% 18.86/5.21 | Equations (109) can reduce 45 to:
% 18.86/5.21 | (110) $false
% 18.86/5.21 |
% 18.86/5.21 |-The branch is then unsatisfiable
% 18.86/5.21 |-Branch two:
% 18.86/5.21 | (45) ~ (xm = sz00)
% 18.86/5.21 | (112) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = all_0_2_2) & ~ (v0 = all_0_3_3) & sdtasdt0(xn, xm) = v1 & sdtasdt0(xm, xl) = v0)
% 18.86/5.21 |
% 18.86/5.21 +-Applying beta-rule and splitting (82), into two cases.
% 18.86/5.21 |-Branch one:
% 18.86/5.21 | (109) xm = sz00
% 18.86/5.21 |
% 18.86/5.21 | Equations (109) can reduce 45 to:
% 18.86/5.21 | (110) $false
% 18.86/5.21 |
% 18.86/5.21 |-The branch is then unsatisfiable
% 18.86/5.21 |-Branch two:
% 18.86/5.21 | (45) ~ (xm = sz00)
% 18.86/5.21 | (116) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xm, xn) = v0 & sdtasdt0(xm, xl) = v1)
% 18.86/5.21 |
% 18.86/5.21 +-Applying beta-rule and splitting (112), into two cases.
% 18.86/5.21 |-Branch one:
% 18.86/5.21 | (117) xn = xl
% 18.86/5.21 |
% 18.86/5.21 | Equations (117) can reduce 14 to:
% 18.86/5.21 | (110) $false
% 18.86/5.21 |
% 18.86/5.21 |-The branch is then unsatisfiable
% 18.86/5.21 |-Branch two:
% 18.86/5.21 | (14) ~ (xn = xl)
% 18.86/5.21 | (120) ? [v0] : ? [v1] : ( ~ (v1 = all_0_2_2) & ~ (v0 = all_0_3_3) & sdtasdt0(xn, xm) = v1 & sdtasdt0(xm, xl) = v0)
% 18.86/5.21 |
% 18.86/5.21 | Instantiating (120) with all_27_0_16, all_27_1_17 yields:
% 18.86/5.21 | (121) ~ (all_27_0_16 = all_0_2_2) & ~ (all_27_1_17 = all_0_3_3) & sdtasdt0(xn, xm) = all_27_0_16 & sdtasdt0(xm, xl) = all_27_1_17
% 18.86/5.21 |
% 18.86/5.21 | Applying alpha-rule on (121) yields:
% 18.86/5.21 | (122) ~ (all_27_0_16 = all_0_2_2)
% 18.86/5.21 | (123) ~ (all_27_1_17 = all_0_3_3)
% 18.86/5.21 | (124) sdtasdt0(xn, xm) = all_27_0_16
% 18.86/5.21 | (125) sdtasdt0(xm, xl) = all_27_1_17
% 18.86/5.21 |
% 18.86/5.21 +-Applying beta-rule and splitting (116), into two cases.
% 18.86/5.21 |-Branch one:
% 18.86/5.21 | (117) xn = xl
% 18.86/5.21 |
% 18.86/5.21 | Equations (117) can reduce 14 to:
% 18.86/5.21 | (110) $false
% 18.86/5.21 |
% 18.86/5.21 |-The branch is then unsatisfiable
% 18.86/5.21 |-Branch two:
% 18.86/5.21 | (14) ~ (xn = xl)
% 18.86/5.21 | (129) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xm, xn) = v0 & sdtasdt0(xm, xl) = v1)
% 18.86/5.21 |
% 18.86/5.21 | Instantiating (129) with all_33_0_18, all_33_1_19 yields:
% 18.86/5.21 | (130) ~ (all_33_0_18 = all_33_1_19) & sdtasdt0(xm, xn) = all_33_1_19 & sdtasdt0(xm, xl) = all_33_0_18
% 18.86/5.21 |
% 18.86/5.21 | Applying alpha-rule on (130) yields:
% 18.86/5.21 | (131) ~ (all_33_0_18 = all_33_1_19)
% 18.86/5.21 | (132) sdtasdt0(xm, xn) = all_33_1_19
% 18.86/5.21 | (133) sdtasdt0(xm, xl) = all_33_0_18
% 18.86/5.21 |
% 18.86/5.21 +-Applying beta-rule and splitting (86), into two cases.
% 18.86/5.21 |-Branch one:
% 18.86/5.21 | (109) xm = sz00
% 18.86/5.21 |
% 18.86/5.21 | Equations (109) can reduce 45 to:
% 18.86/5.21 | (110) $false
% 18.86/5.21 |
% 18.86/5.21 |-The branch is then unsatisfiable
% 18.86/5.21 |-Branch two:
% 18.86/5.21 | (45) ~ (xm = sz00)
% 18.86/5.21 | (137) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xn, xm) = v1 & sdtasdt0(xl, xm) = v0)
% 18.86/5.22 |
% 18.86/5.22 +-Applying beta-rule and splitting (89), into two cases.
% 18.86/5.22 |-Branch one:
% 18.86/5.22 | (109) xm = sz00
% 18.86/5.22 |
% 18.86/5.22 | Equations (109) can reduce 45 to:
% 18.86/5.22 | (110) $false
% 18.86/5.22 |
% 18.86/5.22 |-The branch is then unsatisfiable
% 18.86/5.22 |-Branch two:
% 18.86/5.22 | (45) ~ (xm = sz00)
% 18.86/5.22 | (141) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xn, xm) = v0 & sdtasdt0(xl, xm) = v1)
% 18.86/5.22 |
% 18.86/5.22 +-Applying beta-rule and splitting (75), into two cases.
