TSTP Solution File: NUM476+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM476+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 08:44:54 EDT 2022
% Result : Theorem 23.16s 6.32s
% Output : Proof 46.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM476+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jul 5 12:25:37 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.62/0.61 ____ _
% 0.62/0.61 ___ / __ \_____(_)___ ________ __________
% 0.62/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.62/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.62/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.62/0.61
% 0.62/0.61 A Theorem Prover for First-Order Logic
% 0.62/0.61 (ePrincess v.1.0)
% 0.62/0.61
% 0.62/0.61 (c) Philipp Rümmer, 2009-2015
% 0.62/0.61 (c) Peter Backeman, 2014-2015
% 0.62/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.62/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.62/0.61 Bug reports to peter@backeman.se
% 0.62/0.61
% 0.62/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.62/0.61
% 0.62/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.78/1.04 Prover 0: Preprocessing ...
% 3.43/1.50 Prover 0: Constructing countermodel ...
% 21.30/5.96 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 21.77/6.04 Prover 1: Preprocessing ...
% 22.16/6.17 Prover 1: Constructing countermodel ...
% 23.16/6.32 Prover 1: proved (362ms)
% 23.16/6.32 Prover 0: stopped
% 23.16/6.32
% 23.16/6.32 No countermodel exists, formula is valid
% 23.16/6.32 % SZS status Theorem for theBenchmark
% 23.16/6.32
% 23.16/6.32 Generating proof ... found it (size 413)
% 45.66/12.45
% 45.66/12.45 % SZS output start Proof for theBenchmark
% 45.66/12.46 Assumed formulas after preprocessing and simplification:
% 45.66/12.46 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ( ~ (v3 = 0) & ~ (sz10 = sz00) & sdtsldt0(v0, xl) = v2 & sdtsldt0(xm, xl) = v1 & doDivides0(xl, v0) = 0 & doDivides0(xl, xn) = v3 & doDivides0(xl, xm) = 0 & sdtpldt0(xm, xn) = v0 & aNaturalNumber0(xn) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xl) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v15 = v14 | v13 = sz00 | ~ (sdtlseqdt0(v16, v17) = v18) | ~ (sdtasdt0(v13, v15) = v17) | ~ (sdtasdt0(v13, v14) = v16) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (sdtlseqdt0(v23, v24) = v25 & sdtlseqdt0(v14, v15) = v22 & sdtasdt0(v15, v13) = v24 & sdtasdt0(v14, v13) = v23 & aNaturalNumber0(v15) = v21 & aNaturalNumber0(v14) = v20 & aNaturalNumber0(v13) = v19 & ( ~ (v22 = 0) | ~ (v21 = 0) | ~ (v20 = 0) | ~ (v19 = 0) | (v25 = 0 & v18 = 0 & ~ (v24 = v23) & ~ (v17 = v16))))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v14 = v13 | ~ (sdtlseqdt0(v16, v17) = v18) | ~ (sdtlseqdt0(v13, v14) = 0) | ~ (sdtpldt0(v14, v15) = v17) | ~ (sdtpldt0(v13, v15) = v16) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ((sdtlseqdt0(v20, v21) = v22 & sdtpldt0(v15, v14) = v21 & sdtpldt0(v15, v13) = v20 & aNaturalNumber0(v15) = v19 & ( ~ (v19 = 0) | (v22 = 0 & v18 = 0 & ~ (v21 = v20) & ~ (v17 = v16)))) | (aNaturalNumber0(v14) = v20 & aNaturalNumber0(v13) = v19 & ( ~ (v20 = 0) | ~ (v19 = 0))))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (sdtasdt0(v13, v15) = v17) | ~ (sdtasdt0(v13, v14) = v16) | ~ (sdtpldt0(v16, v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (sdtasdt0(v22, v13) = v24 & sdtasdt0(v15, v13) = v26 & sdtasdt0(v14, v13) = v25 & sdtasdt0(v13, v22) = v23 & sdtpldt0(v25, v26) = v27 & sdtpldt0(v14, v15) = v22 & aNaturalNumber0(v15) = v21 & aNaturalNumber0(v14) = v20 & aNaturalNumber0(v13) = v19 & ( ~ (v21 = 0) | ~ (v20 = 0) | ~ (v19 = 0) | (v27 = v24 & v23 = v18)))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (doDivides0(v13, v16) = v17) | ~ (sdtpldt0(v14, v15) = v16) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (doDivides0(v13, v15) = v22 & doDivides0(v13, v14) = v21 & aNaturalNumber0(v15) = v20 & aNaturalNumber0(v14) = v19 & aNaturalNumber0(v13) = v18 & ( ~ (v22 = 0) | ~ (v21 = 0) | ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0)))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | v13 = sz00 | ~ (sdtasdt0(v13, v15) = v17) | ~ (sdtasdt0(v13, v14) = v16) | ~ (aNaturalNumber0(v13) = 0) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (sdtasdt0(v15, v13) = v21 & sdtasdt0(v14, v13) = v20 & aNaturalNumber0(v15) = v19 & aNaturalNumber0(v14) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0) | ( ~ (v21 = v20) & ~ (v17 = v16))))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (sdtpldt0(v13, v15) = v17) | ~ (sdtpldt0(v13, v14) = v16) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (sdtpldt0(v15, v13) = v22 & sdtpldt0(v14, v13) = v21 & aNaturalNumber0(v15) = v20 & aNaturalNumber0(v14) = v19 & aNaturalNumber0(v13) = v18 & ( ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | ( ~ (v22 = v21) & ~ (v17 = v16))))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (sdtasdt0(v16, v15) = v17) | ~ (sdtasdt0(v13, v14) = v16) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (sdtasdt0(v14, v15) = v21 & sdtasdt0(v13, v21) = v22 & aNaturalNumber0(v15) = v20 & aNaturalNumber0(v14) = v19 & aNaturalNumber0(v13) = v18 & ( ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | v22 = v17))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (sdtpldt0(v16, v15) = v17) | ~ (sdtpldt0(v13, v14) = v16) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (sdtpldt0(v14, v15) = v21 & sdtpldt0(v13, v21) = v22 & aNaturalNumber0(v15) = v20 & aNaturalNumber0(v14) = v19 & aNaturalNumber0(v13) = v18 & ( ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | v22 = v17))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v15 | v13 = sz00 | ~ (sdtsldt0(v14, v13) = v15) | ~ (sdtasdt0(v13, v16) = v14) | ? [v17] : ? [v18] : ? [v19] : (( ~ (v17 = 0) & aNaturalNumber0(v16) = v17) | (doDivides0(v13, v14) = v19 & aNaturalNumber0(v14) = v18 & aNaturalNumber0(v13) = v17 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0))))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v15 | ~ (sdtmndt0(v14, v13) = v15) | ~ (sdtpldt0(v13, v16) = v14) | ? [v17] : ? [v18] : ? [v19] : (( ~ (v17 = 0) & aNaturalNumber0(v16) = v17) | (sdtlseqdt0(v13, v14) = v19 & aNaturalNumber0(v14) = v18 & aNaturalNumber0(v13) = v17 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0))))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v14 | v13 = sz00 | ~ (sdtsldt0(v14, v13) = v15) | ~ (sdtasdt0(v13, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : (doDivides0(v13, v14) = v19 & aNaturalNumber0(v14) = v18 & aNaturalNumber0(v13) = v17 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v14 | ~ (sdtmndt0(v14, v13) = v15) | ~ (sdtpldt0(v13, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : (sdtlseqdt0(v13, v14) = v19 & aNaturalNumber0(v14) = v18 & aNaturalNumber0(v13) = v17 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | v13 = sz00 | ~ (sdtlseqdt0(v14, v15) = v16) | ~ (sdtasdt0(v14, v13) = v15) | ? [v17] : ? [v18] : (aNaturalNumber0(v14) = v18 & aNaturalNumber0(v13) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (doDivides0(v13, v15) = v16) | ~ (doDivides0(v13, v14) = 0) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (doDivides0(v14, v15) = v20 & aNaturalNumber0(v15) = v19 & aNaturalNumber0(v14) = v18 & aNaturalNumber0(v13) = v17 & ( ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (sdtlseqdt0(v13, v15) = v16) | ~ (sdtlseqdt0(v13, v14) = 0) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (sdtlseqdt0(v14, v15) = v20 & aNaturalNumber0(v15) = v19 & aNaturalNumber0(v14) = v18 & aNaturalNumber0(v13) = v17 & ( ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (doDivides0(v13, v14) = v15) | ~ (sdtasdt0(v13, v16) = v14) | ? [v17] : ? [v18] : (( ~ (v17 = 0) & aNaturalNumber0(v16) = v17) | (aNaturalNumber0(v14) = v18 & aNaturalNumber0(v13) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0))))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (sdtlseqdt0(v13, v14) = v15) | ~ (sdtpldt0(v13, v16) = v14) | ? [v17] : ? [v18] : (( ~ (v17 = 0) & aNaturalNumber0(v16) = v17) | (aNaturalNumber0(v14) = v18 & aNaturalNumber0(v13) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0))))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (sdtsldt0(v16, v15) = v14) | ~ (sdtsldt0(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (doDivides0(v16, v15) = v14) | ~ (doDivides0(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (iLess0(v16, v15) = v14) | ~ (iLess0(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (sdtmndt0(v16, v15) = v14) | ~ (sdtmndt0(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (sdtlseqdt0(v16, v15) = v14) | ~ (sdtlseqdt0(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (sdtasdt0(v16, v15) = v14) | ~ (sdtasdt0(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (sdtpldt0(v16, v15) = v14) | ~ (sdtpldt0(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = sz00 | ~ (sdtsldt0(v14, v13) = v15) | ~ (sdtasdt0(v13, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ((v17 = 0 & aNaturalNumber0(v15) = 0) | (doDivides0(v13, v14) = v19 & aNaturalNumber0(v14) = v18 & aNaturalNumber0(v13) = v17 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0))))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (sdtmndt0(v14, v13) = v15) | ~ (sdtpldt0(v13, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ((v17 = 0 & aNaturalNumber0(v15) = 0) | (sdtlseqdt0(v13, v14) = v19 & aNaturalNumber0(v14) = v18 & aNaturalNumber0(v13) = v17 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0))))) & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = v13 | ~ (iLess0(v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : (sdtlseqdt0(v13, v14) = v18 & aNaturalNumber0(v14) = v17 & aNaturalNumber0(v13) = v16 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (sdtlseqdt0(v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : (sdtlseqdt0(v14, v13) = v18 & aNaturalNumber0(v14) = v17 & aNaturalNumber0(v13) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0) | (v18 = 0 & ~ (v14 = v13))))) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (aNaturalNumber0(v15) = v14) | ~ (aNaturalNumber0(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (sdtasdt0(v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : (sdtasdt0(v14, v13) = v18 & aNaturalNumber0(v14) = v17 & aNaturalNumber0(v13) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0) | v18 = v15))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (sdtasdt0(v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : (aNaturalNumber0(v15) = v18 & aNaturalNumber0(v14) = v17 & aNaturalNumber0(v13) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0) | v18 = 0))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (sdtpldt0(v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : (sdtpldt0(v14, v13) = v18 & aNaturalNumber0(v14) = v17 & aNaturalNumber0(v13) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0) | v18 = v15))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (sdtpldt0(v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : (aNaturalNumber0(v15) = v18 & aNaturalNumber0(v14) = v17 & aNaturalNumber0(v13) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0) | v18 = 0))) & ! [v13] : ! [v14] : (v14 = v13 | ~ (sdtlseqdt0(v13, v14) = 0) | ? [v15] : ? [v16] : ? [v17] : (sdtlseqdt0(v14, v13) = v17 & aNaturalNumber0(v14) = v16 & aNaturalNumber0(v13) = v15 & ( ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v13] : ! [v14] : (v14 = sz00 | v13 = sz00 | ~ (sdtasdt0(v13, v14) = sz00) | ? [v15] : ? [v16] : (aNaturalNumber0(v14) = v16 & aNaturalNumber0(v13) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v13] : ! [v14] : (v14 = sz00 | ~ (sdtpldt0(v13, v14) = sz00) | ? [v15] : ? [v16] : (aNaturalNumber0(v14) = v16 & aNaturalNumber0(v13) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v13] : ! [v14] : (v14 = 0 | v13 = sz10 | v13 = sz00 | ~ (sdtlseqdt0(sz10, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & aNaturalNumber0(v13) = v15)) & ! [v13] : ! [v14] : (v14 = 0 | ~ (sdtlseqdt0(v13, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & aNaturalNumber0(v13) = v15)) & ! [v13] : ! [v14] : (v13 = sz00 | ~ (sdtpldt0(v13, v14) = sz00) | ? [v15] : ? [v16] : (aNaturalNumber0(v14) = v16 & aNaturalNumber0(v13) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v13] : ! [v14] : ( ~ (doDivides0(v13, v14) = 0) | ? [v15] : ? [v16] : ? [v17] : ((v17 = v14 & v16 = 0 & sdtasdt0(v13, v15) = v14 & aNaturalNumber0(v15) = 0) | (aNaturalNumber0(v14) = v16 & aNaturalNumber0(v13) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & ! [v13] : ! [v14] : ( ~ (sdtlseqdt0(v13, v14) = 0) | ? [v15] : ? [v16] : ? [v17] : ((v17 = v14 & v16 = 0 & sdtpldt0(v13, v15) = v14 & aNaturalNumber0(v15) = 0) | (aNaturalNumber0(v14) = v16 & aNaturalNumber0(v13) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & ! [v13] : ! [v14] : ( ~ (sdtasdt0(sz10, v13) = v14) | ? [v15] : ? [v16] : (sdtasdt0(v13, sz10) = v16 & aNaturalNumber0(v13) = v15 & ( ~ (v15 = 0) | (v16 = v13 & v14 = v13)))) & ! [v13] : ! [v14] : ( ~ (sdtasdt0(sz00, v13) = v14) | ? [v15] : ? [v16] : (sdtasdt0(v13, sz00) = v16 & aNaturalNumber0(v13) = v15 & ( ~ (v15 = 0) | (v16 = sz00 & v14 = sz00)))) & ! [v13] : ! [v14] : ( ~ (sdtpldt0(sz00, v13) = v14) | ? [v15] : ? [v16] : (sdtpldt0(v13, sz00) = v16 & aNaturalNumber0(v13) = v15 & ( ~ (v15 = 0) | (v16 = v13 & v14 = v13)))) & (xl = sz00 | (v12 = v6 & v11 = xn & v10 = v9 & v8 = 0 & v7 = v2 & v4 = v1 & sdtmndt0(v2, v1) = v9 & sdtlseqdt0(v1, v2) = 0 & sdtasdt0(xl, v9) = xn & sdtasdt0(xl, v1) = v5 & sdtpldt0(v5, xn) = v6)))
% 46.14/12.52 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12 yields:
% 46.14/12.52 | (1) ~ (all_0_9_9 = 0) & ~ (sz10 = sz00) & sdtsldt0(all_0_12_12, xl) = all_0_10_10 & sdtsldt0(xm, xl) = all_0_11_11 & doDivides0(xl, all_0_12_12) = 0 & doDivides0(xl, xn) = all_0_9_9 & doDivides0(xl, xm) = 0 & sdtpldt0(xm, xn) = all_0_12_12 & aNaturalNumber0(xn) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xl) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | v0 = sz00 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (sdtlseqdt0(v10, v11) = v12 & sdtlseqdt0(v1, v2) = v9 & sdtasdt0(v2, v0) = v11 & sdtasdt0(v1, v0) = v10 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v12 = 0 & v5 = 0 & ~ (v11 = v10) & ~ (v4 = v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtlseqdt0(v0, v1) = 0) | ~ (sdtpldt0(v1, v2) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((sdtlseqdt0(v7, v8) = v9 & sdtpldt0(v2, v1) = v8 & sdtpldt0(v2, v0) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0 & ~ (v8 = v7) & ~ (v4 = v3)))) | (aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v9, v0) = v11 & sdtasdt0(v2, v0) = v13 & sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v9) = v10 & sdtpldt0(v12, v13) = v14 & sdtpldt0(v1, v2) = v9 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v14 = v11 & v10 = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (doDivides0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (doDivides0(v0, v2) = v9 & doDivides0(v0, v1) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v8 = v7) & ~ (v4 = v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtpldt0(v2, v0) = v9 & sdtpldt0(v1, v0) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v9 = v8) & ~ (v4 = v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtpldt0(v1, v2) = v8 & sdtpldt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v0 = sz00 | ~ (sdtlseqdt0(v1, v2) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ? [v4] : ? [v5] : (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (doDivides0(v0, v2) = v3) | ~ (doDivides0(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (doDivides0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (sdtlseqdt0(v0, v2) = v3) | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (sdtlseqdt0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (doDivides0(v0, v1) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(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] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (iLess0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtlseqdt0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtlseqdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v5 = 0 & ~ (v1 = v0))))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (sdtlseqdt0(v1, v0) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)) & ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (doDivides0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ! [v0] : ! [v1] : ( ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00)))) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & (xl = sz00 | (all_0_0_0 = all_0_6_6 & all_0_1_1 = xn & all_0_2_2 = all_0_3_3 & all_0_4_4 = 0 & all_0_5_5 = all_0_10_10 & all_0_8_8 = all_0_11_11 & sdtmndt0(all_0_10_10, all_0_11_11) = all_0_3_3 & sdtlseqdt0(all_0_11_11, all_0_10_10) = 0 & sdtasdt0(xl, all_0_3_3) = xn & sdtasdt0(xl, all_0_11_11) = all_0_7_7 & sdtpldt0(all_0_7_7, xn) = all_0_6_6))
% 46.17/12.54 |
% 46.17/12.54 | Applying alpha-rule on (1) yields:
% 46.17/12.54 | (2) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtlseqdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v5 = 0 & ~ (v1 = v0)))))
% 46.17/12.54 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4)))
% 46.17/12.54 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 46.17/12.54 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 46.17/12.54 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (iLess0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtlseqdt0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))))
