%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : NUM492+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n025.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 08:45:05 EDT 2022 % Result : Theorem 6.91s 2.24s % Output : Proof 11.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NUM492+3 : TPTP v8.1.0. Released v4.0.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n025.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 22:56:13 EDT 2022 % 0.13/0.34 % CPUTime : % 0.54/0.62 ____ _ % 0.54/0.62 ___ / __ \_____(_)___ ________ __________ % 0.54/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.62 % 0.54/0.62 A Theorem Prover for First-Order Logic % 0.54/0.62 (ePrincess v.1.0) % 0.54/0.62 % 0.54/0.62 (c) Philipp Rümmer, 2009-2015 % 0.54/0.62 (c) Peter Backeman, 2014-2015 % 0.54/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.54/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.54/0.62 Bug reports to peter@backeman.se % 0.54/0.62 % 0.54/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.54/0.62 % 0.54/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.71/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.07/1.09 Prover 0: Preprocessing ... % 3.90/1.61 Prover 0: Constructing countermodel ... % 6.91/2.24 Prover 0: proved (1544ms) % 6.91/2.24 % 6.91/2.24 No countermodel exists, formula is valid % 6.91/2.24 % SZS status Theorem for theBenchmark % 6.91/2.24 % 6.91/2.24 Generating proof ... found it (size 59) % 11.14/3.20 % 11.14/3.20 % SZS output start Proof for theBenchmark % 11.14/3.20 Assumed formulas after preprocessing and simplification: % 11.14/3.20 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (xr = xn) & ~ (xp = sz10) & ~ (xp = sz00) & ~ (sz10 = sz00) & sdtmndt0(v2, v3) = v4 & sdtmndt0(xn, xp) = xr & sdtasdt0(xr, xm) = v4 & sdtasdt0(xp, v9) = v2 & sdtasdt0(xp, v6) = v2 & sdtasdt0(xp, v5) = v3 & sdtasdt0(xp, xm) = v3 & sdtasdt0(xn, xm) = v2 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, xp) = v1 & sdtpldt0(xr, v7) = xn & sdtpldt0(xp, v8) = xn & sdtpldt0(xp, xr) = xn & sdtpldt0(xn, xm) = v0 & isPrime0(xp) & doDivides0(xp, v3) & doDivides0(xp, v2) & sdtlseqdt0(xr, xn) & sdtlseqdt0(xp, xn) & aNaturalNumber0(v9) & aNaturalNumber0(v8) & aNaturalNumber0(v7) & aNaturalNumber0(v6) & aNaturalNumber0(v5) & aNaturalNumber0(xr) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ isPrime0(sz10) & ~ isPrime0(sz00) & ~ doDivides0(xp, v4) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v10 = sz00 | ~ (sdtsldt0(v14, v10) = v15) | ~ (sdtsldt0(v11, v10) = v12) | ~ (sdtasdt0(v13, v11) = v14) | ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v13) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtasdt0(v13, v12) = v15) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (sdtasdt0(v12, v10) = v14) | ~ (sdtasdt0(v11, v10) = v13) | ~ (sdtpldt0(v13, v14) = v15) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (sdtasdt0(v16, v10) = v15 & sdtasdt0(v10, v16) = v17 & sdtasdt0(v10, v12) = v19 & sdtasdt0(v10, v11) = v18 & sdtpldt0(v18, v19) = v17 & sdtpldt0(v11, v12) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (sdtasdt0(v10, v12) = v14) | ~ (sdtasdt0(v10, v11) = v13) | ~ (sdtpldt0(v13, v14) = v15) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (sdtasdt0(v16, v10) = v17 & sdtasdt0(v12, v10) = v19 & sdtasdt0(v11, v10) = v18 & sdtasdt0(v10, v16) = v15 & sdtpldt0(v18, v19) = v17 & sdtpldt0(v11, v12) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v12, v10) = v14) | ~ (sdtasdt0(v11, v10) = v13) | ~ sdtlseqdt0(v11, v12) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtlseqdt0(v13, v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v12, v10) = v14) | ~ (sdtasdt0(v11, v10) = v13) | ~ sdtlseqdt0(v11, v12) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v15) & sdtasdt0(v10, v12) = v16 & sdtasdt0(v10, v11) = v15 & sdtlseqdt0(v15, v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v12, v10) = v14) | ~ (sdtasdt0(v11, v10) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v15) & sdtasdt0(v10, v12) = v16 & sdtasdt0(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v12, v10) = v14) | ~ (sdtasdt0(v10, v11) = v13) | ~ sdtlseqdt0(v11, v12) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v14) & ~ (v15 = v13) & sdtasdt0(v11, v10) = v16 & sdtasdt0(v10, v12) = v15 & sdtlseqdt0(v16, v14) & sdtlseqdt0(v13, v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v12, v10) = v14) | ~ (sdtasdt0(v10, v11) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v14) & ~ (v15 = v13) & sdtasdt0(v11, v10) = v16 & sdtasdt0(v10, v12) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v11, v10) = v14) | ~ (sdtasdt0(v10, v12) = v13) | ~ sdtlseqdt0(v11, v12) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v14) & ~ (v15 = v13) & sdtasdt0(v12, v10) = v16 & sdtasdt0(v10, v11) = v15 & sdtlseqdt0(v15, v13) & sdtlseqdt0(v14, v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v11, v10) = v14) | ~ (sdtasdt0(v10, v12) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v14) & ~ (v15 = v13) & sdtasdt0(v12, v10) = v16 & sdtasdt0(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v10, v12) = v14) | ~ (sdtasdt0(v10, v11) = v13) | ~ sdtlseqdt0(v11, v12) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtlseqdt0(v13, v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v10, v12) = v14) | ~ (sdtasdt0(v10, v11) = v13) | ~ sdtlseqdt0(v11, v12) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v15) & sdtasdt0(v12, v10) = v16 & sdtasdt0(v11, v10) = v15 & sdtlseqdt0(v15, v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v10, v12) = v14) | ~ (sdtasdt0(v10, v11) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v15) & sdtasdt0(v12, v10) = v16 & sdtasdt0(v11, v10) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (sdtpldt0(v12, v10) = v14) | ~ (sdtpldt0(v11, v10) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v15) & sdtpldt0(v10, v12) = v16 & sdtpldt0(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (sdtpldt0(v12, v10) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v14) & ~ (v15 = v13) & sdtpldt0(v11, v10) = v16 & sdtpldt0(v10, v12) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (sdtpldt0(v11, v10) = v14) | ~ (sdtpldt0(v10, v12) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v14) & ~ (v15 = v13) & sdtpldt0(v12, v10) = v16 & sdtpldt0(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (sdtpldt0(v10, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ( ~ (v16 = v15) & sdtpldt0(v12, v10) = v16 & sdtpldt0(v11, v10) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = sz10 | v12 = sz00 | ~ (sdtpldt0(v13, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ iLess0(v14, v1) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v12, v11) | doDivides0(v12, v10) | ? [v15] : ? [v16] : ? [v17] : ((v17 = v12 & ~ (v15 = v12) & ~ (v15 = sz10) & sdtasdt0(v15, v16) = v12 & doDivides0(v15, v12) & aNaturalNumber0(v16) & aNaturalNumber0(v15)) | (sdtasdt0(v10, v11) = v15 & ~ doDivides0(v12, v15) & ! [v18] : ( ~ (sdtasdt0(v12, v18) = v15) | ~ aNaturalNumber0(v18))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = sz10 | v12 = sz00 | ~ (sdtpldt0(v13, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ iLess0(v14, v1) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v12, v11) | ? [v15] : ? [v16] : ? [v17] : ((v17 = v12 & ~ (v15 = v12) & ~ (v15 = sz10) & sdtasdt0(v15, v16) = v12 & doDivides0(v15, v12) & aNaturalNumber0(v16) & aNaturalNumber0(v15)) | (v16 = v10 & sdtasdt0(v12, v15) = v10 & aNaturalNumber0(v15)) | (sdtasdt0(v10, v11) = v15 & ~ doDivides0(v12, v15) & ! [v18] : ( ~ (sdtasdt0(v12, v18) = v15) | ~ aNaturalNumber0(v18))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = sz10 | v12 = sz00 | ~ (sdtpldt0(v13, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ iLess0(v14, v1) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v12, v10) | ? [v15] : ? [v16] : ? [v17] : ((v17 = v12 & ~ (v15 = v12) & ~ (v15 = sz10) & sdtasdt0(v15, v16) = v12 & doDivides0(v15, v12) & aNaturalNumber0(v16) & aNaturalNumber0(v15)) | (v16 = v11 & sdtasdt0(v12, v15) = v11 & aNaturalNumber0(v15)) | (sdtasdt0(v10, v11) = v15 & ~ doDivides0(v12, v15) & ! [v18] : ( ~ (sdtasdt0(v12, v18) = v15) | ~ aNaturalNumber0(v18))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = sz10 | v12 = sz00 | ~ (sdtpldt0(v13, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ iLess0(v14, v1) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ? [v17] : ((v17 = v12 & ~ (v15 = v12) & ~ (v15 = sz10) & sdtasdt0(v15, v16) = v12 & doDivides0(v15, v12) & aNaturalNumber0(v16) & aNaturalNumber0(v15)) | (v16 = v11 & sdtasdt0(v12, v15) = v11 & aNaturalNumber0(v15)) | (v16 = v10 & sdtasdt0(v12, v15) = v10 & aNaturalNumber0(v15)) | (sdtasdt0(v10, v11) = v15 & ~ doDivides0(v12, v15) & ! [v18] : ( ~ (sdtasdt0(v12, v18) = v15) | ~ aNaturalNumber0(v18))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = sz00 | ~ (sdtsldt0(v11, v10) = v12) | ~ (sdtasdt0(v13, v12) = v14) | ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v13) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : (sdtsldt0(v15, v10) = v14 & sdtasdt0(v13, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtasdt0(v13, v12) = v14) | ~ (sdtasdt0(v10, v11) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : (sdtasdt0(v11, v12) = v15 & sdtasdt0(v10, v15) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtasdt0(v13, v10) = v14) | ~ (sdtpldt0(v11, v12) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (sdtasdt0(v12, v10) = v19 & sdtasdt0(v11, v10) = v18 & sdtasdt0(v10, v13) = v15 & sdtasdt0(v10, v12) = v17 & sdtasdt0(v10, v11) = v16 & sdtpldt0(v18, v19) = v14 & sdtpldt0(v16, v17) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtasdt0(v11, v12) = v13) | ~ (sdtasdt0(v10, v13) = v14) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : (sdtasdt0(v15, v12) = v14 & sdtasdt0(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtasdt0(v10, v13) = v14) | ~ (sdtpldt0(v11, v12) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (sdtasdt0(v13, v10) = v17 & sdtasdt0(v12, v10) = v19 & sdtasdt0(v11, v10) = v18 & sdtasdt0(v10, v12) = v16 & sdtasdt0(v10, v11) = v15 & sdtpldt0(v18, v19) = v17 & sdtpldt0(v15, v16) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtpldt0(v13, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ isPrime0(v12) | ~ iLess0(v14, v1) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v12, v11) | doDivides0(v12, v10) | ? [v15] : (sdtasdt0(v10, v11) = v15 & ~ doDivides0(v12, v15) & ! [v16] : ( ~ (sdtasdt0(v12, v16) = v15) | ~ aNaturalNumber0(v16)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtpldt0(v13, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ isPrime0(v12) | ~ iLess0(v14, v1) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v12, v11) | ? [v15] : ? [v16] : ((v16 = v10 & sdtasdt0(v12, v15) = v10 & aNaturalNumber0(v15)) | (sdtasdt0(v10, v11) = v15 & ~ doDivides0(v12, v15) & ! [v17] : ( ~ (sdtasdt0(v12, v17) = v15) | ~ aNaturalNumber0(v17))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtpldt0(v13, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ isPrime0(v12) | ~ iLess0(v14, v1) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v12, v10) | ? [v15] : ? [v16] : ((v16 = v11 & sdtasdt0(v12, v15) = v11 & aNaturalNumber0(v15)) | (sdtasdt0(v10, v11) = v15 & ~ doDivides0(v12, v15) & ! [v17] : ( ~ (sdtasdt0(v12, v17) = v15) | ~ aNaturalNumber0(v17))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtpldt0(v13, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ isPrime0(v12) | ~ iLess0(v14, v1) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : ? [v16] : ((v16 = v11 & sdtasdt0(v12, v15) = v11 & aNaturalNumber0(v15)) | (v16 = v10 & sdtasdt0(v12, v15) = v10 & aNaturalNumber0(v15)) | (sdtasdt0(v10, v11) = v15 & ~ doDivides0(v12, v15) & ! [v17] : ( ~ (sdtasdt0(v12, v17) = v15) | ~ aNaturalNumber0(v17))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtpldt0(v13, v12) = v14) | ~ (sdtpldt0(v10, v11) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : (sdtpldt0(v11, v12) = v15 & sdtpldt0(v10, v15) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (sdtpldt0(v11, v12) = v13) | ~ (sdtpldt0(v10, v13) = v14) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v15] : (sdtpldt0(v15, v12) = v14 & sdtpldt0(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | v10 = sz00 | ~ (sdtsldt0(v11, v10) = v12) | ~ (sdtasdt0(v10, v13) = v11) | ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v13) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (sdtmndt0(v11, v10) = v12) | ~ (sdtpldt0(v10, v13) = v11) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v13) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | v10 = sz00 | ~ (sdtsldt0(v11, v10) = v12) | ~ (sdtasdt0(v10, v12) = v13) | ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (sdtmndt0(v11, v10) = v12) | ~ (sdtpldt0(v10, v12) = v13) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v12, v10) = v13) | ~ (sdtasdt0(v11, v10) = v13) | ~ sdtlseqdt0(v11, v12) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v12, v10) = v13) | ~ (sdtasdt0(v11, v10) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v10, v12) = v13) | ~ (sdtasdt0(v10, v11) = v13) | ~ sdtlseqdt0(v11, v12) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | v10 = sz00 | ~ (sdtasdt0(v10, v12) = v13) | ~ (sdtasdt0(v10, v11) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (sdtpldt0(v12, v10) = v13) | ~ (sdtpldt0(v11, v10) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (sdtpldt0(v10, v12) = v13) | ~ (sdtpldt0(v10, v11) = v13) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtsldt0(v13, v12) = v11) | ~ (sdtsldt0(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtmndt0(v13, v12) = v11) | ~ (sdtmndt0(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtasdt0(v13, v12) = v11) | ~ (sdtasdt0(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtpldt0(v13, v12) = v11) | ~ (sdtpldt0(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtpldt0(v12, v11) = v13) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v14] : ? [v15] : ? [v16] : ( ~ (v16 = v15) & ~ (v14 = v13) & sdtpldt0(v12, v10) = v14 & sdtpldt0(v11, v12) = v16 & sdtpldt0(v10, v12) = v15 & sdtlseqdt0(v15, v16) & sdtlseqdt0(v14, v13))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtpldt0(v12, v10) = v13) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v14] : ? [v15] : ? [v16] : ( ~ (v16 = v15) & ~ (v14 = v13) & sdtpldt0(v12, v11) = v14 & sdtpldt0(v11, v12) = v16 & sdtpldt0(v10, v12) = v15 & sdtlseqdt0(v15, v16) & sdtlseqdt0(v13, v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtpldt0(v11, v12) = v13) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v14] : ? [v15] : ? [v16] : ( ~ (v16 = v13) & ~ (v15 = v14) & sdtpldt0(v12, v11) = v15 & sdtpldt0(v12, v10) = v14 & sdtpldt0(v10, v12) = v16 & sdtlseqdt0(v16, v13) & sdtlseqdt0(v14, v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (sdtpldt0(v10, v12) = v13) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v14] : ? [v15] : ? [v16] : ( ~ (v16 = v13) & ~ (v15 = v14) & sdtpldt0(v12, v11) = v15 & sdtpldt0(v12, v10) = v14 & sdtpldt0(v11, v12) = v16 & sdtlseqdt0(v14, v15) & sdtlseqdt0(v13, v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = sz00 | ~ (sdtsldt0(v11, v10) = v12) | ~ (sdtasdt0(v10, v12) = v13) | ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | aNaturalNumber0(v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtmndt0(v11, v10) = v12) | ~ (sdtpldt0(v10, v12) = v13) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | aNaturalNumber0(v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtpldt0(v11, v12) = v13) | ~ doDivides0(v10, v13) | ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sdtpldt0(v11, v12) = v13) | ~ doDivides0(v10, v12) | ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v10, v13)) & ! [v10] : ! [v11] : ! [v12] : (v10 = sz00 | ~ (sdtasdt0(v11, v10) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtlseqdt0(v11, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtasdt0(v11, v10) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtasdt0(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtasdt0(v10, v12) = v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtasdt0(v10, v11) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtasdt0(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtasdt0(v10, v11) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | aNaturalNumber0(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtpldt0(v11, v10) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtpldt0(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtpldt0(v10, v12) = v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtlseqdt0(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtpldt0(v10, v11) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtpldt0(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (sdtpldt0(v10, v11) = v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | aNaturalNumber0(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ doDivides0(v11, v12) | ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | doDivides0(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ sdtlseqdt0(v11, v12) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v12) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtlseqdt0(v10, v12)) & ! [v10] : ! [v11] : (v11 = v10 | v11 = sz10 | ~ isPrime0(v10) | ~ doDivides0(v11, v10) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (sdtasdt0(v10, sz10) = v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (sdtasdt0(sz10, v10) = v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (sdtpldt0(v10, sz00) = v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (sdtpldt0(sz00, v10) = v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = v10 | ~ sdtlseqdt0(v11, v10) | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = v10 | ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | iLess0(v10, v11)) & ! [v10] : ! [v11] : (v11 = sz00 | v10 = sz00 | ~ (sdtasdt0(v10, v11) = sz00) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = sz00 | ~ (sdtasdt0(v10, sz00) = v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = sz00 | ~ (sdtasdt0(sz00, v10) = v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = sz00 | ~ (sdtpldt0(v10, v11) = sz00) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v11 = sz00 | ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtlseqdt0(v10, v11)) & ! [v10] : ! [v11] : (v10 = xp | v10 = sz10 | ~ (sdtasdt0(v10, v11) = xp) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : (v10 = sz00 | ~ (sdtpldt0(v10, v11) = sz00) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10)) & ! [v10] : ! [v11] : ( ~ (sdtasdt0(v10, sz10) = v11) | ~ aNaturalNumber0(v10) | sdtasdt0(sz10, v10) = v10) & ! [v10] : ! [v11] : ( ~ (sdtasdt0(v10, sz00) = v11) | ~ aNaturalNumber0(v10) | sdtasdt0(sz00, v10) = sz00) & ! [v10] : ! [v11] : ( ~ (sdtasdt0(sz10, v10) = v11) | ~ aNaturalNumber0(v10) | sdtasdt0(v10, sz10) = v10) & ! [v10] : ! [v11] : ( ~ (sdtasdt0(sz00, v10) = v11) | ~ aNaturalNumber0(v10) | sdtasdt0(v10, sz00) = sz00) & ! [v10] : ! [v11] : ( ~ (sdtpldt0(v10, sz00) = v11) | ~ aNaturalNumber0(v10) | sdtpldt0(sz00, v10) = v10) & ! [v10] : ! [v11] : ( ~ (sdtpldt0(sz00, v10) = v11) | ~ aNaturalNumber0(v10) | sdtpldt0(v10, sz00) = v10) & ! [v10] : ! [v11] : ( ~ doDivides0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v12] : (sdtasdt0(v10, v12) = v11 & aNaturalNumber0(v12))) & ! [v10] : ! [v11] : ( ~ sdtlseqdt0(v10, v11) | ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | ? [v12] : (sdtpldt0(v10, v12) = v11 & aNaturalNumber0(v12))) & ! [v10] : ! [v11] : ( ~ aNaturalNumber0(v11) | ~ aNaturalNumber0(v10) | sdtlseqdt0(v11, v10) | sdtlseqdt0(v10, v11)) & ! [v10] : (v10 = xp | v10 = sz10 | ~ doDivides0(v10, xp) | ~ aNaturalNumber0(v10)) & ! [v10] : (v10 = sz10 | v10 = sz00 | ~ aNaturalNumber0(v10) | isPrime0(v10) | ? [v11] : ( ~ (v11 = v10) & ~ (v11 = sz10) & doDivides0(v11, v10) & aNaturalNumber0(v11))) & ! [v10] : (v10 = sz10 | v10 = sz00 | ~ aNaturalNumber0(v10) | sdtlseqdt0(sz10, v10)) & ! [v10] : (v10 = sz10 | v10 = sz00 | ~ aNaturalNumber0(v10) | ? [v11] : (isPrime0(v11) & doDivides0(v11, v10) & aNaturalNumber0(v11))) & ! [v10] : ( ~ aNaturalNumber0(v10) | sdtlseqdt0(v10, v10)) & ! [v10] : ( ~ aNaturalNumber0(v10) | ? [v11] : ( ~ (v11 = v4) & sdtasdt0(xp, v10) = v11))) % 11.43/3.28 | 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 yields: % 11.43/3.28 | (1) ~ (xr = xn) & ~ (xp = sz10) & ~ (xp = sz00) & ~ (sz10 = sz00) & sdtmndt0(all_0_7_7, all_0_6_6) = all_0_5_5 & sdtmndt0(xn, xp) = xr & sdtasdt0(xr, xm) = all_0_5_5 & sdtasdt0(xp, all_0_0_0) = all_0_7_7 & sdtasdt0(xp, all_0_3_3) = all_0_7_7 & sdtasdt0(xp, all_0_4_4) = all_0_6_6 & sdtasdt0(xp, xm) = all_0_6_6 & sdtasdt0(xn, xm) = all_0_7_7 & sdtpldt0(all_0_6_6, all_0_5_5) = all_0_7_7 & sdtpldt0(all_0_9_9, xp) = all_0_8_8 & sdtpldt0(xr, all_0_2_2) = xn & sdtpldt0(xp, all_0_1_1) = xn & sdtpldt0(xp, xr) = xn & sdtpldt0(xn, xm) = all_0_9_9 & isPrime0(xp) & doDivides0(xp, all_0_6_6) & doDivides0(xp, all_0_7_7) & sdtlseqdt0(xr, xn) & sdtlseqdt0(xp, xn) & aNaturalNumber0(all_0_0_0) & aNaturalNumber0(all_0_1_1) & aNaturalNumber0(all_0_2_2) & aNaturalNumber0(all_0_3_3) & aNaturalNumber0(all_0_4_4) & aNaturalNumber0(xr) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ isPrime0(sz10) & ~ isPrime0(sz00) & ~ doDivides0(xp, all_0_5_5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v3, v2) = v5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtlseqdt0(v6, v4) & sdtlseqdt0(v3, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v3) & sdtlseqdt0(v4, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtlseqdt0(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v0, v2) = v6 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v2) = v4) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtsldt0(v5, v0) = v4 & sdtasdt0(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v6, v7) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) | ? [v5] : (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v6] : ( ~ (sdtasdt0(v2, v6) = v5) | ~ aNaturalNumber0(v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5] : ? [v6] : ((v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ((v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ((v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v1) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v4, v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v0) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v1) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v1, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v0, v2) = v6 & sdtlseqdt0(v6, v3) & sdtlseqdt0(v4, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1)) & ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0] : ! [v1] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1) = xp) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0) & ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2))) & ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2))) & ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) & ! [v0] : (v0 = xp | v0 = sz10 | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0)) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1] : ( ~ (v1 = v0) & ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1))) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1))) & ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_5_5) & sdtasdt0(xp, v0) = v1)) % 11.43/3.31 | % 11.43/3.31 | Applying alpha-rule on (1) yields: % 11.43/3.31 | (2) doDivides0(xp, all_0_7_7) % 11.43/3.31 | (3) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 11.43/3.31 | (4) ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2)) % 11.43/3.31 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v0) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v1) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v3, v4))) % 11.43/3.31 | (6) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) % 11.43/3.31 | (7) sdtasdt0(xp, all_0_3_3) = all_0_7_7 % 11.43/3.31 | (8) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) % 11.43/3.31 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) % 11.43/3.31 | (10) aNaturalNumber0(all_0_2_2) % 11.43/3.31 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v6, v7) = v5)) % 11.43/3.31 | (12) sdtmndt0(xn, xp) = xr % 11.43/3.31 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 11.43/3.31 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2) % 11.43/3.31 | (15) ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2))) % 11.43/3.31 | (16) ! [v0] : (v0 = xp | v0 = sz10 | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0)) % 11.43/3.31 | (17) sdtlseqdt0(xp, xn) % 11.43/3.31 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtlseqdt0(v5, v6))) % 11.43/3.31 | (19) doDivides0(xp, all_0_6_6) % 11.43/3.31 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 11.43/3.31 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtlseqdt0(v6, v4) & sdtlseqdt0(v3, v5))) % 11.43/3.31 | (22) sdtmndt0(all_0_7_7, all_0_6_6) = all_0_5_5 % 11.43/3.31 | (23) sdtpldt0(all_0_9_9, xp) = all_0_8_8 % 11.43/3.31 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) % 11.43/3.32 | (25) ~ (xr = xn) % 11.43/3.32 | (26) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0) % 11.43/3.32 | (27) sdtasdt0(xp, xm) = all_0_6_6 % 11.43/3.32 | (28) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 11.43/3.32 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v0, v2) = v6 & sdtpldt0(v0, v1) = v5)) % 11.43/3.32 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v3, v2) = v5) % 11.43/3.32 | (31) ~ (xp = sz10) % 11.43/3.32 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5)) % 11.43/3.32 | (33) ! [v0] : ! [v1] : (v1 = sz00 | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) % 11.43/3.32 | (34) aNaturalNumber0(xp) % 11.43/3.32 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 11.43/3.32 | (36) isPrime0(xp) % 11.43/3.32 | (37) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0)) % 11.43/3.32 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v3) & sdtlseqdt0(v4, v6))) % 11.43/3.32 | (39) aNaturalNumber0(all_0_4_4) % 11.43/3.32 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 11.43/3.32 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5)) % 11.43/3.32 | (42) sdtpldt0(xp, all_0_1_1) = xn % 11.43/3.32 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ((v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7))))) % 11.43/3.32 | (44) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 11.43/3.32 | (45) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) % 11.43/3.32 | (46) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 11.43/3.32 | (47) ~ (xp = sz00) % 11.43/3.32 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5)) % 11.43/3.32 | (49) sdtasdt0(xp, all_0_0_0) = all_0_7_7 % 11.43/3.32 | (50) ! [v0] : ! [v1] : (v1 = v0 | v1 = sz10 | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 11.43/3.32 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v6))) % 11.43/3.32 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 11.43/3.32 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 11.43/3.32 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) % 11.43/3.32 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 11.43/3.32 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 11.43/3.32 | (57) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0)) % 11.43/3.32 | (58) sdtlseqdt0(xr, xn) % 11.43/3.32 | (59) ~ isPrime0(sz00) % 11.43/3.32 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v3, v2) = v4) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtsldt0(v5, v0) = v4 & sdtasdt0(v3, v1) = v5)) % 11.43/3.32 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5)) % 11.43/3.32 | (62) aNaturalNumber0(sz10) % 11.43/3.32 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2) % 11.43/3.32 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2) % 11.43/3.32 | (65) ! [v0] : ! [v1] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1) = xp) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 11.43/3.32 | (66) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2))) % 11.43/3.32 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v1, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v0, v2) = v6 & sdtlseqdt0(v6, v3) & sdtlseqdt0(v4, v5))) % 11.43/3.32 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 11.43/3.32 | (69) sdtpldt0(xn, xm) = all_0_9_9 % 11.43/3.33 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2) % 11.43/3.33 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ((v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7))))) % 11.43/3.33 | (72) sdtasdt0(xn, xm) = all_0_7_7 % 11.43/3.33 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 11.43/3.33 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5] : ? [v6] : ((v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v7] : ( ~ (sdtasdt0(v2, v7) = v5) | ~ aNaturalNumber0(v7))))) % 11.43/3.34 | (75) sdtpldt0(all_0_6_6, all_0_5_5) = all_0_7_7 % 11.43/3.34 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) % 11.43/3.34 | (77) aNaturalNumber0(all_0_3_3) % 11.43/3.34 | (78) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 11.43/3.34 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ isPrime0(v2) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) | ? [v5] : (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v6] : ( ~ (sdtasdt0(v2, v6) = v5) | ~ aNaturalNumber0(v6)))) % 11.43/3.34 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) % 11.43/3.34 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5)) % 11.43/3.34 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6))) % 11.43/3.34 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v1 & sdtasdt0(v2, v5) = v1 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) % 11.43/3.34 | (84) ~ isPrime0(sz10) % 11.43/3.34 | (85) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2)) % 11.43/3.34 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3)) % 11.43/3.34 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 11.43/3.34 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4)) % 11.43/3.34 | (89) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1] : ( ~ (v1 = v0) & ~ (v1 = sz10) & doDivides0(v1, v0) & aNaturalNumber0(v1))) % 11.43/3.34 | (90) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0) % 11.43/3.34 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 11.43/3.34 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) % 11.43/3.35 | (93) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1)) % 11.43/3.35 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5)) % 11.43/3.35 | (95) ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) % 11.43/3.35 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) % 11.43/3.35 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) % 11.43/3.35 | (98) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) % 11.43/3.35 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v1) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v4, v3))) % 11.43/3.35 | (100) aNaturalNumber0(all_0_0_0) % 11.43/3.35 | (101) sdtasdt0(xp, all_0_4_4) = all_0_6_6 % 11.43/3.35 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 11.43/3.35 | (103) ~ (sz10 = sz00) % 11.43/3.35 | (104) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) % 11.43/3.35 | (105) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00) % 11.43/3.35 | (106) sdtpldt0(xr, all_0_2_2) = xn % 11.43/3.35 | (107) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) % 11.43/3.35 | (108) ~ doDivides0(xp, all_0_5_5) % 11.43/3.35 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v1) = v5)) % 11.43/3.35 | (110) sdtasdt0(xr, xm) = all_0_5_5 % 11.43/3.35 | (111) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) % 11.43/3.35 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) % 11.43/3.35 | (113) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0) % 11.43/3.35 | (114) aNaturalNumber0(xm) % 11.43/3.35 | (115) aNaturalNumber0(sz00) % 11.43/3.35 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) % 11.43/3.35 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4)) % 11.43/3.35 | (118) aNaturalNumber0(xr) % 11.43/3.35 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5)) % 11.43/3.35 | (120) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0) % 11.43/3.35 | (121) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00) % 11.43/3.35 | (122) aNaturalNumber0(xn) % 11.43/3.35 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = sz10 | v2 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ iLess0(v4, all_0_8_8) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v2 & ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = v2 & doDivides0(v5, v2) & aNaturalNumber0(v6) & aNaturalNumber0(v5)) | (v6 = v0 & sdtasdt0(v2, v5) = v0 & aNaturalNumber0(v5)) | (sdtasdt0(v0, v1) = v5 & ~ doDivides0(v2, v5) & ! [v8] : ( ~ (sdtasdt0(v2, v8) = v5) | ~ aNaturalNumber0(v8))))) % 11.43/3.35 | (124) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | ? [v1] : (isPrime0(v1) & doDivides0(v1, v0) & aNaturalNumber0(v1))) % 11.43/3.35 | (125) aNaturalNumber0(all_0_1_1) % 11.43/3.35 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4)) % 11.43/3.35 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5)) % 11.43/3.35 | (128) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) % 11.43/3.35 | (129) ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_5_5) & sdtasdt0(xp, v0) = v1)) % 11.43/3.35 | (130) sdtpldt0(xp, xr) = xn % 11.43/3.35 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 11.43/3.35 | (132) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 11.43/3.35 | % 11.43/3.35 | Instantiating formula (20) with all_0_7_7, all_0_0_0, all_0_3_3, xp and discharging atoms sdtasdt0(xp, all_0_0_0) = all_0_7_7, sdtasdt0(xp, all_0_3_3) = all_0_7_7, aNaturalNumber0(all_0_0_0), aNaturalNumber0(all_0_3_3), aNaturalNumber0(xp), yields: % 11.43/3.35 | (133) all_0_0_0 = all_0_3_3 | xp = sz00 % 11.43/3.35 | % 11.43/3.35 | Instantiating formula (20) with all_0_6_6, all_0_4_4, xm, xp and discharging atoms sdtasdt0(xp, all_0_4_4) = all_0_6_6, sdtasdt0(xp, xm) = all_0_6_6, aNaturalNumber0(all_0_4_4), aNaturalNumber0(xp), aNaturalNumber0(xm), yields: % 11.43/3.35 | (134) all_0_4_4 = xm | xp = sz00 % 11.43/3.35 | % 11.43/3.35 | Instantiating formula (52) with all_0_1_1, xr, xn, xp and discharging atoms sdtmndt0(xn, xp) = xr, sdtpldt0(xp, all_0_1_1) = xn, sdtlseqdt0(xp, xn), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xp), aNaturalNumber0(xn), yields: % 11.43/3.35 | (135) all_0_1_1 = xr % 11.43/3.35 | % 11.43/3.35 | From (135) and (42) follows: % 11.43/3.35 | (130) sdtpldt0(xp, xr) = xn % 11.43/3.35 | % 11.43/3.35 | From (135) and (125) follows: % 11.43/3.35 | (118) aNaturalNumber0(xr) % 11.43/3.35 | % 11.43/3.35 +-Applying beta-rule and splitting (133), into two cases. % 11.43/3.35 |-Branch