%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : NUM465+2 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n029.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 08:44:46 EDT 2022 % Result : Theorem 7.97s 2.52s % Output : Proof 14.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM465+2 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n029.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Wed Jul 6 00:39:57 EDT 2022 % 0.12/0.34 % CPUTime : % 0.52/0.58 ____ _ % 0.52/0.58 ___ / __ \_____(_)___ ________ __________ % 0.52/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.52/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.52/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.52/0.58 % 0.52/0.58 A Theorem Prover for First-Order Logic % 0.52/0.58 (ePrincess v.1.0) % 0.52/0.58 % 0.52/0.58 (c) Philipp Rümmer, 2009-2015 % 0.52/0.58 (c) Peter Backeman, 2014-2015 % 0.52/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.52/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.52/0.58 Bug reports to peter@backeman.se % 0.52/0.58 % 0.52/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.52/0.58 % 0.52/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.52/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.59/0.94 Prover 0: Preprocessing ... % 3.17/1.40 Prover 0: Constructing countermodel ... % 7.97/2.52 Prover 0: proved (1893ms) % 7.97/2.52 % 7.97/2.52 No countermodel exists, formula is valid % 7.97/2.52 % SZS status Theorem for theBenchmark % 7.97/2.52 % 7.97/2.52 Generating proof ... found it (size 66) % 14.00/3.92 % 14.00/3.92 % SZS output start Proof for theBenchmark % 14.00/3.92 Assumed formulas after preprocessing and simplification: % 14.00/3.92 | (0) ? [v0] : ? [v1] : ( ~ (xm = sz00) & ~ (sz10 = sz00) & sdtasdt0(xn, xm) = v0 & sdtpldt0(sz10, v1) = xm & sdtlseqdt0(sz10, xm) & aNaturalNumber0(v1) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ sdtlseqdt0(xn, v0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v4, v2) = v6) | ~ (sdtasdt0(v3, v2) = v5) | ~ (sdtpldt0(v5, v6) = v7) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (sdtasdt0(v8, v2) = v7 & sdtasdt0(v2, v8) = v9 & sdtasdt0(v2, v4) = v11 & sdtasdt0(v2, v3) = v10 & sdtpldt0(v10, v11) = v9 & sdtpldt0(v3, v4) = v8)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v2, v4) = v6) | ~ (sdtasdt0(v2, v3) = v5) | ~ (sdtpldt0(v5, v6) = v7) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (sdtasdt0(v8, v2) = v9 & sdtasdt0(v4, v2) = v11 & sdtasdt0(v3, v2) = v10 & sdtasdt0(v2, v8) = v7 & sdtpldt0(v10, v11) = v9 & sdtpldt0(v3, v4) = v8)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | v2 = sz00 | ~ (sdtasdt0(v4, v2) = v6) | ~ (sdtasdt0(v3, v2) = v5) | ~ sdtlseqdt0(v3, v4) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | sdtlseqdt0(v5, v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | v2 = sz00 | ~ (sdtasdt0(v4, v2) = v6) | ~ (sdtasdt0(v3, v2) = v5) | ~ sdtlseqdt0(v3, v4) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7] : ? [v8] : ( ~ (v8 = v7) & sdtasdt0(v2, v4) = v8 & sdtasdt0(v2, v3) = v7 & sdtlseqdt0(v7, v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | v2 = sz00 | ~ (sdtasdt0(v4, v2) = v6) | ~ (sdtasdt0(v3, v2) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7] : ? [v8] : ( ~ (v8 = v7) & sdtasdt0(v2, v4) = v8 & sdtasdt0(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | v2 = sz00 | ~ (sdtasdt0(v4, v2) = v6) | ~ (sdtasdt0(v2, v3) = v5) | ~ sdtlseqdt0(v3, v4) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7] : ? [v8] : ( ~ (v8 = v6) & ~ (v7 = v5) & sdtasdt0(v3, v2) = v8 & sdtasdt0(v2, v4) = v7 & sdtlseqdt0(v8, v6) & sdtlseqdt0(v5, v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | v2 = sz00 | ~ (sdtasdt0(v4, v2) = v6) | ~ (sdtasdt0(v2, v3) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7] : ? [v8] : ( ~ (v8 = v6) & ~ (v7 = v5) & sdtasdt0(v3, v2) = v8 & sdtasdt0(v2, v4) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | v2 = sz00 | ~ (sdtasdt0(v3, v2) = v6) | ~ (sdtasdt0(v2, v4) = v5) | ~ sdtlseqdt0(v3, v4) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7] : ? [v8] : ( ~ (v8 = v6) & ~ (v7 = v5) & sdtasdt0(v4, v2) = v8 & sdtasdt0(v2, v3) = v7 & sdtlseqdt0(v7, v5) & sdtlseqdt0(v6, v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | v2 = sz00 | ~ (sdtasdt0(v3, v2) = v6) | ~ (sdtasdt0(v2, v4) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7] : ? [v8] : ( ~ (v8 = v6) & ~ (v7 = v5) & sdtasdt0(v4, v2) = v8 & sdtasdt0(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | v2 = sz00 | ~ (sdtasdt0(v2, v4) = v6) | ~ (sdtasdt0(v2, v3) = v5) | ~ sdtlseqdt0(v3, v4) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | sdtlseqdt0(v5, v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | v2 = sz00 | ~ (sdtasdt0(v2, v4) = v6) | ~ (sdtasdt0(v2, v3) = v5) | ~ sdtlseqdt0(v3, v4) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7] : ? [v8] : ( ~ (v8 = v7) & sdtasdt0(v4, v2) = v8 & sdtasdt0(v3, v2) = v7 & sdtlseqdt0(v7, v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | v2 = sz00 | ~ (sdtasdt0(v2, v4) = v6) | ~ (sdtasdt0(v2, v3) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7] : ? [v8] : ( ~ (v8 = v7) & sdtasdt0(v4, v2) = v8 & sdtasdt0(v3, v2) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (sdtpldt0(v4, v2) = v6) | ~ (sdtpldt0(v3, v2) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7] : ? [v8] : ( ~ (v8 = v7) & sdtpldt0(v2, v4) = v8 & sdtpldt0(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (sdtpldt0(v4, v2) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7] : ? [v8] : ( ~ (v8 = v6) & ~ (v7 = v5) & sdtpldt0(v3, v2) = v8 & sdtpldt0(v2, v4) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (sdtpldt0(v3, v2) = v6) | ~ (sdtpldt0(v2, v4) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7] : ? [v8] : ( ~ (v8 = v6) & ~ (v7 = v5) & sdtpldt0(v4, v2) = v8 & sdtpldt0(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (sdtpldt0(v2, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7] : ? [v8] : ( ~ (v8 = v7) & sdtpldt0(v4, v2) = v8 & sdtpldt0(v3, v2) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, v4) = v6) | ~ (sdtasdt0(v2, v3) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7] : (sdtasdt0(v3, v4) = v7 & sdtasdt0(v2, v7) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, v2) = v6) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (sdtasdt0(v4, v2) = v11 & sdtasdt0(v3, v2) = v10 & sdtasdt0(v2, v5) = v7 & sdtasdt0(v2, v4) = v9 & sdtasdt0(v2, v3) = v8 & sdtpldt0(v10, v11) = v6 & sdtpldt0(v8, v9) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v3, v4) = v5) | ~ (sdtasdt0(v2, v5) = v6) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7] : (sdtasdt0(v7, v4) = v6 & sdtasdt0(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v2, v5) = v6) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (sdtasdt0(v5, v2) = v9 & sdtasdt0(v4, v2) = v11 & sdtasdt0(v3, v2) = v10 & sdtasdt0(v2, v4) = v8 & sdtasdt0(v2, v3) = v7 & sdtpldt0(v10, v11) = v9 & sdtpldt0(v7, v8) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7] : (sdtpldt0(v3, v4) = v7 & sdtpldt0(v2, v7) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v3, v4) = v5) | ~ (sdtpldt0(v2, v5) = v6) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7] : (sdtpldt0(v7, v4) = v6 & sdtpldt0(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtmndt0(v3, v2) = v4) | ~ (sdtpldt0(v2, v5) = v3) | ~ sdtlseqdt0(v2, v3) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (sdtmndt0(v3, v2) = v4) | ~ (sdtpldt0(v2, v4) = v5) | ~ sdtlseqdt0(v2, v3) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | v2 = sz00 | ~ (sdtasdt0(v4, v2) = v5) | ~ (sdtasdt0(v3, v2) = v5) | ~ sdtlseqdt0(v3, v4) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | v2 = sz00 | ~ (sdtasdt0(v4, v2) = v5) | ~ (sdtasdt0(v3, v2) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | v2 = sz00 | ~ (sdtasdt0(v2, v4) = v5) | ~ (sdtasdt0(v2, v3) = v5) | ~ sdtlseqdt0(v3, v4) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | v2 = sz00 | ~ (sdtasdt0(v2, v4) = v5) | ~ (sdtasdt0(v2, v3) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (sdtpldt0(v4, v2) = v5) | ~ (sdtpldt0(v3, v2) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (sdtpldt0(v2, v4) = v5) | ~ (sdtpldt0(v2, v3) = v5) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtmndt0(v5, v4) = v3) | ~ (sdtmndt0(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] : (v3 = v2 | ~ (sdtpldt0(v4, v3) = v5) | ~ sdtlseqdt0(v2, v3) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = v7) & ~ (v6 = v5) & sdtpldt0(v4, v2) = v6 & sdtpldt0(v3, v4) = v8 & sdtpldt0(v2, v4) = v7 & sdtlseqdt0(v7, v8) & sdtlseqdt0(v6, v5))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtpldt0(v4, v2) = v5) | ~ sdtlseqdt0(v2, v3) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = v7) & ~ (v6 = v5) & sdtpldt0(v4, v3) = v6 & sdtpldt0(v3, v4) = v8 & sdtpldt0(v2, v4) = v7 & sdtlseqdt0(v7, v8) & sdtlseqdt0(v5, v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtpldt0(v3, v4) = v5) | ~ sdtlseqdt0(v2, v3) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = v5) & ~ (v7 = v6) & sdtpldt0(v4, v3) = v7 & sdtpldt0(v4, v2) = v6 & sdtpldt0(v2, v4) = v8 & sdtlseqdt0(v8, v5) & sdtlseqdt0(v6, v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtpldt0(v2, v4) = v5) | ~ sdtlseqdt0(v2, v3) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = v5) & ~ (v7 = v6) & sdtpldt0(v4, v3) = v7 & sdtpldt0(v4, v2) = v6 & sdtpldt0(v3, v4) = v8 & sdtlseqdt0(v6, v7) & sdtlseqdt0(v5, v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtmndt0(v3, v2) = v4) | ~ (sdtpldt0(v2, v4) = v5) | ~ sdtlseqdt0(v2, v3) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | aNaturalNumber0(v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | sdtasdt0(v2, v3) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v2, v3) = v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | sdtasdt0(v3, v2) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v2, v3) = v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | aNaturalNumber0(v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | sdtpldt0(v2, v3) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v2, v4) = v3) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | sdtlseqdt0(v2, v3)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v2, v3) = v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | sdtpldt0(v3, v2) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v2, v3) = v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | aNaturalNumber0(v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ sdtlseqdt0(v3, v4) | ~ sdtlseqdt0(v2, v3) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | sdtlseqdt0(v2, v4)) & ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtasdt0(v2, sz10) = v3) | ~ aNaturalNumber0(v2)) & ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtasdt0(sz10, v2) = v3) | ~ aNaturalNumber0(v2)) & ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtpldt0(v2, sz00) = v3) | ~ aNaturalNumber0(v2)) & ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtpldt0(sz00, v2) = v3) | ~ aNaturalNumber0(v2)) & ! [v2] : ! [v3] : (v3 = v2 | ~ sdtlseqdt0(v3, v2) | ~ sdtlseqdt0(v2, v3) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2)) & ! [v2] : ! [v3] : (v3 = sz00 | v2 = sz00 | ~ (sdtasdt0(v2, v3) = sz00) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2)) & ! [v2] : ! [v3] : (v3 = sz00 | ~ (sdtasdt0(v2, sz00) = v3) | ~ aNaturalNumber0(v2)) & ! [v2] : ! [v3] : (v3 = sz00 | ~ (sdtasdt0(sz00, v2) = v3) | ~ aNaturalNumber0(v2)) & ! [v2] : ! [v3] : (v3 = sz00 | ~ (sdtpldt0(v2, v3) = sz00) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2)) & ! [v2] : ! [v3] : (v2 = sz00 | ~ (sdtpldt0(v2, v3) = sz00) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2)) & ! [v2] : ! [v3] : ( ~ (sdtasdt0(v2, sz10) = v3) | ~ aNaturalNumber0(v2) | sdtasdt0(sz10, v2) = v2) & ! [v2] : ! [v3] : ( ~ (sdtasdt0(v2, sz00) = v3) | ~ aNaturalNumber0(v2) | sdtasdt0(sz00, v2) = sz00) & ! [v2] : ! [v3] : ( ~ (sdtasdt0(sz10, v2) = v3) | ~ aNaturalNumber0(v2) | sdtasdt0(v2, sz10) = v2) & ! [v2] : ! [v3] : ( ~ (sdtasdt0(sz00, v2) = v3) | ~ aNaturalNumber0(v2) | sdtasdt0(v2, sz00) = sz00) & ! [v2] : ! [v3] : ( ~ (sdtpldt0(v2, sz00) = v3) | ~ aNaturalNumber0(v2) | sdtpldt0(sz00, v2) = v2) & ! [v2] : ! [v3] : ( ~ (sdtpldt0(sz00, v2) = v3) | ~ aNaturalNumber0(v2) | sdtpldt0(v2, sz00) = v2) & ! [v2] : ! [v3] : ( ~ sdtlseqdt0(v2, v3) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v4] : (sdtpldt0(v2, v4) = v3 & aNaturalNumber0(v4))) & ! [v2] : ! [v3] : ( ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | sdtlseqdt0(v3, v2) | sdtlseqdt0(v2, v3)) & ! [v2] : (v2 = sz10 | v2 = sz00 | ~ aNaturalNumber0(v2) | sdtlseqdt0(sz10, v2)) & ! [v2] : ( ~ aNaturalNumber0(v2) | sdtlseqdt0(v2, v2)) & ! [v2] : ( ~ aNaturalNumber0(v2) | ? [v3] : ( ~ (v3 = v0) & sdtpldt0(xn, v2) = v3))) % 14.05/3.98 | Instantiating (0) with all_0_0_0, all_0_1_1 yields: % 14.05/3.98 | (1) ~ (xm = sz00) & ~ (sz10 = sz00) & sdtasdt0(xn, xm) = all_0_1_1 & sdtpldt0(sz10, all_0_0_0) = xm & sdtlseqdt0(sz10, xm) & aNaturalNumber0(all_0_0_0) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ sdtlseqdt0(xn, all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtlseqdt0(v6, v4) & sdtlseqdt0(v3, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v3) & sdtlseqdt0(v4, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtlseqdt0(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v0, v2) = v6 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (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) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (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] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) & ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_1_1) & sdtpldt0(xn, v0) = v1)) % 14.05/4.00 | % 14.05/4.00 | Applying alpha-rule on (1) yields: % 14.05/4.00 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 14.05/4.01 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 14.05/4.01 | (4) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0) % 14.05/4.01 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) % 14.05/4.01 | (6) sdtpldt0(sz10, all_0_0_0) = xm % 14.05/4.01 | (7) ! [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)) % 14.05/4.01 | (8) aNaturalNumber0(all_0_0_0) % 14.05/4.01 | (9) ! [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))) % 14.05/4.01 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 14.05/4.01 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v6, v7) = v5)) % 14.05/4.01 | (12) aNaturalNumber0(sz10) % 14.05/4.01 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 14.05/4.01 | (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)) % 14.05/4.01 | (15) ! [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)) % 14.42/4.01 | (16) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0) % 14.42/4.01 | (17) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) % 14.42/4.01 | (18) ~ (sz10 = sz00) % 14.42/4.01 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0)) % 14.42/4.01 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 14.42/4.01 | (21) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) % 14.42/4.01 | (22) ! [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)) % 14.42/4.01 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) % 14.42/4.01 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 14.42/4.01 | (25) ! [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)) % 14.42/4.01 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 14.42/4.01 | (27) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0)) % 14.42/4.01 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 14.42/4.01 | (29) ! [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))) % 14.42/4.01 | (30) aNaturalNumber0(xn) % 14.42/4.01 | (31) ~ sdtlseqdt0(xn, all_0_1_1) % 14.42/4.01 | (32) ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_1_1) & sdtpldt0(xn, v0) = v1)) % 14.42/4.01 | (33) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 14.42/4.01 | (34) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0) % 14.42/4.02 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v6))) % 14.42/4.02 | (36) ! [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)) % 14.42/4.02 | (37) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2))) % 