% 46.17/12.54 | (7) aNaturalNumber0(xn) = 0
% 46.17/12.55 | (8) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 46.17/12.55 | (9) doDivides0(xl, all_0_12_12) = 0
% 46.17/12.55 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v9, v0) = v11 & sdtasdt0(v2, v0) = v13 & sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v9) = v10 & sdtpldt0(v12, v13) = v14 & sdtpldt0(v1, v2) = v9 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v14 = v11 & v10 = v5))))
% 46.17/12.55 | (11) ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 46.17/12.55 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtpldt0(v2, v0) = v9 & sdtpldt0(v1, v0) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v9 = v8) & ~ (v4 = v3)))))
% 46.17/12.55 | (13) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00))))
% 46.17/12.55 | (14) sdtsldt0(xm, xl) = all_0_11_11
% 46.17/12.55 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 46.17/12.55 | (16) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 46.17/12.55 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (doDivides0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (doDivides0(v0, v2) = v9 & doDivides0(v0, v1) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0))))
% 46.17/12.55 | (18) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 46.17/12.55 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v8 = v7) & ~ (v4 = v3)))))
% 46.17/12.55 | (20) sdtpldt0(xm, xn) = all_0_12_12
% 46.17/12.55 | (21) sdtsldt0(all_0_12_12, xl) = all_0_10_10
% 46.17/12.55 | (22) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 46.17/12.55 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 46.17/12.55 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | v0 = sz00 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (sdtlseqdt0(v10, v11) = v12 & sdtlseqdt0(v1, v2) = v9 & sdtasdt0(v2, v0) = v11 & sdtasdt0(v1, v0) = v10 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v12 = 0 & v5 = 0 & ~ (v11 = v10) & ~ (v4 = v3)))))
% 46.17/12.55 | (25) aNaturalNumber0(sz00) = 0
% 46.17/12.55 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))))
% 46.17/12.55 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 46.17/12.55 | (28) doDivides0(xl, xm) = 0
% 46.17/12.55 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0))
% 46.17/12.55 | (30) aNaturalNumber0(sz10) = 0
% 46.17/12.55 | (31) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 46.17/12.55 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))))
% 46.17/12.55 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 46.17/12.56 | (34) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (sdtlseqdt0(v1, v0) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0))))
% 46.17/12.56 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 46.17/12.56 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))))
% 46.17/12.56 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))))
% 46.17/12.56 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 46.17/12.56 | (39) ! [v0] : ! [v1] : ( ~ (doDivides0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))))
% 46.17/12.56 | (40) doDivides0(xl, xn) = all_0_9_9
% 46.17/12.56 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 46.17/12.56 | (42) ~ (all_0_9_9 = 0)
% 46.17/12.56 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 46.17/12.56 | (44) ~ (sz10 = sz00)
% 46.17/12.56 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtlseqdt0(v0, v1) = 0) | ~ (sdtpldt0(v1, v2) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((sdtlseqdt0(v7, v8) = v9 & sdtpldt0(v2, v1) = v8 & sdtpldt0(v2, v0) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0 & ~ (v8 = v7) & ~ (v4 = v3)))) | (aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))))
% 46.17/12.56 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 46.17/12.56 | (47) aNaturalNumber0(xm) = 0
% 46.17/12.56 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtpldt0(v1, v2) = v8 & sdtpldt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4)))
% 46.17/12.56 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (sdtlseqdt0(v0, v2) = v3) | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (sdtlseqdt0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 46.17/12.56 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (doDivides0(v0, v2) = v3) | ~ (doDivides0(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (doDivides0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 46.17/12.56 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0))
% 46.17/12.56 | (52) aNaturalNumber0(xl) = 0
% 46.17/12.56 | (53) xl = sz00 | (all_0_0_0 = all_0_6_6 & all_0_1_1 = xn & all_0_2_2 = all_0_3_3 & all_0_4_4 = 0 & all_0_5_5 = all_0_10_10 & all_0_8_8 = all_0_11_11 & sdtmndt0(all_0_10_10, all_0_11_11) = all_0_3_3 & sdtlseqdt0(all_0_11_11, all_0_10_10) = 0 & sdtasdt0(xl, all_0_3_3) = xn & sdtasdt0(xl, all_0_11_11) = all_0_7_7 & sdtpldt0(all_0_7_7, xn) = all_0_6_6)
% 46.17/12.56 | (54) ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 46.17/12.56 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0))
% 46.17/12.56 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (doDivides0(v0, v1) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 46.17/12.56 | (57) ! [v0] : ! [v1] : ( ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))))
% 46.17/12.56 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v0 = sz00 | ~ (sdtlseqdt0(v1, v2) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ? [v4] : ? [v5] : (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))
% 46.17/12.57 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0))
% 46.17/12.57 |
% 46.17/12.57 | Instantiating formula (15) with xm, xl, all_0_11_11, all_0_10_10 and discharging atoms sdtsldt0(xm, xl) = all_0_11_11, yields:
% 46.17/12.57 | (60) all_0_10_10 = all_0_11_11 | ~ (sdtsldt0(xm, xl) = all_0_10_10)
% 46.17/12.57 |
% 46.17/12.57 | Instantiating formula (51) with xl, xn, all_0_9_9, 0 and discharging atoms doDivides0(xl, xn) = all_0_9_9, yields:
% 46.17/12.57 | (61) all_0_9_9 = 0 | ~ (doDivides0(xl, xn) = 0)
% 46.17/12.57 |
% 46.17/12.57 | Instantiating formula (39) with all_0_12_12, xl and discharging atoms doDivides0(xl, all_0_12_12) = 0, yields:
% 46.17/12.57 | (62) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_12_12 & v1 = 0 & sdtasdt0(xl, v0) = all_0_12_12 & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_0_12_12) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 46.17/12.57 |
% 46.17/12.57 | Instantiating formula (50) with all_0_9_9, xn, all_0_12_12, xl and discharging atoms doDivides0(xl, all_0_12_12) = 0, doDivides0(xl, xn) = all_0_9_9, yields:
% 46.17/12.57 | (63) all_0_9_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_12_12, xn) = v3 & aNaturalNumber0(all_0_12_12) = v1 & aNaturalNumber0(xn) = v2 & aNaturalNumber0(xl) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 46.17/12.57 |
% 46.17/12.57 | Instantiating formula (50) with all_0_9_9, xn, xm, xl and discharging atoms doDivides0(xl, xn) = all_0_9_9, doDivides0(xl, xm) = 0, yields:
% 46.17/12.57 | (64) all_0_9_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(xm, xn) = v3 & aNaturalNumber0(xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 46.17/12.57 |
% 46.17/12.57 | Instantiating formula (39) with xm, xl and discharging atoms doDivides0(xl, xm) = 0, yields:
% 46.17/12.57 | (65) ? [v0] : ? [v1] : ? [v2] : ((v2 = xm & v1 = 0 & sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 46.17/12.57 |
% 46.17/12.57 | Instantiating formula (48) with xm, xm, xn, xn, xm yields:
% 46.17/12.57 | (66) ~ (sdtpldt0(xm, xn) = xm) | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xn, xn) = v3 & sdtpldt0(xm, v3) = v4 & aNaturalNumber0(xn) = v2 & aNaturalNumber0(xn) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = xm))
% 46.17/12.57 |
% 46.17/12.57 | Instantiating formula (31) with all_0_12_12, xn yields:
% 46.17/12.57 | (67) ~ (sdtpldt0(sz00, xn) = all_0_12_12) | ? [v0] : ? [v1] : (sdtpldt0(xn, sz00) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v0 = 0) | (v1 = xn & all_0_12_12 = xn)))
% 46.17/12.57 |
% 46.17/12.57 | Instantiating formula (33) with all_0_12_12, xn, xm and discharging atoms sdtpldt0(xm, xn) = all_0_12_12, yields:
% 46.17/12.57 | (68) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xn, xm) = v2 & aNaturalNumber0(xn) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_12_12))
% 46.17/12.57 |
% 46.17/12.57 | Instantiating formula (41) with all_0_12_12, xn, xm and discharging atoms sdtpldt0(xm, xn) = all_0_12_12, yields:
% 46.17/12.57 | (69) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_12_12) = v2 & aNaturalNumber0(xn) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 46.17/12.57 |
% 46.17/12.57 | Instantiating (69) with all_8_0_13, all_8_1_14, all_8_2_15 yields:
% 46.17/12.57 | (70) aNaturalNumber0(all_0_12_12) = all_8_0_13 & aNaturalNumber0(xn) = all_8_1_14 & aNaturalNumber0(xm) = all_8_2_15 & ( ~ (all_8_1_14 = 0) | ~ (all_8_2_15 = 0) | all_8_0_13 = 0)
% 46.17/12.57 |
% 46.17/12.57 | Applying alpha-rule on (70) yields:
% 46.17/12.57 | (71) aNaturalNumber0(all_0_12_12) = all_8_0_13
% 46.17/12.57 | (72) aNaturalNumber0(xn) = all_8_1_14
% 46.17/12.57 | (73) aNaturalNumber0(xm) = all_8_2_15
% 46.17/12.57 | (74) ~ (all_8_1_14 = 0) | ~ (all_8_2_15 = 0) | all_8_0_13 = 0
% 46.17/12.57 |
% 46.17/12.57 | Instantiating (68) with all_10_0_16, all_10_1_17, all_10_2_18 yields:
% 46.17/12.57 | (75) sdtpldt0(xn, xm) = all_10_0_16 & aNaturalNumber0(xn) = all_10_1_17 & aNaturalNumber0(xm) = all_10_2_18 & ( ~ (all_10_1_17 = 0) | ~ (all_10_2_18 = 0) | all_10_0_16 = all_0_12_12)
% 46.17/12.57 |
% 46.17/12.57 | Applying alpha-rule on (75) yields:
% 46.17/12.57 | (76) sdtpldt0(xn, xm) = all_10_0_16
% 46.17/12.57 | (77) aNaturalNumber0(xn) = all_10_1_17
% 46.17/12.57 | (78) aNaturalNumber0(xm) = all_10_2_18
% 46.17/12.57 | (79) ~ (all_10_1_17 = 0) | ~ (all_10_2_18 = 0) | all_10_0_16 = all_0_12_12
% 46.17/12.57 |
% 46.17/12.57 | Instantiating (65) with all_12_0_19, all_12_1_20, all_12_2_21 yields:
% 46.17/12.57 | (80) (all_12_0_19 = xm & all_12_1_20 = 0 & sdtasdt0(xl, all_12_2_21) = xm & aNaturalNumber0(all_12_2_21) = 0) | (aNaturalNumber0(xm) = all_12_1_20 & aNaturalNumber0(xl) = all_12_2_21 & ( ~ (all_12_1_20 = 0) | ~ (all_12_2_21 = 0)))
% 46.17/12.57 |
% 46.17/12.57 | Instantiating (62) with all_13_0_22, all_13_1_23, all_13_2_24 yields:
% 46.17/12.57 | (81) (all_13_0_22 = all_0_12_12 & all_13_1_23 = 0 & sdtasdt0(xl, all_13_2_24) = all_0_12_12 & aNaturalNumber0(all_13_2_24) = 0) | (aNaturalNumber0(all_0_12_12) = all_13_1_23 & aNaturalNumber0(xl) = all_13_2_24 & ( ~ (all_13_1_23 = 0) | ~ (all_13_2_24 = 0)))
% 46.17/12.57 |
% 46.17/12.57 +-Applying beta-rule and splitting (63), into two cases.
% 46.17/12.57 |-Branch one:
% 46.17/12.57 | (82) all_0_9_9 = 0
% 46.17/12.57 |
% 46.17/12.57 | Equations (82) can reduce 42 to:
% 46.17/12.57 | (83) $false
% 46.17/12.57 |
% 46.17/12.58 |-The branch is then unsatisfiable
% 46.17/12.58 |-Branch two:
% 46.17/12.58 | (42) ~ (all_0_9_9 = 0)
% 46.17/12.58 | (85) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_12_12, xn) = v3 & aNaturalNumber0(all_0_12_12) = v1 & aNaturalNumber0(xn) = v2 & aNaturalNumber0(xl) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 46.17/12.58 |
% 46.17/12.58 | Instantiating (85) with all_18_0_25, all_18_1_26, all_18_2_27, all_18_3_28 yields:
% 46.17/12.58 | (86) doDivides0(all_0_12_12, xn) = all_18_0_25 & aNaturalNumber0(all_0_12_12) = all_18_2_27 & aNaturalNumber0(xn) = all_18_1_26 & aNaturalNumber0(xl) = all_18_3_28 & ( ~ (all_18_0_25 = 0) | ~ (all_18_1_26 = 0) | ~ (all_18_2_27 = 0) | ~ (all_18_3_28 = 0))
% 46.17/12.58 |
% 46.17/12.58 | Applying alpha-rule on (86) yields:
% 46.17/12.58 | (87) ~ (all_18_0_25 = 0) | ~ (all_18_1_26 = 0) | ~ (all_18_2_27 = 0) | ~ (all_18_3_28 = 0)
% 46.17/12.58 | (88) doDivides0(all_0_12_12, xn) = all_18_0_25
% 46.17/12.58 | (89) aNaturalNumber0(xn) = all_18_1_26
% 46.17/12.58 | (90) aNaturalNumber0(all_0_12_12) = all_18_2_27
% 46.17/12.58 | (91) aNaturalNumber0(xl) = all_18_3_28
% 46.17/12.58 |
% 46.17/12.58 +-Applying beta-rule and splitting (64), into two cases.
% 46.17/12.58 |-Branch one:
% 46.17/12.58 | (82) all_0_9_9 = 0
% 46.17/12.58 |
% 46.17/12.58 | Equations (82) can reduce 42 to:
% 46.17/12.58 | (83) $false
% 46.17/12.58 |
% 46.17/12.58 |-The branch is then unsatisfiable
% 46.17/12.58 |-Branch two:
% 46.17/12.58 | (42) ~ (all_0_9_9 = 0)
% 46.17/12.58 | (95) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(xm, xn) = v3 & aNaturalNumber0(xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 46.17/12.58 |
% 46.17/12.58 | Instantiating (95) with all_23_0_29, all_23_1_30, all_23_2_31, all_23_3_32 yields:
% 46.17/12.58 | (96) doDivides0(xm, xn) = all_23_0_29 & aNaturalNumber0(xn) = all_23_1_30 & aNaturalNumber0(xm) = all_23_2_31 & aNaturalNumber0(xl) = all_23_3_32 & ( ~ (all_23_0_29 = 0) | ~ (all_23_1_30 = 0) | ~ (all_23_2_31 = 0) | ~ (all_23_3_32 = 0))
% 46.17/12.58 |
% 46.17/12.58 | Applying alpha-rule on (96) yields:
% 46.17/12.58 | (97) aNaturalNumber0(xm) = all_23_2_31
% 46.17/12.58 | (98) aNaturalNumber0(xn) = all_23_1_30
% 46.17/12.58 | (99) aNaturalNumber0(xl) = all_23_3_32
% 46.17/12.58 | (100) ~ (all_23_0_29 = 0) | ~ (all_23_1_30 = 0) | ~ (all_23_2_31 = 0) | ~ (all_23_3_32 = 0)
% 46.17/12.58 | (101) doDivides0(xm, xn) = all_23_0_29
% 46.17/12.58 |
% 46.17/12.58 | Instantiating formula (55) with all_0_12_12, all_8_0_13, all_18_2_27 and discharging atoms aNaturalNumber0(all_0_12_12) = all_18_2_27, aNaturalNumber0(all_0_12_12) = all_8_0_13, yields:
% 46.17/12.58 | (102) all_18_2_27 = all_8_0_13
% 46.17/12.58 |
% 46.17/12.58 | Instantiating formula (55) with xn, all_18_1_26, 0 and discharging atoms aNaturalNumber0(xn) = all_18_1_26, aNaturalNumber0(xn) = 0, yields:
% 46.17/12.58 | (103) all_18_1_26 = 0
% 46.17/12.58 |
% 46.17/12.58 | Instantiating formula (55) with xn, all_10_1_17, all_23_1_30 and discharging atoms aNaturalNumber0(xn) = all_23_1_30, aNaturalNumber0(xn) = all_10_1_17, yields:
% 46.17/12.58 | (104) all_23_1_30 = all_10_1_17
% 46.17/12.58 |
% 46.17/12.58 | Instantiating formula (55) with xn, all_10_1_17, all_18_1_26 and discharging atoms aNaturalNumber0(xn) = all_18_1_26, aNaturalNumber0(xn) = all_10_1_17, yields:
% 46.17/12.58 | (105) all_18_1_26 = all_10_1_17
% 46.17/12.58 |
% 46.17/12.58 | Instantiating formula (55) with xn, all_8_1_14, all_23_1_30 and discharging atoms aNaturalNumber0(xn) = all_23_1_30, aNaturalNumber0(xn) = all_8_1_14, yields:
% 46.17/12.58 | (106) all_23_1_30 = all_8_1_14
% 46.17/12.58 |
% 46.17/12.58 | Instantiating formula (55) with xm, all_10_2_18, 0 and discharging atoms aNaturalNumber0(xm) = all_10_2_18, aNaturalNumber0(xm) = 0, yields:
% 46.17/12.58 | (107) all_10_2_18 = 0
% 46.17/12.58 |
% 46.17/12.58 | Instantiating formula (55) with xm, all_10_2_18, all_23_2_31 and discharging atoms aNaturalNumber0(xm) = all_23_2_31, aNaturalNumber0(xm) = all_10_2_18, yields:
% 46.17/12.58 | (108) all_23_2_31 = all_10_2_18
% 46.17/12.58 |
% 46.17/12.58 | Instantiating formula (55) with xm, all_8_2_15, all_23_2_31 and discharging atoms aNaturalNumber0(xm) = all_23_2_31, aNaturalNumber0(xm) = all_8_2_15, yields:
% 46.17/12.58 | (109) all_23_2_31 = all_8_2_15
% 46.17/12.58 |
% 46.17/12.58 | Instantiating formula (55) with xl, all_23_3_32, 0 and discharging atoms aNaturalNumber0(xl) = all_23_3_32, aNaturalNumber0(xl) = 0, yields:
% 46.17/12.58 | (110) all_23_3_32 = 0
% 46.17/12.58 |
% 46.17/12.58 | Instantiating formula (55) with xl, all_18_3_28, all_23_3_32 and discharging atoms aNaturalNumber0(xl) = all_23_3_32, aNaturalNumber0(xl) = all_18_3_28, yields:
% 46.17/12.58 | (111) all_23_3_32 = all_18_3_28
% 46.17/12.58 |
% 46.17/12.58 | Combining equations (104,106) yields a new equation:
% 46.17/12.58 | (112) all_10_1_17 = all_8_1_14
% 46.17/12.58 |
% 46.17/12.58 | Simplifying 112 yields:
% 46.17/12.58 | (113) all_10_1_17 = all_8_1_14
% 46.17/12.58 |
% 46.17/12.58 | Combining equations (108,109) yields a new equation:
% 46.17/12.58 | (114) all_10_2_18 = all_8_2_15
% 46.17/12.58 |
% 46.17/12.58 | Simplifying 114 yields:
% 46.17/12.58 | (115) all_10_2_18 = all_8_2_15
% 46.17/12.58 |
% 46.17/12.58 | Combining equations (111,110) yields a new equation:
% 46.17/12.58 | (116) all_18_3_28 = 0
% 46.17/12.58 |
% 46.17/12.58 | Simplifying 116 yields:
% 46.17/12.58 | (117) all_18_3_28 = 0
% 46.17/12.58 |
% 46.17/12.58 | Combining equations (105,103) yields a new equation:
% 46.17/12.58 | (118) all_10_1_17 = 0
% 46.17/12.58 |
% 46.17/12.58 | Simplifying 118 yields:
% 46.17/12.58 | (119) all_10_1_17 = 0
% 46.17/12.58 |
% 46.17/12.58 | Combining equations (113,119) yields a new equation:
% 46.17/12.58 | (120) all_8_1_14 = 0
% 46.17/12.58 |
% 46.17/12.58 | Simplifying 120 yields:
% 46.17/12.58 | (121) all_8_1_14 = 0
% 46.17/12.58 |
% 46.17/12.58 | Combining equations (107,115) yields a new equation:
% 46.17/12.58 | (122) all_8_2_15 = 0
% 46.17/12.58 |
% 46.17/12.58 | Combining equations (122,115) yields a new equation:
% 46.17/12.58 | (107) all_10_2_18 = 0
% 46.17/12.58 |
% 46.17/12.58 | From (102) and (90) follows:
% 46.17/12.58 | (71) aNaturalNumber0(all_0_12_12) = all_8_0_13
% 46.17/12.58 |
% 46.17/12.58 | From (121) and (72) follows:
% 46.17/12.58 | (7) aNaturalNumber0(xn) = 0
% 46.17/12.58 |
% 46.17/12.58 | From (122) and (73) follows:
% 46.17/12.58 | (47) aNaturalNumber0(xm) = 0
% 46.17/12.58 |
% 46.17/12.58 | From (117) and (91) follows:
% 46.17/12.58 | (52) aNaturalNumber0(xl) = 0
% 46.17/12.58 |
% 46.17/12.58 +-Applying beta-rule and splitting (80), into two cases.
