%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : NUM462+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 08:44:43 EDT 2022 % Result : Theorem 6.72s 2.21s % Output : Proof 13.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : NUM462+1 : TPTP v8.1.0. Released v4.0.0. % 0.10/0.13 % 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 09:11:44 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.59 ____ _ % 0.19/0.59 ___ / __ \_____(_)___ ________ __________ % 0.19/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic % 0.19/0.59 (ePrincess v.1.0) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2015 % 0.19/0.59 (c) Peter Backeman, 2014-2015 % 0.19/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.59 Bug reports to peter@backeman.se % 0.19/0.59 % 0.19/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.69/0.96 Prover 0: Preprocessing ... % 2.77/1.33 Prover 0: Constructing countermodel ... % 6.72/2.21 Prover 0: proved (1567ms) % 6.72/2.21 % 6.72/2.21 No countermodel exists, formula is valid % 6.72/2.21 % SZS status Theorem for theBenchmark % 6.72/2.21 % 6.72/2.21 Generating proof ... found it (size 154) % 12.59/3.58 % 12.59/3.58 % SZS output start Proof for theBenchmark % 12.59/3.58 Assumed formulas after preprocessing and simplification: % 12.59/3.58 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (xn = xl) & ~ (xm = sz00) & ~ (sz10 = sz00) & sdtasdt0(xn, xm) = v3 & sdtasdt0(xl, xm) = v2 & sdtasdt0(xm, xn) = v1 & sdtasdt0(xm, xl) = v0 & sdtlseqdt0(xl, xn) & aNaturalNumber0(xn) & aNaturalNumber0(xl) & aNaturalNumber0(xm) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v6, v4) = v8) | ~ (sdtasdt0(v5, v4) = v7) | ~ (sdtpldt0(v7, v8) = v9) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (sdtasdt0(v10, v4) = v9 & sdtasdt0(v4, v10) = v11 & sdtasdt0(v4, v6) = v13 & sdtasdt0(v4, v5) = v12 & sdtpldt0(v12, v13) = v11 & sdtpldt0(v5, v6) = v10)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v4, v6) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ (sdtpldt0(v7, v8) = v9) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (sdtasdt0(v10, v4) = v11 & sdtasdt0(v6, v4) = v13 & sdtasdt0(v5, v4) = v12 & sdtasdt0(v4, v10) = v9 & sdtpldt0(v12, v13) = v11 & sdtpldt0(v5, v6) = v10)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v8) | ~ (sdtasdt0(v5, v4) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtasdt0(v4, v6) = v10 & sdtasdt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtasdt0(v5, v4) = v10 & sdtasdt0(v4, v6) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v5, v4) = v8) | ~ (sdtasdt0(v4, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtasdt0(v6, v4) = v10 & sdtasdt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v4, v6) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtasdt0(v6, v4) = v10 & sdtasdt0(v5, v4) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v6, v4) = v8) | ~ (sdtpldt0(v5, v4) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtpldt0(v4, v6) = v10 & sdtpldt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v6, v4) = v8) | ~ (sdtpldt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtpldt0(v5, v4) = v10 & sdtpldt0(v4, v6) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v5, v4) = v8) | ~ (sdtpldt0(v4, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtpldt0(v6, v4) = v10 & sdtpldt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v4, v6) = v8) | ~ (sdtpldt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtpldt0(v6, v4) = v10 & sdtpldt0(v5, v4) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v7, v6) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : (sdtasdt0(v5, v6) = v9 & sdtasdt0(v4, v9) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v7, v4) = v8) | ~ (sdtpldt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (sdtasdt0(v6, v4) = v13 & sdtasdt0(v5, v4) = v12 & sdtasdt0(v4, v7) = v9 & sdtasdt0(v4, v6) = v11 & sdtasdt0(v4, v5) = v10 & sdtpldt0(v12, v13) = v8 & sdtpldt0(v10, v11) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v5, v6) = v7) | ~ (sdtasdt0(v4, v7) = v8) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : (sdtasdt0(v9, v6) = v8 & sdtasdt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v4, v7) = v8) | ~ (sdtpldt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (sdtasdt0(v7, v4) = v11 & sdtasdt0(v6, v4) = v13 & sdtasdt0(v5, v4) = v12 & sdtasdt0(v4, v6) = v10 & sdtasdt0(v4, v5) = v9 & sdtpldt0(v12, v13) = v11 & sdtpldt0(v9, v10) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v7, v6) = v8) | ~ (sdtpldt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : (sdtpldt0(v5, v6) = v9 & sdtpldt0(v4, v9) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ (sdtpldt0(v4, v7) = v8) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : (sdtpldt0(v9, v6) = v8 & sdtpldt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (sdtmndt0(v5, v4) = v6) | ~ (sdtpldt0(v4, v7) = v5) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (sdtmndt0(v5, v4) = v6) | ~ (sdtpldt0(v4, v6) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v7) | ~ (sdtasdt0(v5, v4) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v4, v6) = v7) | ~ (sdtasdt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (sdtpldt0(v6, v4) = v7) | ~ (sdtpldt0(v5, v4) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (sdtpldt0(v4, v6) = v7) | ~ (sdtpldt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtmndt0(v7, v6) = v5) | ~ (sdtmndt0(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtasdt0(v7, v6) = v5) | ~ (sdtasdt0(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v7, v6) = v5) | ~ (sdtpldt0(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v6, v5) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = v9) & ~ (v8 = v7) & sdtpldt0(v6, v4) = v8 & sdtpldt0(v5, v6) = v10 & sdtpldt0(v4, v6) = v9 & sdtlseqdt0(v9, v10) & sdtlseqdt0(v8, v7))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v6, v4) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = v9) & ~ (v8 = v7) & sdtpldt0(v6, v5) = v8 & sdtpldt0(v5, v6) = v10 & sdtpldt0(v4, v6) = v9 & sdtlseqdt0(v9, v10) & sdtlseqdt0(v7, v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v5, v6) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = v7) & ~ (v9 = v8) & sdtpldt0(v6, v5) = v9 & sdtpldt0(v6, v4) = v8 & sdtpldt0(v4, v6) = v10 & sdtlseqdt0(v10, v7) & sdtlseqdt0(v8, v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v4, v6) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = v7) & ~ (v9 = v8) & sdtpldt0(v6, v5) = v9 & sdtpldt0(v6, v4) = v8 & sdtpldt0(v5, v6) = v10 & sdtlseqdt0(v8, v9) & sdtlseqdt0(v7, v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtmndt0(v5, v4) = v6) | ~ (sdtpldt0(v4, v6) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | aNaturalNumber0(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, v4) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtasdt0(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v4, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtasdt0(v5, v4) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v4, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | aNaturalNumber0(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v5, v4) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtpldt0(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v4, v6) = v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v4, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtpldt0(v5, v4) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v4, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | aNaturalNumber0(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ sdtlseqdt0(v5, v6) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v4, v6)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtasdt0(v4, sz10) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtasdt0(sz10, v4) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtpldt0(v4, sz00) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtpldt0(sz00, v4) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ sdtlseqdt0(v5, v4) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = sz00 | v4 = sz00 | ~ (sdtasdt0(v4, v5) = sz00) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = sz00 | ~ (sdtasdt0(v4, sz00) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = sz00 | ~ (sdtasdt0(sz00, v4) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = sz00 | ~ (sdtpldt0(v4, v5) = sz00) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v4 = sz00 | ~ (sdtpldt0(v4, v5) = sz00) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ( ~ (sdtasdt0(v4, sz10) = v5) | ~ aNaturalNumber0(v4) | sdtasdt0(sz10, v4) = v4) & ! [v4] : ! [v5] : ( ~ (sdtasdt0(v4, sz00) = v5) | ~ aNaturalNumber0(v4) | sdtasdt0(sz00, v4) = sz00) & ! [v4] : ! [v5] : ( ~ (sdtasdt0(sz10, v4) = v5) | ~ aNaturalNumber0(v4) | sdtasdt0(v4, sz10) = v4) & ! [v4] : ! [v5] : ( ~ (sdtasdt0(sz00, v4) = v5) | ~ aNaturalNumber0(v4) | sdtasdt0(v4, sz00) = sz00) & ! [v4] : ! [v5] : ( ~ (sdtpldt0(v4, sz00) = v5) | ~ aNaturalNumber0(v4) | sdtpldt0(sz00, v4) = v4) & ! [v4] : ! [v5] : ( ~ (sdtpldt0(sz00, v4) = v5) | ~ aNaturalNumber0(v4) | sdtpldt0(v4, sz00) = v4) & ! [v4] : ! [v5] : ( ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v6] : (sdtpldt0(v4, v6) = v5 & aNaturalNumber0(v6))) & ! [v4] : ! [v5] : ( ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v5, v4) | sdtlseqdt0(v4, v5)) & ! [v4] : ( ~ aNaturalNumber0(v4) | sdtlseqdt0(v4, v4)) & (v3 = v2 | v1 = v0 | ~ sdtlseqdt0(v2, v3) | ~ sdtlseqdt0(v0, v1))) % 12.88/3.64 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 12.88/3.64 | (1) ~ (xn = xl) & ~ (xm = sz00) & ~ (sz10 = sz00) & sdtasdt0(xn, xm) = all_0_0_0 & sdtasdt0(xl, xm) = all_0_1_1 & sdtasdt0(xm, xn) = all_0_2_2 & sdtasdt0(xm, xl) = all_0_3_3 & sdtlseqdt0(xl, xn) & aNaturalNumber0(xn) & aNaturalNumber0(xl) & aNaturalNumber0(xm) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v0, v2) = v6 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v6, v7) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v1) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v4, v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v0) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v1) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v1, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v0, v2) = v6 & sdtlseqdt0(v6, v3) & sdtlseqdt0(v4, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0) & ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2))) & ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) & ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) & (all_0_0_0 = all_0_1_1 | all_0_2_2 = all_0_3_3 | ~ sdtlseqdt0(all_0_1_1, all_0_0_0) | ~ sdtlseqdt0(all_0_3_3, all_0_2_2)) % 12.88/3.66 | % 12.88/3.66 | Applying alpha-rule on (1) yields: % 13.26/3.66 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2) % 13.26/3.66 | (3) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0) % 13.26/3.66 | (4) ~ (xm = sz00) % 13.26/3.66 | (5) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) % 13.26/3.67 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5)) % 13.26/3.67 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4)) % 13.26/3.67 | (8) sdtasdt0(xl, xm) = all_0_1_1 % 13.26/3.67 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5)) % 13.26/3.67 | (10) sdtasdt0(xn, xm) = all_0_0_0 % 13.26/3.67 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2) % 13.26/3.67 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 13.26/3.67 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v0) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v1) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v3, v4))) % 13.26/3.67 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4)) % 13.26/3.67 | (15) aNaturalNumber0(xl) % 13.26/3.67 | (16) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2))) % 13.26/3.67 | (17) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 13.26/3.67 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 13.26/3.67 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) % 13.26/3.67 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0)) % 13.26/3.67 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) % 13.26/3.67 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0)) % 13.26/3.67 | (23) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) % 13.26/3.67 