14.42/4.02 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2) % 14.42/4.02 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtlseqdt0(v5, v6))) % 14.42/4.02 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 14.42/4.02 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 14.42/4.02 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2) % 14.42/4.02 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) % 14.42/4.02 | (44) aNaturalNumber0(xm) % 14.42/4.02 | (45) ! [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)) % 14.42/4.02 | (46) ! [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)) % 14.42/4.02 | (47) sdtasdt0(xn, xm) = all_0_1_1 % 14.42/4.02 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5 & sdtlseqdt0(v5, v3) & sdtlseqdt0(v4, v6))) % 14.42/4.02 | (49) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00) % 14.42/4.02 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 14.42/4.02 | (51) aNaturalNumber0(sz00) % 14.42/4.02 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 14.42/4.02 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) % 14.42/4.02 | (54) ! [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)) % 14.42/4.02 | (55) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 14.42/4.02 | (56) ! [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)) % 14.42/4.02 | (57) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) % 14.42/4.02 | (58) ! [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)) % 14.42/4.02 | (59) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00) % 14.42/4.02 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtlseqdt0(v6, v4) & sdtlseqdt0(v3, v5))) % 14.42/4.03 | (61) ! [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))) % 14.42/4.03 | (62) ! [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)) % 14.42/4.03 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2) % 14.42/4.03 | (64) ~ (xm = sz00) % 14.42/4.03 | (65) sdtlseqdt0(sz10, xm) % 14.42/4.03 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) % 14.42/4.03 | (67) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) % 14.42/4.03 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2)) % 14.42/4.03 | (69) ! [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)) % 14.42/4.03 | (70) ! [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)) % 14.42/4.03 | (71) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 14.42/4.03 | (72) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) % 14.42/4.03 | (73) ! [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)) % 14.42/4.03 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2) % 14.42/4.03 | (75) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) % 14.42/4.03 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 14.42/4.03 | (77) ! [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))) % 14.42/4.03 | (78) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0) % 14.42/4.03 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 14.42/4.03 | % 14.42/4.03 | Instantiating formula (38) with all_0_1_1, xn, xm and discharging atoms sdtasdt0(xn, xm) = all_0_1_1, aNaturalNumber0(xn), aNaturalNumber0(xm), yields: % 14.42/4.03 | (80) sdtasdt0(xm, xn) = all_0_1_1 % 14.42/4.03 | % 14.42/4.03 | Instantiating formula (76) with all_0_1_1, xm, xn and discharging atoms sdtasdt0(xn, xm) = all_0_1_1, aNaturalNumber0(xn), aNaturalNumber0(xm), yields: % 14.42/4.03 | (81) aNaturalNumber0(all_0_1_1) % 14.42/4.03 | % 14.42/4.03 | Instantiating formula (45) with all_0_1_1, xm, all_0_0_0, sz10, xn and discharging atoms sdtasdt0(xn, xm) = all_0_1_1, sdtpldt0(sz10, all_0_0_0) = xm, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xn), aNaturalNumber0(sz10), yields: % 14.42/4.03 | (82) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_0_0, xn) = v4 & sdtasdt0(xn, all_0_0_0) = v1 & sdtasdt0(xn, sz10) = v0 & sdtasdt0(xm, xn) = v2 & sdtasdt0(sz10, xn) = v3 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_0_1_1) % 14.42/4.03 | % 14.42/4.03 | Instantiating formula (74) with xm, sz10, all_0_0_0 and discharging