% 46.17/12.58 |-Branch one:
% 46.17/12.58 | (128) all_12_0_19 = xm & all_12_1_20 = 0 & sdtasdt0(xl, all_12_2_21) = xm & aNaturalNumber0(all_12_2_21) = 0
% 46.17/12.59 |
% 46.17/12.59 | Applying alpha-rule on (128) yields:
% 46.17/12.59 | (129) all_12_0_19 = xm
% 46.17/12.59 | (130) all_12_1_20 = 0
% 46.17/12.59 | (131) sdtasdt0(xl, all_12_2_21) = xm
% 46.17/12.59 | (132) aNaturalNumber0(all_12_2_21) = 0
% 46.17/12.59 |
% 46.17/12.59 +-Applying beta-rule and splitting (74), into two cases.
% 46.17/12.59 |-Branch one:
% 46.17/12.59 | (133) ~ (all_8_1_14 = 0)
% 46.17/12.59 |
% 46.17/12.59 | Equations (121) can reduce 133 to:
% 46.17/12.59 | (83) $false
% 46.17/12.59 |
% 46.17/12.59 |-The branch is then unsatisfiable
% 46.17/12.59 |-Branch two:
% 46.17/12.59 | (121) all_8_1_14 = 0
% 46.17/12.59 | (136) ~ (all_8_2_15 = 0) | all_8_0_13 = 0
% 46.17/12.59 |
% 46.17/12.59 +-Applying beta-rule and splitting (136), into two cases.
% 46.17/12.59 |-Branch one:
% 46.17/12.59 | (137) ~ (all_8_2_15 = 0)
% 46.17/12.59 |
% 46.17/12.59 | Equations (122) can reduce 137 to:
% 46.17/12.59 | (83) $false
% 46.17/12.59 |
% 46.17/12.59 |-The branch is then unsatisfiable
% 46.17/12.59 |-Branch two:
% 46.17/12.59 | (122) all_8_2_15 = 0
% 46.17/12.59 | (140) all_8_0_13 = 0
% 46.17/12.59 |
% 46.17/12.59 | From (140) and (71) follows:
% 46.17/12.59 | (141) aNaturalNumber0(all_0_12_12) = 0
% 46.17/12.59 |
% 46.17/12.59 +-Applying beta-rule and splitting (81), into two cases.
% 46.17/12.59 |-Branch one:
% 46.17/12.59 | (142) all_13_0_22 = all_0_12_12 & all_13_1_23 = 0 & sdtasdt0(xl, all_13_2_24) = all_0_12_12 & aNaturalNumber0(all_13_2_24) = 0
% 46.17/12.59 |
% 46.17/12.59 | Applying alpha-rule on (142) yields:
% 46.17/12.59 | (143) all_13_0_22 = all_0_12_12
% 46.17/12.59 | (144) all_13_1_23 = 0
% 46.17/12.59 | (145) sdtasdt0(xl, all_13_2_24) = all_0_12_12
% 46.17/12.59 | (146) aNaturalNumber0(all_13_2_24) = 0
% 46.17/12.59 |
% 46.17/12.59 +-Applying beta-rule and splitting (79), into two cases.
% 46.17/12.59 |-Branch one:
% 46.17/12.59 | (147) ~ (all_10_1_17 = 0)
% 46.17/12.59 |
% 46.17/12.59 | Equations (119) can reduce 147 to:
% 46.17/12.59 | (83) $false
% 46.17/12.59 |
% 46.17/12.59 |-The branch is then unsatisfiable
% 46.17/12.59 |-Branch two:
% 46.17/12.59 | (119) all_10_1_17 = 0
% 46.17/12.59 | (150) ~ (all_10_2_18 = 0) | all_10_0_16 = all_0_12_12
% 46.17/12.59 |
% 46.17/12.59 +-Applying beta-rule and splitting (150), into two cases.
% 46.17/12.59 |-Branch one:
% 46.17/12.59 | (151) ~ (all_10_2_18 = 0)
% 46.17/12.59 |
% 46.17/12.59 | Equations (107) can reduce 151 to:
% 46.17/12.59 | (83) $false
% 46.17/12.59 |
% 46.17/12.59 |-The branch is then unsatisfiable
% 46.17/12.59 |-Branch two:
% 46.17/12.59 | (107) all_10_2_18 = 0
% 46.17/12.59 | (154) all_10_0_16 = all_0_12_12
% 46.17/12.59 |
% 46.17/12.59 | From (154) and (76) follows:
% 46.17/12.59 | (155) sdtpldt0(xn, xm) = all_0_12_12
% 46.17/12.59 |
% 46.17/12.59 | Instantiating formula (26) with all_13_2_24, all_0_10_10, all_0_12_12, xl and discharging atoms sdtsldt0(all_0_12_12, xl) = all_0_10_10, sdtasdt0(xl, all_13_2_24) = all_0_12_12, yields:
% 46.17/12.59 | (156) all_13_2_24 = all_0_10_10 | xl = sz00 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_13_2_24) = v0) | (doDivides0(xl, all_0_12_12) = v2 & aNaturalNumber0(all_0_12_12) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 46.17/12.59 |
% 46.17/12.59 | Instantiating formula (56) with all_13_2_24, all_0_9_9, xn, xl and discharging atoms doDivides0(xl, xn) = all_0_9_9, yields:
% 46.17/12.59 | (157) all_0_9_9 = 0 | ~ (sdtasdt0(xl, all_13_2_24) = xn) | ? [v0] : ? [v1] : (( ~ (v0 = 0) & aNaturalNumber0(all_13_2_24) = v0) | (aNaturalNumber0(xn) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 46.17/12.59 |
% 46.17/12.59 | Instantiating formula (35) with all_0_12_12, all_13_2_24, xl and discharging atoms sdtasdt0(xl, all_13_2_24) = all_0_12_12, yields:
% 46.17/12.59 | (158) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_13_2_24, xl) = v2 & aNaturalNumber0(all_13_2_24) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_12_12))
% 46.17/12.59 |
% 46.17/12.59 | Instantiating formula (26) with all_12_2_21, all_0_11_11, xm, xl and discharging atoms sdtsldt0(xm, xl) = all_0_11_11, sdtasdt0(xl, all_12_2_21) = xm, yields:
% 46.17/12.59 | (159) all_12_2_21 = all_0_11_11 | xl = sz00 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_12_2_21) = v0) | (doDivides0(xl, xm) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 46.17/12.59 |
% 46.17/12.59 | Instantiating formula (13) with xm, all_12_2_21 yields:
% 46.17/12.59 | (160) ~ (sdtasdt0(sz00, all_12_2_21) = xm) | ? [v0] : ? [v1] : (sdtasdt0(all_12_2_21, sz00) = v1 & aNaturalNumber0(all_12_2_21) = v0 & ( ~ (v0 = 0) | (v1 = sz00 & xm = sz00)))
% 46.17/12.59 |
% 46.17/12.59 | Instantiating formula (35) with xm, all_12_2_21, xl and discharging atoms sdtasdt0(xl, all_12_2_21) = xm, yields:
% 46.17/12.59 | (161) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_12_2_21, xl) = v2 & aNaturalNumber0(all_12_2_21) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xm))
% 46.17/12.59 |
% 46.17/12.59 | Instantiating (161) with all_66_0_33, all_66_1_34, all_66_2_35 yields:
% 46.17/12.59 | (162) sdtasdt0(all_12_2_21, xl) = all_66_0_33 & aNaturalNumber0(all_12_2_21) = all_66_1_34 & aNaturalNumber0(xl) = all_66_2_35 & ( ~ (all_66_1_34 = 0) | ~ (all_66_2_35 = 0) | all_66_0_33 = xm)
% 46.17/12.59 |
% 46.17/12.59 | Applying alpha-rule on (162) yields:
% 46.17/12.59 | (163) sdtasdt0(all_12_2_21, xl) = all_66_0_33
% 46.17/12.59 | (164) aNaturalNumber0(all_12_2_21) = all_66_1_34
% 46.17/12.59 | (165) aNaturalNumber0(xl) = all_66_2_35
% 46.17/12.59 | (166) ~ (all_66_1_34 = 0) | ~ (all_66_2_35 = 0) | all_66_0_33 = xm
% 46.17/12.59 |
% 46.17/12.59 | Instantiating (158) with all_68_0_36, all_68_1_37, all_68_2_38 yields:
% 46.17/12.59 | (167) sdtasdt0(all_13_2_24, xl) = all_68_0_36 & aNaturalNumber0(all_13_2_24) = all_68_1_37 & aNaturalNumber0(xl) = all_68_2_38 & ( ~ (all_68_1_37 = 0) | ~ (all_68_2_38 = 0) | all_68_0_36 = all_0_12_12)
% 46.17/12.59 |
% 46.17/12.59 | Applying alpha-rule on (167) yields:
% 46.17/12.59 | (168) sdtasdt0(all_13_2_24, xl) = all_68_0_36
% 46.17/12.59 | (169) aNaturalNumber0(all_13_2_24) = all_68_1_37
% 46.17/12.59 | (170) aNaturalNumber0(xl) = all_68_2_38
% 46.17/12.59 | (171) ~ (all_68_1_37 = 0) | ~ (all_68_2_38 = 0) | all_68_0_36 = all_0_12_12
% 46.17/12.59 |
% 46.17/12.59 | Instantiating formula (55) with all_13_2_24, all_68_1_37, 0 and discharging atoms aNaturalNumber0(all_13_2_24) = all_68_1_37, aNaturalNumber0(all_13_2_24) = 0, yields:
% 46.17/12.59 | (172) all_68_1_37 = 0
% 46.17/12.59 |
% 46.17/12.59 | Instantiating formula (55) with all_12_2_21, all_66_1_34, 0 and discharging atoms aNaturalNumber0(all_12_2_21) = all_66_1_34, aNaturalNumber0(all_12_2_21) = 0, yields:
% 46.17/12.60 | (173) all_66_1_34 = 0
% 46.17/12.60 |
% 46.17/12.60 | Instantiating formula (55) with xl, all_68_2_38, 0 and discharging atoms aNaturalNumber0(xl) = all_68_2_38, aNaturalNumber0(xl) = 0, yields:
% 46.17/12.60 | (174) all_68_2_38 = 0
% 46.17/12.60 |
% 46.17/12.60 | Instantiating formula (55) with xl, all_66_2_35, all_68_2_38 and discharging atoms aNaturalNumber0(xl) = all_68_2_38, aNaturalNumber0(xl) = all_66_2_35, yields:
% 46.17/12.60 | (175) all_68_2_38 = all_66_2_35
% 46.17/12.60 |
% 46.17/12.60 | Combining equations (174,175) yields a new equation:
% 46.17/12.60 | (176) all_66_2_35 = 0
% 46.17/12.60 |
% 46.17/12.60 | Combining equations (176,175) yields a new equation:
% 46.17/12.60 | (174) all_68_2_38 = 0
% 46.17/12.60 |
% 46.17/12.60 | From (172) and (169) follows:
% 46.17/12.60 | (146) aNaturalNumber0(all_13_2_24) = 0
% 46.17/12.60 |
% 46.17/12.60 | From (173) and (164) follows:
% 46.17/12.60 | (132) aNaturalNumber0(all_12_2_21) = 0
% 46.17/12.60 |
% 46.17/12.60 | From (176) and (165) follows:
% 46.17/12.60 | (52) aNaturalNumber0(xl) = 0
% 46.17/12.60 |
% 46.17/12.60 +-Applying beta-rule and splitting (157), into two cases.
% 46.17/12.60 |-Branch one:
% 46.17/12.60 | (181) ~ (sdtasdt0(xl, all_13_2_24) = xn)
% 46.17/12.60 |
% 46.17/12.60 +-Applying beta-rule and splitting (171), into two cases.
% 46.17/12.60 |-Branch one:
% 46.17/12.60 | (182) ~ (all_68_1_37 = 0)
% 46.17/12.60 |
% 46.17/12.60 | Equations (172) can reduce 182 to:
% 46.17/12.60 | (83) $false
% 46.17/12.60 |
% 46.17/12.60 |-The branch is then unsatisfiable
% 46.17/12.60 |-Branch two:
% 46.17/12.60 | (172) all_68_1_37 = 0
% 46.17/12.60 | (185) ~ (all_68_2_38 = 0) | all_68_0_36 = all_0_12_12
% 46.17/12.60 |
% 46.17/12.60 +-Applying beta-rule and splitting (166), into two cases.
% 46.17/12.60 |-Branch one:
% 46.17/12.60 | (186) ~ (all_66_1_34 = 0)
% 46.17/12.60 |
% 46.17/12.60 | Equations (173) can reduce 186 to:
% 46.17/12.60 | (83) $false
% 46.17/12.60 |
% 46.17/12.60 |-The branch is then unsatisfiable
% 46.17/12.60 |-Branch two:
% 46.17/12.60 | (173) all_66_1_34 = 0
% 46.17/12.60 | (189) ~ (all_66_2_35 = 0) | all_66_0_33 = xm
% 46.17/12.60 |
% 46.17/12.60 +-Applying beta-rule and splitting (185), into two cases.
% 46.17/12.60 |-Branch one:
% 46.17/12.60 | (190) ~ (all_68_2_38 = 0)
% 46.17/12.60 |
% 46.17/12.60 | Equations (174) can reduce 190 to:
% 46.17/12.60 | (83) $false
% 46.17/12.60 |
% 46.17/12.60 |-The branch is then unsatisfiable
% 46.17/12.60 |-Branch two:
% 46.17/12.60 | (174) all_68_2_38 = 0
% 46.17/12.60 | (193) all_68_0_36 = all_0_12_12
% 46.17/12.60 |
% 46.17/12.60 | From (193) and (168) follows:
% 46.17/12.60 | (194) sdtasdt0(all_13_2_24, xl) = all_0_12_12
% 46.17/12.60 |
% 46.17/12.60 +-Applying beta-rule and splitting (189), into two cases.
% 46.17/12.60 |-Branch one:
% 46.17/12.60 | (195) ~ (all_66_2_35 = 0)
% 46.17/12.60 |
% 46.17/12.60 | Equations (176) can reduce 195 to:
% 46.17/12.60 | (83) $false
% 46.17/12.60 |
% 46.17/12.60 |-The branch is then unsatisfiable
% 46.17/12.60 |-Branch two:
% 46.17/12.60 | (176) all_66_2_35 = 0
% 46.17/12.60 | (198) all_66_0_33 = xm
% 46.17/12.60 |
% 46.17/12.60 | From (198) and (163) follows:
% 46.17/12.60 | (199) sdtasdt0(all_12_2_21, xl) = xm
% 46.17/12.60 |
% 46.17/12.60 | Using (145) and (181) yields:
% 46.17/12.60 | (200) ~ (all_0_12_12 = xn)
% 46.17/12.60 |
% 46.17/12.60 +-Applying beta-rule and splitting (67), into two cases.
% 46.17/12.60 |-Branch one:
% 46.17/12.60 | (201) ~ (sdtpldt0(sz00, xn) = all_0_12_12)
% 46.17/12.60 |
% 46.17/12.60 | Using (20) and (201) yields:
% 46.17/12.60 | (202) ~ (xm = sz00)
% 46.17/12.60 |
% 46.17/12.60 +-Applying beta-rule and splitting (160), into two cases.
% 46.17/12.60 |-Branch one:
% 46.17/12.60 | (203) ~ (sdtasdt0(sz00, all_12_2_21) = xm)
% 46.17/12.60 |
% 46.17/12.60 | Using (131) and (203) yields:
% 46.17/12.60 | (204) ~ (xl = sz00)
% 46.17/12.60 |
% 46.17/12.60 +-Applying beta-rule and splitting (159), into two cases.
% 46.17/12.60 |-Branch one:
% 46.17/12.60 | (205) xl = sz00
% 46.17/12.60 |
% 46.17/12.60 | Equations (205) can reduce 204 to:
% 46.56/12.60 | (83) $false
% 46.56/12.60 |
% 46.56/12.60 |-The branch is then unsatisfiable
% 46.56/12.60 |-Branch two:
% 46.56/12.60 | (204) ~ (xl = sz00)
% 46.56/12.60 | (208) all_12_2_21 = all_0_11_11 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_12_2_21) = v0) | (doDivides0(xl, xm) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 46.56/12.60 |
% 46.56/12.60 +-Applying beta-rule and splitting (53), into two cases.
