TSTP Solution File: NUM495+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM495+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.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 08:45:07 EDT 2022
% Result : Theorem 26.94s 7.53s
% Output : Proof 280.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM495+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jul 6 01:55:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.59/0.59 ____ _
% 0.59/0.59 ___ / __ \_____(_)___ ________ __________
% 0.59/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.59
% 0.59/0.59 A Theorem Prover for First-Order Logic
% 0.59/0.59 (ePrincess v.1.0)
% 0.59/0.59
% 0.59/0.59 (c) Philipp Rümmer, 2009-2015
% 0.59/0.59 (c) Peter Backeman, 2014-2015
% 0.59/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.59 Bug reports to peter@backeman.se
% 0.59/0.59
% 0.59/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.59
% 0.59/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.77/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.96/1.06 Prover 0: Preprocessing ...
% 3.99/1.60 Prover 0: Constructing countermodel ...
% 20.33/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 20.76/6.03 Prover 1: Preprocessing ...
% 21.22/6.19 Prover 1: Constructing countermodel ...
% 26.94/7.53 Prover 1: proved (1600ms)
% 26.94/7.53 Prover 0: stopped
% 26.94/7.53
% 26.94/7.53 No countermodel exists, formula is valid
% 26.94/7.53 % SZS status Theorem for theBenchmark
% 26.94/7.53
% 26.94/7.53 Generating proof ... found it (size 955)
% 278.19/221.25
% 278.19/221.25 % SZS output start Proof for theBenchmark
% 278.19/221.25 Assumed formulas after preprocessing and simplification:
% 278.19/221.25 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ( ~ (v7 = 0) & ~ (v6 = 0) & ~ (v5 = v1) & ~ (xr = xn) & ~ (xp = sz10) & ~ (xp = sz00) & ~ (sz10 = sz00) & isPrime0(xp) = 0 & doDivides0(xp, v3) = 0 & doDivides0(xp, v2) = 0 & doDivides0(xp, xr) = v6 & doDivides0(xp, xm) = v7 & sdtmndt0(xn, xp) = xr & sdtlseqdt0(v5, v1) = 0 & sdtlseqdt0(xr, xn) = 0 & sdtlseqdt0(xp, xn) = 0 & sdtasdt0(xr, xm) = v3 & sdtasdt0(xp, v12) = v2 & sdtasdt0(xp, v9) = v3 & sdtasdt0(xn, xm) = v2 & sdtpldt0(v5, v8) = v1 & sdtpldt0(v4, xp) = v5 & sdtpldt0(v0, xp) = v1 & sdtpldt0(xr, v10) = xn & sdtpldt0(xr, xm) = v4 & sdtpldt0(xp, v11) = xn & sdtpldt0(xp, xr) = xn & sdtpldt0(xn, xm) = v0 & aNaturalNumber0(v12) = 0 & aNaturalNumber0(v11) = 0 & aNaturalNumber0(v10) = 0 & aNaturalNumber0(v9) = 0 & aNaturalNumber0(v8) = 0 & aNaturalNumber0(xr) = 0 & aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 & ~ (isPrime0(sz10) = 0) & ~ (isPrime0(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] : (v13 = sz00 | ~ (sdtsldt0(v17, v13) = v18) | ~ (sdtsldt0(v14, v13) = v15) | ~ (sdtasdt0(v16, v14) = v17) | ? [v19] : ? [v20] : ? [v21] : ((doDivides0(v13, v14) = v21 & aNaturalNumber0(v14) = v20 & aNaturalNumber0(v13) = v19 & ( ~ (v21 = 0) | ~ (v20 = 0) | ~ (v19 = 0))) | (sdtasdt0(v16, v15) = v20 & aNaturalNumber0(v16) = v19 & ( ~ (v19 = 0) | v20 = v18)))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (doDivides0(v15, v16) = v17) | ~ (sdtasdt0(v15, v18) = v16) | ~ (sdtasdt0(v13, v14) = v16) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : ? [v32] : ? [v33] : (( ~ (v19 = 0) & aNaturalNumber0(v18) = v19) | (isPrime0(v15) = v22 & doDivides0(v15, v14) = v27 & doDivides0(v15, v13) = v26 & iLess0(v24, v1) = v25 & sdtpldt0(v23, v15) = v24 & sdtpldt0(v13, v14) = v23 & aNaturalNumber0(v15) = v21 & aNaturalNumber0(v14) = v20 & aNaturalNumber0(v13) = v19 & ( ~ (v25 = 0) | ~ (v21 = 0) | ~ (v20 = 0) | ~ (v19 = 0) | (v30 = v14 & v29 = 0 & v27 = 0 & sdtasdt0(v15, v28) = v14 & aNaturalNumber0(v28) = 0) | (v30 = v13 & v29 = 0 & v26 = 0 & sdtasdt0(v15, v28) = v13 & aNaturalNumber0(v28) = 0) | ( ~ (v22 = 0) & (v15 = sz10 | v15 = sz00 | (v33 = v15 & v32 = 0 & v30 = 0 & v29 = 0 & ~ (v28 = v15) & ~ (v28 = sz10) & doDivides0(v28, v15) = 0 & sdtasdt0(v28, v31) = v15 & aNaturalNumber0(v31) = 0 & aNaturalNumber0(v28) = 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] : ( ~ (doDivides0(v15, v16) = 0) | ~ (sdtasdt0(v13, v14) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : (isPrime0(v15) = v20 & doDivides0(v15, v14) = v25 & doDivides0(v15, v13) = v24 & iLess0(v22, v1) = v23 & sdtpldt0(v21, v15) = v22 & sdtpldt0(v13, v14) = v21 & aNaturalNumber0(v15) = v19 & aNaturalNumber0(v14) = v18 & aNaturalNumber0(v13) = v17 & ( ~ (v23 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | (v28 = v14 & v27 = 0 & v25 = 0 & sdtasdt0(v15, v26) = v14 & aNaturalNumber0(v26) = 0) | (v28 = v13 & v27 = 0 & v24 = 0 & sdtasdt0(v15, v26) = v13 & aNaturalNumber0(v26) = 0) | ( ~ (v20 = 0) & (v15 = sz10 | v15 = sz00 | (v31 = v15 & v30 = 0 & v28 = 0 & v27 = 0 & ~ (v26 = v15) & ~ (v26 = sz10) & doDivides0(v26, v15) = 0 & sdtasdt0(v26, v29) = v15 & aNaturalNumber0(v29) = 0 & aNaturalNumber0(v26) = 0)))))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (doDivides0(v13, v16) = 0) | ~ (sdtpldt0(v14, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (doDivides0(v13, v15) = v21 & doDivides0(v13, v14) = v20 & aNaturalNumber0(v15) = v19 & aNaturalNumber0(v14) = v18 & aNaturalNumber0(v13) = v17 & ( ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | v21 = 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 | v14 = sz00 | ~ (sdtlseqdt0(v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : (doDivides0(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 | ~ (isPrime0(v15) = v14) | ~ (isPrime0(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (aNaturalNumber0(v15) = v14) | ~ (aNaturalNumber0(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v13 = xp | v13 = sz10 | ~ (doDivides0(v13, xp) = v14) | ~ (sdtasdt0(v13, v15) = xp) | ? [v16] : (( ~ (v16 = 0) & aNaturalNumber0(v15) = v16) | ( ~ (v16 = 0) & aNaturalNumber0(v13) = v16))) & ! [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 | v14 = sz10 | ~ (isPrime0(v13) = 0) | ~ (doDivides0(v14, v13) = 0) | ? [v15] : (( ~ (v15 = 0) & aNaturalNumber0(v14) = v15) | ( ~ (v15 = 0) & aNaturalNumber0(v13) = v15))) & ! [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 | ~ (isPrime0(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & ~ (v15 = v13) & ~ (v15 = sz10) & doDivides0(v15, v13) = 0 & aNaturalNumber0(v15) = 0) | ( ~ (v15 = 0) & aNaturalNumber0(v13) = v15))) & ! [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)))) & ! [v13] : (v13 = xp | v13 = sz10 | ~ (doDivides0(v13, xp) = 0) | ? [v14] : ( ~ (v14 = 0) & aNaturalNumber0(v13) = v14)) & ! [v13] : (v13 = sz10 | v13 = sz00 | ~ (aNaturalNumber0(v13) = 0) | ? [v14] : (isPrime0(v14) = 0 & doDivides0(v14, v13) = 0 & aNaturalNumber0(v14) = 0)) & ! [v13] : ( ~ (sdtasdt0(xp, v13) = xr) | ? [v14] : ( ~ (v14 = 0) & aNaturalNumber0(v13) = v14)) & ! [v13] : ( ~ (sdtasdt0(xp, v13) = xm) | ? [v14] : ( ~ (v14 = 0) & aNaturalNumber0(v13) = v14)))
% 278.52/221.33 | 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:
% 278.52/221.33 | (1) ~ (all_0_5_5 = 0) & ~ (all_0_6_6 = 0) & ~ (all_0_7_7 = all_0_11_11) & ~ (xr = xn) & ~ (xp = sz10) & ~ (xp = sz00) & ~ (sz10 = sz00) & isPrime0(xp) = 0 & doDivides0(xp, all_0_9_9) = 0 & doDivides0(xp, all_0_10_10) = 0 & doDivides0(xp, xr) = all_0_6_6 & doDivides0(xp, xm) = all_0_5_5 & sdtmndt0(xn, xp) = xr & sdtlseqdt0(all_0_7_7, all_0_11_11) = 0 & sdtlseqdt0(xr, xn) = 0 & sdtlseqdt0(xp, xn) = 0 & sdtasdt0(xr, xm) = all_0_9_9 & sdtasdt0(xp, all_0_0_0) = all_0_10_10 & sdtasdt0(xp, all_0_3_3) = all_0_9_9 & sdtasdt0(xn, xm) = all_0_10_10 & sdtpldt0(all_0_7_7, all_0_4_4) = all_0_11_11 & sdtpldt0(all_0_8_8, xp) = all_0_7_7 & sdtpldt0(all_0_12_12, xp) = all_0_11_11 & sdtpldt0(xr, all_0_2_2) = xn & sdtpldt0(xr, xm) = all_0_8_8 & sdtpldt0(xp, all_0_1_1) = xn & sdtpldt0(xp, xr) = xn & sdtpldt0(xn, xm) = all_0_12_12 & aNaturalNumber0(all_0_0_0) = 0 & aNaturalNumber0(all_0_1_1) = 0 & aNaturalNumber0(all_0_2_2) = 0 & aNaturalNumber0(all_0_3_3) = 0 & aNaturalNumber0(all_0_4_4) = 0 & aNaturalNumber0(xr) = 0 & aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 & ~ (isPrime0(sz10) = 0) & ~ (isPrime0(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] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ((doDivides0(v0, v1) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))) | (sdtasdt0(v3, v2) = v7 & aNaturalNumber0(v3) = v6 & ( ~ (v6 = 0) | v7 = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (doDivides0(v2, v3) = v4) | ~ (sdtasdt0(v2, v5) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (( ~ (v6 = 0) & aNaturalNumber0(v5) = v6) | (isPrime0(v2) = v9 & doDivides0(v2, v1) = v14 & doDivides0(v2, v0) = v13 & iLess0(v11, all_0_11_11) = v12 & sdtpldt0(v10, v2) = v11 & sdtpldt0(v0, v1) = v10 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v12 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v17 = v1 & v16 = 0 & v14 = 0 & sdtasdt0(v2, v15) = v1 & aNaturalNumber0(v15) = 0) | (v17 = v0 & v16 = 0 & v13 = 0 & sdtasdt0(v2, v15) = v0 & aNaturalNumber0(v15) = 0) | ( ~ (v9 = 0) & (v2 = sz10 | v2 = sz00 | (v20 = v2 & v19 = 0 & v17 = 0 & v16 = 0 & ~ (v15 = v2) & ~ (v15 = sz10) & doDivides0(v15, v2) = 0 & sdtasdt0(v15, v18) = v2 & aNaturalNumber0(v18) = 0 & aNaturalNumber0(v15) = 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] : ( ~ (doDivides0(v2, v3) = 0) | ~ (sdtasdt0(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (isPrime0(v2) = v7 & doDivides0(v2, v1) = v12 & doDivides0(v2, v0) = v11 & iLess0(v9, all_0_11_11) = v10 & sdtpldt0(v8, v2) = v9 & sdtpldt0(v0, v1) = v8 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v10 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | (v15 = v1 & v14 = 0 & v12 = 0 & sdtasdt0(v2, v13) = v1 & aNaturalNumber0(v13) = 0) | (v15 = v0 & v14 = 0 & v11 = 0 & sdtasdt0(v2, v13) = v0 & aNaturalNumber0(v13) = 0) | ( ~ (v7 = 0) & (v2 = sz10 | v2 = sz00 | (v18 = v2 & v17 = 0 & v15 = 0 & v14 = 0 & ~ (v13 = v2) & ~ (v13 = sz10) & doDivides0(v13, v2) = 0 & sdtasdt0(v13, v16) = v2 & aNaturalNumber0(v16) = 0 & aNaturalNumber0(v13) = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (doDivides0(v0, v3) = 0) | ~ (sdtpldt0(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (doDivides0(v0, v2) = v8 & doDivides0(v0, v1) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v8 = 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 | v1 = sz00 | ~ (sdtlseqdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (doDivides0(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 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v0 = xp | v0 = sz10 | ~ (doDivides0(v0, xp) = v1) | ~ (sdtasdt0(v0, v2) = xp) | ? [v3] : (( ~ (v3 = 0) & aNaturalNumber0(v2) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [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 | v1 = sz10 | ~ (isPrime0(v0) = 0) | ~ (doDivides0(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [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 | ~ (isPrime0(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & ~ (v2 = v0) & ~ (v2 = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [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)))) & ! [v0] : (v0 = xp | v0 = sz10 | ~ (doDivides0(v0, xp) = 0) | ? [v1] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0)) & ! [v0] : ( ~ (sdtasdt0(xp, v0) = xr) | ? [v1] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) & ! [v0] : ( ~ (sdtasdt0(xp, v0) = xm) | ? [v1] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1))
% 278.66/221.36 |
% 278.66/221.36 | Applying alpha-rule on (1) yields:
% 278.66/221.36 | (2) ! [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))))
% 278.66/221.36 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0))
% 278.66/221.36 | (4) ! [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)))
% 278.66/221.36 | (5) sdtpldt0(all_0_7_7, all_0_4_4) = all_0_11_11
% 278.66/221.36 | (6) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 278.66/221.36 | (7) ~ (all_0_7_7 = all_0_11_11)
% 278.66/221.36 | (8) ! [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))))
% 278.66/221.36 | (9) ~ (all_0_5_5 = 0)
% 278.66/221.36 | (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))))
% 278.66/221.36 | (11) ! [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)))
% 278.66/221.36 | (12) sdtasdt0(xp, all_0_0_0) = all_0_10_10
% 278.66/221.36 | (13) isPrime0(xp) = 0
% 278.66/221.36 | (14) ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 278.66/221.36 | (15) sdtpldt0(xp, xr) = xn
% 278.66/221.36 | (16) ! [v0] : (v0 = xp | v0 = sz10 | ~ (doDivides0(v0, xp) = 0) | ? [v1] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1))
% 278.66/221.36 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (doDivides0(v2, v3) = 0) | ~ (sdtasdt0(v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (isPrime0(v2) = v7 & doDivides0(v2, v1) = v12 & doDivides0(v2, v0) = v11 & iLess0(v9, all_0_11_11) = v10 & sdtpldt0(v8, v2) = v9 & sdtpldt0(v0, v1) = v8 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v10 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | (v15 = v1 & v14 = 0 & v12 = 0 & sdtasdt0(v2, v13) = v1 & aNaturalNumber0(v13) = 0) | (v15 = v0 & v14 = 0 & v11 = 0 & sdtasdt0(v2, v13) = v0 & aNaturalNumber0(v13) = 0) | ( ~ (v7 = 0) & (v2 = sz10 | v2 = sz00 | (v18 = v2 & v17 = 0 & v15 = 0 & v14 = 0 & ~ (v13 = v2) & ~ (v13 = sz10) & doDivides0(v13, v2) = 0 & sdtasdt0(v13, v16) = v2 & aNaturalNumber0(v16) = 0 & aNaturalNumber0(v13) = 0))))))
% 278.66/221.37 | (18) doDivides0(xp, all_0_10_10) = 0
% 278.66/221.37 | (19) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 278.66/221.37 | (20) ! [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))))
% 278.66/221.37 | (21) sdtlseqdt0(xr, xn) = 0
% 278.66/221.37 | (22) aNaturalNumber0(sz00) = 0
% 278.66/221.37 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0))
% 278.66/221.37 | (24) aNaturalNumber0(all_0_1_1) = 0
% 278.66/221.37 | (25) doDivides0(xp, xm) = all_0_5_5
% 278.66/221.37 | (26) ! [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)))
% 278.66/221.37 | (27) ~ (xp = sz10)
% 278.66/221.37 | (28) ! [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)))))
% 278.66/221.37 | (29) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ (isPrime0(v0) = 0) | ~ (doDivides0(v1, v0) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 278.66/221.37 | (30) ~ (all_0_6_6 = 0)
% 278.66/221.37 | (31) ! [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)))))
% 278.66/221.37 | (32) ! [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)))))
% 278.66/221.37 | (33) ~ (xp = sz00)
% 278.66/221.37 | (34) aNaturalNumber0(xn) = 0
% 278.66/221.37 | (35) doDivides0(xp, all_0_9_9) = 0
% 278.66/221.37 | (36) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 278.66/221.37 | (37) ~ (isPrime0(sz10) = 0)
% 278.66/221.37 | (38) sdtasdt0(xr, xm) = all_0_9_9
% 278.66/221.37 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 278.66/221.37 | (40) sdtasdt0(xp, all_0_3_3) = all_0_9_9
% 278.66/221.37 | (41) ! [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)))))
% 278.66/221.37 | (42) ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (isPrime0(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & ~ (v2 = v0) & ~ (v2 = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 278.66/221.37 | (43) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 278.66/221.37 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 278.66/221.37 | (45) sdtmndt0(xn, xp) = xr
% 278.66/221.37 | (46) ! [v0] : ! [v1] : ! [v2] : (v0 = xp | v0 = sz10 | ~ (doDivides0(v0, xp) = v1) | ~ (sdtasdt0(v0, v2) = xp) | ? [v3] : (( ~ (v3 = 0) & aNaturalNumber0(v2) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 278.66/221.37 | (47) sdtpldt0(xr, xm) = all_0_8_8
% 278.66/221.37 | (48) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = sz00 | ~ (sdtlseqdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))))
% 278.66/221.38 | (49) sdtpldt0(all_0_8_8, xp) = all_0_7_7
% 278.66/221.38 | (50) ! [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))))
% 278.66/221.38 | (51) ! [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))))
% 278.66/221.38 | (52) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00))))
% 278.66/221.38 | (53) ! [v0] : ( ~ (sdtasdt0(xp, v0) = xr) | ? [v1] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1))
% 278.66/221.38 | (54) ! [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)))))
% 278.66/221.38 | (55) aNaturalNumber0(all_0_4_4) = 0
% 278.66/221.38 | (56) ! [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)))))
% 278.66/221.38 | (57) ! [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)))
% 278.66/221.38 | (58) sdtpldt0(xr, all_0_2_2) = xn
% 278.66/221.38 | (59) ! [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)))))
% 278.66/221.38 | (60) sdtlseqdt0(xp, xn) = 0
% 278.66/221.38 | (61) sdtpldt0(xn, xm) = all_0_12_12
% 278.66/221.38 | (62) ! [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)))))
% 278.66/221.38 | (63) ! [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)))
% 278.66/221.38 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (doDivides0(v0, v3) = 0) | ~ (sdtpldt0(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (doDivides0(v0, v2) = v8 & doDivides0(v0, v1) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v8 = 0)))
% 278.66/221.38 | (65) ! [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)))))
% 278.66/221.38 | (66) ! [v0] : ( ~ (sdtasdt0(xp, v0) = xm) | ? [v1] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1))
% 278.66/221.38 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0))
% 278.66/221.38 | (68) sdtpldt0(all_0_12_12, xp) = all_0_11_11
% 278.66/221.38 | (69) sdtpldt0(xp, all_0_1_1) = xn
% 278.66/221.38 | (70) ! [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))))
% 278.66/221.38 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0))
% 278.66/221.38 | (72) aNaturalNumber0(all_0_0_0) = 0
% 278.66/221.38 | (73) aNaturalNumber0(sz10) = 0
% 278.66/221.39 | (74) ~ (sz10 = sz00)
% 278.66/221.39 | (75) ! [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)))))
% 278.66/221.39 | (76) aNaturalNumber0(xm) = 0
% 278.66/221.39 | (77) ! [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)))))
% 278.66/221.39 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (doDivides0(v2, v3) = v4) | ~ (sdtasdt0(v2, v5) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (( ~ (v6 = 0) & aNaturalNumber0(v5) = v6) | (isPrime0(v2) = v9 & doDivides0(v2, v1) = v14 & doDivides0(v2, v0) = v13 & iLess0(v11, all_0_11_11) = v12 & sdtpldt0(v10, v2) = v11 & sdtpldt0(v0, v1) = v10 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v12 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v17 = v1 & v16 = 0 & v14 = 0 & sdtasdt0(v2, v15) = v1 & aNaturalNumber0(v15) = 0) | (v17 = v0 & v16 = 0 & v13 = 0 & sdtasdt0(v2, v15) = v0 & aNaturalNumber0(v15) = 0) | ( ~ (v9 = 0) & (v2 = sz10 | v2 = sz00 | (v20 = v2 & v19 = 0 & v17 = 0 & v16 = 0 & ~ (v15 = v2) & ~ (v15 = sz10) & doDivides0(v15, v2) = 0 & sdtasdt0(v15, v18) = v2 & aNaturalNumber0(v18) = 0 & aNaturalNumber0(v15) = 0)))))))
% 278.66/221.39 | (79) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 278.66/221.39 | (80) ~ (isPrime0(sz00) = 0)
% 278.66/221.39 | (81) aNaturalNumber0(xr) = 0
% 278.66/221.39 | (82) ! [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))))
% 278.66/221.39 | (83) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ? [v1] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0))
% 278.66/221.39 | (84) sdtlseqdt0(all_0_7_7, all_0_11_11) = 0
% 278.66/221.39 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 278.66/221.39 | (86) sdtasdt0(xn, xm) = all_0_10_10
% 278.66/221.39 | (87) ! [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))))
% 278.66/221.39 | (88) ! [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)))))
% 278.66/221.39 | (89) aNaturalNumber0(all_0_3_3) = 0
% 278.66/221.39 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 278.66/221.39 | (91) ~ (xr = xn)
% 278.66/221.39 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ((doDivides0(v0, v1) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))) | (sdtasdt0(v3, v2) = v7 & aNaturalNumber0(v3) = v6 & ( ~ (v6 = 0) | v7 = v5))))
% 278.66/221.39 | (93) doDivides0(xp, xr) = all_0_6_6
% 278.66/221.39 | (94) aNaturalNumber0(all_0_2_2) = 0
% 278.66/221.39 | (95) ! [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)))))
% 278.66/221.39 | (96) ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))
% 278.66/221.39 | (97) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0))
% 278.66/221.39 | (98) aNaturalNumber0(xp) = 0
% 278.66/221.39 | (99) ! [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)))
% 278.66/221.39 |
% 278.66/221.40 | Instantiating formula (8) with all_0_6_6, xr, all_0_9_9, xp and discharging atoms doDivides0(xp, all_0_9_9) = 0, doDivides0(xp, xr) = all_0_6_6, yields:
% 278.66/221.40 | (100) all_0_6_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_9_9, xr) = v3 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 278.66/221.40 |
% 278.66/221.40 | Instantiating formula (8) with all_0_6_6, xr, all_0_10_10, xp and discharging atoms doDivides0(xp, all_0_10_10) = 0, doDivides0(xp, xr) = all_0_6_6, yields:
% 278.66/221.40 | (101) all_0_6_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_10_10, xr) = v3 & aNaturalNumber0(all_0_10_10) = v1 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 278.66/221.40 |
% 278.66/221.40 | Instantiating formula (8) with all_0_5_5, xm, all_0_9_9, xp and discharging atoms doDivides0(xp, all_0_9_9) = 0, doDivides0(xp, xm) = all_0_5_5, yields:
% 278.66/221.40 | (102) all_0_5_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_9_9, xm) = v3 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 278.66/221.40 |
% 278.66/221.40 | Instantiating formula (8) with all_0_5_5, xm, all_0_10_10, xp and discharging atoms doDivides0(xp, all_0_10_10) = 0, doDivides0(xp, xm) = all_0_5_5, yields:
% 278.66/221.40 | (103) all_0_5_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_10_10, xm) = v3 & aNaturalNumber0(all_0_10_10) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 278.66/221.40 |
% 278.66/221.40 | Instantiating formula (70) with all_0_11_11, all_0_7_7 and discharging atoms sdtlseqdt0(all_0_7_7, all_0_11_11) = 0, yields:
% 278.66/221.40 | (104) all_0_7_7 = all_0_11_11 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_0_11_11, all_0_7_7) = v2 & aNaturalNumber0(all_0_7_7) = v0 & aNaturalNumber0(all_0_11_11) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 278.66/221.40 |
% 278.66/221.40 | Instantiating formula (77) with all_0_11_11, all_0_7_7 and discharging atoms sdtlseqdt0(all_0_7_7, all_0_11_11) = 0, yields:
% 278.66/221.40 | (105) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_11_11 & v1 = 0 & sdtpldt0(all_0_7_7, v0) = all_0_11_11 & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_0_7_7) = v0 & aNaturalNumber0(all_0_11_11) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 278.66/221.40 |
% 278.66/221.40 | Instantiating formula (70) with xn, xr and discharging atoms sdtlseqdt0(xr, xn) = 0, yields:
% 278.66/221.40 | (106) xr = xn | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xn, xr) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 278.66/221.40 |
% 278.66/221.40 | Instantiating formula (17) with all_0_9_9, xp, xm, xr and discharging atoms doDivides0(xp, all_0_9_9) = 0, sdtasdt0(xr, xm) = all_0_9_9, yields:
% 278.66/221.40 | (107) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (isPrime0(xp) = v3 & doDivides0(xp, xr) = v7 & doDivides0(xp, xm) = v8 & iLess0(v5, all_0_11_11) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xr, xm) = v4 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & ( ~ (v6 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v11 = xr & v10 = 0 & v7 = 0 & sdtasdt0(xp, v9) = xr & aNaturalNumber0(v9) = 0) | (v11 = xm & v10 = 0 & v8 = 0 & sdtasdt0(xp, v9) = xm & aNaturalNumber0(v9) = 0) | ( ~ (v3 = 0) & (xp = sz10 | xp = sz00 | (v14 = xp & v13 = 0 & v11 = 0 & v10 = 0 & ~ (v9 = xp) & ~ (v9 = sz10) & doDivides0(v9, xp) = 0 & sdtasdt0(v9, v12) = xp & aNaturalNumber0(v12) = 0 & aNaturalNumber0(v9) = 0)))))
% 278.66/221.40 |
% 278.66/221.40 | Instantiating formula (11) with all_0_9_9, xm, xr and discharging atoms sdtasdt0(xr, xm) = all_0_9_9, yields:
% 278.66/221.40 | (108) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xm, xr) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_9_9))
% 278.66/221.40 |
% 278.66/221.40 | Instantiating formula (26) with all_0_9_9, xm, xr and discharging atoms sdtasdt0(xr, xm) = all_0_9_9, yields:
% 278.66/221.40 | (109) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_9_9) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 278.66/221.40 |
% 278.66/221.40 | Instantiating formula (17) with all_0_10_10, xp, all_0_0_0, xp and discharging atoms doDivides0(xp, all_0_10_10) = 0, sdtasdt0(xp, all_0_0_0) = all_0_10_10, yields:
% 278.66/221.40 | (110) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (isPrime0(xp) = v3 & doDivides0(xp, all_0_0_0) = v8 & doDivides0(xp, xp) = v7 & iLess0(v5, all_0_11_11) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xp, all_0_0_0) = v4 & aNaturalNumber0(all_0_0_0) = v1 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v11 = all_0_0_0 & v10 = 0 & v8 = 0 & sdtasdt0(xp, v9) = all_0_0_0 & aNaturalNumber0(v9) = 0) | (v11 = xp & v10 = 0 & v7 = 0 & sdtasdt0(xp, v9) = xp & aNaturalNumber0(v9) = 0) | ( ~ (v3 = 0) & (xp = sz10 | xp = sz00 | (v14 = xp & v13 = 0 & v11 = 0 & v10 = 0 & ~ (v9 = xp) & ~ (v9 = sz10) & doDivides0(v9, xp) = 0 & sdtasdt0(v9, v12) = xp & aNaturalNumber0(v12) = 0 & aNaturalNumber0(v9) = 0)))))
% 278.66/221.40 |
% 278.66/221.40 | Instantiating formula (78) with all_0_0_0, 0, all_0_10_10, xp, all_0_0_0, xp and discharging atoms doDivides0(xp, all_0_10_10) = 0, sdtasdt0(xp, all_0_0_0) = all_0_10_10, yields:
% 278.66/221.40 | (111) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (( ~ (v0 = 0) & aNaturalNumber0(all_0_0_0) = v0) | (isPrime0(xp) = v3 & doDivides0(xp, all_0_0_0) = v8 & doDivides0(xp, xp) = v7 & iLess0(v5, all_0_11_11) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xp, all_0_0_0) = v4 & aNaturalNumber0(all_0_0_0) = v1 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v11 = all_0_0_0 & v10 = 0 & v8 = 0 & sdtasdt0(xp, v9) = all_0_0_0 & aNaturalNumber0(v9) = 0) | (v11 = xp & v10 = 0 & v7 = 0 & sdtasdt0(xp, v9) = xp & aNaturalNumber0(v9) = 0) | ( ~ (v3 = 0) & (xp = sz10 | xp = sz00 | (v14 = xp & v13 = 0 & v11 = 0 & v10 = 0 & ~ (v9 = xp) & ~ (v9 = sz10) & doDivides0(v9, xp) = 0 & sdtasdt0(v9, v12) = xp & aNaturalNumber0(v12) = 0 & aNaturalNumber0(v9) = 0))))))
% 278.66/221.41 |
% 278.66/221.41 | Instantiating formula (11) with all_0_10_10, all_0_0_0, xp and discharging atoms sdtasdt0(xp, all_0_0_0) = all_0_10_10, yields:
% 278.66/221.41 | (112) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_0_0_0, xp) = v2 & aNaturalNumber0(all_0_0_0) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_10_10))
% 278.66/221.41 |
% 278.66/221.41 | Instantiating formula (26) with all_0_10_10, all_0_0_0, xp and discharging atoms sdtasdt0(xp, all_0_0_0) = all_0_10_10, yields:
% 278.66/221.41 | (113) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_0_0) = v1 & aNaturalNumber0(all_0_10_10) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 278.66/221.41 |
% 278.66/221.41 | Instantiating formula (78) with all_0_3_3, 0, all_0_9_9, xp, all_0_3_3, xp and discharging atoms doDivides0(xp, all_0_9_9) = 0, sdtasdt0(xp, all_0_3_3) = all_0_9_9, yields:
% 278.66/221.41 | (114) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (( ~ (v0 = 0) & aNaturalNumber0(all_0_3_3) = v0) | (isPrime0(xp) = v3 & doDivides0(xp, all_0_3_3) = v8 & doDivides0(xp, xp) = v7 & iLess0(v5, all_0_11_11) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xp, all_0_3_3) = v4 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v11 = all_0_3_3 & v10 = 0 & v8 = 0 & sdtasdt0(xp, v9) = all_0_3_3 & aNaturalNumber0(v9) = 0) | (v11 = xp & v10 = 0 & v7 = 0 & sdtasdt0(xp, v9) = xp & aNaturalNumber0(v9) = 0) | ( ~ (v3 = 0) & (xp = sz10 | xp = sz00 | (v14 = xp & v13 = 0 & v11 = 0 & v10 = 0 & ~ (v9 = xp) & ~ (v9 = sz10) & doDivides0(v9, xp) = 0 & sdtasdt0(v9, v12) = xp & aNaturalNumber0(v12) = 0 & aNaturalNumber0(v9) = 0))))))
% 278.66/221.41 |
% 278.66/221.41 | Instantiating formula (78) with all_0_3_3, 0, all_0_9_9, xp, xm, xr and discharging atoms doDivides0(xp, all_0_9_9) = 0, sdtasdt0(xr, xm) = all_0_9_9, sdtasdt0(xp, all_0_3_3) = all_0_9_9, yields:
% 278.66/221.41 | (115) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (( ~ (v0 = 0) & aNaturalNumber0(all_0_3_3) = v0) | (isPrime0(xp) = v3 & doDivides0(xp, xr) = v7 & doDivides0(xp, xm) = v8 & iLess0(v5, all_0_11_11) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xr, xm) = v4 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & ( ~ (v6 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v11 = xr & v10 = 0 & v7 = 0 & sdtasdt0(xp, v9) = xr & aNaturalNumber0(v9) = 0) | (v11 = xm & v10 = 0 & v8 = 0 & sdtasdt0(xp, v9) = xm & aNaturalNumber0(v9) = 0) | ( ~ (v3 = 0) & (xp = sz10 | xp = sz00 | (v14 = xp & v13 = 0 & v11 = 0 & v10 = 0 & ~ (v9 = xp) & ~ (v9 = sz10) & doDivides0(v9, xp) = 0 & sdtasdt0(v9, v12) = xp & aNaturalNumber0(v12) = 0 & aNaturalNumber0(v9) = 0))))))
% 278.66/221.41 |
% 278.66/221.41 | Instantiating formula (17) with all_0_9_9, xp, all_0_3_3, xp and discharging atoms doDivides0(xp, all_0_9_9) = 0, sdtasdt0(xp, all_0_3_3) = all_0_9_9, yields:
% 278.66/221.41 | (116) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (isPrime0(xp) = v3 & doDivides0(xp, all_0_3_3) = v8 & doDivides0(xp, xp) = v7 & iLess0(v5, all_0_11_11) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xp, all_0_3_3) = v4 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v6 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v11 = all_0_3_3 & v10 = 0 & v8 = 0 & sdtasdt0(xp, v9) = all_0_3_3 & aNaturalNumber0(v9) = 0) | (v11 = xp & v10 = 0 & v7 = 0 & sdtasdt0(xp, v9) = xp & aNaturalNumber0(v9) = 0) | ( ~ (v3 = 0) & (xp = sz10 | xp = sz00 | (v14 = xp & v13 = 0 & v11 = 0 & v10 = 0 & ~ (v9 = xp) & ~ (v9 = sz10) & doDivides0(v9, xp) = 0 & sdtasdt0(v9, v12) = xp & aNaturalNumber0(v12) = 0 & aNaturalNumber0(v9) = 0)))))
% 278.66/221.41 |
% 278.66/221.41 | Instantiating formula (11) with all_0_9_9, all_0_3_3, xp and discharging atoms sdtasdt0(xp, all_0_3_3) = all_0_9_9, yields:
% 278.66/221.41 | (117) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_0_3_3, xp) = v2 & aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_9_9))
% 278.66/221.41 |
% 278.66/221.41 | Instantiating formula (26) with all_0_9_9, all_0_3_3, xp and discharging atoms sdtasdt0(xp, all_0_3_3) = all_0_9_9, yields:
% 278.66/221.41 | (118) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_3_3) = v1 & aNaturalNumber0(all_0_9_9) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 278.66/221.41 |
% 278.66/221.41 | Instantiating formula (17) with all_0_10_10, xp, xm, xn and discharging atoms doDivides0(xp, all_0_10_10) = 0, sdtasdt0(xn, xm) = all_0_10_10, yields:
% 278.66/221.41 | (119) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (isPrime0(xp) = v3 & doDivides0(xp, xm) = v8 & doDivides0(xp, xn) = v7 & iLess0(v5, all_0_11_11) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xn, xm) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v6 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v11 = xm & v10 = 0 & v8 = 0 & sdtasdt0(xp, v9) = xm & aNaturalNumber0(v9) = 0) | (v11 = xn & v10 = 0 & v7 = 0 & sdtasdt0(xp, v9) = xn & aNaturalNumber0(v9) = 0) | ( ~ (v3 = 0) & (xp = sz10 | xp = sz00 | (v14 = xp & v13 = 0 & v11 = 0 & v10 = 0 & ~ (v9 = xp) & ~ (v9 = sz10) & doDivides0(v9, xp) = 0 & sdtasdt0(v9, v12) = xp & aNaturalNumber0(v12) = 0 & aNaturalNumber0(v9) = 0)))))
% 278.66/221.41 |
% 278.66/221.41 | Instantiating formula (78) with all_0_0_0, 0, all_0_10_10, xp, xm, xn and discharging atoms doDivides0(xp, all_0_10_10) = 0, sdtasdt0(xp, all_0_0_0) = all_0_10_10, sdtasdt0(xn, xm) = all_0_10_10, yields:
% 278.66/221.41 | (120) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (( ~ (v0 = 0) & aNaturalNumber0(all_0_0_0) = v0) | (isPrime0(xp) = v3 & doDivides0(xp, xm) = v8 & doDivides0(xp, xn) = v7 & iLess0(v5, all_0_11_11) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xn, xm) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v6 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v11 = xm & v10 = 0 & v8 = 0 & sdtasdt0(xp, v9) = xm & aNaturalNumber0(v9) = 0) | (v11 = xn & v10 = 0 & v7 = 0 & sdtasdt0(xp, v9) = xn & aNaturalNumber0(v9) = 0) | ( ~ (v3 = 0) & (xp = sz10 | xp = sz00 | (v14 = xp & v13 = 0 & v11 = 0 & v10 = 0 & ~ (v9 = xp) & ~ (v9 = sz10) & doDivides0(v9, xp) = 0 & sdtasdt0(v9, v12) = xp & aNaturalNumber0(v12) = 0 & aNaturalNumber0(v9) = 0))))))
% 278.66/221.41 |
% 278.66/221.41 | Instantiating formula (11) with all_0_10_10, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_10_10, yields:
% 278.66/221.41 | (121) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_10_10))
% 278.66/221.41 |
% 278.66/221.41 | Instantiating formula (26) with all_0_10_10, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_10_10, yields:
% 278.66/221.41 | (122) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_10_10) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 278.66/221.41 |
% 278.66/221.41 | Instantiating formula (63) with all_0_11_11, all_0_4_4, all_0_7_7 and discharging atoms sdtpldt0(all_0_7_7, all_0_4_4) = all_0_11_11, yields:
% 278.66/221.41 | (123) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_0_4_4, all_0_7_7) = v2 & aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_11_11))
% 278.66/221.41 |
% 278.66/221.41 | Instantiating formula (57) with all_0_11_11, all_0_4_4, all_0_7_7 and discharging atoms sdtpldt0(all_0_7_7, all_0_4_4) = all_0_11_11, yields:
% 278.66/221.41 | (124) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(all_0_7_7) = v0 & aNaturalNumber0(all_0_11_11) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 278.66/221.41 |
% 278.66/221.41 | Instantiating formula (99) with all_0_11_11, all_0_7_7, all_0_4_4, xp, all_0_8_8 and discharging atoms sdtpldt0(all_0_7_7, all_0_4_4) = all_0_11_11, sdtpldt0(all_0_8_8, xp) = all_0_7_7, yields:
% 278.66/221.41 | (125) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_0_8_8, v3) = v4 & sdtpldt0(xp, all_0_4_4) = v3 & aNaturalNumber0(all_0_4_4) = v2 & aNaturalNumber0(all_0_8_8) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_11_11))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (63) with all_0_7_7, xp, all_0_8_8 and discharging atoms sdtpldt0(all_0_8_8, xp) = all_0_7_7, yields:
% 278.66/221.42 | (126) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, all_0_8_8) = v2 & aNaturalNumber0(all_0_8_8) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_7_7))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (57) with all_0_7_7, xp, all_0_8_8 and discharging atoms sdtpldt0(all_0_8_8, xp) = all_0_7_7, yields:
% 278.66/221.42 | (127) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_7_7) = v2 & aNaturalNumber0(all_0_8_8) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (28) with all_0_11_11, all_0_11_11, xp, all_0_4_4, all_0_12_12 and discharging atoms sdtpldt0(all_0_12_12, xp) = all_0_11_11, yields:
% 278.66/221.42 | (128) all_0_4_4 = xp | ~ (sdtpldt0(all_0_12_12, all_0_4_4) = all_0_11_11) | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_0_4_4, all_0_12_12) = v3 & sdtpldt0(xp, all_0_12_12) = v4 & aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(all_0_12_12) = v0 & aNaturalNumber0(xp) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (99) with all_0_11_11, all_0_12_12, xp, xp, all_0_8_8 and discharging atoms sdtpldt0(all_0_12_12, xp) = all_0_11_11, yields:
% 278.66/221.42 | (129) ~ (sdtpldt0(all_0_8_8, xp) = all_0_12_12) | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_0_8_8, v3) = v4 & sdtpldt0(xp, xp) = v3 & aNaturalNumber0(all_0_8_8) = v0 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_11_11))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (63) with all_0_11_11, xp, all_0_12_12 and discharging atoms sdtpldt0(all_0_12_12, xp) = all_0_11_11, yields:
% 278.66/221.42 | (130) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xp, all_0_12_12) = v2 & aNaturalNumber0(all_0_12_12) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_11_11))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (57) with all_0_11_11, xp, all_0_12_12 and discharging atoms sdtpldt0(all_0_12_12, xp) = all_0_11_11, yields:
% 278.66/221.42 | (131) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_11_11) = v2 & aNaturalNumber0(all_0_12_12) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (63) with xn, all_0_2_2, xr and discharging atoms sdtpldt0(xr, all_0_2_2) = xn, yields:
% 278.66/221.42 | (132) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_0_2_2, xr) = v2 & aNaturalNumber0(all_0_2_2) = v1 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xn))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (99) with all_0_7_7, all_0_8_8, xp, xm, xr and discharging atoms sdtpldt0(all_0_8_8, xp) = all_0_7_7, sdtpldt0(xr, xm) = all_0_8_8, yields:
% 278.66/221.42 | (133) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xr, v3) = v4 & sdtpldt0(xm, xp) = v3 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_7_7))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (63) with all_0_8_8, xm, xr and discharging atoms sdtpldt0(xr, xm) = all_0_8_8, yields:
% 278.66/221.42 | (134) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xm, xr) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_8_8))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (57) with all_0_8_8, xm, xr and discharging atoms sdtpldt0(xr, xm) = all_0_8_8, yields:
% 278.66/221.42 | (135) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_8_8) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (88) with all_0_1_1, xr, xn, xp and discharging atoms sdtmndt0(xn, xp) = xr, sdtpldt0(xp, all_0_1_1) = xn, yields:
% 278.66/221.42 | (136) all_0_1_1 = xr | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_0_1_1) = v0) | (sdtlseqdt0(xp, xn) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (63) with xn, all_0_1_1, xp and discharging atoms sdtpldt0(xp, all_0_1_1) = xn, yields:
% 278.66/221.42 | (137) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_0_1_1, xp) = v2 & aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xn))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (6) with xr, xp yields:
% 278.66/221.42 | (138) xp = sz00 | ~ (sdtpldt0(xp, xr) = sz00) | ? [v0] : ? [v1] : (aNaturalNumber0(xr) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (63) with xn, xr, xp and discharging atoms sdtpldt0(xp, xr) = xn, yields:
% 278.66/221.42 | (139) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xr, xp) = v2 & aNaturalNumber0(xr) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xn))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (99) with all_0_11_11, all_0_12_12, all_0_4_4, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_12_12, yields:
% 278.66/221.42 | (140) ~ (sdtpldt0(all_0_12_12, all_0_4_4) = all_0_11_11) | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xm, all_0_4_4) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(all_0_4_4) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_11_11))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (99) with all_0_11_11, all_0_12_12, xp, xm, xn and discharging atoms sdtpldt0(all_0_12_12, xp) = all_0_11_11, sdtpldt0(xn, xm) = all_0_12_12, yields:
% 278.66/221.42 | (141) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xm, xp) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_11_11))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (99) with all_0_12_12, xn, xm, all_0_2_2, xr and discharging atoms sdtpldt0(xr, all_0_2_2) = xn, sdtpldt0(xn, xm) = all_0_12_12, yields:
% 278.66/221.42 | (142) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_0_2_2, xm) = v3 & sdtpldt0(xr, v3) = v4 & aNaturalNumber0(all_0_2_2) = v1 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_12_12))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (99) with all_0_12_12, xn, xm, all_0_1_1, xp and discharging atoms sdtpldt0(xp, all_0_1_1) = xn, sdtpldt0(xn, xm) = all_0_12_12, yields:
% 278.66/221.42 | (143) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_0_1_1, xm) = v3 & sdtpldt0(xp, v3) = v4 & aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_12_12))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (99) with all_0_12_12, xn, xm, xr, xp and discharging atoms sdtpldt0(xp, xr) = xn, sdtpldt0(xn, xm) = all_0_12_12, yields:
% 278.66/221.42 | (144) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xr, xm) = v3 & sdtpldt0(xp, v3) = v4 & aNaturalNumber0(xr) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_12_12))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (6) with xm, xn yields:
% 278.66/221.42 | (145) xn = sz00 | ~ (sdtpldt0(xn, xm) = sz00) | ? [v0] : ? [v1] : (aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (63) with all_0_12_12, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_12_12, yields:
% 278.66/221.42 | (146) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xm, xn) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_12_12))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (57) with all_0_12_12, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_12_12, yields:
% 278.66/221.42 | (147) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_12_12) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 278.66/221.42 |
% 278.66/221.42 | Instantiating formula (83) with xp and discharging atoms aNaturalNumber0(xp) = 0, yields:
% 278.66/221.42 | (148) xp = sz10 | xp = sz00 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 278.66/221.42 |
% 278.66/221.42 | Instantiating (147) with all_8_0_13, all_8_1_14, all_8_2_15 yields:
% 278.66/221.42 | (149) aNaturalNumber0(all_0_12_12) = all_8_0_13 & aNaturalNumber0(xm) = all_8_1_14 & aNaturalNumber0(xn) = all_8_2_15 & ( ~ (all_8_1_14 = 0) | ~ (all_8_2_15 = 0) | all_8_0_13 = 0)
% 278.66/221.42 |
% 278.66/221.42 | Applying alpha-rule on (149) yields:
% 278.66/221.42 | (150) aNaturalNumber0(all_0_12_12) = all_8_0_13
% 278.66/221.42 | (151) aNaturalNumber0(xm) = all_8_1_14
% 278.66/221.42 | (152) aNaturalNumber0(xn) = all_8_2_15
% 278.66/221.42 | (153) ~ (all_8_1_14 = 0) | ~ (all_8_2_15 = 0) | all_8_0_13 = 0
% 278.66/221.42 |
% 278.66/221.42 | Instantiating (144) with all_10_0_16, all_10_1_17, all_10_2_18, all_10_3_19, all_10_4_20 yields:
% 278.66/221.42 | (154) sdtpldt0(xr, xm) = all_10_1_17 & sdtpldt0(xp, all_10_1_17) = all_10_0_16 & aNaturalNumber0(xr) = all_10_3_19 & aNaturalNumber0(xp) = all_10_4_20 & aNaturalNumber0(xm) = all_10_2_18 & ( ~ (all_10_2_18 = 0) | ~ (all_10_3_19 = 0) | ~ (all_10_4_20 = 0) | all_10_0_16 = all_0_12_12)
% 278.66/221.43 |
% 278.66/221.43 | Applying alpha-rule on (154) yields:
% 278.66/221.43 | (155) aNaturalNumber0(xm) = all_10_2_18
% 278.66/221.43 | (156) ~ (all_10_2_18 = 0) | ~ (all_10_3_19 = 0) | ~ (all_10_4_20 = 0) | all_10_0_16 = all_0_12_12
% 278.66/221.43 | (157) sdtpldt0(xp, all_10_1_17) = all_10_0_16
% 278.66/221.43 | (158) aNaturalNumber0(xr) = all_10_3_19
% 278.66/221.43 | (159) sdtpldt0(xr, xm) = all_10_1_17
% 278.66/221.43 | (160) aNaturalNumber0(xp) = all_10_4_20
% 278.66/221.43 |
% 278.66/221.43 | Instantiating (131) with all_12_0_21, all_12_1_22, all_12_2_23 yields:
% 278.66/221.43 | (161) aNaturalNumber0(all_0_11_11) = all_12_0_21 & aNaturalNumber0(all_0_12_12) = all_12_2_23 & aNaturalNumber0(xp) = all_12_1_22 & ( ~ (all_12_1_22 = 0) | ~ (all_12_2_23 = 0) | all_12_0_21 = 0)
% 278.66/221.43 |
% 278.66/221.43 | Applying alpha-rule on (161) yields:
% 278.66/221.43 | (162) aNaturalNumber0(all_0_11_11) = all_12_0_21
% 278.66/221.43 | (163) aNaturalNumber0(all_0_12_12) = all_12_2_23
% 279.13/221.43 | (164) aNaturalNumber0(xp) = all_12_1_22
% 279.13/221.43 | (165) ~ (all_12_1_22 = 0) | ~ (all_12_2_23 = 0) | all_12_0_21 = 0
% 279.13/221.43 |
% 279.13/221.43 | Instantiating (130) with all_14_0_24, all_14_1_25, all_14_2_26 yields:
% 279.13/221.43 | (166) sdtpldt0(xp, all_0_12_12) = all_14_0_24 & aNaturalNumber0(all_0_12_12) = all_14_2_26 & aNaturalNumber0(xp) = all_14_1_25 & ( ~ (all_14_1_25 = 0) | ~ (all_14_2_26 = 0) | all_14_0_24 = all_0_11_11)
% 279.13/221.43 |
% 279.13/221.43 | Applying alpha-rule on (166) yields:
% 279.13/221.43 | (167) sdtpldt0(xp, all_0_12_12) = all_14_0_24
% 279.13/221.43 | (168) aNaturalNumber0(all_0_12_12) = all_14_2_26
% 279.13/221.43 | (169) aNaturalNumber0(xp) = all_14_1_25
% 279.13/221.43 | (170) ~ (all_14_1_25 = 0) | ~ (all_14_2_26 = 0) | all_14_0_24 = all_0_11_11
% 279.13/221.43 |
% 279.13/221.43 | Instantiating (120) with all_16_0_27, all_16_1_28, all_16_2_29, all_16_3_30, all_16_4_31, all_16_5_32, all_16_6_33, all_16_7_34, all_16_8_35, all_16_9_36, all_16_10_37, all_16_11_38, all_16_12_39, all_16_13_40, all_16_14_41 yields:
% 279.13/221.43 | (171) ( ~ (all_16_14_41 = 0) & aNaturalNumber0(all_0_0_0) = all_16_14_41) | (isPrime0(xp) = all_16_11_38 & doDivides0(xp, xm) = all_16_6_33 & doDivides0(xp, xn) = all_16_7_34 & iLess0(all_16_9_36, all_0_11_11) = all_16_8_35 & sdtpldt0(all_16_10_37, xp) = all_16_9_36 & sdtpldt0(xn, xm) = all_16_10_37 & aNaturalNumber0(xp) = all_16_12_39 & aNaturalNumber0(xm) = all_16_13_40 & aNaturalNumber0(xn) = all_16_14_41 & ( ~ (all_16_8_35 = 0) | ~ (all_16_12_39 = 0) | ~ (all_16_13_40 = 0) | ~ (all_16_14_41 = 0) | (all_16_3_30 = xm & all_16_4_31 = 0 & all_16_6_33 = 0 & sdtasdt0(xp, all_16_5_32) = xm & aNaturalNumber0(all_16_5_32) = 0) | (all_16_3_30 = xn & all_16_4_31 = 0 & all_16_7_34 = 0 & sdtasdt0(xp, all_16_5_32) = xn & aNaturalNumber0(all_16_5_32) = 0) | ( ~ (all_16_11_38 = 0) & (xp = sz10 | xp = sz00 | (all_16_0_27 = xp & all_16_1_28 = 0 & all_16_3_30 = 0 & all_16_4_31 = 0 & ~ (all_16_5_32 = xp) & ~ (all_16_5_32 = sz10) & doDivides0(all_16_5_32, xp) = 0 & sdtasdt0(all_16_5_32, all_16_2_29) = xp & aNaturalNumber0(all_16_2_29) = 0 & aNaturalNumber0(all_16_5_32) = 0)))))
% 279.13/221.43 |
% 279.13/221.43 | Instantiating (118) with all_17_0_42, all_17_1_43, all_17_2_44 yields:
% 279.13/221.43 | (172) aNaturalNumber0(all_0_3_3) = all_17_1_43 & aNaturalNumber0(all_0_9_9) = all_17_0_42 & aNaturalNumber0(xp) = all_17_2_44 & ( ~ (all_17_1_43 = 0) | ~ (all_17_2_44 = 0) | all_17_0_42 = 0)
% 279.13/221.43 |
% 279.13/221.43 | Applying alpha-rule on (172) yields:
% 279.13/221.43 | (173) aNaturalNumber0(all_0_3_3) = all_17_1_43
% 279.13/221.43 | (174) aNaturalNumber0(all_0_9_9) = all_17_0_42
% 279.13/221.43 | (175) aNaturalNumber0(xp) = all_17_2_44
% 279.13/221.43 | (176) ~ (all_17_1_43 = 0) | ~ (all_17_2_44 = 0) | all_17_0_42 = 0
% 279.13/221.43 |
% 279.13/221.43 | Instantiating (119) with all_19_0_45, all_19_1_46, all_19_2_47, all_19_3_48, all_19_4_49, all_19_5_50, all_19_6_51, all_19_7_52, all_19_8_53, all_19_9_54, all_19_10_55, all_19_11_56, all_19_12_57, all_19_13_58, all_19_14_59 yields:
% 279.13/221.43 | (177) isPrime0(xp) = all_19_11_56 & doDivides0(xp, xm) = all_19_6_51 & doDivides0(xp, xn) = all_19_7_52 & iLess0(all_19_9_54, all_0_11_11) = all_19_8_53 & sdtpldt0(all_19_10_55, xp) = all_19_9_54 & sdtpldt0(xn, xm) = all_19_10_55 & aNaturalNumber0(xp) = all_19_12_57 & aNaturalNumber0(xm) = all_19_13_58 & aNaturalNumber0(xn) = all_19_14_59 & ( ~ (all_19_8_53 = 0) | ~ (all_19_12_57 = 0) | ~ (all_19_13_58 = 0) | ~ (all_19_14_59 = 0) | (all_19_3_48 = xm & all_19_4_49 = 0 & all_19_6_51 = 0 & sdtasdt0(xp, all_19_5_50) = xm & aNaturalNumber0(all_19_5_50) = 0) | (all_19_3_48 = xn & all_19_4_49 = 0 & all_19_7_52 = 0 & sdtasdt0(xp, all_19_5_50) = xn & aNaturalNumber0(all_19_5_50) = 0) | ( ~ (all_19_11_56 = 0) & (xp = sz10 | xp = sz00 | (all_19_0_45 = xp & all_19_1_46 = 0 & all_19_3_48 = 0 & all_19_4_49 = 0 & ~ (all_19_5_50 = xp) & ~ (all_19_5_50 = sz10) & doDivides0(all_19_5_50, xp) = 0 & sdtasdt0(all_19_5_50, all_19_2_47) = xp & aNaturalNumber0(all_19_2_47) = 0 & aNaturalNumber0(all_19_5_50) = 0))))
% 279.13/221.43 |
% 279.13/221.43 | Applying alpha-rule on (177) yields:
% 279.13/221.43 | (178) isPrime0(xp) = all_19_11_56
% 279.13/221.43 | (179) sdtpldt0(all_19_10_55, xp) = all_19_9_54
% 279.13/221.43 | (180) aNaturalNumber0(xn) = all_19_14_59
% 279.13/221.43 | (181) sdtpldt0(xn, xm) = all_19_10_55
% 279.13/221.43 | (182) ~ (all_19_8_53 = 0) | ~ (all_19_12_57 = 0) | ~ (all_19_13_58 = 0) | ~ (all_19_14_59 = 0) | (all_19_3_48 = xm & all_19_4_49 = 0 & all_19_6_51 = 0 & sdtasdt0(xp, all_19_5_50) = xm & aNaturalNumber0(all_19_5_50) = 0) | (all_19_3_48 = xn & all_19_4_49 = 0 & all_19_7_52 = 0 & sdtasdt0(xp, all_19_5_50) = xn & aNaturalNumber0(all_19_5_50) = 0) | ( ~ (all_19_11_56 = 0) & (xp = sz10 | xp = sz00 | (all_19_0_45 = xp & all_19_1_46 = 0 & all_19_3_48 = 0 & all_19_4_49 = 0 & ~ (all_19_5_50 = xp) & ~ (all_19_5_50 = sz10) & doDivides0(all_19_5_50, xp) = 0 & sdtasdt0(all_19_5_50, all_19_2_47) = xp & aNaturalNumber0(all_19_2_47) = 0 & aNaturalNumber0(all_19_5_50) = 0)))
% 279.13/221.43 | (183) iLess0(all_19_9_54, all_0_11_11) = all_19_8_53
% 279.13/221.43 | (184) aNaturalNumber0(xm) = all_19_13_58
% 279.13/221.43 | (185) aNaturalNumber0(xp) = all_19_12_57
% 279.13/221.43 | (186) doDivides0(xp, xn) = all_19_7_52
% 279.13/221.43 | (187) doDivides0(xp, xm) = all_19_6_51
% 279.13/221.43 |
% 279.13/221.43 | Instantiating (116) with all_21_0_60, all_21_1_61, all_21_2_62, all_21_3_63, all_21_4_64, all_21_5_65, all_21_6_66, all_21_7_67, all_21_8_68, all_21_9_69, all_21_10_70, all_21_11_71, all_21_12_72, all_21_13_73, all_21_14_74 yields:
% 279.13/221.43 | (188) isPrime0(xp) = all_21_11_71 & doDivides0(xp, all_0_3_3) = all_21_6_66 & doDivides0(xp, xp) = all_21_7_67 & iLess0(all_21_9_69, all_0_11_11) = all_21_8_68 & sdtpldt0(all_21_10_70, xp) = all_21_9_69 & sdtpldt0(xp, all_0_3_3) = all_21_10_70 & aNaturalNumber0(all_0_3_3) = all_21_13_73 & aNaturalNumber0(xp) = all_21_12_72 & aNaturalNumber0(xp) = all_21_14_74 & ( ~ (all_21_8_68 = 0) | ~ (all_21_12_72 = 0) | ~ (all_21_13_73 = 0) | ~ (all_21_14_74 = 0) | (all_21_3_63 = all_0_3_3 & all_21_4_64 = 0 & all_21_6_66 = 0 & sdtasdt0(xp, all_21_5_65) = all_0_3_3 & aNaturalNumber0(all_21_5_65) = 0) | (all_21_3_63 = xp & all_21_4_64 = 0 & all_21_7_67 = 0 & sdtasdt0(xp, all_21_5_65) = xp & aNaturalNumber0(all_21_5_65) = 0) | ( ~ (all_21_11_71 = 0) & (xp = sz10 | xp = sz00 | (all_21_0_60 = xp & all_21_1_61 = 0 & all_21_3_63 = 0 & all_21_4_64 = 0 & ~ (all_21_5_65 = xp) & ~ (all_21_5_65 = sz10) & doDivides0(all_21_5_65, xp) = 0 & sdtasdt0(all_21_5_65, all_21_2_62) = xp & aNaturalNumber0(all_21_2_62) = 0 & aNaturalNumber0(all_21_5_65) = 0))))
% 279.13/221.43 |
% 279.13/221.43 | Applying alpha-rule on (188) yields:
% 279.13/221.43 | (189) sdtpldt0(xp, all_0_3_3) = all_21_10_70
% 279.13/221.43 | (190) sdtpldt0(all_21_10_70, xp) = all_21_9_69
% 279.13/221.43 | (191) aNaturalNumber0(all_0_3_3) = all_21_13_73
% 279.13/221.43 | (192) ~ (all_21_8_68 = 0) | ~ (all_21_12_72 = 0) | ~ (all_21_13_73 = 0) | ~ (all_21_14_74 = 0) | (all_21_3_63 = all_0_3_3 & all_21_4_64 = 0 & all_21_6_66 = 0 & sdtasdt0(xp, all_21_5_65) = all_0_3_3 & aNaturalNumber0(all_21_5_65) = 0) | (all_21_3_63 = xp & all_21_4_64 = 0 & all_21_7_67 = 0 & sdtasdt0(xp, all_21_5_65) = xp & aNaturalNumber0(all_21_5_65) = 0) | ( ~ (all_21_11_71 = 0) & (xp = sz10 | xp = sz00 | (all_21_0_60 = xp & all_21_1_61 = 0 & all_21_3_63 = 0 & all_21_4_64 = 0 & ~ (all_21_5_65 = xp) & ~ (all_21_5_65 = sz10) & doDivides0(all_21_5_65, xp) = 0 & sdtasdt0(all_21_5_65, all_21_2_62) = xp & aNaturalNumber0(all_21_2_62) = 0 & aNaturalNumber0(all_21_5_65) = 0)))
% 279.13/221.43 | (193) iLess0(all_21_9_69, all_0_11_11) = all_21_8_68
% 279.13/221.43 | (194) aNaturalNumber0(xp) = all_21_14_74
% 279.13/221.43 | (195) doDivides0(xp, all_0_3_3) = all_21_6_66
% 279.13/221.43 | (196) isPrime0(xp) = all_21_11_71
% 279.13/221.43 | (197) doDivides0(xp, xp) = all_21_7_67
% 279.13/221.43 | (198) aNaturalNumber0(xp) = all_21_12_72
% 279.13/221.43 |
% 279.13/221.43 | Instantiating (112) with all_23_0_75, all_23_1_76, all_23_2_77 yields:
% 279.13/221.43 | (199) sdtasdt0(all_0_0_0, xp) = all_23_0_75 & aNaturalNumber0(all_0_0_0) = all_23_1_76 & aNaturalNumber0(xp) = all_23_2_77 & ( ~ (all_23_1_76 = 0) | ~ (all_23_2_77 = 0) | all_23_0_75 = all_0_10_10)
% 279.13/221.43 |
% 279.13/221.43 | Applying alpha-rule on (199) yields:
% 279.13/221.43 | (200) sdtasdt0(all_0_0_0, xp) = all_23_0_75
% 279.13/221.43 | (201) aNaturalNumber0(all_0_0_0) = all_23_1_76
% 279.13/221.43 | (202) aNaturalNumber0(xp) = all_23_2_77
% 279.13/221.43 | (203) ~ (all_23_1_76 = 0) | ~ (all_23_2_77 = 0) | all_23_0_75 = all_0_10_10
% 279.13/221.43 |
% 279.13/221.43 | Instantiating (115) with all_25_0_78, all_25_1_79, all_25_2_80, all_25_3_81, all_25_4_82, all_25_5_83, all_25_6_84, all_25_7_85, all_25_8_86, all_25_9_87, all_25_10_88, all_25_11_89, all_25_12_90, all_25_13_91, all_25_14_92 yields:
% 279.13/221.43 | (204) ( ~ (all_25_14_92 = 0) & aNaturalNumber0(all_0_3_3) = all_25_14_92) | (isPrime0(xp) = all_25_11_89 & doDivides0(xp, xr) = all_25_7_85 & doDivides0(xp, xm) = all_25_6_84 & iLess0(all_25_9_87, all_0_11_11) = all_25_8_86 & sdtpldt0(all_25_10_88, xp) = all_25_9_87 & sdtpldt0(xr, xm) = all_25_10_88 & aNaturalNumber0(xr) = all_25_14_92 & aNaturalNumber0(xp) = all_25_12_90 & aNaturalNumber0(xm) = all_25_13_91 & ( ~ (all_25_8_86 = 0) | ~ (all_25_12_90 = 0) | ~ (all_25_13_91 = 0) | ~ (all_25_14_92 = 0) | (all_25_3_81 = xr & all_25_4_82 = 0 & all_25_7_85 = 0 & sdtasdt0(xp, all_25_5_83) = xr & aNaturalNumber0(all_25_5_83) = 0) | (all_25_3_81 = xm & all_25_4_82 = 0 & all_25_6_84 = 0 & sdtasdt0(xp, all_25_5_83) = xm & aNaturalNumber0(all_25_5_83) = 0) | ( ~ (all_25_11_89 = 0) & (xp = sz10 | xp = sz00 | (all_25_0_78 = xp & all_25_1_79 = 0 & all_25_3_81 = 0 & all_25_4_82 = 0 & ~ (all_25_5_83 = xp) & ~ (all_25_5_83 = sz10) & doDivides0(all_25_5_83, xp) = 0 & sdtasdt0(all_25_5_83, all_25_2_80) = xp & aNaturalNumber0(all_25_2_80) = 0 & aNaturalNumber0(all_25_5_83) = 0)))))
% 279.13/221.44 |
% 279.13/221.44 | Instantiating (113) with all_26_0_93, all_26_1_94, all_26_2_95 yields:
% 279.13/221.44 | (205) aNaturalNumber0(all_0_0_0) = all_26_1_94 & aNaturalNumber0(all_0_10_10) = all_26_0_93 & aNaturalNumber0(xp) = all_26_2_95 & ( ~ (all_26_1_94 = 0) | ~ (all_26_2_95 = 0) | all_26_0_93 = 0)
% 279.13/221.44 |
% 279.13/221.44 | Applying alpha-rule on (205) yields:
% 279.13/221.44 | (206) aNaturalNumber0(all_0_0_0) = all_26_1_94
% 279.13/221.44 | (207) aNaturalNumber0(all_0_10_10) = all_26_0_93
% 279.13/221.44 | (208) aNaturalNumber0(xp) = all_26_2_95
% 279.13/221.44 | (209) ~ (all_26_1_94 = 0) | ~ (all_26_2_95 = 0) | all_26_0_93 = 0
% 279.13/221.44 |
% 279.13/221.44 | Instantiating (143) with all_28_0_96, all_28_1_97, all_28_2_98, all_28_3_99, all_28_4_100 yields:
% 279.13/221.44 | (210) sdtpldt0(all_0_1_1, xm) = all_28_1_97 & sdtpldt0(xp, all_28_1_97) = all_28_0_96 & aNaturalNumber0(all_0_1_1) = all_28_3_99 & aNaturalNumber0(xp) = all_28_4_100 & aNaturalNumber0(xm) = all_28_2_98 & ( ~ (all_28_2_98 = 0) | ~ (all_28_3_99 = 0) | ~ (all_28_4_100 = 0) | all_28_0_96 = all_0_12_12)
% 279.13/221.44 |
% 279.13/221.44 | Applying alpha-rule on (210) yields:
% 279.13/221.44 | (211) aNaturalNumber0(xm) = all_28_2_98
% 279.13/221.44 | (212) sdtpldt0(all_0_1_1, xm) = all_28_1_97
% 279.13/221.44 | (213) aNaturalNumber0(all_0_1_1) = all_28_3_99
% 279.13/221.44 | (214) ~ (all_28_2_98 = 0) | ~ (all_28_3_99 = 0) | ~ (all_28_4_100 = 0) | all_28_0_96 = all_0_12_12
% 279.13/221.44 | (215) aNaturalNumber0(xp) = all_28_4_100
% 279.13/221.44 | (216) sdtpldt0(xp, all_28_1_97) = all_28_0_96
% 279.13/221.44 |
% 279.13/221.44 | Instantiating (146) with all_30_0_101, all_30_1_102, all_30_2_103 yields:
% 279.13/221.44 | (217) sdtpldt0(xm, xn) = all_30_0_101 & aNaturalNumber0(xm) = all_30_1_102 & aNaturalNumber0(xn) = all_30_2_103 & ( ~ (all_30_1_102 = 0) | ~ (all_30_2_103 = 0) | all_30_0_101 = all_0_12_12)
% 279.13/221.44 |
% 279.13/221.44 | Applying alpha-rule on (217) yields:
% 279.13/221.44 | (218) sdtpldt0(xm, xn) = all_30_0_101
% 279.13/221.44 | (219) aNaturalNumber0(xm) = all_30_1_102
% 279.13/221.44 | (220) aNaturalNumber0(xn) = all_30_2_103
% 279.13/221.44 | (221) ~ (all_30_1_102 = 0) | ~ (all_30_2_103 = 0) | all_30_0_101 = all_0_12_12
% 279.13/221.44 |
% 279.13/221.44 | Instantiating (127) with all_32_0_104, all_32_1_105, all_32_2_106 yields:
% 279.13/221.44 | (222) aNaturalNumber0(all_0_7_7) = all_32_0_104 & aNaturalNumber0(all_0_8_8) = all_32_2_106 & aNaturalNumber0(xp) = all_32_1_105 & ( ~ (all_32_1_105 = 0) | ~ (all_32_2_106 = 0) | all_32_0_104 = 0)
% 279.13/221.44 |
% 279.13/221.44 | Applying alpha-rule on (222) yields:
% 279.13/221.44 | (223) aNaturalNumber0(all_0_7_7) = all_32_0_104
% 279.13/221.44 | (224) aNaturalNumber0(all_0_8_8) = all_32_2_106
% 279.13/221.44 | (225) aNaturalNumber0(xp) = all_32_1_105
% 279.13/221.44 | (226) ~ (all_32_1_105 = 0) | ~ (all_32_2_106 = 0) | all_32_0_104 = 0
% 279.13/221.44 |
% 279.13/221.44 | Instantiating (126) with all_34_0_107, all_34_1_108, all_34_2_109 yields:
% 279.13/221.44 | (227) sdtpldt0(xp, all_0_8_8) = all_34_0_107 & aNaturalNumber0(all_0_8_8) = all_34_2_109 & aNaturalNumber0(xp) = all_34_1_108 & ( ~ (all_34_1_108 = 0) | ~ (all_34_2_109 = 0) | all_34_0_107 = all_0_7_7)
% 279.13/221.44 |
% 279.13/221.44 | Applying alpha-rule on (227) yields:
% 279.13/221.44 | (228) sdtpldt0(xp, all_0_8_8) = all_34_0_107
% 279.13/221.44 | (229) aNaturalNumber0(all_0_8_8) = all_34_2_109
% 279.13/221.44 | (230) aNaturalNumber0(xp) = all_34_1_108
% 279.13/221.44 | (231) ~ (all_34_1_108 = 0) | ~ (all_34_2_109 = 0) | all_34_0_107 = all_0_7_7
% 279.13/221.44 |
% 279.13/221.44 | Instantiating (125) with all_36_0_110, all_36_1_111, all_36_2_112, all_36_3_113, all_36_4_114 yields:
