%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : NUM473+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n020.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Mon Jul 18 08:44:51 EDT 2022 % Result : Theorem 21.86s 6.23s % Output : Proof 27.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM473+1 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n020.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 : Tue Jul 5 02:36:14 EDT 2022 % 0.13/0.34 % CPUTime : % 0.61/0.61 ____ _ % 0.61/0.61 ___ / __ \_____(_)___ ________ __________ % 0.61/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.61/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.61/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.61/0.61 % 0.61/0.61 A Theorem Prover for First-Order Logic % 0.61/0.61 (ePrincess v.1.0) % 0.61/0.61 % 0.61/0.61 (c) Philipp Rümmer, 2009-2015 % 0.61/0.61 (c) Peter Backeman, 2014-2015 % 0.61/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.61/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.61/0.61 Bug reports to peter@backeman.se % 0.61/0.61 % 0.61/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.61/0.61 % 0.61/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.70/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.82/1.01 Prover 0: Preprocessing ... % 3.73/1.54 Prover 0: Constructing countermodel ... % 20.57/5.95 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 20.81/6.00 Prover 1: Preprocessing ... % 21.32/6.11 Prover 1: Constructing countermodel ... % 21.86/6.23 Prover 1: proved (283ms) % 21.86/6.23 Prover 0: stopped % 21.86/6.23 % 21.86/6.23 No countermodel exists, formula is valid % 21.86/6.23 % SZS status Theorem for theBenchmark % 21.86/6.23 % 21.86/6.23 Generating proof ... found it (size 286) % 26.57/7.33 % 26.57/7.33 % SZS output start Proof for theBenchmark % 26.57/7.33 Assumed formulas after preprocessing and simplification: % 26.57/7.33 | (0) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (xl = sz00) & ~ (sz10 = sz00) & sdtsldt0(v0, xl) = xq & sdtsldt0(xm, xl) = xp & doDivides0(xl, v0) = 0 & doDivides0(xl, xm) = 0 & sdtlseqdt0(xp, xq) = v1 & sdtlseqdt0(xm, v0) = 0 & sdtpldt0(xm, xn) = v0 & aNaturalNumber0(xn) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xl) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v4 = v3 | v2 = sz00 | ~ (sdtlseqdt0(v5, v6) = v7) | ~ (sdtasdt0(v2, v4) = v6) | ~ (sdtasdt0(v2, v3) = v5) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtlseqdt0(v12, v13) = v14 & sdtlseqdt0(v3, v4) = v11 & sdtasdt0(v4, v2) = v13 & sdtasdt0(v3, v2) = v12 & aNaturalNumber0(v4) = v10 & aNaturalNumber0(v3) = v9 & aNaturalNumber0(v2) = v8 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | (v14 = 0 & v7 = 0 & ~ (v13 = v12) & ~ (v6 = v5))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v3 = v2 | ~ (sdtlseqdt0(v5, v6) = v7) | ~ (sdtlseqdt0(v2, v3) = 0) | ~ (sdtpldt0(v3, v4) = v6) | ~ (sdtpldt0(v2, v4) = v5) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((sdtlseqdt0(v9, v10) = v11 & sdtpldt0(v4, v3) = v10 & sdtpldt0(v4, v2) = v9 & aNaturalNumber0(v4) = v8 & ( ~ (v8 = 0) | (v11 = 0 & v7 = 0 & ~ (v10 = v9) & ~ (v6 = v5)))) | (aNaturalNumber0(v3) = v9 & aNaturalNumber0(v2) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v2, v4) = v6) | ~ (sdtasdt0(v2, v3) = v5) | ~ (sdtpldt0(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (sdtasdt0(v11, v2) = v13 & sdtasdt0(v4, v2) = v15 & sdtasdt0(v3, v2) = v14 & sdtasdt0(v2, v11) = v12 & sdtpldt0(v14, v15) = v16 & sdtpldt0(v3, v4) = v11 & aNaturalNumber0(v4) = v10 & aNaturalNumber0(v3) = v9 & aNaturalNumber0(v2) = v8 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | (v16 = v13 & v12 = v7)))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (doDivides0(v2, v5) = v6) | ~ (sdtpldt0(v3, v4) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (doDivides0(v2, v4) = v11 & doDivides0(v2, v3) = v10 & aNaturalNumber0(v4) = v9 & aNaturalNumber0(v3) = v8 & aNaturalNumber0(v2) = v7 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | v2 = sz00 | ~ (sdtasdt0(v2, v4) = v6) | ~ (sdtasdt0(v2, v3) = v5) | ~ (aNaturalNumber0(v2) = 0) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (sdtasdt0(v4, v2) = v10 & sdtasdt0(v3, v2) = v9 & aNaturalNumber0(v4) = v8 & aNaturalNumber0(v3) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | ( ~ (v10 = v9) & ~ (v6 = v5))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (sdtpldt0(v2, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (sdtpldt0(v4, v2) = v11 & sdtpldt0(v3, v2) = v10 & aNaturalNumber0(v4) = v9 & aNaturalNumber0(v3) = v8 & aNaturalNumber0(v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ( ~ (v11 = v10) & ~ (v6 = v5))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, v4) = v6) | ~ (sdtasdt0(v2, v3) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (sdtasdt0(v3, v4) = v10 & sdtasdt0(v2, v10) = v11 & aNaturalNumber0(v4) = v9 & aNaturalNumber0(v3) = v8 & aNaturalNumber0(v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v11 = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (sdtpldt0(v3, v4) = v10 & sdtpldt0(v2, v10) = v11 & aNaturalNumber0(v4) = v9 & aNaturalNumber0(v3) = v8 & aNaturalNumber0(v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v11 = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | v2 = sz00 | ~ (sdtsldt0(v3, v2) = v4) | ~ (sdtasdt0(v2, v5) = v3) | ? [v6] : ? [v7] : ? [v8] : (( ~ (v6 = 0) & aNaturalNumber0(v5) = v6) | (doDivides0(v2, v3) = v8 & aNaturalNumber0(v3) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtmndt0(v3, v2) = v4) | ~ (sdtpldt0(v2, v5) = v3) | ? [v6] : ? [v7] : ? [v8] : (( ~ (v6 = 0) & aNaturalNumber0(v5) = v6) | (sdtlseqdt0(v2, v3) = v8 & aNaturalNumber0(v3) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | v2 = sz00 | ~ (sdtsldt0(v3, v2) = v4) | ~ (sdtasdt0(v2, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : (doDivides0(v2, v3) = v8 & aNaturalNumber0(v3) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (sdtmndt0(v3, v2) = v4) | ~ (sdtpldt0(v2, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : (sdtlseqdt0(v2, v3) = v8 & aNaturalNumber0(v3) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v2 = sz00 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtasdt0(v3, v2) = v4) | ? [v6] : ? [v7] : (aNaturalNumber0(v3) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (doDivides0(v2, v4) = v5) | ~ (doDivides0(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (doDivides0(v3, v4) = v9 & aNaturalNumber0(v4) = v8 & aNaturalNumber0(v3) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (sdtlseqdt0(v2, v4) = v5) | ~ (sdtlseqdt0(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtlseqdt0(v3, v4) = v9 & aNaturalNumber0(v4) = v8 & aNaturalNumber0(v3) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (doDivides0(v2, v3) = v4) | ~ (sdtasdt0(v2, v5) = v3) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & aNaturalNumber0(v5) = v6) | (aNaturalNumber0(v3) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (sdtlseqdt0(v2, v3) = v4) | ~ (sdtpldt0(v2, v5) = v3) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & aNaturalNumber0(v5) = v6) | (aNaturalNumber0(v3) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtsldt0(v5, v4) = v3) | ~ (sdtsldt0(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (doDivides0(v5, v4) = v3) | ~ (doDivides0(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (iLess0(v5, v4) = v3) | ~ (iLess0(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtmndt0(v5, v4) = v3) | ~ (sdtmndt0(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtlseqdt0(v5, v4) = v3) | ~ (sdtlseqdt0(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtasdt0(v5, v4) = v3) | ~ (sdtasdt0(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtpldt0(v5, v4) = v3) | ~ (sdtpldt0(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = sz00 | ~ (sdtsldt0(v3, v2) = v4) | ~ (sdtasdt0(v2, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ((v6 = 0 & aNaturalNumber0(v4) = 0) | (doDivides0(v2, v3) = v8 & aNaturalNumber0(v3) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtmndt0(v3, v2) = v4) | ~ (sdtpldt0(v2, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ((v6 = 0 & aNaturalNumber0(v4) = 0) | (sdtlseqdt0(v2, v3) = v8 & aNaturalNumber0(v3) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = v2 | ~ (iLess0(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (sdtlseqdt0(v2, v3) = v7 & aNaturalNumber0(v3) = v6 & aNaturalNumber0(v2) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (sdtlseqdt0(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (sdtlseqdt0(v3, v2) = v7 & aNaturalNumber0(v3) = v6 & aNaturalNumber0(v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & ~ (v3 = v2))))) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (aNaturalNumber0(v4) = v3) | ~ (aNaturalNumber0(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (sdtasdt0(v3, v2) = v7 & aNaturalNumber0(v3) = v6 & aNaturalNumber0(v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = v4))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (aNaturalNumber0(v4) = v7 & aNaturalNumber0(v3) = v6 & aNaturalNumber0(v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (sdtpldt0(v3, v2) = v7 & aNaturalNumber0(v3) = v6 & aNaturalNumber0(v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = v4))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (aNaturalNumber0(v4) = v7 & aNaturalNumber0(v3) = v6 & aNaturalNumber0(v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0))) & ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtlseqdt0(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v3, v2) = v6 & aNaturalNumber0(v3) = v5 & aNaturalNumber0(v2) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v2] : ! [v3] : (v3 = sz00 | v2 = sz00 | ~ (sdtasdt0(v2, v3) = sz00) | ? [v4] : ? [v5] : (aNaturalNumber0(v3) = v5 & aNaturalNumber0(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v2] : ! [v3] : (v3 = sz00 | ~ (sdtpldt0(v2, v3) = sz00) | ? [v4] : ? [v5] : (aNaturalNumber0(v3) = v5 & aNaturalNumber0(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v2] : ! [v3] : (v3 = 0 | v2 = sz10 | v2 = sz00 | ~ (sdtlseqdt0(sz10, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4)) & ! [v2] : ! [v3] : (v3 = 0 | ~ (sdtlseqdt0(v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4)) & ! [v2] : ! [v3] : (v2 = sz00 | ~ (sdtpldt0(v2, v3) = sz00) | ? [v4] : ? [v5] : (aNaturalNumber0(v3) = v5 & aNaturalNumber0(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v2] : ! [v3] : ( ~ (doDivides0(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = v3 & v5 = 0 & sdtasdt0(v2, v4) = v3 & aNaturalNumber0(v4) = 0) | (aNaturalNumber0(v3) = v5 & aNaturalNumber0(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v2] : ! [v3] : ( ~ (sdtlseqdt0(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = v3 & v5 = 0 & sdtpldt0(v2, v4) = v3 & aNaturalNumber0(v4) = 0) | (aNaturalNumber0(v3) = v5 & aNaturalNumber0(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v2] : ! [v3] : ( ~ (sdtasdt0(sz10, v2) = v3) | ? [v4] : ? [v5] : (sdtasdt0(v2, sz10) = v5 & aNaturalNumber0(v2) = v4 & ( ~ (v4 = 0) | (v5 = v2 & v3 = v2)))) & ! [v2] : ! [v3] : ( ~ (sdtasdt0(sz00, v2) = v3) | ? [v4] : ? [v5] : (sdtasdt0(v2, sz00) = v5 & aNaturalNumber0(v2) = v4 & ( ~ (v4 = 0) | (v5 = sz00 & v3 = sz00)))) & ! [v2] : ! [v3] : ( ~ (sdtpldt0(sz00, v2) = v3) | ? [v4] : ? [v5] : (sdtpldt0(v2, sz00) = v5 & aNaturalNumber0(v2) = v4 & ( ~ (v4 = 0) | (v5 = v2 & v3 = v2))))) % 26.57/7.39 | Instantiating (0) with all_0_0_0, all_0_1_1 yields: % 26.57/7.39 | (1) ~ (all_0_0_0 = 0) & ~ (xl = sz00) & ~ (sz10 = sz00) & sdtsldt0(all_0_1_1, xl) = xq & sdtsldt0(xm, xl) = xp & doDivides0(xl, all_0_1_1) = 0 & doDivides0(xl, xm) = 0 & sdtlseqdt0(xp, xq) = all_0_0_0 & sdtlseqdt0(xm, all_0_1_1) = 0 & sdtpldt0(xm, xn) = all_0_1_1 & aNaturalNumber0(xn) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xl) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | v0 = sz00 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (sdtlseqdt0(v10, v11) = v12 & sdtlseqdt0(v1, v2) = v9 & sdtasdt0(v2, v0) = v11 & sdtasdt0(v1, v0) = v10 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v12 = 0 & v5 = 0 & ~ (v11 = v10) & ~ (v4 = v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (sdtlseqdt0(v3, v4) = v5) | ~ (sdtlseqdt0(v0, v1) = 0) | ~ (sdtpldt0(v1, v2) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((sdtlseqdt0(v7, v8) = v9 & sdtpldt0(v2, v1) = v8 & sdtpldt0(v2, v0) = v7 & aNaturalNumber0(v2) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0 & ~ (v8 = v7) & ~ (v4 = v3)))) | (aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v9, v0) = v11 & sdtasdt0(v2, v0) = v13 & sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v9) = v10 & sdtpldt0(v12, v13) = v14 & sdtpldt0(v1, v2) = v9 & aNaturalNumber0(v2) = v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (v14 = v11 & v10 = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (doDivides0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (doDivides0(v0, v2) = v9 & doDivides0(v0, v1) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v8 = v7) & ~ (v4 = v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtpldt0(v2, v0) = v9 & sdtpldt0(v1, v0) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v9 = v8) & ~ (v4 = v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtpldt0(v1, v2) = v8 & sdtpldt0(v0, v8) = v9 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v0 = sz00 | ~ (sdtlseqdt0(v1, v2) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ? [v4] : ? [v5] : (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (doDivides0(v0, v2) = v3) | ~ (doDivides0(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (doDivides0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (sdtlseqdt0(v0, v2) = v3) | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (sdtlseqdt0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (doDivides0(v0, v1) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (doDivides0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | (sdtlseqdt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (iLess0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtlseqdt0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtlseqdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v5 = 0 & ~ (v1 = v0))))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (sdtlseqdt0(v1, v0) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)) & ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (doDivides0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ! [v0] : ! [v1] : ( ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00)))) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) % 27.04/7.40 | % 27.04/7.40 | Applying alpha-rule on (1) yields: % 27.04/7.40 | (2) sdtlseqdt0(xm, all_0_1_1) = 0 % 27.04/7.40 | (3) ! [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))) % 27.04/7.40 | (4) ! [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)))) % 27.04/7.40 | (5) ! [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)))) % 27.04/7.40 | (6) aNaturalNumber0(sz00) = 0 % 27.04/7.40 | (7) ! [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))))) % 27.04/7.40 | (8) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 27.04/7.40 | (9) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 27.04/7.40 | (10) ~ (xl = sz00) % 27.04/7.40 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) % 27.04/7.41 | (12) ! [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))) % 27.04/7.41 | (13) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : ? [v3] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 27.04/7.41 | (14) ! [v0] : ! [v1] : (v1 = 0 | ~ (sdtlseqdt0(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)) % 27.04/7.41 | (15) doDivides0(xl, all_0_1_1) = 0 % 27.04/7.41 | (16) ! [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))))) % 27.04/7.41 | (17) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00)))) % 27.04/7.41 | (18) aNaturalNumber0(xl) = 0 % 27.04/7.41 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) % 27.04/7.41 | (20) ! [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))))) % 27.04/7.41 | (21) ~ (all_0_0_0 = 0) % 27.04/7.41 | (22) ! [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))))) % 27.04/7.41 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) % 27.04/7.41 | (24) ! [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))) % 27.04/7.41 | (25) ! [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))))) % 27.04/7.41 | (26) aNaturalNumber0(sz10) = 0 % 27.04/7.41 | (27) ! [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))))) % 27.04/7.41 | (28) sdtsldt0(xm, xl) = xp % 27.04/7.41 | (29) ! [v0] : ! [v1] : (v1 = 0 | v0 = sz10 | v0 = sz00 | ~ (sdtlseqdt0(sz10, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)) % 27.04/7.41 | (30) ! [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)))) % 27.04/7.41 | (31) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ? [v3] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) % 27.04/7.41 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 27.04/7.41 | (33) ! [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)))) % 27.04/7.41 | (34) aNaturalNumber0(xm) = 0 % 27.04/7.41 | (35) ! [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))))) % 27.04/7.41 | (36) ! [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)))) % 27.04/7.41 | (37) doDivides0(xl, xm) = 0 % 27.04/7.41 | (38) ! [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))))) % 27.04/7.42 | (39) sdtlseqdt0(xp, xq) = all_0_0_0 % 27.04/7.42 | (40) ! [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)))) % 27.04/7.42 | (41) ! [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))))) % 27.04/7.42 | (42) ! [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))))) % 27.04/7.42 | (43) ! [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))))) % 27.04/7.42 | (44) ! [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)))) % 27.04/7.42 | (45) ! [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)))) % 27.04/7.42 | (46) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ? [v3] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) % 27.04/7.42 | (47) ! [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))))) % 27.04/7.42 | (48) ! [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))) % 27.04/7.42 | (49) ~ (sz10 = sz00) % 27.04/7.42 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 27.04/7.42 | (51) aNaturalNumber0(xn) = 0 % 27.04/7.42 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) % 27.04/7.42 | (53) ! [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)))) % 27.04/7.42 | (54) sdtpldt0(xm, xn) = all_0_1_1 % 27.04/7.42 | (55) sdtsldt0(all_0_1_1, xl) = xq % 27.04/7.42 | (56) ! [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))) % 27.04/7.42 | (57) ! [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))) % 27.04/7.42 | (58) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) % 27.04/7.42 | (59) ! [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))))) % 27.04/7.42 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) % 27.04/7.42 | % 27.04/7.42 | Instantiating formula (52) with xm, xl, xp, xq and discharging atoms sdtsldt0(xm, xl) = xp, yields: % 27.04/7.43 | (61) xq = xp | ~ (sdtsldt0(xm, xl) = xq) % 27.04/7.43 | % 27.04/7.43 | Instantiating formula (42) with all_0_1_1, xl and discharging atoms doDivides0(xl, all_0_1_1) = 0, yields: % 27.04/7.43 | (62) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_1_1 & v1 = 0 & sdtasdt0(xl, v0) = all_0_1_1 & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 27.04/7.43 | % 27.04/7.43 | Instantiating formula (42) with xm, xl and discharging atoms doDivides0(xl, xm) = 0, yields: % 27.04/7.43 | (63) ? [v0] : ? [v1] : ? [v2] : ((v2 = xm & v1 = 0 & sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 27.04/7.43 | % 27.04/7.43 | Instantiating formula (47) with all_0_0_0, xq, xp and discharging atoms sdtlseqdt0(xp, xq) = all_0_0_0, yields: % 27.04/7.43 | (64) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xq, xp) = v2 & aNaturalNumber0(xq) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xq = xp)))) % 27.04/7.43 | % 27.04/7.43 | Instantiating formula (30) with all_0_1_1, xm and discharging atoms sdtlseqdt0(xm, all_0_1_1) = 0, yields: % 27.04/7.43 | (65) all_0_1_1 = xm | ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_0_1_1, xm) = v2 & aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 27.04/7.43 | % 27.04/7.43 | Instantiating formula (38) with all_0_1_1, xm and discharging atoms sdtlseqdt0(xm, all_0_1_1) = 0, yields: % 27.04/7.43 | (66) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_1_1 & v1 = 0 & sdtpldt0(xm, v0) = all_0_1_1 & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 27.04/7.43 | % 27.04/7.43 | Instantiating formula (3) with all_0_1_1, xn, xm and discharging atoms sdtpldt0(xm, xn) = all_0_1_1, yields: % 27.04/7.43 | (67) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(xn, xm) = v2 & aNaturalNumber0(xn) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_1_1)) % 27.04/7.43 | % 27.04/7.43 | Instantiating formula (48) with all_0_1_1, xn, xm and discharging atoms sdtpldt0(xm, xn) = all_0_1_1, yields: % 27.04/7.43 | (68) ? [v0] : ? [v1] : ? [v2] : (aNaturalNumber0(all_0_1_1) = v2 & aNaturalNumber0(xn) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 27.04/7.43 | % 27.04/7.43 | Instantiating (68) with all_8_0_2, all_8_1_3, all_8_2_4 yields: % 27.04/7.43 | (69) aNaturalNumber0(all_0_1_1) = all_8_0_2 & aNaturalNumber0(xn) = all_8_1_3 & aNaturalNumber0(xm) = all_8_2_4 & ( ~ (all_8_1_3 = 0) | ~ (all_8_2_4 = 0) | all_8_0_2 = 0) % 27.04/7.43 | % 27.04/7.43 | Applying alpha-rule on (69) yields: % 27.04/7.43 | (70) aNaturalNumber0(all_0_1_1) = all_8_0_2 % 27.04/7.43 | (71) aNaturalNumber0(xn) = all_8_1_3 % 27.04/7.43 | (72) aNaturalNumber0(xm) = all_8_2_4 % 27.04/7.43 | (73) ~ (all_8_1_3 = 0) | ~ (all_8_2_4 = 0) | all_8_0_2 = 0 % 27.04/7.43 | % 27.04/7.43 | Instantiating (67) with all_10_0_5, all_10_1_6, all_10_2_7 yields: % 27.04/7.43 | (74) sdtpldt0(xn, xm) = all_10_0_5 & aNaturalNumber0(xn) = all_10_1_6 & aNaturalNumber0(xm) = all_10_2_7 & ( ~ (all_10_1_6 = 0) | ~ (all_10_2_7 = 0) | all_10_0_5 = all_0_1_1) % 27.04/7.43 | % 27.04/7.43 | Applying alpha-rule on (74) yields: % 27.04/7.43 | (75) sdtpldt0(xn, xm) = all_10_0_5 % 27.04/7.43 | (76) aNaturalNumber0(xn) = all_10_1_6 % 27.04/7.43 | (77) aNaturalNumber0(xm) = all_10_2_7 % 27.04/7.43 | (78) ~ (all_10_1_6 = 0) | ~ (all_10_2_7 = 0) | all_10_0_5 = all_0_1_1 % 27.04/7.43 | % 27.04/7.43 | Instantiating (63) with all_12_0_8, all_12_1_9, all_12_2_10 yields: % 27.04/7.43 | (79) (all_12_0_8 = xm & all_12_1_9 = 0 & sdtasdt0(xl, all_12_2_10) = xm & aNaturalNumber0(all_12_2_10) = 0) | (aNaturalNumber0(xm) = all_12_1_9 & aNaturalNumber0(xl) = all_12_2_10 & ( ~ (all_12_1_9 = 0) | ~ (all_12_2_10 = 0))) % 27.04/7.43 | % 27.04/7.43 | Instantiating (62) with all_13_0_11, all_13_1_12, all_13_2_13 yields: % 27.04/7.43 | (80) (all_13_0_11 = all_0_1_1 & all_13_1_12 = 0 & sdtasdt0(xl, all_13_2_13) = all_0_1_1 & aNaturalNumber0(all_13_2_13) = 0) | (aNaturalNumber0(all_0_1_1) = all_13_1_12 & aNaturalNumber0(xl) = all_13_2_13 & ( ~ (all_13_1_12 = 0) | ~ (all_13_2_13 = 0))) % 27.04/7.43 | % 27.04/7.43 | Instantiating (66) with all_14_0_14, all_14_1_15, all_14_2_16 yields: % 27.04/7.43 | (81) (all_14_0_14 = all_0_1_1 & all_14_1_15 = 0 & sdtpldt0(xm, all_14_2_16) = all_0_1_1 & aNaturalNumber0(all_14_2_16) = 0) | (aNaturalNumber0(all_0_1_1) = all_14_1_15 & aNaturalNumber0(xm) = all_14_2_16 & ( ~ (all_14_1_15 = 0) | ~ (all_14_2_16 = 0))) % 27.04/7.43 | % 27.04/7.43 +-Applying beta-rule and splitting (64), into two cases. % 27.04/7.43 |-Branch one: % 27.04/7.43 | (82) all_0_0_0 = 0 % 27.04/7.43 | % 27.04/7.43 | Equations (82) can reduce 21 to: % 27.04/7.43 | (83) $false % 27.04/7.43 | % 27.04/7.43 |-The branch is then unsatisfiable % 27.04/7.43 |-Branch two: % 27.04/7.43 | (21) ~ (all_0_0_0 = 0) % 27.04/7.43 | (85) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(xq, xp) = v2 & aNaturalNumber0(xq) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xq = xp)))) % 27.04/7.43 | % 27.04/7.43 | Instantiating (85) with all_19_0_17, all_19_1_18, all_19_2_19 yields: % 27.04/7.43 | (86) sdtlseqdt0(xq, xp) = all_19_0_17 & aNaturalNumber0(xq) = all_19_1_18 & aNaturalNumber0(xp) = all_19_2_19 & ( ~ (all_19_1_18 = 0) | ~ (all_19_2_19 = 0) | (all_19_0_17 = 0 & ~ (xq = xp))) % 27.04/7.43 | % 27.04/7.43 | Applying alpha-rule on (86) yields: % 27.04/7.43 | (87) sdtlseqdt0(xq, xp) = all_19_0_17 % 27.04/7.43 | (88) aNaturalNumber0(xq) = all_19_1_18 % 27.04/7.43 | (89) aNaturalNumber0(xp) = all_19_2_19 % 27.04/7.43 | (90) ~ (all_19_1_18 = 0) | ~ (all_19_2_19 = 0) | (all_19_0_17 = 0 & ~ (xq = xp)) % 27.04/7.43 | % 27.04/7.43 | Instantiating formula (58) with xq, all_19_1_18, all_8_0_2 and discharging atoms aNaturalNumber0(xq) = all_19_1_18, yields: % 27.04/7.43 | (91) all_19_1_18 = all_8_0_2 | ~ (aNaturalNumber0(xq) = all_8_0_2) % 27.04/7.44 | % 27.04/7.44 | Instantiating formula (58) with xn, all_10_1_6, 0 and discharging atoms aNaturalNumber0(xn) = all_10_1_6, aNaturalNumber0(xn) = 0, yields: % 27.04/7.44 | (92) all_10_1_6 = 0 % 27.04/7.44 | % 27.04/7.44 | Instantiating formula (58) with xn, all_8_1_3, all_10_1_6 and discharging atoms aNaturalNumber0(xn) = all_10_1_6, aNaturalNumber0(xn) = all_8_1_3, yields: % 27.04/7.44 | (93) all_10_1_6 = all_8_1_3 % 27.04/7.44 | % 27.04/7.44 | Instantiating formula (58) with xm, all_10_2_7, 0 and discharging atoms aNaturalNumber0(xm) = all_10_2_7, aNaturalNumber0(xm) = 0, yields: % 27.04/7.44 | (94) all_10_2_7 = 0 % 27.04/7.44 | % 27.04/7.44 | Instantiating formula (58) with xm, all_8_2_4, all_10_2_7 and discharging atoms aNaturalNumber0(xm) = all_10_2_7, aNaturalNumber0(xm) = all_8_2_4, yields: % 27.04/7.44 | (95) all_10_2_7 = all_8_2_4 % 27.04/7.44 | % 27.04/7.44 | Combining equations (92,93) yields a new equation: % 27.04/7.44 | (96) all_8_1_3 = 0 % 27.04/7.44 | % 27.04/7.44 | Combining equations (94,95) yields a new equation: % 27.04/7.44 | (97) all_8_2_4 = 0 % 27.04/7.44 | % 27.04/7.44 | From (97) and (72) follows: % 27.04/7.44 | (34) aNaturalNumber0(xm) = 0 % 27.04/7.44 | % 27.04/7.44 +-Applying beta-rule and splitting (79), into two cases. % 27.04/7.44 |-Branch one: % 27.04/7.44 | (99) all_12_0_8 = xm & all_12_1_9 = 0 & sdtasdt0(xl, all_12_2_10) = xm & aNaturalNumber0(all_12_2_10) = 0 % 27.04/7.44 | % 27.04/7.44 | Applying alpha-rule on (99) yields: % 27.04/7.44 | (100) all_12_0_8 = xm % 27.04/7.44 | (101) all_12_1_9 = 0 % 27.04/7.44 | (102) sdtasdt0(xl, all_12_2_10) = xm % 27.04/7.44 | (103) aNaturalNumber0(all_12_2_10) = 0 % 27.04/7.44 | % 27.04/7.44 +-Applying beta-rule and splitting (73), into two cases. % 27.04/7.44 |-Branch one: % 27.04/7.44 | (104) ~ (all_8_1_3 = 0) % 27.04/7.44 | % 27.04/7.44 | Equations (96) can reduce 104 to: % 27.04/7.44 | (83) $false % 27.04/7.44 | % 27.04/7.44 |-The branch is then unsatisfiable % 27.04/7.44 |-Branch two: % 27.04/7.44 | (96) all_8_1_3 = 0 % 27.04/7.44 | (107) ~ (all_8_2_4 = 0) | all_8_0_2 = 0 % 27.04/7.44 | % 27.04/7.44 +-Applying beta-rule and splitting (107), into two cases. % 27.04/7.44 |-Branch one: % 27.04/7.44 | (108) ~ (all_8_2_4 = 0) % 27.04/7.44 | % 27.04/7.44 | Equations (97) can reduce 108 to: % 27.04/7.44 | (83) $false % 27.04/7.44 | % 27.04/7.44 |-The branch is then unsatisfiable % 27.04/7.44 |-Branch two: % 27.04/7.44 | (97) all_8_2_4 = 0 % 27.04/7.44 | (111) all_8_0_2 = 0 % 27.04/7.44 | % 27.04/7.44 | From (111) and (70) follows: % 27.04/7.44 | (112) aNaturalNumber0(all_0_1_1) = 0 % 27.04/7.44 | % 27.04/7.44 +-Applying beta-rule and splitting (80), into two cases. % 27.04/7.44 |-Branch one: % 27.04/7.44 | (113) all_13_0_11 = all_0_1_1 & all_13_1_12 = 0 & sdtasdt0(xl, all_13_2_13) = all_0_1_1 & aNaturalNumber0(all_13_2_13) = 0 % 27.04/7.44 | % 27.04/7.44 | Applying alpha-rule on (113) yields: % 27.04/7.44 | (114) all_13_0_11 = all_0_1_1 % 27.04/7.44 | (115) all_13_1_12 = 0 % 27.04/7.44 | (116) sdtasdt0(xl, all_13_2_13) = all_0_1_1 % 27.04/7.44 | (117) aNaturalNumber0(all_13_2_13) = 0 % 27.04/7.44 | % 27.04/7.44 +-Applying beta-rule and splitting (81), into two cases. % 27.04/7.44 |-Branch one: % 27.04/7.44 | (118) all_14_0_14 = all_0_1_1 & all_14_1_15 = 0 & sdtpldt0(xm, all_14_2_16) = all_0_1_1 & aNaturalNumber0(all_14_2_16) = 0 % 27.04/7.44 | % 27.04/7.44 | Applying alpha-rule on (118) yields: % 27.04/7.44 | (119) all_14_0_14 = all_0_1_1 % 27.04/7.44 | (120) all_14_1_15 = 0 % 27.04/7.44 | (121) sdtpldt0(xm, all_14_2_16) = all_0_1_1 % 27.04/7.44 | (122) aNaturalNumber0(all_14_2_16) = 0 % 27.04/7.44 | % 27.04/7.44 | Instantiating formula (38) with xp, xq yields: % 27.04/7.44 | (123) ~ (sdtlseqdt0(xq, xp) = 0) | ? [v0] : ? [v1] : ? [v2] : ((v2 = xp & v1 = 0 & sdtpldt0(xq, v0) = xp & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xq) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 27.04/7.44 | % 27.04/7.44 | Instantiating formula (43) with all_13_2_13, xq, all_0_1_1, xl and discharging atoms sdtsldt0(all_0_1_1, xl) = xq, sdtasdt0(xl, all_13_2_13) = all_0_1_1, yields: % 27.04/7.44 | (124) all_13_2_13 = xq | xl = sz00 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_13_2_13) = v0) | (doDivides0(xl, all_0_1_1) = v2 & aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))) % 27.04/7.44 | % 27.04/7.44 | Instantiating formula (43) with all_13_2_13, xp, xm, xl and discharging atoms sdtsldt0(xm, xl) = xp, yields: % 27.04/7.44 | (125) all_13_2_13 = xp | xl = sz00 | ~ (sdtasdt0(xl, all_13_2_13) = xm) | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_13_2_13) = v0) | (doDivides0(xl, xm) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))) % 27.04/7.44 | % 27.04/7.44 | Instantiating formula (56) with all_0_1_1, all_13_2_13, xl and discharging atoms sdtasdt0(xl, all_13_2_13) = all_0_1_1, yields: % 27.04/7.44 | (126) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_13_2_13, xl) = v2 & aNaturalNumber0(all_13_2_13) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_1_1)) % 27.04/7.44 | % 27.04/7.44 | Instantiating formula (27) with xm, all_0_1_1, all_12_2_10, all_13_2_13, xl and discharging atoms sdtasdt0(xl, all_13_2_13) = all_0_1_1, sdtasdt0(xl, all_12_2_10) = xm, aNaturalNumber0(xl) = 0, yields: % 27.04/7.44 | (127) all_13_2_13 = all_12_2_10 | xl = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_13_2_13, xl) = v2 & sdtasdt0(all_12_2_10, xl) = v3 & aNaturalNumber0(all_13_2_13) = v0 & aNaturalNumber0(all_12_2_10) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = v2) & ~ (all_0_1_1 = xm)))) % 27.04/7.44 | % 27.04/7.44 | Instantiating formula (27) with all_0_1_1, xm, all_13_2_13, all_12_2_10, xl and discharging atoms sdtasdt0(xl, all_13_2_13) = all_0_1_1, sdtasdt0(xl, all_12_2_10) = xm, aNaturalNumber0(xl) = 0, yields: % 27.04/7.44 | (128) all_13_2_13 = all_12_2_10 | xl = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_13_2_13, xl) = v3 & sdtasdt0(all_12_2_10, xl) = v2 & aNaturalNumber0(all_13_2_13) = v1 & aNaturalNumber0(all_12_2_10) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = v2) & ~ (all_0_1_1 = xm)))) % 27.04/7.44 | % 27.04/7.44 | Instantiating formula (40) with xm, xq, all_0_1_1, xl and discharging atoms sdtsldt0(all_0_1_1, xl) = xq, yields: % 27.04/7.44 | (129) all_0_1_1 = xm | xl = sz00 | ~ (sdtasdt0(xl, xq) = xm) | ? [v0] : ? [v1] : ? [v2] : (doDivides0(xl, all_0_1_1) = v2 & aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 27.04/7.44 | % 27.04/7.44 | Instantiating formula (43) with all_12_2_10, xp, xm, xl and discharging atoms sdtsldt0(xm, xl) = xp, sdtasdt0(xl, all_12_2_10) = xm, yields: % 27.04/7.44 | (130) all_12_2_10 = xp | xl = sz00 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_12_2_10) = v0) | (doDivides0(xl, xm) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))) % 27.04/7.44 | % 27.04/7.44 | Instantiating formula (56) with xm, all_12_2_10, xl and discharging atoms sdtasdt0(xl, all_12_2_10) = xm, yields: % 27.04/7.44 | (131) ? [v0] : ? [v1] : ? [v2] : (sdtasdt0(all_12_2_10, xl) = v2 & aNaturalNumber0(all_12_2_10) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xm)) % 27.04/7.44 | % 27.04/7.44 | Instantiating formula (3) with all_0_1_1, all_14_2_16, xm and discharging atoms sdtpldt0(xm, all_14_2_16) = all_0_1_1, yields: % 27.04/7.44 | (132) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_14_2_16, xm) = v2 & aNaturalNumber0(all_14_2_16) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_0_1_1)) % 27.04/7.44 | % 27.04/7.44 | Instantiating (132) with all_58_0_20, all_58_1_21, all_58_2_22 yields: % 27.04/7.44 | (133) sdtpldt0(all_14_2_16, xm) = all_58_0_20 & aNaturalNumber0(all_14_2_16) = all_58_1_21 & aNaturalNumber0(xm) = all_58_2_22 & ( ~ (all_58_1_21 = 0) | ~ (all_58_2_22 = 0) | all_58_0_20 = all_0_1_1) % 27.04/7.45 | % 27.04/7.45 | Applying alpha-rule on (133) yields: % 27.04/7.45 | (134) sdtpldt0(all_14_2_16, xm) = all_58_0_20 % 27.04/7.45 | (135) aNaturalNumber0(all_14_2_16) = all_58_1_21 % 27.04/7.45 | (136) aNaturalNumber0(xm) = all_58_2_22 % 27.04/7.45 | (137) ~ (all_58_1_21 = 0) | ~ (all_58_2_22 = 0) | all_58_0_20 = all_0_1_1 % 27.04/7.45 | % 27.04/7.45 | Instantiating (131) with all_60_0_23, all_60_1_24, all_60_2_25 yields: % 27.04/7.45 | (138) sdtasdt0(all_12_2_10, xl) = all_60_0_23 & aNaturalNumber0(all_12_2_10) = all_60_1_24 & aNaturalNumber0(xl) = all_60_2_25 & ( ~ (all_60_1_24 = 0) | ~ (all_60_2_25 = 0) | all_60_0_23 = xm) % 27.04/7.45 | % 27.04/7.45 | Applying alpha-rule on (138) yields: % 27.04/7.45 | (139) sdtasdt0(all_12_2_10, xl) = all_60_0_23 % 27.04/7.45 | (140) aNaturalNumber0(all_12_2_10) = all_60_1_24 % 27.04/7.45 | (141) aNaturalNumber0(xl) = all_60_2_25 % 27.04/7.45 | (142) ~ (all_60_1_24 = 0) | ~ (all_60_2_25 = 0) | all_60_0_23 = xm % 27.04/7.45 | % 27.04/7.45 | Instantiating (126) with all_62_0_26, all_62_1_27, all_62_2_28 yields: % 27.04/7.45 | (143) sdtasdt0(all_13_2_13, xl) = all_62_0_26 & aNaturalNumber0(all_13_2_13) = all_62_1_27 & aNaturalNumber0(xl) = all_62_2_28 & ( ~ (all_62_1_27 = 0) | ~ (all_62_2_28 = 0) | all_62_0_26 = all_0_1_1) % 27.04/7.45 | % 27.04/7.45 | Applying alpha-rule on (143) yields: % 27.04/7.45 | (144) sdtasdt0(all_13_2_13, xl) = all_62_0_26 % 27.04/7.45 | (145) aNaturalNumber0(all_13_2_13) = all_62_1_27 % 27.04/7.45 | (146) aNaturalNumber0(xl) = all_62_2_28 % 27.04/7.45 | (147) ~ (all_62_1_27 = 0) | ~ (all_62_2_28 = 0) | all_62_0_26 = all_0_1_1 % 27.04/7.45 | % 27.04/7.45 | Instantiating formula (58) with all_13_2_13, all_62_1_27, 0 and discharging atoms aNaturalNumber0(all_13_2_13) = all_62_1_27, aNaturalNumber0(all_13_2_13) = 0, yields: % 27.04/7.45 | (148) all_62_1_27 = 0 % 27.04/7.45 | % 27.04/7.45 | Instantiating formula (58) with all_12_2_10, all_60_1_24, 0 and discharging atoms aNaturalNumber0(all_12_2_10) = all_60_1_24, aNaturalNumber0(all_12_2_10) = 0, yields: % 27.04/7.45 | (149) all_60_1_24 = 0 % 27.04/7.45 | % 27.04/7.45 | Instantiating formula (58) with xp, all_60_1_24, all_19_2_19 and discharging atoms aNaturalNumber0(xp) = all_19_2_19, yields: % 27.04/7.45 | (150) all_60_1_24 = all_19_2_19 | ~ (aNaturalNumber0(xp) = all_60_1_24) % 27.04/7.45 | % 27.04/7.45 | Instantiating formula (58) with xm, all_58_2_22, 0 and discharging atoms aNaturalNumber0(xm) = all_58_2_22, aNaturalNumber0(xm) = 0, yields: % 27.04/7.45 | (151) all_58_2_22 = 0 % 27.04/7.45 | % 27.04/7.45 | Instantiating formula (58) with xl, all_62_2_28, 0 and discharging atoms aNaturalNumber0(xl) = all_62_2_28, aNaturalNumber0(xl) = 0, yields: % 27.04/7.45 | (152) all_62_2_28 = 0 % 27.04/7.45 | % 27.04/7.45 | Instantiating formula (58) with xl, all_60_2_25, all_62_2_28 and discharging atoms aNaturalNumber0(xl) = all_62_2_28, aNaturalNumber0(xl) = all_60_2_25, yields: % 27.04/7.45 | (153) all_62_2_28 = all_60_2_25 % 27.04/7.45 | % 27.04/7.45 | Combining equations (152,153) yields a new equation: % 27.04/7.45 | (154) all_60_2_25 = 0 % 27.04/7.45 | % 27.04/7.45 | From (148) and (145) follows: % 27.04/7.45 | (117) aNaturalNumber0(all_13_2_13) = 0 % 27.04/7.45 | % 27.04/7.45 | From (149) and (140) follows: % 27.04/7.45 | (103) aNaturalNumber0(all_12_2_10) = 0 % 27.04/7.45 | % 27.04/7.45 | From (151) and (136) follows: % 27.04/7.45 | (34) aNaturalNumber0(xm) = 0 % 27.04/7.45 | % 27.04/7.45 | From (154) and (141) follows: % 27.04/7.45 | (18) aNaturalNumber0(xl) = 0 % 27.04/7.45 | % 27.04/7.45 +-Applying beta-rule and splitting (142), into two cases. % 27.04/7.45 |-Branch one: % 27.04/7.45 | (159) ~ (all_60_1_24 = 0) % 27.04/7.45 | % 27.04/7.45 | Equations (149) can reduce 159 to: % 27.04/7.45 | (83) $false % 27.04/7.45 | % 27.04/7.45 |-The branch is then unsatisfiable % 27.04/7.45 |-Branch two: % 27.04/7.45 | (149) all_60_1_24 = 0 % 27.04/7.45 | (162) ~ (all_60_2_25 = 0) | all_60_0_23 = xm % 27.04/7.45 | % 27.04/7.45 +-Applying beta-rule and splitting (124), into two cases. % 27.04/7.45 |-Branch one: % 27.04/7.45 | (163) xl = sz00 % 27.04/7.45 | % 27.04/7.45 | Equations (163) can reduce 10 to: % 27.04/7.45 | (83) $false % 27.04/7.45 | % 27.04/7.45 |-The branch is then unsatisfiable % 27.04/7.45 |-Branch two: % 27.04/7.45 | (10) ~ (xl = sz00) % 27.04/7.45 | (166) all_13_2_13 = xq | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_13_2_13) = v0) | (doDivides0(xl, all_0_1_1) = v2 & aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))) % 27.04/7.45 | % 27.04/7.45 +-Applying beta-rule and splitting (130), into two cases. % 27.04/7.45 |-Branch one: % 27.04/7.45 | (163) xl = sz00 % 27.04/7.45 | % 27.04/7.45 | Equations (163) can reduce 10 to: % 27.04/7.45 | (83) $false % 27.04/7.45 | % 27.04/7.45 |-The branch is then unsatisfiable % 27.04/7.45 |-Branch two: % 27.04/7.45 | (10) ~ (xl = sz00) % 27.04/7.45 | (170) all_12_2_10 = xp | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_12_2_10) = v0) | (doDivides0(xl, xm) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))) % 27.04/7.45 | % 27.04/7.45 +-Applying beta-rule and splitting (166), into two cases. % 27.04/7.45 |-Branch one: % 27.04/7.45 | (171) all_13_2_13 = xq % 27.04/7.45 | % 27.04/7.45 | From (171) and (116) follows: % 27.04/7.45 | (172) sdtasdt0(xl, xq) = all_0_1_1 % 27.04/7.45 | % 27.04/7.45 | From (171) and (117) follows: % 27.04/7.45 | (173) aNaturalNumber0(xq) = 0 % 27.04/7.45 | % 27.04/7.45 +-Applying beta-rule and splitting (170), into two cases. % 27.04/7.45 |-Branch one: % 27.04/7.45 | (174) all_12_2_10 = xp % 27.04/7.45 | % 27.04/7.45 | From (174) and (102) follows: % 27.04/7.45 | (175) sdtasdt0(xl, xp) = xm % 27.04/7.45 | % 27.04/7.45 | From (174) and (103) follows: % 27.04/7.45 | (176) aNaturalNumber0(xp) = 0 % 27.04/7.45 | % 27.04/7.45 +-Applying beta-rule and splitting (150), into two cases. % 27.04/7.45 |-Branch one: % 27.04/7.45 | (177) ~ (aNaturalNumber0(xp) = all_60_1_24) % 27.04/7.45 | % 27.04/7.45 | From (149) and (177) follows: % 27.04/7.45 | (178) ~ (aNaturalNumber0(xp) = 0) % 27.04/7.45 | % 27.04/7.45 | Using (176) and (178) yields: % 27.04/7.45 | (179) $false % 27.04/7.45 | % 27.04/7.45 |-The branch is then unsatisfiable % 27.04/7.45 |-Branch two: % 27.04/7.45 | (180) aNaturalNumber0(xp) = all_60_1_24 % 27.04/7.45 | (181) all_60_1_24 = all_19_2_19 % 27.04/7.45 | % 27.04/7.45 | Combining equations (149,181) yields a new equation: % 27.04/7.45 | (182) all_19_2_19 = 0 % 27.04/7.45 | % 27.04/7.45 | From (182) and (89) follows: % 27.04/7.45 | (176) aNaturalNumber0(xp) = 0 % 27.04/7.45 | % 27.04/7.45 +-Applying beta-rule and splitting (91), into two cases. % 27.04/7.45 |-Branch one: % 27.04/7.45 | (184) ~ (aNaturalNumber0(xq) = all_8_0_2) % 27.04/7.45 | % 27.04/7.45 | From (111) and (184) follows: % 27.04/7.45 | (185) ~ (aNaturalNumber0(xq) = 0) % 27.04/7.45 | % 27.04/7.45 | Using (173) and (185) yields: % 27.04/7.45 | (179) $false % 27.04/7.45 | % 27.04/7.45 |-The branch is then unsatisfiable % 27.04/7.45 |-Branch two: % 27.04/7.45 | (187) aNaturalNumber0(xq) = all_8_0_2 % 27.04/7.45 | (188) all_19_1_18 = all_8_0_2 % 27.04/7.45 | % 27.04/7.45 | Combining equations (111,188) yields a new equation: % 27.04/7.45 | (189) all_19_1_18 = 0 % 27.04/7.45 | % 27.04/7.45 | From (111) and (187) follows: % 27.04/7.45 | (173) aNaturalNumber0(xq) = 0 % 27.04/7.45 | % 27.04/7.45 +-Applying beta-rule and splitting (90), into two cases. % 27.04/7.45 |-Branch one: % 27.04/7.45 | (191) ~ (all_19_1_18 = 0) % 27.04/7.45 | % 27.04/7.45 | Equations (189) can reduce 191 to: % 27.04/7.45 | (83) $false % 27.04/7.45 | % 27.04/7.45 |-The branch is then unsatisfiable % 27.04/7.45 |-Branch two: % 27.04/7.45 | (189) all_19_1_18 = 0 % 27.04/7.45 | (194) ~ (all_19_2_19 = 0) | (all_19_0_17 = 0 & ~ (xq = xp)) % 27.04/7.45 | % 27.04/7.45 +-Applying beta-rule and splitting (194), into two cases. % 27.04/7.45 |-Branch one: % 27.04/7.45 | (195) ~ (all_19_2_19 = 0) % 27.04/7.45 | % 27.04/7.45 | Equations (182) can reduce 195 to: % 27.04/7.45 | (83) $false % 27.04/7.45 | % 27.04/7.45 |-The branch is then unsatisfiable % 27.04/7.45 |-Branch two: % 27.04/7.46 | (182) all_19_2_19 = 0 % 27.04/7.46 | (198) all_19_0_17 = 0 & ~ (xq = xp) % 27.04/7.46 | % 27.04/7.46 | Applying alpha-rule on (198) yields: % 27.04/7.46 | (199) all_19_0_17 = 0 % 27.04/7.46 | (200) ~ (xq = xp) % 27.04/7.46 | % 27.04/7.46 | From (199) and (87) follows: % 27.04/7.46 | (201) sdtlseqdt0(xq, xp) = 0 % 27.04/7.46 | % 27.04/7.46 +-Applying beta-rule and splitting (125), into two cases. % 27.04/7.46 |-Branch one: % 27.04/7.46 | (202) ~ (sdtasdt0(xl, all_13_2_13) = xm) % 27.04/7.46 | % 27.04/7.46 | From (171) and (202) follows: % 27.04/7.46 | (203) ~ (sdtasdt0(xl, xq) = xm) % 27.04/7.46 | % 27.04/7.46 +-Applying beta-rule and splitting (127), into two cases. % 27.04/7.46 |-Branch one: % 27.04/7.46 | (163) xl = sz00 % 27.04/7.46 | % 27.04/7.46 | Equations (163) can reduce 10 to: % 27.04/7.46 | (83) $false % 27.04/7.46 | % 27.04/7.46 |-The branch is then unsatisfiable % 27.04/7.46 |-Branch two: % 27.04/7.46 | (10) ~ (xl = sz00) % 27.04/7.46 | (207) all_13_2_13 = all_12_2_10 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_13_2_13, xl) = v2 & sdtasdt0(all_12_2_10, xl) = v3 & aNaturalNumber0(all_13_2_13) = v0 & aNaturalNumber0(all_12_2_10) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = v2) & ~ (all_0_1_1 = xm)))) % 27.04/7.46 | % 27.04/7.46 +-Applying beta-rule and splitting (128), into two cases. % 27.04/7.46 |-Branch one: % 27.04/7.46 | (163) xl = sz00 % 27.04/7.46 | % 27.04/7.46 | Equations (163) can reduce 10 to: % 27.04/7.46 | (83) $false % 27.04/7.46 | % 27.04/7.46 |-The branch is then unsatisfiable % 27.04/7.46 |-Branch two: % 27.04/7.46 | (10) ~ (xl = sz00) % 27.04/7.46 | (211) all_13_2_13 = all_12_2_10 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_13_2_13, xl) = v3 & sdtasdt0(all_12_2_10, xl) = v2 & aNaturalNumber0(all_13_2_13) = v1 & aNaturalNumber0(all_12_2_10) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = v2) & ~ (all_0_1_1 = xm)))) % 27.04/7.46 | % 27.04/7.46 +-Applying beta-rule and splitting (211), into two cases. % 27.04/7.46 |-Branch one: % 27.04/7.46 | (212) all_13_2_13 = all_12_2_10 % 27.04/7.46 | % 27.04/7.46 | Combining equations (171,212) yields a new equation: % 27.04/7.46 | (213) all_12_2_10 = xq % 27.04/7.46 | % 27.04/7.46 | Combining equations (213,174) yields a new equation: % 27.04/7.46 | (214) xq = xp % 27.04/7.46 | % 27.04/7.46 | Simplifying 214 yields: % 27.04/7.46 | (215) xq = xp % 27.04/7.46 | % 27.04/7.46 | Equations (215) can reduce 200 to: % 27.04/7.46 | (83) $false % 27.04/7.46 | % 27.04/7.46 |-The branch is then unsatisfiable % 27.04/7.46 |-Branch two: % 27.04/7.46 | (217) ~ (all_13_2_13 = all_12_2_10) % 27.04/7.46 | (218) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_13_2_13, xl) = v3 & sdtasdt0(all_12_2_10, xl) = v2 & aNaturalNumber0(all_13_2_13) = v1 & aNaturalNumber0(all_12_2_10) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = v2) & ~ (all_0_1_1 = xm)))) % 27.04/7.46 | % 27.04/7.46 | Instantiating (218) with all_148_0_29, all_148_1_30, all_148_2_31, all_148_3_32 yields: % 27.04/7.46 | (219) sdtasdt0(all_13_2_13, xl) = all_148_0_29 & sdtasdt0(all_12_2_10, xl) = all_148_1_30 & aNaturalNumber0(all_13_2_13) = all_148_2_31 & aNaturalNumber0(all_12_2_10) = all_148_3_32 & ( ~ (all_148_2_31 = 0) | ~ (all_148_3_32 = 0) | ( ~ (all_148_0_29 = all_148_1_30) & ~ (all_0_1_1 = xm))) % 27.04/7.46 | % 27.04/7.46 | Applying alpha-rule on (219) yields: % 27.04/7.46 | (220) sdtasdt0(all_13_2_13, xl) = all_148_0_29 % 27.04/7.46 | (221) aNaturalNumber0(all_13_2_13) = all_148_2_31 % 27.04/7.46 | (222) aNaturalNumber0(all_12_2_10) = all_148_3_32 % 27.04/7.46 | (223) ~ (all_148_2_31 = 0) | ~ (all_148_3_32 = 0) | ( ~ (all_148_0_29 = all_148_1_30) & ~ (all_0_1_1 = xm)) % 27.04/7.46 | (224) sdtasdt0(all_12_2_10, xl) = all_148_1_30 % 27.04/7.46 | % 27.04/7.46 | Equations (171,174) can reduce 217 to: % 27.04/7.46 | (200) ~ (xq = xp) % 27.04/7.46 | % 27.04/7.46 | From (171) and (221) follows: % 27.04/7.46 | (226) aNaturalNumber0(xq) = all_148_2_31 % 27.04/7.46 | % 27.04/7.46 | From (174) and (222) follows: % 27.04/7.46 | (227) aNaturalNumber0(xp) = all_148_3_32 % 27.04/7.46 | % 27.04/7.46 +-Applying beta-rule and splitting (123), into two cases. % 27.04/7.46 |-Branch one: % 27.04/7.46 | (228) ~ (sdtlseqdt0(xq, xp) = 0) % 27.04/7.46 | % 27.04/7.46 | Using (201) and (228) yields: % 27.04/7.46 | (179) $false % 27.04/7.46 | % 27.04/7.46 |-The branch is then unsatisfiable % 27.04/7.46 |-Branch two: % 27.04/7.46 | (201) sdtlseqdt0(xq, xp) = 0 % 27.04/7.46 | (231) ? [v0] : ? [v1] : ? [v2] : ((v2 = xp & v1 = 0 & sdtpldt0(xq, v0) = xp & aNaturalNumber0(v0) = 0) | (aNaturalNumber0(xq) = v0 & aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 27.04/7.46 | % 27.04/7.46 | Instantiating (231) with all_154_0_33, all_154_1_34, all_154_2_35 yields: % 27.04/7.46 | (232) (all_154_0_33 = xp & all_154_1_34 = 0 & sdtpldt0(xq, all_154_2_35) = xp & aNaturalNumber0(all_154_2_35) = 0) | (aNaturalNumber0(xq) = all_154_2_35 & aNaturalNumber0(xp) = all_154_1_34 & ( ~ (all_154_1_34 = 0) | ~ (all_154_2_35 = 0))) % 27.04/7.46 | % 27.04/7.46 | Instantiating formula (58) with xq, all_148_2_31, 0 and discharging atoms aNaturalNumber0(xq) = all_148_2_31, aNaturalNumber0(xq) = 0, yields: % 27.04/7.46 | (233) all_148_2_31 = 0 % 27.04/7.46 | % 27.04/7.46 | Instantiating formula (58) with xp, all_148_3_32, 0 and discharging atoms aNaturalNumber0(xp) = all_148_3_32, aNaturalNumber0(xp) = 0, yields: % 27.04/7.46 | (234) all_148_3_32 = 0 % 27.04/7.46 | % 27.04/7.46 | Using (172) and (203) yields: % 27.04/7.46 | (235) ~ (all_0_1_1 = xm) % 27.04/7.46 | % 27.04/7.46 | From (233) and (226) follows: % 27.04/7.46 | (173) aNaturalNumber0(xq) = 0 % 27.04/7.46 | % 27.04/7.46 | From (234) and (227) follows: % 27.04/7.46 | (176) aNaturalNumber0(xp) = 0 % 27.04/7.46 | % 27.04/7.46 +-Applying beta-rule and splitting (232), into two cases. % 27.04/7.46 |-Branch one: % 27.04/7.46 | (238) all_154_0_33 = xp & all_154_1_34 = 0 & sdtpldt0(xq, all_154_2_35) = xp & aNaturalNumber0(all_154_2_35) = 0 % 27.04/7.46 | % 27.04/7.46 | Applying alpha-rule on (238) yields: % 27.04/7.46 | (239) all_154_0_33 = xp % 27.04/7.46 | (240) all_154_1_34 = 0 % 27.04/7.46 | (241) sdtpldt0(xq, all_154_2_35) = xp % 27.04/7.46 | (242) aNaturalNumber0(all_154_2_35) = 0 % 27.04/7.46 | % 27.04/7.46 +-Applying beta-rule and splitting (65), into two cases. % 27.04/7.46 |-Branch one: % 27.04/7.46 | (243) all_0_1_1 = xm % 27.04/7.46 | % 27.04/7.46 | Equations (243) can reduce 235 to: % 27.04/7.46 | (83) $false % 27.04/7.46 | % 27.04/7.46 |-The branch is then unsatisfiable % 27.04/7.46 |-Branch two: % 27.04/7.46 | (235) ~ (all_0_1_1 = xm) % 27.04/7.46 | (246) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_0_1_1, xm) = v2 & aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 27.04/7.46 | % 27.04/7.46 | Instantiating (246) with all_170_0_36, all_170_1_37, all_170_2_38 yields: % 27.04/7.46 | (247) sdtlseqdt0(all_0_1_1, xm) = all_170_0_36 & aNaturalNumber0(all_0_1_1) = all_170_1_37 & aNaturalNumber0(xm) = all_170_2_38 & ( ~ (all_170_0_36 = 0) | ~ (all_170_1_37 = 0) | ~ (all_170_2_38 = 0)) % 27.04/7.46 | % 27.04/7.46 | Applying alpha-rule on (247) yields: % 27.04/7.46 | (248) sdtlseqdt0(all_0_1_1, xm) = all_170_0_36 % 27.04/7.46 | (249) aNaturalNumber0(all_0_1_1) = all_170_1_37 % 27.04/7.46 | (250) aNaturalNumber0(xm) = all_170_2_38 % 27.04/7.46 | (251) ~ (all_170_0_36 = 0) | ~ (all_170_1_37 = 0) | ~ (all_170_2_38 = 0) % 27.04/7.46 | % 27.04/7.46 | Instantiating formula (58) with all_0_1_1, all_170_1_37, 0 and discharging atoms aNaturalNumber0(all_0_1_1) = all_170_1_37, aNaturalNumber0(all_0_1_1) = 0, yields: % 27.04/7.46 | (252) all_170_1_37 = 0 % 27.04/7.46 | % 27.04/7.46 | Instantiating formula (58) with xm, all_170_2_38, 0 and discharging atoms aNaturalNumber0(xm) = all_170_2_38, aNaturalNumber0(xm) = 0, yields: % 27.04/7.46 | (253) all_170_2_38 = 0 % 27.04/7.46 | % 27.04/7.46 +-Applying beta-rule and splitting (251), into two cases. % 27.04/7.46 |-Branch one: % 27.04/7.46 | (254) ~ (all_170_0_36 = 0) % 27.04/7.46 | % 27.04/7.46 | Instantiating formula (16) with all_170_0_36, xm, all_0_1_1, xp, xq, xl and discharging atoms sdtlseqdt0(all_0_1_1, xm) = all_170_0_36, sdtasdt0(xl, xq) = all_0_1_1, sdtasdt0(xl, xp) = xm, yields: % 27.04/7.46 | (255) xq = xp | xl = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v4, v5) = v6 & sdtlseqdt0(xq, xp) = v3 & sdtasdt0(xq, xl) = v4 & sdtasdt0(xp, xl) = v5 & aNaturalNumber0(xq) = v1 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xl) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v6 = 0 & all_170_0_36 = 0 & ~ (v5 = v4) & ~ (all_0_1_1 = xm)))) % 27.04/7.46 | % 27.04/7.46 | Instantiating formula (3) with xp, all_154_2_35, xq and discharging atoms sdtpldt0(xq, all_154_2_35) = xp, yields: % 27.04/7.46 | (256) ? [v0] : ? [v1] : ? [v2] : (sdtpldt0(all_154_2_35, xq) = v2 & aNaturalNumber0(all_154_2_35) = v1 & aNaturalNumber0(xq) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xp)) % 27.04/7.46 | % 27.04/7.46 | Instantiating (256) with all_197_0_39, all_197_1_40, all_197_2_41 yields: % 27.04/7.46 | (257) sdtpldt0(all_154_2_35, xq) = all_197_0_39 & aNaturalNumber0(all_154_2_35) = all_197_1_40 & aNaturalNumber0(xq) = all_197_2_41 & ( ~ (all_197_1_40 = 0) | ~ (all_197_2_41 = 0) | all_197_0_39 = xp) % 27.04/7.46 | % 27.04/7.46 | Applying alpha-rule on (257) yields: % 27.04/7.46 | (258) sdtpldt0(all_154_2_35, xq) = all_197_0_39 % 27.04/7.46 | (259) aNaturalNumber0(all_154_2_35) = all_197_1_40 % 27.04/7.46 | (260) aNaturalNumber0(xq) = all_197_2_41 % 27.04/7.46 | (261) ~ (all_197_1_40 = 0) | ~ (all_197_2_41 = 0) | all_197_0_39 = xp % 27.04/7.46 | % 27.04/7.46 +-Applying beta-rule and splitting (255), into two cases. % 27.04/7.46 |-Branch one: % 27.04/7.46 | (163) xl = sz00 % 27.04/7.46 | % 27.04/7.46 | Equations (163) can reduce 10 to: % 27.04/7.46 | (83) $false % 27.04/7.46 | % 27.04/7.46 |-The branch is then unsatisfiable % 27.04/7.46 |-Branch two: % 27.04/7.46 | (10) ~ (xl = sz00) % 27.04/7.46 | (265) xq = xp | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v4, v5) = v6 & sdtlseqdt0(xq, xp) = v3 & sdtasdt0(xq, xl) = v4 & sdtasdt0(xp, xl) = v5 & aNaturalNumber0(xq) = v1 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xl) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v6 = 0 & all_170_0_36 = 0 & ~ (v5 = v4) & ~ (all_0_1_1 = xm)))) % 27.04/7.47 | % 27.04/7.47 +-Applying beta-rule and splitting (265), into two cases. % 27.04/7.47 |-Branch one: % 27.04/7.47 | (215) xq = xp % 27.04/7.47 | % 27.04/7.47 | Equations (215) can reduce 200 to: % 27.04/7.47 | (83) $false % 27.04/7.47 | % 27.04/7.47 |-The branch is then unsatisfiable % 27.04/7.47 |-Branch two: % 27.04/7.47 | (200) ~ (xq = xp) % 27.04/7.47 | (269) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (sdtlseqdt0(v4, v5) = v6 & sdtlseqdt0(xq, xp) = v3 & sdtasdt0(xq, xl) = v4 & sdtasdt0(xp, xl) = v5 & aNaturalNumber0(xq) = v1 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xl) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v6 = 0 & all_170_0_36 = 0 & ~ (v5 = v4) & ~ (all_0_1_1 = xm)))) % 27.04/7.47 | % 27.04/7.47 | Instantiating (269) with all_219_0_42, all_219_1_43, all_219_2_44, all_219_3_45, all_219_4_46, all_219_5_47, all_219_6_48 yields: % 27.04/7.47 | (270) sdtlseqdt0(all_219_2_44, all_219_1_43) = all_219_0_42 & sdtlseqdt0(xq, xp) = all_219_3_45 & sdtasdt0(xq, xl) = all_219_2_44 & sdtasdt0(xp, xl) = all_219_1_43 & aNaturalNumber0(xq) = all_219_5_47 & aNaturalNumber0(xp) = all_219_4_46 & aNaturalNumber0(xl) = all_219_6_48 & ( ~ (all_219_3_45 = 0) | ~ (all_219_4_46 = 0) | ~ (all_219_5_47 = 0) | ~ (all_219_6_48 = 0) | (all_219_0_42 = 0 & all_170_0_36 = 0 & ~ (all_219_1_43 = all_219_2_44) & ~ (all_0_1_1 = xm))) % 27.04/7.47 | % 27.04/7.47 | Applying alpha-rule on (270) yields: % 27.04/7.47 | (271) aNaturalNumber0(xp) = all_219_4_46 % 27.04/7.47 | (272) sdtlseqdt0(xq, xp) = all_219_3_45 % 27.04/7.47 | (273) ~ (all_219_3_45 = 0) | ~ (all_219_4_46 = 0) | ~ (all_219_5_47 = 0) | ~ (all_219_6_48 = 0) | (all_219_0_42 = 0 & all_170_0_36 = 0 & ~ (all_219_1_43 = all_219_2_44) & ~ (all_0_1_1 = xm)) % 27.04/7.47 | (274) sdtlseqdt0(all_219_2_44, all_219_1_43) = all_219_0_42 % 27.04/7.47 | (275) aNaturalNumber0(xq) = all_219_5_47 % 27.04/7.47 | (276) sdtasdt0(xq, xl) = all_219_2_44 % 27.04/7.47 | (277) aNaturalNumber0(xl) = all_219_6_48 % 27.04/7.47 | (278) sdtasdt0(xp, xl) = all_219_1_43 % 27.04/7.47 | % 27.04/7.47 | Instantiating formula (23) with xq, xp, all_219_3_45, 0 and discharging atoms sdtlseqdt0(xq, xp) = all_219_3_45, sdtlseqdt0(xq, xp) = 0, yields: % 27.04/7.47 | (279) all_219_3_45 = 0 % 27.04/7.47 | % 27.04/7.47 | Instantiating formula (58) with xq, all_219_5_47, 0 and discharging atoms aNaturalNumber0(xq) = all_219_5_47, aNaturalNumber0(xq) = 0, yields: % 27.04/7.47 | (280) all_219_5_47 = 0 % 27.04/7.47 | % 27.04/7.47 | Instantiating formula (58) with xq, all_197_2_41, all_219_5_47 and discharging atoms aNaturalNumber0(xq) = all_219_5_47, aNaturalNumber0(xq) = all_197_2_41, yields: % 27.04/7.47 | (281) all_219_5_47 = all_197_2_41 % 27.04/7.47 | % 27.04/7.47 | Instantiating formula (58) with xp, all_219_4_46, 0 and discharging atoms aNaturalNumber0(xp) = all_219_4_46, aNaturalNumber0(xp) = 0, yields: % 27.04/7.47 | (282) all_219_4_46 = 0 % 27.04/7.47 | % 27.04/7.47 | Instantiating formula (58) with xl, all_219_6_48, 0 and discharging atoms aNaturalNumber0(xl) = all_219_6_48, aNaturalNumber0(xl) = 0, yields: % 27.04/7.47 | (283) all_219_6_48 = 0 % 27.04/7.47 | % 27.04/7.47 | Combining equations (280,281) yields a new equation: % 27.04/7.47 | (284) all_197_2_41 = 0 % 27.04/7.47 | % 27.04/7.47 | Combining equations (284,281) yields a new equation: % 27.04/7.47 | (280) all_219_5_47 = 0 % 27.04/7.47 | % 27.04/7.47 +-Applying beta-rule and splitting (273), into two cases. % 27.04/7.47 |-Branch one: % 27.04/7.47 | (286) ~ (all_219_3_45 = 0) % 27.04/7.47 | % 27.04/7.47 | Equations (279) can reduce 286 to: % 27.04/7.47 | (83) $false % 27.04/7.47 | % 27.04/7.47 |-The branch is then unsatisfiable % 27.04/7.47 |-Branch two: % 27.04/7.47 | (279) all_219_3_45 = 0 % 27.04/7.47 | (289) ~ (all_219_4_46 = 0) | ~ (all_219_5_47 = 0) | ~ (all_219_6_48 = 0) | (all_219_0_42 = 0 & all_170_0_36 = 0 & ~ (all_219_1_43 = all_219_2_44) & ~ (all_0_1_1 = xm)) % 27.04/7.47 | % 27.04/7.47 +-Applying beta-rule and splitting (289), into two cases. % 27.04/7.47 |-Branch one: % 27.04/7.47 | (290) ~ (all_219_4_46 = 0) % 27.04/7.47 | % 27.04/7.47 | Equations (282) can reduce 290 to: % 27.04/7.47 | (83) $false % 27.04/7.47 | % 27.04/7.47 |-The branch is then unsatisfiable % 27.04/7.47 |-Branch two: % 27.04/7.47 | (282) all_219_4_46 = 0 % 27.04/7.47 | (293) ~ (all_219_5_47 = 0) | ~ (all_219_6_48 = 0) | (all_219_0_42 = 0 & all_170_0_36 = 0 & ~ (all_219_1_43 = all_219_2_44) & ~ (all_0_1_1 = xm)) % 27.04/7.47 | % 27.04/7.47 +-Applying beta-rule and splitting (293), into two cases. % 27.04/7.47 |-Branch one: % 27.04/7.47 | (294) ~ (all_219_5_47 = 0) % 27.04/7.47 | % 27.04/7.47 | Equations (280) can reduce 294 to: % 27.04/7.47 | (83) $false % 27.04/7.47 | % 27.04/7.47 |-The branch is then unsatisfiable % 27.04/7.47 |-Branch two: % 27.04/7.47 | (280) all_219_5_47 = 0 % 27.04/7.47 | (297) ~ (all_219_6_48 = 0) | (all_219_0_42 = 0 & all_170_0_36 = 0 & ~ (all_219_1_43 = all_219_2_44) & ~ (all_0_1_1 = xm)) % 27.04/7.47 | % 27.04/7.47 +-Applying beta-rule and splitting (297), into two cases. % 27.04/7.47 |-Branch one: % 27.04/7.47 | (298) ~ (all_219_6_48 = 0) % 27.04/7.47 | % 27.04/7.47 | Equations (283) can reduce 298 to: % 27.04/7.47 | (83) $false % 27.04/7.47 | % 27.04/7.47 |-The branch is then unsatisfiable % 27.04/7.47 |-Branch two: % 27.04/7.47 | (283) all_219_6_48 = 0 % 27.04/7.47 | (301) all_219_0_42 = 0 & all_170_0_36 = 0 & ~ (all_219_1_43 = all_219_2_44) & ~ (all_0_1_1 = xm) % 27.04/7.47 | % 27.04/7.47 | Applying alpha-rule on (301) yields: % 27.04/7.47 | (302) all_219_0_42 = 0 % 27.04/7.47 | (303) all_170_0_36 = 0 % 27.04/7.47 | (304) ~ (all_219_1_43 = all_219_2_44) % 27.04/7.47 | (235) ~ (all_0_1_1 = xm) % 27.04/7.47 | % 27.04/7.47 | Equations (303) can reduce 254 to: % 27.04/7.47 | (83) $false % 27.04/7.47 | % 27.04/7.47 |-The branch is then unsatisfiable % 27.04/7.47 |-Branch two: % 27.04/7.47 | (303) all_170_0_36 = 0 % 27.04/7.47 | (308) ~ (all_170_1_37 = 0) | ~ (all_170_2_38 = 0) % 27.04/7.47 | % 27.04/7.47 +-Applying beta-rule and splitting (308), into two cases. % 27.04/7.47 |-Branch one: % 27.04/7.47 | (309) ~ (all_170_1_37 = 0) % 27.04/7.47 | % 27.04/7.47 | Equations (252) can reduce 309 to: % 27.04/7.47 | (83) $false % 27.04/7.47 | % 27.04/7.47 |-The branch is then unsatisfiable % 27.04/7.47 |-Branch two: % 27.04/7.47 | (252) all_170_1_37 = 0 % 27.04/7.47 | (312) ~ (all_170_2_38 = 0) % 27.04/7.47 | % 27.04/7.47 | Equations (253) can reduce 312 to: % 27.04/7.47 | (83) $false % 27.04/7.47 | % 27.04/7.47 |-The branch is then unsatisfiable % 27.04/7.47 |-Branch two: % 27.04/7.47 | (314) aNaturalNumber0(xq) = all_154_2_35 & aNaturalNumber0(xp) = all_154_1_34 & ( ~ (all_154_1_34 = 0) | ~ (all_154_2_35 = 0)) % 27.04/7.47 | % 27.04/7.47 | Applying alpha-rule on (314) yields: % 27.04/7.47 | (315) aNaturalNumber0(xq) = all_154_2_35 % 27.04/7.47 | (316) aNaturalNumber0(xp) = all_154_1_34 % 27.04/7.47 | (317) ~ (all_154_1_34 = 0) | ~ (all_154_2_35 = 0) % 27.04/7.47 | % 27.04/7.47 | Instantiating formula (58) with xq, all_154_2_35, 0 and discharging atoms aNaturalNumber0(xq) = all_154_2_35, aNaturalNumber0(xq) = 0, yields: % 27.04/7.47 | (318) all_154_2_35 = 0 % 27.04/7.47 | % 27.04/7.47 | Instantiating formula (58) with xp, all_154_1_34, 0 and discharging atoms aNaturalNumber0(xp) = all_154_1_34, aNaturalNumber0(xp) = 0, yields: % 27.04/7.47 | (240) all_154_1_34 = 0 % 27.04/7.47 | % 27.04/7.47 +-Applying beta-rule and splitting (317), into two cases. % 27.04/7.47 |-Branch one: % 27.04/7.47 | (320) ~ (all_154_1_34 = 0) % 27.04/7.47 | % 27.04/7.47 | Equations (240) can reduce 320 to: % 27.04/7.47 | (83) $false % 27.04/7.47 | % 27.04/7.47 |-The branch is then unsatisfiable % 27.04/7.47 |-Branch two: % 27.04/7.47 | (240) all_154_1_34 = 0 % 27.04/7.47 | (323) ~ (all_154_2_35 = 0) % 27.04/7.47 | % 27.04/7.47 | Equations (318) can reduce 323 to: % 27.04/7.47 | (83) $false % 27.04/7.47 | % 27.04/7.47 |-The branch is then unsatisfiable % 27.04/7.47 |-Branch two: % 27.04/7.47 | (325) sdtasdt0(xl, all_13_2_13) = xm % 27.04/7.47 | (326) all_13_2_13 = xp | xl = sz00 | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_13_2_13) = v0) | (doDivides0(xl, xm) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))) % 27.04/7.47 | % 27.04/7.47 | From (171) and (325) follows: % 27.04/7.47 | (327) sdtasdt0(xl, xq) = xm % 27.04/7.47 | % 27.04/7.47 +-Applying beta-rule and splitting (127), into two cases. % 27.04/7.47 |-Branch one: % 27.04/7.47 | (163) xl = sz00 % 27.04/7.47 | % 27.04/7.47 | Equations (163) can reduce 10 to: % 27.04/7.47 | (83) $false % 27.04/7.47 | % 27.04/7.47 |-The branch is then unsatisfiable % 27.04/7.47 |-Branch two: % 27.04/7.47 | (10) ~ (xl = sz00) % 27.04/7.47 | (207) all_13_2_13 = all_12_2_10 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_13_2_13, xl) = v2 & sdtasdt0(all_12_2_10, xl) = v3 & aNaturalNumber0(all_13_2_13) = v0 & aNaturalNumber0(all_12_2_10) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = v2) & ~ (all_0_1_1 = xm)))) % 27.04/7.47 | % 27.04/7.47 +-Applying beta-rule and splitting (128), into two cases. % 27.04/7.47 |-Branch one: % 27.04/7.47 | (163) xl = sz00 % 27.04/7.47 | % 27.04/7.47 | Equations (163) can reduce 10 to: % 27.04/7.47 | (83) $false % 27.04/7.47 | % 27.04/7.47 |-The branch is then unsatisfiable % 27.04/7.47 |-Branch two: % 27.04/7.47 | (10) ~ (xl = sz00) % 27.04/7.47 | (211) all_13_2_13 = all_12_2_10 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_13_2_13, xl) = v3 & sdtasdt0(all_12_2_10, xl) = v2 & aNaturalNumber0(all_13_2_13) = v1 & aNaturalNumber0(all_12_2_10) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = v2) & ~ (all_0_1_1 = xm)))) % 27.04/7.47 | % 27.04/7.47 +-Applying beta-rule and splitting (211), into two cases. % 27.04/7.47 |-Branch one: % 27.04/7.47 | (212) all_13_2_13 = all_12_2_10 % 27.04/7.47 | % 27.04/7.47 | Combining equations (171,212) yields a new equation: % 27.04/7.47 | (213) all_12_2_10 = xq % 27.04/7.47 | % 27.04/7.47 | Combining equations (213,174) yields a new equation: % 27.04/7.47 | (214) xq = xp % 27.04/7.47 | % 27.04/7.47 | Simplifying 214 yields: % 27.04/7.47 | (215) xq = xp % 27.04/7.47 | % 27.04/7.47 | Equations (215) can reduce 200 to: % 27.04/7.47 | (83) $false % 27.04/7.47 | % 27.04/7.47 |-The branch is then unsatisfiable % 27.04/7.47 |-Branch two: % 27.04/7.47 | (217) ~ (all_13_2_13 = all_12_2_10) % 27.04/7.47 | (218) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(all_13_2_13, xl) = v3 & sdtasdt0(all_12_2_10, xl) = v2 & aNaturalNumber0(all_13_2_13) = v1 & aNaturalNumber0(all_12_2_10) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ~ (v3 = v2) & ~ (all_0_1_1 = xm)))) % 27.04/7.47 | % 27.04/7.47 | Equations (171,174) can reduce 217 to: % 27.04/7.47 | (200) ~ (xq = xp) % 27.04/7.47 | % 27.04/7.47 +-Applying beta-rule and splitting (129), into two cases. % 27.04/7.47 |-Branch one: % 27.04/7.47 | (203) ~ (sdtasdt0(xl, xq) = xm) % 27.04/7.47 | % 27.04/7.47 | Using (327) and (203) yields: % 27.04/7.47 | (179) $false % 27.04/7.47 | % 27.04/7.47 |-The branch is then unsatisfiable % 27.04/7.47 |-Branch two: % 27.04/7.47 | (327) sdtasdt0(xl, xq) = xm % 27.04/7.47 | (347) all_0_1_1 = xm | xl = sz00 | ? [v0] : ? [v1] : ? [v2] : (doDivides0(xl, all_0_1_1) = v2 & aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 27.04/7.48 | % 27.04/7.48 +-Applying beta-rule and splitting (326), into two cases. % 27.04/7.48 |-Branch one: % 27.04/7.48 | (163) xl = sz00 % 27.04/7.48 | % 27.04/7.48 | Equations (163) can reduce 10 to: % 27.04/7.48 | (83) $false % 27.04/7.48 | % 27.04/7.48 |-The branch is then unsatisfiable % 27.04/7.48 |-Branch two: % 27.04/7.48 | (10) ~ (xl = sz00) % 27.04/7.48 | (351) all_13_2_13 = xp | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_13_2_13) = v0) | (doDivides0(xl, xm) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))) % 27.04/7.48 | % 27.04/7.48 +-Applying beta-rule and splitting (347), into two cases. % 27.04/7.48 |-Branch one: % 27.04/7.48 | (163) xl = sz00 % 27.04/7.48 | % 27.04/7.48 | Equations (163) can reduce 10 to: % 27.04/7.48 | (83) $false % 27.04/7.48 | % 27.04/7.48 |-The branch is then unsatisfiable % 27.04/7.48 |-Branch two: % 27.04/7.48 | (10) ~ (xl = sz00) % 27.04/7.48 | (355) all_0_1_1 = xm | ? [v0] : ? [v1] : ? [v2] : (doDivides0(xl, all_0_1_1) = v2 & aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 27.04/7.48 | % 27.04/7.48 +-Applying beta-rule and splitting (355), into two cases. % 27.04/7.48 |-Branch one: % 27.04/7.48 | (243) all_0_1_1 = xm % 27.04/7.48 | % 27.04/7.48 | From (243) and (55) follows: % 27.04/7.48 | (357) sdtsldt0(xm, xl) = xq % 27.04/7.48 | % 27.04/7.48 +-Applying beta-rule and splitting (61), into two cases. % 27.04/7.48 |-Branch one: % 27.04/7.48 | (358) ~ (sdtsldt0(xm, xl) = xq) % 27.04/7.48 | % 27.04/7.48 | Using (357) and (358) yields: % 27.04/7.48 | (179) $false % 27.04/7.48 | % 27.04/7.48 |-The branch is then unsatisfiable % 27.04/7.48 |-Branch two: % 27.04/7.48 | (357) sdtsldt0(xm, xl) = xq % 27.04/7.48 | (215) xq = xp % 27.04/7.48 | % 27.04/7.48 | Equations (215) can reduce 200 to: % 27.04/7.48 | (83) $false % 27.04/7.48 | % 27.04/7.48 |-The branch is then unsatisfiable % 27.04/7.48 |-Branch two: % 27.04/7.48 | (235) ~ (all_0_1_1 = xm) % 27.04/7.48 | (364) ? [v0] : ? [v1] : ? [v2] : (doDivides0(xl, all_0_1_1) = v2 & aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 27.04/7.48 | % 27.04/7.48 +-Applying beta-rule and splitting (65), into two cases. % 27.04/7.48 |-Branch one: % 27.04/7.48 | (243) all_0_1_1 = xm % 27.04/7.48 | % 27.04/7.48 | Equations (243) can reduce 235 to: % 27.04/7.48 | (83) $false % 27.04/7.48 | % 27.04/7.48 |-The branch is then unsatisfiable % 27.04/7.48 |-Branch two: % 27.04/7.48 | (235) ~ (all_0_1_1 = xm) % 27.04/7.48 | (246) ? [v0] : ? [v1] : ? [v2] : (sdtlseqdt0(all_0_1_1, xm) = v2 & aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 27.04/7.48 | % 27.04/7.48 | Instantiating formula (50) with xl, xq, xm, all_0_1_1 and discharging atoms sdtasdt0(xl, xq) = all_0_1_1, sdtasdt0(xl, xq) = xm, yields: % 27.04/7.48 | (243) all_0_1_1 = xm % 27.04/7.48 | % 27.04/7.48 | Equations (243) can reduce 235 to: % 27.04/7.48 | (83) $false % 27.04/7.48 | % 27.04/7.48 |-The branch is then unsatisfiable % 27.04/7.48 |-Branch two: % 27.04/7.48 | (371) ~ (all_12_2_10 = xp) % 27.04/7.48 | (372) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_12_2_10) = v0) | (doDivides0(xl, xm) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))) % 27.04/7.48 | % 27.04/7.48 | Instantiating (372) with all_112_0_68, all_112_1_69, all_112_2_70 yields: % 27.04/7.48 | (373) ( ~ (all_112_2_70 = 0) & aNaturalNumber0(all_12_2_10) = all_112_2_70) | (doDivides0(xl, xm) = all_112_0_68 & aNaturalNumber0(xm) = all_112_1_69 & aNaturalNumber0(xl) = all_112_2_70 & ( ~ (all_112_0_68 = 0) | ~ (all_112_1_69 = 0) | ~ (all_112_2_70 = 0))) % 27.04/7.48 | % 27.04/7.48 +-Applying beta-rule and splitting (373), into two cases. % 27.04/7.48 |-Branch one: % 27.04/7.48 | (374) ~ (all_112_2_70 = 0) & aNaturalNumber0(all_12_2_10) = all_112_2_70 % 27.04/7.48 | % 27.04/7.48 | Applying alpha-rule on (374) yields: % 27.04/7.48 | (375) ~ (all_112_2_70 = 0) % 27.04/7.48 | (376) aNaturalNumber0(all_12_2_10) = all_112_2_70 % 27.04/7.48 | % 27.04/7.48 | Instantiating formula (58) with all_12_2_10, all_112_2_70, 0 and discharging atoms aNaturalNumber0(all_12_2_10) = all_112_2_70, aNaturalNumber0(all_12_2_10) = 0, yields: % 27.04/7.48 | (377) all_112_2_70 = 0 % 27.04/7.48 | % 27.04/7.48 | Equations (377) can reduce 375 to: % 27.04/7.48 | (83) $false % 27.04/7.48 | % 27.04/7.48 |-The branch is then unsatisfiable % 27.04/7.48 |-Branch two: % 27.04/7.48 | (379) doDivides0(xl, xm) = all_112_0_68 & aNaturalNumber0(xm) = all_112_1_69 & aNaturalNumber0(xl) = all_112_2_70 & ( ~ (all_112_0_68 = 0) | ~ (all_112_1_69 = 0) | ~ (all_112_2_70 = 0)) % 27.04/7.48 | % 27.04/7.48 | Applying alpha-rule on (379) yields: % 27.04/7.48 | (380) doDivides0(xl, xm) = all_112_0_68 % 27.04/7.48 | (381) aNaturalNumber0(xm) = all_112_1_69 % 27.04/7.48 | (382) aNaturalNumber0(xl) = all_112_2_70 % 27.04/7.48 | (383) ~ (all_112_0_68 = 0) | ~ (all_112_1_69 = 0) | ~ (all_112_2_70 = 0) % 27.04/7.48 | % 27.04/7.48 | Instantiating formula (19) with xl, xm, all_112_0_68, 0 and