% 46.56/12.60 |-Branch one:
% 46.56/12.60 | (205) xl = sz00
% 46.56/12.60 |
% 46.56/12.60 | Equations (205) can reduce 204 to:
% 46.56/12.60 | (83) $false
% 46.56/12.60 |
% 46.56/12.60 |-The branch is then unsatisfiable
% 46.56/12.60 |-Branch two:
% 46.56/12.60 | (204) ~ (xl = sz00)
% 46.56/12.60 | (212) all_0_0_0 = all_0_6_6 & all_0_1_1 = xn & all_0_2_2 = all_0_3_3 & all_0_4_4 = 0 & all_0_5_5 = all_0_10_10 & all_0_8_8 = all_0_11_11 & sdtmndt0(all_0_10_10, all_0_11_11) = all_0_3_3 & sdtlseqdt0(all_0_11_11, all_0_10_10) = 0 & sdtasdt0(xl, all_0_3_3) = xn & sdtasdt0(xl, all_0_11_11) = all_0_7_7 & sdtpldt0(all_0_7_7, xn) = all_0_6_6
% 46.56/12.60 |
% 46.56/12.60 | Applying alpha-rule on (212) yields:
% 46.56/12.60 | (213) all_0_8_8 = all_0_11_11
% 46.56/12.60 | (214) all_0_1_1 = xn
% 46.56/12.60 | (215) sdtpldt0(all_0_7_7, xn) = all_0_6_6
% 46.56/12.60 | (216) sdtlseqdt0(all_0_11_11, all_0_10_10) = 0
% 46.56/12.60 | (217) sdtasdt0(xl, all_0_3_3) = xn
% 46.56/12.60 | (218) sdtasdt0(xl, all_0_11_11) = all_0_7_7
% 46.56/12.60 | (219) all_0_5_5 = all_0_10_10
% 46.56/12.61 | (220) all_0_2_2 = all_0_3_3
% 46.56/12.61 | (221) sdtmndt0(all_0_10_10, all_0_11_11) = all_0_3_3
% 46.56/12.61 | (222) all_0_0_0 = all_0_6_6
% 46.56/12.61 | (223) all_0_4_4 = 0
% 46.56/12.61 |
% 46.56/12.61 +-Applying beta-rule and splitting (208), into two cases.
% 46.56/12.61 |-Branch one:
% 46.56/12.61 | (224) all_12_2_21 = all_0_11_11
% 46.56/12.61 |
% 46.56/12.61 | From (224) and (199) follows:
% 46.56/12.61 | (225) sdtasdt0(all_0_11_11, xl) = xm
% 46.56/12.61 |
% 46.56/12.61 | From (224) and (131) follows:
% 46.56/12.61 | (226) sdtasdt0(xl, all_0_11_11) = xm
% 46.56/12.61 |
% 46.56/12.61 | From (224) and (132) follows:
% 46.56/12.61 | (227) aNaturalNumber0(all_0_11_11) = 0
% 46.56/12.61 |
% 46.56/12.61 +-Applying beta-rule and splitting (156), into two cases.
% 46.56/12.61 |-Branch one:
% 46.56/12.61 | (205) xl = sz00
% 46.56/12.61 |
% 46.56/12.61 | Equations (205) can reduce 204 to:
% 46.56/12.61 | (83) $false
% 46.56/12.61 |
% 46.56/12.61 |-The branch is then unsatisfiable
% 46.56/12.61 |-Branch two:
% 46.56/12.61 | (204) ~ (xl = sz00)
% 46.56/12.61 | (231) all_13_2_24 = all_0_10_10 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_13_2_24) = v0) | (doDivides0(xl, all_0_12_12) = v2 & aNaturalNumber0(all_0_12_12) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 46.56/12.61 |
% 46.56/12.61 +-Applying beta-rule and splitting (231), into two cases.
% 46.56/12.61 |-Branch one:
% 46.56/12.61 | (232) all_13_2_24 = all_0_10_10
% 46.56/12.61 |
% 46.56/12.61 | From (232) and (194) follows:
% 46.56/12.61 | (233) sdtasdt0(all_0_10_10, xl) = all_0_12_12
% 46.56/12.61 |
% 46.56/12.61 | From (232) and (146) follows:
% 46.56/12.61 | (234) aNaturalNumber0(all_0_10_10) = 0
% 46.56/12.61 |
% 46.56/12.61 | Instantiating formula (23) with xl, all_0_11_11, xm, all_0_7_7 and discharging atoms sdtasdt0(xl, all_0_11_11) = all_0_7_7, sdtasdt0(xl, all_0_11_11) = xm, yields:
% 46.56/12.61 | (235) all_0_7_7 = xm
% 46.56/12.61 |
% 46.56/12.61 | Instantiating formula (46) with xm, xn, all_0_6_6, all_0_12_12 and discharging atoms sdtpldt0(xm, xn) = all_0_12_12, yields:
% 46.56/12.61 | (236) all_0_6_6 = all_0_12_12 | ~ (sdtpldt0(xm, xn) = all_0_6_6)
% 46.56/12.61 |
% 46.56/12.61 | From (235) and (218) follows:
% 46.56/12.61 | (226) sdtasdt0(xl, all_0_11_11) = xm
% 46.56/12.61 |
% 46.56/12.61 | From (235) and (215) follows:
% 46.56/12.61 | (238) sdtpldt0(xm, xn) = all_0_6_6
% 46.56/12.61 |
% 46.56/12.61 +-Applying beta-rule and splitting (236), into two cases.
% 46.56/12.61 |-Branch one:
% 46.56/12.61 | (239) ~ (sdtpldt0(xm, xn) = all_0_6_6)
% 46.56/12.61 |
% 46.56/12.61 | Using (238) and (239) yields:
% 46.56/12.61 | (240) $false
% 46.56/12.61 |
% 46.56/12.61 |-The branch is then unsatisfiable
% 46.56/12.61 |-Branch two:
% 46.56/12.61 | (238) sdtpldt0(xm, xn) = all_0_6_6
% 46.56/12.61 | (242) all_0_6_6 = all_0_12_12
% 46.56/12.61 |
% 46.56/12.61 | From (242) and (238) follows:
% 46.56/12.61 | (20) sdtpldt0(xm, xn) = all_0_12_12
% 46.56/12.61 |
% 46.56/12.61 | Instantiating formula (34) with all_0_10_10, all_0_11_11 and discharging atoms sdtlseqdt0(all_0_11_11, all_0_10_10) = 0, yields:
% 46.56/12.61 | (244) all_0_10_10 = all_0_11_11 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_0_10_10, all_0_11_11) = v2 & aNaturalNumber0(all_0_10_10) = v1 & aNaturalNumber0(all_0_11_11) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 46.56/12.61 |
% 46.56/12.61 | Instantiating formula (57) with all_0_10_10, all_0_11_11 and discharging atoms sdtlseqdt0(all_0_11_11, all_0_10_10) = 0, yields:
% 46.56/12.61 | (245) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_10_10 & v1 = 0 & sdtpldt0(all_0_11_11, v0) = all_0_10_10 & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_0_10_10) = v1 & aNaturalNumber0(all_0_11_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 46.56/12.61 |
% 46.56/12.61 | Instantiating formula (56) with all_0_3_3, all_0_9_9, xn, xl and discharging atoms doDivides0(xl, xn) = all_0_9_9, sdtasdt0(xl, all_0_3_3) = xn, yields:
% 46.56/12.61 | (246) all_0_9_9 = 0 | ? [v0] : ? [v1] : (( ~ (v0 = 0) & aNaturalNumber0(all_0_3_3) = v0) | (aNaturalNumber0(xn) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 46.56/12.61 |
% 46.56/12.61 | Instantiating formula (35) with xn, all_0_3_3, xl and discharging atoms sdtasdt0(xl, all_0_3_3) = xn, yields:
% 46.56/12.61 | (247) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_0_3_3, xl) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xn))
% 46.56/12.61 |
% 46.56/12.61 | Instantiating formula (38) with xn, all_0_3_3, xl and discharging atoms sdtasdt0(xl, all_0_3_3) = xn, yields:
% 46.56/12.61 | (248) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xn) = v2 & aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 46.56/12.61 |
% 46.56/12.61 | Instantiating formula (10) with all_0_12_12, xm, xn, all_0_11_11, all_0_3_3, xl and discharging atoms sdtasdt0(xl, all_0_3_3) = xn, sdtasdt0(xl, all_0_11_11) = xm, sdtpldt0(xn, xm) = all_0_12_12, yields:
% 46.56/12.61 | (249) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (sdtasdt0(v3, xl) = v5 & sdtasdt0(all_0_3_3, xl) = v6 & sdtasdt0(all_0_11_11, xl) = v7 & sdtasdt0(xl, v3) = v4 & sdtpldt0(v6, v7) = v8 & sdtpldt0(all_0_3_3, all_0_11_11) = v3 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(all_0_11_11) = v2 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v8 = v5 & v4 = all_0_12_12)))
% 46.56/12.61 |
% 46.56/12.61 | Instantiating formula (10) with all_0_12_12, xn, xm, all_0_3_3, all_0_11_11, xl and discharging atoms sdtasdt0(xl, all_0_3_3) = xn, sdtasdt0(xl, all_0_11_11) = xm, sdtpldt0(xm, xn) = all_0_12_12, yields:
% 46.56/12.61 | (250) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (sdtasdt0(v3, xl) = v5 & sdtasdt0(all_0_3_3, xl) = v7 & sdtasdt0(all_0_11_11, xl) = v6 & sdtasdt0(xl, v3) = v4 & sdtpldt0(v6, v7) = v8 & sdtpldt0(all_0_11_11, all_0_3_3) = v3 & aNaturalNumber0(all_0_3_3) = v2 & aNaturalNumber0(all_0_11_11) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v8 = v5 & v4 = all_0_12_12)))
% 46.56/12.61 |
% 46.56/12.61 | Instantiating (250) with all_159_0_39, all_159_1_40, all_159_2_41, all_159_3_42, all_159_4_43, all_159_5_44, all_159_6_45, all_159_7_46, all_159_8_47 yields:
% 46.56/12.61 | (251) sdtasdt0(all_159_5_44, xl) = all_159_3_42 & sdtasdt0(all_0_3_3, xl) = all_159_1_40 & sdtasdt0(all_0_11_11, xl) = all_159_2_41 & sdtasdt0(xl, all_159_5_44) = all_159_4_43 & sdtpldt0(all_159_2_41, all_159_1_40) = all_159_0_39 & sdtpldt0(all_0_11_11, all_0_3_3) = all_159_5_44 & aNaturalNumber0(all_0_3_3) = all_159_6_45 & aNaturalNumber0(all_0_11_11) = all_159_7_46 & aNaturalNumber0(xl) = all_159_8_47 & ( ~ (all_159_6_45 = 0) | ~ (all_159_7_46 = 0) | ~ (all_159_8_47 = 0) | (all_159_0_39 = all_159_3_42 & all_159_4_43 = all_0_12_12))
% 46.56/12.61 |
% 46.56/12.61 | Applying alpha-rule on (251) yields:
% 46.56/12.61 | (252) aNaturalNumber0(all_0_3_3) = all_159_6_45
% 46.56/12.61 | (253) aNaturalNumber0(xl) = all_159_8_47
% 46.56/12.61 | (254) aNaturalNumber0(all_0_11_11) = all_159_7_46
% 46.56/12.62 | (255) sdtpldt0(all_0_11_11, all_0_3_3) = all_159_5_44
% 46.56/12.62 | (256) ~ (all_159_6_45 = 0) | ~ (all_159_7_46 = 0) | ~ (all_159_8_47 = 0) | (all_159_0_39 = all_159_3_42 & all_159_4_43 = all_0_12_12)
% 46.56/12.62 | (257) sdtasdt0(all_159_5_44, xl) = all_159_3_42
% 46.56/12.62 | (258) sdtasdt0(xl, all_159_5_44) = all_159_4_43
% 46.56/12.62 | (259) sdtasdt0(all_0_11_11, xl) = all_159_2_41
% 46.56/12.62 | (260) sdtasdt0(all_0_3_3, xl) = all_159_1_40
% 46.56/12.62 | (261) sdtpldt0(all_159_2_41, all_159_1_40) = all_159_0_39
% 46.56/12.62 |
% 46.56/12.62 | Instantiating (249) with all_161_0_48, all_161_1_49, all_161_2_50, all_161_3_51, all_161_4_52, all_161_5_53, all_161_6_54, all_161_7_55, all_161_8_56 yields:
% 46.56/12.62 | (262) sdtasdt0(all_161_5_53, xl) = all_161_3_51 & sdtasdt0(all_0_3_3, xl) = all_161_2_50 & sdtasdt0(all_0_11_11, xl) = all_161_1_49 & sdtasdt0(xl, all_161_5_53) = all_161_4_52 & sdtpldt0(all_161_2_50, all_161_1_49) = all_161_0_48 & sdtpldt0(all_0_3_3, all_0_11_11) = all_161_5_53 & aNaturalNumber0(all_0_3_3) = all_161_7_55 & aNaturalNumber0(all_0_11_11) = all_161_6_54 & aNaturalNumber0(xl) = all_161_8_56 & ( ~ (all_161_6_54 = 0) | ~ (all_161_7_55 = 0) | ~ (all_161_8_56 = 0) | (all_161_0_48 = all_161_3_51 & all_161_4_52 = all_0_12_12))
% 46.56/12.62 |
% 46.56/12.62 | Applying alpha-rule on (262) yields:
% 46.56/12.62 | (263) aNaturalNumber0(all_0_11_11) = all_161_6_54
% 46.56/12.62 | (264) sdtpldt0(all_161_2_50, all_161_1_49) = all_161_0_48
% 46.56/12.62 | (265) sdtasdt0(all_0_11_11, xl) = all_161_1_49
% 46.56/12.62 | (266) sdtpldt0(all_0_3_3, all_0_11_11) = all_161_5_53
% 46.56/12.62 | (267) sdtasdt0(xl, all_161_5_53) = all_161_4_52
% 46.56/12.62 | (268) aNaturalNumber0(xl) = all_161_8_56
% 46.56/12.62 | (269) sdtasdt0(all_161_5_53, xl) = all_161_3_51
% 46.56/12.62 | (270) aNaturalNumber0(all_0_3_3) = all_161_7_55
% 46.56/12.62 | (271) sdtasdt0(all_0_3_3, xl) = all_161_2_50
% 46.56/12.62 | (272) ~ (all_161_6_54 = 0) | ~ (all_161_7_55 = 0) | ~ (all_161_8_56 = 0) | (all_161_0_48 = all_161_3_51 & all_161_4_52 = all_0_12_12)
% 46.56/12.62 |
% 46.56/12.62 | Instantiating (248) with all_163_0_57, all_163_1_58, all_163_2_59 yields:
% 46.56/12.62 | (273) aNaturalNumber0(all_0_3_3) = all_163_1_58 & aNaturalNumber0(xn) = all_163_0_57 & aNaturalNumber0(xl) = all_163_2_59 & ( ~ (all_163_1_58 = 0) | ~ (all_163_2_59 = 0) | all_163_0_57 = 0)
% 46.56/12.62 |
% 46.56/12.62 | Applying alpha-rule on (273) yields:
% 46.56/12.62 | (274) aNaturalNumber0(all_0_3_3) = all_163_1_58
% 46.56/12.62 | (275) aNaturalNumber0(xn) = all_163_0_57
% 46.56/12.62 | (276) aNaturalNumber0(xl) = all_163_2_59
% 46.56/12.62 | (277) ~ (all_163_1_58 = 0) | ~ (all_163_2_59 = 0) | all_163_0_57 = 0
% 46.56/12.62 |
% 46.56/12.62 | Instantiating (247) with all_165_0_60, all_165_1_61, all_165_2_62 yields:
% 46.56/12.62 | (278) sdtasdt0(all_0_3_3, xl) = all_165_0_60 & aNaturalNumber0(all_0_3_3) = all_165_1_61 & aNaturalNumber0(xl) = all_165_2_62 & ( ~ (all_165_1_61 = 0) | ~ (all_165_2_62 = 0) | all_165_0_60 = xn)
% 46.56/12.62 |
% 46.56/12.62 | Applying alpha-rule on (278) yields:
% 46.56/12.62 | (279) sdtasdt0(all_0_3_3, xl) = all_165_0_60
% 46.56/12.62 | (280) aNaturalNumber0(all_0_3_3) = all_165_1_61
% 46.56/12.62 | (281) aNaturalNumber0(xl) = all_165_2_62
% 46.56/12.62 | (282) ~ (all_165_1_61 = 0) | ~ (all_165_2_62 = 0) | all_165_0_60 = xn
% 46.56/12.62 |
% 46.56/12.62 | Instantiating (245) with all_167_0_63, all_167_1_64, all_167_2_65 yields:
% 46.56/12.62 | (283) (all_167_0_63 = all_0_10_10 & all_167_1_64 = 0 & sdtpldt0(all_0_11_11, all_167_2_65) = all_0_10_10 & aNaturalNumber0(all_167_2_65) = 0) | (aNaturalNumber0(all_0_10_10) = all_167_1_64 & aNaturalNumber0(all_0_11_11) = all_167_2_65 & ( ~ (all_167_1_64 = 0) | ~ (all_167_2_65 = 0)))
% 46.56/12.62 |
% 46.56/12.62 +-Applying beta-rule and splitting (246), into two cases.