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6))) % 13.26/3.67 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2)) % 13.26/3.67 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 13.26/3.67 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 13.26/3.67 | (28) aNaturalNumber0(sz00) % 13.26/3.67 | (29) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) % 13.26/3.67 | (30) sdtasdt0(xm, xl) = all_0_3_3 % 13.26/3.67 | (31) aNaturalNumber0(xn) % 13.26/3.67 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5)) % 13.26/3.68 | (33) sdtasdt0(xm, xn) = all_0_2_2 % 13.32/3.68 | (34) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0) % 13.32/3.68 | (35) aNaturalNumber0(xm) % 13.32/3.68 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5)) % 13.32/3.68 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v2, v1) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v4, v3))) % 13.32/3.68 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v1) = v5)) % 13.32/3.68 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2) % 13.32/3.68 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5)) % 13.32/3.68 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5)) % 13.32/3.68 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) % 13.32/3.68 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5)) % 13.32/3.68 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 13.32/3.68 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v6, v7) = v5)) % 13.32/3.68 | (46) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0) % 13.32/3.68 | (47) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 13.32/3.68 | (48) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 13.32/3.68 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 13.32/3.68 | (50) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00) % 13.32/3.68 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 13.32/3.68 | (52) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 13.32/3.68 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2) % 13.32/3.69 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) % 13.32/3.69 | (55) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0) % 13.32/3.69 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 13.32/3.69 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) % 13.32/3.69 | (58) sdtlseqdt0(xl, xn) % 13.32/3.69 | (59) ~ (xn = xl) % 13.32/3.69 | (60) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00) % 13.32/3.69 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 13.32/3.69 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 13.32/3.69 | (63) all_0_0_0 = all_0_1_1 | all_0_2_2 = all_0_3_3 | ~ sdtlseqdt0(all_0_1_1, all_0_0_0) | ~ sdtlseqdt0(all_0_3_3, all_0_2_2) % 13.32/3.69 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5)) % 13.32/3.69 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v0, v2) = v6 & sdtpldt0(v0, v1) = v5)) % 13.32/3.69 | (66) ~ (sz10 = sz00) % 13.32/3.69 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 13.32/3.69 | (68) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) % 13.32/3.69 | (69) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) % 13.32/3.69 | (70) aNaturalNumber0(sz10) % 13.32/3.69 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v1, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v0, v2) = v6 & sdtlseqdt0(v6, v3) & sdtlseqdt0(v4, v5))) % 13.32/3.69 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4)) % 13.32/3.69 | % 13.32/3.69 | Instantiating formula (16) with xn, xl and discharging atoms sdtlseqdt0(xl, xn), aNaturalNumber0(xn), aNaturalNumber0(xl), yields: % 13.32/3.69 | (73) ? [v0] : (sdtpldt0(xl, v0) = xn & aNaturalNumber0(v0)) % 13.32/3.69 | % 13.32/3.69 | Instantiating formula (9) with all_0_0_0, all_0_1_1, xn, xl, xm and discharging atoms sdtasdt0(xn, xm) = all_0_0_0, sdtasdt0(xl, xm) = all_0_1_1, aNaturalNumber0(xn), aNaturalNumber0(xl), aNaturalNumber0(xm), yields: % 13.32/3.69 | (74) xn = xl | xm = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xm, xn) = v1 & sdtasdt0(xm, xl) = v0) % 13.32/3.69 | % 13.32/3.69 | Instantiating formula (40) with all_0_0_0, all_0_3_3, xn, xl, xm and discharging atoms sdtasdt0(xn, xm) = all_0_0_0, sdtasdt0(xm, xl) = all_0_3_3, aNaturalNumber0(xn), aNaturalNumber0(xl), aNaturalNumber0(xm), yields: % 13.32/3.69 | (75) xn = xl | xm = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = all_0_0_0) & ~ (v0 = all_0_3_3) & sdtasdt0(xl, xm) = v1 & sdtasdt0(xm, xn) = v0) % 13.32/3.69 | % 13.32/3.69 | Instantiating formula (39) with all_0_0_0, xn, xm and discharging atoms sdtasdt0(xn, xm) = all_0_0_0, aNaturalNumber0(xn), aNaturalNumber0(xm), yields: % 13.32/3.69 | (76) sdtasdt0(xm, xn) = all_0_0_0 % 13.32/3.69 | % 13.32/3.69 | Instantiating formula (56) with all_0_0_0, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_0_0, aNaturalNumber0(xn), aNaturalNumber0(xm), yields: % 13.32/3.69 | (77) aNaturalNumber0(all_0_0_0) % 13.32/3.70 | % 13.32/3.70 | Instantiating formula (9) with all_0_1_1, all_0_0_0, xl, xn, xm and discharging atoms sdtasdt0(xn, xm) = all_0_0_0, sdtasdt0(xl, xm) = all_0_1_1, aNaturalNumber0(xn), aNaturalNumber0(xl), aNaturalNumber0(xm), yields: % 13.32/3.70 | (78) xn = xl | xm = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xm, xn) = v0 & sdtasdt0(xm, xl) = v1) % 13.32/3.70 | % 13.32/3.70 | Instantiating formula (41) with all_0_1_1, all_0_2_2, xn, xl, xm and discharging atoms sdtasdt0(xl, xm) = all_0_1_1, sdtasdt0(xm, xn) = all_0_2_2, aNaturalNumber0(xn), aNaturalNumber0(xl), aNaturalNumber0(xm), yields: % 13.32/3.70 | (79) xn = xl | xm = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = all_0_1_1) & ~ (v0 = all_0_2_2) & sdtasdt0(xn, xm) = v1 & sdtasdt0(xm, xl) = v0) % 13.32/3.70 | % 13.32/3.70 | Instantiating formula (56) with all_0_1_1, xm, xl and discharging atoms sdtasdt0(xl, xm) = all_0_1_1, aNaturalNumber0(xl), aNaturalNumber0(xm), yields: % 13.32/3.70 | (80) aNaturalNumber0(all_0_1_1) % 13.32/3.70 | % 13.32/3.70 | Instantiating formula (39) with all_0_2_2, xm, xn and discharging atoms sdtasdt0(xm, xn) = all_0_2_2, aNaturalNumber0(xn), aNaturalNumber0(xm), yields: % 13.32/3.70 | (81) sdtasdt0(xn, xm) = all_0_2_2 % 13.32/3.70 | % 13.32/3.70 | Instantiating formula (64) with all_0_3_3, all_0_2_2, xl, xn, xm and discharging atoms sdtasdt0(xm, xn) = all_0_2_2, sdtasdt0(xm, xl) = all_0_3_3, aNaturalNumber0(xn), aNaturalNumber0(xl), aNaturalNumber0(xm), yields: % 13.32/3.70 | (82) xn = xl | xm = sz00 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xn, xm) = v0 & sdtasdt0(xl, xm) = v1) % 13.32/3.70 | % 13.32/3.70 | Instantiating formula (39) with all_0_3_3, xm, xl and discharging atoms sdtasdt0(xm, xl) = all_0_3_3, aNaturalNumber0(xl), aNaturalNumber0(xm), yields: % 13.32/3.70 | (83) sdtasdt0(xl, xm) = all_0_3_3 % 13.32/3.70 | % 13.32/3.70 | Instantiating formula (23) with xm, xm and discharging atoms aNaturalNumber0(xm), yields: % 13.32/3.70 | (84) sdtlseqdt0(xm, xm) % 13.32/3.70 | % 13.32/3.70 | Instantiating (73) with all_9_0_4 yields: % 13.32/3.70 | (85) sdtpldt0(xl, all_9_0_4) = xn & aNaturalNumber0(all_9_0_4) % 13.32/3.70 | % 13.32/3.70 | Applying alpha-rule on (85) yields: % 13.32/3.70 | (86) sdtpldt0(xl, all_9_0_4) = xn % 13.32/3.70 | (87) aNaturalNumber0(all_9_0_4) % 13.32/3.70 | % 13.32/3.70 +-Applying beta-rule and splitting (82), into two cases. % 13.32/3.70 |-Branch one: % 13.32/3.70 | (88) xm = sz00 % 13.32/3.70 | % 13.32/3.70 | Equations (88) can reduce 4 to: % 13.32/3.70 | (89) $false % 13.32/3.70 | % 13.32/3.70 |-The branch is then unsatisfiable % 13.32/3.70 |-Branch two: % 13.32/3.70 | (4) ~ (xm = sz00) % 13.32/3.70 | (91) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xn, xm) = v0 & sdtasdt0(xl, xm) = v1) % 13.32/3.70 | % 13.32/3.70 +-Applying beta-rule and splitting (91), into two cases. % 13.32/3.70 |-Branch one: % 13.32/3.70 | (92) xn = xl % 13.32/3.70 | % 13.32/3.70 | Equations (92) can reduce 59 to: % 13.32/3.70 | (89) $false % 13.32/3.70 | % 13.32/3.70 |-The branch is then unsatisfiable % 13.32/3.70 |-Branch two: % 13.32/3.70 | (59) ~ (xn = xl) % 13.32/3.70 | (95) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xn, xm) = v0 & sdtasdt0(xl, xm) = v1) % 13.32/3.70 | % 13.32/3.70 | Instantiating (95) with all_19_0_5, all_19_1_6 yields: % 13.32/3.70 | (96) ~ (all_19_0_5 = all_19_1_6) & sdtasdt0(xn, xm) = all_19_1_6 & sdtasdt0(xl, xm) = all_19_0_5 % 13.32/3.70 | % 13.32/3.70 | Applying alpha-rule on (96) yields: % 13.32/3.70 | (97) ~ (all_19_0_5 = all_19_1_6) % 13.32/3.70 | (98) sdtasdt0(xn, xm) = all_19_1_6 % 13.32/3.70 | (99) sdtasdt0(xl, xm) = all_19_0_5 % 13.32/3.70 | % 13.32/3.70 +-Applying beta-rule and splitting (79), into two cases. % 13.32/3.70 |-Branch one: % 13.32/3.70 | (88) xm = sz00 % 13.32/3.70 | % 13.32/3.70 | Equations (88) can reduce 4 to: % 13.32/3.70 | (89) $false % 13.32/3.70 | % 13.32/3.70 |-The branch is then unsatisfiable % 13.32/3.70 |-Branch two: % 13.32/3.70 | (4) ~ (xm = sz00) % 13.32/3.70 | (103) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = all_0_1_1) & ~ (v0 = all_0_2_2) & sdtasdt0(xn, xm) = v1 & sdtasdt0(xm, xl) = v0) % 13.32/3.70 | % 13.32/3.70 +-Applying beta-rule and splitting (78), into two cases. % 13.32/3.70 |-Branch one: % 13.32/3.70 | (88) xm = sz00 % 13.32/3.70 | % 13.32/3.70 | Equations (88) can reduce 4 to: % 13.32/3.70 | (89) $false % 13.32/3.70 | % 13.32/3.70 |-The branch is then unsatisfiable % 13.32/3.70 |-Branch two: % 13.32/3.70 | (4) ~ (xm = sz00) % 13.32/3.70 | (107) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xm, xn) = v0 & sdtasdt0(xm, xl) = v1) % 13.32/3.70 | % 13.32/3.70 +-Applying beta-rule and splitting (107), into two cases. % 13.32/3.70 |-Branch one: % 13.32/3.70 | (92) xn = xl % 13.32/3.70 | % 13.32/3.70 | Equations (92) can reduce 59 to: % 13.32/3.70 | (89) $false % 13.32/3.70 | % 13.32/3.70 |-The branch is then unsatisfiable % 13.32/3.70 |-Branch two: % 13.32/3.70 | (59) ~ (xn = xl) % 13.32/3.70 | (111) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xm, xn) = v0 & sdtasdt0(xm, xl) = v1) % 13.32/3.70 | % 13.32/3.70 +-Applying beta-rule and splitting (103), into two cases. % 13.32/3.70 |-Branch one: % 13.32/3.70 | (92) xn = xl % 13.32/3.70 | % 13.32/3.70 | Equations (92) can reduce 59 to: % 13.32/3.70 | (89) $false % 13.32/3.70 | % 13.32/3.70 |-The branch is then unsatisfiable % 13.32/3.70 |-Branch two: % 13.32/3.70 | (59) ~ (xn = xl) % 13.32/3.70 | (115) ? [v0] : ? [v1] : ( ~ (v1 = all_0_1_1) & ~ (v0 = all_0_2_2) & sdtasdt0(xn, xm) = v1 & sdtasdt0(xm, xl) = v0) % 13.32/3.70 | % 13.32/3.70 | Instantiating (115) with all_39_0_9, all_39_1_10 yields: % 13.32/3.70 | (116) ~ (all_39_0_9 = all_0_1_1) & ~ (all_39_1_10 = all_0_2_2) & sdtasdt0(xn, xm) = all_39_0_9 & sdtasdt0(xm, xl) = all_39_1_10 % 13.32/3.71 | % 13.32/3.71 | Applying alpha-rule on (116) yields: % 13.32/3.71 | (117) ~ (all_39_0_9 = all_0_1_1) % 13.32/3.71 | (118) ~ (all_39_1_10 = all_0_2_2) % 13.32/3.71 | (119) sdtasdt0(xn, xm) = all_39_0_9 % 13.32/3.71 | (120) sdtasdt0(xm, xl) = all_39_1_10 % 13.32/3.71 | % 13.32/3.71 +-Applying beta-rule and splitting (75), into two cases. % 13.32/3.71 |-Branch one: % 13.32/3.71 | (88) xm = sz00 % 13.32/3.71 | % 13.32/3.71 | Equations (88) can reduce 4 to: % 13.32/3.71 | (89) $false % 13.32/3.71 | % 13.32/3.71 |-The branch is then unsatisfiable % 13.32/3.71 |-Branch two: % 13.32/3.71 | (4) ~ (xm = sz00) % 13.32/3.71 | (124) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = all_0_0_0) & ~ (v0 = all_0_3_3) & sdtasdt0(xl, xm) = v1 & sdtasdt0(xm, xn) = v0) % 13.32/3.71 | % 13.32/3.71 +-Applying beta-rule and splitting (74), into two cases. % 13.32/3.71 |-Branch one: % 13.32/3.71 | (88) xm = sz00 % 13.32/3.71 | % 13.32/3.71 | Equations (88) can reduce 4 to: % 13.32/3.71 | (89) $false % 13.32/3.71 | % 13.32/3.71 |-The branch is then unsatisfiable % 13.32/3.71 |-Branch two: % 13.32/3.71 | (4) ~ (xm = sz00) % 13.32/3.71 | (128) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xm, xn) = v1 & sdtasdt0(xm, xl) = v0) % 13.32/3.71 | % 13.32/3.71 +-Applying beta-rule and splitting (124), into two cases. % 13.32/3.71 |-Branch one: % 13.32/3.71 | (92) xn = xl % 13.32/3.71 | % 13.32/3.71 | Equations (92) can reduce 59 to: % 13.32/3.71 | (89) $false % 13.32/3.71 | % 13.32/3.71 |-The branch is then unsatisfiable % 13.32/3.71 |-Branch two: % 13.32/3.71 | (59) ~ (xn = xl) % 13.32/3.71 | (132) ? [v0] : ? [v1] : ( ~ (v1 = all_0_0_0) & ~ (v0 = all_0_3_3) & sdtasdt0(xl, xm) = v1 & sdtasdt0(xm, xn) = v0) % 13.32/3.71 | % 13.32/3.71 | Instantiating (132) with all_53_0_11, all_53_1_12 yields: % 13.32/3.71 | (133) ~ (all_53_0_11 = all_0_0_0) & ~ (all_53_1_12 = all_0_3_3) & sdtasdt0(xl, xm) = all_53_0_11 & sdtasdt0(xm, xn) = all_53_1_12 % 13.32/3.71 | % 13.32/3.71 | Applying alpha-rule on (133) yields: % 13.32/3.71 | (134) ~ (all_53_0_11 = all_0_0_0) % 13.32/3.71 | (135) ~ (all_53_1_12 = all_0_3_3) % 13.32/3.71 | (136) sdtasdt0(xl, xm) = all_53_0_11 % 13.49/3.71 | (137) sdtasdt0(xm, xn) = all_53_1_12 % 13.49/3.71 | % 13.49/3.71 +-Applying beta-rule and splitting (128), into two cases. % 13.49/3.71 |-Branch one: % 13.49/3.71 | (92) xn = xl % 13.49/3.71 | % 13.49/3.71 | Equations (92) can reduce 59 to: % 13.49/3.71 | (89) $false % 13.49/3.71 | % 13.49/3.71 |-The branch is then unsatisfiable % 13.49/3.71 |-Branch two: % 13.49/3.71 | (59) ~ (xn = xl) % 13.49/3.71 | (141) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtasdt0(xm, xn) = v1 & sdtasdt0(xm, xl) = v0) % 13.49/3.71 | % 13.49/3.71 | Instantiating formula (61) with xn, xm, all_19_1_6, all_0_0_0 and discharging atoms sdtasdt0(xn, xm) = all_19_1_6, sdtasdt0(xn, xm) = all_0_0_0, yields: % 13.49/3.71 | (142) all_19_1_6 = all_0_0_0 % 13.49/3.71 | % 13.49/3.71 | Instantiating formula (61) with xn, xm, all_19_1_6, all_39_0_9 and discharging atoms sdtasdt0(xn, xm) = all_39_0_9, sdtasdt0(xn, xm) = all_19_1_6, yields: % 13.49/3.71 | (143) all_39_0_9 = all_19_1_6 % 13.49/3.71 | % 13.49/3.71 | Instantiating formula (61) with xn, xm, all_0_2_2, all_39_0_9 and discharging atoms sdtasdt0(xn, xm) = all_39_0_9, sdtasdt0(xn, xm) = all_0_2_2, yields: % 13.49/3.71 | (144) all_39_0_9 = all_0_2_2 % 13.49/3.71 | % 13.49/3.71 | Instantiating formula (61) with xl, xm, all_53_0_11, all_0_1_1 and discharging atoms sdtasdt0(xl, xm) = all_53_0_11, sdtasdt0(xl, xm) = all_0_1_1, yields: % 13.49/3.71 | (145) all_53_0_11 = all_0_1_1 % 13.49/3.71 | % 13.49/3.71 | Instantiating formula (61) with xl, xm, all_19_0_5, all_53_0_11 and discharging atoms sdtasdt0(xl, xm) = all_53_0_11, sdtasdt0(xl, xm) = all_19_0_5, yields: % 13.49/3.71 | (146) all_53_0_11 = all_19_0_5 % 13.49/3.71 | % 13.49/3.71 | Instantiating formula (61) with xl, xm, all_0_3_3, all_19_0_5 and discharging atoms sdtasdt0(xl, xm) = all_19_0_5, sdtasdt0(xl, xm) = all_0_3_3, yields: % 13.49/3.71 | (147) all_19_0_5 = all_0_3_3 % 13.49/3.71 | % 13.49/3.71 | Combining equations (146,145) yields a new equation: % 13.49/3.71 | (148) all_19_0_5 = all_0_1_1 % 13.49/3.71 | % 13.49/3.71 | Simplifying 148 yields: % 13.49/3.71 | (149) all_19_0_5 = all_0_1_1 % 13.49/3.71 | % 13.49/3.71 | Combining equations (143,144) yields a new equation: % 13.49/3.71 | (150) all_19_1_6 = all_0_2_2 % 13.49/3.71 | % 13.49/3.71 | Simplifying 150 yields: % 13.49/3.71 | (151) all_19_1_6 = all_0_2_2 % 13.49/3.71 | % 13.49/3.71 | Combining equations (147,149) yields a new equation: % 13.49/3.71 | (152) all_0_1_1 = all_0_3_3 % 13.49/3.71 | % 13.49/3.71 | Combining equations (142,151) yields a new equation: % 13.49/3.71 | (153) all_0_0_0 = all_0_2_2 % 13.49/3.71 | % 13.49/3.71 | Simplifying 153 yields: % 13.49/3.71 | (154) all_0_0_0 = all_0_2_2 % 13.49/3.71 | % 13.49/3.71 | Combining equations (152,149) yields a new equation: % 13.49/3.71 | (147) all_19_0_5 = all_0_3_3 % 13.49/3.71 | % 13.49/3.71 | Equations (147,151) can reduce 97 to: % 13.49/3.71 | (156) ~ (all_0_2_2 = all_0_3_3) % 13.49/3.71 | % 13.49/3.71 | Simplifying 156 yields: % 13.49/3.71 | (157) ~ (all_0_2_2 = all_0_3_3) % 13.49/3.71 | % 13.49/3.71 | From (154) and (10) follows: % 13.49/3.71 | (81) sdtasdt0(xn, xm) = all_0_2_2 % 13.49/3.71 | % 13.49/3.71 | From (152) and (8) follows: % 13.49/3.71 | (83) sdtasdt0(xl, xm) = all_0_3_3 % 13.49/3.71 | % 13.49/3.71 | From (154) and (76) follows: % 13.49/3.71 | (33) sdtasdt0(xm, xn) = all_0_2_2 % 13.49/3.71 | % 13.49/3.71 | From (154) and (77) follows: % 13.49/3.71 | (161) aNaturalNumber0(all_0_2_2) % 13.49/3.71 | % 13.49/3.71 | From (152) and (80) follows: % 13.49/3.72 | (162) aNaturalNumber0(all_0_3_3) % 13.49/3.72 | % 13.49/3.72 +-Applying beta-rule and splitting (63), into two cases. % 13.49/3.72 |-Branch one: % 13.49/3.72 | (163) ~ sdtlseqdt0(all_0_1_1, all_0_0_0) % 13.49/3.72 | % 13.49/3.72 | From (152)(154) and (163) follows: % 13.49/3.72 | (164) ~ sdtlseqdt0(all_0_3_3, all_0_2_2) % 13.49/3.72 | % 13.49/3.72 | Instantiating formula (16) with xm, xm and discharging atoms sdtlseqdt0(xm, xm), aNaturalNumber0(xm), yields: % 13.49/3.72 | (165) ? [v0] : (sdtpldt0(xm, v0) = xm & aNaturalNumber0(v0)) % 13.49/3.72 | % 13.49/3.72 | Instantiating formula (72) with all_0_2_2, xn, all_9_0_4, xl, xm and discharging atoms sdtasdt0(xm, xn) = all_0_2_2, sdtpldt0(xl, all_9_0_4) = xn, aNaturalNumber0(all_9_0_4), aNaturalNumber0(xl), aNaturalNumber0(xm), yields: % 13.49/3.72 | (166) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_9_0_4, xm) = v4 & sdtasdt0(xn, xm) = v2 & sdtasdt0(xl, xm) = v3 & sdtasdt0(xm, all_9_0_4) = v1 & sdtasdt0(xm, xl) = v0 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_0_2_2) % 13.49/3.72 | % 13.49/3.72 | Instantiating formula (45) with all_0_2_2, xn, all_9_0_4, xl, xm and discharging atoms sdtasdt0(xn, xm) = all_0_2_2, sdtpldt0(xl, all_9_0_4) = xn, aNaturalNumber0(all_9_0_4), aNaturalNumber0(xl), aNaturalNumber0(xm), yields: % 13.49/3.72 | (167) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_9_0_4, xm) = v4 & sdtasdt0(xl, xm) = v3 & sdtasdt0(xm, all_9_0_4) = v2 & sdtasdt0(xm, xn) = v0 & sdtasdt0(xm, xl) = v1 & sdtpldt0(v3, v4) = all_0_2_2 & sdtpldt0(v1, v2) = v0) % 13.49/3.72 | % 13.49/3.72 | Instantiating formula (24) with xn, all_9_0_4, xn, xl and discharging atoms sdtpldt0(xl, all_9_0_4) = xn, sdtlseqdt0(xl, xn), aNaturalNumber0(all_9_0_4), aNaturalNumber0(xn), aNaturalNumber0(xl), yields: % 13.49/3.72 | (168) xn = xl | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xn) & ~ (v1 = v0) & sdtpldt0(all_9_0_4, xn) = v1 & sdtpldt0(all_9_0_4, xl) = v0 & sdtpldt0(xn, all_9_0_4) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xn, v2)) % 