% 18.86/5.22 |-Branch one:
% 18.86/5.22 | (117) xn = xl
% 18.86/5.22 |
% 18.86/5.22 | Equations (117) can reduce 14 to:
% 18.86/5.22 | (110) $false
% 18.86/5.22 |
% 18.86/5.22 |-The branch is then unsatisfiable
% 18.86/5.22 |-Branch two:
% 18.86/5.22 | (14) ~ (xn = xl)
% 18.86/5.22 | (145) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xn) & ~ (v1 = v0) & sdtpldt0(all_0_0_0, xn) = v1 & sdtpldt0(all_0_0_0, xl) = v0 & sdtpldt0(xn, all_0_0_0) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xn, v2))
% 18.86/5.22 |
% 18.86/5.22 | Instantiating (145) with all_46_0_20, all_46_1_21, all_46_2_22 yields:
% 18.86/5.22 | (146) ~ (all_46_0_20 = xn) & ~ (all_46_1_21 = all_46_2_22) & sdtpldt0(all_0_0_0, xn) = all_46_1_21 & sdtpldt0(all_0_0_0, xl) = all_46_2_22 & sdtpldt0(xn, all_0_0_0) = all_46_0_20 & sdtlseqdt0(all_46_2_22, all_46_1_21) & sdtlseqdt0(xn, all_46_0_20)
% 18.86/5.22 |
% 18.86/5.22 | Applying alpha-rule on (146) yields:
% 18.86/5.22 | (147) sdtpldt0(all_0_0_0, xl) = all_46_2_22
% 18.86/5.22 | (148) ~ (all_46_0_20 = xn)
% 18.86/5.22 | (149) sdtpldt0(xn, all_0_0_0) = all_46_0_20
% 18.86/5.22 | (150) ~ (all_46_1_21 = all_46_2_22)
% 18.86/5.22 | (151) sdtpldt0(all_0_0_0, xn) = all_46_1_21
% 18.86/5.22 | (152) sdtlseqdt0(all_46_2_22, all_46_1_21)
% 18.86/5.22 | (153) sdtlseqdt0(xn, all_46_0_20)
% 18.86/5.22 |
% 18.86/5.22 +-Applying beta-rule and splitting (137), into two cases.
% 18.86/5.22 |-Branch one:
% 18.86/5.22 | (117) xn = xl
% 18.86/5.22 |
% 18.86/5.22 | Equations (117) can reduce 14 to:
% 18.86/5.22 | (110) $false
% 18.86/5.22 |
% 18.86/5.22 |-The branch is then unsatisfiable
% 18.86/5.22 |-Branch two:
% 18.86/5.22 | (14) ~ (xn = xl)
% 18.86/5.22 | (157) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xn, xm) = v1 & sdtasdt0(xl, xm) = v0)
% 18.86/5.22 |
% 18.86/5.22 | Instantiating (157) with all_52_0_23, all_52_1_24 yields:
% 18.86/5.22 | (158) ~ (all_52_0_23 = all_52_1_24) & sdtasdt0(xn, xm) = all_52_0_23 & sdtasdt0(xl, xm) = all_52_1_24
% 18.86/5.22 |
% 18.86/5.22 | Applying alpha-rule on (158) yields:
% 18.86/5.22 | (159) ~ (all_52_0_23 = all_52_1_24)
% 18.86/5.22 | (160) sdtasdt0(xn, xm) = all_52_0_23
% 18.86/5.22 | (161) sdtasdt0(xl, xm) = all_52_1_24
% 18.86/5.22 |
% 18.86/5.22 +-Applying beta-rule and splitting (78), into two cases.
% 18.86/5.22 |-Branch one:
% 18.86/5.22 | (109) xm = sz00
% 18.86/5.22 |
% 18.86/5.22 | Equations (109) can reduce 45 to:
% 18.86/5.22 | (110) $false
% 18.86/5.22 |
% 18.86/5.22 |-The branch is then unsatisfiable
% 18.86/5.22 |-Branch two:
% 18.86/5.22 | (45) ~ (xm = sz00)
% 18.86/5.22 | (165) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = all_0_1_1) & ~ (v0 = all_0_4_4) & sdtasdt0(xl, xm) = v1 & sdtasdt0(xm, xn) = v0)
% 18.86/5.22 |
% 18.86/5.22 +-Applying beta-rule and splitting (165), into two cases.