% 46.56/12.62 |-Branch one:
% 46.56/12.62 | (82) all_0_9_9 = 0
% 46.56/12.62 |
% 46.56/12.62 | Equations (82) can reduce 42 to:
% 46.56/12.62 | (83) $false
% 46.56/12.62 |
% 46.56/12.62 |-The branch is then unsatisfiable
% 46.56/12.62 |-Branch two:
% 46.56/12.62 | (42) ~ (all_0_9_9 = 0)
% 46.56/12.62 | (287) ? [v0] : ? [v1] : (( ~ (v0 = 0) & aNaturalNumber0(all_0_3_3) = v0) | (aNaturalNumber0(xn) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 46.56/12.62 |
% 46.56/12.62 | Instantiating (287) with all_172_0_66, all_172_1_67 yields:
% 46.56/12.62 | (288) ( ~ (all_172_1_67 = 0) & aNaturalNumber0(all_0_3_3) = all_172_1_67) | (aNaturalNumber0(xn) = all_172_0_66 & aNaturalNumber0(xl) = all_172_1_67 & ( ~ (all_172_0_66 = 0) | ~ (all_172_1_67 = 0)))
% 46.56/12.62 |
% 46.56/12.62 | Instantiating formula (23) with all_0_11_11, xl, all_161_1_49, all_0_12_12 and discharging atoms sdtasdt0(all_0_11_11, xl) = all_161_1_49, yields:
% 46.56/12.62 | (289) all_161_1_49 = all_0_12_12 | ~ (sdtasdt0(all_0_11_11, xl) = all_0_12_12)
% 46.56/12.62 |
% 46.56/12.62 | Instantiating formula (23) with all_0_11_11, xl, all_161_1_49, xm and discharging atoms sdtasdt0(all_0_11_11, xl) = all_161_1_49, sdtasdt0(all_0_11_11, xl) = xm, yields:
% 46.56/12.62 | (290) all_161_1_49 = xm
% 46.56/12.62 |
% 46.56/12.62 | Instantiating formula (55) with all_0_3_3, all_163_1_58, all_165_1_61 and discharging atoms aNaturalNumber0(all_0_3_3) = all_165_1_61, aNaturalNumber0(all_0_3_3) = all_163_1_58, yields:
% 46.56/12.62 | (291) all_165_1_61 = all_163_1_58
% 46.56/12.62 |
% 46.56/12.62 | Instantiating formula (55) with all_0_3_3, all_161_7_55, all_165_1_61 and discharging atoms aNaturalNumber0(all_0_3_3) = all_165_1_61, aNaturalNumber0(all_0_3_3) = all_161_7_55, yields:
% 46.56/12.62 | (292) all_165_1_61 = all_161_7_55
% 46.56/12.62 |
% 46.56/12.62 | Instantiating formula (55) with xm, all_159_6_45, 0 and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 46.56/12.62 | (293) all_159_6_45 = 0 | ~ (aNaturalNumber0(xm) = all_159_6_45)
% 46.56/12.62 |
% 46.56/12.62 | Instantiating formula (55) with all_0_3_3, all_159_6_45, all_165_1_61 and discharging atoms aNaturalNumber0(all_0_3_3) = all_165_1_61, aNaturalNumber0(all_0_3_3) = all_159_6_45, yields:
% 46.56/12.62 | (294) all_165_1_61 = all_159_6_45
% 46.56/12.62 |
% 46.56/12.62 | Instantiating formula (55) with all_0_11_11, all_161_6_54, 0 and discharging atoms aNaturalNumber0(all_0_11_11) = all_161_6_54, aNaturalNumber0(all_0_11_11) = 0, yields:
% 46.56/12.62 | (295) all_161_6_54 = 0
% 46.56/12.62 |
% 46.56/12.62 | Instantiating formula (55) with all_0_11_11, all_159_7_46, all_161_6_54 and discharging atoms aNaturalNumber0(all_0_11_11) = all_161_6_54, aNaturalNumber0(all_0_11_11) = all_159_7_46, yields:
% 46.56/12.62 | (296) all_161_6_54 = all_159_7_46
% 46.56/12.62 |
% 46.56/12.62 | Instantiating formula (55) with xn, all_163_0_57, 0 and discharging atoms aNaturalNumber0(xn) = all_163_0_57, aNaturalNumber0(xn) = 0, yields:
% 46.56/12.62 | (297) all_163_0_57 = 0
% 46.56/12.62 |
% 46.56/12.62 | Instantiating formula (55) with xl, all_163_2_59, 0 and discharging atoms aNaturalNumber0(xl) = all_163_2_59, aNaturalNumber0(xl) = 0, yields:
% 46.56/12.62 | (298) all_163_2_59 = 0
% 46.56/12.62 |
% 46.56/12.62 | Instantiating formula (55) with xl, all_163_2_59, all_165_2_62 and discharging atoms aNaturalNumber0(xl) = all_165_2_62, aNaturalNumber0(xl) = all_163_2_59, yields:
% 46.56/12.62 | (299) all_165_2_62 = all_163_2_59
% 46.56/12.62 |
% 46.56/12.62 | Instantiating formula (55) with xl, all_161_8_56, all_165_2_62 and discharging atoms aNaturalNumber0(xl) = all_165_2_62, aNaturalNumber0(xl) = all_161_8_56, yields:
% 46.56/12.62 | (300) all_165_2_62 = all_161_8_56
% 46.56/12.62 |
% 46.56/12.62 | Instantiating formula (55) with xl, all_159_8_47, all_165_2_62 and discharging atoms aNaturalNumber0(xl) = all_165_2_62, aNaturalNumber0(xl) = all_159_8_47, yields:
% 46.56/12.62 | (301) all_165_2_62 = all_159_8_47
% 46.56/12.62 |
% 46.56/12.62 | Combining equations (294,291) yields a new equation:
% 46.56/12.62 | (302) all_163_1_58 = all_159_6_45
% 46.56/12.62 |
% 46.56/12.62 | Combining equations (292,291) yields a new equation:
% 46.56/12.62 | (303) all_163_1_58 = all_161_7_55
% 46.56/12.62 |
% 46.56/12.62 | Combining equations (301,300) yields a new equation:
% 46.56/12.62 | (304) all_161_8_56 = all_159_8_47
% 46.56/12.62 |
% 46.56/12.62 | Combining equations (299,300) yields a new equation:
% 46.56/12.62 | (305) all_163_2_59 = all_161_8_56
% 46.56/12.62 |
% 46.56/12.62 | Simplifying 305 yields:
% 46.56/12.62 | (306) all_163_2_59 = all_161_8_56
% 46.56/12.62 |
% 46.56/12.62 | Combining equations (302,303) yields a new equation:
% 46.56/12.62 | (307) all_161_7_55 = all_159_6_45
% 46.56/12.62 |
% 46.56/12.62 | Combining equations (306,298) yields a new equation:
% 46.56/12.62 | (308) all_161_8_56 = 0
% 46.56/12.62 |
% 46.56/12.62 | Simplifying 308 yields:
% 46.56/12.62 | (309) all_161_8_56 = 0
% 46.56/12.62 |
% 46.56/12.62 | Combining equations (295,296) yields a new equation:
% 46.56/12.62 | (310) all_159_7_46 = 0
% 46.56/12.62 |
% 46.56/12.62 | Combining equations (309,304) yields a new equation:
% 46.56/12.62 | (311) all_159_8_47 = 0
% 46.56/12.62 |
% 46.56/12.62 | From (307) and (270) follows:
% 46.56/12.62 | (252) aNaturalNumber0(all_0_3_3) = all_159_6_45
% 46.56/12.62 |
% 46.56/12.62 | From (310) and (254) follows:
% 46.56/12.62 | (227) aNaturalNumber0(all_0_11_11) = 0
% 46.56/12.62 |
% 46.56/12.62 | From (297) and (275) follows:
% 46.56/12.62 | (7) aNaturalNumber0(xn) = 0
% 46.56/12.62 |
% 46.56/12.62 | From (311) and (253) follows:
% 46.56/12.62 | (52) aNaturalNumber0(xl) = 0
% 46.56/12.62 |
% 46.56/12.62 +-Applying beta-rule and splitting (288), into two cases.
% 46.56/12.62 |-Branch one:
% 46.56/12.62 | (316) ~ (all_172_1_67 = 0) & aNaturalNumber0(all_0_3_3) = all_172_1_67
% 46.56/12.62 |
% 46.56/12.62 | Applying alpha-rule on (316) yields:
% 46.56/12.62 | (317) ~ (all_172_1_67 = 0)
% 46.56/12.62 | (318) aNaturalNumber0(all_0_3_3) = all_172_1_67
% 46.56/12.62 |
% 46.56/12.62 +-Applying beta-rule and splitting (283), into two cases.
% 46.56/12.62 |-Branch one:
% 46.56/12.62 | (319) all_167_0_63 = all_0_10_10 & all_167_1_64 = 0 & sdtpldt0(all_0_11_11, all_167_2_65) = all_0_10_10 & aNaturalNumber0(all_167_2_65) = 0
% 46.56/12.62 |
% 46.56/12.62 | Applying alpha-rule on (319) yields:
% 46.56/12.62 | (320) all_167_0_63 = all_0_10_10
% 46.56/12.62 | (321) all_167_1_64 = 0
% 46.56/12.62 | (322) sdtpldt0(all_0_11_11, all_167_2_65) = all_0_10_10
% 46.56/12.62 | (323) aNaturalNumber0(all_167_2_65) = 0
% 46.56/12.62 |
% 46.56/12.62 | Instantiating formula (55) with all_0_3_3, 0, all_159_6_45 and discharging atoms aNaturalNumber0(all_0_3_3) = all_159_6_45, yields:
% 46.56/12.62 | (324) all_159_6_45 = 0 | ~ (aNaturalNumber0(all_0_3_3) = 0)
% 46.56/12.62 |
% 46.56/12.62 | Instantiating formula (55) with all_0_3_3, all_172_1_67, all_159_6_45 and discharging atoms aNaturalNumber0(all_0_3_3) = all_172_1_67, aNaturalNumber0(all_0_3_3) = all_159_6_45, yields:
% 46.56/12.63 | (325) all_172_1_67 = all_159_6_45
% 46.56/12.63 |
% 46.56/12.63 | Instantiating formula (55) with all_0_11_11, all_172_1_67, 0 and discharging atoms aNaturalNumber0(all_0_11_11) = 0, yields:
% 46.56/12.63 | (326) all_172_1_67 = 0 | ~ (aNaturalNumber0(all_0_11_11) = all_172_1_67)
% 46.56/12.63 |
% 46.56/12.63 | Instantiating formula (55) with all_0_3_3, all_172_1_67, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_172_1_67, yields:
% 46.56/12.63 | (327) all_172_1_67 = 0 | ~ (aNaturalNumber0(all_0_3_3) = 0)
% 46.56/12.63 |
% 46.56/12.63 | Equations (325) can reduce 317 to:
% 46.56/12.63 | (328) ~ (all_159_6_45 = 0)
% 46.56/12.63 |
% 46.56/12.63 +-Applying beta-rule and splitting (60), into two cases.
% 46.56/12.63 |-Branch one:
% 46.56/12.63 | (329) ~ (sdtsldt0(xm, xl) = all_0_10_10)
% 46.56/12.63 |
% 46.56/12.63 | Using (14) and (329) yields:
% 46.56/12.63 | (330) ~ (all_0_10_10 = all_0_11_11)
% 46.56/12.63 |
% 46.56/12.63 +-Applying beta-rule and splitting (244), into two cases.
% 46.56/12.63 |-Branch one:
% 46.56/12.63 | (331) all_0_10_10 = all_0_11_11
% 46.56/12.63 |
% 46.56/12.63 | Equations (331) can reduce 330 to:
% 46.56/12.63 | (83) $false
% 46.56/12.63 |
% 46.56/12.63 |-The branch is then unsatisfiable
% 46.56/12.63 |-Branch two:
% 46.56/12.63 | (330) ~ (all_0_10_10 = all_0_11_11)
% 46.56/12.63 | (334) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_0_10_10, all_0_11_11) = v2 & aNaturalNumber0(all_0_10_10) = v1 & aNaturalNumber0(all_0_11_11) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 46.56/12.63 |
% 46.56/12.63 | Instantiating (334) with all_215_0_68, all_215_1_69, all_215_2_70 yields:
% 46.56/12.63 | (335) sdtlseqdt0(all_0_10_10, all_0_11_11) = all_215_0_68 & aNaturalNumber0(all_0_10_10) = all_215_1_69 & aNaturalNumber0(all_0_11_11) = all_215_2_70 & ( ~ (all_215_0_68 = 0) | ~ (all_215_1_69 = 0) | ~ (all_215_2_70 = 0))
% 46.56/12.63 |
% 46.56/12.63 | Applying alpha-rule on (335) yields:
% 46.56/12.63 | (336) sdtlseqdt0(all_0_10_10, all_0_11_11) = all_215_0_68
% 46.56/12.63 | (337) aNaturalNumber0(all_0_10_10) = all_215_1_69
% 46.56/12.63 | (338) aNaturalNumber0(all_0_11_11) = all_215_2_70
% 46.56/12.63 | (339) ~ (all_215_0_68 = 0) | ~ (all_215_1_69 = 0) | ~ (all_215_2_70 = 0)
% 46.56/12.63 |
% 46.56/12.63 +-Applying beta-rule and splitting (326), into two cases.
% 46.56/12.63 |-Branch one:
% 46.56/12.63 | (340) ~ (aNaturalNumber0(all_0_11_11) = all_172_1_67)
% 46.56/12.63 |
% 46.56/12.63 | From (325) and (340) follows:
% 46.56/12.63 | (341) ~ (aNaturalNumber0(all_0_11_11) = all_159_6_45)
% 46.56/12.63 |
% 46.56/12.63 | Instantiating formula (55) with all_0_10_10, all_215_1_69, 0 and discharging atoms aNaturalNumber0(all_0_10_10) = all_215_1_69, aNaturalNumber0(all_0_10_10) = 0, yields:
% 46.56/12.63 | (342) all_215_1_69 = 0
% 46.56/12.63 |
% 46.56/12.63 | Instantiating formula (55) with all_0_11_11, all_215_2_70, 0 and discharging atoms aNaturalNumber0(all_0_11_11) = all_215_2_70, aNaturalNumber0(all_0_11_11) = 0, yields:
% 46.56/12.63 | (343) all_215_2_70 = 0
% 46.56/12.63 |
% 46.56/12.63 | Using (338) and (341) yields:
% 46.56/12.63 | (344) ~ (all_215_2_70 = all_159_6_45)
% 46.56/12.63 |
% 46.56/12.63 | Equations (343) can reduce 344 to:
% 46.56/12.63 | (345) ~ (all_159_6_45 = 0)
% 46.56/12.63 |
% 46.56/12.63 | Simplifying 345 yields:
% 46.56/12.63 | (328) ~ (all_159_6_45 = 0)
% 46.56/12.63 |
% 46.56/12.63 | From (342) and (337) follows:
% 46.56/12.63 | (234) aNaturalNumber0(all_0_10_10) = 0
% 46.56/12.63 |
% 46.56/12.63 | From (343) and (338) follows:
% 46.56/12.63 | (227) aNaturalNumber0(all_0_11_11) = 0
% 46.56/12.63 |
% 46.56/12.63 | Instantiating formula (41) with all_161_5_53, all_0_11_11, all_0_3_3 and discharging atoms sdtpldt0(all_0_3_3, all_0_11_11) = all_161_5_53, yields:
% 46.56/12.63 | (349) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_161_5_53) = v2 & aNaturalNumber0(all_0_3_3) = v0 & aNaturalNumber0(all_0_11_11) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 46.56/12.63 |
% 46.56/12.63 | Instantiating formula (32) with all_159_5_44, all_0_3_3, all_0_10_10, all_0_11_11 and discharging atoms sdtmndt0(all_0_10_10, all_0_11_11) = all_0_3_3, sdtpldt0(all_0_11_11, all_0_3_3) = all_159_5_44, yields:
% 46.56/12.63 | (350) ? [v0] : ? [v1] : ? [v2] : ((v0 = 0 & aNaturalNumber0(all_0_3_3) = 0) | (sdtlseqdt0(all_0_11_11, all_0_10_10) = v2 & aNaturalNumber0(all_0_10_10) = v1 & aNaturalNumber0(all_0_11_11) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 46.56/12.63 |
% 46.56/12.63 | Instantiating (349) with all_798_0_77, all_798_1_78, all_798_2_79 yields:
% 46.56/12.63 | (351) aNaturalNumber0(all_161_5_53) = all_798_0_77 & aNaturalNumber0(all_0_3_3) = all_798_2_79 & aNaturalNumber0(all_0_11_11) = all_798_1_78 & ( ~ (all_798_1_78 = 0) | ~ (all_798_2_79 = 0) | all_798_0_77 = 0)
% 46.56/12.63 |
% 46.56/12.63 | Applying alpha-rule on (351) yields:
% 46.56/12.63 | (352) aNaturalNumber0(all_161_5_53) = all_798_0_77
% 46.56/12.63 | (353) aNaturalNumber0(all_0_3_3) = all_798_2_79
% 46.56/12.63 | (354) aNaturalNumber0(all_0_11_11) = all_798_1_78
% 46.56/12.63 | (355) ~ (all_798_1_78 = 0) | ~ (all_798_2_79 = 0) | all_798_0_77 = 0
% 46.56/12.63 |
% 46.56/12.63 | Instantiating (350) with all_820_0_110, all_820_1_111, all_820_2_112 yields:
% 46.56/12.63 | (356) (all_820_2_112 = 0 & aNaturalNumber0(all_0_3_3) = 0) | (sdtlseqdt0(all_0_11_11, all_0_10_10) = all_820_0_110 & aNaturalNumber0(all_0_10_10) = all_820_1_111 & aNaturalNumber0(all_0_11_11) = all_820_2_112 & ( ~ (all_820_0_110 = 0) | ~ (all_820_1_111 = 0) | ~ (all_820_2_112 = 0)))
% 46.56/12.63 |
% 46.56/12.63 +-Applying beta-rule and splitting (356), into two cases.
% 46.56/12.63 |-Branch one:
% 46.56/12.63 | (357) all_820_2_112 = 0 & aNaturalNumber0(all_0_3_3) = 0
% 46.56/12.63 |
% 46.56/12.63 | Applying alpha-rule on (357) yields:
% 46.56/12.63 | (358) all_820_2_112 = 0
% 46.56/12.63 | (359) aNaturalNumber0(all_0_3_3) = 0
% 46.56/12.63 |
% 46.56/12.63 +-Applying beta-rule and splitting (327), into two cases.
% 46.56/12.63 |-Branch one:
% 46.56/12.63 | (360) ~ (aNaturalNumber0(all_0_3_3) = 0)
% 46.56/12.63 |
% 46.56/12.63 | Using (359) and (360) yields:
% 46.56/12.63 | (240) $false
% 46.56/12.63 |
% 46.56/12.63 |-The branch is then unsatisfiable
% 46.56/12.63 |-Branch two:
% 46.56/12.63 | (359) aNaturalNumber0(all_0_3_3) = 0
% 46.56/12.63 | (363) all_172_1_67 = 0
% 46.56/12.63 |
% 46.56/12.63 | Combining equations (363,325) yields a new equation:
% 46.56/12.63 | (364) all_159_6_45 = 0
% 46.56/12.63 |
% 46.56/12.63 | Equations (364) can reduce 328 to:
% 46.56/12.63 | (83) $false
% 46.56/12.63 |
% 46.56/12.63 |-The branch is then unsatisfiable
% 46.56/12.63 |-Branch two:
% 46.56/12.63 | (366) sdtlseqdt0(all_0_11_11, all_0_10_10) = all_820_0_110 & aNaturalNumber0(all_0_10_10) = all_820_1_111 & aNaturalNumber0(all_0_11_11) = all_820_2_112 & ( ~ (all_820_0_110 = 0) | ~ (all_820_1_111 = 0) | ~ (all_820_2_112 = 0))
% 46.56/12.63 |
% 46.56/12.63 | Applying alpha-rule on (366) yields:
% 46.56/12.63 | (367) sdtlseqdt0(all_0_11_11, all_0_10_10) = all_820_0_110
% 46.56/12.63 | (368) aNaturalNumber0(all_0_10_10) = all_820_1_111
% 46.56/12.63 | (369) aNaturalNumber0(all_0_11_11) = all_820_2_112
% 46.56/12.63 | (370) ~ (all_820_0_110 = 0) | ~ (all_820_1_111 = 0) | ~ (all_820_2_112 = 0)
% 46.56/12.63 |
% 46.56/12.63 | Instantiating formula (59) with all_0_11_11, all_0_10_10, all_820_0_110, 0 and discharging atoms sdtlseqdt0(all_0_11_11, all_0_10_10) = all_820_0_110, sdtlseqdt0(all_0_11_11, all_0_10_10) = 0, yields:
% 46.56/12.63 | (371) all_820_0_110 = 0
% 46.56/12.63 |
% 46.56/12.63 | Instantiating formula (55) with all_0_10_10, all_820_1_111, 0 and discharging atoms aNaturalNumber0(all_0_10_10) = all_820_1_111, aNaturalNumber0(all_0_10_10) = 0, yields:
% 46.56/12.63 | (372) all_820_1_111 = 0
% 46.56/12.63 |
% 46.56/12.63 | Instantiating formula (55) with all_0_11_11, all_820_2_112, 0 and discharging atoms aNaturalNumber0(all_0_11_11) = all_820_2_112, aNaturalNumber0(all_0_11_11) = 0, yields:
% 46.56/12.63 | (358) all_820_2_112 = 0
% 46.56/12.63 |
% 46.56/12.63 | Instantiating formula (55) with all_0_11_11, all_798_1_78, all_820_2_112 and discharging atoms aNaturalNumber0(all_0_11_11) = all_820_2_112, aNaturalNumber0(all_0_11_11) = all_798_1_78, yields:
% 46.56/12.63 | (374) all_820_2_112 = all_798_1_78
% 46.56/12.63 |
% 46.56/12.63 | Combining equations (358,374) yields a new equation:
% 46.56/12.63 | (375) all_798_1_78 = 0
% 46.56/12.63 |
% 46.56/12.63 | Combining equations (375,374) yields a new equation:
% 46.56/12.63 | (358) all_820_2_112 = 0
% 46.56/12.63 |
% 46.56/12.63 +-Applying beta-rule and splitting (370), into two cases.