atoms sdtpldt0(sz10, all_0_0_0) = xm, aNaturalNumber0(all_0_0_0), aNaturalNumber0(sz10), yields: % 14.42/4.03 | (83) sdtpldt0(all_0_0_0, sz10) = xm % 14.42/4.03 | % 14.42/4.04 | Instantiating formula (37) with xm, sz10 and discharging atoms sdtlseqdt0(sz10, xm), aNaturalNumber0(xm), aNaturalNumber0(sz10), yields: % 14.42/4.04 | (84) ? [v0] : (sdtpldt0(sz10, v0) = xm & aNaturalNumber0(v0)) % 14.42/4.04 | % 14.42/4.04 | Instantiating formula (32) with sz00 and discharging atoms aNaturalNumber0(sz00), yields: % 14.42/4.04 | (85) ? [v0] : ( ~ (v0 = all_0_1_1) & sdtpldt0(xn, sz00) = v0) % 14.42/4.04 | % 14.42/4.04 | Instantiating (84) with all_11_0_3 yields: % 14.42/4.04 | (86) sdtpldt0(sz10, all_11_0_3) = xm & aNaturalNumber0(all_11_0_3) % 14.42/4.04 | % 14.42/4.04 | Applying alpha-rule on (86) yields: % 14.42/4.04 | (87) sdtpldt0(sz10, all_11_0_3) = xm % 14.42/4.04 | (88) aNaturalNumber0(all_11_0_3) % 14.42/4.04 | % 14.42/4.04 | Instantiating (85) with all_15_0_5 yields: % 14.42/4.04 | (89) ~ (all_15_0_5 = all_0_1_1) & sdtpldt0(xn, sz00) = all_15_0_5 % 14.42/4.04 | % 14.42/4.04 | Applying alpha-rule on (89) yields: % 14.42/4.04 | (90) ~ (all_15_0_5 = all_0_1_1) % 14.42/4.04 | (91) sdtpldt0(xn, sz00) = all_15_0_5 % 14.42/4.04 | % 14.42/4.04 | Instantiating (82) with all_17_0_6, all_17_1_7, all_17_2_8, all_17_3_9, all_17_4_10 yields: % 14.42/4.04 | (92) sdtasdt0(all_0_0_0, xn) = all_17_0_6 & sdtasdt0(xn, all_0_0_0) = all_17_3_9 & sdtasdt0(xn, sz10) = all_17_4_10 & sdtasdt0(xm, xn) = all_17_2_8 & sdtasdt0(sz10, xn) = all_17_1_7 & sdtpldt0(all_17_1_7, all_17_0_6) = all_17_2_8 & sdtpldt0(all_17_4_10, all_17_3_9) = all_0_1_1 % 14.42/4.04 | % 14.42/4.04 | Applying alpha-rule on (92) yields: % 14.42/4.04 | (93) sdtasdt0(xn, sz10) = all_17_4_10 % 14.42/4.04 | (94) sdtasdt0(xm, xn) = all_17_2_8 % 14.42/4.04 | (95) sdtpldt0(all_17_1_7, all_17_0_6) = all_17_2_8 % 14.42/4.04 | (96) sdtasdt0(sz10, xn) = all_17_1_7 % 14.42/4.04 | (97) sdtpldt0(all_17_4_10, all_17_3_9) = all_0_1_1 % 14.42/4.04 | (98) sdtasdt0(all_0_0_0, xn) = all_17_0_6 % 14.42/4.04 | (99) sdtasdt0(xn, all_0_0_0) = all_17_3_9 % 14.42/4.04 | % 14.42/4.04 | Instantiating formula (10) with xm, xn, all_0_1_1, all_17_2_8 and discharging atoms sdtasdt0(xm, xn) = all_17_2_8, sdtasdt0(xm, xn) = all_0_1_1, yields: % 14.42/4.04 | (100) all_17_2_8 = all_0_1_1 % 14.42/4.04 | % 14.42/4.04 | Instantiating formula (19) with all_17_1_7, xn and discharging atoms sdtasdt0(sz10, xn) = all_17_1_7, aNaturalNumber0(xn), yields: % 14.42/4.04 | (101) all_17_1_7 = xn % 14.42/4.04 | % 14.42/4.04 | Instantiating formula (17) with all_15_0_5, xn and discharging atoms sdtpldt0(xn, sz00) = all_15_0_5, aNaturalNumber0(xn), yields: % 14.42/4.04 | (102) all_15_0_5 = xn % 14.42/4.04 | % 14.42/4.04 | Instantiating formula (50) with xm, all_0_0_0, all_11_0_3, sz10 and discharging atoms sdtpldt0(sz10, all_11_0_3) = xm, sdtpldt0(sz10, all_0_0_0) = xm, aNaturalNumber0(all_11_0_3), aNaturalNumber0(all_0_0_0), aNaturalNumber0(sz10), yields: % 14.42/4.04 | (103) all_11_0_3 = all_0_0_0 % 14.42/4.04 | % 14.42/4.04 | From (100) and (94) follows: % 14.42/4.04 | (80) sdtasdt0(xm, xn) = all_0_1_1 % 14.42/4.04 | % 14.42/4.04 | From (101) and (96) follows: % 14.42/4.04 | (105) sdtasdt0(sz10, xn) = xn % 14.42/4.04 | % 14.42/4.04 | From (101)(100) and (95) follows: % 14.42/4.04 | (106) sdtpldt0(xn, all_17_0_6) = all_0_1_1 % 14.42/4.04 | % 14.42/4.04 | From (102) and (91) follows: % 14.42/4.04 | (107) sdtpldt0(xn, sz00) = xn % 14.42/4.04 | % 14.42/4.04 | From (103) and (88) follows: % 14.42/4.04 | (8) aNaturalNumber0(all_0_0_0) % 14.42/4.04 | % 14.42/4.04 | Instantiating formula (38) with all_17_0_6, all_0_0_0, xn and discharging atoms sdtasdt0(all_0_0_0, xn) = all_17_0_6, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xn), yields: % 14.42/4.04 | (109) sdtasdt0(xn, all_0_0_0) = all_17_0_6 % 14.42/4.04 | % 14.42/4.04 | Instantiating formula (76) with all_17_0_6, xn, all_0_0_0 and discharging atoms sdtasdt0(all_0_0_0, xn) = all_17_0_6, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xn), yields: % 