% 18.86/5.22 |-Branch one:
% 18.86/5.22 | (117) xn = xl
% 18.86/5.22 |
% 18.86/5.22 | Equations (117) can reduce 14 to:
% 18.86/5.22 | (110) $false
% 18.86/5.22 |
% 18.86/5.22 |-The branch is then unsatisfiable
% 18.86/5.22 |-Branch two:
% 18.86/5.22 | (14) ~ (xn = xl)
% 18.86/5.22 | (169) ? [v0] : ? [v1] : ( ~ (v1 = all_0_1_1) & ~ (v0 = all_0_4_4) & sdtasdt0(xl, xm) = v1 & sdtasdt0(xm, xn) = v0)
% 18.86/5.22 |
% 18.86/5.22 | Instantiating (169) with all_62_0_25, all_62_1_26 yields:
% 18.86/5.22 | (170) ~ (all_62_0_25 = all_0_1_1) & ~ (all_62_1_26 = all_0_4_4) & sdtasdt0(xl, xm) = all_62_0_25 & sdtasdt0(xm, xn) = all_62_1_26
% 18.86/5.22 |
% 18.86/5.22 | Applying alpha-rule on (170) yields:
% 18.86/5.22 | (171) ~ (all_62_0_25 = all_0_1_1)
% 18.86/5.22 | (172) ~ (all_62_1_26 = all_0_4_4)
% 18.86/5.22 | (173) sdtasdt0(xl, xm) = all_62_0_25
% 18.86/5.22 | (174) sdtasdt0(xm, xn) = all_62_1_26
% 18.86/5.22 |
% 18.86/5.22 | Instantiating formula (32) with all_0_0_0, xm, all_9_0_5, all_11_0_10 and discharging atoms sdtasdt0(all_0_0_0, xm) = all_11_0_10, sdtasdt0(all_0_0_0, xm) = all_9_0_5, yields:
% 18.86/5.22 | (175) all_11_0_10 = all_9_0_5
% 18.86/5.22 |
% 18.86/5.22 | Instantiating formula (32) with xn, xm, all_52_0_23, all_0_1_1 and discharging atoms sdtasdt0(xn, xm) = all_52_0_23, sdtasdt0(xn, xm) = all_0_1_1, yields:
% 18.86/5.22 | (176) all_52_0_23 = all_0_1_1
% 18.86/5.22 |
% 18.86/5.22 | Instantiating formula (32) with xn, xm, all_27_0_16, all_52_0_23 and discharging atoms sdtasdt0(xn, xm) = all_52_0_23, sdtasdt0(xn, xm) = all_27_0_16, yields:
% 18.86/5.22 | (177) all_52_0_23 = all_27_0_16
% 18.86/5.22 |
% 18.86/5.22 | Instantiating formula (32) with xn, xm, all_9_2_7, all_27_0_16 and discharging atoms sdtasdt0(xn, xm) = all_27_0_16, sdtasdt0(xn, xm) = all_9_2_7, yields:
% 18.86/5.22 | (178) all_27_0_16 = all_9_2_7
% 18.86/5.22 |
% 18.86/5.22 | Instantiating formula (32) with xn, xm, all_0_3_3, all_27_0_16 and discharging atoms sdtasdt0(xn, xm) = all_27_0_16, sdtasdt0(xn, xm) = all_0_3_3, yields:
% 18.86/5.22 | (179) all_27_0_16 = all_0_3_3
% 18.86/5.22 |
% 18.86/5.22 | Instantiating formula (32) with xl, xm, all_52_1_24, all_0_2_2 and discharging atoms sdtasdt0(xl, xm) = all_52_1_24, sdtasdt0(xl, xm) = all_0_2_2, yields:
% 18.86/5.22 | (180) all_52_1_24 = all_0_2_2
% 18.86/5.22 |
% 18.86/5.22 | Instantiating formula (32) with xl, xm, all_52_1_24, all_62_0_25 and discharging atoms sdtasdt0(xl, xm) = all_62_0_25, sdtasdt0(xl, xm) = all_52_1_24, yields:
% 18.86/5.22 | (181) all_62_0_25 = all_52_1_24
% 18.86/5.22 |
% 18.86/5.22 | Instantiating formula (32) with xl, xm, all_11_1_11, all_62_0_25 and discharging atoms sdtasdt0(xl, xm) = all_62_0_25, sdtasdt0(xl, xm) = all_11_1_11, yields:
% 18.86/5.22 | (182) all_62_0_25 = all_11_1_11
% 18.86/5.22 |
% 18.86/5.22 | Instantiating formula (32) with xl, xm, all_9_1_6, all_62_0_25 and discharging atoms sdtasdt0(xl, xm) = all_62_0_25, sdtasdt0(xl, xm) = all_9_1_6, yields:
% 18.86/5.22 | (183) all_62_0_25 = all_9_1_6
% 18.86/5.22 |
% 18.86/5.22 | Instantiating formula (32) with xm, all_0_0_0, all_9_3_8, all_11_2_12 and discharging atoms sdtasdt0(xm, all_0_0_0) = all_11_2_12, sdtasdt0(xm, all_0_0_0) = all_9_3_8, yields:
% 18.86/5.22 | (184) all_11_2_12 = all_9_3_8
% 18.86/5.22 |
% 18.86/5.22 | Instantiating formula (32) with xm, xl, all_27_1_17, all_33_0_18 and discharging atoms sdtasdt0(xm, xl) = all_33_0_18, sdtasdt0(xm, xl) = all_27_1_17, yields:
% 18.86/5.22 | (185) all_33_0_18 = all_27_1_17
% 18.86/5.22 |
% 18.86/5.22 | Instantiating formula (32) with xm, xl, all_11_3_13, all_33_0_18 and discharging atoms sdtasdt0(xm, xl) = all_33_0_18, sdtasdt0(xm, xl) = all_11_3_13, yields:
% 18.86/5.22 | (186) all_33_0_18 = all_11_3_13
% 18.86/5.22 |
% 18.86/5.22 | Instantiating formula (32) with xm, xl, all_9_4_9, all_0_4_4 and discharging atoms sdtasdt0(xm, xl) = all_9_4_9, sdtasdt0(xm, xl) = all_0_4_4, yields:
% 18.86/5.22 | (187) all_9_4_9 = all_0_4_4
% 18.86/5.22 |
% 18.86/5.22 | Instantiating formula (32) with xm, xl, all_9_4_9, all_27_1_17 and discharging atoms sdtasdt0(xm, xl) = all_27_1_17, sdtasdt0(xm, xl) = all_9_4_9, yields:
% 18.86/5.22 | (188) all_27_1_17 = all_9_4_9
% 18.86/5.22 |
% 18.86/5.22 | Instantiating formula (32) with xm, xl, all_0_2_2, all_27_1_17 and discharging atoms sdtasdt0(xm, xl) = all_27_1_17, sdtasdt0(xm, xl) = all_0_2_2, yields:
% 19.33/5.22 | (189) all_27_1_17 = all_0_2_2
% 19.33/5.22 |
% 19.33/5.22 | Instantiating formula (48) with all_0_0_0, xl, xn, all_46_2_22 and discharging atoms sdtpldt0(all_0_0_0, xl) = all_46_2_22, sdtpldt0(all_0_0_0, xl) = xn, yields:
% 19.33/5.22 | (190) all_46_2_22 = xn
% 19.33/5.22 |
% 19.33/5.22 | Instantiating formula (62) with xn, all_0_0_0, all_13_0_15, xl and discharging atoms sdtpldt0(xl, all_13_0_15) = xn, sdtpldt0(xl, all_0_0_0) = xn, aNaturalNumber0(all_13_0_15), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), yields:
% 19.33/5.23 | (191) all_13_0_15 = all_0_0_0
% 19.33/5.23 |
% 19.33/5.23 | Combining equations (181,182) yields a new equation:
% 19.33/5.23 | (192) all_52_1_24 = all_11_1_11
% 19.33/5.23 |
% 19.33/5.23 | Simplifying 192 yields:
% 19.33/5.23 | (193) all_52_1_24 = all_11_1_11
% 19.33/5.23 |
% 19.33/5.23 | Combining equations (183,182) yields a new equation:
% 19.33/5.23 | (194) all_11_1_11 = all_9_1_6
% 19.33/5.23 |
% 19.33/5.23 | Combining equations (177,176) yields a new equation:
% 19.33/5.23 | (195) all_27_0_16 = all_0_1_1
% 19.33/5.23 |
% 19.33/5.23 | Simplifying 195 yields:
% 19.33/5.23 | (196) all_27_0_16 = all_0_1_1
% 19.33/5.23 |
% 19.33/5.23 | Combining equations (193,180) yields a new equation:
% 19.33/5.23 | (197) all_11_1_11 = all_0_2_2
% 19.33/5.23 |
% 19.33/5.23 | Simplifying 197 yields:
% 19.33/5.23 | (198) all_11_1_11 = all_0_2_2
% 19.33/5.23 |
% 19.33/5.23 | Combining equations (185,186) yields a new equation:
% 19.33/5.23 | (199) all_27_1_17 = all_11_3_13
% 19.33/5.23 |
% 19.33/5.23 | Simplifying 199 yields:
% 19.33/5.23 | (200) all_27_1_17 = all_11_3_13
% 19.33/5.23 |
% 19.33/5.23 | Combining equations (179,178) yields a new equation:
% 19.33/5.23 | (201) all_9_2_7 = all_0_3_3
% 19.33/5.23 |
% 19.33/5.23 | Combining equations (196,178) yields a new equation:
% 19.33/5.23 | (202) all_9_2_7 = all_0_1_1
% 19.33/5.23 |
% 19.33/5.23 | Combining equations (188,200) yields a new equation:
% 19.33/5.23 | (203) all_11_3_13 = all_9_4_9
% 19.33/5.23 |
% 19.33/5.23 | Combining equations (189,200) yields a new equation:
% 19.33/5.23 | (204) all_11_3_13 = all_0_2_2
% 19.33/5.23 |
% 19.33/5.23 | Combining equations (194,198) yields a new equation:
% 19.33/5.23 | (205) all_9_1_6 = all_0_2_2
% 19.33/5.23 |
% 19.33/5.23 | Simplifying 205 yields:
% 19.33/5.23 | (206) all_9_1_6 = all_0_2_2
% 19.33/5.23 |
% 19.33/5.23 | Combining equations (203,204) yields a new equation:
% 19.33/5.23 | (207) all_9_4_9 = all_0_2_2
% 19.33/5.23 |
% 19.33/5.23 | Simplifying 207 yields:
% 19.33/5.23 | (208) all_9_4_9 = all_0_2_2
% 19.33/5.23 |
% 19.33/5.23 | Combining equations (201,202) yields a new equation:
% 19.33/5.23 | (209) all_0_1_1 = all_0_3_3
% 19.33/5.23 |
% 19.33/5.23 | Combining equations (187,208) yields a new equation:
% 19.33/5.23 | (210) all_0_2_2 = all_0_4_4
% 19.33/5.23 |