% 46.56/12.63 |-Branch one:
% 46.56/12.63 | (377) ~ (all_820_0_110 = 0)
% 46.56/12.63 |
% 46.56/12.63 | Equations (371) can reduce 377 to:
% 46.56/12.63 | (83) $false
% 46.56/12.63 |
% 46.56/12.63 |-The branch is then unsatisfiable
% 46.56/12.63 |-Branch two:
% 46.56/12.63 | (371) all_820_0_110 = 0
% 46.56/12.63 | (380) ~ (all_820_1_111 = 0) | ~ (all_820_2_112 = 0)
% 46.56/12.63 |
% 46.56/12.63 +-Applying beta-rule and splitting (380), into two cases.
% 46.56/12.63 |-Branch one:
% 46.56/12.63 | (381) ~ (all_820_1_111 = 0)
% 46.56/12.63 |
% 46.56/12.63 | Equations (372) can reduce 381 to:
% 46.56/12.63 | (83) $false
% 46.56/12.63 |
% 46.56/12.63 |-The branch is then unsatisfiable
% 46.56/12.63 |-Branch two:
% 46.56/12.63 | (372) all_820_1_111 = 0
% 46.56/12.63 | (384) ~ (all_820_2_112 = 0)
% 46.56/12.63 |
% 46.56/12.63 | Equations (358) can reduce 384 to:
% 46.56/12.63 | (83) $false
% 46.56/12.63 |
% 46.56/12.63 |-The branch is then unsatisfiable
% 46.56/12.63 |-Branch two:
% 46.56/12.63 | (386) aNaturalNumber0(all_0_11_11) = all_172_1_67
% 46.56/12.63 | (363) all_172_1_67 = 0
% 46.56/12.63 |
% 46.56/12.63 | Combining equations (363,325) yields a new equation:
% 46.56/12.63 | (364) all_159_6_45 = 0
% 46.56/12.63 |
% 46.56/12.63 | Equations (364) can reduce 328 to:
% 46.56/12.63 | (83) $false
% 46.56/12.63 |
% 46.56/12.63 |-The branch is then unsatisfiable
% 46.56/12.63 |-Branch two:
% 46.56/12.63 | (390) sdtsldt0(xm, xl) = all_0_10_10
% 46.56/12.63 | (331) all_0_10_10 = all_0_11_11
% 46.56/12.63 |
% 46.56/12.63 | From (331) and (221) follows:
% 46.56/12.63 | (392) sdtmndt0(all_0_11_11, all_0_11_11) = all_0_3_3
% 46.56/12.63 |
% 46.56/12.63 | From (331) and (216) follows:
% 46.56/12.63 | (393) sdtlseqdt0(all_0_11_11, all_0_11_11) = 0
% 46.56/12.63 |
% 46.56/12.63 | From (331) and (233) follows:
% 46.56/12.63 | (394) sdtasdt0(all_0_11_11, xl) = all_0_12_12
% 46.56/12.63 |
% 46.56/12.64 | From (331) and (322) follows:
% 46.56/12.64 | (395) sdtpldt0(all_0_11_11, all_167_2_65) = all_0_11_11
% 46.56/12.64 |
% 46.56/12.64 | From (331) and (234) follows:
% 46.56/12.64 | (227) aNaturalNumber0(all_0_11_11) = 0
% 46.56/12.64 |
% 46.56/12.64 +-Applying beta-rule and splitting (289), into two cases.
% 46.56/12.64 |-Branch one:
% 46.56/12.64 | (397) ~ (sdtasdt0(all_0_11_11, xl) = all_0_12_12)
% 46.56/12.64 |
% 46.56/12.64 | Using (394) and (397) yields:
% 46.56/12.64 | (240) $false
% 46.56/12.64 |
% 46.56/12.64 |-The branch is then unsatisfiable
% 46.56/12.64 |-Branch two:
% 46.56/12.64 | (394) sdtasdt0(all_0_11_11, xl) = all_0_12_12
% 46.56/12.64 | (400) all_161_1_49 = all_0_12_12
% 46.56/12.64 |
% 46.56/12.64 | Combining equations (400,290) yields a new equation:
% 46.56/12.64 | (401) all_0_12_12 = xm
% 46.56/12.64 |
% 46.56/12.64 | Simplifying 401 yields:
% 46.56/12.64 | (402) all_0_12_12 = xm
% 46.56/12.64 |
% 46.56/12.64 | From (402) and (20) follows:
% 46.56/12.64 | (403) sdtpldt0(xm, xn) = xm
% 46.56/12.64 |
% 46.56/12.64 | From (402) and (141) follows:
% 46.56/12.64 | (47) aNaturalNumber0(xm) = 0
% 46.56/12.64 |
% 46.56/12.64 +-Applying beta-rule and splitting (66), into two cases.
% 46.56/12.64 |-Branch one:
% 46.56/12.64 | (405) ~ (sdtpldt0(xm, xn) = xm)
% 46.56/12.64 |
% 46.56/12.64 | Using (403) and (405) yields:
% 46.56/12.64 | (240) $false
% 46.56/12.64 |
% 46.56/12.64 |-The branch is then unsatisfiable
% 46.56/12.64 |-Branch two:
% 46.56/12.64 | (403) sdtpldt0(xm, xn) = xm
% 46.56/12.64 | (408) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xn, xn) = v3 & sdtpldt0(xm, v3) = v4 & aNaturalNumber0(xn) = v2 & aNaturalNumber0(xn) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = xm))
% 46.56/12.64 |
% 46.56/12.64 | Instantiating (408) with all_215_0_122, all_215_1_123, all_215_2_124, all_215_3_125, all_215_4_126 yields:
% 46.56/12.64 | (409) sdtpldt0(xn, xn) = all_215_1_123 & sdtpldt0(xm, all_215_1_123) = all_215_0_122 & aNaturalNumber0(xn) = all_215_2_124 & aNaturalNumber0(xn) = all_215_3_125 & aNaturalNumber0(xm) = all_215_4_126 & ( ~ (all_215_2_124 = 0) | ~ (all_215_3_125 = 0) | ~ (all_215_4_126 = 0) | all_215_0_122 = xm)
% 46.56/12.64 |
% 46.56/12.64 | Applying alpha-rule on (409) yields:
% 46.56/12.64 | (410) ~ (all_215_2_124 = 0) | ~ (all_215_3_125 = 0) | ~ (all_215_4_126 = 0) | all_215_0_122 = xm
% 46.56/12.64 | (411) aNaturalNumber0(xn) = all_215_3_125
% 46.56/12.64 | (412) aNaturalNumber0(xn) = all_215_2_124
% 46.56/12.64 | (413) sdtpldt0(xn, xn) = all_215_1_123
% 46.56/12.64 | (414) aNaturalNumber0(xm) = all_215_4_126
% 46.56/12.64 | (415) sdtpldt0(xm, all_215_1_123) = all_215_0_122
% 46.56/12.64 |
% 46.56/12.64 +-Applying beta-rule and splitting (293), into two cases.
% 46.56/12.64 |-Branch one:
% 46.56/12.64 | (416) ~ (aNaturalNumber0(xm) = all_159_6_45)
% 46.56/12.64 |
% 46.56/12.64 | Instantiating formula (55) with xm, all_215_4_126, 0 and discharging atoms aNaturalNumber0(xm) = all_215_4_126, aNaturalNumber0(xm) = 0, yields:
% 46.56/12.64 | (417) all_215_4_126 = 0
% 46.56/12.64 |
% 46.56/12.64 | Using (414) and (416) yields:
% 46.56/12.64 | (418) ~ (all_215_4_126 = all_159_6_45)
% 46.56/12.64 |
% 46.56/12.64 | Equations (417) can reduce 418 to:
% 46.56/12.64 | (345) ~ (all_159_6_45 = 0)
% 46.56/12.64 |
% 46.56/12.64 | Simplifying 345 yields:
% 46.56/12.64 | (328) ~ (all_159_6_45 = 0)
% 46.56/12.64 |
% 46.56/12.64 | Instantiating formula (41) with all_161_5_53, all_0_11_11, all_0_3_3 and discharging atoms sdtpldt0(all_0_3_3, all_0_11_11) = all_161_5_53, yields:
% 46.56/12.64 | (349) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_161_5_53) = v2 & aNaturalNumber0(all_0_3_3) = v0 & aNaturalNumber0(all_0_11_11) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 46.56/12.64 |
% 46.56/12.64 | Instantiating formula (48) with all_0_11_11, all_0_11_11, all_167_2_65, all_167_2_65, all_0_11_11 and discharging atoms sdtpldt0(all_0_11_11, all_167_2_65) = all_0_11_11, yields:
% 46.56/12.64 | (422) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_167_2_65, all_167_2_65) = v3 & sdtpldt0(all_0_11_11, v3) = v4 & aNaturalNumber0(all_167_2_65) = v2 & aNaturalNumber0(all_167_2_65) = v1 & aNaturalNumber0(all_0_11_11) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_11_11))
% 46.56/12.64 |
% 46.56/12.64 | Instantiating formula (33) with all_0_11_11, all_167_2_65, all_0_11_11 and discharging atoms sdtpldt0(all_0_11_11, all_167_2_65) = all_0_11_11, yields:
% 46.56/12.64 | (423) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_167_2_65, all_0_11_11) = v2 & aNaturalNumber0(all_167_2_65) = v1 & aNaturalNumber0(all_0_11_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_11_11))
% 46.56/12.64 |
% 46.56/12.64 | Instantiating formula (48) with all_159_5_44, all_0_11_11, all_0_3_3, all_167_2_65, all_0_11_11 and discharging atoms sdtpldt0(all_0_11_11, all_167_2_65) = all_0_11_11, sdtpldt0(all_0_11_11, all_0_3_3) = all_159_5_44, yields:
% 46.56/12.64 | (424) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_167_2_65, all_0_3_3) = v3 & sdtpldt0(all_0_11_11, v3) = v4 & aNaturalNumber0(all_167_2_65) = v1 & aNaturalNumber0(all_0_3_3) = v2 & aNaturalNumber0(all_0_11_11) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_159_5_44))
% 46.56/12.64 |
% 46.56/12.64 | Instantiating formula (32) with all_159_5_44, all_0_3_3, all_0_11_11, all_0_11_11 and discharging atoms sdtmndt0(all_0_11_11, all_0_11_11) = all_0_3_3, sdtpldt0(all_0_11_11, all_0_3_3) = all_159_5_44, yields:
% 46.56/12.64 | (425) ? [v0] : ? [v1] : ? [v2] : ((v0 = 0 & aNaturalNumber0(all_0_3_3) = 0) | (sdtlseqdt0(all_0_11_11, all_0_11_11) = v2 & aNaturalNumber0(all_0_11_11) = v1 & aNaturalNumber0(all_0_11_11) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 46.56/12.64 |
% 46.56/12.64 | Instantiating formula (41) with all_159_5_44, all_0_3_3, all_0_11_11 and discharging atoms sdtpldt0(all_0_11_11, all_0_3_3) = all_159_5_44, yields:
% 46.56/12.64 | (426) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_159_5_44) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(all_0_11_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 46.56/12.64 |
% 46.56/12.64 | Instantiating (426) with all_808_0_170, all_808_1_171, all_808_2_172 yields:
% 46.56/12.64 | (427) aNaturalNumber0(all_159_5_44) = all_808_0_170 & aNaturalNumber0(all_0_3_3) = all_808_1_171 & aNaturalNumber0(all_0_11_11) = all_808_2_172 & ( ~ (all_808_1_171 = 0) | ~ (all_808_2_172 = 0) | all_808_0_170 = 0)
% 46.56/12.64 |
% 46.56/12.64 | Applying alpha-rule on (427) yields:
% 46.56/12.64 | (428) aNaturalNumber0(all_159_5_44) = all_808_0_170
% 46.56/12.64 | (429) aNaturalNumber0(all_0_3_3) = all_808_1_171
% 46.56/12.64 | (430) aNaturalNumber0(all_0_11_11) = all_808_2_172
% 46.56/12.64 | (431) ~ (all_808_1_171 = 0) | ~ (all_808_2_172 = 0) | all_808_0_170 = 0
% 46.56/12.64 |
% 46.56/12.64 | Instantiating (425) with all_810_0_173, all_810_1_174, all_810_2_175 yields:
% 46.56/12.64 | (432) (all_810_2_175 = 0 & aNaturalNumber0(all_0_3_3) = 0) | (sdtlseqdt0(all_0_11_11, all_0_11_11) = all_810_0_173 & aNaturalNumber0(all_0_11_11) = all_810_1_174 & aNaturalNumber0(all_0_11_11) = all_810_2_175 & ( ~ (all_810_0_173 = 0) | ~ (all_810_1_174 = 0) | ~ (all_810_2_175 = 0)))
% 46.56/12.64 |
% 46.56/12.64 | Instantiating (423) with all_811_0_176, all_811_1_177, all_811_2_178 yields:
% 46.56/12.64 | (433) sdtpldt0(all_167_2_65, all_0_11_11) = all_811_0_176 & aNaturalNumber0(all_167_2_65) = all_811_1_177 & aNaturalNumber0(all_0_11_11) = all_811_2_178 & ( ~ (all_811_1_177 = 0) | ~ (all_811_2_178 = 0) | all_811_0_176 = all_0_11_11)
% 46.56/12.64 |
% 46.56/12.64 | Applying alpha-rule on (433) yields:
% 46.56/12.64 | (434) sdtpldt0(all_167_2_65, all_0_11_11) = all_811_0_176
% 46.56/12.64 | (435) aNaturalNumber0(all_167_2_65) = all_811_1_177
% 46.56/12.64 | (436) aNaturalNumber0(all_0_11_11) = all_811_2_178
% 46.56/12.64 | (437) ~ (all_811_1_177 = 0) | ~ (all_811_2_178 = 0) | all_811_0_176 = all_0_11_11
% 46.56/12.64 |
% 46.56/12.64 | Instantiating (422) with all_821_0_193, all_821_1_194, all_821_2_195, all_821_3_196, all_821_4_197 yields:
% 46.56/12.64 | (438) sdtpldt0(all_167_2_65, all_167_2_65) = all_821_1_194 & sdtpldt0(all_0_11_11, all_821_1_194) = all_821_0_193 & aNaturalNumber0(all_167_2_65) = all_821_2_195 & aNaturalNumber0(all_167_2_65) = all_821_3_196 & aNaturalNumber0(all_0_11_11) = all_821_4_197 & ( ~ (all_821_2_195 = 0) | ~ (all_821_3_196 = 0) | ~ (all_821_4_197 = 0) | all_821_0_193 = all_0_11_11)
% 46.56/12.64 |
% 46.56/12.64 | Applying alpha-rule on (438) yields:
% 46.56/12.64 | (439) aNaturalNumber0(all_167_2_65) = all_821_2_195
% 46.56/12.64 | (440) sdtpldt0(all_167_2_65, all_167_2_65) = all_821_1_194
% 46.56/12.64 | (441) aNaturalNumber0(all_0_11_11) = all_821_4_197
% 46.56/12.64 | (442) sdtpldt0(all_0_11_11, all_821_1_194) = all_821_0_193
% 46.56/12.64 | (443) aNaturalNumber0(all_167_2_65) = all_821_3_196
% 46.56/12.64 | (444) ~ (all_821_2_195 = 0) | ~ (all_821_3_196 = 0) | ~ (all_821_4_197 = 0) | all_821_0_193 = all_0_11_11
% 46.56/12.64 |
% 46.56/12.64 | Instantiating (349) with all_823_0_198, all_823_1_199, all_823_2_200 yields:
% 46.56/12.64 | (445) aNaturalNumber0(all_161_5_53) = all_823_0_198 & aNaturalNumber0(all_0_3_3) = all_823_2_200 & aNaturalNumber0(all_0_11_11) = all_823_1_199 & ( ~ (all_823_1_199 = 0) | ~ (all_823_2_200 = 0) | all_823_0_198 = 0)
% 46.56/12.64 |
% 46.56/12.64 | Applying alpha-rule on (445) yields:
% 46.56/12.64 | (446) aNaturalNumber0(all_161_5_53) = all_823_0_198
% 46.56/12.64 | (447) aNaturalNumber0(all_0_3_3) = all_823_2_200
% 46.56/12.64 | (448) aNaturalNumber0(all_0_11_11) = all_823_1_199
% 46.56/12.64 | (449) ~ (all_823_1_199 = 0) | ~ (all_823_2_200 = 0) | all_823_0_198 = 0
% 46.56/12.64 |
% 46.56/12.64 | Instantiating (424) with all_825_0_201, all_825_1_202, all_825_2_203, all_825_3_204, all_825_4_205 yields:
% 46.56/12.64 | (450) sdtpldt0(all_167_2_65, all_0_3_3) = all_825_1_202 & sdtpldt0(all_0_11_11, all_825_1_202) = all_825_0_201 & aNaturalNumber0(all_167_2_65) = all_825_3_204 & aNaturalNumber0(all_0_3_3) = all_825_2_203 & aNaturalNumber0(all_0_11_11) = all_825_4_205 & ( ~ (all_825_2_203 = 0) | ~ (all_825_3_204 = 0) | ~ (all_825_4_205 = 0) | all_825_0_201 = all_159_5_44)
% 46.56/12.64 |
% 46.56/12.64 | Applying alpha-rule on (450) yields:
% 46.56/12.64 | (451) ~ (all_825_2_203 = 0) | ~ (all_825_3_204 = 0) | ~ (all_825_4_205 = 0) | all_825_0_201 = all_159_5_44
% 46.56/12.64 | (452) aNaturalNumber0(all_0_3_3) = all_825_2_203
% 46.56/12.64 | (453) aNaturalNumber0(all_0_11_11) = all_825_4_205
% 46.56/12.64 | (454) sdtpldt0(all_0_11_11, all_825_1_202) = all_825_0_201
% 46.56/12.64 | (455) aNaturalNumber0(all_167_2_65) = all_825_3_204
% 46.56/12.64 | (456) sdtpldt0(all_167_2_65, all_0_3_3) = all_825_1_202
% 46.56/12.64 |
% 46.56/12.64 +-Applying beta-rule and splitting (432), into two cases.