% 279.13/221.44 | (232) sdtpldt0(all_0_8_8, all_36_1_111) = all_36_0_110 & sdtpldt0(xp, all_0_4_4) = all_36_1_111 & aNaturalNumber0(all_0_4_4) = all_36_2_112 & aNaturalNumber0(all_0_8_8) = all_36_4_114 & aNaturalNumber0(xp) = all_36_3_113 & ( ~ (all_36_2_112 = 0) | ~ (all_36_3_113 = 0) | ~ (all_36_4_114 = 0) | all_36_0_110 = all_0_11_11)
% 279.13/221.44 |
% 279.13/221.44 | Applying alpha-rule on (232) yields:
% 279.13/221.44 | (233) sdtpldt0(xp, all_0_4_4) = all_36_1_111
% 279.13/221.44 | (234) aNaturalNumber0(all_0_4_4) = all_36_2_112
% 279.13/221.44 | (235) ~ (all_36_2_112 = 0) | ~ (all_36_3_113 = 0) | ~ (all_36_4_114 = 0) | all_36_0_110 = all_0_11_11
% 279.13/221.44 | (236) aNaturalNumber0(xp) = all_36_3_113
% 279.13/221.44 | (237) aNaturalNumber0(all_0_8_8) = all_36_4_114
% 279.13/221.44 | (238) sdtpldt0(all_0_8_8, all_36_1_111) = all_36_0_110
% 279.13/221.44 |
% 279.13/221.44 | Instantiating (114) with all_38_0_115, all_38_1_116, all_38_2_117, all_38_3_118, all_38_4_119, all_38_5_120, all_38_6_121, all_38_7_122, all_38_8_123, all_38_9_124, all_38_10_125, all_38_11_126, all_38_12_127, all_38_13_128, all_38_14_129 yields:
% 279.13/221.44 | (239) ( ~ (all_38_14_129 = 0) & aNaturalNumber0(all_0_3_3) = all_38_14_129) | (isPrime0(xp) = all_38_11_126 & doDivides0(xp, all_0_3_3) = all_38_6_121 & doDivides0(xp, xp) = all_38_7_122 & iLess0(all_38_9_124, all_0_11_11) = all_38_8_123 & sdtpldt0(all_38_10_125, xp) = all_38_9_124 & sdtpldt0(xp, all_0_3_3) = all_38_10_125 & aNaturalNumber0(all_0_3_3) = all_38_13_128 & aNaturalNumber0(xp) = all_38_12_127 & aNaturalNumber0(xp) = all_38_14_129 & ( ~ (all_38_8_123 = 0) | ~ (all_38_12_127 = 0) | ~ (all_38_13_128 = 0) | ~ (all_38_14_129 = 0) | (all_38_3_118 = all_0_3_3 & all_38_4_119 = 0 & all_38_6_121 = 0 & sdtasdt0(xp, all_38_5_120) = all_0_3_3 & aNaturalNumber0(all_38_5_120) = 0) | (all_38_3_118 = xp & all_38_4_119 = 0 & all_38_7_122 = 0 & sdtasdt0(xp, all_38_5_120) = xp & aNaturalNumber0(all_38_5_120) = 0) | ( ~ (all_38_11_126 = 0) & (xp = sz10 | xp = sz00 | (all_38_0_115 = xp & all_38_1_116 = 0 & all_38_3_118 = 0 & all_38_4_119 = 0 & ~ (all_38_5_120 = xp) & ~ (all_38_5_120 = sz10) & doDivides0(all_38_5_120, xp) = 0 & sdtasdt0(all_38_5_120, all_38_2_117) = xp & aNaturalNumber0(all_38_2_117) = 0 & aNaturalNumber0(all_38_5_120) = 0)))))
% 279.13/221.44 |
% 279.13/221.44 | Instantiating (122) with all_39_0_130, all_39_1_131, all_39_2_132 yields:
% 279.13/221.44 | (240) aNaturalNumber0(all_0_10_10) = all_39_0_130 & aNaturalNumber0(xm) = all_39_1_131 & aNaturalNumber0(xn) = all_39_2_132 & ( ~ (all_39_1_131 = 0) | ~ (all_39_2_132 = 0) | all_39_0_130 = 0)
% 279.13/221.44 |
% 279.13/221.44 | Applying alpha-rule on (240) yields:
% 279.13/221.44 | (241) aNaturalNumber0(all_0_10_10) = all_39_0_130
% 279.13/221.44 | (242) aNaturalNumber0(xm) = all_39_1_131
% 279.13/221.44 | (243) aNaturalNumber0(xn) = all_39_2_132
% 279.13/221.44 | (244) ~ (all_39_1_131 = 0) | ~ (all_39_2_132 = 0) | all_39_0_130 = 0
% 279.13/221.44 |
% 279.13/221.44 | Instantiating (124) with all_41_0_133, all_41_1_134, all_41_2_135 yields:
% 279.13/221.44 | (245) aNaturalNumber0(all_0_4_4) = all_41_1_134 & aNaturalNumber0(all_0_7_7) = all_41_2_135 & aNaturalNumber0(all_0_11_11) = all_41_0_133 & ( ~ (all_41_1_134 = 0) | ~ (all_41_2_135 = 0) | all_41_0_133 = 0)
% 279.13/221.44 |
% 279.13/221.44 | Applying alpha-rule on (245) yields:
% 279.13/221.44 | (246) aNaturalNumber0(all_0_4_4) = all_41_1_134
% 279.13/221.44 | (247) aNaturalNumber0(all_0_7_7) = all_41_2_135
% 279.13/221.44 | (248) aNaturalNumber0(all_0_11_11) = all_41_0_133
% 279.13/221.44 | (249) ~ (all_41_1_134 = 0) | ~ (all_41_2_135 = 0) | all_41_0_133 = 0
% 279.13/221.44 |
% 279.13/221.44 | Instantiating (123) with all_43_0_136, all_43_1_137, all_43_2_138 yields:
% 279.13/221.44 | (250) sdtpldt0(all_0_4_4, all_0_7_7) = all_43_0_136 & aNaturalNumber0(all_0_4_4) = all_43_1_137 & aNaturalNumber0(all_0_7_7) = all_43_2_138 & ( ~ (all_43_1_137 = 0) | ~ (all_43_2_138 = 0) | all_43_0_136 = all_0_11_11)
% 279.13/221.44 |
% 279.13/221.44 | Applying alpha-rule on (250) yields:
% 279.13/221.44 | (251) sdtpldt0(all_0_4_4, all_0_7_7) = all_43_0_136
% 279.13/221.44 | (252) aNaturalNumber0(all_0_4_4) = all_43_1_137
% 279.13/221.44 | (253) aNaturalNumber0(all_0_7_7) = all_43_2_138
% 279.13/221.44 | (254) ~ (all_43_1_137 = 0) | ~ (all_43_2_138 = 0) | all_43_0_136 = all_0_11_11
% 279.13/221.44 |
% 279.13/221.44 | Instantiating (117) with all_45_0_139, all_45_1_140, all_45_2_141 yields:
% 279.13/221.44 | (255) sdtasdt0(all_0_3_3, xp) = all_45_0_139 & aNaturalNumber0(all_0_3_3) = all_45_1_140 & aNaturalNumber0(xp) = all_45_2_141 & ( ~ (all_45_1_140 = 0) | ~ (all_45_2_141 = 0) | all_45_0_139 = all_0_9_9)
% 279.13/221.44 |
% 279.13/221.44 | Applying alpha-rule on (255) yields:
% 279.13/221.44 | (256) sdtasdt0(all_0_3_3, xp) = all_45_0_139
% 279.13/221.44 | (257) aNaturalNumber0(all_0_3_3) = all_45_1_140
% 279.13/221.44 | (258) aNaturalNumber0(xp) = all_45_2_141
% 279.13/221.44 | (259) ~ (all_45_1_140 = 0) | ~ (all_45_2_141 = 0) | all_45_0_139 = all_0_9_9
% 279.13/221.44 |
% 279.13/221.44 | Instantiating (111) with all_47_0_142, all_47_1_143, all_47_2_144, all_47_3_145, all_47_4_146, all_47_5_147, all_47_6_148, all_47_7_149, all_47_8_150, all_47_9_151, all_47_10_152, all_47_11_153, all_47_12_154, all_47_13_155, all_47_14_156 yields:
% 279.13/221.44 | (260) ( ~ (all_47_14_156 = 0) & aNaturalNumber0(all_0_0_0) = all_47_14_156) | (isPrime0(xp) = all_47_11_153 & doDivides0(xp, all_0_0_0) = all_47_6_148 & doDivides0(xp, xp) = all_47_7_149 & iLess0(all_47_9_151, all_0_11_11) = all_47_8_150 & sdtpldt0(all_47_10_152, xp) = all_47_9_151 & sdtpldt0(xp, all_0_0_0) = all_47_10_152 & aNaturalNumber0(all_0_0_0) = all_47_13_155 & aNaturalNumber0(xp) = all_47_12_154 & aNaturalNumber0(xp) = all_47_14_156 & ( ~ (all_47_8_150 = 0) | ~ (all_47_12_154 = 0) | ~ (all_47_13_155 = 0) | ~ (all_47_14_156 = 0) | (all_47_3_145 = all_0_0_0 & all_47_4_146 = 0 & all_47_6_148 = 0 & sdtasdt0(xp, all_47_5_147) = all_0_0_0 & aNaturalNumber0(all_47_5_147) = 0) | (all_47_3_145 = xp & all_47_4_146 = 0 & all_47_7_149 = 0 & sdtasdt0(xp, all_47_5_147) = xp & aNaturalNumber0(all_47_5_147) = 0) | ( ~ (all_47_11_153 = 0) & (xp = sz10 | xp = sz00 | (all_47_0_142 = xp & all_47_1_143 = 0 & all_47_3_145 = 0 & all_47_4_146 = 0 & ~ (all_47_5_147 = xp) & ~ (all_47_5_147 = sz10) & doDivides0(all_47_5_147, xp) = 0 & sdtasdt0(all_47_5_147, all_47_2_144) = xp & aNaturalNumber0(all_47_2_144) = 0 & aNaturalNumber0(all_47_5_147) = 0)))))
% 279.13/221.44 |
% 279.13/221.44 | Instantiating (110) with all_48_0_157, all_48_1_158, all_48_2_159, all_48_3_160, all_48_4_161, all_48_5_162, all_48_6_163, all_48_7_164, all_48_8_165, all_48_9_166, all_48_10_167, all_48_11_168, all_48_12_169, all_48_13_170, all_48_14_171 yields:
% 279.13/221.44 | (261) isPrime0(xp) = all_48_11_168 & doDivides0(xp, all_0_0_0) = all_48_6_163 & doDivides0(xp, xp) = all_48_7_164 & iLess0(all_48_9_166, all_0_11_11) = all_48_8_165 & sdtpldt0(all_48_10_167, xp) = all_48_9_166 & sdtpldt0(xp, all_0_0_0) = all_48_10_167 & aNaturalNumber0(all_0_0_0) = all_48_13_170 & aNaturalNumber0(xp) = all_48_12_169 & aNaturalNumber0(xp) = all_48_14_171 & ( ~ (all_48_8_165 = 0) | ~ (all_48_12_169 = 0) | ~ (all_48_13_170 = 0) | ~ (all_48_14_171 = 0) | (all_48_3_160 = all_0_0_0 & all_48_4_161 = 0 & all_48_6_163 = 0 & sdtasdt0(xp, all_48_5_162) = all_0_0_0 & aNaturalNumber0(all_48_5_162) = 0) | (all_48_3_160 = xp & all_48_4_161 = 0 & all_48_7_164 = 0 & sdtasdt0(xp, all_48_5_162) = xp & aNaturalNumber0(all_48_5_162) = 0) | ( ~ (all_48_11_168 = 0) & (xp = sz10 | xp = sz00 | (all_48_0_157 = xp & all_48_1_158 = 0 & all_48_3_160 = 0 & all_48_4_161 = 0 & ~ (all_48_5_162 = xp) & ~ (all_48_5_162 = sz10) & doDivides0(all_48_5_162, xp) = 0 & sdtasdt0(all_48_5_162, all_48_2_159) = xp & aNaturalNumber0(all_48_2_159) = 0 & aNaturalNumber0(all_48_5_162) = 0))))
% 279.13/221.44 |
% 279.13/221.44 | Applying alpha-rule on (261) yields:
% 279.13/221.44 | (262) doDivides0(xp, all_0_0_0) = all_48_6_163
% 279.13/221.44 | (263) doDivides0(xp, xp) = all_48_7_164
% 279.13/221.44 | (264) sdtpldt0(xp, all_0_0_0) = all_48_10_167
% 279.13/221.44 | (265) aNaturalNumber0(xp) = all_48_14_171
% 279.13/221.44 | (266) iLess0(all_48_9_166, all_0_11_11) = all_48_8_165
% 279.13/221.45 | (267) isPrime0(xp) = all_48_11_168
% 279.13/221.45 | (268) sdtpldt0(all_48_10_167, xp) = all_48_9_166
% 279.13/221.45 | (269) aNaturalNumber0(all_0_0_0) = all_48_13_170
% 279.13/221.45 | (270) ~ (all_48_8_165 = 0) | ~ (all_48_12_169 = 0) | ~ (all_48_13_170 = 0) | ~ (all_48_14_171 = 0) | (all_48_3_160 = all_0_0_0 & all_48_4_161 = 0 & all_48_6_163 = 0 & sdtasdt0(xp, all_48_5_162) = all_0_0_0 & aNaturalNumber0(all_48_5_162) = 0) | (all_48_3_160 = xp & all_48_4_161 = 0 & all_48_7_164 = 0 & sdtasdt0(xp, all_48_5_162) = xp & aNaturalNumber0(all_48_5_162) = 0) | ( ~ (all_48_11_168 = 0) & (xp = sz10 | xp = sz00 | (all_48_0_157 = xp & all_48_1_158 = 0 & all_48_3_160 = 0 & all_48_4_161 = 0 & ~ (all_48_5_162 = xp) & ~ (all_48_5_162 = sz10) & doDivides0(all_48_5_162, xp) = 0 & sdtasdt0(all_48_5_162, all_48_2_159) = xp & aNaturalNumber0(all_48_2_159) = 0 & aNaturalNumber0(all_48_5_162) = 0)))
% 279.13/221.45 | (271) aNaturalNumber0(xp) = all_48_12_169
% 279.13/221.45 |
% 279.13/221.45 | Instantiating (107) with all_50_0_172, all_50_1_173, all_50_2_174, all_50_3_175, all_50_4_176, all_50_5_177, all_50_6_178, all_50_7_179, all_50_8_180, all_50_9_181, all_50_10_182, all_50_11_183, all_50_12_184, all_50_13_185, all_50_14_186 yields:
% 279.13/221.45 | (272) isPrime0(xp) = all_50_11_183 & doDivides0(xp, xr) = all_50_7_179 & doDivides0(xp, xm) = all_50_6_178 & iLess0(all_50_9_181, all_0_11_11) = all_50_8_180 & sdtpldt0(all_50_10_182, xp) = all_50_9_181 & sdtpldt0(xr, xm) = all_50_10_182 & aNaturalNumber0(xr) = all_50_14_186 & aNaturalNumber0(xp) = all_50_12_184 & aNaturalNumber0(xm) = all_50_13_185 & ( ~ (all_50_8_180 = 0) | ~ (all_50_12_184 = 0) | ~ (all_50_13_185 = 0) | ~ (all_50_14_186 = 0) | (all_50_3_175 = xr & all_50_4_176 = 0 & all_50_7_179 = 0 & sdtasdt0(xp, all_50_5_177) = xr & aNaturalNumber0(all_50_5_177) = 0) | (all_50_3_175 = xm & all_50_4_176 = 0 & all_50_6_178 = 0 & sdtasdt0(xp, all_50_5_177) = xm & aNaturalNumber0(all_50_5_177) = 0) | ( ~ (all_50_11_183 = 0) & (xp = sz10 | xp = sz00 | (all_50_0_172 = xp & all_50_1_173 = 0 & all_50_3_175 = 0 & all_50_4_176 = 0 & ~ (all_50_5_177 = xp) & ~ (all_50_5_177 = sz10) & doDivides0(all_50_5_177, xp) = 0 & sdtasdt0(all_50_5_177, all_50_2_174) = xp & aNaturalNumber0(all_50_2_174) = 0 & aNaturalNumber0(all_50_5_177) = 0))))
% 279.13/221.45 |
% 279.13/221.45 | Applying alpha-rule on (272) yields:
% 279.13/221.45 | (273) doDivides0(xp, xm) = all_50_6_178
% 279.13/221.45 | (274) ~ (all_50_8_180 = 0) | ~ (all_50_12_184 = 0) | ~ (all_50_13_185 = 0) | ~ (all_50_14_186 = 0) | (all_50_3_175 = xr & all_50_4_176 = 0 & all_50_7_179 = 0 & sdtasdt0(xp, all_50_5_177) = xr & aNaturalNumber0(all_50_5_177) = 0) | (all_50_3_175 = xm & all_50_4_176 = 0 & all_50_6_178 = 0 & sdtasdt0(xp, all_50_5_177) = xm & aNaturalNumber0(all_50_5_177) = 0) | ( ~ (all_50_11_183 = 0) & (xp = sz10 | xp = sz00 | (all_50_0_172 = xp & all_50_1_173 = 0 & all_50_3_175 = 0 & all_50_4_176 = 0 & ~ (all_50_5_177 = xp) & ~ (all_50_5_177 = sz10) & doDivides0(all_50_5_177, xp) = 0 & sdtasdt0(all_50_5_177, all_50_2_174) = xp & aNaturalNumber0(all_50_2_174) = 0 & aNaturalNumber0(all_50_5_177) = 0)))
% 279.13/221.45 | (275) aNaturalNumber0(xm) = all_50_13_185
% 279.13/221.45 | (276) isPrime0(xp) = all_50_11_183
% 279.13/221.45 | (277) iLess0(all_50_9_181, all_0_11_11) = all_50_8_180
% 279.13/221.45 | (278) doDivides0(xp, xr) = all_50_7_179
% 279.13/221.45 | (279) sdtpldt0(all_50_10_182, xp) = all_50_9_181
% 279.13/221.45 | (280) aNaturalNumber0(xp) = all_50_12_184
% 279.13/221.45 | (281) aNaturalNumber0(xr) = all_50_14_186
% 279.13/221.45 | (282) sdtpldt0(xr, xm) = all_50_10_182
% 279.13/221.45 |
% 279.13/221.45 | Instantiating (108) with all_52_0_187, all_52_1_188, all_52_2_189 yields:
% 279.13/221.45 | (283) sdtasdt0(xm, xr) = all_52_0_187 & aNaturalNumber0(xr) = all_52_2_189 & aNaturalNumber0(xm) = all_52_1_188 & ( ~ (all_52_1_188 = 0) | ~ (all_52_2_189 = 0) | all_52_0_187 = all_0_9_9)
% 279.13/221.45 |
% 279.13/221.45 | Applying alpha-rule on (283) yields:
% 279.13/221.45 | (284) sdtasdt0(xm, xr) = all_52_0_187
% 279.13/221.45 | (285) aNaturalNumber0(xr) = all_52_2_189
% 279.13/221.45 | (286) aNaturalNumber0(xm) = all_52_1_188
% 279.13/221.45 | (287) ~ (all_52_1_188 = 0) | ~ (all_52_2_189 = 0) | all_52_0_187 = all_0_9_9
% 279.13/221.45 |
% 279.13/221.45 | Instantiating (109) with all_54_0_190, all_54_1_191, all_54_2_192 yields:
% 279.13/221.45 | (288) aNaturalNumber0(all_0_9_9) = all_54_0_190 & aNaturalNumber0(xr) = all_54_2_192 & aNaturalNumber0(xm) = all_54_1_191 & ( ~ (all_54_1_191 = 0) | ~ (all_54_2_192 = 0) | all_54_0_190 = 0)
% 279.13/221.45 |
% 279.13/221.45 | Applying alpha-rule on (288) yields:
% 279.13/221.45 | (289) aNaturalNumber0(all_0_9_9) = all_54_0_190
% 279.13/221.45 | (290) aNaturalNumber0(xr) = all_54_2_192
% 279.13/221.45 | (291) aNaturalNumber0(xm) = all_54_1_191
% 279.13/221.45 | (292) ~ (all_54_1_191 = 0) | ~ (all_54_2_192 = 0) | all_54_0_190 = 0
% 279.13/221.45 |
% 279.13/221.45 | Instantiating (121) with all_56_0_193, all_56_1_194, all_56_2_195 yields:
% 279.13/221.45 | (293) sdtasdt0(xm, xn) = all_56_0_193 & aNaturalNumber0(xm) = all_56_1_194 & aNaturalNumber0(xn) = all_56_2_195 & ( ~ (all_56_1_194 = 0) | ~ (all_56_2_195 = 0) | all_56_0_193 = all_0_10_10)
% 279.13/221.45 |
% 279.13/221.45 | Applying alpha-rule on (293) yields:
% 279.13/221.45 | (294) sdtasdt0(xm, xn) = all_56_0_193
% 279.13/221.45 | (295) aNaturalNumber0(xm) = all_56_1_194
% 279.13/221.45 | (296) aNaturalNumber0(xn) = all_56_2_195
% 279.13/221.45 | (297) ~ (all_56_1_194 = 0) | ~ (all_56_2_195 = 0) | all_56_0_193 = all_0_10_10
% 279.13/221.45 |
% 279.13/221.45 | Instantiating (105) with all_58_0_196, all_58_1_197, all_58_2_198 yields:
% 279.13/221.45 | (298) (all_58_0_196 = all_0_11_11 & all_58_1_197 = 0 & sdtpldt0(all_0_7_7, all_58_2_198) = all_0_11_11 & aNaturalNumber0(all_58_2_198) = 0) | (aNaturalNumber0(all_0_7_7) = all_58_2_198 & aNaturalNumber0(all_0_11_11) = all_58_1_197 & ( ~ (all_58_1_197 = 0) | ~ (all_58_2_198 = 0)))
% 279.13/221.45 |
% 279.13/221.45 | Instantiating (137) with all_61_0_205, all_61_1_206, all_61_2_207 yields:
% 279.13/221.45 | (299) sdtpldt0(all_0_1_1, xp) = all_61_0_205 & aNaturalNumber0(all_0_1_1) = all_61_1_206 & aNaturalNumber0(xp) = all_61_2_207 & ( ~ (all_61_1_206 = 0) | ~ (all_61_2_207 = 0) | all_61_0_205 = xn)
% 279.13/221.45 |
% 279.13/221.45 | Applying alpha-rule on (299) yields:
% 279.13/221.45 | (300) sdtpldt0(all_0_1_1, xp) = all_61_0_205
% 279.13/221.45 | (301) aNaturalNumber0(all_0_1_1) = all_61_1_206
% 279.13/221.45 | (302) aNaturalNumber0(xp) = all_61_2_207
% 279.13/221.45 | (303) ~ (all_61_1_206 = 0) | ~ (all_61_2_207 = 0) | all_61_0_205 = xn
% 279.13/221.45 |
% 279.13/221.45 | Instantiating (142) with all_63_0_208, all_63_1_209, all_63_2_210, all_63_3_211, all_63_4_212 yields:
% 279.13/221.45 | (304) sdtpldt0(all_0_2_2, xm) = all_63_1_209 & sdtpldt0(xr, all_63_1_209) = all_63_0_208 & aNaturalNumber0(all_0_2_2) = all_63_3_211 & aNaturalNumber0(xr) = all_63_4_212 & aNaturalNumber0(xm) = all_63_2_210 & ( ~ (all_63_2_210 = 0) | ~ (all_63_3_211 = 0) | ~ (all_63_4_212 = 0) | all_63_0_208 = all_0_12_12)
% 279.13/221.45 |
% 279.13/221.45 | Applying alpha-rule on (304) yields:
% 279.13/221.45 | (305) ~ (all_63_2_210 = 0) | ~ (all_63_3_211 = 0) | ~ (all_63_4_212 = 0) | all_63_0_208 = all_0_12_12
% 279.13/221.45 | (306) sdtpldt0(all_0_2_2, xm) = all_63_1_209
% 279.13/221.45 | (307) sdtpldt0(xr, all_63_1_209) = all_63_0_208
% 279.13/221.45 | (308) aNaturalNumber0(all_0_2_2) = all_63_3_211
% 279.13/221.45 | (309) aNaturalNumber0(xm) = all_63_2_210
% 279.13/221.45 | (310) aNaturalNumber0(xr) = all_63_4_212
% 279.13/221.45 |
% 279.13/221.45 | Instantiating (139) with all_65_0_213, all_65_1_214, all_65_2_215 yields:
% 279.13/221.45 | (311) sdtpldt0(xr, xp) = all_65_0_213 & aNaturalNumber0(xr) = all_65_1_214 & aNaturalNumber0(xp) = all_65_2_215 & ( ~ (all_65_1_214 = 0) | ~ (all_65_2_215 = 0) | all_65_0_213 = xn)
% 279.13/221.45 |
% 279.13/221.45 | Applying alpha-rule on (311) yields:
% 279.13/221.45 | (312) sdtpldt0(xr, xp) = all_65_0_213
% 279.13/221.45 | (313) aNaturalNumber0(xr) = all_65_1_214
% 279.13/221.45 | (314) aNaturalNumber0(xp) = all_65_2_215
% 279.13/221.45 | (315) ~ (all_65_1_214 = 0) | ~ (all_65_2_215 = 0) | all_65_0_213 = xn
% 279.13/221.45 |
% 279.13/221.45 | Instantiating (141) with all_67_0_216, all_67_1_217, all_67_2_218, all_67_3_219, all_67_4_220 yields:
% 279.13/221.45 | (316) sdtpldt0(xm, xp) = all_67_1_217 & sdtpldt0(xn, all_67_1_217) = all_67_0_216 & aNaturalNumber0(xp) = all_67_2_218 & aNaturalNumber0(xm) = all_67_3_219 & aNaturalNumber0(xn) = all_67_4_220 & ( ~ (all_67_2_218 = 0) | ~ (all_67_3_219 = 0) | ~ (all_67_4_220 = 0) | all_67_0_216 = all_0_11_11)
% 279.13/221.45 |
% 279.13/221.45 | Applying alpha-rule on (316) yields:
% 279.13/221.45 | (317) aNaturalNumber0(xp) = all_67_2_218
% 279.13/221.45 | (318) aNaturalNumber0(xm) = all_67_3_219
% 279.13/221.45 | (319) aNaturalNumber0(xn) = all_67_4_220
% 279.13/221.45 | (320) sdtpldt0(xm, xp) = all_67_1_217
% 279.13/221.45 | (321) ~ (all_67_2_218 = 0) | ~ (all_67_3_219 = 0) | ~ (all_67_4_220 = 0) | all_67_0_216 = all_0_11_11
% 279.13/221.45 | (322) sdtpldt0(xn, all_67_1_217) = all_67_0_216
% 279.13/221.45 |
% 279.13/221.45 | Instantiating (135) with all_69_0_221, all_69_1_222, all_69_2_223 yields:
% 279.13/221.45 | (323) aNaturalNumber0(all_0_8_8) = all_69_0_221 & aNaturalNumber0(xr) = all_69_2_223 & aNaturalNumber0(xm) = all_69_1_222 & ( ~ (all_69_1_222 = 0) | ~ (all_69_2_223 = 0) | all_69_0_221 = 0)
% 279.13/221.45 |
% 279.13/221.45 | Applying alpha-rule on (323) yields:
% 279.13/221.45 | (324) aNaturalNumber0(all_0_8_8) = all_69_0_221
% 279.13/221.45 | (325) aNaturalNumber0(xr) = all_69_2_223
% 279.13/221.45 | (326) aNaturalNumber0(xm) = all_69_1_222
% 279.13/221.45 | (327) ~ (all_69_1_222 = 0) | ~ (all_69_2_223 = 0) | all_69_0_221 = 0
% 279.13/221.45 |
% 279.13/221.45 | Instantiating (134) with all_73_0_230, all_73_1_231, all_73_2_232 yields:
% 279.13/221.45 | (328) sdtpldt0(xm, xr) = all_73_0_230 & aNaturalNumber0(xr) = all_73_2_232 & aNaturalNumber0(xm) = all_73_1_231 & ( ~ (all_73_1_231 = 0) | ~ (all_73_2_232 = 0) | all_73_0_230 = all_0_8_8)
% 279.13/221.45 |
% 279.13/221.45 | Applying alpha-rule on (328) yields:
% 279.13/221.45 | (329) sdtpldt0(xm, xr) = all_73_0_230
% 279.13/221.45 | (330) aNaturalNumber0(xr) = all_73_2_232
% 279.13/221.45 | (331) aNaturalNumber0(xm) = all_73_1_231
% 279.13/221.45 | (332) ~ (all_73_1_231 = 0) | ~ (all_73_2_232 = 0) | all_73_0_230 = all_0_8_8
% 279.13/221.45 |
% 279.13/221.45 | Instantiating (133) with all_75_0_233, all_75_1_234, all_75_2_235, all_75_3_236, all_75_4_237 yields:
% 279.13/221.45 | (333) sdtpldt0(xr, all_75_1_234) = all_75_0_233 & sdtpldt0(xm, xp) = all_75_1_234 & aNaturalNumber0(xr) = all_75_4_237 & aNaturalNumber0(xp) = all_75_2_235 & aNaturalNumber0(xm) = all_75_3_236 & ( ~ (all_75_2_235 = 0) | ~ (all_75_3_236 = 0) | ~ (all_75_4_237 = 0) | all_75_0_233 = all_0_7_7)
% 279.13/221.45 |
% 279.13/221.45 | Applying alpha-rule on (333) yields:
% 279.13/221.45 | (334) aNaturalNumber0(xr) = all_75_4_237
% 279.13/221.45 | (335) aNaturalNumber0(xp) = all_75_2_235
% 279.13/221.45 | (336) aNaturalNumber0(xm) = all_75_3_236
% 279.13/221.45 | (337) sdtpldt0(xm, xp) = all_75_1_234
% 279.13/221.46 | (338) sdtpldt0(xr, all_75_1_234) = all_75_0_233
% 279.13/221.46 | (339) ~ (all_75_2_235 = 0) | ~ (all_75_3_236 = 0) | ~ (all_75_4_237 = 0) | all_75_0_233 = all_0_7_7
% 279.13/221.46 |
% 279.13/221.46 | Instantiating (132) with all_77_0_238, all_77_1_239, all_77_2_240 yields:
% 279.13/221.46 | (340) sdtpldt0(all_0_2_2, xr) = all_77_0_238 & aNaturalNumber0(all_0_2_2) = all_77_1_239 & aNaturalNumber0(xr) = all_77_2_240 & ( ~ (all_77_1_239 = 0) | ~ (all_77_2_240 = 0) | all_77_0_238 = xn)
% 279.13/221.46 |
% 279.13/221.46 | Applying alpha-rule on (340) yields:
% 279.13/221.46 | (341) sdtpldt0(all_0_2_2, xr) = all_77_0_238
% 279.13/221.46 | (342) aNaturalNumber0(all_0_2_2) = all_77_1_239
% 279.13/221.46 | (343) aNaturalNumber0(xr) = all_77_2_240
% 279.13/221.46 | (344) ~ (all_77_1_239 = 0) | ~ (all_77_2_240 = 0) | all_77_0_238 = xn
% 279.13/221.46 |
% 279.13/221.46 +-Applying beta-rule and splitting (100), into two cases.
% 279.13/221.46 |-Branch one:
% 279.13/221.46 | (345) all_0_6_6 = 0
% 279.13/221.46 |
% 279.13/221.46 | Equations (345) can reduce 30 to:
% 279.13/221.46 | (346) $false
% 279.13/221.46 |
% 279.13/221.46 |-The branch is then unsatisfiable
% 279.13/221.46 |-Branch two:
% 279.13/221.46 | (30) ~ (all_0_6_6 = 0)
% 279.13/221.46 | (348) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_9_9, xr) = v3 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 279.13/221.46 |
% 279.13/221.46 | Instantiating (348) with all_83_0_241, all_83_1_242, all_83_2_243, all_83_3_244 yields:
% 279.13/221.46 | (349) doDivides0(all_0_9_9, xr) = all_83_0_241 & aNaturalNumber0(all_0_9_9) = all_83_2_243 & aNaturalNumber0(xr) = all_83_1_242 & aNaturalNumber0(xp) = all_83_3_244 & ( ~ (all_83_0_241 = 0) | ~ (all_83_1_242 = 0) | ~ (all_83_2_243 = 0) | ~ (all_83_3_244 = 0))
% 279.13/221.46 |
% 279.13/221.46 | Applying alpha-rule on (349) yields:
% 279.13/221.46 | (350) aNaturalNumber0(all_0_9_9) = all_83_2_243
% 279.13/221.46 | (351) ~ (all_83_0_241 = 0) | ~ (all_83_1_242 = 0) | ~ (all_83_2_243 = 0) | ~ (all_83_3_244 = 0)
% 279.13/221.46 | (352) aNaturalNumber0(xr) = all_83_1_242
% 279.13/221.46 | (353) aNaturalNumber0(xp) = all_83_3_244
% 279.13/221.46 | (354) doDivides0(all_0_9_9, xr) = all_83_0_241
% 279.13/221.46 |
% 279.13/221.46 +-Applying beta-rule and splitting (101), into two cases.
% 279.13/221.46 |-Branch one:
% 279.13/221.46 | (345) all_0_6_6 = 0
% 279.13/221.46 |
% 279.13/221.46 | Equations (345) can reduce 30 to:
% 279.13/221.46 | (346) $false
% 279.13/221.46 |
% 279.13/221.46 |-The branch is then unsatisfiable
% 279.13/221.46 |-Branch two:
% 279.13/221.46 | (30) ~ (all_0_6_6 = 0)
% 279.13/221.46 | (358) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_10_10, xr) = v3 & aNaturalNumber0(all_0_10_10) = v1 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 279.13/221.46 |
% 279.13/221.46 | Instantiating (358) with all_88_0_245, all_88_1_246, all_88_2_247, all_88_3_248 yields:
% 279.13/221.46 | (359) doDivides0(all_0_10_10, xr) = all_88_0_245 & aNaturalNumber0(all_0_10_10) = all_88_2_247 & aNaturalNumber0(xr) = all_88_1_246 & aNaturalNumber0(xp) = all_88_3_248 & ( ~ (all_88_0_245 = 0) | ~ (all_88_1_246 = 0) | ~ (all_88_2_247 = 0) | ~ (all_88_3_248 = 0))
% 279.13/221.46 |
% 279.13/221.46 | Applying alpha-rule on (359) yields:
% 279.13/221.46 | (360) ~ (all_88_0_245 = 0) | ~ (all_88_1_246 = 0) | ~ (all_88_2_247 = 0) | ~ (all_88_3_248 = 0)
% 279.13/221.46 | (361) aNaturalNumber0(xp) = all_88_3_248
% 279.13/221.46 | (362) doDivides0(all_0_10_10, xr) = all_88_0_245
% 279.13/221.46 | (363) aNaturalNumber0(all_0_10_10) = all_88_2_247
% 279.13/221.46 | (364) aNaturalNumber0(xr) = all_88_1_246
% 279.13/221.46 |
% 279.13/221.46 +-Applying beta-rule and splitting (102), into two cases.
% 279.13/221.46 |-Branch one:
% 279.13/221.46 | (365) all_0_5_5 = 0
% 279.13/221.46 |
% 279.13/221.46 | Equations (365) can reduce 9 to:
% 279.13/221.46 | (346) $false
% 279.13/221.46 |
% 279.13/221.46 |-The branch is then unsatisfiable
% 279.13/221.46 |-Branch two:
% 279.13/221.46 | (9) ~ (all_0_5_5 = 0)
% 279.13/221.46 | (368) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_9_9, xm) = v3 & aNaturalNumber0(all_0_9_9) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 279.13/221.46 |
% 279.13/221.46 | Instantiating (368) with all_93_0_249, all_93_1_250, all_93_2_251, all_93_3_252 yields:
% 279.13/221.46 | (369) doDivides0(all_0_9_9, xm) = all_93_0_249 & aNaturalNumber0(all_0_9_9) = all_93_2_251 & aNaturalNumber0(xp) = all_93_3_252 & aNaturalNumber0(xm) = all_93_1_250 & ( ~ (all_93_0_249 = 0) | ~ (all_93_1_250 = 0) | ~ (all_93_2_251 = 0) | ~ (all_93_3_252 = 0))
% 279.13/221.46 |
% 279.13/221.46 | Applying alpha-rule on (369) yields:
% 279.13/221.46 | (370) doDivides0(all_0_9_9, xm) = all_93_0_249
% 279.13/221.46 | (371) aNaturalNumber0(xm) = all_93_1_250
% 279.13/221.46 | (372) ~ (all_93_0_249 = 0) | ~ (all_93_1_250 = 0) | ~ (all_93_2_251 = 0) | ~ (all_93_3_252 = 0)
% 279.13/221.46 | (373) aNaturalNumber0(xp) = all_93_3_252
% 279.13/221.46 | (374) aNaturalNumber0(all_0_9_9) = all_93_2_251
% 279.13/221.46 |
% 279.13/221.46 +-Applying beta-rule and splitting (103), into two cases.
% 279.13/221.46 |-Branch one:
% 279.13/221.46 | (365) all_0_5_5 = 0
% 279.13/221.46 |
% 279.13/221.46 | Equations (365) can reduce 9 to:
% 279.13/221.46 | (346) $false
% 279.13/221.46 |
% 279.13/221.46 |-The branch is then unsatisfiable
% 279.13/221.46 |-Branch two:
% 279.13/221.46 | (9) ~ (all_0_5_5 = 0)
% 279.13/221.46 | (378) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (doDivides0(all_0_10_10, xm) = v3 & aNaturalNumber0(all_0_10_10) = v1 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 279.13/221.46 |
% 279.13/221.46 | Instantiating (378) with all_98_0_253, all_98_1_254, all_98_2_255, all_98_3_256 yields:
% 279.13/221.46 | (379) doDivides0(all_0_10_10, xm) = all_98_0_253 & aNaturalNumber0(all_0_10_10) = all_98_2_255 & aNaturalNumber0(xp) = all_98_3_256 & aNaturalNumber0(xm) = all_98_1_254 & ( ~ (all_98_0_253 = 0) | ~ (all_98_1_254 = 0) | ~ (all_98_2_255 = 0) | ~ (all_98_3_256 = 0))
% 279.13/221.46 |
% 279.13/221.46 | Applying alpha-rule on (379) yields:
% 279.13/221.46 | (380) doDivides0(all_0_10_10, xm) = all_98_0_253
% 279.13/221.46 | (381) aNaturalNumber0(xm) = all_98_1_254
% 279.13/221.46 | (382) aNaturalNumber0(xp) = all_98_3_256
% 279.13/221.46 | (383) ~ (all_98_0_253 = 0) | ~ (all_98_1_254 = 0) | ~ (all_98_2_255 = 0) | ~ (all_98_3_256 = 0)
% 279.13/221.46 | (384) aNaturalNumber0(all_0_10_10) = all_98_2_255
% 279.13/221.46 |
% 279.13/221.46 +-Applying beta-rule and splitting (104), into two cases.
% 279.13/221.46 |-Branch one:
% 279.13/221.46 | (385) all_0_7_7 = all_0_11_11
% 279.13/221.46 |
% 279.13/221.46 | Equations (385) can reduce 7 to:
% 279.13/221.46 | (346) $false
% 279.13/221.46 |
% 279.13/221.46 |-The branch is then unsatisfiable
% 279.13/221.46 |-Branch two:
% 279.13/221.46 | (7) ~ (all_0_7_7 = all_0_11_11)
% 279.13/221.46 | (388) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_0_11_11, all_0_7_7) = v2 & aNaturalNumber0(all_0_7_7) = v0 & aNaturalNumber0(all_0_11_11) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 279.13/221.46 |
% 279.13/221.46 | Instantiating (388) with all_103_0_257, all_103_1_258, all_103_2_259 yields:
% 279.13/221.46 | (389) sdtlseqdt0(all_0_11_11, all_0_7_7) = all_103_0_257 & aNaturalNumber0(all_0_7_7) = all_103_2_259 & aNaturalNumber0(all_0_11_11) = all_103_1_258 & ( ~ (all_103_0_257 = 0) | ~ (all_103_1_258 = 0) | ~ (all_103_2_259 = 0))
% 279.13/221.46 |
% 279.13/221.46 | Applying alpha-rule on (389) yields:
% 279.13/221.46 | (390) sdtlseqdt0(all_0_11_11, all_0_7_7) = all_103_0_257
% 279.13/221.46 | (391) aNaturalNumber0(all_0_7_7) = all_103_2_259
% 279.13/221.46 | (392) aNaturalNumber0(all_0_11_11) = all_103_1_258
% 279.13/221.46 | (393) ~ (all_103_0_257 = 0) | ~ (all_103_1_258 = 0) | ~ (all_103_2_259 = 0)
% 279.13/221.46 |
% 279.13/221.46 +-Applying beta-rule and splitting (106), into two cases.
% 279.13/221.46 |-Branch one:
% 279.13/221.46 | (394) xr = xn
% 279.13/221.46 |
% 279.13/221.46 | Equations (394) can reduce 91 to:
% 279.13/221.46 | (346) $false
% 279.13/221.46 |
% 279.13/221.46 |-The branch is then unsatisfiable
% 279.13/221.46 |-Branch two:
% 279.13/221.46 | (91) ~ (xr = xn)
% 279.13/221.46 | (397) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xn, xr) = v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 279.13/221.46 |
% 279.13/221.46 | Instantiating (397) with all_108_0_260, all_108_1_261, all_108_2_262 yields:
% 279.13/221.46 | (398) sdtlseqdt0(xn, xr) = all_108_0_260 & aNaturalNumber0(xr) = all_108_2_262 & aNaturalNumber0(xn) = all_108_1_261 & ( ~ (all_108_0_260 = 0) | ~ (all_108_1_261 = 0) | ~ (all_108_2_262 = 0))
% 279.13/221.46 |
% 279.13/221.46 | Applying alpha-rule on (398) yields:
% 279.13/221.46 | (399) sdtlseqdt0(xn, xr) = all_108_0_260
% 279.13/221.46 | (400) aNaturalNumber0(xr) = all_108_2_262
% 279.13/221.46 | (401) aNaturalNumber0(xn) = all_108_1_261
% 279.13/221.46 | (402) ~ (all_108_0_260 = 0) | ~ (all_108_1_261 = 0) | ~ (all_108_2_262 = 0)
% 279.13/221.46 |
% 279.13/221.46 +-Applying beta-rule and splitting (148), into two cases.