% 19.33/5.23 | Combining equations (209,202) yields a new equation:
% 19.33/5.23 | (201) all_9_2_7 = all_0_3_3
% 19.33/5.23 |
% 19.33/5.23 | Combining equations (210,206) yields a new equation:
% 19.33/5.23 | (212) all_9_1_6 = all_0_4_4
% 19.33/5.23 |
% 19.33/5.23 | Combining equations (210,204) yields a new equation:
% 19.33/5.23 | (213) all_11_3_13 = all_0_4_4
% 19.33/5.23 |
% 19.33/5.23 | Combining equations (213,200) yields a new equation:
% 19.33/5.23 | (214) all_27_1_17 = all_0_4_4
% 19.33/5.23 |
% 19.33/5.23 | Equations (214) can reduce 123 to:
% 19.33/5.23 | (215) ~ (all_0_3_3 = all_0_4_4)
% 19.33/5.23 |
% 19.33/5.23 | Simplifying 215 yields:
% 19.33/5.23 | (216) ~ (all_0_3_3 = all_0_4_4)
% 19.33/5.23 |
% 19.33/5.23 | From (175) and (102) follows:
% 19.33/5.23 | (97) sdtasdt0(all_0_0_0, xm) = all_9_0_5
% 19.33/5.23 |
% 19.33/5.23 | From (209) and (73) follows:
% 19.33/5.23 | (88) sdtasdt0(xn, xm) = all_0_3_3
% 19.33/5.23 |
% 19.33/5.23 | From (184) and (101) follows:
% 19.33/5.23 | (93) sdtasdt0(xm, all_0_0_0) = all_9_3_8
% 19.33/5.23 |
% 19.33/5.23 | From (209) and (80) follows:
% 19.33/5.23 | (51) sdtasdt0(xm, xn) = all_0_3_3
% 19.33/5.23 |
% 19.33/5.23 | From (212)(201) and (94) follows:
% 19.33/5.23 | (221) sdtpldt0(all_0_4_4, all_9_0_5) = all_0_3_3
% 19.33/5.23 |
% 19.33/5.23 | From (190) and (147) follows:
% 19.33/5.23 | (76) sdtpldt0(all_0_0_0, xl) = xn
% 19.33/5.23 |
% 19.33/5.23 | From (191) and (108) follows:
% 19.33/5.23 | (17) aNaturalNumber0(all_0_0_0)
% 19.33/5.23 |
% 19.33/5.23 | From (209) and (81) follows:
% 19.33/5.23 | (224) aNaturalNumber0(all_0_3_3)
% 19.33/5.23 |
% 19.33/5.23 | From (210) and (85) follows:
% 19.33/5.23 | (225) aNaturalNumber0(all_0_4_4)
% 19.33/5.23 |
% 19.33/5.23 +-Applying beta-rule and splitting (70), into two cases.
% 19.33/5.23 |-Branch one:
% 19.33/5.23 | (226) all_0_1_1 = all_0_2_2
% 19.33/5.23 |
% 19.33/5.23 | Combining equations (209,226) yields a new equation:
% 19.33/5.23 | (227) all_0_2_2 = all_0_3_3
% 19.33/5.23 |
% 19.33/5.23 | Combining equations (227,210) yields a new equation:
% 19.33/5.23 | (228) all_0_3_3 = all_0_4_4
% 19.33/5.23 |
% 19.33/5.23 | Simplifying 228 yields:
% 19.33/5.23 | (229) all_0_3_3 = all_0_4_4
% 19.33/5.23 |
% 19.33/5.23 | Equations (229) can reduce 216 to:
% 19.33/5.23 | (110) $false
% 19.33/5.23 |
% 19.33/5.23 |-The branch is then unsatisfiable
% 19.33/5.23 |-Branch two:
% 19.33/5.23 | (231) ~ (all_0_1_1 = all_0_2_2)
% 19.33/5.23 | (232) all_0_3_3 = all_0_4_4 | ( ~ sdtlseqdt0(all_0_2_2, all_0_1_1) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_1_1) & sdtpldt0(all_0_2_2, v0) = v1))) | ( ~ sdtlseqdt0(all_0_4_4, all_0_3_3) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_3_3) & sdtpldt0(all_0_4_4, v0) = v1)))
% 19.33/5.23 |
% 19.33/5.23 | Equations (209,210) can reduce 231 to:
% 19.33/5.23 | (216) ~ (all_0_3_3 = all_0_4_4)
% 19.33/5.23 |
% 19.33/5.23 +-Applying beta-rule and splitting (232), into two cases.
% 19.33/5.23 |-Branch one:
% 19.33/5.23 | (229) all_0_3_3 = all_0_4_4
% 19.33/5.23 |
% 19.33/5.23 | Equations (229) can reduce 216 to:
% 19.33/5.23 | (110) $false
% 19.33/5.23 |
% 19.33/5.23 |-The branch is then unsatisfiable
% 19.33/5.23 |-Branch two:
% 19.33/5.23 | (216) ~ (all_0_3_3 = all_0_4_4)
% 19.33/5.23 | (237) ( ~ sdtlseqdt0(all_0_2_2, all_0_1_1) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_1_1) & sdtpldt0(all_0_2_2, v0) = v1))) | ( ~ sdtlseqdt0(all_0_4_4, all_0_3_3) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_3_3) & sdtpldt0(all_0_4_4, v0) = v1)))
% 19.33/5.23 |
% 19.33/5.23 +-Applying beta-rule and splitting (237), into two cases.