% 46.56/12.64 |-Branch one:
% 46.56/12.65 | (457) all_810_2_175 = 0 & aNaturalNumber0(all_0_3_3) = 0
% 46.56/12.65 |
% 46.56/12.65 | Applying alpha-rule on (457) yields:
% 46.56/12.65 | (458) all_810_2_175 = 0
% 46.56/12.65 | (359) aNaturalNumber0(all_0_3_3) = 0
% 46.56/12.65 |
% 46.56/12.65 +-Applying beta-rule and splitting (324), into two cases.
% 46.56/12.65 |-Branch one:
% 46.56/12.65 | (360) ~ (aNaturalNumber0(all_0_3_3) = 0)
% 46.56/12.65 |
% 46.56/12.65 | Using (359) and (360) yields:
% 46.56/12.65 | (240) $false
% 46.56/12.65 |
% 46.56/12.65 |-The branch is then unsatisfiable
% 46.56/12.65 |-Branch two:
% 46.56/12.65 | (359) aNaturalNumber0(all_0_3_3) = 0
% 46.56/12.65 | (364) all_159_6_45 = 0
% 46.56/12.65 |
% 46.56/12.65 | Equations (364) can reduce 328 to:
% 46.56/12.65 | (83) $false
% 46.56/12.65 |
% 46.56/12.65 |-The branch is then unsatisfiable
% 46.56/12.65 |-Branch two:
% 46.56/12.65 | (465) sdtlseqdt0(all_0_11_11, all_0_11_11) = all_810_0_173 & aNaturalNumber0(all_0_11_11) = all_810_1_174 & aNaturalNumber0(all_0_11_11) = all_810_2_175 & ( ~ (all_810_0_173 = 0) | ~ (all_810_1_174 = 0) | ~ (all_810_2_175 = 0))
% 46.56/12.65 |
% 46.56/12.65 | Applying alpha-rule on (465) yields:
% 46.56/12.65 | (466) sdtlseqdt0(all_0_11_11, all_0_11_11) = all_810_0_173
% 46.56/12.65 | (467) aNaturalNumber0(all_0_11_11) = all_810_1_174
% 46.56/12.65 | (468) aNaturalNumber0(all_0_11_11) = all_810_2_175
% 46.56/12.65 | (469) ~ (all_810_0_173 = 0) | ~ (all_810_1_174 = 0) | ~ (all_810_2_175 = 0)
% 46.56/12.65 |
% 46.56/12.65 | Instantiating formula (59) with all_0_11_11, all_0_11_11, all_810_0_173, 0 and discharging atoms sdtlseqdt0(all_0_11_11, all_0_11_11) = all_810_0_173, sdtlseqdt0(all_0_11_11, all_0_11_11) = 0, yields:
% 46.56/12.65 | (470) all_810_0_173 = 0
% 46.56/12.65 |
% 46.56/12.65 | Instantiating formula (55) with all_0_11_11, all_825_4_205, 0 and discharging atoms aNaturalNumber0(all_0_11_11) = all_825_4_205, aNaturalNumber0(all_0_11_11) = 0, yields:
% 46.56/12.65 | (471) all_825_4_205 = 0
% 46.56/12.65 |
% 46.56/12.65 | Instantiating formula (55) with all_0_11_11, all_823_1_199, all_825_4_205 and discharging atoms aNaturalNumber0(all_0_11_11) = all_825_4_205, aNaturalNumber0(all_0_11_11) = all_823_1_199, yields:
% 46.56/12.65 | (472) all_825_4_205 = all_823_1_199
% 46.56/12.65 |
% 46.56/12.65 | Instantiating formula (55) with all_0_11_11, all_811_2_178, all_821_4_197 and discharging atoms aNaturalNumber0(all_0_11_11) = all_821_4_197, aNaturalNumber0(all_0_11_11) = all_811_2_178, yields:
% 46.56/12.65 | (473) all_821_4_197 = all_811_2_178
% 46.56/12.65 |
% 46.56/12.65 | Instantiating formula (55) with all_0_11_11, all_810_1_174, all_825_4_205 and discharging atoms aNaturalNumber0(all_0_11_11) = all_825_4_205, aNaturalNumber0(all_0_11_11) = all_810_1_174, yields:
% 46.56/12.65 | (474) all_825_4_205 = all_810_1_174
% 46.56/12.65 |
% 46.56/12.65 | Instantiating formula (55) with all_0_11_11, all_810_2_175, all_825_4_205 and discharging atoms aNaturalNumber0(all_0_11_11) = all_825_4_205, aNaturalNumber0(all_0_11_11) = all_810_2_175, yields:
% 46.56/12.65 | (475) all_825_4_205 = all_810_2_175
% 46.56/12.65 |
% 46.56/12.65 | Instantiating formula (55) with all_0_11_11, all_810_2_175, all_811_2_178 and discharging atoms aNaturalNumber0(all_0_11_11) = all_811_2_178, aNaturalNumber0(all_0_11_11) = all_810_2_175, yields:
% 46.56/12.65 | (476) all_811_2_178 = all_810_2_175
% 46.56/12.65 |
% 46.56/12.65 | Instantiating formula (55) with all_0_11_11, all_808_2_172, all_821_4_197 and discharging atoms aNaturalNumber0(all_0_11_11) = all_821_4_197, aNaturalNumber0(all_0_11_11) = all_808_2_172, yields:
% 46.56/12.65 | (477) all_821_4_197 = all_808_2_172
% 46.56/12.65 |
% 46.56/12.65 | Combining equations (471,472) yields a new equation:
% 46.56/12.65 | (478) all_823_1_199 = 0
% 46.56/12.65 |
% 46.56/12.65 | Combining equations (475,472) yields a new equation:
% 46.56/12.65 | (479) all_823_1_199 = all_810_2_175
% 46.56/12.65 |
% 46.56/12.65 | Combining equations (474,472) yields a new equation:
% 46.56/12.65 | (480) all_823_1_199 = all_810_1_174
% 46.56/12.65 |
% 46.56/12.65 | Combining equations (479,480) yields a new equation:
% 46.56/12.65 | (481) all_810_1_174 = all_810_2_175
% 46.56/12.65 |
% 46.56/12.65 | Combining equations (478,480) yields a new equation:
% 46.56/12.65 | (482) all_810_1_174 = 0
% 46.56/12.65 |
% 46.56/12.65 | Combining equations (473,477) yields a new equation:
% 46.56/12.65 | (483) all_811_2_178 = all_808_2_172
% 46.56/12.65 |
% 46.56/12.65 | Simplifying 483 yields:
% 46.56/12.65 | (484) all_811_2_178 = all_808_2_172
% 46.56/12.65 |
% 46.56/12.65 | Combining equations (476,484) yields a new equation:
% 46.56/12.65 | (485) all_810_2_175 = all_808_2_172
% 46.56/12.65 |
% 46.56/12.65 | Simplifying 485 yields:
% 46.56/12.65 | (486) all_810_2_175 = all_808_2_172
% 46.56/12.65 |
% 46.56/12.65 | Combining equations (481,482) yields a new equation:
% 46.56/12.65 | (487) all_810_2_175 = 0
% 46.56/12.65 |
% 46.56/12.65 | Simplifying 487 yields:
% 46.56/12.65 | (458) all_810_2_175 = 0
% 46.56/12.65 |
% 46.56/12.65 | Combining equations (458,486) yields a new equation:
% 46.56/12.65 | (489) all_808_2_172 = 0
% 46.56/12.65 |
% 46.56/12.65 | Combining equations (489,486) yields a new equation:
% 46.56/12.65 | (458) all_810_2_175 = 0
% 46.56/12.65 |
% 46.56/12.65 +-Applying beta-rule and splitting (469), into two cases.
% 46.56/12.65 |-Branch one:
% 46.56/12.65 | (491) ~ (all_810_0_173 = 0)
% 46.56/12.65 |
% 46.56/12.65 | Equations (470) can reduce 491 to:
% 46.56/12.65 | (83) $false
% 46.56/12.65 |
% 46.56/12.65 |-The branch is then unsatisfiable
% 46.56/12.65 |-Branch two:
% 46.56/12.65 | (470) all_810_0_173 = 0
% 46.56/12.65 | (494) ~ (all_810_1_174 = 0) | ~ (all_810_2_175 = 0)
% 46.56/12.65 |
% 46.56/12.65 +-Applying beta-rule and splitting (494), into two cases.
% 46.56/12.65 |-Branch one:
% 46.56/12.65 | (495) ~ (all_810_1_174 = 0)
% 46.56/12.65 |
% 46.56/12.65 | Equations (482) can reduce 495 to:
% 46.56/12.65 | (83) $false
% 46.56/12.65 |
% 46.56/12.65 |-The branch is then unsatisfiable
% 46.56/12.65 |-Branch two:
% 46.56/12.65 | (482) all_810_1_174 = 0
% 46.56/12.65 | (498) ~ (all_810_2_175 = 0)
% 46.56/12.65 |
% 46.56/12.65 | Equations (458) can reduce 498 to:
% 46.56/12.65 | (83) $false
% 46.56/12.65 |
% 46.56/12.65 |-The branch is then unsatisfiable
% 46.56/12.65 |-Branch two:
% 46.56/12.65 | (500) aNaturalNumber0(xm) = all_159_6_45
% 46.56/12.65 | (364) all_159_6_45 = 0
% 46.56/12.65 |
% 46.56/12.65 | Equations (364) can reduce 328 to:
% 46.56/12.65 | (83) $false
% 46.56/12.65 |
% 46.56/12.65 |-The branch is then unsatisfiable
% 46.56/12.65 |-Branch two:
% 46.56/12.65 | (503) aNaturalNumber0(all_0_10_10) = all_167_1_64 & aNaturalNumber0(all_0_11_11) = all_167_2_65 & ( ~ (all_167_1_64 = 0) | ~ (all_167_2_65 = 0))
% 46.56/12.65 |
% 46.56/12.65 | Applying alpha-rule on (503) yields:
% 46.56/12.65 | (504) aNaturalNumber0(all_0_10_10) = all_167_1_64
% 46.56/12.65 | (505) aNaturalNumber0(all_0_11_11) = all_167_2_65
% 46.56/12.65 | (506) ~ (all_167_1_64 = 0) | ~ (all_167_2_65 = 0)
% 46.56/12.65 |
% 46.56/12.65 | Instantiating formula (55) with all_0_10_10, all_167_1_64, 0 and discharging atoms aNaturalNumber0(all_0_10_10) = all_167_1_64, aNaturalNumber0(all_0_10_10) = 0, yields:
% 46.56/12.65 | (321) all_167_1_64 = 0
% 46.56/12.65 |
% 46.56/12.65 | Instantiating formula (55) with all_0_11_11, all_167_2_65, 0 and discharging atoms aNaturalNumber0(all_0_11_11) = all_167_2_65, aNaturalNumber0(all_0_11_11) = 0, yields:
% 46.56/12.65 | (508) all_167_2_65 = 0
% 46.56/12.65 |
% 46.56/12.65 +-Applying beta-rule and splitting (506), into two cases.
% 46.56/12.65 |-Branch one:
% 46.56/12.65 | (509) ~ (all_167_1_64 = 0)
% 46.56/12.65 |
% 46.56/12.65 | Equations (321) can reduce 509 to:
% 46.56/12.65 | (83) $false
% 46.56/12.65 |
% 46.56/12.65 |-The branch is then unsatisfiable
% 46.56/12.65 |-Branch two:
% 46.56/12.65 | (321) all_167_1_64 = 0
% 46.56/12.65 | (512) ~ (all_167_2_65 = 0)
% 46.56/12.65 |
% 46.56/12.65 | Equations (508) can reduce 512 to:
% 46.56/12.65 | (83) $false
% 46.56/12.65 |
% 46.56/12.65 |-The branch is then unsatisfiable
% 46.56/12.65 |-Branch two:
% 46.56/12.65 | (514) aNaturalNumber0(xn) = all_172_0_66 & aNaturalNumber0(xl) = all_172_1_67 & ( ~ (all_172_0_66 = 0) | ~ (all_172_1_67 = 0))
% 46.56/12.65 |
% 46.56/12.65 | Applying alpha-rule on (514) yields:
% 46.56/12.65 | (515) aNaturalNumber0(xn) = all_172_0_66
% 46.56/12.65 | (516) aNaturalNumber0(xl) = all_172_1_67
% 46.56/12.65 | (517) ~ (all_172_0_66 = 0) | ~ (all_172_1_67 = 0)
% 46.56/12.65 |
% 46.56/12.65 | Instantiating formula (55) with xn, all_172_0_66, 0 and discharging atoms aNaturalNumber0(xn) = all_172_0_66, aNaturalNumber0(xn) = 0, yields:
% 46.56/12.65 | (518) all_172_0_66 = 0
% 46.56/12.65 |
% 46.56/12.65 | Instantiating formula (55) with xl, all_172_1_67, 0 and discharging atoms aNaturalNumber0(xl) = all_172_1_67, aNaturalNumber0(xl) = 0, yields:
% 46.56/12.65 | (363) all_172_1_67 = 0
% 46.56/12.65 |
% 46.56/12.65 +-Applying beta-rule and splitting (517), into two cases.
% 46.56/12.65 |-Branch one:
% 46.56/12.65 | (520) ~ (all_172_0_66 = 0)
% 46.56/12.65 |
% 46.56/12.65 | Equations (518) can reduce 520 to:
% 46.56/12.65 | (83) $false
% 46.56/12.65 |
% 46.56/12.65 |-The branch is then unsatisfiable
% 46.56/12.65 |-Branch two:
% 46.56/12.65 | (518) all_172_0_66 = 0
% 46.56/12.65 | (317) ~ (all_172_1_67 = 0)
% 46.56/12.65 |
% 46.56/12.65 | Equations (363) can reduce 317 to:
% 46.56/12.65 | (83) $false
% 46.56/12.65 |
% 46.56/12.65 |-The branch is then unsatisfiable
% 46.56/12.65 |-Branch two:
% 46.56/12.65 | (525) ~ (all_13_2_24 = all_0_10_10)
% 46.56/12.65 | (526) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_13_2_24) = v0) | (doDivides0(xl, all_0_12_12) = v2 & aNaturalNumber0(all_0_12_12) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 46.56/12.65 |
% 46.56/12.65 | Instantiating (526) with all_146_0_254, all_146_1_255, all_146_2_256 yields:
% 46.56/12.65 | (527) ( ~ (all_146_2_256 = 0) & aNaturalNumber0(all_13_2_24) = all_146_2_256) | (doDivides0(xl, all_0_12_12) = all_146_0_254 & aNaturalNumber0(all_0_12_12) = all_146_1_255 & aNaturalNumber0(xl) = all_146_2_256 & ( ~ (all_146_0_254 = 0) | ~ (all_146_1_255 = 0) | ~ (all_146_2_256 = 0)))
% 46.56/12.65 |
% 46.56/12.65 +-Applying beta-rule and splitting (527), into two cases.
% 46.56/12.65 |-Branch one:
% 46.56/12.65 | (528) ~ (all_146_2_256 = 0) & aNaturalNumber0(all_13_2_24) = all_146_2_256
% 46.56/12.65 |
% 46.56/12.65 | Applying alpha-rule on (528) yields:
% 46.56/12.65 | (529) ~ (all_146_2_256 = 0)
% 46.56/12.65 | (530) aNaturalNumber0(all_13_2_24) = all_146_2_256
% 46.56/12.65 |
% 46.56/12.65 | Instantiating formula (55) with all_13_2_24, all_146_2_256, 0 and discharging atoms aNaturalNumber0(all_13_2_24) = all_146_2_256, aNaturalNumber0(all_13_2_24) = 0, yields:
% 46.56/12.66 | (531) all_146_2_256 = 0
% 46.56/12.66 |
% 46.56/12.66 | Equations (531) can reduce 529 to:
% 46.56/12.66 | (83) $false
% 46.56/12.66 |
% 46.56/12.66 |-The branch is then unsatisfiable
% 46.56/12.66 |-Branch two:
% 46.56/12.66 | (533) doDivides0(xl, all_0_12_12) = all_146_0_254 & aNaturalNumber0(all_0_12_12) = all_146_1_255 & aNaturalNumber0(xl) = all_146_2_256 & ( ~ (all_146_0_254 = 0) | ~ (all_146_1_255 = 0) | ~ (all_146_2_256 = 0))
% 46.56/12.66 |
% 46.56/12.66 | Applying alpha-rule on (533) yields:
% 46.56/12.66 | (534) doDivides0(xl, all_0_12_12) = all_146_0_254
% 46.56/12.66 | (535) aNaturalNumber0(all_0_12_12) = all_146_1_255
% 46.56/12.66 | (536) aNaturalNumber0(xl) = all_146_2_256
% 46.56/12.66 | (537) ~ (all_146_0_254 = 0) | ~ (all_146_1_255 = 0) | ~ (all_146_2_256 = 0)
% 46.56/12.66 |
% 46.56/12.66 | Instantiating formula (51) with xl, all_0_12_12, all_146_0_254, 0 and discharging atoms doDivides0(xl, all_0_12_12) = all_146_0_254, doDivides0(xl, all_0_12_12) = 0, yields:
% 46.56/12.66 | (538) all_146_0_254 = 0
% 46.56/12.66 |
% 46.56/12.66 | Instantiating formula (55) with all_0_12_12, all_146_1_255, 0 and discharging atoms aNaturalNumber0(all_0_12_12) = all_146_1_255, aNaturalNumber0(all_0_12_12) = 0, yields:
% 46.56/12.66 | (539) all_146_1_255 = 0
% 46.56/12.66 |
% 46.56/12.66 | Instantiating formula (55) with xl, all_146_2_256, 0 and discharging atoms aNaturalNumber0(xl) = all_146_2_256, aNaturalNumber0(xl) = 0, yields:
% 46.56/12.66 | (531) all_146_2_256 = 0
% 46.56/12.66 |
% 46.56/12.66 +-Applying beta-rule and splitting (537), into two cases.