discharging atoms doDivides0(xl, xm) = all_112_0_68, doDivides0(xl, xm) = 0, yields: % 27.04/7.48 | (384) all_112_0_68 = 0 % 27.04/7.48 | % 27.04/7.48 | Instantiating formula (58) with xm, all_112_1_69, 0 and discharging atoms aNaturalNumber0(xm) = all_112_1_69, aNaturalNumber0(xm) = 0, yields: % 27.04/7.48 | (385) all_112_1_69 = 0 % 27.04/7.48 | % 27.04/7.48 | Instantiating formula (58) with xl, all_112_2_70, 0 and discharging atoms aNaturalNumber0(xl) = all_112_2_70, aNaturalNumber0(xl) = 0, yields: % 27.04/7.48 | (377) all_112_2_70 = 0 % 27.04/7.48 | % 27.04/7.48 +-Applying beta-rule and splitting (383), into two cases. % 27.04/7.48 |-Branch one: % 27.04/7.48 | (387) ~ (all_112_0_68 = 0) % 27.04/7.48 | % 27.04/7.48 | Equations (384) can reduce 387 to: % 27.04/7.48 | (83) $false % 27.04/7.48 | % 27.04/7.48 |-The branch is then unsatisfiable % 27.04/7.48 |-Branch two: % 27.04/7.48 | (384) all_112_0_68 = 0 % 27.04/7.48 | (390) ~ (all_112_1_69 = 0) | ~ (all_112_2_70 = 0) % 27.04/7.48 | % 27.04/7.48 +-Applying beta-rule and splitting (390), into two cases. % 27.04/7.48 |-Branch one: % 27.04/7.48 | (391) ~ (all_112_1_69 = 0) % 27.04/7.48 | % 27.04/7.48 | Equations (385) can reduce 391 to: % 27.04/7.48 | (83) $false % 27.04/7.48 | % 27.04/7.48 |-The branch is then unsatisfiable % 27.04/7.48 |-Branch two: % 27.04/7.48 | (385) all_112_1_69 = 0 % 27.04/7.48 | (375) ~ (all_112_2_70 = 0) % 27.04/7.48 | % 27.04/7.48 | Equations (377) can reduce 375 to: % 27.04/7.48 | (83) $false % 27.04/7.48 | % 27.04/7.48 |-The branch is then unsatisfiable % 27.04/7.48 |-Branch two: % 27.04/7.48 | (396) ~ (all_13_2_13 = xq) % 27.04/7.48 | (397) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & aNaturalNumber0(all_13_2_13) = v0) | (doDivides0(xl, all_0_1_1) = v2 & aNaturalNumber0(all_0_1_1) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))) % 27.04/7.48 | % 27.04/7.48 | Instantiating (397) with all_108_0_74, all_108_1_75, all_108_2_76 yields: % 27.04/7.48 | (398) ( ~ (all_108_2_76 = 0) & aNaturalNumber0(all_13_2_13) = all_108_2_76) | (doDivides0(xl, all_0_1_1) = all_108_0_74 & aNaturalNumber0(all_0_1_1) = all_108_1_75 & aNaturalNumber0(xl) = all_108_2_76 & ( ~ (all_108_0_74 = 0) | ~ (all_108_1_75 = 0) | ~ (all_108_2_76 = 0))) % 27.04/7.48 | % 27.04/7.48 +-Applying beta-rule and splitting (398), into two cases. % 27.04/7.48 |-Branch one: % 27.04/7.48 | (399) ~ (all_108_2_76 = 0) & aNaturalNumber0(all_13_2_13) = all_108_2_76 % 27.04/7.48 | % 27.04/7.48 | Applying alpha-rule on (399) yields: % 27.04/7.48 | (400) ~ (all_108_2_76 = 0) % 27.04/7.48 | (401) aNaturalNumber0(all_13_2_13) = all_108_2_76 % 27.04/7.48 | % 27.04/7.48 | Instantiating formula (58) with all_13_2_13, all_108_2_76, 0 and discharging atoms aNaturalNumber0(all_13_2_13) = all_108_2_76, aNaturalNumber0(all_13_2_13) = 0, yields: % 27.04/7.48 | (402) all_108_2_76 = 0 % 27.04/7.48 | % 27.04/7.48 | Equations (402) can reduce 400 to: % 27.04/7.48 | (83) $false % 27.04/7.48 | % 27.04/7.48 |-The branch is then unsatisfiable % 27.04/7.48 |-Branch two: % 27.04/7.48 | (404) doDivides0(xl, all_0_1_1) = all_108_0_74 & aNaturalNumber0(all_0_1_1) = all_108_1_75 & aNaturalNumber0(xl) = all_108_2_76 & ( ~ (all_108_0_74 = 0) | ~ (all_108_1_75 = 0) | ~ (all_108_2_76 = 0)) % 27.04/7.48 | % 27.04/7.48 | Applying alpha-rule on (404) yields: % 27.04/7.48 | (405) doDivides0(xl, all_0_1_1) = all_108_0_74 % 27.04/7.48 | (406) aNaturalNumber0(all_0_1_1) = all_108_1_75 % 27.04/7.48 | (407) aNaturalNumber0(xl) = all_108_2_76 % 27.04/7.48 | (408) ~ (all_108_0_74 = 0) | ~ (all_108_1_75 = 0) | ~ (all_108_2_76 = 0) % 27.04/7.48 | % 27.04/7.48 | Instantiating formula (19) with xl, all_0_1_1, all_108_0_74, 0 and discharging atoms doDivides0(xl, all_0_1_1) = all_108_0_74, doDivides0(xl, all_0_1_1) = 0, yields: % 27.04/7.48 | (409) all_108_0_74 = 0 % 27.04/7.48 | % 27.04/7.48 | Instantiating formula (58) with all_0_1_1, all_108_1_75, 0 and discharging atoms aNaturalNumber0(all_0_1_1) = all_108_1_75, aNaturalNumber0(all_0_1_1) = 0, yields: % 27.04/7.48 | (410) all_108_1_75 = 0 % 27.04/7.48 | % 27.04/7.48 | Instantiating formula (58) with xl, all_108_2_76, 0 and discharging atoms aNaturalNumber0(xl) = all_108_2_76, aNaturalNumber0(xl) = 0, yields: % 27.04/7.48 | (402) all_108_2_76 = 0 % 27.04/7.48 | % 27.04/7.48 +-Applying beta-rule and splitting (408), into two cases. % 27.04/7.48 |-Branch one: % 27.04/7.48 | (412) ~ (all_108_0_74 = 0) % 27.04/7.48 | % 27.04/7.48 | Equations (409) can reduce 412 to: % 27.04/7.48 | (83) $false % 27.04/7.48 | % 27.04/7.48 |-The branch is then unsatisfiable % 27.04/7.48 |-Branch two: % 27.04/7.48 | (409) all_108_0_74 = 0 % 27.04/7.48 | (415) ~ (all_108_1_75 = 0) | ~ (all_108_2_76 = 0) % 27.04/7.48 | % 27.04/7.48 +-Applying beta-rule and splitting (415), into two cases. % 27.04/7.48 |-Branch one: % 27.04/7.48 | (416) ~ (all_108_1_75 = 0) % 27.04/7.48 | % 27.04/7.48 | Equations (410) can reduce 416 to: % 27.04/7.48 | (83) $false % 27.04/7.48 | % 27.04/7.48 |-The branch is then unsatisfiable % 27.04/7.48 |-Branch two: % 27.04/7.48 | (410) all_108_1_75 = 0 % 27.04/7.48 | (400) ~ (all_108_2_76 = 0) % 27.04/7.48 | % 27.04/7.48 | Equations (402) can reduce 400 to: % 27.04/7.48 | (83) $false % 27.04/7.48 | % 27.04/7.48 |-The branch is then unsatisfiable % 27.04/7.49 |-Branch two: % 27.04/7.49 | (421) aNaturalNumber0(all_0_1_1) = all_14_1_15 & aNaturalNumber0(xm) = all_14_2_16 & ( ~ (all_14_1_15 = 0) | ~ (all_14_2_16 = 0)) % 27.04/7.49 | % 27.04/7.49 | Applying alpha-rule on (421) yields: % 27.04/7.49 | (422) aNaturalNumber0(all_0_1_1) = all_14_1_15 % 27.04/7.49 | (423) aNaturalNumber0(xm) = all_14_2_16 % 27.04/7.49 | (424) ~ (all_14_1_15 = 0) | ~ (all_14_2_16 = 0) % 27.04/7.49 | % 27.04/7.49 | Instantiating formula (58) with all_0_1_1, all_14_1_15, 0 and discharging atoms aNaturalNumber0(all_0_1_1) = all_14_1_15, aNaturalNumber0(all_0_1_1) = 0, yields: % 27.04/7.49 | (120) all_14_1_15 = 0 % 27.04/7.49 | % 27.04/7.49 | Instantiating formula (58) with xm, all_14_2_16, 0 and discharging atoms aNaturalNumber0(xm) = all_14_2_16, aNaturalNumber0(xm) = 0, yields: % 27.04/7.49 | (426) all_14_2_16 = 0 % 27.04/7.49 | % 27.04/7.49 +-Applying beta-rule and splitting (424), into two cases. % 27.04/7.49 |-Branch one: % 27.04/7.49 | (427) ~ (all_14_1_15 = 0) % 27.04/7.49 | % 27.04/7.49 | Equations (120) can reduce 427 to: % 27.04/7.49 | (83) $false % 27.04/7.49 | % 27.04/7.49 |-The branch is then unsatisfiable % 27.04/7.49 |-Branch two: % 27.04/7.49 | (120) all_14_1_15 = 0 % 27.04/7.49 | (430) ~ (all_14_2_16 = 0) % 27.04/7.49 | % 27.04/7.49 | Equations (426) can reduce 430 to: % 27.04/7.49 | (83) $false % 27.04/7.49 | % 27.04/7.49 |-The branch is then unsatisfiable % 27.04/7.49 |-Branch two: % 27.04/7.49 | (432) aNaturalNumber0(all_0_1_1) = all_13_1_12 & aNaturalNumber0(xl) = all_13_2_13 & ( ~ (all_13_1_12 = 0) | ~ (all_13_2_13 = 0)) % 27.04/7.49 | % 27.04/7.49 | Applying alpha-rule on (432) yields: % 27.04/7.49 | (433) aNaturalNumber0(all_0_1_1) = all_13_1_12 % 27.04/7.49 | (434) aNaturalNumber0(xl) = all_13_2_13 % 27.04/7.49 | (435) ~ (all_13_1_12 = 0) | ~ (all_13_2_13 = 0) % 27.04/7.49 | % 27.04/7.49 | Instantiating formula (58) with all_0_1_1, all_13_1_12, 0 and discharging atoms aNaturalNumber0(all_0_1_1) = all_13_1_12, aNaturalNumber0(all_0_1_1) = 0, yields: % 27.04/7.49 | (115) all_13_1_12 = 0 % 27.04/7.49 | % 27.04/7.49 | Instantiating formula (58) with xl, all_13_2_13, 0 and discharging atoms aNaturalNumber0(xl) = all_13_2_13, aNaturalNumber0(xl) = 0, yields: % 27.04/7.49 | (437) all_13_2_13 = 0 % 27.04/7.49 | % 27.04/7.49 +-Applying beta-rule and splitting (435), into two cases. % 27.04/7.49 |-Branch one: % 27.04/7.49 | (438) ~ (all_13_1_12 = 0) % 27.04/7.49 | % 27.04/7.49 | Equations (115) can reduce 438 to: % 27.04/7.49 | (83) $false % 27.04/7.49 | % 27.04/7.49 |-The branch is then unsatisfiable % 27.04/7.49 |-Branch two: % 27.04/7.49 | (115) all_13_1_12 = 0 % 27.04/7.49 | (441) ~ (all_13_2_13 = 0) % 27.04/7.49 | % 27.04/7.49 | Equations (437) can reduce 441 to: % 27.04/7.49 | (83) $false % 27.04/7.49 | % 27.04/7.49 |-The branch is then unsatisfiable % 27.04/7.49 |-Branch two: % 27.04/7.49 | (443) aNaturalNumber0(xm) = all_12_1_9 & aNaturalNumber0(xl) = all_12_2_10 & ( ~ (all_12_1_9 = 0) | ~ (all_12_2_10 = 0)) % 27.04/7.49 | % 27.04/7.49 | Applying alpha-rule on (443) yields: % 27.04/7.49 | (444) aNaturalNumber0(xm) = all_12_1_9 % 27.04/7.49 | (445) aNaturalNumber0(xl) = all_12_2_10 % 27.04/7.49 | (446) ~ (all_12_1_9 = 0) | ~ (all_12_2_10 = 0) % 27.04/7.49 | % 27.04/7.49 | Instantiating formula (58) with xm, all_12_1_9, 0 and discharging atoms aNaturalNumber0(xm) = all_12_1_9, aNaturalNumber0(xm) = 0, yields: % 27.04/7.49 | (101) all_12_1_9 = 0 % 27.04/7.49 | % 27.04/7.49 | Instantiating formula (58) with xl, all_12_2_10, 0 and discharging atoms aNaturalNumber0(xl) = all_12_2_10, aNaturalNumber0(xl) = 0, yields: % 27.04/7.49 | (448) all_12_2_10 = 0 % 27.04/7.49 | % 27.04/7.49 +-Applying beta-rule and splitting (446), into two cases. % 27.04/7.49 |-Branch one: % 27.04/7.49 | (449) ~ (all_12_1_9 = 0) % 27.04/7.49 | % 27.04/7.49 | Equations (101) can reduce 449 to: % 27.04/7.49 | (83) $false % 27.04/7.49 | % 27.04/7.49 |-The branch is then unsatisfiable % 27.04/7.49 |-Branch two: % 27.04/7.49 | (101) all_12_1_9 = 0 % 27.04/7.49 | (452) ~ (all_12_2_10 = 0) % 27.04/7.49 | % 27.04/7.49 | Equations (448) can reduce 452 to: % 27.04/7.49 | (83) $false % 27.04/7.49 | % 27.04/7.49 |-The branch is then unsatisfiable % 27.04/7.49 % SZS output end Proof for theBenchmark % 27.04/7.49 % 27.04/7.49 6871ms 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