% 19.33/5.23 |-Branch one:
% 19.33/5.23 | (238) ~ sdtlseqdt0(all_0_2_2, all_0_1_1) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_1_1) & sdtpldt0(all_0_2_2, v0) = v1))
% 19.33/5.23 |
% 19.33/5.23 | Applying alpha-rule on (238) yields:
% 19.33/5.23 | (239) ~ sdtlseqdt0(all_0_2_2, all_0_1_1)
% 19.33/5.23 | (240) ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_1_1) & sdtpldt0(all_0_2_2, v0) = v1))
% 19.33/5.23 |
% 19.33/5.23 | From (210)(209) and (239) follows:
% 19.33/5.23 | (241) ~ sdtlseqdt0(all_0_4_4, all_0_3_3)
% 19.33/5.23 |
% 19.33/5.23 | Instantiating formula (43) with all_9_0_5, all_0_0_0, xm and discharging atoms sdtasdt0(all_0_0_0, xm) = all_9_0_5, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xm), yields:
% 19.33/5.23 | (242) sdtasdt0(xm, all_0_0_0) = all_9_0_5
% 19.33/5.23 |
% 19.33/5.23 | Instantiating formula (30) with all_9_0_5, xm, all_0_0_0 and discharging atoms sdtasdt0(all_0_0_0, xm) = all_9_0_5, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xm), yields:
% 19.33/5.23 | (243) aNaturalNumber0(all_9_0_5)
% 19.33/5.23 |
% 19.33/5.23 | Instantiating formula (56) with all_0_3_3, xn, xl, all_0_0_0, xm and discharging atoms sdtasdt0(xm, xn) = all_0_3_3, sdtpldt0(all_0_0_0, xl) = xn, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), aNaturalNumber0(xm), yields:
% 19.33/5.23 | (244) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_0_0, xm) = v3 & sdtasdt0(xn, xm) = v2 & sdtasdt0(xl, xm) = v4 & sdtasdt0(xm, all_0_0_0) = v0 & sdtasdt0(xm, xl) = v1 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_0_3_3)
% 19.33/5.23 |
% 19.33/5.23 | Instantiating formula (2) with all_0_3_3, xn, xl, all_0_0_0, xm and discharging atoms sdtasdt0(xn, xm) = all_0_3_3, sdtpldt0(all_0_0_0, xl) = xn, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), aNaturalNumber0(xm), yields:
% 19.33/5.23 | (245) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_0_0, xm) = v3 & sdtasdt0(xl, xm) = v4 & sdtasdt0(xm, all_0_0_0) = v1 & sdtasdt0(xm, xn) = v0 & sdtasdt0(xm, xl) = v2 & sdtpldt0(v3, v4) = all_0_3_3 & sdtpldt0(v1, v2) = v0)
% 19.33/5.23 |
% 19.33/5.23 | Instantiating (245) with all_119_0_41, all_119_1_42, all_119_2_43, all_119_3_44, all_119_4_45 yields:
% 19.33/5.23 | (246) sdtasdt0(all_0_0_0, xm) = all_119_1_42 & sdtasdt0(xl, xm) = all_119_0_41 & sdtasdt0(xm, all_0_0_0) = all_119_3_44 & sdtasdt0(xm, xn) = all_119_4_45 & sdtasdt0(xm, xl) = all_119_2_43 & sdtpldt0(all_119_1_42, all_119_0_41) = all_0_3_3 & sdtpldt0(all_119_3_44, all_119_2_43) = all_119_4_45
% 19.33/5.24 |
% 19.33/5.24 | Applying alpha-rule on (246) yields:
% 19.33/5.24 | (247) sdtasdt0(xm, all_0_0_0) = all_119_3_44
% 19.33/5.24 | (248) sdtpldt0(all_119_3_44, all_119_2_43) = all_119_4_45
% 19.33/5.24 | (249) sdtasdt0(all_0_0_0, xm) = all_119_1_42
% 19.33/5.24 | (250) sdtasdt0(xl, xm) = all_119_0_41
% 19.33/5.24 | (251) sdtpldt0(all_119_1_42, all_119_0_41) = all_0_3_3
% 19.33/5.24 | (252) sdtasdt0(xm, xn) = all_119_4_45
% 19.33/5.24 | (253) sdtasdt0(xm, xl) = all_119_2_43
% 19.33/5.24 |
% 19.33/5.24 | Instantiating (244) with all_143_0_57, all_143_1_58, all_143_2_59, all_143_3_60, all_143_4_61 yields:
% 19.33/5.24 | (254) sdtasdt0(all_0_0_0, xm) = all_143_1_58 & sdtasdt0(xn, xm) = all_143_2_59 & sdtasdt0(xl, xm) = all_143_0_57 & sdtasdt0(xm, all_0_0_0) = all_143_4_61 & sdtasdt0(xm, xl) = all_143_3_60 & sdtpldt0(all_143_1_58, all_143_0_57) = all_143_2_59 & sdtpldt0(all_143_4_61, all_143_3_60) = all_0_3_3
% 19.33/5.24 |
% 19.33/5.24 | Applying alpha-rule on (254) yields:
% 19.33/5.24 | (255) sdtpldt0(all_143_4_61, all_143_3_60) = all_0_3_3
% 19.33/5.24 | (256) sdtasdt0(xl, xm) = all_143_0_57
% 19.33/5.24 | (257) sdtpldt0(all_143_1_58, all_143_0_57) = all_143_2_59
% 19.33/5.24 | (258) sdtasdt0(xn, xm) = all_143_2_59
% 19.33/5.24 | (259) sdtasdt0(xm, xl) = all_143_3_60
% 19.33/5.24 | (260) sdtasdt0(all_0_0_0, xm) = all_143_1_58