% 279.13/221.46 |-Branch one:
% 279.13/221.46 | (403) xp = sz00
% 279.13/221.46 |
% 279.13/221.46 | Equations (403) can reduce 33 to:
% 279.13/221.46 | (346) $false
% 279.13/221.46 |
% 279.13/221.46 |-The branch is then unsatisfiable
% 279.13/221.46 |-Branch two:
% 279.13/221.46 | (33) ~ (xp = sz00)
% 279.13/221.46 | (406) xp = sz10 | ? [v0] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0)
% 279.13/221.46 |
% 279.13/221.46 | Instantiating formula (3) with xp, all_50_11_183, 0 and discharging atoms isPrime0(xp) = all_50_11_183, isPrime0(xp) = 0, yields:
% 279.13/221.47 | (407) all_50_11_183 = 0
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (67) with xp, xr, all_50_7_179, all_0_6_6 and discharging atoms doDivides0(xp, xr) = all_50_7_179, doDivides0(xp, xr) = all_0_6_6, yields:
% 279.13/221.47 | (408) all_50_7_179 = all_0_6_6
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (67) with xp, xm, all_50_6_178, all_0_5_5 and discharging atoms doDivides0(xp, xm) = all_50_6_178, doDivides0(xp, xm) = all_0_5_5, yields:
% 279.13/221.47 | (409) all_50_6_178 = all_0_5_5
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (67) with xp, xm, all_19_6_51, all_50_6_178 and discharging atoms doDivides0(xp, xm) = all_50_6_178, doDivides0(xp, xm) = all_19_6_51, yields:
% 279.13/221.47 | (410) all_50_6_178 = all_19_6_51
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (39) with all_0_8_8, xp, all_50_9_181, all_0_7_7 and discharging atoms sdtpldt0(all_0_8_8, xp) = all_0_7_7, yields:
% 279.13/221.47 | (411) all_50_9_181 = all_0_7_7 | ~ (sdtpldt0(all_0_8_8, xp) = all_50_9_181)
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (39) with xr, xm, all_50_10_182, all_0_8_8 and discharging atoms sdtpldt0(xr, xm) = all_50_10_182, sdtpldt0(xr, xm) = all_0_8_8, yields:
% 279.13/221.47 | (412) all_50_10_182 = all_0_8_8
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (39) with xr, xm, all_50_10_182, all_28_1_97 and discharging atoms sdtpldt0(xr, xm) = all_50_10_182, yields:
% 279.13/221.47 | (413) all_50_10_182 = all_28_1_97 | ~ (sdtpldt0(xr, xm) = all_28_1_97)
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (39) with xr, xm, all_10_1_17, all_50_10_182 and discharging atoms sdtpldt0(xr, xm) = all_50_10_182, sdtpldt0(xr, xm) = all_10_1_17, yields:
% 279.13/221.47 | (414) all_50_10_182 = all_10_1_17
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (39) with xp, all_0_8_8, all_34_0_107, all_10_0_16 and discharging atoms sdtpldt0(xp, all_0_8_8) = all_34_0_107, yields:
% 279.13/221.47 | (415) all_34_0_107 = all_10_0_16 | ~ (sdtpldt0(xp, all_0_8_8) = all_10_0_16)
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (39) with xm, xp, all_67_1_217, all_75_1_234 and discharging atoms sdtpldt0(xm, xp) = all_75_1_234, sdtpldt0(xm, xp) = all_67_1_217, yields:
% 279.13/221.47 | (416) all_75_1_234 = all_67_1_217
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (39) with xn, xm, all_19_10_55, all_0_12_12 and discharging atoms sdtpldt0(xn, xm) = all_19_10_55, sdtpldt0(xn, xm) = all_0_12_12, yields:
% 279.13/221.47 | (417) all_19_10_55 = all_0_12_12
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (39) with xn, xm, all_19_10_55, all_67_0_216 and discharging atoms sdtpldt0(xn, xm) = all_19_10_55, yields:
% 279.13/221.47 | (418) all_67_0_216 = all_19_10_55 | ~ (sdtpldt0(xn, xm) = all_67_0_216)
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_0_0, all_48_13_170, 0 and discharging atoms aNaturalNumber0(all_0_0_0) = all_48_13_170, aNaturalNumber0(all_0_0_0) = 0, yields:
% 279.13/221.47 | (419) all_48_13_170 = 0
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_0_0, all_26_1_94, all_48_13_170 and discharging atoms aNaturalNumber0(all_0_0_0) = all_48_13_170, aNaturalNumber0(all_0_0_0) = all_26_1_94, yields:
% 279.13/221.47 | (420) all_48_13_170 = all_26_1_94
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_0_0, all_23_1_76, all_48_13_170 and discharging atoms aNaturalNumber0(all_0_0_0) = all_48_13_170, aNaturalNumber0(all_0_0_0) = all_23_1_76, yields:
% 279.13/221.47 | (421) all_48_13_170 = all_23_1_76
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_1_1, all_61_1_206, 0 and discharging atoms aNaturalNumber0(all_0_1_1) = all_61_1_206, aNaturalNumber0(all_0_1_1) = 0, yields:
% 279.13/221.47 | (422) all_61_1_206 = 0
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_1_1, all_28_3_99, all_61_1_206 and discharging atoms aNaturalNumber0(all_0_1_1) = all_61_1_206, aNaturalNumber0(all_0_1_1) = all_28_3_99, yields:
% 279.13/221.47 | (423) all_61_1_206 = all_28_3_99
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_2_2, all_77_1_239, 0 and discharging atoms aNaturalNumber0(all_0_2_2) = all_77_1_239, aNaturalNumber0(all_0_2_2) = 0, yields:
% 279.13/221.47 | (424) all_77_1_239 = 0
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_2_2, all_63_3_211, all_77_1_239 and discharging atoms aNaturalNumber0(all_0_2_2) = all_77_1_239, aNaturalNumber0(all_0_2_2) = all_63_3_211, yields:
% 279.13/221.47 | (425) all_77_1_239 = all_63_3_211
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_3_3, all_21_13_73, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_21_13_73, aNaturalNumber0(all_0_3_3) = 0, yields:
% 279.13/221.47 | (426) all_21_13_73 = 0
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_3_3, all_21_13_73, all_45_1_140 and discharging atoms aNaturalNumber0(all_0_3_3) = all_45_1_140, aNaturalNumber0(all_0_3_3) = all_21_13_73, yields:
% 279.13/221.47 | (427) all_45_1_140 = all_21_13_73
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_3_3, all_17_1_43, all_45_1_140 and discharging atoms aNaturalNumber0(all_0_3_3) = all_45_1_140, aNaturalNumber0(all_0_3_3) = all_17_1_43, yields:
% 279.13/221.47 | (428) all_45_1_140 = all_17_1_43
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_4_4, all_43_1_137, 0 and discharging atoms aNaturalNumber0(all_0_4_4) = all_43_1_137, aNaturalNumber0(all_0_4_4) = 0, yields:
% 279.13/221.47 | (429) all_43_1_137 = 0
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_4_4, all_41_1_134, all_43_1_137 and discharging atoms aNaturalNumber0(all_0_4_4) = all_43_1_137, aNaturalNumber0(all_0_4_4) = all_41_1_134, yields:
% 279.13/221.47 | (430) all_43_1_137 = all_41_1_134
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_4_4, all_36_2_112, all_43_1_137 and discharging atoms aNaturalNumber0(all_0_4_4) = all_43_1_137, aNaturalNumber0(all_0_4_4) = all_36_2_112, yields:
% 279.13/221.47 | (431) all_43_1_137 = all_36_2_112
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_7_7, all_43_2_138, all_103_2_259 and discharging atoms aNaturalNumber0(all_0_7_7) = all_103_2_259, aNaturalNumber0(all_0_7_7) = all_43_2_138, yields:
% 279.13/221.47 | (432) all_103_2_259 = all_43_2_138
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_7_7, all_41_2_135, all_103_2_259 and discharging atoms aNaturalNumber0(all_0_7_7) = all_103_2_259, aNaturalNumber0(all_0_7_7) = all_41_2_135, yields:
% 279.13/221.47 | (433) all_103_2_259 = all_41_2_135
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_7_7, all_32_0_104, all_103_2_259 and discharging atoms aNaturalNumber0(all_0_7_7) = all_103_2_259, aNaturalNumber0(all_0_7_7) = all_32_0_104, yields:
% 279.13/221.47 | (434) all_103_2_259 = all_32_0_104
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_8_8, all_36_4_114, all_69_0_221 and discharging atoms aNaturalNumber0(all_0_8_8) = all_69_0_221, aNaturalNumber0(all_0_8_8) = all_36_4_114, yields:
% 279.13/221.47 | (435) all_69_0_221 = all_36_4_114
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_8_8, all_34_2_109, all_36_4_114 and discharging atoms aNaturalNumber0(all_0_8_8) = all_36_4_114, aNaturalNumber0(all_0_8_8) = all_34_2_109, yields:
% 279.13/221.47 | (436) all_36_4_114 = all_34_2_109
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_8_8, all_32_2_106, all_69_0_221 and discharging atoms aNaturalNumber0(all_0_8_8) = all_69_0_221, aNaturalNumber0(all_0_8_8) = all_32_2_106, yields:
% 279.13/221.47 | (437) all_69_0_221 = all_32_2_106
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_11_11, all_41_0_133, all_103_1_258 and discharging atoms aNaturalNumber0(all_0_11_11) = all_103_1_258, aNaturalNumber0(all_0_11_11) = all_41_0_133, yields:
% 279.13/221.47 | (438) all_103_1_258 = all_41_0_133
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with all_0_11_11, all_12_0_21, all_103_1_258 and discharging atoms aNaturalNumber0(all_0_11_11) = all_103_1_258, aNaturalNumber0(all_0_11_11) = all_12_0_21, yields:
% 279.13/221.47 | (439) all_103_1_258 = all_12_0_21
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xr, all_83_1_242, all_108_2_262 and discharging atoms aNaturalNumber0(xr) = all_108_2_262, aNaturalNumber0(xr) = all_83_1_242, yields:
% 279.13/221.47 | (440) all_108_2_262 = all_83_1_242
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xr, all_75_4_237, all_77_2_240 and discharging atoms aNaturalNumber0(xr) = all_77_2_240, aNaturalNumber0(xr) = all_75_4_237, yields:
% 279.13/221.47 | (441) all_77_2_240 = all_75_4_237
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xr, all_73_2_232, all_88_1_246 and discharging atoms aNaturalNumber0(xr) = all_88_1_246, aNaturalNumber0(xr) = all_73_2_232, yields:
% 279.13/221.47 | (442) all_88_1_246 = all_73_2_232
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xr, all_69_2_223, 0 and discharging atoms aNaturalNumber0(xr) = all_69_2_223, aNaturalNumber0(xr) = 0, yields:
% 279.13/221.47 | (443) all_69_2_223 = 0
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xr, all_69_2_223, all_83_1_242 and discharging atoms aNaturalNumber0(xr) = all_83_1_242, aNaturalNumber0(xr) = all_69_2_223, yields:
% 279.13/221.47 | (444) all_83_1_242 = all_69_2_223
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xr, all_69_2_223, all_75_4_237 and discharging atoms aNaturalNumber0(xr) = all_75_4_237, aNaturalNumber0(xr) = all_69_2_223, yields:
% 279.13/221.47 | (445) all_75_4_237 = all_69_2_223
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xr, all_69_2_223, all_73_2_232 and discharging atoms aNaturalNumber0(xr) = all_73_2_232, aNaturalNumber0(xr) = all_69_2_223, yields:
% 279.13/221.47 | (446) all_73_2_232 = all_69_2_223
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xr, all_65_1_214, all_108_2_262 and discharging atoms aNaturalNumber0(xr) = all_108_2_262, aNaturalNumber0(xr) = all_65_1_214, yields:
% 279.13/221.47 | (447) all_108_2_262 = all_65_1_214
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xr, all_63_4_212, all_88_1_246 and discharging atoms aNaturalNumber0(xr) = all_88_1_246, aNaturalNumber0(xr) = all_63_4_212, yields:
% 279.13/221.47 | (448) all_88_1_246 = all_63_4_212
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xr, all_54_2_192, all_77_2_240 and discharging atoms aNaturalNumber0(xr) = all_77_2_240, aNaturalNumber0(xr) = all_54_2_192, yields:
% 279.13/221.47 | (449) all_77_2_240 = all_54_2_192
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xr, all_52_2_189, all_75_4_237 and discharging atoms aNaturalNumber0(xr) = all_75_4_237, aNaturalNumber0(xr) = all_52_2_189, yields:
% 279.13/221.47 | (450) all_75_4_237 = all_52_2_189
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xr, all_50_14_186, all_52_2_189 and discharging atoms aNaturalNumber0(xr) = all_52_2_189, aNaturalNumber0(xr) = all_50_14_186, yields:
% 279.13/221.47 | (451) all_52_2_189 = all_50_14_186
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xr, all_10_3_19, all_50_14_186 and discharging atoms aNaturalNumber0(xr) = all_50_14_186, aNaturalNumber0(xr) = all_10_3_19, yields:
% 279.13/221.47 | (452) all_50_14_186 = all_10_3_19
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xp, all_88_3_248, all_98_3_256 and discharging atoms aNaturalNumber0(xp) = all_98_3_256, aNaturalNumber0(xp) = all_88_3_248, yields:
% 279.13/221.47 | (453) all_98_3_256 = all_88_3_248
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xp, all_83_3_244, all_93_3_252 and discharging atoms aNaturalNumber0(xp) = all_93_3_252, aNaturalNumber0(xp) = all_83_3_244, yields:
% 279.13/221.47 | (454) all_93_3_252 = all_83_3_244
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xp, all_67_2_218, all_75_2_235 and discharging atoms aNaturalNumber0(xp) = all_75_2_235, aNaturalNumber0(xp) = all_67_2_218, yields:
% 279.13/221.47 | (455) all_75_2_235 = all_67_2_218
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xp, all_65_2_215, all_67_2_218 and discharging atoms aNaturalNumber0(xp) = all_67_2_218, aNaturalNumber0(xp) = all_65_2_215, yields:
% 279.13/221.47 | (456) all_67_2_218 = all_65_2_215
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xp, all_61_2_207, all_65_2_215 and discharging atoms aNaturalNumber0(xp) = all_65_2_215, aNaturalNumber0(xp) = all_61_2_207, yields:
% 279.13/221.47 | (457) all_65_2_215 = all_61_2_207
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xp, all_50_12_184, all_88_3_248 and discharging atoms aNaturalNumber0(xp) = all_88_3_248, aNaturalNumber0(xp) = all_50_12_184, yields:
% 279.13/221.47 | (458) all_88_3_248 = all_50_12_184
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xp, all_48_14_171, all_48_12_169 and discharging atoms aNaturalNumber0(xp) = all_48_12_169, aNaturalNumber0(xp) = all_48_14_171, yields:
% 279.13/221.47 | (459) all_48_12_169 = all_48_14_171
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xp, all_45_2_141, all_83_3_244 and discharging atoms aNaturalNumber0(xp) = all_83_3_244, aNaturalNumber0(xp) = all_45_2_141, yields:
% 279.13/221.47 | (460) all_83_3_244 = all_45_2_141
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xp, all_36_3_113, all_50_12_184 and discharging atoms aNaturalNumber0(xp) = all_50_12_184, aNaturalNumber0(xp) = all_36_3_113, yields:
% 279.13/221.47 | (461) all_50_12_184 = all_36_3_113
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xp, all_34_1_108, all_48_14_171 and discharging atoms aNaturalNumber0(xp) = all_48_14_171, aNaturalNumber0(xp) = all_34_1_108, yields:
% 279.13/221.47 | (462) all_48_14_171 = all_34_1_108
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xp, all_34_1_108, all_45_2_141 and discharging atoms aNaturalNumber0(xp) = all_45_2_141, aNaturalNumber0(xp) = all_34_1_108, yields:
% 279.13/221.47 | (463) all_45_2_141 = all_34_1_108
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xp, all_32_1_105, all_61_2_207 and discharging atoms aNaturalNumber0(xp) = all_61_2_207, aNaturalNumber0(xp) = all_32_1_105, yields:
% 279.13/221.47 | (464) all_61_2_207 = all_32_1_105
% 279.13/221.47 |
% 279.13/221.47 | Instantiating formula (97) with xp, all_28_4_100, 0 and discharging atoms aNaturalNumber0(xp) = all_28_4_100, aNaturalNumber0(xp) = 0, yields:
% 279.13/221.48 | (465) all_28_4_100 = 0
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xp, all_26_2_95, all_48_12_169 and discharging atoms aNaturalNumber0(xp) = all_48_12_169, aNaturalNumber0(xp) = all_26_2_95, yields:
% 279.13/221.48 | (466) all_48_12_169 = all_26_2_95
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xp, all_23_2_77, all_36_3_113 and discharging atoms aNaturalNumber0(xp) = all_36_3_113, aNaturalNumber0(xp) = all_23_2_77, yields:
% 279.13/221.48 | (467) all_36_3_113 = all_23_2_77
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xp, all_21_12_72, all_28_4_100 and discharging atoms aNaturalNumber0(xp) = all_28_4_100, aNaturalNumber0(xp) = all_21_12_72, yields:
% 279.13/221.48 | (468) all_28_4_100 = all_21_12_72
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xp, all_21_12_72, all_23_2_77 and discharging atoms aNaturalNumber0(xp) = all_23_2_77, aNaturalNumber0(xp) = all_21_12_72, yields:
% 279.13/221.48 | (469) all_23_2_77 = all_21_12_72
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xp, all_21_14_74, all_48_14_171 and discharging atoms aNaturalNumber0(xp) = all_48_14_171, aNaturalNumber0(xp) = all_21_14_74, yields:
% 279.13/221.48 | (470) all_48_14_171 = all_21_14_74
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xp, all_21_14_74, all_21_12_72 and discharging atoms aNaturalNumber0(xp) = all_21_12_72, aNaturalNumber0(xp) = all_21_14_74, yields:
% 279.13/221.48 | (471) all_21_12_72 = all_21_14_74
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xp, all_19_12_57, all_98_3_256 and discharging atoms aNaturalNumber0(xp) = all_98_3_256, aNaturalNumber0(xp) = all_19_12_57, yields:
% 279.13/221.48 | (472) all_98_3_256 = all_19_12_57
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xp, all_17_2_44, all_32_1_105 and discharging atoms aNaturalNumber0(xp) = all_32_1_105, aNaturalNumber0(xp) = all_17_2_44, yields:
% 279.13/221.48 | (473) all_32_1_105 = all_17_2_44
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xp, all_17_2_44, all_28_4_100 and discharging atoms aNaturalNumber0(xp) = all_28_4_100, aNaturalNumber0(xp) = all_17_2_44, yields:
% 279.13/221.48 | (474) all_28_4_100 = all_17_2_44
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xp, all_14_1_25, all_28_4_100 and discharging atoms aNaturalNumber0(xp) = all_28_4_100, aNaturalNumber0(xp) = all_14_1_25, yields:
% 279.13/221.48 | (475) all_28_4_100 = all_14_1_25
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xp, all_12_1_22, all_75_2_235 and discharging atoms aNaturalNumber0(xp) = all_75_2_235, aNaturalNumber0(xp) = all_12_1_22, yields:
% 279.13/221.48 | (476) all_75_2_235 = all_12_1_22
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xp, all_10_4_20, all_93_3_252 and discharging atoms aNaturalNumber0(xp) = all_93_3_252, aNaturalNumber0(xp) = all_10_4_20, yields:
% 279.13/221.48 | (477) all_93_3_252 = all_10_4_20
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xm, all_93_1_250, all_98_1_254 and discharging atoms aNaturalNumber0(xm) = all_98_1_254, aNaturalNumber0(xm) = all_93_1_250, yields:
% 279.13/221.48 | (478) all_98_1_254 = all_93_1_250
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xm, all_75_3_236, all_93_1_250 and discharging atoms aNaturalNumber0(xm) = all_93_1_250, aNaturalNumber0(xm) = all_75_3_236, yields:
% 279.13/221.48 | (479) all_93_1_250 = all_75_3_236
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xm, all_69_1_222, 0 and discharging atoms aNaturalNumber0(xm) = all_69_1_222, aNaturalNumber0(xm) = 0, yields:
% 279.13/221.48 | (480) all_69_1_222 = 0
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xm, all_69_1_222, all_75_3_236 and discharging atoms aNaturalNumber0(xm) = all_75_3_236, aNaturalNumber0(xm) = all_69_1_222, yields:
% 279.13/221.48 | (481) all_75_3_236 = all_69_1_222
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xm, all_69_1_222, all_73_1_231 and discharging atoms aNaturalNumber0(xm) = all_73_1_231, aNaturalNumber0(xm) = all_69_1_222, yields:
% 279.13/221.48 | (482) all_73_1_231 = all_69_1_222
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xm, all_67_3_219, all_73_1_231 and discharging atoms aNaturalNumber0(xm) = all_73_1_231, aNaturalNumber0(xm) = all_67_3_219, yields:
% 279.13/221.48 | (483) all_73_1_231 = all_67_3_219
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xm, all_63_2_210, all_73_1_231 and discharging atoms aNaturalNumber0(xm) = all_73_1_231, aNaturalNumber0(xm) = all_63_2_210, yields:
% 279.13/221.48 | (484) all_73_1_231 = all_63_2_210
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xm, all_56_1_194, all_98_1_254 and discharging atoms aNaturalNumber0(xm) = all_98_1_254, aNaturalNumber0(xm) = all_56_1_194, yields:
% 279.13/221.48 | (485) all_98_1_254 = all_56_1_194
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xm, all_54_1_191, all_67_3_219 and discharging atoms aNaturalNumber0(xm) = all_67_3_219, aNaturalNumber0(xm) = all_54_1_191, yields:
% 279.13/221.48 | (486) all_67_3_219 = all_54_1_191
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xm, all_52_1_188, all_69_1_222 and discharging atoms aNaturalNumber0(xm) = all_69_1_222, aNaturalNumber0(xm) = all_52_1_188, yields:
% 279.13/221.48 | (487) all_69_1_222 = all_52_1_188
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xm, all_50_13_185, all_52_1_188 and discharging atoms aNaturalNumber0(xm) = all_52_1_188, aNaturalNumber0(xm) = all_50_13_185, yields:
% 279.13/221.48 | (488) all_52_1_188 = all_50_13_185
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xm, all_30_1_102, all_50_13_185 and discharging atoms aNaturalNumber0(xm) = all_50_13_185, aNaturalNumber0(xm) = all_30_1_102, yields:
% 279.13/221.48 | (489) all_50_13_185 = all_30_1_102
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xm, all_28_2_98, all_39_1_131 and discharging atoms aNaturalNumber0(xm) = all_39_1_131, aNaturalNumber0(xm) = all_28_2_98, yields:
% 279.13/221.48 | (490) all_39_1_131 = all_28_2_98
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xm, all_28_2_98, all_30_1_102 and discharging atoms aNaturalNumber0(xm) = all_30_1_102, aNaturalNumber0(xm) = all_28_2_98, yields:
% 279.13/221.48 | (491) all_30_1_102 = all_28_2_98
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xm, all_19_13_58, all_39_1_131 and discharging atoms aNaturalNumber0(xm) = all_39_1_131, aNaturalNumber0(xm) = all_19_13_58, yields:
% 279.13/221.48 | (492) all_39_1_131 = all_19_13_58
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xm, all_10_2_18, all_39_1_131 and discharging atoms aNaturalNumber0(xm) = all_39_1_131, aNaturalNumber0(xm) = all_10_2_18, yields:
% 279.13/221.48 | (493) all_39_1_131 = all_10_2_18
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xm, all_8_1_14, all_10_2_18 and discharging atoms aNaturalNumber0(xm) = all_10_2_18, aNaturalNumber0(xm) = all_8_1_14, yields:
% 279.13/221.48 | (494) all_10_2_18 = all_8_1_14
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xn, all_67_4_220, all_108_1_261 and discharging atoms aNaturalNumber0(xn) = all_108_1_261, aNaturalNumber0(xn) = all_67_4_220, yields:
% 279.13/221.48 | (495) all_108_1_261 = all_67_4_220
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xn, all_56_2_195, 0 and discharging atoms aNaturalNumber0(xn) = all_56_2_195, aNaturalNumber0(xn) = 0, yields:
% 279.13/221.48 | (496) all_56_2_195 = 0
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xn, all_39_2_132, all_67_4_220 and discharging atoms aNaturalNumber0(xn) = all_67_4_220, aNaturalNumber0(xn) = all_39_2_132, yields:
% 279.13/221.48 | (497) all_67_4_220 = all_39_2_132
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xn, all_30_2_103, all_56_2_195 and discharging atoms aNaturalNumber0(xn) = all_56_2_195, aNaturalNumber0(xn) = all_30_2_103, yields:
% 279.13/221.48 | (498) all_56_2_195 = all_30_2_103
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xn, all_19_14_59, all_56_2_195 and discharging atoms aNaturalNumber0(xn) = all_56_2_195, aNaturalNumber0(xn) = all_19_14_59, yields:
% 279.13/221.48 | (499) all_56_2_195 = all_19_14_59
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xn, all_19_14_59, all_39_2_132 and discharging atoms aNaturalNumber0(xn) = all_39_2_132, aNaturalNumber0(xn) = all_19_14_59, yields:
% 279.13/221.48 | (500) all_39_2_132 = all_19_14_59
% 279.13/221.48 |
% 279.13/221.48 | Instantiating formula (97) with xn, all_8_2_15, all_108_1_261 and discharging atoms aNaturalNumber0(xn) = all_108_1_261, aNaturalNumber0(xn) = all_8_2_15, yields:
% 279.13/221.48 | (501) all_108_1_261 = all_8_2_15
% 279.13/221.48 |
% 279.13/221.48 | Combining equations (495,501) yields a new equation:
% 279.13/221.48 | (502) all_67_4_220 = all_8_2_15
% 279.13/221.48 |
% 279.13/221.48 | Simplifying 502 yields:
% 279.13/221.48 | (503) all_67_4_220 = all_8_2_15
% 279.13/221.48 |
% 279.13/221.48 | Combining equations (440,447) yields a new equation:
% 279.13/221.48 | (504) all_83_1_242 = all_65_1_214
% 279.13/221.48 |
% 279.13/221.48 | Simplifying 504 yields:
% 279.13/221.48 | (505) all_83_1_242 = all_65_1_214
% 279.13/221.48 |
% 279.13/221.48 | Combining equations (438,439) yields a new equation:
% 279.13/221.48 | (506) all_41_0_133 = all_12_0_21
% 279.13/221.48 |
% 279.13/221.48 | Simplifying 506 yields:
% 279.13/221.48 | (507) all_41_0_133 = all_12_0_21
% 279.13/221.48 |
% 279.13/221.48 | Combining equations (434,432) yields a new equation:
% 279.13/221.48 | (508) all_43_2_138 = all_32_0_104
% 279.13/221.48 |
% 279.13/221.48 | Combining equations (433,432) yields a new equation:
% 279.13/221.48 | (509) all_43_2_138 = all_41_2_135
% 279.13/221.48 |
% 279.13/221.48 | Combining equations (478,485) yields a new equation:
% 279.13/221.48 | (510) all_93_1_250 = all_56_1_194
% 279.13/221.48 |
% 279.13/221.48 | Simplifying 510 yields:
% 279.13/221.48 | (511) all_93_1_250 = all_56_1_194
% 279.13/221.48 |
% 279.13/221.48 | Combining equations (453,472) yields a new equation:
% 279.13/221.48 | (512) all_88_3_248 = all_19_12_57
% 279.13/221.48 |
% 279.13/221.48 | Simplifying 512 yields:
% 279.13/221.48 | (513) all_88_3_248 = all_19_12_57
% 279.13/221.48 |
% 279.13/221.48 | Combining equations (479,511) yields a new equation:
% 279.13/221.48 | (514) all_75_3_236 = all_56_1_194
% 279.13/221.48 |
% 279.13/221.48 | Simplifying 514 yields:
% 279.13/221.48 | (515) all_75_3_236 = all_56_1_194
% 279.13/221.48 |
% 279.13/221.48 | Combining equations (454,477) yields a new equation:
% 279.13/221.48 | (516) all_83_3_244 = all_10_4_20
% 279.13/221.48 |
% 279.13/221.48 | Simplifying 516 yields:
% 279.13/221.48 | (517) all_83_3_244 = all_10_4_20
% 279.13/221.48 |
% 279.13/221.48 | Combining equations (442,448) yields a new equation:
% 279.13/221.48 | (518) all_73_2_232 = all_63_4_212
% 279.13/221.48 |
% 279.13/221.48 | Simplifying 518 yields:
% 279.13/221.48 | (519) all_73_2_232 = all_63_4_212
% 279.13/221.48 |
% 279.13/221.48 | Combining equations (458,513) yields a new equation:
% 279.13/221.48 | (520) all_50_12_184 = all_19_12_57
% 279.13/221.48 |
% 279.13/221.48 | Simplifying 520 yields:
% 279.13/221.48 | (521) all_50_12_184 = all_19_12_57
% 279.13/221.48 |
% 279.13/221.48 | Combining equations (444,505) yields a new equation:
% 279.13/221.48 | (522) all_69_2_223 = all_65_1_214
% 279.13/221.48 |
% 279.13/221.48 | Simplifying 522 yields:
% 279.13/221.48 | (523) all_69_2_223 = all_65_1_214
% 279.13/221.48 |
% 279.13/221.48 | Combining equations (460,517) yields a new equation:
% 279.13/221.48 | (524) all_45_2_141 = all_10_4_20
% 279.13/221.48 |
% 279.13/221.48 | Simplifying 524 yields:
% 279.13/221.48 | (525) all_45_2_141 = all_10_4_20
% 279.13/221.48 |
% 279.13/221.48 | Combining equations (424,425) yields a new equation:
% 279.13/221.48 | (526) all_63_3_211 = 0
% 279.13/221.48 |
% 279.13/221.48 | Combining equations (441,449) yields a new equation:
% 279.13/221.48 | (527) all_75_4_237 = all_54_2_192
% 279.13/221.48 |
% 279.13/221.48 | Simplifying 527 yields:
% 279.13/221.48 | (528) all_75_4_237 = all_54_2_192
% 279.13/221.48 |
% 279.13/221.48 | Combining equations (455,476) yields a new equation:
% 279.13/221.48 | (529) all_67_2_218 = all_12_1_22
% 279.13/221.49 |
% 279.13/221.49 | Simplifying 529 yields:
% 279.13/221.49 | (530) all_67_2_218 = all_12_1_22
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (481,515) yields a new equation:
% 279.13/221.49 | (531) all_69_1_222 = all_56_1_194
% 279.13/221.49 |
% 279.13/221.49 | Simplifying 531 yields:
% 279.13/221.49 | (532) all_69_1_222 = all_56_1_194
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (450,528) yields a new equation:
% 279.13/221.49 | (533) all_54_2_192 = all_52_2_189
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (445,528) yields a new equation:
% 279.13/221.49 | (534) all_69_2_223 = all_54_2_192
% 279.13/221.49 |
% 279.13/221.49 | Simplifying 534 yields:
% 279.13/221.49 | (535) all_69_2_223 = all_54_2_192
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (483,484) yields a new equation:
% 279.13/221.49 | (536) all_67_3_219 = all_63_2_210
% 279.13/221.49 |
% 279.13/221.49 | Simplifying 536 yields:
% 279.13/221.49 | (537) all_67_3_219 = all_63_2_210
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (482,484) yields a new equation:
% 279.13/221.49 | (538) all_69_1_222 = all_63_2_210
% 279.13/221.49 |
% 279.13/221.49 | Simplifying 538 yields:
% 279.13/221.49 | (539) all_69_1_222 = all_63_2_210
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (446,519) yields a new equation:
% 279.13/221.49 | (540) all_69_2_223 = all_63_4_212
% 279.13/221.49 |
% 279.13/221.49 | Simplifying 540 yields:
% 279.13/221.49 | (541) all_69_2_223 = all_63_4_212
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (435,437) yields a new equation:
% 279.13/221.49 | (542) all_36_4_114 = all_32_2_106
% 279.13/221.49 |
% 279.13/221.49 | Simplifying 542 yields:
% 279.13/221.49 | (543) all_36_4_114 = all_32_2_106
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (480,532) yields a new equation:
% 279.13/221.49 | (544) all_56_1_194 = 0
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (539,532) yields a new equation:
% 279.13/221.49 | (545) all_63_2_210 = all_56_1_194
% 279.13/221.49 |
% 279.13/221.49 | Simplifying 545 yields:
% 279.13/221.49 | (546) all_63_2_210 = all_56_1_194
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (487,532) yields a new equation:
% 279.13/221.49 | (547) all_56_1_194 = all_52_1_188
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (535,523) yields a new equation:
% 279.13/221.49 | (548) all_65_1_214 = all_54_2_192
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (443,523) yields a new equation:
% 279.13/221.49 | (549) all_65_1_214 = 0
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (541,523) yields a new equation:
% 279.13/221.49 | (550) all_65_1_214 = all_63_4_212
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (456,530) yields a new equation:
% 279.13/221.49 | (551) all_65_2_215 = all_12_1_22
% 279.13/221.49 |
% 279.13/221.49 | Simplifying 551 yields:
% 279.13/221.49 | (552) all_65_2_215 = all_12_1_22
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (537,486) yields a new equation:
% 279.13/221.49 | (553) all_63_2_210 = all_54_1_191
% 279.13/221.49 |
% 279.13/221.49 | Simplifying 553 yields:
% 279.13/221.49 | (554) all_63_2_210 = all_54_1_191
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (497,503) yields a new equation:
% 279.13/221.49 | (555) all_39_2_132 = all_8_2_15
% 279.13/221.49 |
% 279.13/221.49 | Simplifying 555 yields:
% 279.13/221.49 | (556) all_39_2_132 = all_8_2_15
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (548,550) yields a new equation:
% 279.13/221.49 | (557) all_63_4_212 = all_54_2_192
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (549,550) yields a new equation:
% 279.13/221.49 | (558) all_63_4_212 = 0
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (457,552) yields a new equation:
% 279.13/221.49 | (559) all_61_2_207 = all_12_1_22
% 279.13/221.49 |
% 279.13/221.49 | Simplifying 559 yields:
% 279.13/221.49 | (560) all_61_2_207 = all_12_1_22
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (546,554) yields a new equation:
% 279.13/221.49 | (561) all_56_1_194 = all_54_1_191
% 279.13/221.49 |
% 279.13/221.49 | Simplifying 561 yields:
% 279.13/221.49 | (562) all_56_1_194 = all_54_1_191
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (557,558) yields a new equation:
% 279.13/221.49 | (563) all_54_2_192 = 0
% 279.13/221.49 |
% 279.13/221.49 | Simplifying 563 yields:
% 279.13/221.49 | (564) all_54_2_192 = 0
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (422,423) yields a new equation:
% 279.13/221.49 | (565) all_28_3_99 = 0
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (464,560) yields a new equation:
% 279.13/221.49 | (566) all_32_1_105 = all_12_1_22
% 279.13/221.49 |
% 279.13/221.49 | Simplifying 566 yields:
% 279.13/221.49 | (567) all_32_1_105 = all_12_1_22
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (544,562) yields a new equation:
% 279.13/221.49 | (568) all_54_1_191 = 0
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (547,562) yields a new equation:
% 279.13/221.49 | (569) all_54_1_191 = all_52_1_188
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (499,498) yields a new equation:
% 279.13/221.49 | (570) all_30_2_103 = all_19_14_59
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (496,498) yields a new equation:
% 279.13/221.49 | (571) all_30_2_103 = 0
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (569,568) yields a new equation:
% 279.13/221.49 | (572) all_52_1_188 = 0
% 279.13/221.49 |
% 279.13/221.49 | Simplifying 572 yields:
% 279.13/221.49 | (573) all_52_1_188 = 0
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (533,564) yields a new equation:
% 279.13/221.49 | (574) all_52_2_189 = 0
% 279.13/221.49 |
% 279.13/221.49 | Simplifying 574 yields:
% 279.13/221.49 | (575) all_52_2_189 = 0
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (488,573) yields a new equation:
% 279.13/221.49 | (576) all_50_13_185 = 0
% 279.13/221.49 |
% 279.13/221.49 | Simplifying 576 yields:
% 279.13/221.49 | (577) all_50_13_185 = 0
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (451,575) yields a new equation:
% 279.13/221.49 | (578) all_50_14_186 = 0
% 279.13/221.49 |
% 279.13/221.49 | Simplifying 578 yields:
% 279.13/221.49 | (579) all_50_14_186 = 0
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (409,410) yields a new equation:
% 279.13/221.49 | (580) all_19_6_51 = all_0_5_5
% 279.13/221.49 |
% 279.13/221.49 | Combining equations (412,414) yields a new equation:
% 279.13/221.49 | (581) all_10_1_17 = all_0_8_8
% 279.43/221.49 |
% 279.43/221.49 | Combining equations (461,521) yields a new equation:
% 279.43/221.49 | (582) all_36_3_113 = all_19_12_57
% 279.43/221.49 |
% 279.43/221.49 | Simplifying 582 yields:
% 279.43/221.49 | (583) all_36_3_113 = all_19_12_57
% 279.43/221.49 |
% 279.43/221.49 | Combining equations (489,577) yields a new equation:
% 279.43/221.49 | (584) all_30_1_102 = 0
% 279.43/221.49 |
% 279.43/221.49 | Simplifying 584 yields:
% 279.43/221.49 | (585) all_30_1_102 = 0
% 279.43/221.49 |
% 279.43/221.49 | Combining equations (452,579) yields a new equation:
% 279.43/221.49 | (586) all_10_3_19 = 0
% 279.43/221.49 |
% 279.43/221.49 | Simplifying 586 yields:
% 279.43/221.49 | (587) all_10_3_19 = 0
% 279.43/221.49 |
% 279.43/221.49 | Combining equations (459,466) yields a new equation:
% 279.43/221.49 | (588) all_48_14_171 = all_26_2_95
% 279.43/221.49 |
% 279.43/221.49 | Simplifying 588 yields:
% 279.43/221.49 | (589) all_48_14_171 = all_26_2_95
% 279.43/221.49 |
% 279.43/221.49 | Combining equations (421,420) yields a new equation:
% 279.43/221.49 | (590) all_26_1_94 = all_23_1_76
% 279.43/221.49 |
% 279.43/221.49 | Combining equations (419,420) yields a new equation:
% 279.43/221.49 | (591) all_26_1_94 = 0
% 279.43/221.49 |
% 279.43/221.49 | Combining equations (462,589) yields a new equation:
% 279.43/221.49 | (592) all_34_1_108 = all_26_2_95
% 279.43/221.49 |
% 279.43/221.49 | Simplifying 592 yields:
% 279.43/221.49 | (593) all_34_1_108 = all_26_2_95
% 279.43/221.49 |
% 279.43/221.49 | Combining equations (470,589) yields a new equation:
% 279.43/221.49 | (594) all_26_2_95 = all_21_14_74
% 279.43/221.49 |
% 279.43/221.49 | Combining equations (427,428) yields a new equation:
% 279.43/221.49 | (595) all_21_13_73 = all_17_1_43
% 279.43/221.49 |
% 279.43/221.49 | Simplifying 595 yields:
% 279.43/221.49 | (596) all_21_13_73 = all_17_1_43
% 279.43/221.49 |
% 279.43/221.49 | Combining equations (463,525) yields a new equation:
% 279.43/221.49 | (597) all_34_1_108 = all_10_4_20
% 279.43/221.49 |
% 279.43/221.49 | Simplifying 597 yields:
% 279.43/221.49 | (598) all_34_1_108 = all_10_4_20
% 279.43/221.49 |
% 279.43/221.49 | Combining equations (431,430) yields a new equation:
% 279.43/221.49 | (599) all_41_1_134 = all_36_2_112
% 279.43/221.49 |
% 279.43/221.49 | Combining equations (429,430) yields a new equation:
% 279.43/221.49 | (600) all_41_1_134 = 0
% 279.43/221.49 |
% 279.43/221.49 | Combining equations (509,508) yields a new equation:
% 279.43/221.50 | (601) all_41_2_135 = all_32_0_104
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 601 yields:
% 279.43/221.50 | (602) all_41_2_135 = all_32_0_104
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (599,600) yields a new equation:
% 279.43/221.50 | (603) all_36_2_112 = 0
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 603 yields:
% 279.43/221.50 | (604) all_36_2_112 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (490,492) yields a new equation:
% 279.43/221.50 | (605) all_28_2_98 = all_19_13_58
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 605 yields:
% 279.43/221.50 | (606) all_28_2_98 = all_19_13_58
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (493,492) yields a new equation:
% 279.43/221.50 | (607) all_19_13_58 = all_10_2_18
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (500,556) yields a new equation:
% 279.43/221.50 | (608) all_19_14_59 = all_8_2_15
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 608 yields:
% 279.43/221.50 | (609) all_19_14_59 = all_8_2_15
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (467,583) yields a new equation:
% 279.43/221.50 | (610) all_23_2_77 = all_19_12_57
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 610 yields:
% 279.43/221.50 | (611) all_23_2_77 = all_19_12_57
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (436,543) yields a new equation:
% 279.43/221.50 | (612) all_34_2_109 = all_32_2_106
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 612 yields:
% 279.43/221.50 | (613) all_34_2_109 = all_32_2_106
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (593,598) yields a new equation:
% 279.43/221.50 | (614) all_26_2_95 = all_10_4_20
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 614 yields:
% 279.43/221.50 | (615) all_26_2_95 = all_10_4_20
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (473,567) yields a new equation:
% 279.43/221.50 | (616) all_17_2_44 = all_12_1_22
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 616 yields:
% 279.43/221.50 | (617) all_17_2_44 = all_12_1_22
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (491,585) yields a new equation:
% 279.43/221.50 | (618) all_28_2_98 = 0
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 618 yields:
% 279.43/221.50 | (619) all_28_2_98 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (570,571) yields a new equation:
% 279.43/221.50 | (620) all_19_14_59 = 0
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 620 yields:
% 279.43/221.50 | (621) all_19_14_59 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (606,619) yields a new equation:
% 279.43/221.50 | (622) all_19_13_58 = 0
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 622 yields:
% 279.43/221.50 | (623) all_19_13_58 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (474,475) yields a new equation:
% 279.43/221.50 | (624) all_17_2_44 = all_14_1_25
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 624 yields:
% 279.43/221.50 | (625) all_17_2_44 = all_14_1_25
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (465,475) yields a new equation:
% 279.43/221.50 | (626) all_14_1_25 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (468,475) yields a new equation:
% 279.43/221.50 | (627) all_21_12_72 = all_14_1_25
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 627 yields:
% 279.43/221.50 | (628) all_21_12_72 = all_14_1_25
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (590,591) yields a new equation:
% 279.43/221.50 | (629) all_23_1_76 = 0
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 629 yields:
% 279.43/221.50 | (630) all_23_1_76 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (594,615) yields a new equation:
% 279.43/221.50 | (631) all_21_14_74 = all_10_4_20
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 631 yields:
% 279.43/221.50 | (632) all_21_14_74 = all_10_4_20
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (469,611) yields a new equation:
% 279.43/221.50 | (633) all_21_12_72 = all_19_12_57
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 633 yields:
% 279.43/221.50 | (634) all_21_12_72 = all_19_12_57
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (471,634) yields a new equation:
% 279.43/221.50 | (635) all_21_14_74 = all_19_12_57
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 635 yields:
% 279.43/221.50 | (636) all_21_14_74 = all_19_12_57
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (628,634) yields a new equation:
% 279.43/221.50 | (637) all_19_12_57 = all_14_1_25
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (426,596) yields a new equation:
% 279.43/221.50 | (638) all_17_1_43 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (636,632) yields a new equation:
% 279.43/221.50 | (639) all_19_12_57 = all_10_4_20
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 639 yields:
% 279.43/221.50 | (640) all_19_12_57 = all_10_4_20
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (637,640) yields a new equation:
% 279.43/221.50 | (641) all_14_1_25 = all_10_4_20
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 641 yields:
% 279.43/221.50 | (642) all_14_1_25 = all_10_4_20
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (607,623) yields a new equation:
% 279.43/221.50 | (643) all_10_2_18 = 0
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 643 yields:
% 279.43/221.50 | (644) all_10_2_18 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (609,621) yields a new equation:
% 279.43/221.50 | (645) all_8_2_15 = 0
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 645 yields:
% 279.43/221.50 | (646) all_8_2_15 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (625,617) yields a new equation:
% 279.43/221.50 | (647) all_14_1_25 = all_12_1_22
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 647 yields:
% 279.43/221.50 | (648) all_14_1_25 = all_12_1_22
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (626,648) yields a new equation:
% 279.43/221.50 | (649) all_12_1_22 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (642,648) yields a new equation:
% 279.43/221.50 | (650) all_12_1_22 = all_10_4_20
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (649,650) yields a new equation:
% 279.43/221.50 | (651) all_10_4_20 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (494,644) yields a new equation:
% 279.43/221.50 | (652) all_8_1_14 = 0
% 279.43/221.50 |
% 279.43/221.50 | Simplifying 652 yields:
% 279.43/221.50 | (653) all_8_1_14 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (651,650) yields a new equation:
% 279.43/221.50 | (649) all_12_1_22 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (649,648) yields a new equation:
% 279.43/221.50 | (626) all_14_1_25 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (651,640) yields a new equation:
% 279.43/221.50 | (656) all_19_12_57 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (626,475) yields a new equation:
% 279.43/221.50 | (465) all_28_4_100 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (649,567) yields a new equation:
% 279.43/221.50 | (658) all_32_1_105 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (651,598) yields a new equation:
% 279.43/221.50 | (659) all_34_1_108 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (656,521) yields a new equation:
% 279.43/221.50 | (660) all_50_12_184 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (581,414) yields a new equation:
% 279.43/221.50 | (412) all_50_10_182 = all_0_8_8
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (580,410) yields a new equation:
% 279.43/221.50 | (409) all_50_6_178 = all_0_5_5
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (568,562) yields a new equation:
% 279.43/221.50 | (544) all_56_1_194 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (568,554) yields a new equation:
% 279.43/221.50 | (664) all_63_2_210 = 0
% 279.43/221.50 |
% 279.43/221.50 | Combining equations (558,550) yields a new equation:
% 279.43/221.50 | (549) all_65_1_214 = 0
% 279.43/221.50 |
% 279.43/221.51 | Combining equations (646,503) yields a new equation:
% 279.43/221.51 | (666) all_67_4_220 = 0
% 279.43/221.51 |
% 279.43/221.51 | Combining equations (568,486) yields a new equation:
% 279.43/221.51 | (667) all_67_3_219 = 0
% 279.43/221.51 |
% 279.43/221.51 | Combining equations (649,530) yields a new equation:
% 279.43/221.51 | (668) all_67_2_218 = 0
% 279.43/221.51 |
% 279.43/221.51 | Combining equations (549,523) yields a new equation:
% 279.43/221.51 | (443) all_69_2_223 = 0
% 279.43/221.51 |
% 279.43/221.51 | Combining equations (544,532) yields a new equation:
% 279.43/221.51 | (480) all_69_1_222 = 0
% 279.43/221.51 |
% 279.43/221.51 | Combining equations (564,528) yields a new equation:
% 279.43/221.51 | (671) all_75_4_237 = 0
% 279.43/221.51 |
% 279.43/221.51 | Combining equations (544,515) yields a new equation:
% 279.43/221.51 | (672) all_75_3_236 = 0
% 279.43/221.51 |
% 279.43/221.51 | Combining equations (649,476) yields a new equation:
% 279.43/221.51 | (673) all_75_2_235 = 0
% 279.43/221.51 |
% 279.43/221.51 | Combining equations (508,432) yields a new equation:
% 279.43/221.51 | (434) all_103_2_259 = all_32_0_104
% 279.43/221.51 |
% 279.43/221.51 | From (412) and (279) follows:
% 279.43/221.51 | (675) sdtpldt0(all_0_8_8, xp) = all_50_9_181
% 279.43/221.51 |
% 279.43/221.51 | From (416) and (338) follows:
% 279.43/221.51 | (676) sdtpldt0(xr, all_67_1_217) = all_75_0_233
% 279.43/221.51 |
% 279.43/221.51 | From (581) and (157) follows:
% 279.43/221.51 | (677) sdtpldt0(xp, all_0_8_8) = all_10_0_16
% 279.43/221.51 |
% 279.43/221.51 | From (416) and (337) follows:
% 279.43/221.51 | (320) sdtpldt0(xm, xp) = all_67_1_217
% 279.43/221.51 |
% 279.43/221.51 | From (417) and (181) follows:
% 279.43/221.51 | (61) sdtpldt0(xn, xm) = all_0_12_12
% 279.43/221.51 |
% 279.43/221.51 | From (630) and (201) follows:
% 279.43/221.51 | (72) aNaturalNumber0(all_0_0_0) = 0
% 279.43/221.51 |
% 279.43/221.51 | From (565) and (213) follows:
% 279.43/221.51 | (24) aNaturalNumber0(all_0_1_1) = 0
% 279.43/221.51 |
% 279.43/221.51 | From (638) and (173) follows:
% 279.43/221.51 | (89) aNaturalNumber0(all_0_3_3) = 0
% 279.43/221.51 |
% 279.43/221.51 | From (604) and (234) follows:
% 279.43/221.51 | (55) aNaturalNumber0(all_0_4_4) = 0
% 279.43/221.51 |
% 279.43/221.51 | From (602) and (247) follows:
% 279.43/221.51 | (223) aNaturalNumber0(all_0_7_7) = all_32_0_104
% 279.43/221.51 |
% 279.43/221.51 | From (613) and (229) follows:
% 279.43/221.51 | (224) aNaturalNumber0(all_0_8_8) = all_32_2_106
% 279.43/221.51 |
% 279.43/221.51 | From (507) and (248) follows:
% 279.43/221.51 | (162) aNaturalNumber0(all_0_11_11) = all_12_0_21
% 279.43/221.51 |
% 279.43/221.51 | From (651) and (160) follows:
% 279.43/221.51 | (98) aNaturalNumber0(xp) = 0
% 279.43/221.51 |
% 279.43/221.51 | From (653) and (151) follows:
% 279.43/221.51 | (76) aNaturalNumber0(xm) = 0
% 279.43/221.51 |
% 279.43/221.51 | From (646) and (152) follows:
% 279.43/221.51 | (34) aNaturalNumber0(xn) = 0
% 279.43/221.51 |
% 279.43/221.51 +-Applying beta-rule and splitting (136), into two cases.