one: % 11.43/3.35 | (138) xp = sz00 % 11.43/3.36 | % 11.43/3.36 | Equations (138) can reduce 47 to: % 11.43/3.36 | (139) $false % 11.43/3.36 | % 11.43/3.36 |-The branch is then unsatisfiable % 11.43/3.36 |-Branch two: % 11.43/3.36 | (47) ~ (xp = sz00) % 11.43/3.36 | (141) all_0_0_0 = all_0_3_3 % 11.43/3.36 | % 11.43/3.36 +-Applying beta-rule and splitting (134), into two cases. % 11.43/3.36 |-Branch one: % 11.43/3.36 | (138) xp = sz00 % 11.43/3.36 | % 11.43/3.36 | Equations (138) can reduce 47 to: % 11.43/3.36 | (139) $false % 11.43/3.36 | % 11.43/3.36 |-The branch is then unsatisfiable % 11.43/3.36 |-Branch two: % 11.43/3.36 | (47) ~ (xp = sz00) % 11.43/3.36 | (145) all_0_4_4 = xm % 11.43/3.36 | % 11.43/3.36 | From (145) and (101) follows: % 11.43/3.36 | (27) sdtasdt0(xp, xm) = all_0_6_6 % 11.43/3.36 | % 11.43/3.36 | From (145) and (39) follows: % 11.43/3.36 | (114) aNaturalNumber0(xm) % 11.43/3.36 | % 11.43/3.36 | Instantiating formula (70) with xn, xp, xr and discharging atoms sdtpldt0(xp, xr) = xn, aNaturalNumber0(xr), aNaturalNumber0(xp), yields: % 11.43/3.36 | (148) sdtpldt0(xr, xp) = xn % 11.43/3.36 | % 11.43/3.36 | Instantiating formula (112) with all_0_7_7, all_0_5_5, all_0_6_6, xr, xp, xm and discharging atoms sdtasdt0(xr, xm) = all_0_5_5, sdtasdt0(xp, xm) = all_0_6_6, sdtpldt0(all_0_6_6, all_0_5_5) = all_0_7_7, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xm), yields: % 11.43/3.36 | (149) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v0, xm) = all_0_7_7 & sdtasdt0(xm, v0) = v1 & sdtasdt0(xm, xr) = v3 & sdtasdt0(xm, xp) = v2 & sdtpldt0(v2, v3) = v1 & sdtpldt0(xp, xr) = v0) % 11.43/3.36 | % 11.43/3.36 | Instantiating formula (64) with all_0_5_5, xr, xm and discharging atoms sdtasdt0(xr, xm) = all_0_5_5, aNaturalNumber0(xr), aNaturalNumber0(xm), yields: % 11.43/3.36 | (150) sdtasdt0(xm, xr) = all_0_5_5 % 11.43/3.36 | % 11.43/3.36 | Instantiating formula (78) with all_0_5_5, xm, xr and discharging atoms sdtasdt0(xr, xm) = all_0_5_5, aNaturalNumber0(xr), aNaturalNumber0(xm), yields: % 11.43/3.36 | (151) aNaturalNumber0(all_0_5_5) % 11.43/3.36 | % 11.43/3.36 | Instantiating formula (64) with all_0_6_6, xp, xm and discharging atoms sdtasdt0(xp, xm) = all_0_6_6, aNaturalNumber0(xp), aNaturalNumber0(xm), yields: % 11.43/3.36 | (152) sdtasdt0(xm, xp) = all_0_6_6 % 11.43/3.36 | % 11.43/3.36 | Instantiating formula (78) with all_0_6_6, xm, xp and discharging atoms sdtasdt0(xp, xm) = all_0_6_6, aNaturalNumber0(xp), aNaturalNumber0(xm), yields: % 11.43/3.36 | (153) aNaturalNumber0(all_0_6_6) % 11.43/3.36 | % 11.43/3.36 | Instantiating formula (11) with all_0_7_7, xn, all_0_2_2, xr, xm and discharging atoms sdtasdt0(xn, xm) = all_0_7_7, sdtpldt0(xr, all_0_2_2) = xn, aNaturalNumber0(all_0_2_2), aNaturalNumber0(xr), aNaturalNumber0(xm), yields: % 11.43/3.36 | (154) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_2_2, xm) = v4 & sdtasdt0(xr, xm) = v3 & sdtasdt0(xm, all_0_2_2) = v2 & sdtasdt0(xm, xr) = v1 & sdtasdt0(xm, xn) = v0 & sdtpldt0(v3, v4) = all_0_7_7 & sdtpldt0(v1, v2) = v0) % 11.43/3.36 | % 11.43/3.36 | Instantiating formula (11) with all_0_7_7, xn, xr, xp, xm and discharging atoms sdtasdt0(xn, xm) = all_0_7_7, sdtpldt0(xp, xr) = xn, aNaturalNumber0(xr), aNaturalNumber0(xp), aNaturalNumber0(xm), yields: % 11.43/3.36 | (155) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(xr, xm) = v4 & sdtasdt0(xp, xm) = v3 & sdtasdt0(xm, xr) = v2 & sdtasdt0(xm, xp) = v1 & sdtasdt0(xm, xn) = v0 & sdtpldt0(v3, v4) = all_0_7_7 & sdtpldt0(v1, v2) = v0) % 11.43/3.36 | % 11.43/3.36 | Instantiating formula (64) with all_0_7_7, xn, xm and discharging atoms sdtasdt0(xn, xm) = all_0_7_7, aNaturalNumber0(xm), aNaturalNumber0(xn), yields: % 11.43/3.36 | (156) sdtasdt0(xm, xn) = all_0_7_7 % 11.43/3.36 | % 11.43/3.36 | Instantiating formula (66) with xn, xr and discharging atoms sdtlseqdt0(xr, xn), aNaturalNumber0(xr), aNaturalNumber0(xn), yields: % 11.43/3.36 | (157) ? [v0] : (sdtpldt0(xr, v0) = xn & aNaturalNumber0(v0)) % 11.43/3.36 | % 11.43/3.36 | Instantiating (157) with all_23_0_11 yields: % 11.43/3.36 | (158) sdtpldt0(xr, all_23_0_11) = xn & aNaturalNumber0(all_23_0_11) % 11.43/3.36 | % 11.43/3.36 | Applying alpha-rule on (158) yields: % 11.43/3.36 | (159) sdtpldt0(xr, all_23_0_11) = xn % 11.43/3.36 | (160) aNaturalNumber0(all_23_0_11) % 11.43/3.36 | % 11.43/3.36 | Instantiating (149) with all_35_0_17, all_35_1_18, all_35_2_19, all_35_3_20 yields: % 11.43/3.36 | (161) sdtasdt0(all_35_3_20, xm) = all_0_7_7 & sdtasdt0(xm, all_35_3_20) = all_35_2_19 & sdtasdt0(xm, xr) = all_35_0_17 & sdtasdt0(xm, xp) = all_35_1_18 & sdtpldt0(all_35_1_18, all_35_0_17) = all_35_2_19 & sdtpldt0(xp, xr) = all_35_3_20 % 11.43/3.36 | % 11.43/3.36 | Applying alpha-rule on (161) yields: % 11.43/3.36 | (162) sdtasdt0(xm, xp) = all_35_1_18 % 11.43/3.36 | (163) sdtasdt0(xm, xr) = all_35_0_17 % 11.43/3.36 | (164) sdtasdt0(all_35_3_20, xm) = all_0_7_7 % 11.43/3.36 | (165) sdtpldt0(all_35_1_18, all_35_0_17) = all_35_2_19 % 11.43/3.36 | (166) sdtpldt0(xp, xr) = all_35_3_20 % 11.43/3.36 | (167) sdtasdt0(xm, all_35_3_20) = all_35_2_19 % 11.43/3.36 | % 11.43/3.36 | Instantiating (155) with all_49_0_27, all_49_1_28, all_49_2_29, all_49_3_30, all_49_4_31 yields: % 11.43/3.36 | (168) sdtasdt0(xr, xm) = all_49_0_27 & sdtasdt0(xp, xm) = all_49_1_28 & sdtasdt0(xm, xr) = all_49_2_29 & sdtasdt0(xm, xp) = all_49_3_30 & sdtasdt0(xm, xn) = all_49_4_31 & sdtpldt0(all_49_1_28, all_49_0_27) = all_0_7_7 & sdtpldt0(all_49_3_30, all_49_2_29) = all_49_4_31 % 11.43/3.36 | % 11.43/3.36 | Applying alpha-rule on (168) yields: % 11.43/3.36 | (169) sdtasdt0(xm, xp) = all_49_3_30 % 11.43/3.36 | (170) sdtpldt0(all_49_3_30, all_49_2_29) = all_49_4_31 % 11.43/3.36 | (171) sdtasdt0(xm, xr) = all_49_2_29 % 11.43/3.36 | (172) sdtasdt0(xm, xn) = all_49_4_31 % 11.43/3.36 | (173) sdtpldt0(all_49_1_28, all_49_0_27) = all_0_7_7 % 11.43/3.36 | (174) sdtasdt0(xp, xm) = all_49_1_28 % 11.43/3.36 | (175) sdtasdt0(xr, xm) = all_49_0_27 % 11.43/3.36 | % 11.43/3.36 | Instantiating (154) with all_51_0_32, all_51_1_33, all_51_2_34, all_51_3_35, all_51_4_36 yields: % 11.43/3.36 | (176) sdtasdt0(all_0_2_2, xm) = all_51_0_32 & sdtasdt0(xr, xm) = all_51_1_33 & sdtasdt0(xm, all_0_2_2) = all_51_2_34 & sdtasdt0(xm, xr) = all_51_3_35 & sdtasdt0(xm, xn) = all_51_4_36 & sdtpldt0(all_51_1_33, all_51_0_32) = all_0_7_7 & sdtpldt0(all_51_3_35, all_51_2_34) = all_51_4_36 % 11.43/3.36 | % 11.43/3.36 | Applying alpha-rule on (176) yields: % 11.43/3.36 | (177) sdtasdt0(all_0_2_2, xm) = all_51_0_32 % 11.43/3.36 | (178) sdtpldt0(all_51_1_33, all_51_0_32) = all_0_7_7 % 11.43/3.36 | (179) sdtasdt0(xm, xn) = all_51_4_36 % 11.43/3.36 | (180) sdtasdt0(xr, xm) = all_51_1_33 % 11.43/3.36 | (181) sdtpldt0(all_51_3_35, all_51_2_34) = all_51_4_36 % 11.43/3.36 | (182) sdtasdt0(xm, all_0_2_2) = all_51_2_34 % 11.43/3.36 | (183) sdtasdt0(xm, xr) = all_51_3_35 % 11.43/3.36 | % 11.43/3.36 | Instantiating formula (131) with xm, xr, all_49_2_29, all_51_3_35 and discharging atoms sdtasdt0(xm, xr) = all_51_3_35, sdtasdt0(xm, xr) = all_49_2_29, yields: % 11.43/3.36 | (184) all_51_3_35 = all_49_2_29 % 11.43/3.36 | % 11.43/3.36 | Instantiating formula (131) with xm, xr, all_35_0_17, all_51_3_35 and discharging atoms sdtasdt0(xm, xr) = all_51_3_35, sdtasdt0(xm, xr) = all_35_0_17, yields: % 11.43/3.36 | (185) all_51_3_35 = all_35_0_17 % 11.43/3.36 | % 11.43/3.36 | Instantiating formula (131) with xm, xr, all_0_5_5, all_51_3_35 and discharging atoms sdtasdt0(xm, xr) = all_51_3_35, sdtasdt0(xm, xr) = all_0_5_5, yields: % 11.43/3.36 | (186) all_51_3_35 = all_0_5_5 % 11.43/3.36 | % 11.43/3.36 | Instantiating formula (131) with xm, xp, all_35_1_18, all_49_3_30 and discharging atoms sdtasdt0(xm, xp) = all_49_3_30, sdtasdt0(xm, xp) = all_35_1_18, yields: % 11.43/3.36 | (187) all_49_3_30 = all_35_1_18 % 11.43/3.36 | % 11.43/3.36 | Instantiating formula (131) with xm, xp, all_0_6_6, all_49_3_30 and discharging atoms sdtasdt0(xm, xp) = all_49_3_30, sdtasdt0(xm, xp) = all_0_6_6, yields: % 11.43/3.36 | (188) all_49_3_30 = all_0_6_6 % 11.43/3.36 | % 11.43/3.36 | Instantiating formula (131) with xm, xn, all_49_4_31, all_51_4_36 and discharging atoms sdtasdt0(xm, xn) = all_51_4_36, sdtasdt0(xm, xn) = all_49_4_31, yields: % 11.43/3.36 | (189) all_51_4_36 = all_49_4_31 % 11.43/3.36 | % 11.43/3.36 | Instantiating formula (131) with xm, xn, all_0_7_7, all_51_4_36 and discharging atoms sdtasdt0(xm, xn) = all_51_4_36, sdtasdt0(xm, xn) = all_0_7_7, yields: % 11.43/3.36 | (190) all_51_4_36 = all_0_7_7 % 11.43/3.36 | % 11.43/3.36 | Instantiating formula (35) with xn, all_0_2_2, all_23_0_11, xr and discharging atoms sdtpldt0(xr, all_23_0_11) = xn, sdtpldt0(xr, all_0_2_2) = xn, aNaturalNumber0(all_23_0_11), aNaturalNumber0(all_0_2_2), aNaturalNumber0(xr), yields: % 11.43/3.36 | (191) all_23_0_11 = all_0_2_2 % 11.43/3.36 | % 11.43/3.36 | Instantiating formula (35) with xn, all_23_0_11, xp, xr and discharging atoms sdtpldt0(xr, all_23_0_11) = xn, sdtpldt0(xr, xp) = xn, aNaturalNumber0(all_23_0_11), aNaturalNumber0(xr), aNaturalNumber0(xp), yields: % 11.43/3.36 | (192) all_23_0_11 = xp % 11.43/3.36 | % 11.43/3.36 | Combining equations (185,184) yields a new equation: % 11.43/3.36 | (193) all_49_2_29 = all_35_0_17 % 11.43/3.36 | % 11.43/3.36 | Combining equations (186,184) yields a new equation: % 11.43/3.36 | (194) all_49_2_29 = all_0_5_5 % 11.43/3.36 | % 11.43/3.36 | Combining equations (189,190) yields a new equation: % 11.43/3.36 | (195) all_49_4_31 = all_0_7_7 % 11.43/3.36 | % 11.43/3.36 | Simplifying 195 yields: % 11.43/3.36 | (196) all_49_4_31 = all_0_7_7 % 11.43/3.36 | % 11.43/3.36 | Combining equations (193,194) yields a new equation: % 11.43/3.36 | (197) all_35_0_17 = all_0_5_5 % 11.43/3.36 | % 11.43/3.36 | Simplifying 197 yields: % 11.43/3.36 | (198) all_35_0_17 = all_0_5_5 % 11.43/3.36 | % 11.43/3.36 | Combining equations (188,187) yields a new equation: % 11.43/3.36 | (199) all_35_1_18 = all_0_6_6 % 11.43/3.36 | % 11.43/3.36 | Combining equations (191,192) yields a new equation: % 11.43/3.36 | (200) all_0_2_2 = xp % 11.43/3.36 | % 11.43/3.36 | Simplifying 200 yields: % 11.43/3.36 | (201) all_0_2_2 = xp % 11.43/3.36 | % 11.43/3.36 | Combining equations (199,187) yields a new equation: % 11.43/3.36 | (188) all_49_3_30 = all_0_6_6 % 11.43/3.36 | % 11.43/3.36 | From (188)(194)(196) and (170) follows: % 11.43/3.36 | (75) sdtpldt0(all_0_6_6, all_0_5_5) = all_0_7_7 % 11.43/3.36 | % 11.43/3.36 | From (199)(198) and (165) follows: % 11.43/3.36 | (204) sdtpldt0(all_0_6_6, all_0_5_5) = all_35_2_19 % 11.43/3.36 | % 11.43/3.36 | From (201) and (10) follows: % 11.43/3.36 | (34) aNaturalNumber0(xp) % 11.43/3.36 | % 11.43/3.37 | Instantiating formula (87) with all_0_6_6, all_0_5_5, all_35_2_19, all_0_7_7 and discharging atoms sdtpldt0(all_0_6_6, all_0_5_5) = all_35_2_19, sdtpldt0(all_0_6_6, all_0_5_5) = all_0_7_7, yields: % 11.43/3.37 | (206) all_35_2_19 = all_0_7_7 % 11.43/3.37 | % 11.43/3.37 | From (206) and (204) follows: % 11.43/3.37 | (75) sdtpldt0(all_0_6_6, all_0_5_5) = all_0_7_7 % 11.43/3.37 | % 11.43/3.37 | Instantiating formula (24) with all_0_7_7, all_0_5_5, all_0_6_6, xp and discharging atoms sdtpldt0(all_0_6_6, all_0_5_5) = all_0_7_7, doDivides0(xp, all_0_6_6), doDivides0(xp, all_0_7_7), aNaturalNumber0(all_0_5_5), aNaturalNumber0(all_0_6_6), aNaturalNumber0(xp), ~ doDivides0(xp, all_0_5_5), yields: % 11.43/3.37 | (208) $false % 11.43/3.37 | % 11.43/3.37 |-The branch is then unsatisfiable % 11.43/3.37 % SZS output end Proof for theBenchmark % 11.43/3.37 % 11.43/3.37 2728ms %------------------------------------------------------------------------------