% 19.33/5.24 | (261) sdtasdt0(xm, all_0_0_0) = all_143_4_61
% 19.33/5.24 |
% 19.33/5.24 | Instantiating formula (32) with xm, all_0_0_0, all_143_4_61, all_9_3_8 and discharging atoms sdtasdt0(xm, all_0_0_0) = all_143_4_61, sdtasdt0(xm, all_0_0_0) = all_9_3_8, yields:
% 19.33/5.24 | (262) all_143_4_61 = all_9_3_8
% 19.33/5.24 |
% 19.33/5.24 | Instantiating formula (32) with xm, all_0_0_0, all_119_3_44, all_143_4_61 and discharging atoms sdtasdt0(xm, all_0_0_0) = all_143_4_61, sdtasdt0(xm, all_0_0_0) = all_119_3_44, yields:
% 19.33/5.24 | (263) all_143_4_61 = all_119_3_44
% 19.33/5.24 |
% 19.33/5.24 | Instantiating formula (32) with xm, all_0_0_0, all_9_0_5, all_119_3_44 and discharging atoms sdtasdt0(xm, all_0_0_0) = all_119_3_44, sdtasdt0(xm, all_0_0_0) = all_9_0_5, yields:
% 19.33/5.24 | (264) all_119_3_44 = all_9_0_5
% 19.33/5.24 |
% 19.33/5.24 | Combining equations (263,262) yields a new equation:
% 19.33/5.24 | (265) all_119_3_44 = all_9_3_8
% 19.33/5.24 |
% 19.33/5.24 | Simplifying 265 yields:
% 19.33/5.24 | (266) all_119_3_44 = all_9_3_8
% 19.33/5.24 |
% 19.33/5.24 | Combining equations (264,266) yields a new equation:
% 19.33/5.24 | (267) all_9_0_5 = all_9_3_8
% 19.33/5.24 |
% 19.33/5.24 | Simplifying 267 yields:
% 19.33/5.24 | (268) all_9_0_5 = all_9_3_8
% 19.33/5.24 |
% 19.33/5.24 | From (268) and (221) follows:
% 19.33/5.24 | (269) sdtpldt0(all_0_4_4, all_9_3_8) = all_0_3_3
% 19.33/5.24 |
% 19.33/5.24 | From (268) and (243) follows:
% 19.33/5.24 | (270) aNaturalNumber0(all_9_3_8)
% 19.33/5.24 |
% 19.33/5.24 | Instantiating formula (27) with all_9_3_8, all_0_3_3, all_0_4_4 and discharging atoms sdtpldt0(all_0_4_4, all_9_3_8) = all_0_3_3, aNaturalNumber0(all_9_3_8), aNaturalNumber0(all_0_3_3), aNaturalNumber0(all_0_4_4), ~ sdtlseqdt0(all_0_4_4, all_0_3_3), yields:
% 19.33/5.24 | (271) $false
% 19.33/5.24 |
% 19.33/5.24 |-The branch is then unsatisfiable
% 19.33/5.24 |-Branch two:
% 19.33/5.24 | (272) ~ sdtlseqdt0(all_0_4_4, all_0_3_3) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_3_3) & sdtpldt0(all_0_4_4, v0) = v1))
% 19.33/5.24 |
% 19.33/5.24 | Applying alpha-rule on (272) yields:
% 19.33/5.24 | (241) ~ sdtlseqdt0(all_0_4_4, all_0_3_3)
% 19.33/5.24 | (274) ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_3_3) & sdtpldt0(all_0_4_4, v0) = v1))
% 19.33/5.24 |
% 19.33/5.24 | Instantiating formula (43) with all_9_0_5, all_0_0_0, xm and discharging atoms sdtasdt0(all_0_0_0, xm) = all_9_0_5, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xm), yields:
% 19.33/5.24 | (242) sdtasdt0(xm, all_0_0_0) = all_9_0_5
% 19.33/5.24 |
% 19.33/5.24 | Instantiating formula (30) with all_9_0_5, xm, all_0_0_0 and discharging atoms sdtasdt0(all_0_0_0, xm) = all_9_0_5, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xm), yields:
% 19.33/5.24 | (243) aNaturalNumber0(all_9_0_5)
% 19.33/5.24 |
% 19.33/5.24 | Instantiating formula (56) with all_0_3_3, xn, xl, all_0_0_0, xm and discharging atoms sdtasdt0(xm, xn) = all_0_3_3, sdtpldt0(all_0_0_0, xl) = xn, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), aNaturalNumber0(xm), yields:
% 19.33/5.24 | (244) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_0_0, xm) = v3 & sdtasdt0(xn, xm) = v2 & sdtasdt0(xl, xm) = v4 & sdtasdt0(xm, all_0_0_0) = v0 & sdtasdt0(xm, xl) = v1 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_0_3_3)
% 19.33/5.24 |
% 19.33/5.24 | Instantiating formula (2) with all_0_3_3, xn, xl, all_0_0_0, xm and discharging atoms sdtasdt0(xn, xm) = all_0_3_3, sdtpldt0(all_0_0_0, xl) = xn, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), aNaturalNumber0(xm), yields:
% 19.33/5.24 | (245) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_0_0, xm) = v3 & sdtasdt0(xl, xm) = v4 & sdtasdt0(xm, all_0_0_0) = v1 & sdtasdt0(xm, xn) = v0 & sdtasdt0(xm, xl) = v2 & sdtpldt0(v3, v4) = all_0_3_3 & sdtpldt0(v1, v2) = v0)
% 19.33/5.24 |