% 279.43/221.51 |-Branch one:
% 279.43/221.51 | (690) all_0_1_1 = xr
% 279.43/221.51 |
% 279.43/221.51 | From (690) and (212) follows:
% 279.43/221.51 | (691) sdtpldt0(xr, xm) = all_28_1_97
% 279.43/221.51 |
% 279.43/221.51 | From (690) and (69) follows:
% 279.43/221.51 | (15) sdtpldt0(xp, xr) = xn
% 279.43/221.51 |
% 279.43/221.51 | From (690) and (24) follows:
% 279.43/221.51 | (81) aNaturalNumber0(xr) = 0
% 279.43/221.51 |
% 279.43/221.51 +-Applying beta-rule and splitting (413), into two cases.
% 279.43/221.51 |-Branch one:
% 279.43/221.51 | (694) ~ (sdtpldt0(xr, xm) = all_28_1_97)
% 279.43/221.51 |
% 279.43/221.51 | Using (691) and (694) yields:
% 279.43/221.51 | (695) $false
% 279.43/221.51 |
% 279.43/221.51 |-The branch is then unsatisfiable
% 279.43/221.51 |-Branch two:
% 279.43/221.51 | (691) sdtpldt0(xr, xm) = all_28_1_97
% 279.43/221.51 | (697) all_50_10_182 = all_28_1_97
% 279.43/221.51 |
% 279.43/221.51 | Combining equations (697,412) yields a new equation:
% 279.43/221.51 | (698) all_28_1_97 = all_0_8_8
% 279.43/221.51 |
% 279.43/221.51 | Simplifying 698 yields:
% 279.43/221.51 | (699) all_28_1_97 = all_0_8_8
% 279.43/221.51 |
% 279.43/221.51 | From (699) and (691) follows:
% 279.43/221.51 | (47) sdtpldt0(xr, xm) = all_0_8_8
% 279.43/221.51 |
% 279.43/221.51 | From (699) and (216) follows:
% 279.43/221.51 | (701) sdtpldt0(xp, all_0_8_8) = all_28_0_96
% 279.43/221.51 |
% 279.43/221.51 +-Applying beta-rule and splitting (327), into two cases.
% 279.43/221.51 |-Branch one:
% 279.43/221.51 | (702) ~ (all_69_1_222 = 0)
% 279.43/221.51 |
% 279.43/221.51 | Equations (480) can reduce 702 to:
% 279.43/221.51 | (346) $false
% 279.43/221.51 |
% 279.43/221.51 |-The branch is then unsatisfiable
% 279.43/221.51 |-Branch two:
% 279.43/221.51 | (480) all_69_1_222 = 0
% 279.43/221.51 | (705) ~ (all_69_2_223 = 0) | all_69_0_221 = 0
% 279.43/221.51 |
% 279.43/221.51 +-Applying beta-rule and splitting (705), into two cases.
% 279.43/221.51 |-Branch one:
% 279.43/221.51 | (706) ~ (all_69_2_223 = 0)
% 279.43/221.51 |
% 279.43/221.51 | Equations (443) can reduce 706 to:
% 279.43/221.51 | (346) $false
% 279.43/221.51 |
% 279.43/221.51 |-The branch is then unsatisfiable
% 279.43/221.51 |-Branch two:
% 279.43/221.51 | (443) all_69_2_223 = 0
% 279.43/221.51 | (709) all_69_0_221 = 0
% 279.43/221.51 |
% 279.43/221.51 | Combining equations (709,437) yields a new equation:
% 279.43/221.51 | (710) all_32_2_106 = 0
% 279.43/221.51 |
% 279.43/221.51 | Combining equations (710,613) yields a new equation:
% 279.43/221.51 | (711) all_34_2_109 = 0
% 279.43/221.51 |
% 279.43/221.51 | From (710) and (224) follows:
% 279.43/221.51 | (712) aNaturalNumber0(all_0_8_8) = 0
% 279.43/221.51 |
% 279.43/221.51 +-Applying beta-rule and splitting (305), into two cases.
% 279.43/221.51 |-Branch one:
% 279.43/221.51 | (713) ~ (all_63_2_210 = 0)
% 279.43/221.51 |
% 279.43/221.51 | Equations (664) can reduce 713 to:
% 279.43/221.51 | (346) $false
% 279.43/221.51 |
% 279.43/221.51 |-The branch is then unsatisfiable
% 279.43/221.51 |-Branch two:
% 279.43/221.51 | (664) all_63_2_210 = 0
% 279.43/221.51 | (716) ~ (all_63_3_211 = 0) | ~ (all_63_4_212 = 0) | all_63_0_208 = all_0_12_12
% 279.43/221.51 |
% 279.43/221.51 +-Applying beta-rule and splitting (716), into two cases.
% 279.43/221.51 |-Branch one:
% 279.43/221.51 | (717) ~ (all_63_3_211 = 0)
% 279.43/221.51 |
% 279.43/221.51 | Equations (526) can reduce 717 to:
% 279.43/221.51 | (346) $false
% 279.43/221.51 |
% 279.43/221.51 |-The branch is then unsatisfiable
% 279.43/221.51 |-Branch two:
% 279.43/221.51 | (526) all_63_3_211 = 0
% 279.43/221.51 | (720) ~ (all_63_4_212 = 0) | all_63_0_208 = all_0_12_12
% 279.43/221.51 |
% 279.43/221.51 +-Applying beta-rule and splitting (720), into two cases.
% 279.43/221.51 |-Branch one:
% 279.43/221.51 | (721) ~ (all_63_4_212 = 0)
% 279.43/221.51 |
% 279.43/221.51 | Equations (558) can reduce 721 to:
% 279.43/221.51 | (346) $false
% 279.43/221.51 |
% 279.43/221.51 |-The branch is then unsatisfiable
% 279.43/221.51 |-Branch two:
% 279.43/221.51 | (558) all_63_4_212 = 0
% 279.43/221.51 | (724) all_63_0_208 = all_0_12_12
% 279.43/221.51 |
% 279.43/221.51 | From (724) and (307) follows:
% 279.43/221.51 | (725) sdtpldt0(xr, all_63_1_209) = all_0_12_12
% 279.43/221.51 |
% 279.43/221.51 +-Applying beta-rule and splitting (231), into two cases.
% 279.43/221.51 |-Branch one:
% 279.43/221.51 | (726) ~ (all_34_1_108 = 0)
% 279.43/221.51 |
% 279.43/221.51 | Equations (659) can reduce 726 to:
% 279.43/221.51 | (346) $false
% 279.43/221.51 |
% 279.43/221.51 |-The branch is then unsatisfiable
% 279.43/221.51 |-Branch two:
% 279.43/221.51 | (659) all_34_1_108 = 0
% 279.43/221.51 | (729) ~ (all_34_2_109 = 0) | all_34_0_107 = all_0_7_7
% 279.43/221.51 |
% 279.43/221.51 +-Applying beta-rule and splitting (729), into two cases.
% 279.43/221.51 |-Branch one:
% 279.43/221.51 | (730) ~ (all_34_2_109 = 0)
% 279.43/221.51 |
% 279.43/221.51 | Equations (711) can reduce 730 to:
% 279.43/221.51 | (346) $false
% 279.43/221.51 |
% 279.43/221.51 |-The branch is then unsatisfiable
% 279.43/221.51 |-Branch two:
% 279.43/221.51 | (711) all_34_2_109 = 0
% 279.43/221.52 | (733) all_34_0_107 = all_0_7_7
% 279.43/221.52 |
% 279.43/221.52 +-Applying beta-rule and splitting (138), into two cases.
% 279.43/221.52 |-Branch one:
% 279.43/221.52 | (734) ~ (sdtpldt0(xp, xr) = sz00)
% 279.43/221.52 |
% 279.43/221.52 +-Applying beta-rule and splitting (274), into two cases.
% 279.43/221.52 |-Branch one:
% 279.43/221.52 | (735) ~ (all_50_8_180 = 0)
% 279.43/221.52 |
% 279.43/221.52 +-Applying beta-rule and splitting (260), into two cases.
% 279.43/221.52 |-Branch one:
% 279.43/221.52 | (736) ~ (all_47_14_156 = 0) & aNaturalNumber0(all_0_0_0) = all_47_14_156
% 279.43/221.52 |
% 279.43/221.52 | Applying alpha-rule on (736) yields:
% 279.43/221.52 | (737) ~ (all_47_14_156 = 0)
% 279.43/221.52 | (738) aNaturalNumber0(all_0_0_0) = all_47_14_156
% 279.43/221.52 |
% 279.43/221.52 | Instantiating formula (97) with all_0_0_0, all_47_14_156, 0 and discharging atoms aNaturalNumber0(all_0_0_0) = all_47_14_156, aNaturalNumber0(all_0_0_0) = 0, yields:
% 279.43/221.52 | (739) all_47_14_156 = 0
% 279.43/221.52 |
% 279.43/221.52 | Equations (739) can reduce 737 to:
% 279.43/221.52 | (346) $false
% 279.43/221.52 |
% 279.43/221.52 |-The branch is then unsatisfiable
% 279.43/221.52 |-Branch two:
% 279.43/221.52 | (741) isPrime0(xp) = all_47_11_153 & doDivides0(xp, all_0_0_0) = all_47_6_148 & doDivides0(xp, xp) = all_47_7_149 & iLess0(all_47_9_151, all_0_11_11) = all_47_8_150 & sdtpldt0(all_47_10_152, xp) = all_47_9_151 & sdtpldt0(xp, all_0_0_0) = all_47_10_152 & aNaturalNumber0(all_0_0_0) = all_47_13_155 & aNaturalNumber0(xp) = all_47_12_154 & aNaturalNumber0(xp) = all_47_14_156 & ( ~ (all_47_8_150 = 0) | ~ (all_47_12_154 = 0) | ~ (all_47_13_155 = 0) | ~ (all_47_14_156 = 0) | (all_47_3_145 = all_0_0_0 & all_47_4_146 = 0 & all_47_6_148 = 0 & sdtasdt0(xp, all_47_5_147) = all_0_0_0 & aNaturalNumber0(all_47_5_147) = 0) | (all_47_3_145 = xp & all_47_4_146 = 0 & all_47_7_149 = 0 & sdtasdt0(xp, all_47_5_147) = xp & aNaturalNumber0(all_47_5_147) = 0) | ( ~ (all_47_11_153 = 0) & (xp = sz10 | xp = sz00 | (all_47_0_142 = xp & all_47_1_143 = 0 & all_47_3_145 = 0 & all_47_4_146 = 0 & ~ (all_47_5_147 = xp) & ~ (all_47_5_147 = sz10) & doDivides0(all_47_5_147, xp) = 0 & sdtasdt0(all_47_5_147, all_47_2_144) = xp & aNaturalNumber0(all_47_2_144) = 0 & aNaturalNumber0(all_47_5_147) = 0))))
% 279.43/221.52 |
% 279.43/221.52 | Applying alpha-rule on (741) yields:
% 279.43/221.52 | (742) aNaturalNumber0(xp) = all_47_12_154
% 279.43/221.52 | (743) aNaturalNumber0(all_0_0_0) = all_47_13_155
% 279.43/221.52 | (744) sdtpldt0(all_47_10_152, xp) = all_47_9_151
% 279.43/221.52 | (745) aNaturalNumber0(xp) = all_47_14_156
% 279.43/221.52 | (746) sdtpldt0(xp, all_0_0_0) = all_47_10_152
% 279.43/221.52 | (747) doDivides0(xp, all_0_0_0) = all_47_6_148
% 279.43/221.52 | (748) isPrime0(xp) = all_47_11_153
% 279.43/221.52 | (749) ~ (all_47_8_150 = 0) | ~ (all_47_12_154 = 0) | ~ (all_47_13_155 = 0) | ~ (all_47_14_156 = 0) | (all_47_3_145 = all_0_0_0 & all_47_4_146 = 0 & all_47_6_148 = 0 & sdtasdt0(xp, all_47_5_147) = all_0_0_0 & aNaturalNumber0(all_47_5_147) = 0) | (all_47_3_145 = xp & all_47_4_146 = 0 & all_47_7_149 = 0 & sdtasdt0(xp, all_47_5_147) = xp & aNaturalNumber0(all_47_5_147) = 0) | ( ~ (all_47_11_153 = 0) & (xp = sz10 | xp = sz00 | (all_47_0_142 = xp & all_47_1_143 = 0 & all_47_3_145 = 0 & all_47_4_146 = 0 & ~ (all_47_5_147 = xp) & ~ (all_47_5_147 = sz10) & doDivides0(all_47_5_147, xp) = 0 & sdtasdt0(all_47_5_147, all_47_2_144) = xp & aNaturalNumber0(all_47_2_144) = 0 & aNaturalNumber0(all_47_5_147) = 0)))
% 279.43/221.52 | (750) iLess0(all_47_9_151, all_0_11_11) = all_47_8_150
% 279.43/221.52 | (751) doDivides0(xp, xp) = all_47_7_149
% 279.43/221.52 |
% 279.43/221.52 +-Applying beta-rule and splitting (226), into two cases.
% 279.43/221.52 |-Branch one:
% 279.43/221.52 | (752) ~ (all_32_1_105 = 0)
% 279.43/221.52 |
% 279.43/221.52 | Equations (658) can reduce 752 to:
% 279.43/221.52 | (346) $false
% 279.43/221.52 |
% 279.43/221.52 |-The branch is then unsatisfiable
% 279.43/221.52 |-Branch two:
% 279.43/221.52 | (658) all_32_1_105 = 0
% 279.43/221.52 | (755) ~ (all_32_2_106 = 0) | all_32_0_104 = 0
% 279.43/221.52 |
% 279.43/221.52 +-Applying beta-rule and splitting (321), into two cases.
% 279.43/221.52 |-Branch one:
% 279.43/221.52 | (756) ~ (all_67_2_218 = 0)
% 279.43/221.52 |
% 279.43/221.52 | Equations (668) can reduce 756 to:
% 279.43/221.52 | (346) $false
% 279.43/221.52 |
% 279.43/221.52 |-The branch is then unsatisfiable
% 279.43/221.52 |-Branch two:
% 279.43/221.52 | (668) all_67_2_218 = 0
% 279.43/221.52 | (759) ~ (all_67_3_219 = 0) | ~ (all_67_4_220 = 0) | all_67_0_216 = all_0_11_11
% 279.43/221.52 |
% 279.43/221.52 +-Applying beta-rule and splitting (204), into two cases.
% 279.43/221.52 |-Branch one:
% 279.43/221.52 | (760) ~ (all_25_14_92 = 0) & aNaturalNumber0(all_0_3_3) = all_25_14_92
% 279.43/221.52 |
% 279.43/221.52 | Applying alpha-rule on (760) yields:
% 279.43/221.52 | (761) ~ (all_25_14_92 = 0)
% 279.43/221.52 | (762) aNaturalNumber0(all_0_3_3) = all_25_14_92
% 279.43/221.52 |
% 279.43/221.52 | Instantiating formula (97) with all_0_3_3, all_25_14_92, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_25_14_92, aNaturalNumber0(all_0_3_3) = 0, yields:
% 279.43/221.52 | (763) all_25_14_92 = 0
% 279.43/221.52 |
% 279.43/221.52 | Equations (763) can reduce 761 to:
% 279.43/221.52 | (346) $false
% 279.43/221.52 |
% 279.43/221.52 |-The branch is then unsatisfiable
% 279.43/221.52 |-Branch two:
% 279.43/221.52 | (765) isPrime0(xp) = all_25_11_89 & doDivides0(xp, xr) = all_25_7_85 & doDivides0(xp, xm) = all_25_6_84 & iLess0(all_25_9_87, all_0_11_11) = all_25_8_86 & sdtpldt0(all_25_10_88, xp) = all_25_9_87 & sdtpldt0(xr, xm) = all_25_10_88 & aNaturalNumber0(xr) = all_25_14_92 & aNaturalNumber0(xp) = all_25_12_90 & aNaturalNumber0(xm) = all_25_13_91 & ( ~ (all_25_8_86 = 0) | ~ (all_25_12_90 = 0) | ~ (all_25_13_91 = 0) | ~ (all_25_14_92 = 0) | (all_25_3_81 = xr & all_25_4_82 = 0 & all_25_7_85 = 0 & sdtasdt0(xp, all_25_5_83) = xr & aNaturalNumber0(all_25_5_83) = 0) | (all_25_3_81 = xm & all_25_4_82 = 0 & all_25_6_84 = 0 & sdtasdt0(xp, all_25_5_83) = xm & aNaturalNumber0(all_25_5_83) = 0) | ( ~ (all_25_11_89 = 0) & (xp = sz10 | xp = sz00 | (all_25_0_78 = xp & all_25_1_79 = 0 & all_25_3_81 = 0 & all_25_4_82 = 0 & ~ (all_25_5_83 = xp) & ~ (all_25_5_83 = sz10) & doDivides0(all_25_5_83, xp) = 0 & sdtasdt0(all_25_5_83, all_25_2_80) = xp & aNaturalNumber0(all_25_2_80) = 0 & aNaturalNumber0(all_25_5_83) = 0))))
% 279.43/221.52 |
% 279.43/221.52 | Applying alpha-rule on (765) yields:
% 279.43/221.52 | (766) aNaturalNumber0(xm) = all_25_13_91
% 279.43/221.52 | (767) doDivides0(xp, xm) = all_25_6_84
% 279.43/221.52 | (768) isPrime0(xp) = all_25_11_89
% 279.43/221.52 | (769) sdtpldt0(xr, xm) = all_25_10_88
% 279.43/221.52 | (770) iLess0(all_25_9_87, all_0_11_11) = all_25_8_86
% 279.43/221.52 | (771) doDivides0(xp, xr) = all_25_7_85
% 279.43/221.52 | (772) sdtpldt0(all_25_10_88, xp) = all_25_9_87
% 279.43/221.52 | (773) aNaturalNumber0(xr) = all_25_14_92
% 279.43/221.52 | (774) aNaturalNumber0(xp) = all_25_12_90
% 279.43/221.52 | (775) ~ (all_25_8_86 = 0) | ~ (all_25_12_90 = 0) | ~ (all_25_13_91 = 0) | ~ (all_25_14_92 = 0) | (all_25_3_81 = xr & all_25_4_82 = 0 & all_25_7_85 = 0 & sdtasdt0(xp, all_25_5_83) = xr & aNaturalNumber0(all_25_5_83) = 0) | (all_25_3_81 = xm & all_25_4_82 = 0 & all_25_6_84 = 0 & sdtasdt0(xp, all_25_5_83) = xm & aNaturalNumber0(all_25_5_83) = 0) | ( ~ (all_25_11_89 = 0) & (xp = sz10 | xp = sz00 | (all_25_0_78 = xp & all_25_1_79 = 0 & all_25_3_81 = 0 & all_25_4_82 = 0 & ~ (all_25_5_83 = xp) & ~ (all_25_5_83 = sz10) & doDivides0(all_25_5_83, xp) = 0 & sdtasdt0(all_25_5_83, all_25_2_80) = xp & aNaturalNumber0(all_25_2_80) = 0 & aNaturalNumber0(all_25_5_83) = 0)))
% 279.43/221.52 |
% 279.43/221.52 +-Applying beta-rule and splitting (759), into two cases.
% 279.43/221.52 |-Branch one:
% 279.43/221.52 | (776) ~ (all_67_3_219 = 0)
% 279.43/221.52 |
% 279.43/221.52 | Equations (667) can reduce 776 to:
% 279.43/221.52 | (346) $false
% 279.43/221.52 |
% 279.43/221.52 |-The branch is then unsatisfiable
% 279.43/221.52 |-Branch two:
% 279.43/221.52 | (667) all_67_3_219 = 0
% 279.43/221.52 | (779) ~ (all_67_4_220 = 0) | all_67_0_216 = all_0_11_11
% 279.43/221.52 |
% 279.43/221.52 +-Applying beta-rule and splitting (779), into two cases.
% 279.43/221.52 |-Branch one:
% 279.43/221.52 | (780) ~ (all_67_4_220 = 0)
% 279.43/221.52 |
% 279.43/221.52 | Equations (666) can reduce 780 to:
% 279.43/221.52 | (346) $false
% 279.43/221.52 |
% 279.43/221.52 |-The branch is then unsatisfiable
% 279.43/221.52 |-Branch two:
% 279.43/221.52 | (666) all_67_4_220 = 0
% 279.43/221.52 | (783) all_67_0_216 = all_0_11_11
% 279.43/221.52 |
% 279.43/221.52 +-Applying beta-rule and splitting (755), into two cases.
% 279.43/221.52 |-Branch one:
% 279.43/221.52 | (784) ~ (all_32_2_106 = 0)
% 279.43/221.52 |
% 279.43/221.52 | Equations (710) can reduce 784 to:
% 279.43/221.52 | (346) $false
% 279.43/221.52 |
% 279.43/221.52 |-The branch is then unsatisfiable
% 279.43/221.52 |-Branch two:
% 279.43/221.52 | (710) all_32_2_106 = 0
% 279.43/221.52 | (787) all_32_0_104 = 0
% 279.43/221.52 |
% 279.43/221.53 | Combining equations (787,602) yields a new equation:
% 279.43/221.53 | (788) all_41_2_135 = 0
% 279.43/221.53 |
% 279.43/221.53 | Combining equations (787,434) yields a new equation:
% 279.43/221.53 | (789) all_103_2_259 = 0
% 279.43/221.53 |
% 279.43/221.53 | From (787) and (223) follows:
% 279.43/221.53 | (790) aNaturalNumber0(all_0_7_7) = 0
% 279.43/221.53 |
% 279.43/221.53 +-Applying beta-rule and splitting (156), into two cases.
% 279.43/221.53 |-Branch one:
% 279.43/221.53 | (791) ~ (all_10_2_18 = 0)
% 279.43/221.53 |
% 279.43/221.53 | Equations (644) can reduce 791 to:
% 279.43/221.53 | (346) $false
% 279.43/221.53 |
% 279.43/221.53 |-The branch is then unsatisfiable
% 279.43/221.53 |-Branch two:
% 279.43/221.53 | (644) all_10_2_18 = 0
% 279.43/221.53 | (794) ~ (all_10_3_19 = 0) | ~ (all_10_4_20 = 0) | all_10_0_16 = all_0_12_12
% 279.43/221.53 |
% 279.43/221.53 +-Applying beta-rule and splitting (794), into two cases.
% 279.43/221.53 |-Branch one:
% 279.43/221.53 | (795) ~ (all_10_3_19 = 0)
% 279.43/221.53 |
% 279.43/221.53 | Equations (587) can reduce 795 to:
% 279.43/221.53 | (346) $false
% 279.43/221.53 |
% 279.43/221.53 |-The branch is then unsatisfiable
% 279.43/221.53 |-Branch two:
% 279.43/221.53 | (587) all_10_3_19 = 0
% 279.43/221.53 | (798) ~ (all_10_4_20 = 0) | all_10_0_16 = all_0_12_12
% 279.43/221.53 |
% 279.43/221.53 +-Applying beta-rule and splitting (798), into two cases.
% 279.43/221.53 |-Branch one:
% 279.43/221.53 | (799) ~ (all_10_4_20 = 0)
% 279.43/221.53 |
% 279.43/221.53 | Equations (651) can reduce 799 to:
% 279.43/221.53 | (346) $false
% 279.43/221.53 |
% 279.43/221.53 |-The branch is then unsatisfiable
% 279.43/221.53 |-Branch two:
% 279.43/221.53 | (651) all_10_4_20 = 0
% 279.43/221.53 | (802) all_10_0_16 = all_0_12_12
% 279.43/221.53 |
% 279.43/221.53 +-Applying beta-rule and splitting (339), into two cases.
% 279.43/221.53 |-Branch one:
% 279.43/221.53 | (803) ~ (all_75_2_235 = 0)
% 279.43/221.53 |
% 279.43/221.53 | Equations (673) can reduce 803 to:
% 279.43/221.53 | (346) $false
% 279.43/221.53 |
% 279.43/221.53 |-The branch is then unsatisfiable
% 279.43/221.53 |-Branch two:
% 279.43/221.53 | (673) all_75_2_235 = 0
% 279.43/221.53 | (806) ~ (all_75_3_236 = 0) | ~ (all_75_4_237 = 0) | all_75_0_233 = all_0_7_7
% 279.43/221.53 |
% 279.43/221.53 +-Applying beta-rule and splitting (239), into two cases.
% 279.43/221.53 |-Branch one:
% 279.43/221.53 | (807) ~ (all_38_14_129 = 0) & aNaturalNumber0(all_0_3_3) = all_38_14_129
% 279.43/221.53 |
% 279.43/221.53 | Applying alpha-rule on (807) yields:
% 279.43/221.53 | (808) ~ (all_38_14_129 = 0)
% 279.43/221.53 | (809) aNaturalNumber0(all_0_3_3) = all_38_14_129
% 279.43/221.53 |
% 279.43/221.53 | Instantiating formula (97) with all_0_3_3, all_38_14_129, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_38_14_129, aNaturalNumber0(all_0_3_3) = 0, yields:
% 279.43/221.53 | (810) all_38_14_129 = 0
% 279.43/221.53 |
% 279.43/221.53 | Equations (810) can reduce 808 to:
% 279.43/221.53 | (346) $false
% 279.43/221.53 |
% 279.43/221.53 |-The branch is then unsatisfiable
% 279.43/221.53 |-Branch two:
% 279.43/221.53 | (812) isPrime0(xp) = all_38_11_126 & doDivides0(xp, all_0_3_3) = all_38_6_121 & doDivides0(xp, xp) = all_38_7_122 & iLess0(all_38_9_124, all_0_11_11) = all_38_8_123 & sdtpldt0(all_38_10_125, xp) = all_38_9_124 & sdtpldt0(xp, all_0_3_3) = all_38_10_125 & aNaturalNumber0(all_0_3_3) = all_38_13_128 & aNaturalNumber0(xp) = all_38_12_127 & aNaturalNumber0(xp) = all_38_14_129 & ( ~ (all_38_8_123 = 0) | ~ (all_38_12_127 = 0) | ~ (all_38_13_128 = 0) | ~ (all_38_14_129 = 0) | (all_38_3_118 = all_0_3_3 & all_38_4_119 = 0 & all_38_6_121 = 0 & sdtasdt0(xp, all_38_5_120) = all_0_3_3 & aNaturalNumber0(all_38_5_120) = 0) | (all_38_3_118 = xp & all_38_4_119 = 0 & all_38_7_122 = 0 & sdtasdt0(xp, all_38_5_120) = xp & aNaturalNumber0(all_38_5_120) = 0) | ( ~ (all_38_11_126 = 0) & (xp = sz10 | xp = sz00 | (all_38_0_115 = xp & all_38_1_116 = 0 & all_38_3_118 = 0 & all_38_4_119 = 0 & ~ (all_38_5_120 = xp) & ~ (all_38_5_120 = sz10) & doDivides0(all_38_5_120, xp) = 0 & sdtasdt0(all_38_5_120, all_38_2_117) = xp & aNaturalNumber0(all_38_2_117) = 0 & aNaturalNumber0(all_38_5_120) = 0))))
% 279.43/221.53 |
% 279.43/221.53 | Applying alpha-rule on (812) yields:
% 279.43/221.53 | (813) doDivides0(xp, all_0_3_3) = all_38_6_121
% 279.43/221.53 | (814) doDivides0(xp, xp) = all_38_7_122
% 279.43/221.53 | (815) aNaturalNumber0(all_0_3_3) = all_38_13_128
% 279.43/221.53 | (816) iLess0(all_38_9_124, all_0_11_11) = all_38_8_123
% 279.43/221.53 | (817) sdtpldt0(all_38_10_125, xp) = all_38_9_124
% 279.43/221.53 | (818) sdtpldt0(xp, all_0_3_3) = all_38_10_125
% 279.43/221.53 | (819) aNaturalNumber0(xp) = all_38_14_129
% 279.43/221.53 | (820) isPrime0(xp) = all_38_11_126
% 279.43/221.53 | (821) aNaturalNumber0(xp) = all_38_12_127
% 279.43/221.53 | (822) ~ (all_38_8_123 = 0) | ~ (all_38_12_127 = 0) | ~ (all_38_13_128 = 0) | ~ (all_38_14_129 = 0) | (all_38_3_118 = all_0_3_3 & all_38_4_119 = 0 & all_38_6_121 = 0 & sdtasdt0(xp, all_38_5_120) = all_0_3_3 & aNaturalNumber0(all_38_5_120) = 0) | (all_38_3_118 = xp & all_38_4_119 = 0 & all_38_7_122 = 0 & sdtasdt0(xp, all_38_5_120) = xp & aNaturalNumber0(all_38_5_120) = 0) | ( ~ (all_38_11_126 = 0) & (xp = sz10 | xp = sz00 | (all_38_0_115 = xp & all_38_1_116 = 0 & all_38_3_118 = 0 & all_38_4_119 = 0 & ~ (all_38_5_120 = xp) & ~ (all_38_5_120 = sz10) & doDivides0(all_38_5_120, xp) = 0 & sdtasdt0(all_38_5_120, all_38_2_117) = xp & aNaturalNumber0(all_38_2_117) = 0 & aNaturalNumber0(all_38_5_120) = 0)))
% 279.43/221.53 |
% 279.43/221.53 +-Applying beta-rule and splitting (249), into two cases.
% 279.43/221.53 |-Branch one:
% 279.43/221.53 | (823) ~ (all_41_1_134 = 0)
% 279.43/221.53 |
% 279.43/221.53 | Equations (600) can reduce 823 to:
% 279.43/221.53 | (346) $false
% 279.43/221.53 |
% 279.43/221.53 |-The branch is then unsatisfiable
% 279.43/221.53 |-Branch two:
% 279.43/221.53 | (600) all_41_1_134 = 0
% 279.43/221.53 | (826) ~ (all_41_2_135 = 0) | all_41_0_133 = 0
% 279.43/221.53 |
% 279.43/221.53 +-Applying beta-rule and splitting (806), into two cases.
% 279.43/221.53 |-Branch one:
% 279.43/221.53 | (827) ~ (all_75_3_236 = 0)
% 279.43/221.53 |
% 279.43/221.53 | Equations (672) can reduce 827 to:
% 279.43/221.53 | (346) $false
% 279.43/221.53 |
% 279.43/221.53 |-The branch is then unsatisfiable
% 279.43/221.53 |-Branch two:
% 279.43/221.53 | (672) all_75_3_236 = 0
% 279.43/221.53 | (830) ~ (all_75_4_237 = 0) | all_75_0_233 = all_0_7_7
% 279.43/221.53 |
% 279.43/221.53 +-Applying beta-rule and splitting (830), into two cases.
% 279.43/221.53 |-Branch one:
% 279.43/221.53 | (831) ~ (all_75_4_237 = 0)
% 279.43/221.53 |
% 279.43/221.53 | Equations (671) can reduce 831 to:
% 279.43/221.53 | (346) $false
% 279.43/221.53 |
% 279.43/221.53 |-The branch is then unsatisfiable
% 279.43/221.53 |-Branch two:
% 279.43/221.53 | (671) all_75_4_237 = 0
% 279.43/221.53 | (834) all_75_0_233 = all_0_7_7
% 279.43/221.53 |
% 279.43/221.53 | From (834) and (676) follows:
% 279.43/221.53 | (835) sdtpldt0(xr, all_67_1_217) = all_0_7_7
% 279.43/221.53 |
% 279.43/221.53 +-Applying beta-rule and splitting (214), into two cases.
% 279.43/221.53 |-Branch one:
% 279.43/221.53 | (836) ~ (all_28_2_98 = 0)
% 279.43/221.53 |
% 279.43/221.53 | Equations (619) can reduce 836 to:
% 279.43/221.53 | (346) $false
% 279.43/221.53 |
% 279.43/221.53 |-The branch is then unsatisfiable
% 279.43/221.53 |-Branch two:
% 279.43/221.53 | (619) all_28_2_98 = 0
% 279.43/221.53 | (839) ~ (all_28_3_99 = 0) | ~ (all_28_4_100 = 0) | all_28_0_96 = all_0_12_12
% 279.43/221.53 |
% 279.43/221.53 +-Applying beta-rule and splitting (839), into two cases.
% 279.43/221.53 |-Branch one:
% 279.43/221.53 | (840) ~ (all_28_3_99 = 0)
% 279.43/221.53 |
% 279.43/221.53 | Equations (565) can reduce 840 to:
% 279.43/221.53 | (346) $false
% 279.43/221.53 |
% 279.43/221.53 |-The branch is then unsatisfiable
% 279.43/221.53 |-Branch two:
% 279.43/221.53 | (565) all_28_3_99 = 0
% 279.43/221.53 | (843) ~ (all_28_4_100 = 0) | all_28_0_96 = all_0_12_12
% 279.43/221.53 |
% 279.43/221.53 +-Applying beta-rule and splitting (843), into two cases.
% 279.43/221.53 |-Branch one:
% 279.43/221.53 | (844) ~ (all_28_4_100 = 0)
% 279.43/221.53 |
% 279.43/221.53 | Equations (465) can reduce 844 to:
% 279.43/221.53 | (346) $false
% 279.43/221.53 |
% 279.43/221.53 |-The branch is then unsatisfiable
% 279.43/221.53 |-Branch two:
% 279.43/221.53 | (465) all_28_4_100 = 0
% 279.43/221.53 | (847) all_28_0_96 = all_0_12_12
% 279.43/221.53 |
% 279.43/221.53 | From (847) and (701) follows:
% 279.43/221.53 | (848) sdtpldt0(xp, all_0_8_8) = all_0_12_12
% 279.43/221.53 |
% 279.43/221.53 +-Applying beta-rule and splitting (415), into two cases.
% 279.43/221.53 |-Branch one:
% 279.43/221.53 | (849) ~ (sdtpldt0(xp, all_0_8_8) = all_10_0_16)
% 279.43/221.53 |
% 279.43/221.53 | From (802) and (849) follows:
% 279.43/221.53 | (850) ~ (sdtpldt0(xp, all_0_8_8) = all_0_12_12)
% 279.43/221.54 |
% 279.43/221.54 | Using (848) and (850) yields:
% 279.43/221.54 | (695) $false
% 279.43/221.54 |
% 279.43/221.54 |-The branch is then unsatisfiable
% 279.43/221.54 |-Branch two:
% 279.43/221.54 | (677) sdtpldt0(xp, all_0_8_8) = all_10_0_16
% 279.43/221.54 | (853) all_34_0_107 = all_10_0_16
% 279.43/221.54 |
% 279.43/221.54 | Combining equations (733,853) yields a new equation:
% 279.43/221.54 | (854) all_10_0_16 = all_0_7_7
% 279.43/221.54 |
% 279.43/221.54 | Combining equations (854,802) yields a new equation:
% 279.43/221.54 | (855) all_0_7_7 = all_0_12_12
% 279.43/221.54 |
% 279.43/221.54 | Simplifying 855 yields:
% 279.43/221.54 | (856) all_0_7_7 = all_0_12_12
% 279.43/221.54 |
% 279.43/221.54 | Equations (856) can reduce 7 to:
% 279.43/221.54 | (857) ~ (all_0_11_11 = all_0_12_12)
% 279.43/221.54 |
% 279.43/221.54 | Simplifying 857 yields:
% 279.43/221.54 | (858) ~ (all_0_11_11 = all_0_12_12)
% 279.43/221.54 |
% 279.43/221.54 | From (856) and (84) follows:
% 279.43/221.54 | (859) sdtlseqdt0(all_0_12_12, all_0_11_11) = 0
% 279.43/221.54 |
% 279.43/221.54 | From (856) and (390) follows:
% 279.43/221.54 | (860) sdtlseqdt0(all_0_11_11, all_0_12_12) = all_103_0_257
% 279.43/221.54 |
% 279.43/221.54 | From (856) and (5) follows:
% 279.43/221.54 | (861) sdtpldt0(all_0_12_12, all_0_4_4) = all_0_11_11
% 279.43/221.54 |
% 279.43/221.54 | From (856) and (49) follows:
% 279.43/221.54 | (862) sdtpldt0(all_0_8_8, xp) = all_0_12_12
% 279.43/221.54 |
% 279.43/221.54 | From (856) and (835) follows:
% 279.43/221.54 | (863) sdtpldt0(xr, all_67_1_217) = all_0_12_12
% 279.43/221.54 |
% 279.43/221.54 | From (856) and (790) follows:
% 279.43/221.54 | (864) aNaturalNumber0(all_0_12_12) = 0
% 279.43/221.54 |
% 279.43/221.54 +-Applying beta-rule and splitting (826), into two cases.
% 279.43/221.54 |-Branch one:
% 279.43/221.54 | (865) ~ (all_41_2_135 = 0)
% 279.43/221.54 |
% 279.43/221.54 | Equations (788) can reduce 865 to:
% 279.43/221.54 | (346) $false
% 279.43/221.54 |
% 279.43/221.54 |-The branch is then unsatisfiable
% 279.43/221.54 |-Branch two:
% 279.43/221.54 | (788) all_41_2_135 = 0
% 279.43/221.54 | (868) all_41_0_133 = 0
% 279.43/221.54 |
% 279.43/221.54 | Combining equations (507,868) yields a new equation:
% 279.43/221.54 | (869) all_12_0_21 = 0
% 279.43/221.54 |
% 279.43/221.54 | Simplifying 869 yields:
% 279.43/221.54 | (870) all_12_0_21 = 0
% 279.43/221.54 |
% 279.43/221.54 | Combining equations (870,439) yields a new equation:
% 279.43/221.54 | (871) all_103_1_258 = 0
% 279.43/221.54 |
% 279.43/221.54 | From (870) and (162) follows:
% 279.43/221.54 | (872) aNaturalNumber0(all_0_11_11) = 0
% 279.43/221.54 |
% 279.43/221.54 +-Applying beta-rule and splitting (140), into two cases.
% 279.43/221.54 |-Branch one:
% 279.43/221.54 | (873) ~ (sdtpldt0(all_0_12_12, all_0_4_4) = all_0_11_11)
% 279.43/221.54 |
% 279.43/221.54 | Using (861) and (873) yields:
% 279.43/221.54 | (695) $false
% 279.43/221.54 |
% 279.43/221.54 |-The branch is then unsatisfiable
% 279.43/221.54 |-Branch two:
% 279.43/221.54 | (861) sdtpldt0(all_0_12_12, all_0_4_4) = all_0_11_11
% 279.43/221.54 | (876) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xm, all_0_4_4) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(all_0_4_4) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_11_11))
% 279.43/221.54 |
% 279.43/221.54 | Instantiating (876) with all_414_0_295, all_414_1_296, all_414_2_297, all_414_3_298, all_414_4_299 yields:
% 279.43/221.54 | (877) sdtpldt0(xm, all_0_4_4) = all_414_1_296 & sdtpldt0(xn, all_414_1_296) = all_414_0_295 & aNaturalNumber0(all_0_4_4) = all_414_2_297 & aNaturalNumber0(xm) = all_414_3_298 & aNaturalNumber0(xn) = all_414_4_299 & ( ~ (all_414_2_297 = 0) | ~ (all_414_3_298 = 0) | ~ (all_414_4_299 = 0) | all_414_0_295 = all_0_11_11)
% 279.43/221.54 |
% 279.43/221.54 | Applying alpha-rule on (877) yields:
% 279.43/221.54 | (878) aNaturalNumber0(all_0_4_4) = all_414_2_297
% 279.43/221.54 | (879) aNaturalNumber0(xm) = all_414_3_298
% 279.43/221.54 | (880) ~ (all_414_2_297 = 0) | ~ (all_414_3_298 = 0) | ~ (all_414_4_299 = 0) | all_414_0_295 = all_0_11_11
% 279.43/221.54 | (881) aNaturalNumber0(xn) = all_414_4_299
% 279.43/221.54 | (882) sdtpldt0(xm, all_0_4_4) = all_414_1_296
% 279.43/221.54 | (883) sdtpldt0(xn, all_414_1_296) = all_414_0_295
% 279.43/221.54 |
% 279.43/221.54 +-Applying beta-rule and splitting (393), into two cases.
% 279.43/221.54 |-Branch one:
% 279.43/221.54 | (884) ~ (all_103_0_257 = 0)
% 279.43/221.54 |
% 279.43/221.54 +-Applying beta-rule and splitting (129), into two cases.