13.49/3.72 | % 13.49/3.72 | Instantiating formula (53) with xn, xl, all_9_0_4 and discharging atoms sdtpldt0(xl, all_9_0_4) = xn, aNaturalNumber0(all_9_0_4), aNaturalNumber0(xl), yields: % 13.49/3.72 | (169) sdtpldt0(all_9_0_4, xl) = xn % 13.49/3.72 | % 13.49/3.72 | Instantiating (167) with all_75_0_15, all_75_1_16, all_75_2_17, all_75_3_18, all_75_4_19 yields: % 13.49/3.72 | (170) sdtasdt0(all_9_0_4, xm) = all_75_0_15 & sdtasdt0(xl, xm) = all_75_1_16 & sdtasdt0(xm, all_9_0_4) = all_75_2_17 & sdtasdt0(xm, xn) = all_75_4_19 & sdtasdt0(xm, xl) = all_75_3_18 & sdtpldt0(all_75_1_16, all_75_0_15) = all_0_2_2 & sdtpldt0(all_75_3_18, all_75_2_17) = all_75_4_19 % 13.49/3.72 | % 13.49/3.72 | Applying alpha-rule on (170) yields: % 13.49/3.72 | (171) sdtasdt0(all_9_0_4, xm) = all_75_0_15 % 13.49/3.72 | (172) sdtasdt0(xm, xl) = all_75_3_18 % 13.49/3.72 | (173) sdtpldt0(all_75_1_16, all_75_0_15) = all_0_2_2 % 13.49/3.72 | (174) sdtasdt0(xm, xn) = all_75_4_19 % 13.49/3.72 | (175) sdtasdt0(xm, all_9_0_4) = all_75_2_17 % 13.49/3.72 | (176) sdtpldt0(all_75_3_18, all_75_2_17) = all_75_4_19 % 13.49/3.72 | (177) sdtasdt0(xl, xm) = all_75_1_16 % 13.49/3.72 | % 13.49/3.72 | Instantiating (166) with all_83_0_23, all_83_1_24, all_83_2_25, all_83_3_26, all_83_4_27 yields: % 13.49/3.72 | (178) sdtasdt0(all_9_0_4, xm) = all_83_0_23 & sdtasdt0(xn, xm) = all_83_2_25 & sdtasdt0(xl, xm) = all_83_1_24 & sdtasdt0(xm, all_9_0_4) = all_83_3_26 & sdtasdt0(xm, xl) = all_83_4_27 & sdtpldt0(all_83_1_24, all_83_0_23) = all_83_2_25 & sdtpldt0(all_83_4_27, all_83_3_26) = all_0_2_2 % 13.49/3.72 | % 13.49/3.72 | Applying alpha-rule on (178) yields: % 13.49/3.72 | (179) sdtasdt0(xm, xl) = all_83_4_27 % 13.49/3.72 | (180) sdtpldt0(all_83_4_27, all_83_3_26) = all_0_2_2 % 13.49/3.72 | (181) sdtasdt0(xn, xm) = all_83_2_25 % 13.49/3.72 | (182) sdtasdt0(xm, all_9_0_4) = all_83_3_26 % 13.49/3.72 | (183) sdtasdt0(all_9_0_4, xm) = all_83_0_23 % 13.49/3.72 | (184) sdtasdt0(xl, xm) = all_83_1_24 % 13.49/3.72 | (185) sdtpldt0(all_83_1_24, all_83_0_23) = all_83_2_25 % 13.49/3.72 | % 13.49/3.72 | Instantiating (165) with all_85_0_28 yields: % 13.49/3.72 | (186) sdtpldt0(xm, all_85_0_28) = xm & aNaturalNumber0(all_85_0_28) % 13.49/3.72 | % 13.49/3.72 | Applying alpha-rule on (186) yields: % 13.49/3.72 | (187) sdtpldt0(xm, all_85_0_28) = xm % 13.49/3.72 | (188) aNaturalNumber0(all_85_0_28) % 13.49/3.72 | % 13.49/3.72 +-Applying beta-rule and splitting (168), into two cases. % 13.49/3.72 |-Branch one: % 13.49/3.72 | (92) xn = xl % 13.49/3.72 | % 13.49/3.72 | Equations (92) can reduce 59 to: % 13.49/3.72 | (89) $false % 13.49/3.72 | % 13.49/3.72 |-The branch is then unsatisfiable % 13.49/3.72 |-Branch two: % 13.49/3.72 | (59) ~ (xn = xl) % 13.49/3.72 | (192) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xn) & ~ (v1 = v0) & sdtpldt0(all_9_0_4, xn) = v1 & sdtpldt0(all_9_0_4, xl) = v0 & sdtpldt0(xn, all_9_0_4) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xn, v2)) % 13.49/3.72 | % 13.49/3.72 | Instantiating (192) with all_93_0_30, all_93_1_31, all_93_2_32 yields: % 13.49/3.72 | (193) ~ (all_93_0_30 = xn) & ~ (all_93_1_31 = all_93_2_32) & sdtpldt0(all_9_0_4, xn) = all_93_1_31 & sdtpldt0(all_9_0_4, xl) = all_93_2_32 & sdtpldt0(xn, all_9_0_4) = all_93_0_30 & sdtlseqdt0(all_93_2_32, all_93_1_31) & sdtlseqdt0(xn, all_93_0_30) % 13.49/3.72 | % 13.49/3.72 | Applying alpha-rule on (193) yields: % 13.49/3.72 | (194) sdtpldt0(xn, all_9_0_4) = all_93_0_30 % 13.49/3.73 | (195) sdtlseqdt0(all_93_2_32, all_93_1_31) % 13.49/3.73 | (196) sdtlseqdt0(xn, all_93_0_30) % 13.49/3.73 | (197) sdtpldt0(all_9_0_4, xn) = all_93_1_31 % 13.49/3.73 | (198) ~ (all_93_0_30 = xn) % 13.49/3.73 | (199) sdtpldt0(all_9_0_4, xl) = all_93_2_32 % 13.49/3.73 | (200) ~ (all_93_1_31 = all_93_2_32) % 13.49/3.73 | % 13.49/3.73 | Instantiating formula (61) with all_9_0_4, xm, all_75_0_15, all_83_0_23 and discharging atoms sdtasdt0(all_9_0_4, xm) = all_83_0_23, sdtasdt0(all_9_0_4, xm) = all_75_0_15, yields: % 13.49/3.73 | (201) all_83_0_23 = all_75_0_15 % 13.49/3.73 | % 13.49/3.73 | Instantiating formula (61) with xn, xm, all_83_2_25, all_0_2_2 and discharging atoms sdtasdt0(xn, xm) = all_83_2_25, sdtasdt0(xn, xm) = all_0_2_2, yields: % 13.49/3.73 | (202) all_83_2_25 = all_0_2_2 % 13.49/3.73 | % 13.49/3.73 | Instantiating formula (61) with xl, xm, all_83_1_24, all_0_3_3 and discharging atoms sdtasdt0(xl, xm) = all_83_1_24, sdtasdt0(xl, xm) = all_0_3_3, yields: % 13.49/3.73 | (203) all_83_1_24 = all_0_3_3 % 13.49/3.73 | % 13.49/3.73 | Instantiating formula (61) with xl, xm, all_75_1_16, all_83_1_24 and discharging atoms sdtasdt0(xl, xm) = all_83_1_24, sdtasdt0(xl, xm) = all_75_1_16, yields: % 13.49/3.73 | (204) all_83_1_24 = all_75_1_16 % 13.49/3.73 | % 13.49/3.73 | Instantiating formula (61) with xm, all_9_0_4, all_75_2_17, all_83_3_26 and discharging atoms sdtasdt0(xm, all_9_0_4) = all_83_3_26, sdtasdt0(xm, all_9_0_4) = all_75_2_17, yields: % 13.49/3.73 | (205) all_83_3_26 = all_75_2_17 % 13.49/3.73 | % 13.49/3.73 | Instantiating formula (61) with xm, xn, all_75_4_19, all_0_2_2 and discharging atoms sdtasdt0(xm, xn) = all_75_4_19, sdtasdt0(xm, xn) = all_0_2_2, yields: % 13.49/3.73 | (206) all_75_4_19 = all_0_2_2 % 13.49/3.73 | % 13.49/3.73 | Instantiating formula (27) with all_9_0_4, xl, xn, all_93_2_32 and discharging atoms sdtpldt0(all_9_0_4, xl) = all_93_2_32, sdtpldt0(all_9_0_4, xl) = xn, yields: % 13.49/3.73 | (207) all_93_2_32 = xn % 13.49/3.73 | % 13.49/3.73 | Combining equations (204,203) yields a new equation: % 13.49/3.73 | (208) all_75_1_16 = all_0_3_3 % 13.49/3.73 | % 13.49/3.73 | Simplifying 208 yields: % 13.49/3.73 | (209) all_75_1_16 = all_0_3_3 % 13.49/3.73 | % 13.49/3.73 | From (201) and (183) follows: % 13.49/3.73 | (171) sdtasdt0(all_9_0_4, xm) = all_75_0_15 % 13.49/3.73 | % 13.49/3.73 | From (202) and (181) follows: % 13.49/3.73 | (81) sdtasdt0(xn, xm) = all_0_2_2 % 13.49/3.73 | % 13.49/3.73 | From (205) and (182) follows: % 13.49/3.73 | (175) sdtasdt0(xm, all_9_0_4) = all_75_2_17 % 13.49/3.73 | % 13.49/3.73 | From (206) and (174) follows: % 13.49/3.73 | (33) sdtasdt0(xm, xn) = all_0_2_2 % 13.49/3.73 | % 