% 19.33/5.24 | Instantiating (245) with all_119_0_93, all_119_1_94, all_119_2_95, all_119_3_96, all_119_4_97 yields:
% 19.33/5.24 | (279) sdtasdt0(all_0_0_0, xm) = all_119_1_94 & sdtasdt0(xl, xm) = all_119_0_93 & sdtasdt0(xm, all_0_0_0) = all_119_3_96 & sdtasdt0(xm, xn) = all_119_4_97 & sdtasdt0(xm, xl) = all_119_2_95 & sdtpldt0(all_119_1_94, all_119_0_93) = all_0_3_3 & sdtpldt0(all_119_3_96, all_119_2_95) = all_119_4_97
% 19.33/5.24 |
% 19.33/5.24 | Applying alpha-rule on (279) yields:
% 19.33/5.24 | (280) sdtpldt0(all_119_1_94, all_119_0_93) = all_0_3_3
% 19.33/5.24 | (281) sdtasdt0(xm, xl) = all_119_2_95
% 19.33/5.24 | (282) sdtpldt0(all_119_3_96, all_119_2_95) = all_119_4_97
% 19.33/5.24 | (283) sdtasdt0(xm, all_0_0_0) = all_119_3_96
% 19.33/5.24 | (284) sdtasdt0(xm, xn) = all_119_4_97
% 19.33/5.24 | (285) sdtasdt0(xl, xm) = all_119_0_93
% 19.33/5.24 | (286) sdtasdt0(all_0_0_0, xm) = all_119_1_94
% 19.33/5.24 |
% 19.33/5.24 | Instantiating (244) with all_143_0_109, all_143_1_110, all_143_2_111, all_143_3_112, all_143_4_113 yields:
% 19.33/5.24 | (287) sdtasdt0(all_0_0_0, xm) = all_143_1_110 & sdtasdt0(xn, xm) = all_143_2_111 & sdtasdt0(xl, xm) = all_143_0_109 & sdtasdt0(xm, all_0_0_0) = all_143_4_113 & sdtasdt0(xm, xl) = all_143_3_112 & sdtpldt0(all_143_1_110, all_143_0_109) = all_143_2_111 & sdtpldt0(all_143_4_113, all_143_3_112) = all_0_3_3
% 19.33/5.24 |
% 19.33/5.24 | Applying alpha-rule on (287) yields:
% 19.33/5.24 | (288) sdtpldt0(all_143_1_110, all_143_0_109) = all_143_2_111
% 19.33/5.24 | (289) sdtasdt0(xm, all_0_0_0) = all_143_4_113
% 19.33/5.24 | (290) sdtasdt0(all_0_0_0, xm) = all_143_1_110
% 19.33/5.24 | (291) sdtasdt0(xn, xm) = all_143_2_111
% 19.33/5.24 | (292) sdtpldt0(all_143_4_113, all_143_3_112) = all_0_3_3
% 19.33/5.24 | (293) sdtasdt0(xl, xm) = all_143_0_109
% 19.33/5.24 | (294) sdtasdt0(xm, xl) = all_143_3_112
% 19.33/5.24 |
% 19.33/5.24 | Instantiating formula (32) with xm, all_0_0_0, all_143_4_113, all_9_3_8 and discharging atoms sdtasdt0(xm, all_0_0_0) = all_143_4_113, sdtasdt0(xm, all_0_0_0) = all_9_3_8, yields:
% 19.33/5.24 | (295) all_143_4_113 = all_9_3_8
% 19.33/5.24 |
% 19.33/5.24 | Instantiating formula (32) with xm, all_0_0_0, all_119_3_96, all_143_4_113 and discharging atoms sdtasdt0(xm, all_0_0_0) = all_143_4_113, sdtasdt0(xm, all_0_0_0) = all_119_3_96, yields:
% 19.33/5.24 | (296) all_143_4_113 = all_119_3_96
% 19.33/5.24 |
% 19.33/5.24 | Instantiating formula (32) with xm, all_0_0_0, all_9_0_5, all_119_3_96 and discharging atoms sdtasdt0(xm, all_0_0_0) = all_119_3_96, sdtasdt0(xm, all_0_0_0) = all_9_0_5, yields:
% 19.33/5.24 | (297) all_119_3_96 = all_9_0_5
% 19.33/5.24 |
% 19.33/5.24 | Combining equations (296,295) yields a new equation:
% 19.33/5.24 | (298) all_119_3_96 = all_9_3_8
% 19.33/5.24 |
% 19.33/5.24 | Simplifying 298 yields:
% 19.33/5.24 | (299) all_119_3_96 = all_9_3_8
% 19.33/5.24 |
% 19.33/5.24 | Combining equations (297,299) yields a new equation:
% 19.33/5.24 | (267) all_9_0_5 = all_9_3_8
% 19.33/5.24 |
% 19.33/5.24 | Simplifying 267 yields:
% 19.33/5.24 | (268) all_9_0_5 = all_9_3_8
% 19.33/5.24 |
% 19.33/5.24 | From (268) and (221) follows:
% 19.33/5.24 | (269) sdtpldt0(all_0_4_4, all_9_3_8) = all_0_3_3
% 19.33/5.24 |
% 19.33/5.24 | From (268) and (243) follows:
% 19.33/5.24 | (270) aNaturalNumber0(all_9_3_8)
% 19.33/5.24 |
% 19.33/5.24 | Instantiating formula (27) with all_9_3_8, all_0_3_3, all_0_4_4 and discharging atoms sdtpldt0(all_0_4_4, all_9_3_8) = all_0_3_3, aNaturalNumber0(all_9_3_8), aNaturalNumber0(all_0_3_3), aNaturalNumber0(all_0_4_4), ~ sdtlseqdt0(all_0_4_4, all_0_3_3), yields:
% 19.33/5.24 | (271) $false
% 19.33/5.24 |
% 19.33/5.24 |-The branch is then unsatisfiable
% 19.33/5.25 % SZS output end Proof for theBenchmark
% 19.33/5.25
% 19.33/5.25 4634ms
%------------------------------------------------------------------------------