% 279.43/221.54 |-Branch one:
% 279.43/221.54 | (885) ~ (sdtpldt0(all_0_8_8, xp) = all_0_12_12)
% 279.43/221.54 |
% 279.43/221.54 | Using (862) and (885) yields:
% 279.43/221.54 | (695) $false
% 279.43/221.54 |
% 279.43/221.54 |-The branch is then unsatisfiable
% 279.43/221.54 |-Branch two:
% 279.43/221.54 | (862) sdtpldt0(all_0_8_8, xp) = all_0_12_12
% 279.43/221.54 | (888) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_0_8_8, v3) = v4 & sdtpldt0(xp, xp) = v3 & aNaturalNumber0(all_0_8_8) = v0 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_11_11))
% 279.43/221.54 |
% 279.43/221.54 | Instantiating (888) with all_423_0_300, all_423_1_301, all_423_2_302, all_423_3_303, all_423_4_304 yields:
% 279.43/221.54 | (889) sdtpldt0(all_0_8_8, all_423_1_301) = all_423_0_300 & sdtpldt0(xp, xp) = all_423_1_301 & aNaturalNumber0(all_0_8_8) = all_423_4_304 & aNaturalNumber0(xp) = all_423_2_302 & aNaturalNumber0(xp) = all_423_3_303 & ( ~ (all_423_2_302 = 0) | ~ (all_423_3_303 = 0) | ~ (all_423_4_304 = 0) | all_423_0_300 = all_0_11_11)
% 279.43/221.54 |
% 279.43/221.54 | Applying alpha-rule on (889) yields:
% 279.43/221.54 | (890) aNaturalNumber0(xp) = all_423_2_302
% 279.43/221.54 | (891) aNaturalNumber0(all_0_8_8) = all_423_4_304
% 279.43/221.54 | (892) ~ (all_423_2_302 = 0) | ~ (all_423_3_303 = 0) | ~ (all_423_4_304 = 0) | all_423_0_300 = all_0_11_11
% 279.43/221.54 | (893) sdtpldt0(xp, xp) = all_423_1_301
% 279.43/221.54 | (894) aNaturalNumber0(xp) = all_423_3_303
% 279.43/221.54 | (895) sdtpldt0(all_0_8_8, all_423_1_301) = all_423_0_300
% 279.43/221.54 |
% 279.43/221.54 +-Applying beta-rule and splitting (298), into two cases.
% 279.43/221.54 |-Branch one:
% 279.43/221.54 | (896) all_58_0_196 = all_0_11_11 & all_58_1_197 = 0 & sdtpldt0(all_0_7_7, all_58_2_198) = all_0_11_11 & aNaturalNumber0(all_58_2_198) = 0
% 279.43/221.54 |
% 279.43/221.54 | Applying alpha-rule on (896) yields:
% 279.43/221.54 | (897) all_58_0_196 = all_0_11_11
% 279.43/221.54 | (898) all_58_1_197 = 0
% 279.43/221.54 | (899) sdtpldt0(all_0_7_7, all_58_2_198) = all_0_11_11
% 279.43/221.54 | (900) aNaturalNumber0(all_58_2_198) = 0
% 279.43/221.54 |
% 279.43/221.54 | From (856) and (899) follows:
% 279.43/221.54 | (901) sdtpldt0(all_0_12_12, all_58_2_198) = all_0_11_11
% 279.43/221.54 |
% 279.43/221.54 +-Applying beta-rule and splitting (411), into two cases.
% 279.43/221.54 |-Branch one:
% 279.43/221.54 | (902) ~ (sdtpldt0(all_0_8_8, xp) = all_50_9_181)
% 279.43/221.55 |
% 279.43/221.55 | Using (675) and (902) yields:
% 279.43/221.55 | (695) $false
% 279.43/221.55 |
% 279.43/221.55 |-The branch is then unsatisfiable
% 279.43/221.55 |-Branch two:
% 279.43/221.55 | (675) sdtpldt0(all_0_8_8, xp) = all_50_9_181
% 279.43/221.55 | (905) all_50_9_181 = all_0_7_7
% 279.43/221.55 |
% 279.43/221.55 | Combining equations (856,905) yields a new equation:
% 279.43/221.55 | (906) all_50_9_181 = all_0_12_12
% 279.43/221.55 |
% 279.43/221.55 | From (906) and (277) follows:
% 279.43/221.55 | (907) iLess0(all_0_12_12, all_0_11_11) = all_50_8_180
% 279.43/221.55 |
% 279.43/221.55 | From (906) and (675) follows:
% 279.43/221.55 | (862) sdtpldt0(all_0_8_8, xp) = all_0_12_12
% 279.43/221.55 |
% 279.43/221.55 | Instantiating formula (71) with all_0_12_12, all_0_11_11, all_50_8_180, all_25_8_86 and discharging atoms iLess0(all_0_12_12, all_0_11_11) = all_50_8_180, yields:
% 279.43/221.55 | (909) all_50_8_180 = all_25_8_86 | ~ (iLess0(all_0_12_12, all_0_11_11) = all_25_8_86)
% 279.43/221.55 |
% 279.43/221.55 | Instantiating formula (39) with all_0_8_8, xp, all_0_12_12, all_25_9_87 and discharging atoms sdtpldt0(all_0_8_8, xp) = all_0_12_12, yields:
% 279.43/221.55 | (910) all_25_9_87 = all_0_12_12 | ~ (sdtpldt0(all_0_8_8, xp) = all_25_9_87)
% 279.43/221.55 |
% 279.43/221.55 | Instantiating formula (39) with xr, xm, all_25_10_88, all_0_8_8 and discharging atoms sdtpldt0(xr, xm) = all_25_10_88, sdtpldt0(xr, xm) = all_0_8_8, yields:
% 279.43/221.55 | (911) all_25_10_88 = all_0_8_8
% 279.43/221.55 |
% 279.43/221.55 | Instantiating formula (39) with xp, xp, all_423_1_301, all_36_1_111 and discharging atoms sdtpldt0(xp, xp) = all_423_1_301, yields:
% 279.43/221.55 | (912) all_423_1_301 = all_36_1_111 | ~ (sdtpldt0(xp, xp) = all_36_1_111)
% 279.43/221.55 |
% 279.43/221.55 | Instantiating formula (39) with xm, xp, all_414_1_296, all_67_1_217 and discharging atoms sdtpldt0(xm, xp) = all_67_1_217, yields:
% 279.43/221.55 | (913) all_414_1_296 = all_67_1_217 | ~ (sdtpldt0(xm, xp) = all_414_1_296)
% 279.43/221.55 |
% 279.43/221.55 | Instantiating formula (97) with all_0_0_0, all_47_13_155, 0 and discharging atoms aNaturalNumber0(all_0_0_0) = all_47_13_155, aNaturalNumber0(all_0_0_0) = 0, yields:
% 279.43/221.55 | (914) all_47_13_155 = 0
% 279.43/221.55 |
% 279.43/221.55 | Instantiating formula (97) with all_0_4_4, all_414_2_297, 0 and discharging atoms aNaturalNumber0(all_0_4_4) = all_414_2_297, aNaturalNumber0(all_0_4_4) = 0, yields:
% 279.43/221.55 | (915) all_414_2_297 = 0
% 279.43/221.55 |
% 279.43/221.55 | Instantiating formula (97) with all_0_8_8, all_423_4_304, 0 and discharging atoms aNaturalNumber0(all_0_8_8) = all_423_4_304, aNaturalNumber0(all_0_8_8) = 0, yields:
% 279.43/221.55 | (916) all_423_4_304 = 0
% 279.43/221.55 |
% 279.43/221.55 | Instantiating formula (97) with xp, all_423_3_303, all_423_2_302 and discharging atoms aNaturalNumber0(xp) = all_423_2_302, aNaturalNumber0(xp) = all_423_3_303, yields:
% 279.43/221.55 | (917) all_423_2_302 = all_423_3_303
% 279.43/221.55 |
% 279.43/221.55 | Instantiating formula (97) with xp, all_47_12_154, all_423_3_303 and discharging atoms aNaturalNumber0(xp) = all_423_3_303, aNaturalNumber0(xp) = all_47_12_154, yields:
% 279.43/221.55 | (918) all_423_3_303 = all_47_12_154
% 279.43/221.55 |
% 279.43/221.55 | Instantiating formula (97) with xp, all_47_14_156, all_47_12_154 and discharging atoms aNaturalNumber0(xp) = all_47_12_154, aNaturalNumber0(xp) = all_47_14_156, yields:
% 279.43/221.55 | (919) all_47_12_154 = all_47_14_156
% 279.43/221.55 |
% 279.43/221.55 | Instantiating formula (97) with xp, all_38_12_127, all_47_14_156 and discharging atoms aNaturalNumber0(xp) = all_47_14_156, aNaturalNumber0(xp) = all_38_12_127, yields:
% 279.43/221.55 | (920) all_47_14_156 = all_38_12_127
% 279.43/221.55 |
% 279.43/221.55 | Instantiating formula (97) with xp, all_38_14_129, 0 and discharging atoms aNaturalNumber0(xp) = all_38_14_129, aNaturalNumber0(xp) = 0, yields:
% 279.43/221.55 | (810) all_38_14_129 = 0
% 279.43/221.55 |
% 279.43/221.55 | Instantiating formula (97) with xp, all_38_14_129, all_47_14_156 and discharging atoms aNaturalNumber0(xp) = all_47_14_156, aNaturalNumber0(xp) = all_38_14_129, yields:
% 279.43/221.55 | (922) all_47_14_156 = all_38_14_129
% 279.43/221.55 |
% 279.43/221.55 | Instantiating formula (97) with xp, all_25_12_90, all_423_2_302 and discharging atoms aNaturalNumber0(xp) = all_423_2_302, aNaturalNumber0(xp) = all_25_12_90, yields:
% 279.43/221.55 | (923) all_423_2_302 = all_25_12_90
% 279.43/221.55 |
% 279.43/221.55 | Instantiating formula (97) with xm, all_414_3_298, 0 and discharging atoms aNaturalNumber0(xm) = all_414_3_298, aNaturalNumber0(xm) = 0, yields:
% 279.43/221.55 | (924) all_414_3_298 = 0
% 279.43/221.55 |
% 279.43/221.55 | Instantiating formula (97) with xm, all_25_13_91, all_414_3_298 and discharging atoms aNaturalNumber0(xm) = all_414_3_298, aNaturalNumber0(xm) = all_25_13_91, yields:
% 279.43/221.55 | (925) all_414_3_298 = all_25_13_91
% 279.43/221.55 |
% 279.43/221.55 | Instantiating formula (97) with xn, all_414_4_299, 0 and discharging atoms aNaturalNumber0(xn) = all_414_4_299, aNaturalNumber0(xn) = 0, yields:
% 279.43/221.55 | (926) all_414_4_299 = 0
% 279.43/221.55 |
% 279.43/221.55 | Using (15) and (734) yields:
% 279.43/221.55 | (927) ~ (xn = sz00)
% 279.43/221.55 |
% 279.43/221.55 | Combining equations (917,923) yields a new equation:
% 279.43/221.55 | (928) all_423_3_303 = all_25_12_90
% 279.43/221.55 |
% 279.43/221.55 | Simplifying 928 yields:
% 279.43/221.55 | (929) all_423_3_303 = all_25_12_90
% 279.43/221.55 |
% 279.43/221.55 | Combining equations (918,929) yields a new equation:
% 279.43/221.55 | (930) all_47_12_154 = all_25_12_90
% 279.43/221.55 |
% 279.43/221.55 | Simplifying 930 yields:
% 279.43/221.55 | (931) all_47_12_154 = all_25_12_90
% 279.43/221.55 |
% 279.43/221.55 | Combining equations (925,924) yields a new equation:
% 279.43/221.55 | (932) all_25_13_91 = 0
% 279.43/221.55 |
% 279.43/221.55 | Simplifying 932 yields:
% 279.43/221.55 | (933) all_25_13_91 = 0
% 279.43/221.55 |
% 279.43/221.55 | Combining equations (919,931) yields a new equation:
% 279.43/221.55 | (934) all_47_14_156 = all_25_12_90
% 279.43/221.55 |
% 279.43/221.55 | Simplifying 934 yields:
% 279.43/221.55 | (935) all_47_14_156 = all_25_12_90
% 279.43/221.55 |
% 279.43/221.55 | Combining equations (922,920) yields a new equation:
% 279.43/221.55 | (936) all_38_12_127 = all_38_14_129
% 279.43/221.55 |
% 279.43/221.55 | Combining equations (935,920) yields a new equation:
% 279.43/221.55 | (937) all_38_12_127 = all_25_12_90
% 279.43/221.55 |
% 279.43/221.55 | Combining equations (936,937) yields a new equation:
% 279.43/221.55 | (938) all_38_14_129 = all_25_12_90
% 279.43/221.55 |
% 279.43/221.55 | Simplifying 938 yields:
% 279.43/221.55 | (939) all_38_14_129 = all_25_12_90
% 279.43/221.55 |
% 279.43/221.55 | Combining equations (810,939) yields a new equation:
% 279.43/221.55 | (940) all_25_12_90 = 0
% 279.43/221.55 |
% 279.43/221.55 | Combining equations (940,929) yields a new equation:
% 279.43/221.55 | (941) all_423_3_303 = 0
% 279.43/221.55 |
% 279.43/221.55 | Combining equations (940,923) yields a new equation:
% 279.43/221.55 | (942) all_423_2_302 = 0
% 279.43/221.55 |
% 279.43/221.55 | From (911) and (772) follows:
% 279.43/221.55 | (943) sdtpldt0(all_0_8_8, xp) = all_25_9_87
% 279.43/221.55 |
% 279.43/221.55 | From (914) and (743) follows:
% 279.43/221.55 | (72) aNaturalNumber0(all_0_0_0) = 0
% 279.43/221.55 |
% 279.43/221.55 | From (915) and (878) follows:
% 279.43/221.55 | (55) aNaturalNumber0(all_0_4_4) = 0
% 279.43/221.55 |
% 279.43/221.55 | From (940) and (774) follows:
% 279.43/221.55 | (98) aNaturalNumber0(xp) = 0
% 279.43/221.55 |
% 279.43/221.55 | From (933) and (766) follows:
% 279.43/221.55 | (76) aNaturalNumber0(xm) = 0
% 279.43/221.55 |
% 279.43/221.55 | From (926) and (881) follows:
% 279.43/221.55 | (34) aNaturalNumber0(xn) = 0
% 279.43/221.55 |
% 279.43/221.55 +-Applying beta-rule and splitting (128), into two cases.
% 279.43/221.55 |-Branch one:
% 279.43/221.55 | (873) ~ (sdtpldt0(all_0_12_12, all_0_4_4) = all_0_11_11)
% 279.43/221.55 |
% 279.43/221.55 | Using (861) and (873) yields:
% 279.43/221.55 | (695) $false
% 279.43/221.55 |
% 279.43/221.55 |-The branch is then unsatisfiable
% 279.43/221.55 |-Branch two:
% 279.43/221.55 | (861) sdtpldt0(all_0_12_12, all_0_4_4) = all_0_11_11
% 279.43/221.56 | (952) all_0_4_4 = xp | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_0_4_4, all_0_12_12) = v3 & sdtpldt0(xp, all_0_12_12) = v4 & aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(all_0_12_12) = v0 & aNaturalNumber0(xp) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 279.43/221.56 |
% 279.43/221.56 +-Applying beta-rule and splitting (952), into two cases.
% 279.43/221.56 |-Branch one:
% 279.43/221.56 | (953) all_0_4_4 = xp
% 279.43/221.56 |
% 279.43/221.56 | From (953) and (233) follows:
% 279.43/221.56 | (954) sdtpldt0(xp, xp) = all_36_1_111
% 279.43/221.56 |
% 279.43/221.56 | From (953) and (882) follows:
% 279.43/221.56 | (955) sdtpldt0(xm, xp) = all_414_1_296
% 279.43/221.56 |
% 279.43/221.56 +-Applying beta-rule and splitting (145), into two cases.
% 279.43/221.56 |-Branch one:
% 279.43/221.56 | (956) ~ (sdtpldt0(xn, xm) = sz00)
% 279.43/221.56 |
% 279.43/221.56 +-Applying beta-rule and splitting (913), into two cases.
% 279.43/221.56 |-Branch one:
% 279.43/221.56 | (957) ~ (sdtpldt0(xm, xp) = all_414_1_296)
% 279.43/221.56 |
% 279.43/221.56 | Using (955) and (957) yields:
% 279.43/221.56 | (695) $false
% 279.43/221.56 |
% 279.43/221.56 |-The branch is then unsatisfiable
% 279.43/221.56 |-Branch two:
% 279.43/221.56 | (955) sdtpldt0(xm, xp) = all_414_1_296
% 279.43/221.56 | (960) all_414_1_296 = all_67_1_217
% 279.43/221.56 |
% 279.43/221.56 | From (960) and (883) follows:
% 279.43/221.56 | (961) sdtpldt0(xn, all_67_1_217) = all_414_0_295
% 279.43/221.56 |
% 279.43/221.56 +-Applying beta-rule and splitting (880), into two cases.
% 279.43/221.56 |-Branch one:
% 279.43/221.56 | (962) ~ (all_414_2_297 = 0)
% 279.43/221.56 |
% 279.43/221.56 | Equations (915) can reduce 962 to:
% 279.43/221.56 | (346) $false
% 279.43/221.56 |
% 279.43/221.56 |-The branch is then unsatisfiable
% 279.43/221.56 |-Branch two:
% 279.43/221.56 | (915) all_414_2_297 = 0
% 279.43/221.56 | (965) ~ (all_414_3_298 = 0) | ~ (all_414_4_299 = 0) | all_414_0_295 = all_0_11_11
% 279.43/221.56 |
% 279.43/221.56 +-Applying beta-rule and splitting (965), into two cases.
% 279.43/221.56 |-Branch one:
% 279.43/221.56 | (966) ~ (all_414_3_298 = 0)
% 279.43/221.56 |
% 279.43/221.56 | Equations (924) can reduce 966 to:
% 279.43/221.56 | (346) $false
% 279.43/221.56 |
% 279.43/221.56 |-The branch is then unsatisfiable
% 279.43/221.56 |-Branch two:
% 279.43/221.56 | (924) all_414_3_298 = 0
% 279.43/221.56 | (969) ~ (all_414_4_299 = 0) | all_414_0_295 = all_0_11_11
% 279.43/221.56 |
% 279.43/221.56 +-Applying beta-rule and splitting (969), into two cases.
% 279.43/221.56 |-Branch one:
% 279.43/221.56 | (970) ~ (all_414_4_299 = 0)
% 279.43/221.56 |
% 279.43/221.56 | Equations (926) can reduce 970 to:
% 279.43/221.56 | (346) $false
% 279.43/221.56 |
% 279.43/221.56 |-The branch is then unsatisfiable
% 279.43/221.56 |-Branch two:
% 279.43/221.56 | (926) all_414_4_299 = 0
% 279.43/221.56 | (973) all_414_0_295 = all_0_11_11
% 279.43/221.56 |
% 279.43/221.56 | From (973) and (961) follows:
% 279.43/221.56 | (974) sdtpldt0(xn, all_67_1_217) = all_0_11_11
% 279.43/221.56 |
% 279.43/221.56 +-Applying beta-rule and splitting (910), into two cases.
% 279.43/221.56 |-Branch one:
% 279.43/221.56 | (975) ~ (sdtpldt0(all_0_8_8, xp) = all_25_9_87)
% 279.43/221.56 |
% 279.43/221.56 | Using (943) and (975) yields:
% 279.43/221.56 | (695) $false
% 279.43/221.56 |
% 279.43/221.56 |-The branch is then unsatisfiable
% 279.43/221.56 |-Branch two:
% 279.43/221.56 | (943) sdtpldt0(all_0_8_8, xp) = all_25_9_87
% 279.43/221.56 | (978) all_25_9_87 = all_0_12_12
% 279.43/221.56 |
% 279.43/221.56 | From (978) and (770) follows:
% 279.43/221.56 | (979) iLess0(all_0_12_12, all_0_11_11) = all_25_8_86
% 279.43/221.56 |
% 279.43/221.56 +-Applying beta-rule and splitting (171), into two cases.
% 279.43/221.56 |-Branch one:
% 279.43/221.56 | (980) ~ (all_16_14_41 = 0) & aNaturalNumber0(all_0_0_0) = all_16_14_41
% 279.43/221.56 |
% 279.43/221.56 | Applying alpha-rule on (980) yields:
% 279.43/221.56 | (981) ~ (all_16_14_41 = 0)
% 279.43/221.56 | (982) aNaturalNumber0(all_0_0_0) = all_16_14_41
% 279.43/221.56 |
% 279.43/221.56 | Instantiating formula (97) with all_0_0_0, all_16_14_41, 0 and discharging atoms aNaturalNumber0(all_0_0_0) = all_16_14_41, aNaturalNumber0(all_0_0_0) = 0, yields:
% 279.43/221.56 | (983) all_16_14_41 = 0
% 279.43/221.56 |
% 279.43/221.56 | Equations (983) can reduce 981 to:
% 279.43/221.56 | (346) $false
% 279.43/221.56 |
% 279.43/221.56 |-The branch is then unsatisfiable
% 279.43/221.56 |-Branch two:
% 279.43/221.56 | (985) isPrime0(xp) = all_16_11_38 & doDivides0(xp, xm) = all_16_6_33 & doDivides0(xp, xn) = all_16_7_34 & iLess0(all_16_9_36, all_0_11_11) = all_16_8_35 & sdtpldt0(all_16_10_37, xp) = all_16_9_36 & sdtpldt0(xn, xm) = all_16_10_37 & aNaturalNumber0(xp) = all_16_12_39 & aNaturalNumber0(xm) = all_16_13_40 & aNaturalNumber0(xn) = all_16_14_41 & ( ~ (all_16_8_35 = 0) | ~ (all_16_12_39 = 0) | ~ (all_16_13_40 = 0) | ~ (all_16_14_41 = 0) | (all_16_3_30 = xm & all_16_4_31 = 0 & all_16_6_33 = 0 & sdtasdt0(xp, all_16_5_32) = xm & aNaturalNumber0(all_16_5_32) = 0) | (all_16_3_30 = xn & all_16_4_31 = 0 & all_16_7_34 = 0 & sdtasdt0(xp, all_16_5_32) = xn & aNaturalNumber0(all_16_5_32) = 0) | ( ~ (all_16_11_38 = 0) & (xp = sz10 | xp = sz00 | (all_16_0_27 = xp & all_16_1_28 = 0 & all_16_3_30 = 0 & all_16_4_31 = 0 & ~ (all_16_5_32 = xp) & ~ (all_16_5_32 = sz10) & doDivides0(all_16_5_32, xp) = 0 & sdtasdt0(all_16_5_32, all_16_2_29) = xp & aNaturalNumber0(all_16_2_29) = 0 & aNaturalNumber0(all_16_5_32) = 0))))
% 279.43/221.56 |
% 279.43/221.56 | Applying alpha-rule on (985) yields:
% 279.43/221.56 | (986) aNaturalNumber0(xn) = all_16_14_41
% 279.43/221.56 | (987) sdtpldt0(xn, xm) = all_16_10_37
% 279.73/221.56 | (988) aNaturalNumber0(xp) = all_16_12_39
% 279.73/221.56 | (989) doDivides0(xp, xn) = all_16_7_34
% 279.73/221.56 | (990) iLess0(all_16_9_36, all_0_11_11) = all_16_8_35
% 279.73/221.56 | (991) ~ (all_16_8_35 = 0) | ~ (all_16_12_39 = 0) | ~ (all_16_13_40 = 0) | ~ (all_16_14_41 = 0) | (all_16_3_30 = xm & all_16_4_31 = 0 & all_16_6_33 = 0 & sdtasdt0(xp, all_16_5_32) = xm & aNaturalNumber0(all_16_5_32) = 0) | (all_16_3_30 = xn & all_16_4_31 = 0 & all_16_7_34 = 0 & sdtasdt0(xp, all_16_5_32) = xn & aNaturalNumber0(all_16_5_32) = 0) | ( ~ (all_16_11_38 = 0) & (xp = sz10 | xp = sz00 | (all_16_0_27 = xp & all_16_1_28 = 0 & all_16_3_30 = 0 & all_16_4_31 = 0 & ~ (all_16_5_32 = xp) & ~ (all_16_5_32 = sz10) & doDivides0(all_16_5_32, xp) = 0 & sdtasdt0(all_16_5_32, all_16_2_29) = xp & aNaturalNumber0(all_16_2_29) = 0 & aNaturalNumber0(all_16_5_32) = 0)))
% 279.73/221.56 | (992) isPrime0(xp) = all_16_11_38
% 279.73/221.56 | (993) sdtpldt0(all_16_10_37, xp) = all_16_9_36
% 279.73/221.56 | (994) aNaturalNumber0(xm) = all_16_13_40
% 279.73/221.56 | (995) doDivides0(xp, xm) = all_16_6_33
% 279.73/221.56 |
% 279.73/221.56 +-Applying beta-rule and splitting (892), into two cases.
% 279.73/221.56 |-Branch one:
% 279.73/221.56 | (996) ~ (all_423_2_302 = 0)
% 279.73/221.56 |
% 279.73/221.56 | Equations (942) can reduce 996 to:
% 279.73/221.56 | (346) $false
% 279.73/221.56 |
% 279.73/221.56 |-The branch is then unsatisfiable
% 279.73/221.56 |-Branch two:
% 279.73/221.56 | (942) all_423_2_302 = 0
% 279.73/221.56 | (999) ~ (all_423_3_303 = 0) | ~ (all_423_4_304 = 0) | all_423_0_300 = all_0_11_11
% 279.73/221.56 |
% 279.73/221.56 +-Applying beta-rule and splitting (999), into two cases.
% 279.73/221.56 |-Branch one:
% 279.73/221.56 | (1000) ~ (all_423_3_303 = 0)
% 279.73/221.57 |
% 279.73/221.57 | Equations (941) can reduce 1000 to:
% 279.73/221.57 | (346) $false
% 279.73/221.57 |
% 279.73/221.57 |-The branch is then unsatisfiable
% 279.73/221.57 |-Branch two:
% 279.73/221.57 | (941) all_423_3_303 = 0
% 279.73/221.57 | (1003) ~ (all_423_4_304 = 0) | all_423_0_300 = all_0_11_11
% 279.73/221.57 |
% 279.73/221.57 +-Applying beta-rule and splitting (1003), into two cases.
% 279.73/221.57 |-Branch one:
% 279.73/221.57 | (1004) ~ (all_423_4_304 = 0)
% 279.73/221.57 |
% 279.73/221.57 | Equations (916) can reduce 1004 to:
% 279.73/221.57 | (346) $false
% 279.73/221.57 |
% 279.73/221.57 |-The branch is then unsatisfiable
% 279.73/221.57 |-Branch two:
% 279.73/221.57 | (916) all_423_4_304 = 0
% 279.73/221.57 | (1007) all_423_0_300 = all_0_11_11
% 279.73/221.57 |
% 279.73/221.57 | From (1007) and (895) follows:
% 279.73/221.57 | (1008) sdtpldt0(all_0_8_8, all_423_1_301) = all_0_11_11
% 279.73/221.57 |
% 279.73/221.57 +-Applying beta-rule and splitting (418), into two cases.
% 279.73/221.57 |-Branch one:
% 279.73/221.57 | (1009) ~ (sdtpldt0(xn, xm) = all_67_0_216)
% 279.73/221.57 |
% 279.73/221.57 | From (783) and (1009) follows:
% 279.73/221.57 | (1010) ~ (sdtpldt0(xn, xm) = all_0_11_11)
% 279.73/221.57 |
% 279.73/221.57 +-Applying beta-rule and splitting (912), into two cases.
% 279.73/221.57 |-Branch one:
% 279.73/221.57 | (1011) ~ (sdtpldt0(xp, xp) = all_36_1_111)
% 279.73/221.57 |
% 279.75/221.57 | Using (954) and (1011) yields:
% 279.75/221.57 | (695) $false
% 279.75/221.57 |
% 279.75/221.57 |-The branch is then unsatisfiable
% 279.75/221.57 |-Branch two:
% 279.75/221.57 | (954) sdtpldt0(xp, xp) = all_36_1_111
% 279.75/221.57 | (1014) all_423_1_301 = all_36_1_111
% 279.75/221.57 |
% 279.75/221.57 | From (1014) and (1008) follows:
% 279.75/221.57 | (1015) sdtpldt0(all_0_8_8, all_36_1_111) = all_0_11_11
% 279.75/221.57 |
% 279.75/221.57 +-Applying beta-rule and splitting (909), into two cases.
% 279.75/221.57 |-Branch one:
% 279.75/221.57 | (1016) ~ (iLess0(all_0_12_12, all_0_11_11) = all_25_8_86)
% 279.75/221.57 |
% 279.75/221.57 | Using (979) and (1016) yields:
% 279.75/221.57 | (695) $false
% 279.75/221.57 |
% 279.75/221.57 |-The branch is then unsatisfiable
% 279.75/221.57 |-Branch two:
% 279.75/221.57 | (979) iLess0(all_0_12_12, all_0_11_11) = all_25_8_86
% 279.75/221.57 | (1019) all_50_8_180 = all_25_8_86
% 279.75/221.57 |
% 279.75/221.57 | Equations (1019) can reduce 735 to:
% 279.75/221.57 | (1020) ~ (all_25_8_86 = 0)
% 279.75/221.57 |
% 279.75/221.57 | From (1019) and (907) follows:
% 279.75/221.57 | (979) iLess0(all_0_12_12, all_0_11_11) = all_25_8_86
% 279.75/221.57 |
% 279.75/221.57 | Instantiating formula (39) with xn, xm, all_16_10_37, all_0_12_12 and discharging atoms sdtpldt0(xn, xm) = all_16_10_37, sdtpldt0(xn, xm) = all_0_12_12, yields:
% 279.75/221.57 | (1022) all_16_10_37 = all_0_12_12
% 279.75/221.57 |
% 279.75/221.57 | Using (987) and (1010) yields:
% 279.75/221.57 | (1023) ~ (all_16_10_37 = all_0_11_11)
% 279.75/221.57 |
% 279.75/221.57 | Using (987) and (956) yields:
% 279.75/221.57 | (1024) ~ (all_16_10_37 = sz00)
% 279.75/221.57 |
% 279.75/221.57 | Equations (1022) can reduce 1023 to:
% 279.75/221.57 | (857) ~ (all_0_11_11 = all_0_12_12)
% 279.75/221.57 |
% 279.75/221.57 | Simplifying 857 yields:
% 279.75/221.57 | (858) ~ (all_0_11_11 = all_0_12_12)
% 279.75/221.57 |
% 279.75/221.57 | Equations (1022) can reduce 1024 to:
% 279.75/221.57 | (1027) ~ (all_0_12_12 = sz00)
% 279.75/221.57 |
% 279.75/221.57 | Instantiating formula (82) with all_25_8_86, all_0_11_11, all_0_12_12 and discharging atoms iLess0(all_0_12_12, all_0_11_11) = all_25_8_86, yields:
% 279.75/221.57 | (1028) all_25_8_86 = 0 | all_0_11_11 = all_0_12_12 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_0_12_12, all_0_11_11) = v2 & aNaturalNumber0(all_0_11_11) = v1 & aNaturalNumber0(all_0_12_12) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 279.75/221.57 |
% 279.75/221.57 | Instantiating formula (48) with all_103_0_257, all_0_12_12, all_0_11_11 and discharging atoms sdtlseqdt0(all_0_11_11, all_0_12_12) = all_103_0_257, yields:
% 279.75/221.57 | (1029) all_103_0_257 = 0 | all_0_12_12 = sz00 | ? [v0] : ? [v1] : ? [v2] : (doDivides0(all_0_11_11, all_0_12_12) = v2 & aNaturalNumber0(all_0_11_11) = v0 & aNaturalNumber0(all_0_12_12) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 279.75/221.57 |
% 279.75/221.57 | Instantiating formula (57) with all_0_11_11, all_36_1_111, all_0_8_8 and discharging atoms sdtpldt0(all_0_8_8, all_36_1_111) = all_0_11_11, yields:
% 279.75/221.57 | (1030) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_36_1_111) = v1 & aNaturalNumber0(all_0_8_8) = v0 & aNaturalNumber0(all_0_11_11) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 279.75/221.57 |
% 279.75/221.57 | Instantiating formula (63) with all_0_11_11, all_58_2_198, all_0_12_12 and discharging atoms sdtpldt0(all_0_12_12, all_58_2_198) = all_0_11_11, yields:
% 279.75/221.57 | (1031) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_58_2_198, all_0_12_12) = v2 & aNaturalNumber0(all_58_2_198) = v1 & aNaturalNumber0(all_0_12_12) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_11_11))
% 279.75/221.57 |
% 279.75/221.57 | Instantiating formula (57) with all_0_12_12, all_67_1_217, xr and discharging atoms sdtpldt0(xr, all_67_1_217) = all_0_12_12, yields:
% 279.75/221.57 | (1032) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_67_1_217) = v1 & aNaturalNumber0(all_0_12_12) = v2 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 279.75/221.57 |
% 279.75/221.57 | Instantiating formula (57) with all_0_12_12, all_63_1_209, xr and discharging atoms sdtpldt0(xr, all_63_1_209) = all_0_12_12, yields:
% 279.75/221.57 | (1033) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_63_1_209) = v1 & aNaturalNumber0(all_0_12_12) = v2 & aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 279.75/221.57 |
% 279.75/221.57 | Instantiating formula (57) with all_0_11_11, all_67_1_217, xn and discharging atoms sdtpldt0(xn, all_67_1_217) = all_0_11_11, yields:
% 279.75/221.57 | (1034) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_67_1_217) = v1 & aNaturalNumber0(all_0_11_11) = v2 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 279.75/221.57 |
% 279.75/221.57 | Instantiating (1034) with all_595_0_308, all_595_1_309, all_595_2_310 yields:
% 279.75/221.57 | (1035) aNaturalNumber0(all_67_1_217) = all_595_1_309 & aNaturalNumber0(all_0_11_11) = all_595_0_308 & aNaturalNumber0(xn) = all_595_2_310 & ( ~ (all_595_1_309 = 0) | ~ (all_595_2_310 = 0) | all_595_0_308 = 0)
% 279.75/221.57 |
% 279.75/221.57 | Applying alpha-rule on (1035) yields:
% 279.75/221.57 | (1036) aNaturalNumber0(all_67_1_217) = all_595_1_309
% 279.75/221.57 | (1037) aNaturalNumber0(all_0_11_11) = all_595_0_308
% 279.75/221.57 | (1038) aNaturalNumber0(xn) = all_595_2_310
% 279.75/221.57 | (1039) ~ (all_595_1_309 = 0) | ~ (all_595_2_310 = 0) | all_595_0_308 = 0
% 279.75/221.57 |
% 279.75/221.57 | Instantiating (1032) with all_605_0_327, all_605_1_328, all_605_2_329 yields:
% 279.75/221.57 | (1040) aNaturalNumber0(all_67_1_217) = all_605_1_328 & aNaturalNumber0(all_0_12_12) = all_605_0_327 & aNaturalNumber0(xr) = all_605_2_329 & ( ~ (all_605_1_328 = 0) | ~ (all_605_2_329 = 0) | all_605_0_327 = 0)
% 279.75/221.57 |
% 279.75/221.57 | Applying alpha-rule on (1040) yields:
% 279.75/221.57 | (1041) aNaturalNumber0(all_67_1_217) = all_605_1_328
% 279.75/221.58 | (1042) aNaturalNumber0(all_0_12_12) = all_605_0_327
% 279.75/221.58 | (1043) aNaturalNumber0(xr) = all_605_2_329
% 279.75/221.58 | (1044) ~ (all_605_1_328 = 0) | ~ (all_605_2_329 = 0) | all_605_0_327 = 0
% 279.75/221.58 |
% 279.75/221.58 | Instantiating (1033) with all_619_0_356, all_619_1_357, all_619_2_358 yields:
% 279.75/221.58 | (1045) aNaturalNumber0(all_63_1_209) = all_619_1_357 & aNaturalNumber0(all_0_12_12) = all_619_0_356 & aNaturalNumber0(xr) = all_619_2_358 & ( ~ (all_619_1_357 = 0) | ~ (all_619_2_358 = 0) | all_619_0_356 = 0)
% 279.75/221.58 |
% 279.75/221.58 | Applying alpha-rule on (1045) yields:
% 279.75/221.58 | (1046) aNaturalNumber0(all_63_1_209) = all_619_1_357
% 279.75/221.58 | (1047) aNaturalNumber0(all_0_12_12) = all_619_0_356
% 279.75/221.58 | (1048) aNaturalNumber0(xr) = all_619_2_358
% 279.75/221.58 | (1049) ~ (all_619_1_357 = 0) | ~ (all_619_2_358 = 0) | all_619_0_356 = 0
% 279.75/221.58 |
% 279.75/221.58 | Instantiating (1030) with all_629_0_373, all_629_1_374, all_629_2_375 yields:
% 279.75/221.58 | (1050) aNaturalNumber0(all_36_1_111) = all_629_1_374 & aNaturalNumber0(all_0_8_8) = all_629_2_375 & aNaturalNumber0(all_0_11_11) = all_629_0_373 & ( ~ (all_629_1_374 = 0) | ~ (all_629_2_375 = 0) | all_629_0_373 = 0)
% 279.75/221.58 |
% 279.75/221.58 | Applying alpha-rule on (1050) yields:
% 279.75/221.58 | (1051) aNaturalNumber0(all_36_1_111) = all_629_1_374
% 279.75/221.58 | (1052) aNaturalNumber0(all_0_8_8) = all_629_2_375
% 279.75/221.58 | (1053) aNaturalNumber0(all_0_11_11) = all_629_0_373
% 279.75/221.58 | (1054) ~ (all_629_1_374 = 0) | ~ (all_629_2_375 = 0) | all_629_0_373 = 0
% 279.75/221.58 |
% 279.75/221.58 | Instantiating (1031) with all_727_0_802, all_727_1_803, all_727_2_804 yields:
% 279.75/221.58 | (1055) sdtpldt0(all_58_2_198, all_0_12_12) = all_727_0_802 & aNaturalNumber0(all_58_2_198) = all_727_1_803 & aNaturalNumber0(all_0_12_12) = all_727_2_804 & ( ~ (all_727_1_803 = 0) | ~ (all_727_2_804 = 0) | all_727_0_802 = all_0_11_11)
% 279.75/221.58 |
% 279.75/221.58 | Applying alpha-rule on (1055) yields:
% 279.75/221.58 | (1056) sdtpldt0(all_58_2_198, all_0_12_12) = all_727_0_802
% 279.75/221.58 | (1057) aNaturalNumber0(all_58_2_198) = all_727_1_803
% 279.75/221.58 | (1058) aNaturalNumber0(all_0_12_12) = all_727_2_804
% 279.75/221.58 | (1059) ~ (all_727_1_803 = 0) | ~ (all_727_2_804 = 0) | all_727_0_802 = all_0_11_11
% 279.75/221.58 |
% 279.75/221.58 +-Applying beta-rule and splitting (1029), into two cases.
% 279.75/221.58 |-Branch one:
% 279.75/221.58 | (1060) all_0_12_12 = sz00
% 279.75/221.58 |
% 279.75/221.58 | Equations (1060) can reduce 1027 to:
% 279.75/221.58 | (346) $false
% 279.75/221.58 |
% 279.75/221.58 |-The branch is then unsatisfiable
% 279.75/221.58 |-Branch two:
% 279.75/221.58 | (1027) ~ (all_0_12_12 = sz00)
% 279.75/221.58 | (1063) all_103_0_257 = 0 | ? [v0] : ? [v1] : ? [v2] : (doDivides0(all_0_11_11, all_0_12_12) = v2 & aNaturalNumber0(all_0_11_11) = v0 & aNaturalNumber0(all_0_12_12) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 279.75/221.58 |
% 279.75/221.58 +-Applying beta-rule and splitting (1063), into two cases.