% 46.56/12.66 |-Branch one:
% 46.56/12.66 | (541) ~ (all_146_0_254 = 0)
% 46.56/12.66 |
% 46.56/12.66 | Equations (538) can reduce 541 to:
% 46.56/12.66 | (83) $false
% 46.56/12.66 |
% 46.56/12.66 |-The branch is then unsatisfiable
% 46.56/12.66 |-Branch two:
% 46.56/12.66 | (538) all_146_0_254 = 0
% 46.56/12.66 | (544) ~ (all_146_1_255 = 0) | ~ (all_146_2_256 = 0)
% 46.56/12.66 |
% 46.56/12.66 +-Applying beta-rule and splitting (544), into two cases.
% 46.56/12.66 |-Branch one:
% 46.56/12.66 | (545) ~ (all_146_1_255 = 0)
% 46.56/12.66 |
% 46.56/12.66 | Equations (539) can reduce 545 to:
% 46.56/12.66 | (83) $false
% 46.56/12.66 |
% 46.56/12.66 |-The branch is then unsatisfiable
% 46.56/12.66 |-Branch two:
% 46.56/12.66 | (539) all_146_1_255 = 0
% 46.56/12.66 | (529) ~ (all_146_2_256 = 0)
% 46.56/12.66 |
% 46.56/12.66 | Equations (531) can reduce 529 to:
% 46.56/12.66 | (83) $false
% 46.56/12.66 |
% 46.56/12.66 |-The branch is then unsatisfiable
% 46.56/12.66 |-Branch two:
% 46.56/12.66 | (550) ~ (all_12_2_21 = all_0_11_11)
% 46.56/12.66 | (551) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_12_2_21) = v0) | (doDivides0(xl, xm) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 46.56/12.66 |
% 46.56/12.66 | Instantiating (551) with all_138_0_257, all_138_1_258, all_138_2_259 yields:
% 46.56/12.66 | (552) ( ~ (all_138_2_259 = 0) & aNaturalNumber0(all_12_2_21) = all_138_2_259) | (doDivides0(xl, xm) = all_138_0_257 & aNaturalNumber0(xm) = all_138_1_258 & aNaturalNumber0(xl) = all_138_2_259 & ( ~ (all_138_0_257 = 0) | ~ (all_138_1_258 = 0) | ~ (all_138_2_259 = 0)))
% 46.56/12.66 |
% 46.56/12.66 +-Applying beta-rule and splitting (552), into two cases.
% 46.56/12.66 |-Branch one:
% 46.56/12.66 | (553) ~ (all_138_2_259 = 0) & aNaturalNumber0(all_12_2_21) = all_138_2_259
% 46.56/12.66 |
% 46.56/12.66 | Applying alpha-rule on (553) yields:
% 46.56/12.66 | (554) ~ (all_138_2_259 = 0)
% 46.56/12.66 | (555) aNaturalNumber0(all_12_2_21) = all_138_2_259
% 46.56/12.66 |
% 46.56/12.66 | Instantiating formula (55) with all_12_2_21, all_138_2_259, 0 and discharging atoms aNaturalNumber0(all_12_2_21) = all_138_2_259, aNaturalNumber0(all_12_2_21) = 0, yields:
% 46.56/12.66 | (556) all_138_2_259 = 0
% 46.56/12.66 |
% 46.56/12.66 | Equations (556) can reduce 554 to:
% 46.56/12.66 | (83) $false
% 46.56/12.66 |
% 46.56/12.66 |-The branch is then unsatisfiable
% 46.56/12.66 |-Branch two:
% 46.56/12.66 | (558) doDivides0(xl, xm) = all_138_0_257 & aNaturalNumber0(xm) = all_138_1_258 & aNaturalNumber0(xl) = all_138_2_259 & ( ~ (all_138_0_257 = 0) | ~ (all_138_1_258 = 0) | ~ (all_138_2_259 = 0))
% 46.56/12.66 |
% 46.56/12.66 | Applying alpha-rule on (558) yields:
% 46.56/12.66 | (559) doDivides0(xl, xm) = all_138_0_257
% 46.56/12.66 | (560) aNaturalNumber0(xm) = all_138_1_258
% 46.56/12.66 | (561) aNaturalNumber0(xl) = all_138_2_259
% 46.56/12.66 | (562) ~ (all_138_0_257 = 0) | ~ (all_138_1_258 = 0) | ~ (all_138_2_259 = 0)
% 46.56/12.66 |
% 46.56/12.66 | Instantiating formula (51) with xl, xm, all_138_0_257, 0 and discharging atoms doDivides0(xl, xm) = all_138_0_257, doDivides0(xl, xm) = 0, yields:
% 46.56/12.66 | (563) all_138_0_257 = 0
% 46.56/12.66 |
% 46.56/12.66 | Instantiating formula (55) with xm, all_138_1_258, 0 and discharging atoms aNaturalNumber0(xm) = all_138_1_258, aNaturalNumber0(xm) = 0, yields:
% 46.56/12.66 | (564) all_138_1_258 = 0
% 46.56/12.66 |
% 46.56/12.66 | Instantiating formula (55) with xl, all_138_2_259, 0 and discharging atoms aNaturalNumber0(xl) = all_138_2_259, aNaturalNumber0(xl) = 0, yields:
% 46.56/12.66 | (556) all_138_2_259 = 0
% 46.56/12.66 |
% 46.56/12.66 +-Applying beta-rule and splitting (562), into two cases.
% 46.56/12.66 |-Branch one:
% 46.56/12.66 | (566) ~ (all_138_0_257 = 0)
% 46.56/12.66 |
% 46.56/12.66 | Equations (563) can reduce 566 to:
% 46.56/12.66 | (83) $false
% 46.56/12.66 |
% 46.56/12.66 |-The branch is then unsatisfiable
% 46.56/12.66 |-Branch two:
% 46.56/12.66 | (563) all_138_0_257 = 0
% 46.56/12.66 | (569) ~ (all_138_1_258 = 0) | ~ (all_138_2_259 = 0)
% 46.56/12.66 |
% 46.56/12.66 +-Applying beta-rule and splitting (569), into two cases.
% 46.56/12.66 |-Branch one:
% 46.56/12.66 | (570) ~ (all_138_1_258 = 0)
% 46.56/12.66 |
% 46.56/12.66 | Equations (564) can reduce 570 to:
% 46.56/12.66 | (83) $false
% 46.56/12.66 |
% 46.56/12.66 |-The branch is then unsatisfiable
% 46.56/12.66 |-Branch two:
% 46.56/12.66 | (564) all_138_1_258 = 0
% 46.56/12.66 | (554) ~ (all_138_2_259 = 0)
% 46.56/12.66 |
% 46.56/12.66 | Equations (556) can reduce 554 to:
% 46.56/12.66 | (83) $false
% 46.56/12.66 |
% 46.56/12.66 |-The branch is then unsatisfiable
% 46.56/12.66 |-Branch two:
% 46.56/12.66 | (575) sdtasdt0(sz00, all_12_2_21) = xm
% 46.56/12.66 | (576) ? [v0] : ? [v1] : (sdtasdt0(all_12_2_21, sz00) = v1 & aNaturalNumber0(all_12_2_21) = v0 & ( ~ (v0 = 0) | (v1 = sz00 & xm = sz00)))
% 46.56/12.66 |
% 46.56/12.66 | Instantiating (576) with all_114_0_260, all_114_1_261 yields:
% 46.56/12.66 | (577) sdtasdt0(all_12_2_21, sz00) = all_114_0_260 & aNaturalNumber0(all_12_2_21) = all_114_1_261 & ( ~ (all_114_1_261 = 0) | (all_114_0_260 = sz00 & xm = sz00))
% 46.56/12.66 |
% 46.56/12.66 | Applying alpha-rule on (577) yields:
% 46.56/12.66 | (578) sdtasdt0(all_12_2_21, sz00) = all_114_0_260
% 46.56/12.66 | (579) aNaturalNumber0(all_12_2_21) = all_114_1_261
% 46.56/12.66 | (580) ~ (all_114_1_261 = 0) | (all_114_0_260 = sz00 & xm = sz00)
% 46.56/12.66 |
% 46.56/12.66 +-Applying beta-rule and splitting (580), into two cases.
% 46.56/12.66 |-Branch one:
% 46.56/12.66 | (581) ~ (all_114_1_261 = 0)
% 46.56/12.66 |
% 46.56/12.66 | Instantiating formula (55) with all_12_2_21, all_114_1_261, 0 and discharging atoms aNaturalNumber0(all_12_2_21) = all_114_1_261, aNaturalNumber0(all_12_2_21) = 0, yields:
% 46.56/12.66 | (582) all_114_1_261 = 0
% 46.56/12.66 |
% 46.56/12.66 | Equations (582) can reduce 581 to:
% 46.56/12.66 | (83) $false
% 46.56/12.66 |
% 46.56/12.66 |-The branch is then unsatisfiable
% 46.56/12.66 |-Branch two:
% 46.56/12.66 | (582) all_114_1_261 = 0
% 46.56/12.66 | (585) all_114_0_260 = sz00 & xm = sz00
% 46.56/12.66 |
% 46.56/12.66 | Applying alpha-rule on (585) yields:
% 46.56/12.66 | (586) all_114_0_260 = sz00
% 46.56/12.66 | (587) xm = sz00
% 46.56/12.66 |
% 46.56/12.66 | Equations (587) can reduce 202 to:
% 46.56/12.66 | (83) $false
% 46.56/12.66 |
% 46.56/12.66 |-The branch is then unsatisfiable
% 46.56/12.66 |-Branch two:
% 46.56/12.66 | (589) sdtpldt0(sz00, xn) = all_0_12_12
% 46.56/12.66 | (590) ? [v0] : ? [v1] : (sdtpldt0(xn, sz00) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v0 = 0) | (v1 = xn & all_0_12_12 = xn)))
% 46.56/12.66 |
% 46.56/12.66 | Instantiating (590) with all_102_0_262, all_102_1_263 yields:
% 46.56/12.66 | (591) sdtpldt0(xn, sz00) = all_102_0_262 & aNaturalNumber0(xn) = all_102_1_263 & ( ~ (all_102_1_263 = 0) | (all_102_0_262 = xn & all_0_12_12 = xn))
% 46.56/12.66 |
% 46.56/12.66 | Applying alpha-rule on (591) yields:
% 46.56/12.66 | (592) sdtpldt0(xn, sz00) = all_102_0_262
% 46.56/12.66 | (593) aNaturalNumber0(xn) = all_102_1_263
% 46.56/12.66 | (594) ~ (all_102_1_263 = 0) | (all_102_0_262 = xn & all_0_12_12 = xn)
% 46.56/12.66 |
% 46.56/12.66 +-Applying beta-rule and splitting (594), into two cases.
% 46.56/12.66 |-Branch one:
% 46.56/12.66 | (595) ~ (all_102_1_263 = 0)
% 46.56/12.66 |
% 46.56/12.66 | Instantiating formula (55) with xn, all_102_1_263, 0 and discharging atoms aNaturalNumber0(xn) = all_102_1_263, aNaturalNumber0(xn) = 0, yields:
% 46.56/12.66 | (596) all_102_1_263 = 0
% 46.56/12.66 |
% 46.56/12.66 | Equations (596) can reduce 595 to:
% 46.56/12.66 | (83) $false
% 46.56/12.66 |
% 46.56/12.66 |-The branch is then unsatisfiable
% 46.56/12.66 |-Branch two:
% 46.56/12.66 | (596) all_102_1_263 = 0
% 46.56/12.67 | (599) all_102_0_262 = xn & all_0_12_12 = xn
% 46.56/12.67 |
% 46.56/12.67 | Applying alpha-rule on (599) yields:
% 46.56/12.67 | (600) all_102_0_262 = xn
% 46.56/12.67 | (601) all_0_12_12 = xn
% 46.56/12.67 |
% 46.56/12.67 | Equations (601) can reduce 200 to:
% 46.56/12.67 | (83) $false
% 46.56/12.67 |
% 46.56/12.67 |-The branch is then unsatisfiable
% 46.56/12.67 |-Branch two:
% 46.56/12.67 | (603) sdtasdt0(xl, all_13_2_24) = xn
% 46.56/12.67 | (604) all_0_9_9 = 0 | ? [v0] : ? [v1] : (( ~ (v0 = 0) & aNaturalNumber0(all_13_2_24) = v0) | (aNaturalNumber0(xn) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 46.56/12.67 |
% 46.56/12.67 +-Applying beta-rule and splitting (604), into two cases.
% 46.56/12.67 |-Branch one:
% 46.56/12.67 | (82) all_0_9_9 = 0
% 46.56/12.67 |
% 46.56/12.67 | Equations (82) can reduce 42 to:
% 46.56/12.67 | (83) $false
% 46.56/12.67 |
% 46.56/12.67 |-The branch is then unsatisfiable
% 46.56/12.67 |-Branch two:
% 46.56/12.67 | (42) ~ (all_0_9_9 = 0)
% 46.56/12.67 | (608) ? [v0] : ? [v1] : (( ~ (v0 = 0) & aNaturalNumber0(all_13_2_24) = v0) | (aNaturalNumber0(xn) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 46.56/12.67 |
% 46.56/12.67 | Instantiating formula (23) with xl, all_13_2_24, xn, all_0_12_12 and discharging atoms sdtasdt0(xl, all_13_2_24) = all_0_12_12, sdtasdt0(xl, all_13_2_24) = xn, yields:
% 46.56/12.67 | (601) all_0_12_12 = xn
% 46.56/12.67 |
% 46.56/12.67 | From (601) and (9) follows:
% 46.56/12.67 | (610) doDivides0(xl, xn) = 0
% 46.56/12.67 |
% 46.56/12.67 +-Applying beta-rule and splitting (61), into two cases.
% 46.56/12.67 |-Branch one:
% 46.56/12.67 | (611) ~ (doDivides0(xl, xn) = 0)
% 46.56/12.67 |
% 46.56/12.67 | Using (610) and (611) yields:
% 46.56/12.67 | (240) $false
% 46.56/12.67 |
% 46.56/12.67 |-The branch is then unsatisfiable
% 46.56/12.67 |-Branch two:
% 46.56/12.67 | (610) doDivides0(xl, xn) = 0
% 46.56/12.67 | (82) all_0_9_9 = 0
% 46.56/12.67 |
% 46.56/12.67 | Equations (82) can reduce 42 to:
% 46.56/12.67 | (83) $false
% 46.56/12.67 |
% 46.56/12.67 |-The branch is then unsatisfiable
% 46.56/12.67 |-Branch two:
% 46.56/12.67 | (616) aNaturalNumber0(all_0_12_12) = all_13_1_23 & aNaturalNumber0(xl) = all_13_2_24 & ( ~ (all_13_1_23 = 0) | ~ (all_13_2_24 = 0))
% 46.56/12.67 |
% 46.56/12.67 | Applying alpha-rule on (616) yields:
% 46.56/12.67 | (617) aNaturalNumber0(all_0_12_12) = all_13_1_23
% 46.56/12.67 | (618) aNaturalNumber0(xl) = all_13_2_24
% 46.56/12.67 | (619) ~ (all_13_1_23 = 0) | ~ (all_13_2_24 = 0)
% 46.56/12.67 |
% 46.56/12.67 | Instantiating formula (55) with all_0_12_12, all_13_1_23, 0 and discharging atoms aNaturalNumber0(all_0_12_12) = all_13_1_23, aNaturalNumber0(all_0_12_12) = 0, yields:
% 46.56/12.67 | (144) all_13_1_23 = 0
% 46.56/12.67 |
% 46.56/12.67 | Instantiating formula (55) with xl, all_13_2_24, 0 and discharging atoms aNaturalNumber0(xl) = all_13_2_24, aNaturalNumber0(xl) = 0, yields:
% 46.56/12.67 | (621) all_13_2_24 = 0
% 46.56/12.67 |
% 46.56/12.67 +-Applying beta-rule and splitting (619), into two cases.
% 46.56/12.67 |-Branch one:
% 46.56/12.67 | (622) ~ (all_13_1_23 = 0)
% 46.56/12.67 |
% 46.56/12.67 | Equations (144) can reduce 622 to:
% 46.56/12.67 | (83) $false
% 46.56/12.67 |
% 46.56/12.67 |-The branch is then unsatisfiable
% 46.56/12.67 |-Branch two:
% 46.56/12.67 | (144) all_13_1_23 = 0
% 46.56/12.67 | (625) ~ (all_13_2_24 = 0)
% 46.56/12.67 |
% 46.56/12.67 | Equations (621) can reduce 625 to:
% 46.56/12.67 | (83) $false
% 46.56/12.67 |
% 46.56/12.67 |-The branch is then unsatisfiable
% 46.56/12.67 |-Branch two:
% 46.56/12.67 | (627) aNaturalNumber0(xm) = all_12_1_20 & aNaturalNumber0(xl) = all_12_2_21 & ( ~ (all_12_1_20 = 0) | ~ (all_12_2_21 = 0))
% 46.56/12.67 |
% 46.56/12.67 | Applying alpha-rule on (627) yields:
% 46.56/12.67 | (628) aNaturalNumber0(xm) = all_12_1_20
% 46.56/12.67 | (629) aNaturalNumber0(xl) = all_12_2_21
% 46.56/12.67 | (630) ~ (all_12_1_20 = 0) | ~ (all_12_2_21 = 0)
% 46.56/12.67 |
% 46.56/12.67 | Instantiating formula (55) with xm, all_12_1_20, 0 and discharging atoms aNaturalNumber0(xm) = all_12_1_20, aNaturalNumber0(xm) = 0, yields:
% 46.56/12.67 | (130) all_12_1_20 = 0
% 46.56/12.67 |
% 46.56/12.67 | Instantiating formula (55) with xl, all_12_2_21, 0 and discharging atoms aNaturalNumber0(xl) = all_12_2_21, aNaturalNumber0(xl) = 0, yields:
% 46.56/12.67 | (632) all_12_2_21 = 0
% 46.56/12.67 |
% 46.56/12.67 +-Applying beta-rule and splitting (630), into two cases.
% 46.56/12.67 |-Branch one:
% 46.56/12.67 | (633) ~ (all_12_1_20 = 0)
% 46.56/12.67 |
% 46.56/12.67 | Equations (130) can reduce 633 to:
% 46.56/12.67 | (83) $false
% 46.56/12.67 |
% 46.56/12.67 |-The branch is then unsatisfiable
% 46.56/12.67 |-Branch two:
% 46.56/12.67 | (130) all_12_1_20 = 0
% 46.56/12.67 | (636) ~ (all_12_2_21 = 0)
% 46.56/12.67 |
% 46.56/12.67 | Equations (632) can reduce 636 to:
% 46.56/12.67 | (83) $false
% 46.56/12.67 |
% 46.56/12.67 |-The branch is then unsatisfiable
% 46.56/12.67 % SZS output end Proof for theBenchmark
% 46.56/12.67
% 46.56/12.67 12046ms
%------------------------------------------------------------------------------