13.49/3.73 | From (209) and (173) follows: % 13.49/3.73 | (214) sdtpldt0(all_0_3_3, all_75_0_15) = all_0_2_2 % 13.59/3.73 | % 13.59/3.73 | From (207) and (199) follows: % 13.59/3.73 | (169) sdtpldt0(all_9_0_4, xl) = xn % 13.59/3.73 | % 13.59/3.73 | Instantiating formula (56) with all_75_0_15, xm, all_9_0_4 and discharging atoms sdtasdt0(all_9_0_4, xm) = all_75_0_15, aNaturalNumber0(all_9_0_4), aNaturalNumber0(xm), yields: % 13.59/3.73 | (216) aNaturalNumber0(all_75_0_15) % 13.59/3.73 | % 13.59/3.73 | Instantiating formula (2) with all_75_2_17, all_9_0_4, xm and discharging atoms sdtasdt0(xm, all_9_0_4) = all_75_2_17, aNaturalNumber0(all_9_0_4), aNaturalNumber0(xm), yields: % 13.59/3.73 | (217) sdtasdt0(all_9_0_4, xm) = all_75_2_17 % 13.59/3.73 | % 13.59/3.73 | Instantiating formula (45) with all_0_2_2, xn, xl, all_9_0_4, xm and discharging atoms sdtasdt0(xn, xm) = all_0_2_2, sdtpldt0(all_9_0_4, xl) = xn, aNaturalNumber0(all_9_0_4), aNaturalNumber0(xl), aNaturalNumber0(xm), yields: % 13.59/3.73 | (218) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_9_0_4, xm) = v3 & sdtasdt0(xl, xm) = v4 & sdtasdt0(xm, all_9_0_4) = v1 & sdtasdt0(xm, xn) = v0 & sdtasdt0(xm, xl) = v2 & sdtpldt0(v3, v4) = all_0_2_2 & sdtpldt0(v1, v2) = v0) % 13.59/3.73 | % 13.59/3.73 | Instantiating formula (72) with all_0_2_2, xn, xl, all_9_0_4, xm and discharging atoms sdtasdt0(xm, xn) = all_0_2_2, sdtpldt0(all_9_0_4, xl) = xn, aNaturalNumber0(all_9_0_4), aNaturalNumber0(xl), aNaturalNumber0(xm), yields: % 13.59/3.73 | (219) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_9_0_4, xm) = v3 & sdtasdt0(xn, xm) = v2 & sdtasdt0(xl, xm) = v4 & sdtasdt0(xm, all_9_0_4) = v0 & sdtasdt0(xm, xl) = v1 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_0_2_2) % 13.59/3.73 | % 13.59/3.73 | Instantiating formula (72) with all_75_0_15, xm, all_85_0_28, xm, all_9_0_4 and discharging atoms sdtasdt0(all_9_0_4, xm) = all_75_0_15, sdtpldt0(xm, all_85_0_28) = xm, aNaturalNumber0(all_85_0_28), aNaturalNumber0(all_9_0_4), aNaturalNumber0(xm), yields: % 13.59/3.73 | (220) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_85_0_28, all_9_0_4) = v4 & sdtasdt0(all_9_0_4, all_85_0_28) = v1 & sdtasdt0(all_9_0_4, xm) = v0 & sdtasdt0(xm, all_9_0_4) = v3 & sdtasdt0(xm, all_9_0_4) = v2 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_75_0_15) % 13.59/3.73 | % 13.59/3.73 | Instantiating formula (45) with all_75_2_17, xm, all_85_0_28, xm, all_9_0_4 and discharging atoms sdtasdt0(xm, all_9_0_4) = all_75_2_17, sdtpldt0(xm, all_85_0_28) = xm, aNaturalNumber0(all_85_0_28), aNaturalNumber0(all_9_0_4), aNaturalNumber0(xm), yields: % 13.59/3.74 | (221) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_85_0_28, all_9_0_4) = v4 & sdtasdt0(all_9_0_4, all_85_0_28) = v2 & sdtasdt0(all_9_0_4, xm) = v1 & sdtasdt0(all_9_0_4, xm) = v0 & sdtasdt0(xm, all_9_0_4) = v3 & sdtpldt0(v3, v4) = all_75_2_17 & sdtpldt0(v1, v2) = v0) % 13.59/3.74 | % 13.59/3.74 | Instantiating (220) with all_107_0_34, all_107_1_35, all_107_2_36, all_107_3_37, all_107_4_38 yields: % 13.59/3.74 | (222) sdtasdt0(all_85_0_28, all_9_0_4) = all_107_0_34 & sdtasdt0(all_9_0_4, all_85_0_28) = all_107_3_37 & sdtasdt0(all_9_0_4, xm) = all_107_4_38 & sdtasdt0(xm, all_9_0_4) = all_107_1_35 & sdtasdt0(xm, all_9_0_4) = all_107_2_36 & sdtpldt0(all_107_1_35, all_107_0_34) = all_107_2_36 & sdtpldt0(all_107_4_38, all_107_3_37) = all_75_0_15 % 13.59/3.74 | % 13.59/3.74 | Applying alpha-rule on (222) yields: % 13.59/3.74 | (223) sdtasdt0(xm, all_9_0_4) = all_107_2_36 % 13.59/3.74 | (224) sdtasdt0(all_85_0_28, all_9_0_4) = all_107_0_34 % 13.59/3.74 | (225) sdtpldt0(all_107_1_35, all_107_0_34) = all_107_2_36 % 13.59/3.74 | (226) sdtpldt0(all_107_4_38, all_107_3_37) = all_75_0_15 % 13.59/3.74 | (227) sdtasdt0(xm, all_9_0_4) = all_107_1_35 % 13.59/3.74 | (228) sdtasdt0(all_9_0_4, xm) = all_107_4_38 % 13.59/3.74 | (229) sdtasdt0(all_9_0_4, all_85_0_28) = all_107_3_37 % 13.59/3.74 | % 13.59/3.74 | Instantiating (218) with all_127_0_56, all_127_1_57, all_127_2_58, all_127_3_59, all_127_4_60 yields: % 13.59/3.74 | (230) sdtasdt0(all_9_0_4, xm) = all_127_1_57 & sdtasdt0(xl, xm) = all_127_0_56 & sdtasdt0(xm, all_9_0_4) = all_127_3_59 & sdtasdt0(xm, xn) = all_127_4_60 & sdtasdt0(xm, xl) = all_127_2_58 & sdtpldt0(all_127_1_57, all_127_0_56) = all_0_2_2 & sdtpldt0(all_127_3_59, all_127_2_58) = all_127_4_60 % 13.59/3.74 | % 13.59/3.74 | Applying alpha-rule on (230) yields: % 13.59/3.74 | (231) sdtasdt0(all_9_0_4, xm) = all_127_1_57 % 13.59/3.74 | (232) sdtasdt0(xm, xn) = all_127_4_60 % 13.59/3.74 | (233) sdtpldt0(all_127_1_57, all_127_0_56) = all_0_2_2 % 13.59/3.74 | (234) sdtasdt0(xm, all_9_0_4) = all_127_3_59 % 13.59/3.74 | (235) sdtasdt0(xm, xl) = all_127_2_58 % 13.59/3.74 | (236) sdtpldt0(all_127_3_59, all_127_2_58) = all_127_4_60 % 13.59/3.74 | (237) sdtasdt0(xl, xm) = all_127_0_56 % 13.59/3.74 | % 13.59/3.74 | Instantiating (221) with all_143_0_76, all_143_1_77, all_143_2_78, all_143_3_79, all_143_4_80 yields: % 13.59/3.74 | (238) sdtasdt0(all_85_0_28, all_9_0_4) = all_143_0_76 & sdtasdt0(all_9_0_4, all_85_0_28) = all_143_2_78 & sdtasdt0(all_9_0_4, xm) = all_143_3_79 & sdtasdt0(all_9_0_4, xm) = all_143_4_80 & sdtasdt0(xm, all_9_0_4) = all_143_1_77 & sdtpldt0(all_143_1_77, all_143_0_76) = all_75_2_17 & sdtpldt0(all_143_3_79, all_143_2_78) = all_143_4_80 % 13.59/3.74 | % 13.59/3.74 | Applying alpha-rule on (238) yields: % 13.59/3.74 | (239) sdtpldt0(all_143_1_77, all_143_0_76) = all_75_2_17 % 13.59/3.74 | (240) sdtasdt0(all_9_0_4, xm) = all_143_3_79 % 13.59/3.74 | (241) sdtasdt0(all_85_0_28, all_9_0_4) = all_143_0_76 % 13.59/3.74 | (242) sdtpldt0(all_143_3_79, all_143_2_78) = all_143_4_80 % 13.59/3.74 | (243) sdtasdt0(all_9_0_4, all_85_0_28) = all_143_2_78 % 13.59/3.74 | (244) sdtasdt0(xm, all_9_0_4) = all_143_1_77 % 13.59/3.74 | (245) sdtasdt0(all_9_0_4, xm) = all_143_4_80 % 13.59/3.74 | % 13.59/3.74 | Instantiating (219) with all_159_0_104, all_159_1_105, all_159_2_106, all_159_3_107, all_159_4_108 yields: % 13.59/3.74 | (246) sdtasdt0(all_9_0_4, xm) = all_159_1_105 & sdtasdt0(xn, xm) = all_159_2_106 & sdtasdt0(xl, xm) = all_159_0_104 & sdtasdt0(xm, all_9_0_4) = all_159_4_108 & sdtasdt0(xm, xl) = all_159_3_107 & sdtpldt0(all_159_1_105, all_159_0_104) = all_159_2_106 & sdtpldt0(all_159_4_108, all_159_3_107) = all_0_2_2 % 13.59/3.74 | % 13.59/3.74 | Applying alpha-rule on (246) yields: % 13.59/3.74 | (247) sdtasdt0(xm, all_9_0_4) = all_159_4_108 % 13.59/3.74 | (248) sdtasdt0(xn, xm) = all_159_2_106 % 13.59/3.74 | (249) sdtasdt0(xm, xl) = all_159_3_107 % 13.59/3.74 | (250) sdtasdt0(all_9_0_4, xm) = all_159_1_105 % 13.59/3.74 | (251) sdtpldt0(all_159_4_108, all_159_3_107) = all_0_2_2 % 13.59/3.74 | (252) sdtpldt0(all_159_1_105, all_159_0_104) = all_159_2_106 % 13.59/3.74 | (253) sdtasdt0(xl, xm) = all_159_0_104 % 13.59/3.74 | % 13.59/3.74 | Instantiating formula (61) with all_9_0_4, xm, all_159_1_105, all_75_0_15 and discharging atoms sdtasdt0(all_9_0_4, xm) = all_159_1_105, sdtasdt0(all_9_0_4, xm) = all_75_0_15, yields: % 13.59/3.74 | (254) all_159_1_105 = all_75_0_15 % 13.59/3.74 | % 13.59/3.74 | Instantiating formula (61) with all_9_0_4, xm, all_143_3_79, all_159_1_105 and discharging atoms sdtasdt0(all_9_0_4, xm) = all_159_1_105, sdtasdt0(all_9_0_4, xm) = all_143_3_79, yields: % 13.59/3.74 | (255) all_159_1_105 = all_143_3_79 % 13.59/3.74 | % 13.59/3.74 | Instantiating formula (61) with all_9_0_4, xm, all_143_4_80, all_143_3_79 and discharging atoms sdtasdt0(all_9_0_4, xm) = all_143_3_79, sdtasdt0(all_9_0_4, xm) = all_143_4_80, yields: % 13.59/3.74 | (256) all_143_3_79 = all_143_4_80 % 13.59/3.74 | % 13.59/3.74 | Instantiating formula (61) with all_9_0_4, xm, all_127_1_57, all_143_3_79 and discharging atoms sdtasdt0(all_9_0_4, xm) = all_143_3_79, sdtasdt0(all_9_0_4, xm) = all_127_1_57, yields: % 13.59/3.74 | (257) all_143_3_79 = all_127_1_57 % 13.59/3.74 | % 13.59/3.74 | Instantiating formula (61) with all_9_0_4, xm, all_107_4_38, all_159_1_105 and discharging atoms sdtasdt0(all_9_0_4, xm) = all_159_1_105, sdtasdt0(all_9_0_4, xm) = all_107_4_38, yields: % 13.59/3.74 | (258) all_159_1_105 = all_107_4_38 % 13.59/3.74 | % 13.59/3.74 | Instantiating formula (61) with all_9_0_4, xm, all_75_2_17, all_143_4_80 and discharging atoms sdtasdt0(all_9_0_4, xm) = all_143_4_80, sdtasdt0(all_9_0_4, xm) = all_75_2_17, yields: % 13.59/3.74 | (259) all_143_4_80 = all_75_2_17 % 13.59/3.74 | % 13.59/3.75 | Combining equations (255,258) yields a new equation: % 13.59/3.75 | (260) all_143_3_79 = all_107_4_38 % 13.59/3.75 | % 13.59/3.75 | Simplifying 260 yields: % 13.59/3.75 | (261) all_143_3_79 = all_107_4_38 % 13.59/3.75 | % 13.59/3.75 | Combining equations (254,258) yields a new equation: % 13.59/3.75 | (262) all_107_4_38 = all_75_0_15 % 13.59/3.75 | % 13.59/3.75 | Combining equations (256,257) yields a new equation: % 13.59/3.75 | (263) all_143_4_80 = all_127_1_57 % 13.59/3.75 | % 13.59/3.75 | Simplifying 263 yields: % 13.59/3.75 | (264) all_143_4_80 = all_127_1_57 % 13.59/3.75 | % 13.59/3.75 | Combining equations (261,257) yields a new equation: % 13.59/3.75 | (265) all_127_1_57 = all_107_4_38 % 13.59/3.75 | % 13.59/3.75 | Combining equations (264,259) yields a new equation: % 13.59/3.75 | (266) all_127_1_57 = all_75_2_17 % 13.59/3.75 | % 13.59/3.75 | Simplifying 266 yields: % 13.59/3.75 | (267) all_127_1_57 = all_75_2_17 % 13.59/3.75 | % 13.59/3.75 | Combining equations (265,267) yields a new equation: % 13.59/3.75 | (268) all_107_4_38 = all_75_2_17 % 13.59/3.75 | % 13.59/3.75 | Simplifying 268 yields: % 13.59/3.75 | (269) all_107_4_38 = all_75_2_17 % 13.59/3.75 | % 13.59/3.75 | Combining equations (269,262) yields a new equation: % 13.59/3.75 | (270) all_75_0_15 = all_75_2_17 % 13.59/3.75 | % 13.59/3.75 | From (270) and (214) follows: % 13.59/3.75 | (271) sdtpldt0(all_0_3_3, all_75_2_17) = all_0_2_2 % 13.59/3.75 | % 13.59/3.75 | From (270) and (216) follows: % 13.59/3.75 | (272) aNaturalNumber0(all_75_2_17) % 13.59/3.75 | % 13.59/3.75 | Instantiating formula (21) with all_75_2_17, all_0_2_2, all_0_3_3 and discharging atoms sdtpldt0(all_0_3_3, all_75_2_17) = all_0_2_2, aNaturalNumber0(all_75_2_17), aNaturalNumber0(all_0_2_2), aNaturalNumber0(all_0_3_3), ~ sdtlseqdt0(all_0_3_3, all_0_2_2), yields: % 13.59/3.75 | (273) $false % 13.59/3.75 | % 13.59/3.75 |-The branch is then unsatisfiable % 13.59/3.75 |-Branch two: % 13.59/3.75 | (274) sdtlseqdt0(all_0_1_1, all_0_0_0) % 13.59/3.75 | (275) all_0_0_0 = all_0_1_1 | all_0_2_2 = all_0_3_3 | ~ sdtlseqdt0(all_0_3_3, all_0_2_2) % 13.59/3.75 | % 13.59/3.75 | From (152)(154) and (274) follows: % 13.59/3.75 | (276) sdtlseqdt0(all_0_3_3, all_0_2_2) % 13.59/3.75 | % 13.59/3.75 +-Applying beta-rule and splitting (275), into two cases. % 13.59/3.75 |-Branch one: % 13.59/3.75 | (164) ~ sdtlseqdt0(all_0_3_3, all_0_2_2) % 13.59/3.75 | % 13.59/3.75 | Using (276) and (164) yields: % 13.59/3.75 | (273) $false % 13.59/3.75 | % 13.59/3.75 |-The branch is then unsatisfiable % 13.59/3.75 |-Branch two: % 13.59/3.75 | (276) sdtlseqdt0(all_0_3_3, all_0_2_2) % 13.59/3.75 | (280) all_0_0_0 = all_0_1_1 | all_0_2_2 = all_0_3_3 % 13.59/3.75 | % 13.59/3.75 +-Applying beta-rule and splitting (280), into two cases. % 13.59/3.75 |-Branch one: % 13.59/3.75 | (281) all_0_0_0 = all_0_1_1 % 13.59/3.75 | % 13.59/3.75 | Combining equations (281,154) yields a new equation: % 13.59/3.75 | (282) all_0_1_1 = all_0_2_2 % 13.59/3.75 | % 13.59/3.75 | Simplifying 282 yields: % 13.59/3.75 | (283) all_0_1_1 = all_0_2_2 % 13.59/3.75 | % 13.59/3.75 | Combining equations (283,152) yields a new equation: % 13.59/3.75 | (284) all_0_2_2 = all_0_3_3 % 13.59/3.75 | % 13.59/3.75 | Simplifying 284 yields: % 13.59/3.75 | (285) all_0_2_2 = all_0_3_3 % 13.59/3.75 | % 13.59/3.75 | Equations (285) can reduce 157 to: % 13.59/3.75 | (89) $false % 13.59/3.75 | % 13.59/3.75 |-The branch is then unsatisfiable % 13.59/3.75 |-Branch two: % 13.59/3.75 | (287) ~ (all_0_0_0 = all_0_1_1) % 13.59/3.75 | (285) all_0_2_2 = all_0_3_3 % 13.59/3.75 | % 13.59/3.75 | Equations (285) can reduce 157 to: % 13.59/3.75 | (89) $false % 13.59/3.75 | % 13.59/3.75 |-The branch is then unsatisfiable % 13.59/3.75 % SZS output end Proof for theBenchmark % 13.59/3.75 % 13.59/3.75 3150ms %------------------------------------------------------------------------------