% 279.75/221.58 |-Branch one:
% 279.75/221.58 | (1064) all_103_0_257 = 0
% 279.75/221.58 |
% 279.75/221.58 | Equations (1064) can reduce 884 to:
% 279.75/221.58 | (346) $false
% 279.75/221.58 |
% 279.75/221.58 |-The branch is then unsatisfiable
% 279.75/221.58 |-Branch two:
% 279.75/221.58 | (884) ~ (all_103_0_257 = 0)
% 279.75/221.58 | (1067) ? [v0] : ? [v1] : ? [v2] : (doDivides0(all_0_11_11, all_0_12_12) = v2 & aNaturalNumber0(all_0_11_11) = v0 & aNaturalNumber0(all_0_12_12) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 279.75/221.58 |
% 279.75/221.58 | Instantiating (1067) with all_772_0_817, all_772_1_818, all_772_2_819 yields:
% 279.75/221.58 | (1068) doDivides0(all_0_11_11, all_0_12_12) = all_772_0_817 & aNaturalNumber0(all_0_11_11) = all_772_2_819 & aNaturalNumber0(all_0_12_12) = all_772_1_818 & ( ~ (all_772_0_817 = 0) | ~ (all_772_1_818 = 0) | ~ (all_772_2_819 = 0))
% 279.75/221.58 |
% 279.75/221.58 | Applying alpha-rule on (1068) yields:
% 279.75/221.58 | (1069) doDivides0(all_0_11_11, all_0_12_12) = all_772_0_817
% 279.75/221.58 | (1070) aNaturalNumber0(all_0_11_11) = all_772_2_819
% 279.75/221.58 | (1071) aNaturalNumber0(all_0_12_12) = all_772_1_818
% 279.75/221.58 | (1072) ~ (all_772_0_817 = 0) | ~ (all_772_1_818 = 0) | ~ (all_772_2_819 = 0)
% 279.75/221.58 |
% 279.75/221.58 | Instantiating formula (97) with all_0_11_11, all_629_0_373, 0 and discharging atoms aNaturalNumber0(all_0_11_11) = all_629_0_373, aNaturalNumber0(all_0_11_11) = 0, yields:
% 279.75/221.58 | (1073) all_629_0_373 = 0
% 279.75/221.58 |
% 279.75/221.58 | Instantiating formula (97) with all_0_11_11, all_629_0_373, all_772_2_819 and discharging atoms aNaturalNumber0(all_0_11_11) = all_772_2_819, aNaturalNumber0(all_0_11_11) = all_629_0_373, yields:
% 279.75/221.58 | (1074) all_772_2_819 = all_629_0_373
% 279.75/221.58 |
% 279.75/221.58 | Instantiating formula (97) with all_0_11_11, all_595_0_308, all_772_2_819 and discharging atoms aNaturalNumber0(all_0_11_11) = all_772_2_819, aNaturalNumber0(all_0_11_11) = all_595_0_308, yields:
% 279.75/221.58 | (1075) all_772_2_819 = all_595_0_308
% 279.75/221.58 |
% 279.75/221.58 | Instantiating formula (97) with all_0_12_12, all_772_1_818, 0 and discharging atoms aNaturalNumber0(all_0_12_12) = all_772_1_818, aNaturalNumber0(all_0_12_12) = 0, yields:
% 279.75/221.58 | (1076) all_772_1_818 = 0
% 279.75/221.58 |
% 279.75/221.58 | Instantiating formula (97) with all_0_12_12, all_727_2_804, all_772_1_818 and discharging atoms aNaturalNumber0(all_0_12_12) = all_772_1_818, aNaturalNumber0(all_0_12_12) = all_727_2_804, yields:
% 279.75/221.58 | (1077) all_772_1_818 = all_727_2_804
% 279.75/221.58 |
% 279.75/221.58 | Instantiating formula (97) with all_0_12_12, all_619_0_356, all_772_1_818 and discharging atoms aNaturalNumber0(all_0_12_12) = all_772_1_818, aNaturalNumber0(all_0_12_12) = all_619_0_356, yields:
% 279.75/221.58 | (1078) all_772_1_818 = all_619_0_356
% 279.75/221.58 |
% 279.75/221.58 | Instantiating formula (97) with all_0_12_12, all_605_0_327, all_619_0_356 and discharging atoms aNaturalNumber0(all_0_12_12) = all_619_0_356, aNaturalNumber0(all_0_12_12) = all_605_0_327, yields:
% 279.75/221.58 | (1079) all_619_0_356 = all_605_0_327
% 279.75/221.58 |
% 279.75/221.58 | Combining equations (1076,1077) yields a new equation:
% 279.75/221.58 | (1080) all_727_2_804 = 0
% 279.75/221.58 |
% 279.75/221.58 | Combining equations (1078,1077) yields a new equation:
% 279.75/221.58 | (1081) all_727_2_804 = all_619_0_356
% 279.75/221.58 |
% 279.75/221.58 | Combining equations (1074,1075) yields a new equation:
% 279.75/221.58 | (1082) all_629_0_373 = all_595_0_308
% 279.75/221.58 |
% 279.75/221.58 | Simplifying 1082 yields:
% 279.75/221.58 | (1083) all_629_0_373 = all_595_0_308
% 279.75/221.58 |
% 279.75/221.58 | Combining equations (1081,1080) yields a new equation:
% 279.75/221.58 | (1084) all_619_0_356 = 0
% 279.75/221.58 |
% 279.75/221.58 | Simplifying 1084 yields:
% 279.75/221.58 | (1085) all_619_0_356 = 0
% 279.75/221.58 |
% 279.75/221.58 | Combining equations (1073,1083) yields a new equation:
% 279.75/221.58 | (1086) all_595_0_308 = 0
% 279.75/221.58 |
% 279.75/221.58 | Combining equations (1079,1085) yields a new equation:
% 279.75/221.58 | (1087) all_605_0_327 = 0
% 279.75/221.58 |
% 279.75/221.58 | Simplifying 1087 yields:
% 279.75/221.58 | (1088) all_605_0_327 = 0
% 279.75/221.58 |
% 279.75/221.58 | From (1086) and (1037) follows:
% 279.75/221.58 | (872) aNaturalNumber0(all_0_11_11) = 0
% 279.75/221.58 |
% 279.75/221.58 | From (1088) and (1042) follows:
% 279.75/221.59 | (864) aNaturalNumber0(all_0_12_12) = 0
% 279.75/221.59 |
% 279.75/221.59 +-Applying beta-rule and splitting (1028), into two cases.
% 279.75/221.59 |-Branch one:
% 279.75/221.59 | (1091) all_25_8_86 = 0
% 279.75/221.59 |
% 279.75/221.59 | Equations (1091) can reduce 1020 to:
% 279.75/221.59 | (346) $false
% 279.75/221.59 |
% 279.75/221.59 |-The branch is then unsatisfiable
% 279.75/221.59 |-Branch two:
% 279.75/221.59 | (1020) ~ (all_25_8_86 = 0)
% 279.75/221.59 | (1094) all_0_11_11 = all_0_12_12 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_0_12_12, all_0_11_11) = v2 & aNaturalNumber0(all_0_11_11) = v1 & aNaturalNumber0(all_0_12_12) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 279.75/221.59 |
% 279.75/221.59 +-Applying beta-rule and splitting (1094), into two cases.
% 279.75/221.59 |-Branch one:
% 279.75/221.59 | (1095) all_0_11_11 = all_0_12_12
% 279.75/221.59 |
% 279.75/221.59 | Equations (1095) can reduce 858 to:
% 279.75/221.59 | (346) $false
% 279.75/221.59 |
% 279.75/221.59 |-The branch is then unsatisfiable
% 279.75/221.59 |-Branch two:
% 279.75/221.59 | (858) ~ (all_0_11_11 = all_0_12_12)
% 279.75/221.59 | (1098) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_0_12_12, all_0_11_11) = v2 & aNaturalNumber0(all_0_11_11) = v1 & aNaturalNumber0(all_0_12_12) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 279.75/221.59 |
% 279.75/221.59 | Instantiating (1098) with all_1053_0_952, all_1053_1_953, all_1053_2_954 yields:
% 279.75/221.59 | (1099) sdtlseqdt0(all_0_12_12, all_0_11_11) = all_1053_0_952 & aNaturalNumber0(all_0_11_11) = all_1053_1_953 & aNaturalNumber0(all_0_12_12) = all_1053_2_954 & ( ~ (all_1053_0_952 = 0) | ~ (all_1053_1_953 = 0) | ~ (all_1053_2_954 = 0))
% 279.75/221.59 |
% 279.75/221.59 | Applying alpha-rule on (1099) yields:
% 279.75/221.59 | (1100) sdtlseqdt0(all_0_12_12, all_0_11_11) = all_1053_0_952
% 279.75/221.59 | (1101) aNaturalNumber0(all_0_11_11) = all_1053_1_953
% 279.75/221.59 | (1102) aNaturalNumber0(all_0_12_12) = all_1053_2_954
% 279.75/221.59 | (1103) ~ (all_1053_0_952 = 0) | ~ (all_1053_1_953 = 0) | ~ (all_1053_2_954 = 0)
% 279.75/221.59 |
% 279.75/221.59 | Instantiating formula (23) with all_0_12_12, all_0_11_11, all_1053_0_952, 0 and discharging atoms sdtlseqdt0(all_0_12_12, all_0_11_11) = all_1053_0_952, sdtlseqdt0(all_0_12_12, all_0_11_11) = 0, yields:
% 279.75/221.59 | (1104) all_1053_0_952 = 0
% 279.75/221.59 |
% 279.75/221.59 | Instantiating formula (97) with all_0_11_11, all_1053_1_953, 0 and discharging atoms aNaturalNumber0(all_0_11_11) = all_1053_1_953, aNaturalNumber0(all_0_11_11) = 0, yields:
% 279.75/221.59 | (1105) all_1053_1_953 = 0
% 279.75/221.59 |
% 279.75/221.59 | Instantiating formula (97) with all_0_12_12, all_1053_2_954, 0 and discharging atoms aNaturalNumber0(all_0_12_12) = all_1053_2_954, aNaturalNumber0(all_0_12_12) = 0, yields:
% 279.75/221.59 | (1106) all_1053_2_954 = 0
% 279.75/221.59 |
% 279.75/221.59 +-Applying beta-rule and splitting (1103), into two cases.
% 279.75/221.59 |-Branch one:
% 279.75/221.59 | (1107) ~ (all_1053_0_952 = 0)
% 279.75/221.59 |
% 279.75/221.59 | Equations (1104) can reduce 1107 to:
% 279.75/221.59 | (346) $false
% 279.75/221.59 |
% 279.75/221.59 |-The branch is then unsatisfiable
% 279.75/221.59 |-Branch two:
% 279.75/221.59 | (1104) all_1053_0_952 = 0
% 279.75/221.59 | (1110) ~ (all_1053_1_953 = 0) | ~ (all_1053_2_954 = 0)
% 279.75/221.59 |
% 279.75/221.59 +-Applying beta-rule and splitting (1110), into two cases.
% 279.75/221.59 |-Branch one:
% 279.75/221.59 | (1111) ~ (all_1053_1_953 = 0)
% 279.75/221.59 |
% 279.75/221.59 | Equations (1105) can reduce 1111 to:
% 279.75/221.59 | (346) $false
% 279.75/221.59 |
% 279.75/221.59 |-The branch is then unsatisfiable
% 279.75/221.59 |-Branch two:
% 279.75/221.59 | (1105) all_1053_1_953 = 0
% 279.75/221.59 | (1114) ~ (all_1053_2_954 = 0)
% 279.75/221.59 |
% 279.75/221.59 | Equations (1106) can reduce 1114 to:
% 279.75/221.59 | (346) $false
% 279.75/221.59 |
% 279.75/221.59 |-The branch is then unsatisfiable
% 279.75/221.59 |-Branch two:
% 279.75/221.59 | (1116) sdtpldt0(xn, xm) = all_67_0_216
% 279.75/221.59 | (1117) all_67_0_216 = all_19_10_55
% 279.75/221.59 |
% 279.75/221.59 | Combining equations (783,1117) yields a new equation:
% 279.75/221.59 | (1118) all_19_10_55 = all_0_11_11
% 279.75/221.59 |
% 279.75/221.59 | Combining equations (417,1118) yields a new equation:
% 279.75/221.59 | (1095) all_0_11_11 = all_0_12_12
% 279.75/221.59 |
% 279.75/221.59 | Equations (1095) can reduce 858 to:
% 279.75/221.59 | (346) $false
% 279.75/221.59 |
% 279.75/221.59 |-The branch is then unsatisfiable
% 279.75/221.59 |-Branch two:
% 279.75/221.59 | (1121) sdtpldt0(xn, xm) = sz00
% 279.75/221.59 | (1122) xn = sz00 | ? [v0] : ? [v1] : (aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 279.75/221.59 |
% 279.75/221.59 +-Applying beta-rule and splitting (1122), into two cases.
% 279.75/221.59 |-Branch one:
% 279.75/221.59 | (1123) xn = sz00
% 279.75/221.59 |
% 279.75/221.59 | Equations (1123) can reduce 927 to:
% 279.75/221.59 | (346) $false
% 279.75/221.59 |
% 279.75/221.59 |-The branch is then unsatisfiable
% 279.75/221.59 |-Branch two:
% 279.75/221.59 | (927) ~ (xn = sz00)
% 279.75/221.59 | (1126) ? [v0] : ? [v1] : (aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 279.75/221.59 |
% 279.75/221.59 | Instantiating (1126) with all_469_0_964, all_469_1_965 yields:
% 279.75/221.59 | (1127) aNaturalNumber0(xm) = all_469_0_964 & aNaturalNumber0(xn) = all_469_1_965 & ( ~ (all_469_0_964 = 0) | ~ (all_469_1_965 = 0))
% 279.75/221.60 |
% 279.75/221.60 | Applying alpha-rule on (1127) yields:
% 279.75/221.60 | (1128) aNaturalNumber0(xm) = all_469_0_964
% 279.75/221.60 | (1129) aNaturalNumber0(xn) = all_469_1_965
% 279.75/221.60 | (1130) ~ (all_469_0_964 = 0) | ~ (all_469_1_965 = 0)
% 279.75/221.60 |
% 279.75/221.60 +-Applying beta-rule and splitting (171), into two cases.
% 279.75/221.60 |-Branch one:
% 279.75/221.60 | (980) ~ (all_16_14_41 = 0) & aNaturalNumber0(all_0_0_0) = all_16_14_41
% 279.75/221.60 |
% 279.75/221.60 | Applying alpha-rule on (980) yields:
% 279.75/221.60 | (981) ~ (all_16_14_41 = 0)
% 279.75/221.60 | (982) aNaturalNumber0(all_0_0_0) = all_16_14_41
% 279.75/221.60 |
% 279.75/221.60 | Instantiating formula (97) with all_0_0_0, all_16_14_41, 0 and discharging atoms aNaturalNumber0(all_0_0_0) = all_16_14_41, aNaturalNumber0(all_0_0_0) = 0, yields:
% 279.75/221.60 | (983) all_16_14_41 = 0
% 279.75/221.60 |
% 279.75/221.60 | Equations (983) can reduce 981 to:
% 279.75/221.60 | (346) $false
% 279.75/221.60 |
% 279.75/221.60 |-The branch is then unsatisfiable
% 279.75/221.60 |-Branch two:
% 279.75/221.60 | (985) isPrime0(xp) = all_16_11_38 & doDivides0(xp, xm) = all_16_6_33 & doDivides0(xp, xn) = all_16_7_34 & iLess0(all_16_9_36, all_0_11_11) = all_16_8_35 & sdtpldt0(all_16_10_37, xp) = all_16_9_36 & sdtpldt0(xn, xm) = all_16_10_37 & aNaturalNumber0(xp) = all_16_12_39 & aNaturalNumber0(xm) = all_16_13_40 & aNaturalNumber0(xn) = all_16_14_41 & ( ~ (all_16_8_35 = 0) | ~ (all_16_12_39 = 0) | ~ (all_16_13_40 = 0) | ~ (all_16_14_41 = 0) | (all_16_3_30 = xm & all_16_4_31 = 0 & all_16_6_33 = 0 & sdtasdt0(xp, all_16_5_32) = xm & aNaturalNumber0(all_16_5_32) = 0) | (all_16_3_30 = xn & all_16_4_31 = 0 & all_16_7_34 = 0 & sdtasdt0(xp, all_16_5_32) = xn & aNaturalNumber0(all_16_5_32) = 0) | ( ~ (all_16_11_38 = 0) & (xp = sz10 | xp = sz00 | (all_16_0_27 = xp & all_16_1_28 = 0 & all_16_3_30 = 0 & all_16_4_31 = 0 & ~ (all_16_5_32 = xp) & ~ (all_16_5_32 = sz10) & doDivides0(all_16_5_32, xp) = 0 & sdtasdt0(all_16_5_32, all_16_2_29) = xp & aNaturalNumber0(all_16_2_29) = 0 & aNaturalNumber0(all_16_5_32) = 0))))
% 279.75/221.60 |
% 279.75/221.60 | Applying alpha-rule on (985) yields:
% 279.75/221.60 | (986) aNaturalNumber0(xn) = all_16_14_41
% 279.75/221.60 | (987) sdtpldt0(xn, xm) = all_16_10_37
% 279.75/221.60 | (988) aNaturalNumber0(xp) = all_16_12_39
% 279.75/221.60 | (989) doDivides0(xp, xn) = all_16_7_34
% 279.75/221.60 | (990) iLess0(all_16_9_36, all_0_11_11) = all_16_8_35
% 279.75/221.60 | (991) ~ (all_16_8_35 = 0) | ~ (all_16_12_39 = 0) | ~ (all_16_13_40 = 0) | ~ (all_16_14_41 = 0) | (all_16_3_30 = xm & all_16_4_31 = 0 & all_16_6_33 = 0 & sdtasdt0(xp, all_16_5_32) = xm & aNaturalNumber0(all_16_5_32) = 0) | (all_16_3_30 = xn & all_16_4_31 = 0 & all_16_7_34 = 0 & sdtasdt0(xp, all_16_5_32) = xn & aNaturalNumber0(all_16_5_32) = 0) | ( ~ (all_16_11_38 = 0) & (xp = sz10 | xp = sz00 | (all_16_0_27 = xp & all_16_1_28 = 0 & all_16_3_30 = 0 & all_16_4_31 = 0 & ~ (all_16_5_32 = xp) & ~ (all_16_5_32 = sz10) & doDivides0(all_16_5_32, xp) = 0 & sdtasdt0(all_16_5_32, all_16_2_29) = xp & aNaturalNumber0(all_16_2_29) = 0 & aNaturalNumber0(all_16_5_32) = 0)))
% 279.75/221.60 | (992) isPrime0(xp) = all_16_11_38
% 279.75/221.60 | (993) sdtpldt0(all_16_10_37, xp) = all_16_9_36
% 279.75/221.60 | (994) aNaturalNumber0(xm) = all_16_13_40
% 279.75/221.60 | (995) doDivides0(xp, xm) = all_16_6_33
% 279.75/221.60 |
% 279.75/221.60 | Instantiating formula (97) with xm, all_469_0_964, 0 and discharging atoms aNaturalNumber0(xm) = all_469_0_964, aNaturalNumber0(xm) = 0, yields:
% 279.75/221.60 | (1147) all_469_0_964 = 0
% 279.75/221.60 |
% 279.75/221.60 | Instantiating formula (97) with xm, all_16_13_40, all_469_0_964 and discharging atoms aNaturalNumber0(xm) = all_469_0_964, aNaturalNumber0(xm) = all_16_13_40, yields:
% 279.75/221.60 | (1148) all_469_0_964 = all_16_13_40
% 279.75/221.60 |
% 279.75/221.60 | Instantiating formula (97) with xn, all_469_1_965, 0 and discharging atoms aNaturalNumber0(xn) = all_469_1_965, aNaturalNumber0(xn) = 0, yields:
% 279.75/221.60 | (1149) all_469_1_965 = 0
% 279.75/221.60 |
% 279.75/221.60 | Combining equations (1147,1148) yields a new equation:
% 279.75/221.60 | (1150) all_16_13_40 = 0
% 279.75/221.60 |
% 279.75/221.60 | Combining equations (1150,1148) yields a new equation:
% 279.75/221.60 | (1147) all_469_0_964 = 0
% 279.75/221.60 |
% 279.75/221.60 +-Applying beta-rule and splitting (1130), into two cases.
% 279.75/221.60 |-Branch one:
% 279.75/221.60 | (1152) ~ (all_469_0_964 = 0)
% 279.75/221.60 |
% 279.75/221.60 | Equations (1147) can reduce 1152 to:
% 279.75/221.60 | (346) $false
% 279.75/221.60 |
% 279.75/221.60 |-The branch is then unsatisfiable
% 279.75/221.60 |-Branch two:
% 279.75/221.60 | (1147) all_469_0_964 = 0
% 279.75/221.60 | (1155) ~ (all_469_1_965 = 0)
% 279.75/221.60 |
% 279.75/221.60 | Equations (1149) can reduce 1155 to:
% 279.75/221.60 | (346) $false
% 279.75/221.60 |
% 279.75/221.60 |-The branch is then unsatisfiable
% 279.89/221.60 |-Branch two:
% 279.89/221.60 | (1157) ~ (all_0_4_4 = xp)
% 279.89/221.60 | (1158) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_0_4_4, all_0_12_12) = v3 & sdtpldt0(xp, all_0_12_12) = v4 & aNaturalNumber0(all_0_4_4) = v1 & aNaturalNumber0(all_0_12_12) = v0 & aNaturalNumber0(xp) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 279.89/221.60 |
% 279.89/221.60 | Instantiating (1158) with all_457_0_971, all_457_1_972, all_457_2_973, all_457_3_974, all_457_4_975 yields:
% 279.89/221.60 | (1159) sdtpldt0(all_0_4_4, all_0_12_12) = all_457_1_972 & sdtpldt0(xp, all_0_12_12) = all_457_0_971 & aNaturalNumber0(all_0_4_4) = all_457_3_974 & aNaturalNumber0(all_0_12_12) = all_457_4_975 & aNaturalNumber0(xp) = all_457_2_973 & ( ~ (all_457_2_973 = 0) | ~ (all_457_3_974 = 0) | ~ (all_457_4_975 = 0))
% 279.89/221.60 |
% 279.89/221.60 | Applying alpha-rule on (1159) yields:
% 279.89/221.60 | (1160) sdtpldt0(xp, all_0_12_12) = all_457_0_971
% 279.89/221.60 | (1161) aNaturalNumber0(all_0_4_4) = all_457_3_974
% 279.89/221.60 | (1162) sdtpldt0(all_0_4_4, all_0_12_12) = all_457_1_972
% 279.89/221.60 | (1163) ~ (all_457_2_973 = 0) | ~ (all_457_3_974 = 0) | ~ (all_457_4_975 = 0)
% 279.89/221.60 | (1164) aNaturalNumber0(all_0_12_12) = all_457_4_975
% 279.89/221.60 | (1165) aNaturalNumber0(xp) = all_457_2_973
% 279.89/221.60 |
% 279.89/221.60 | Instantiating formula (97) with all_0_4_4, all_457_3_974, 0 and discharging atoms aNaturalNumber0(all_0_4_4) = all_457_3_974, aNaturalNumber0(all_0_4_4) = 0, yields:
% 279.89/221.60 | (1166) all_457_3_974 = 0
% 279.89/221.60 |
% 279.89/221.60 | Instantiating formula (97) with all_0_12_12, all_457_4_975, 0 and discharging atoms aNaturalNumber0(all_0_12_12) = all_457_4_975, aNaturalNumber0(all_0_12_12) = 0, yields:
% 279.89/221.60 | (1167) all_457_4_975 = 0
% 279.89/221.60 |
% 279.89/221.60 | Instantiating formula (97) with xp, all_457_2_973, 0 and discharging atoms aNaturalNumber0(xp) = all_457_2_973, aNaturalNumber0(xp) = 0, yields:
% 279.89/221.60 | (1168) all_457_2_973 = 0
% 279.89/221.60 |
% 279.89/221.61 +-Applying beta-rule and splitting (1163), into two cases.
% 279.89/221.61 |-Branch one:
% 279.89/221.61 | (1169) ~ (all_457_2_973 = 0)
% 279.89/221.61 |
% 279.89/221.61 | Equations (1168) can reduce 1169 to:
% 279.89/221.61 | (346) $false
% 279.89/221.61 |
% 279.89/221.61 |-The branch is then unsatisfiable
% 279.89/221.61 |-Branch two:
% 279.89/221.61 | (1168) all_457_2_973 = 0
% 279.89/221.61 | (1172) ~ (all_457_3_974 = 0) | ~ (all_457_4_975 = 0)
% 279.89/221.61 |
% 279.89/221.61 +-Applying beta-rule and splitting (1172), into two cases.
% 279.89/221.61 |-Branch one:
% 279.89/221.61 | (1173) ~ (all_457_3_974 = 0)
% 279.89/221.61 |
% 279.89/221.61 | Equations (1166) can reduce 1173 to:
% 279.89/221.61 | (346) $false
% 279.89/221.61 |
% 279.89/221.61 |-The branch is then unsatisfiable
% 279.89/221.61 |-Branch two:
% 279.89/221.61 | (1166) all_457_3_974 = 0
% 279.89/221.61 | (1176) ~ (all_457_4_975 = 0)
% 279.89/221.61 |
% 279.89/221.61 | Equations (1167) can reduce 1176 to:
% 279.89/221.61 | (346) $false
% 279.89/221.61 |
% 279.89/221.61 |-The branch is then unsatisfiable
% 279.89/221.61 |-Branch two:
% 279.89/221.61 | (1178) aNaturalNumber0(all_0_7_7) = all_58_2_198 & aNaturalNumber0(all_0_11_11) = all_58_1_197 & ( ~ (all_58_1_197 = 0) | ~ (all_58_2_198 = 0))
% 279.89/221.61 |
% 279.89/221.61 | Applying alpha-rule on (1178) yields:
% 279.89/221.61 | (1179) aNaturalNumber0(all_0_7_7) = all_58_2_198
% 279.89/221.61 | (1180) aNaturalNumber0(all_0_11_11) = all_58_1_197
% 279.89/221.61 | (1181) ~ (all_58_1_197 = 0) | ~ (all_58_2_198 = 0)
% 279.89/221.61 |
% 279.89/221.61 | From (856) and (1179) follows:
% 279.89/221.61 | (1182) aNaturalNumber0(all_0_12_12) = all_58_2_198
% 279.89/221.61 |
% 279.89/221.61 | Instantiating formula (97) with all_0_11_11, all_58_1_197, 0 and discharging atoms aNaturalNumber0(all_0_11_11) = all_58_1_197, aNaturalNumber0(all_0_11_11) = 0, yields:
% 279.89/221.61 | (898) all_58_1_197 = 0
% 279.89/221.61 |
% 279.89/221.61 | Instantiating formula (97) with all_0_12_12, all_58_2_198, 0 and discharging atoms aNaturalNumber0(all_0_12_12) = all_58_2_198, aNaturalNumber0(all_0_12_12) = 0, yields:
% 279.89/221.61 | (1184) all_58_2_198 = 0
% 279.89/221.61 |
% 279.89/221.61 +-Applying beta-rule and splitting (1181), into two cases.
% 279.89/221.61 |-Branch one:
% 279.89/221.61 | (1185) ~ (all_58_1_197 = 0)
% 279.89/221.61 |
% 279.89/221.61 | Equations (898) can reduce 1185 to:
% 279.89/221.61 | (346) $false
% 279.89/221.61 |
% 279.89/221.61 |-The branch is then unsatisfiable
% 279.89/221.61 |-Branch two:
% 279.89/221.61 | (898) all_58_1_197 = 0
% 279.89/221.61 | (1188) ~ (all_58_2_198 = 0)
% 279.89/221.61 |
% 279.89/221.61 | Equations (1184) can reduce 1188 to:
% 279.89/221.61 | (346) $false
% 279.89/221.61 |
% 279.89/221.61 |-The branch is then unsatisfiable
% 279.89/221.61 |-Branch two:
% 279.89/221.61 | (1064) all_103_0_257 = 0
% 279.89/221.61 | (1191) ~ (all_103_1_258 = 0) | ~ (all_103_2_259 = 0)
% 279.89/221.61 |
% 279.89/221.61 +-Applying beta-rule and splitting (1191), into two cases.
% 279.89/221.61 |-Branch one:
% 279.89/221.61 | (1192) ~ (all_103_1_258 = 0)
% 279.89/221.61 |
% 279.89/221.61 | Equations (871) can reduce 1192 to:
% 279.89/221.61 | (346) $false
% 279.89/221.61 |
% 279.89/221.61 |-The branch is then unsatisfiable
% 279.89/221.61 |-Branch two:
% 279.89/221.61 | (871) all_103_1_258 = 0
% 279.89/221.61 | (1195) ~ (all_103_2_259 = 0)
% 279.89/221.61 |
% 279.89/221.61 | Equations (789) can reduce 1195 to:
% 279.89/221.61 | (346) $false
% 279.89/221.61 |
% 279.89/221.61 |-The branch is then unsatisfiable
% 279.89/221.61 |-Branch two:
% 279.89/221.61 | (1197) all_50_8_180 = 0
% 279.89/221.61 | (1198) ~ (all_50_12_184 = 0) | ~ (all_50_13_185 = 0) | ~ (all_50_14_186 = 0) | (all_50_3_175 = xr & all_50_4_176 = 0 & all_50_7_179 = 0 & sdtasdt0(xp, all_50_5_177) = xr & aNaturalNumber0(all_50_5_177) = 0) | (all_50_3_175 = xm & all_50_4_176 = 0 & all_50_6_178 = 0 & sdtasdt0(xp, all_50_5_177) = xm & aNaturalNumber0(all_50_5_177) = 0) | ( ~ (all_50_11_183 = 0) & (xp = sz10 | xp = sz00 | (all_50_0_172 = xp & all_50_1_173 = 0 & all_50_3_175 = 0 & all_50_4_176 = 0 & ~ (all_50_5_177 = xp) & ~ (all_50_5_177 = sz10) & doDivides0(all_50_5_177, xp) = 0 & sdtasdt0(all_50_5_177, all_50_2_174) = xp & aNaturalNumber0(all_50_2_174) = 0 & aNaturalNumber0(all_50_5_177) = 0)))
% 279.89/221.62 |
% 279.89/221.62 +-Applying beta-rule and splitting (1198), into two cases.
% 279.89/221.62 |-Branch one:
% 279.89/221.62 | (1199) ~ (all_50_12_184 = 0)
% 279.89/221.62 |
% 279.89/221.62 | Equations (660) can reduce 1199 to:
% 279.89/221.62 | (346) $false
% 279.89/221.62 |
% 279.89/221.62 |-The branch is then unsatisfiable
% 279.89/221.62 |-Branch two:
% 279.89/221.62 | (660) all_50_12_184 = 0
% 279.89/221.62 | (1202) ~ (all_50_13_185 = 0) | ~ (all_50_14_186 = 0) | (all_50_3_175 = xr & all_50_4_176 = 0 & all_50_7_179 = 0 & sdtasdt0(xp, all_50_5_177) = xr & aNaturalNumber0(all_50_5_177) = 0) | (all_50_3_175 = xm & all_50_4_176 = 0 & all_50_6_178 = 0 & sdtasdt0(xp, all_50_5_177) = xm & aNaturalNumber0(all_50_5_177) = 0) | ( ~ (all_50_11_183 = 0) & (xp = sz10 | xp = sz00 | (all_50_0_172 = xp & all_50_1_173 = 0 & all_50_3_175 = 0 & all_50_4_176 = 0 & ~ (all_50_5_177 = xp) & ~ (all_50_5_177 = sz10) & doDivides0(all_50_5_177, xp) = 0 & sdtasdt0(all_50_5_177, all_50_2_174) = xp & aNaturalNumber0(all_50_2_174) = 0 & aNaturalNumber0(all_50_5_177) = 0)))
% 279.89/221.62 |
% 279.89/221.62 +-Applying beta-rule and splitting (1202), into two cases.
% 279.89/221.62 |-Branch one:
% 279.89/221.62 | (1203) ~ (all_50_13_185 = 0)
% 279.89/221.62 |
% 279.89/221.62 | Equations (577) can reduce 1203 to:
% 279.89/221.62 | (346) $false
% 279.89/221.62 |
% 279.89/221.62 |-The branch is then unsatisfiable
% 279.89/221.62 |-Branch two:
% 279.89/221.62 | (577) all_50_13_185 = 0
% 279.89/221.62 | (1206) ~ (all_50_14_186 = 0) | (all_50_3_175 = xr & all_50_4_176 = 0 & all_50_7_179 = 0 & sdtasdt0(xp, all_50_5_177) = xr & aNaturalNumber0(all_50_5_177) = 0) | (all_50_3_175 = xm & all_50_4_176 = 0 & all_50_6_178 = 0 & sdtasdt0(xp, all_50_5_177) = xm & aNaturalNumber0(all_50_5_177) = 0) | ( ~ (all_50_11_183 = 0) & (xp = sz10 | xp = sz00 | (all_50_0_172 = xp & all_50_1_173 = 0 & all_50_3_175 = 0 & all_50_4_176 = 0 & ~ (all_50_5_177 = xp) & ~ (all_50_5_177 = sz10) & doDivides0(all_50_5_177, xp) = 0 & sdtasdt0(all_50_5_177, all_50_2_174) = xp & aNaturalNumber0(all_50_2_174) = 0 & aNaturalNumber0(all_50_5_177) = 0)))
% 279.89/221.62 |
% 279.89/221.62 +-Applying beta-rule and splitting (1206), into two cases.
% 279.89/221.62 |-Branch one:
% 279.89/221.62 | (1207) ~ (all_50_14_186 = 0)
% 279.89/221.62 |
% 279.89/221.62 | Equations (579) can reduce 1207 to:
% 279.89/221.62 | (346) $false
% 279.89/221.62 |
% 279.89/221.62 |-The branch is then unsatisfiable
% 279.89/221.62 |-Branch two:
% 279.89/221.62 | (579) all_50_14_186 = 0
% 279.89/221.62 | (1210) (all_50_3_175 = xr & all_50_4_176 = 0 & all_50_7_179 = 0 & sdtasdt0(xp, all_50_5_177) = xr & aNaturalNumber0(all_50_5_177) = 0) | (all_50_3_175 = xm & all_50_4_176 = 0 & all_50_6_178 = 0 & sdtasdt0(xp, all_50_5_177) = xm & aNaturalNumber0(all_50_5_177) = 0) | ( ~ (all_50_11_183 = 0) & (xp = sz10 | xp = sz00 | (all_50_0_172 = xp & all_50_1_173 = 0 & all_50_3_175 = 0 & all_50_4_176 = 0 & ~ (all_50_5_177 = xp) & ~ (all_50_5_177 = sz10) & doDivides0(all_50_5_177, xp) = 0 & sdtasdt0(all_50_5_177, all_50_2_174) = xp & aNaturalNumber0(all_50_2_174) = 0 & aNaturalNumber0(all_50_5_177) = 0)))
% 279.89/221.62 |
% 279.89/221.62 +-Applying beta-rule and splitting (1210), into two cases.
% 279.89/221.62 |-Branch one:
% 279.89/221.62 | (1211) (all_50_3_175 = xr & all_50_4_176 = 0 & all_50_7_179 = 0 & sdtasdt0(xp, all_50_5_177) = xr & aNaturalNumber0(all_50_5_177) = 0) | (all_50_3_175 = xm & all_50_4_176 = 0 & all_50_6_178 = 0 & sdtasdt0(xp, all_50_5_177) = xm & aNaturalNumber0(all_50_5_177) = 0)
% 279.89/221.62 |
% 279.89/221.62 +-Applying beta-rule and splitting (1211), into two cases.
% 279.89/221.62 |-Branch one:
% 279.89/221.62 | (1212) all_50_3_175 = xr & all_50_4_176 = 0 & all_50_7_179 = 0 & sdtasdt0(xp, all_50_5_177) = xr & aNaturalNumber0(all_50_5_177) = 0
% 279.89/221.62 |
% 279.89/221.62 | Applying alpha-rule on (1212) yields:
% 279.89/221.62 | (1213) aNaturalNumber0(all_50_5_177) = 0
% 279.89/221.62 | (1214) all_50_3_175 = xr
% 279.89/221.62 | (1215) all_50_4_176 = 0
% 279.89/221.62 | (1216) sdtasdt0(xp, all_50_5_177) = xr
% 279.89/221.62 | (1217) all_50_7_179 = 0
% 279.89/221.62 |
% 279.89/221.62 | Combining equations (408,1217) yields a new equation:
% 279.89/221.62 | (1218) all_0_6_6 = 0
% 279.89/221.62 |
% 279.89/221.62 | Simplifying 1218 yields:
% 279.89/221.62 | (345) all_0_6_6 = 0
% 279.89/221.62 |
% 279.89/221.62 | Equations (345) can reduce 30 to:
% 279.89/221.62 | (346) $false
% 279.89/221.62 |
% 279.89/221.62 |-The branch is then unsatisfiable
% 279.89/221.62 |-Branch two:
% 279.89/221.62 | (1221) all_50_3_175 = xm & all_50_4_176 = 0 & all_50_6_178 = 0 & sdtasdt0(xp, all_50_5_177) = xm & aNaturalNumber0(all_50_5_177) = 0
% 279.89/221.62 |
% 279.89/221.62 | Applying alpha-rule on (1221) yields:
% 279.89/221.62 | (1213) aNaturalNumber0(all_50_5_177) = 0
% 279.89/221.62 | (1215) all_50_4_176 = 0
% 279.89/221.62 | (1224) all_50_3_175 = xm
% 279.89/221.62 | (1225) sdtasdt0(xp, all_50_5_177) = xm
% 279.89/221.62 | (1226) all_50_6_178 = 0
% 279.89/221.62 |
% 279.89/221.62 | Combining equations (409,1226) yields a new equation:
% 279.89/221.62 | (1227) all_0_5_5 = 0
% 279.89/221.62 |
% 279.89/221.62 | Simplifying 1227 yields:
% 279.89/221.62 | (365) all_0_5_5 = 0
% 279.89/221.62 |
% 279.89/221.62 | Equations (365) can reduce 9 to:
% 279.89/221.62 | (346) $false
% 279.89/221.62 |
% 279.89/221.62 |-The branch is then unsatisfiable
% 279.89/221.62 |-Branch two:
% 279.89/221.62 | (1230) ~ (all_50_11_183 = 0) & (xp = sz10 | xp = sz00 | (all_50_0_172 = xp & all_50_1_173 = 0 & all_50_3_175 = 0 & all_50_4_176 = 0 & ~ (all_50_5_177 = xp) & ~ (all_50_5_177 = sz10) & doDivides0(all_50_5_177, xp) = 0 & sdtasdt0(all_50_5_177, all_50_2_174) = xp & aNaturalNumber0(all_50_2_174) = 0 & aNaturalNumber0(all_50_5_177) = 0))
% 279.89/221.62 |
% 279.89/221.62 | Applying alpha-rule on (1230) yields:
% 279.89/221.62 | (1231) ~ (all_50_11_183 = 0)
% 279.89/221.62 | (1232) xp = sz10 | xp = sz00 | (all_50_0_172 = xp & all_50_1_173 = 0 & all_50_3_175 = 0 & all_50_4_176 = 0 & ~ (all_50_5_177 = xp) & ~ (all_50_5_177 = sz10) & doDivides0(all_50_5_177, xp) = 0 & sdtasdt0(all_50_5_177, all_50_2_174) = xp & aNaturalNumber0(all_50_2_174) = 0 & aNaturalNumber0(all_50_5_177) = 0)
% 279.89/221.62 |
% 279.89/221.62 | Equations (407) can reduce 1231 to:
% 279.89/221.62 | (346) $false
% 279.89/221.62 |
% 279.89/221.62 |-The branch is then unsatisfiable
% 279.89/221.62 |-Branch two:
% 279.89/221.62 | (1234) sdtpldt0(xp, xr) = sz00
% 279.89/221.62 | (1235) xp = sz00 | ? [v0] : ? [v1] : (aNaturalNumber0(xr) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 279.89/221.62 |
% 279.89/221.62 +-Applying beta-rule and splitting (1235), into two cases.
% 279.89/221.62 |-Branch one:
% 279.89/221.62 | (403) xp = sz00
% 279.89/221.62 |
% 279.89/221.62 | Equations (403) can reduce 33 to:
% 279.89/221.62 | (346) $false
% 279.89/221.62 |
% 279.89/221.62 |-The branch is then unsatisfiable
% 279.89/221.62 |-Branch two:
% 279.89/221.62 | (33) ~ (xp = sz00)
% 279.89/221.62 | (1239) ? [v0] : ? [v1] : (aNaturalNumber0(xr) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 279.89/221.62 |
% 279.89/221.62 | Instantiating (1239) with all_235_0_982, all_235_1_983 yields:
% 279.89/221.62 | (1240) aNaturalNumber0(xr) = all_235_0_982 & aNaturalNumber0(xp) = all_235_1_983 & ( ~ (all_235_0_982 = 0) | ~ (all_235_1_983 = 0))
% 279.89/221.62 |
% 279.89/221.63 | Applying alpha-rule on (1240) yields:
% 279.89/221.63 | (1241) aNaturalNumber0(xr) = all_235_0_982
% 279.89/221.63 | (1242) aNaturalNumber0(xp) = all_235_1_983
% 279.89/221.63 | (1243) ~ (all_235_0_982 = 0) | ~ (all_235_1_983 = 0)
% 279.89/221.63 |
% 279.89/221.63 +-Applying beta-rule and splitting (260), into two cases.
% 279.89/221.63 |-Branch one:
% 279.89/221.63 | (736) ~ (all_47_14_156 = 0) & aNaturalNumber0(all_0_0_0) = all_47_14_156
% 279.89/221.63 |
% 279.89/221.63 | Applying alpha-rule on (736) yields:
% 279.89/221.63 | (737) ~ (all_47_14_156 = 0)
% 279.89/221.63 | (738) aNaturalNumber0(all_0_0_0) = all_47_14_156
% 279.89/221.63 |
% 279.89/221.63 | Instantiating formula (97) with all_0_0_0, all_47_14_156, 0 and discharging atoms aNaturalNumber0(all_0_0_0) = all_47_14_156, aNaturalNumber0(all_0_0_0) = 0, yields:
% 279.89/221.63 | (739) all_47_14_156 = 0
% 279.89/221.63 |
% 279.89/221.63 | Equations (739) can reduce 737 to:
% 279.89/221.63 | (346) $false
% 279.89/221.63 |
% 279.89/221.63 |-The branch is then unsatisfiable
% 279.89/221.63 |-Branch two:
% 279.89/221.63 | (741) isPrime0(xp) = all_47_11_153 & doDivides0(xp, all_0_0_0) = all_47_6_148 & doDivides0(xp, xp) = all_47_7_149 & iLess0(all_47_9_151, all_0_11_11) = all_47_8_150 & sdtpldt0(all_47_10_152, xp) = all_47_9_151 & sdtpldt0(xp, all_0_0_0) = all_47_10_152 & aNaturalNumber0(all_0_0_0) = all_47_13_155 & aNaturalNumber0(xp) = all_47_12_154 & aNaturalNumber0(xp) = all_47_14_156 & ( ~ (all_47_8_150 = 0) | ~ (all_47_12_154 = 0) | ~ (all_47_13_155 = 0) | ~ (all_47_14_156 = 0) | (all_47_3_145 = all_0_0_0 & all_47_4_146 = 0 & all_47_6_148 = 0 & sdtasdt0(xp, all_47_5_147) = all_0_0_0 & aNaturalNumber0(all_47_5_147) = 0) | (all_47_3_145 = xp & all_47_4_146 = 0 & all_47_7_149 = 0 & sdtasdt0(xp, all_47_5_147) = xp & aNaturalNumber0(all_47_5_147) = 0) | ( ~ (all_47_11_153 = 0) & (xp = sz10 | xp = sz00 | (all_47_0_142 = xp & all_47_1_143 = 0 & all_47_3_145 = 0 & all_47_4_146 = 0 & ~ (all_47_5_147 = xp) & ~ (all_47_5_147 = sz10) & doDivides0(all_47_5_147, xp) = 0 & sdtasdt0(all_47_5_147, all_47_2_144) = xp & aNaturalNumber0(all_47_2_144) = 0 & aNaturalNumber0(all_47_5_147) = 0))))
% 279.89/221.63 |
% 279.89/221.63 | Applying alpha-rule on (741) yields:
% 279.89/221.63 | (742) aNaturalNumber0(xp) = all_47_12_154
% 279.89/221.63 | (743) aNaturalNumber0(all_0_0_0) = all_47_13_155
% 279.89/221.63 | (744) sdtpldt0(all_47_10_152, xp) = all_47_9_151
% 279.89/221.63 | (745) aNaturalNumber0(xp) = all_47_14_156
% 279.89/221.63 | (746) sdtpldt0(xp, all_0_0_0) = all_47_10_152
% 279.89/221.63 | (747) doDivides0(xp, all_0_0_0) = all_47_6_148
% 279.89/221.63 | (748) isPrime0(xp) = all_47_11_153
% 279.89/221.63 | (749) ~ (all_47_8_150 = 0) | ~ (all_47_12_154 = 0) | ~ (all_47_13_155 = 0) | ~ (all_47_14_156 = 0) | (all_47_3_145 = all_0_0_0 & all_47_4_146 = 0 & all_47_6_148 = 0 & sdtasdt0(xp, all_47_5_147) = all_0_0_0 & aNaturalNumber0(all_47_5_147) = 0) | (all_47_3_145 = xp & all_47_4_146 = 0 & all_47_7_149 = 0 & sdtasdt0(xp, all_47_5_147) = xp & aNaturalNumber0(all_47_5_147) = 0) | ( ~ (all_47_11_153 = 0) & (xp = sz10 | xp = sz00 | (all_47_0_142 = xp & all_47_1_143 = 0 & all_47_3_145 = 0 & all_47_4_146 = 0 & ~ (all_47_5_147 = xp) & ~ (all_47_5_147 = sz10) & doDivides0(all_47_5_147, xp) = 0 & sdtasdt0(all_47_5_147, all_47_2_144) = xp & aNaturalNumber0(all_47_2_144) = 0 & aNaturalNumber0(all_47_5_147) = 0)))
% 279.89/221.63 | (750) iLess0(all_47_9_151, all_0_11_11) = all_47_8_150
% 279.89/221.63 | (751) doDivides0(xp, xp) = all_47_7_149
% 279.89/221.63 |
% 279.89/221.63 +-Applying beta-rule and splitting (239), into two cases.
% 279.89/221.63 |-Branch one:
% 279.89/221.63 | (807) ~ (all_38_14_129 = 0) & aNaturalNumber0(all_0_3_3) = all_38_14_129
% 279.89/221.63 |
% 279.89/221.63 | Applying alpha-rule on (807) yields:
% 279.89/221.63 | (808) ~ (all_38_14_129 = 0)
% 279.89/221.63 | (809) aNaturalNumber0(all_0_3_3) = all_38_14_129
% 279.89/221.63 |
% 279.89/221.63 | Instantiating formula (97) with all_0_3_3, all_38_14_129, 0 and discharging atoms aNaturalNumber0(all_0_3_3) = all_38_14_129, aNaturalNumber0(all_0_3_3) = 0, yields:
% 279.89/221.63 | (810) all_38_14_129 = 0
% 279.89/221.63 |
% 279.89/221.63 | Equations (810) can reduce 808 to:
% 279.89/221.63 | (346) $false
% 279.89/221.63 |
% 279.89/221.63 |-The branch is then unsatisfiable
% 279.89/221.63 |-Branch two:
% 279.89/221.63 | (812) isPrime0(xp) = all_38_11_126 & doDivides0(xp, all_0_3_3) = all_38_6_121 & doDivides0(xp, xp) = all_38_7_122 & iLess0(all_38_9_124, all_0_11_11) = all_38_8_123 & sdtpldt0(all_38_10_125, xp) = all_38_9_124 & sdtpldt0(xp, all_0_3_3) = all_38_10_125 & aNaturalNumber0(all_0_3_3) = all_38_13_128 & aNaturalNumber0(xp) = all_38_12_127 & aNaturalNumber0(xp) = all_38_14_129 & ( ~ (all_38_8_123 = 0) | ~ (all_38_12_127 = 0) | ~ (all_38_13_128 = 0) | ~ (all_38_14_129 = 0) | (all_38_3_118 = all_0_3_3 & all_38_4_119 = 0 & all_38_6_121 = 0 & sdtasdt0(xp, all_38_5_120) = all_0_3_3 & aNaturalNumber0(all_38_5_120) = 0) | (all_38_3_118 = xp & all_38_4_119 = 0 & all_38_7_122 = 0 & sdtasdt0(xp, all_38_5_120) = xp & aNaturalNumber0(all_38_5_120) = 0) | ( ~ (all_38_11_126 = 0) & (xp = sz10 | xp = sz00 | (all_38_0_115 = xp & all_38_1_116 = 0 & all_38_3_118 = 0 & all_38_4_119 = 0 & ~ (all_38_5_120 = xp) & ~ (all_38_5_120 = sz10) & doDivides0(all_38_5_120, xp) = 0 & sdtasdt0(all_38_5_120, all_38_2_117) = xp & aNaturalNumber0(all_38_2_117) = 0 & aNaturalNumber0(all_38_5_120) = 0))))
% 279.89/221.63 |
% 279.89/221.63 | Applying alpha-rule on (812) yields:
% 279.89/221.63 | (813) doDivides0(xp, all_0_3_3) = all_38_6_121
% 280.01/221.63 | (814) doDivides0(xp, xp) = all_38_7_122
% 280.01/221.63 | (815) aNaturalNumber0(all_0_3_3) = all_38_13_128
% 280.01/221.63 | (816) iLess0(all_38_9_124, all_0_11_11) = all_38_8_123
% 280.01/221.63 | (817) sdtpldt0(all_38_10_125, xp) = all_38_9_124
% 280.01/221.63 | (818) sdtpldt0(xp, all_0_3_3) = all_38_10_125
% 280.01/221.63 | (819) aNaturalNumber0(xp) = all_38_14_129
% 280.01/221.63 | (820) isPrime0(xp) = all_38_11_126
% 280.01/221.63 | (821) aNaturalNumber0(xp) = all_38_12_127
% 280.01/221.63 | (822) ~ (all_38_8_123 = 0) | ~ (all_38_12_127 = 0) | ~ (all_38_13_128 = 0) | ~ (all_38_14_129 = 0) | (all_38_3_118 = all_0_3_3 & all_38_4_119 = 0 & all_38_6_121 = 0 & sdtasdt0(xp, all_38_5_120) = all_0_3_3 & aNaturalNumber0(all_38_5_120) = 0) | (all_38_3_118 = xp & all_38_4_119 = 0 & all_38_7_122 = 0 & sdtasdt0(xp, all_38_5_120) = xp & aNaturalNumber0(all_38_5_120) = 0) | ( ~ (all_38_11_126 = 0) & (xp = sz10 | xp = sz00 | (all_38_0_115 = xp & all_38_1_116 = 0 & all_38_3_118 = 0 & all_38_4_119 = 0 & ~ (all_38_5_120 = xp) & ~ (all_38_5_120 = sz10) & doDivides0(all_38_5_120, xp) = 0 & sdtasdt0(all_38_5_120, all_38_2_117) = xp & aNaturalNumber0(all_38_2_117) = 0 & aNaturalNumber0(all_38_5_120) = 0)))
% 280.01/221.63 |
% 280.01/221.63 +-Applying beta-rule and splitting (411), into two cases.
% 280.01/221.63 |-Branch one:
% 280.01/221.63 | (902) ~ (sdtpldt0(all_0_8_8, xp) = all_50_9_181)
% 280.01/221.63 |
% 280.01/221.63 | Using (675) and (902) yields:
% 280.01/221.63 | (695) $false
% 280.01/221.63 |
% 280.01/221.63 |-The branch is then unsatisfiable
% 280.01/221.63 |-Branch two:
% 280.01/221.63 | (675) sdtpldt0(all_0_8_8, xp) = all_50_9_181
% 280.01/221.63 | (905) all_50_9_181 = all_0_7_7
% 280.01/221.63 |
% 280.01/221.63 | From (905) and (675) follows:
% 280.01/221.63 | (49) sdtpldt0(all_0_8_8, xp) = all_0_7_7
% 280.01/221.63 |
% 280.01/221.63 +-Applying beta-rule and splitting (415), into two cases.
% 280.01/221.63 |-Branch one:
% 280.01/221.63 | (849) ~ (sdtpldt0(xp, all_0_8_8) = all_10_0_16)
% 280.01/221.63 |
% 280.01/221.63 | Using (677) and (849) yields:
% 280.01/221.63 | (695) $false
% 280.01/221.63 |
% 280.01/221.63 |-The branch is then unsatisfiable
% 280.01/221.63 |-Branch two:
% 280.01/221.63 | (677) sdtpldt0(xp, all_0_8_8) = all_10_0_16
% 280.01/221.63 | (853) all_34_0_107 = all_10_0_16
% 280.01/221.63 |
% 280.01/221.63 | Combining equations (733,853) yields a new equation:
% 280.01/221.63 | (854) all_10_0_16 = all_0_7_7
% 280.01/221.63 |
% 280.01/221.63 +-Applying beta-rule and splitting (156), into two cases.
% 280.01/221.63 |-Branch one:
% 280.01/221.63 | (791) ~ (all_10_2_18 = 0)
% 280.01/221.64 |
% 280.01/221.64 | Equations (644) can reduce 791 to:
% 280.01/221.64 | (346) $false
% 280.01/221.64 |
% 280.01/221.64 |-The branch is then unsatisfiable
% 280.01/221.64 |-Branch two:
% 280.01/221.64 | (644) all_10_2_18 = 0
% 280.01/221.64 | (794) ~ (all_10_3_19 = 0) | ~ (all_10_4_20 = 0) | all_10_0_16 = all_0_12_12
% 280.01/221.64 |
% 280.01/221.64 +-Applying beta-rule and splitting (794), into two cases.
% 280.01/221.64 |-Branch one:
% 280.01/221.64 | (795) ~ (all_10_3_19 = 0)
% 280.01/221.64 |
% 280.01/221.64 | Equations (587) can reduce 795 to:
% 280.01/221.64 | (346) $false
% 280.01/221.64 |
% 280.01/221.64 |-The branch is then unsatisfiable
% 280.01/221.64 |-Branch two:
% 280.01/221.64 | (587) all_10_3_19 = 0
% 280.01/221.64 | (798) ~ (all_10_4_20 = 0) | all_10_0_16 = all_0_12_12
% 280.01/221.64 |
% 280.01/221.64 +-Applying beta-rule and splitting (798), into two cases.
% 280.01/221.64 |-Branch one:
% 280.01/221.64 | (799) ~ (all_10_4_20 = 0)
% 280.01/221.64 |
% 280.01/221.64 | Equations (651) can reduce 799 to:
% 280.01/221.64 | (346) $false
% 280.01/221.64 |
% 280.01/221.64 |-The branch is then unsatisfiable
% 280.01/221.64 |-Branch two:
% 280.01/221.64 | (651) all_10_4_20 = 0
% 280.01/221.64 | (802) all_10_0_16 = all_0_12_12
% 280.01/221.64 |
% 280.01/221.64 | Combining equations (802,854) yields a new equation:
% 280.01/221.64 | (856) all_0_7_7 = all_0_12_12
% 280.01/221.64 |
% 280.01/221.64 | From (856) and (49) follows:
% 280.01/221.64 | (862) sdtpldt0(all_0_8_8, xp) = all_0_12_12
% 280.01/221.64 |
% 280.01/221.64 +-Applying beta-rule and splitting (129), into two cases.
% 280.01/221.64 |-Branch one:
% 280.01/221.64 | (885) ~ (sdtpldt0(all_0_8_8, xp) = all_0_12_12)
% 280.01/221.64 |
% 280.01/221.64 | Using (862) and (885) yields:
% 280.01/221.64 | (695) $false
% 280.01/221.64 |
% 280.01/221.64 |-The branch is then unsatisfiable
% 280.01/221.64 |-Branch two:
% 280.01/221.64 | (862) sdtpldt0(all_0_8_8, xp) = all_0_12_12
% 280.01/221.64 | (888) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_0_8_8, v3) = v4 & sdtpldt0(xp, xp) = v3 & aNaturalNumber0(all_0_8_8) = v0 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_11_11))
% 280.01/221.64 |
% 280.01/221.64 | Instantiating (888) with all_416_0_1014, all_416_1_1015, all_416_2_1016, all_416_3_1017, all_416_4_1018 yields:
% 280.01/221.64 | (1304) sdtpldt0(all_0_8_8, all_416_1_1015) = all_416_0_1014 & sdtpldt0(xp, xp) = all_416_1_1015 & aNaturalNumber0(all_0_8_8) = all_416_4_1018 & aNaturalNumber0(xp) = all_416_2_1016 & aNaturalNumber0(xp) = all_416_3_1017 & ( ~ (all_416_2_1016 = 0) | ~ (all_416_3_1017 = 0) | ~ (all_416_4_1018 = 0) | all_416_0_1014 = all_0_11_11)
% 280.01/221.64 |
% 280.01/221.64 | Applying alpha-rule on (1304) yields:
% 280.01/221.64 | (1305) aNaturalNumber0(all_0_8_8) = all_416_4_1018
% 280.01/221.64 | (1306) aNaturalNumber0(xp) = all_416_3_1017
% 280.01/221.64 | (1307) aNaturalNumber0(xp) = all_416_2_1016
% 280.01/221.64 | (1308) sdtpldt0(all_0_8_8, all_416_1_1015) = all_416_0_1014
% 280.01/221.64 | (1309) sdtpldt0(xp, xp) = all_416_1_1015
% 280.01/221.64 | (1310) ~ (all_416_2_1016 = 0) | ~ (all_416_3_1017 = 0) | ~ (all_416_4_1018 = 0) | all_416_0_1014 = all_0_11_11
% 280.01/221.64 |
% 280.01/221.64 | Instantiating formula (97) with xr, all_235_0_982, 0 and discharging atoms aNaturalNumber0(xr) = all_235_0_982, aNaturalNumber0(xr) = 0, yields:
% 280.01/221.64 | (1311) all_235_0_982 = 0
% 280.01/221.64 |
% 280.01/221.64 | Instantiating formula (97) with xp, all_416_2_1016, 0 and discharging atoms aNaturalNumber0(xp) = all_416_2_1016, aNaturalNumber0(xp) = 0, yields:
% 280.01/221.64 | (1312) all_416_2_1016 = 0
% 280.01/221.64 |
% 280.01/221.64 | Instantiating formula (97) with xp, all_416_3_1017, all_416_2_1016 and discharging atoms aNaturalNumber0(xp) = all_416_2_1016, aNaturalNumber0(xp) = all_416_3_1017, yields:
% 280.01/221.64 | (1313) all_416_2_1016 = all_416_3_1017
% 280.01/221.64 |
% 280.01/221.64 | Instantiating formula (97) with xp, all_235_1_983, all_416_2_1016 and discharging atoms aNaturalNumber0(xp) = all_416_2_1016, aNaturalNumber0(xp) = all_235_1_983, yields:
% 280.01/221.64 | (1314) all_416_2_1016 = all_235_1_983
% 280.01/221.64 |
% 280.01/221.64 | Instantiating formula (97) with xp, all_47_12_154, all_416_2_1016 and discharging atoms aNaturalNumber0(xp) = all_416_2_1016, aNaturalNumber0(xp) = all_47_12_154, yields:
% 280.01/221.64 | (1315) all_416_2_1016 = all_47_12_154
% 280.01/221.64 |
% 280.01/221.64 | Instantiating formula (97) with xp, all_47_14_156, all_416_3_1017 and discharging atoms aNaturalNumber0(xp) = all_416_3_1017, aNaturalNumber0(xp) = all_47_14_156, yields:
% 280.01/221.64 | (1316) all_416_3_1017 = all_47_14_156
% 280.01/221.64 |
% 280.01/221.64 | Instantiating formula (97) with xp, all_38_12_127, all_235_1_983 and discharging atoms aNaturalNumber0(xp) = all_235_1_983, aNaturalNumber0(xp) = all_38_12_127, yields:
% 280.01/221.64 | (1317) all_235_1_983 = all_38_12_127
% 280.01/221.64 |
% 280.01/221.64 | Instantiating formula (97) with xp, all_38_14_129, all_416_2_1016 and discharging atoms aNaturalNumber0(xp) = all_416_2_1016, aNaturalNumber0(xp) = all_38_14_129, yields:
% 280.01/221.64 | (1318) all_416_2_1016 = all_38_14_129
% 280.01/221.64 |
% 280.01/221.64 | Combining equations (1314,1315) yields a new equation:
% 280.01/221.64 | (1319) all_235_1_983 = all_47_12_154
% 280.01/221.64 |
% 280.01/221.64 | Simplifying 1319 yields:
% 280.01/221.64 | (1320) all_235_1_983 = all_47_12_154
% 280.01/221.64 |
% 280.01/221.64 | Combining equations (1313,1315) yields a new equation:
% 280.01/221.64 | (1321) all_416_3_1017 = all_47_12_154
% 280.01/221.64 |
% 280.01/221.64 | Simplifying 1321 yields:
% 280.01/221.64 | (1322) all_416_3_1017 = all_47_12_154
% 280.01/221.64 |
% 280.01/221.64 | Combining equations (1312,1315) yields a new equation:
% 280.01/221.64 | (1323) all_47_12_154 = 0
% 280.01/221.64 |
% 280.01/221.64 | Combining equations (1318,1315) yields a new equation:
% 280.01/221.64 | (1324) all_47_12_154 = all_38_14_129
% 280.01/221.64 |
% 280.01/221.64 | Combining equations (1322,1316) yields a new equation:
% 280.01/221.64 | (1325) all_47_12_154 = all_47_14_156
% 280.01/221.64 |
% 280.01/221.64 | Simplifying 1325 yields:
% 280.01/221.64 | (919) all_47_12_154 = all_47_14_156
% 280.01/221.64 |
% 280.01/221.64 | Combining equations (1320,1317) yields a new equation:
% 280.01/221.64 | (1327) all_47_12_154 = all_38_12_127
% 280.01/221.64 |
% 280.01/221.64 | Simplifying 1327 yields:
% 280.01/221.64 | (1328) all_47_12_154 = all_38_12_127
% 280.01/221.64 |
% 280.01/221.64 | Combining equations (1324,919) yields a new equation:
% 280.01/221.65 | (922) all_47_14_156 = all_38_14_129
% 280.01/221.65 |
% 280.01/221.65 | Combining equations (1323,919) yields a new equation:
% 280.01/221.65 | (739) all_47_14_156 = 0
% 280.01/221.65 |
% 280.01/221.65 | Combining equations (1328,919) yields a new equation:
% 280.01/221.65 | (920) all_47_14_156 = all_38_12_127
% 280.01/221.65 |
% 280.01/221.65 | Combining equations (739,920) yields a new equation:
% 280.01/221.65 | (1332) all_38_12_127 = 0
% 280.01/221.65 |
% 280.01/221.65 | Combining equations (922,920) yields a new equation:
% 280.01/221.65 | (936) all_38_12_127 = all_38_14_129
% 280.01/221.65 |
% 280.01/221.65 | Combining equations (1332,936) yields a new equation:
% 280.01/221.65 | (810) all_38_14_129 = 0
% 280.01/221.65 |
% 280.01/221.65 | Combining equations (810,936) yields a new equation:
% 280.01/221.65 | (1332) all_38_12_127 = 0
% 280.01/221.65 |
% 280.01/221.65 | Combining equations (1332,1317) yields a new equation:
% 280.01/221.65 | (1336) all_235_1_983 = 0
% 280.01/221.65 |
% 280.01/221.65 +-Applying beta-rule and splitting (1243), into two cases.
% 280.01/221.65 |-Branch one:
% 280.01/221.65 | (1337) ~ (all_235_0_982 = 0)
% 280.01/221.65 |
% 280.01/221.65 | Equations (1311) can reduce 1337 to:
% 280.01/221.65 | (346) $false
% 280.01/221.65 |
% 280.01/221.65 |-The branch is then unsatisfiable
% 280.01/221.65 |-Branch two:
% 280.01/221.65 | (1311) all_235_0_982 = 0
% 280.01/221.65 | (1340) ~ (all_235_1_983 = 0)
% 280.01/221.65 |
% 280.01/221.65 | Equations (1336) can reduce 1340 to:
% 280.01/221.65 | (346) $false
% 280.01/221.65 |
% 280.01/221.65 |-The branch is then unsatisfiable
% 280.01/221.65 |-Branch two:
% 280.01/221.65 | (1342) ~ (all_0_1_1 = xr)
% 280.01/221.65 | (1343) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_0_1_1) = v0) | (sdtlseqdt0(xp, xn) = v2 & aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))))
% 280.01/221.65 |
% 280.01/221.65 | Instantiating (1343) with all_151_0_1033, all_151_1_1034, all_151_2_1035 yields:
% 280.01/221.65 | (1344) ( ~ (all_151_2_1035 = 0) & aNaturalNumber0(all_0_1_1) = all_151_2_1035) | (sdtlseqdt0(xp, xn) = all_151_0_1033 & aNaturalNumber0(xp) = all_151_2_1035 & aNaturalNumber0(xn) = all_151_1_1034 & ( ~ (all_151_0_1033 = 0) | ~ (all_151_1_1034 = 0) | ~ (all_151_2_1035 = 0)))
% 280.01/221.65 |
% 280.01/221.65 +-Applying beta-rule and splitting (327), into two cases.
% 280.01/221.65 |-Branch one:
% 280.01/221.65 | (702) ~ (all_69_1_222 = 0)
% 280.01/221.65 |
% 280.01/221.65 | Equations (480) can reduce 702 to:
% 280.01/221.65 | (346) $false
% 280.01/221.65 |
% 280.01/221.65 |-The branch is then unsatisfiable
% 280.01/221.65 |-Branch two:
% 280.01/221.65 | (480) all_69_1_222 = 0
% 280.01/221.65 | (705) ~ (all_69_2_223 = 0) | all_69_0_221 = 0
% 280.01/221.65 |
% 280.01/221.65 +-Applying beta-rule and splitting (1344), into two cases.
% 280.01/221.65 |-Branch one:
% 280.01/221.65 | (1349) ~ (all_151_2_1035 = 0) & aNaturalNumber0(all_0_1_1) = all_151_2_1035
% 280.01/221.65 |
% 280.01/221.65 | Applying alpha-rule on (1349) yields:
% 280.01/221.65 | (1350) ~ (all_151_2_1035 = 0)
% 280.01/221.65 | (1351) aNaturalNumber0(all_0_1_1) = all_151_2_1035
% 280.01/221.65 |
% 280.01/221.65 | Instantiating formula (97) with all_0_1_1, all_151_2_1035, 0 and discharging atoms aNaturalNumber0(all_0_1_1) = all_151_2_1035, aNaturalNumber0(all_0_1_1) = 0, yields:
% 280.01/221.65 | (1352) all_151_2_1035 = 0
% 280.01/221.65 |
% 280.01/221.65 | Equations (1352) can reduce 1350 to:
% 280.01/221.65 | (346) $false
% 280.01/221.65 |
% 280.01/221.65 |-The branch is then unsatisfiable
% 280.01/221.65 |-Branch two:
% 280.01/221.65 | (1354) sdtlseqdt0(xp, xn) = all_151_0_1033 & aNaturalNumber0(xp) = all_151_2_1035 & aNaturalNumber0(xn) = all_151_1_1034 & ( ~ (all_151_0_1033 = 0) | ~ (all_151_1_1034 = 0) | ~ (all_151_2_1035 = 0))
% 280.01/221.65 |
% 280.01/221.65 | Applying alpha-rule on (1354) yields:
% 280.01/221.65 | (1355) sdtlseqdt0(xp, xn) = all_151_0_1033
% 280.01/221.65 | (1356) aNaturalNumber0(xp) = all_151_2_1035
% 280.01/221.65 | (1357) aNaturalNumber0(xn) = all_151_1_1034
% 280.01/221.65 | (1358) ~ (all_151_0_1033 = 0) | ~ (all_151_1_1034 = 0) | ~ (all_151_2_1035 = 0)
% 280.01/221.65 |
% 280.01/221.65 +-Applying beta-rule and splitting (705), into two cases.
% 280.01/221.65 |-Branch one:
% 280.01/221.65 | (706) ~ (all_69_2_223 = 0)
% 280.01/221.65 |
% 280.01/221.65 | Equations (443) can reduce 706 to:
% 280.01/221.65 | (346) $false
% 280.01/221.65 |
% 280.01/221.65 |-The branch is then unsatisfiable
% 280.01/221.65 |-Branch two:
% 280.01/221.65 | (443) all_69_2_223 = 0
% 280.01/221.65 | (709) all_69_0_221 = 0
% 280.01/221.65 |
% 280.01/221.65 | Combining equations (709,437) yields a new equation:
% 280.01/221.65 | (710) all_32_2_106 = 0
% 280.01/221.65 |
% 280.01/221.65 | Combining equations (710,613) yields a new equation:
% 280.01/221.65 | (711) all_34_2_109 = 0
% 280.01/221.65 |
% 280.01/221.65 +-Applying beta-rule and splitting (231), into two cases.
% 280.01/221.65 |-Branch one:
% 280.01/221.65 | (726) ~ (all_34_1_108 = 0)
% 280.01/221.65 |
% 280.01/221.65 | Equations (659) can reduce 726 to:
% 280.01/221.65 | (346) $false
% 280.01/221.65 |
% 280.01/221.65 |-The branch is then unsatisfiable
% 280.01/221.65 |-Branch two:
% 280.01/221.65 | (659) all_34_1_108 = 0
% 280.01/221.65 | (729) ~ (all_34_2_109 = 0) | all_34_0_107 = all_0_7_7
% 280.01/221.65 |
% 280.01/221.65 +-Applying beta-rule and splitting (729), into two cases.
% 280.01/221.65 |-Branch one:
% 280.01/221.65 | (730) ~ (all_34_2_109 = 0)
% 280.01/221.65 |
% 280.01/221.65 | Equations (711) can reduce 730 to:
% 280.01/221.65 | (346) $false
% 280.01/221.65 |
% 280.01/221.65 |-The branch is then unsatisfiable
% 280.01/221.65 |-Branch two:
% 280.01/221.65 | (711) all_34_2_109 = 0
% 280.01/221.65 | (733) all_34_0_107 = all_0_7_7
% 280.01/221.65 |
% 280.01/221.65 +-Applying beta-rule and splitting (156), into two cases.
% 280.01/221.65 |-Branch one:
% 280.01/221.65 | (791) ~ (all_10_2_18 = 0)
% 280.01/221.65 |
% 280.01/221.65 | Equations (644) can reduce 791 to:
% 280.01/221.65 | (346) $false
% 280.01/221.65 |
% 280.01/221.65 |-The branch is then unsatisfiable
% 280.01/221.65 |-Branch two:
% 280.01/221.65 | (644) all_10_2_18 = 0
% 280.01/221.65 | (794) ~ (all_10_3_19 = 0) | ~ (all_10_4_20 = 0) | all_10_0_16 = all_0_12_12
% 280.01/221.65 |
% 280.01/221.65 +-Applying beta-rule and splitting (794), into two cases.
% 280.01/221.65 |-Branch one:
% 280.01/221.65 | (795) ~ (all_10_3_19 = 0)
% 280.01/221.65 |
% 280.01/221.65 | Equations (587) can reduce 795 to:
% 280.01/221.65 | (346) $false
% 280.01/221.65 |
% 280.01/221.65 |-The branch is then unsatisfiable
% 280.01/221.65 |-Branch two:
% 280.01/221.65 | (587) all_10_3_19 = 0
% 280.01/221.65 | (798) ~ (all_10_4_20 = 0) | all_10_0_16 = all_0_12_12
% 280.01/221.65 |
% 280.01/221.65 +-Applying beta-rule and splitting (798), into two cases.
% 280.01/221.65 |-Branch one:
% 280.01/221.65 | (799) ~ (all_10_4_20 = 0)
% 280.01/221.66 |
% 280.01/221.66 | Equations (651) can reduce 799 to:
% 280.01/221.66 | (346) $false
% 280.01/221.66 |
% 280.01/221.66 |-The branch is then unsatisfiable
% 280.01/221.66 |-Branch two:
% 280.01/221.66 | (651) all_10_4_20 = 0
% 280.01/221.66 | (802) all_10_0_16 = all_0_12_12
% 280.01/221.66 |
% 280.01/221.66 | From (802) and (677) follows:
% 280.01/221.66 | (848) sdtpldt0(xp, all_0_8_8) = all_0_12_12
% 280.01/221.66 |
% 280.01/221.66 +-Applying beta-rule and splitting (415), into two cases.
% 280.01/221.66 |-Branch one:
% 280.01/221.66 | (849) ~ (sdtpldt0(xp, all_0_8_8) = all_10_0_16)
% 280.01/221.66 |
% 280.01/221.66 | From (802) and (849) follows:
% 280.01/221.66 | (850) ~ (sdtpldt0(xp, all_0_8_8) = all_0_12_12)
% 280.01/221.66 |
% 280.01/221.66 | Using (848) and (850) yields:
% 280.01/221.66 | (695) $false
% 280.01/221.66 |
% 280.01/221.66 |-The branch is then unsatisfiable
% 280.01/221.66 |-Branch two:
% 280.01/221.66 | (677) sdtpldt0(xp, all_0_8_8) = all_10_0_16
% 280.01/221.66 | (853) all_34_0_107 = all_10_0_16
% 280.01/221.66 |
% 280.01/221.66 | Combining equations (733,853) yields a new equation:
% 280.01/221.66 | (854) all_10_0_16 = all_0_7_7
% 280.01/221.66 |
% 280.01/221.66 | Combining equations (802,854) yields a new equation:
% 280.01/221.66 | (856) all_0_7_7 = all_0_12_12
% 280.01/221.66 |
% 280.01/221.66 | From (856) and (5) follows:
% 280.01/221.66 | (861) sdtpldt0(all_0_12_12, all_0_4_4) = all_0_11_11
% 280.01/221.66 |
% 280.01/221.66 | From (856) and (49) follows:
% 280.01/221.66 | (862) sdtpldt0(all_0_8_8, xp) = all_0_12_12
% 280.01/221.66 |
% 280.01/221.66 +-Applying beta-rule and splitting (129), into two cases.
% 280.01/221.66 |-Branch one:
% 280.01/221.66 | (885) ~ (sdtpldt0(all_0_8_8, xp) = all_0_12_12)
% 280.01/221.66 |
% 280.01/221.66 | Using (862) and (885) yields:
% 280.01/221.66 | (695) $false
% 280.01/221.66 |
% 280.01/221.66 |-The branch is then unsatisfiable
% 280.01/221.66 |-Branch two:
% 280.01/221.66 | (862) sdtpldt0(all_0_8_8, xp) = all_0_12_12
% 280.01/221.66 | (888) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(all_0_8_8, v3) = v4 & sdtpldt0(xp, xp) = v3 & aNaturalNumber0(all_0_8_8) = v0 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_11_11))
% 280.01/221.66 |
% 280.01/221.66 | Instantiating (888) with all_419_0_1141, all_419_1_1142, all_419_2_1143, all_419_3_1144, all_419_4_1145 yields:
% 280.01/221.66 | (1399) sdtpldt0(all_0_8_8, all_419_1_1142) = all_419_0_1141 & sdtpldt0(xp, xp) = all_419_1_1142 & aNaturalNumber0(all_0_8_8) = all_419_4_1145 & aNaturalNumber0(xp) = all_419_2_1143 & aNaturalNumber0(xp) = all_419_3_1144 & ( ~ (all_419_2_1143 = 0) | ~ (all_419_3_1144 = 0) | ~ (all_419_4_1145 = 0) | all_419_0_1141 = all_0_11_11)
% 280.01/221.66 |
% 280.01/221.66 | Applying alpha-rule on (1399) yields:
% 280.01/221.66 | (1400) aNaturalNumber0(xp) = all_419_3_1144
% 280.01/221.66 | (1401) aNaturalNumber0(all_0_8_8) = all_419_4_1145
% 280.01/221.66 | (1402) aNaturalNumber0(xp) = all_419_2_1143
% 280.01/221.66 | (1403) sdtpldt0(all_0_8_8, all_419_1_1142) = all_419_0_1141
% 280.01/221.66 | (1404) ~ (all_419_2_1143 = 0) | ~ (all_419_3_1144 = 0) | ~ (all_419_4_1145 = 0) | all_419_0_1141 = all_0_11_11
% 280.01/221.66 | (1405) sdtpldt0(xp, xp) = all_419_1_1142
% 280.01/221.66 |
% 280.01/221.66 +-Applying beta-rule and splitting (140), into two cases.
% 280.01/221.66 |-Branch one:
% 280.01/221.66 | (873) ~ (sdtpldt0(all_0_12_12, all_0_4_4) = all_0_11_11)
% 280.01/221.66 |
% 280.01/221.66 | Using (861) and (873) yields:
% 280.01/221.66 | (695) $false
% 280.01/221.66 |
% 280.01/221.66 |-The branch is then unsatisfiable
% 280.01/221.66 |-Branch two:
% 280.01/221.66 | (861) sdtpldt0(all_0_12_12, all_0_4_4) = all_0_11_11
% 280.01/221.66 | (876) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtpldt0(xm, all_0_4_4) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(all_0_4_4) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_0_11_11))
% 280.01/221.66 |
% 280.01/221.66 | Instantiating (876) with all_424_0_1146, all_424_1_1147, all_424_2_1148, all_424_3_1149, all_424_4_1150 yields:
% 280.01/221.66 | (1410) sdtpldt0(xm, all_0_4_4) = all_424_1_1147 & sdtpldt0(xn, all_424_1_1147) = all_424_0_1146 & aNaturalNumber0(all_0_4_4) = all_424_2_1148 & aNaturalNumber0(xm) = all_424_3_1149 & aNaturalNumber0(xn) = all_424_4_1150 & ( ~ (all_424_2_1148 = 0) | ~ (all_424_3_1149 = 0) | ~ (all_424_4_1150 = 0) | all_424_0_1146 = all_0_11_11)
% 280.01/221.66 |
% 280.01/221.66 | Applying alpha-rule on (1410) yields:
% 280.01/221.66 | (1411) aNaturalNumber0(all_0_4_4) = all_424_2_1148
% 280.01/221.66 | (1412) sdtpldt0(xn, all_424_1_1147) = all_424_0_1146
% 280.01/221.66 | (1413) aNaturalNumber0(xm) = all_424_3_1149
% 280.01/221.66 | (1414) ~ (all_424_2_1148 = 0) | ~ (all_424_3_1149 = 0) | ~ (all_424_4_1150 = 0) | all_424_0_1146 = all_0_11_11
% 280.01/221.66 | (1415) sdtpldt0(xm, all_0_4_4) = all_424_1_1147
% 280.01/221.66 | (1416) aNaturalNumber0(xn) = all_424_4_1150
% 280.01/221.66 |
% 280.01/221.66 | Instantiating formula (23) with xp, xn, all_151_0_1033, 0 and discharging atoms sdtlseqdt0(xp, xn) = all_151_0_1033, sdtlseqdt0(xp, xn) = 0, yields:
% 280.01/221.66 | (1417) all_151_0_1033 = 0
% 280.01/221.66 |
% 280.01/221.66 | Instantiating formula (97) with xp, all_419_3_1144, 0 and discharging atoms aNaturalNumber0(xp) = all_419_3_1144, aNaturalNumber0(xp) = 0, yields:
% 280.01/221.66 | (1418) all_419_3_1144 = 0
% 280.01/221.66 |
% 280.01/221.66 | Instantiating formula (97) with xp, all_151_2_1035, all_419_3_1144 and discharging atoms aNaturalNumber0(xp) = all_419_3_1144, aNaturalNumber0(xp) = all_151_2_1035, yields:
% 280.01/221.66 | (1419) all_419_3_1144 = all_151_2_1035
% 280.01/221.66 |
% 280.01/221.66 | Instantiating formula (97) with xn, all_424_4_1150, 0 and discharging atoms aNaturalNumber0(xn) = all_424_4_1150, aNaturalNumber0(xn) = 0, yields:
% 280.01/221.66 | (1420) all_424_4_1150 = 0
% 280.01/221.66 |
% 280.01/221.66 | Instantiating formula (97) with xn, all_151_1_1034, all_424_4_1150 and discharging atoms aNaturalNumber0(xn) = all_424_4_1150, aNaturalNumber0(xn) = all_151_1_1034, yields:
% 280.01/221.66 | (1421) all_424_4_1150 = all_151_1_1034
% 280.01/221.66 |
% 280.01/221.66 | Combining equations (1421,1420) yields a new equation:
% 280.01/221.66 | (1422) all_151_1_1034 = 0
% 280.01/221.66 |
% 280.01/221.66 | Simplifying 1422 yields:
% 280.01/221.66 | (1423) all_151_1_1034 = 0
% 280.01/221.66 |
% 280.01/221.66 | Combining equations (1418,1419) yields a new equation:
% 280.01/221.66 | (1352) all_151_2_1035 = 0
% 280.01/221.66 |
% 280.01/221.66 +-Applying beta-rule and splitting (1358), into two cases.
% 280.01/221.66 |-Branch one:
% 280.01/221.66 | (1425) ~ (all_151_0_1033 = 0)
% 280.01/221.66 |
% 280.01/221.66 | Equations (1417) can reduce 1425 to:
% 280.01/221.66 | (346) $false
% 280.01/221.66 |
% 280.01/221.66 |-The branch is then unsatisfiable
% 280.01/221.66 |-Branch two:
% 280.01/221.66 | (1417) all_151_0_1033 = 0
% 280.01/221.66 | (1428) ~ (all_151_1_1034 = 0) | ~ (all_151_2_1035 = 0)
% 280.01/221.66 |
% 280.01/221.66 +-Applying beta-rule and splitting (1428), into two cases.
% 280.01/221.66 |-Branch one:
% 280.01/221.66 | (1429) ~ (all_151_1_1034 = 0)
% 280.01/221.66 |
% 280.01/221.66 | Equations (1423) can reduce 1429 to:
% 280.01/221.66 | (346) $false
% 280.01/221.66 |
% 280.01/221.66 |-The branch is then unsatisfiable
% 280.01/221.66 |-Branch two:
% 280.01/221.66 | (1423) all_151_1_1034 = 0
% 280.01/221.66 | (1350) ~ (all_151_2_1035 = 0)
% 280.01/221.66 |
% 280.01/221.67 | Equations (1352) can reduce 1350 to:
% 280.01/221.67 | (346) $false
% 280.01/221.67 |
% 280.01/221.67 |-The branch is then unsatisfiable
% 280.01/221.67 % SZS output end Proof for theBenchmark
% 280.01/221.67
% 280.01/221.67 221068ms
%------------------------------------------------------------------------------