14.42/4.04 | (110) aNaturalNumber0(all_17_0_6) % 14.42/4.04 | % 14.42/4.04 | Instantiating formula (14) with all_17_3_9, xn, all_0_0_0, xn, sz10 and discharging atoms sdtasdt0(xn, all_0_0_0) = all_17_3_9, sdtasdt0(sz10, xn) = xn, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xn), aNaturalNumber0(sz10), yields: % 14.42/4.04 | (111) ? [v0] : (sdtasdt0(xn, all_0_0_0) = v0 & sdtasdt0(sz10, v0) = all_17_3_9) % 14.42/4.04 | % 14.42/4.04 | Instantiating formula (45) with all_0_1_1, xm, sz10, all_0_0_0, xn and discharging atoms sdtasdt0(xn, xm) = all_0_1_1, sdtpldt0(all_0_0_0, sz10) = xm, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xn), aNaturalNumber0(sz10), yields: % 14.42/4.04 | (112) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_0_0, xn) = v3 & sdtasdt0(xn, all_0_0_0) = v0 & sdtasdt0(xn, sz10) = v1 & sdtasdt0(xm, xn) = v2 & sdtasdt0(sz10, xn) = v4 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_0_1_1) % 14.42/4.04 | % 14.42/4.04 | Instantiating formula (11) with all_0_1_1, xm, sz10, all_0_0_0, xn and discharging atoms sdtasdt0(xm, xn) = all_0_1_1, sdtpldt0(all_0_0_0, sz10) = xm, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xn), aNaturalNumber0(sz10), yields: % 14.42/4.04 | (113) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_0_0, xn) = v3 & sdtasdt0(xn, all_0_0_0) = v1 & sdtasdt0(xn, xm) = v0 & sdtasdt0(xn, sz10) = v2 & sdtasdt0(sz10, xn) = v4 & sdtpldt0(v3, v4) = all_0_1_1 & sdtpldt0(v1, v2) = v0) % 14.42/4.04 | % 14.42/4.04 | Instantiating formula (45) with all_17_0_6, xn, sz00, xn, all_0_0_0 and discharging atoms sdtasdt0(all_0_0_0, xn) = all_17_0_6, sdtpldt0(xn, sz00) = xn, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xn), aNaturalNumber0(sz00), yields: % 14.42/4.04 | (114) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_0_0, xn) = v0 & sdtasdt0(all_0_0_0, sz00) = v1 & sdtasdt0(xn, all_0_0_0) = v3 & sdtasdt0(xn, all_0_0_0) = v2 & sdtasdt0(sz00, all_0_0_0) = v4 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_17_0_6) % 14.42/4.04 | % 14.42/4.04 | Instantiating formula (11) with all_17_3_9, xn, sz00, xn, all_0_0_0 and discharging atoms sdtasdt0(xn, all_0_0_0) = all_17_3_9, sdtpldt0(xn, sz00) = xn, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xn), aNaturalNumber0(sz00), yields: % 14.42/4.04 | (115) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_0_0_0, xn) = v1 & sdtasdt0(all_0_0_0, xn) = v0 & sdtasdt0(all_0_0_0, sz00) = v2 & sdtasdt0(xn, all_0_0_0) = v3 & sdtasdt0(sz00, all_0_0_0) = v4 & sdtpldt0(v3, v4) = all_17_3_9 & sdtpldt0(v1, v2) = v0) % 14.42/4.04 | % 14.42/4.04 | Instantiating (113) with all_55_0_37, all_55_1_38, all_55_2_39, all_55_3_40, all_55_4_41 yields: % 14.42/4.04 | (116) sdtasdt0(all_0_0_0, xn) = all_55_1_38 & sdtasdt0(xn, all_0_0_0) = all_55_3_40 & sdtasdt0(xn, xm) = all_55_4_41 & sdtasdt0(xn, sz10) = all_55_2_39 & sdtasdt0(sz10, xn) = all_55_0_37 & sdtpldt0(all_55_1_38, all_55_0_37) = all_0_1_1 & sdtpldt0(all_55_3_40, all_55_2_39) = all_55_4_41 % 14.42/4.04 | % 14.42/4.04 | Applying alpha-rule on (116) yields: % 14.42/4.04 | (117) sdtpldt0(all_55_3_40, all_55_2_39) = all_55_4_41 % 14.42/4.04 | (118) sdtasdt0(xn, sz10) = all_55_2_39 % 14.42/4.04 | (119) sdtasdt0(xn, all_0_0_0) = all_55_3_40 % 14.42/4.04 | (120) sdtasdt0(xn, xm) = all_55_4_41 % 14.42/4.05 | (121) sdtpldt0(all_55_1_38, all_55_0_37) = all_0_1_1 % 14.42/4.05 | (122) sdtasdt0(all_0_0_0, xn) = all_55_1_38 % 14.42/4.05 | (123) sdtasdt0(sz10, xn) = all_55_0_37 % 14.42/4.05 | % 14.42/4.05 | Instantiating (115) with all_77_0_63, all_77_1_64, all_77_2_65, all_77_3_66, all_77_4_67 yields: % 14.42/4.05 | (124) sdtasdt0(all_0_0_0, xn) = all_77_3_66 & sdtasdt0(all_0_0_0, xn) = all_77_4_67 & sdtasdt0(all_0_0_0, sz00) = all_77_2_65 & sdtasdt0(xn, all_0_0_0) = all_77_1_64 & sdtasdt0(sz00, all_0_0_0) = all_77_0_63 & sdtpldt0(all_77_1_64, all_77_0_63) = all_17_3_9 & sdtpldt0(all_77_3_66, all_77_2_65) = all_77_4_67 % 14.42/4.05 | % 14.42/4.05 | Applying alpha-rule on (124) yields: % 14.42/4.05 | (125) sdtasdt0(all_0_0_0, xn) = all_77_3_66 % 14.42/4.05 | (126) sdtpldt0(all_77_1_64, all_77_0_63) = all_17_3_9 % 14.42/4.05 | (127) sdtasdt0(all_0_0_0, sz00) = all_77_2_65 % 14.42/4.05 | (128) sdtpldt0(all_77_3_66, all_77_2_65) = all_77_4_67 % 14.42/4.05 | (129) sdtasdt0(sz00, all_0_0_0) = all_77_0_63 % 14.42/4.05 | (130) sdtasdt0(xn, all_0_0_0) = all_77_1_64 % 14.42/4.05 | (131) sdtasdt0(all_0_0_0, xn) = all_77_4_67 % 14.42/4.05 | % 14.42/4.05 | Instantiating (114) with all_79_0_68, all_79_1_69, all_79_2_70, all_79_3_71, all_79_4_72 yields: % 14.42/4.05 | (132) sdtasdt0(all_0_0_0, xn) = all_79_4_72 & sdtasdt0(all_0_0_0, sz00) = all_79_3_71 & sdtasdt0(xn, all_0_0_0) = all_79_1_69 & sdtasdt0(xn, all_0_0_0) = all_79_2_70 & sdtasdt0(sz00, all_0_0_0) = all_79_0_68 & sdtpldt0(all_79_1_69, all_79_0_68) = all_79_2_70 & sdtpldt0(all_79_4_72, all_79_3_71) = all_17_0_6 % 14.42/4.05 | % 14.42/4.05 | Applying alpha-rule on (132) yields: % 14.42/4.05 | (133) sdtpldt0(all_79_4_72, all_79_3_71) = all_17_0_6 % 14.42/4.05 | (134) sdtasdt0(xn, all_0_0_0) = all_79_2_70 % 14.42/4.05 | (135) sdtasdt0(sz00, all_0_0_0) = all_79_0_68 % 14.42/4.05 | (136) sdtasdt0(all_0_0_0, sz00) = all_79_3_71 % 14.42/4.05 | (137) sdtasdt0(all_0_0_0, xn) = all_79_4_72 % 14.42/4.05 | (138) sdtasdt0(xn, all_0_0_0) = all_79_1_69 % 14.42/4.05 | (139) sdtpldt0(all_79_1_69, all_79_0_68) = all_79_2_70 % 14.42/4.05 | % 14.42/4.05 | Instantiating (112) with all_85_0_75, all_85_1_76, all_85_2_77, all_85_3_78, all_85_4_79 yields: % 14.42/4.05 | (140) sdtasdt0(all_0_0_0, xn) = all_85_1_76 & sdtasdt0(xn, all_0_0_0) = all_85_4_79 & sdtasdt0(xn, sz10) = all_85_3_78 & sdtasdt0(xm, xn) = all_85_2_77 & sdtasdt0(sz10, xn) = all_85_0_75 & sdtpldt0(all_85_1_76, all_85_0_75) = all_85_2_77 & sdtpldt0(all_85_4_79, all_85_3_78) = all_0_1_1 % 14.42/4.05 | % 14.42/4.05 | Applying alpha-rule on (140) yields: % 14.42/4.05 | (141) sdtasdt0(sz10, xn) = all_85_0_75 % 14.42/4.05 | (142) sdtasdt0(xn, all_0_0_0) = all_85_4_79 % 14.42/4.05 | (143) sdtasdt0(all_0_0_0, xn) = all_85_1_76 % 14.42/4.05 | (144) sdtasdt0(xn, sz10) = all_85_3_78 % 14.42/4.05 | (145) sdtasdt0(xm, xn) = all_85_2_77 % 14.42/4.05 | (146) sdtpldt0(all_85_1_76, all_85_0_75) = all_85_2_77 % 14.42/4.05 | (147) sdtpldt0(all_85_4_79, all_85_3_78) = all_0_1_1 % 14.42/4.05 | % 14.42/4.05 | Instantiating (111) with all_89_0_81 yields: % 14.42/4.05 | (148) sdtasdt0(xn, all_0_0_0) = all_89_0_81 & sdtasdt0(sz10, all_89_0_81) = all_17_3_9 % 14.42/4.05 | % 14.42/4.05 | Applying alpha-rule on (148) yields: % 14.42/4.05 | (149) sdtasdt0(xn, all_0_0_0) = all_89_0_81 % 14.42/4.05 | (150) sdtasdt0(sz10, all_89_0_81) = all_17_3_9 % 14.42/4.05 | % 14.42/4.05 | Instantiating formula (10) with xn, all_0_0_0, all_85_4_79, all_17_3_9 and discharging atoms sdtasdt0(xn, all_0_0_0) = all_85_4_79, sdtasdt0(xn, all_0_0_0) = all_17_3_9, yields: % 14.42/4.05 | (151) all_85_4_79 = all_17_3_9 % 14.42/4.05 | % 14.42/4.05 | Instantiating formula (10) with xn, all_0_0_0, all_79_1_69, all_89_0_81 and discharging atoms sdtasdt0(xn, all_0_0_0) = all_89_0_81, sdtasdt0(xn, all_0_0_0) = all_79_1_69, yields: % 14.42/4.05 | (152) all_89_0_81 = all_79_1_69 % 14.42/4.05 | % 14.42/4.05 | Instantiating formula (10) with xn, all_0_0_0, all_79_2_70, all_89_0_81 and discharging atoms sdtasdt0(xn, all_0_0_0) = all_89_0_81, sdtasdt0(xn, all_0_0_0) = all_79_2_70, yields: % 14.42/4.05 | (153) all_89_0_81 = all_79_2_70 % 14.42/4.05 | % 14.42/4.05 | Instantiating formula (10) with xn, all_0_0_0, all_77_1_64, all_85_4_79 and discharging atoms sdtasdt0(xn, all_0_0_0) = all_85_4_79, sdtasdt0(xn, all_0_0_0) = all_77_1_64, yields: % 14.42/4.05 | (154) all_85_4_79 = all_77_1_64 % 14.42/4.05 | % 14.42/4.05 | Instantiating formula (10) with xn, all_0_0_0, all_77_1_64, all_79_1_69 and discharging atoms sdtasdt0(xn, all_0_0_0) = all_79_1_69, sdtasdt0(xn, all_0_0_0) = all_77_1_64, yields: % 14.42/4.05 | (155) all_79_1_69 = all_77_1_64 % 14.42/4.05 | % 14.42/4.05 | Instantiating formula (10) with xn, all_0_0_0, all_55_3_40, all_79_1_69 and discharging atoms sdtasdt0(xn, all_0_0_0) = all_79_1_69, sdtasdt0(xn, all_0_0_0) = all_55_3_40, yields: % 14.42/4.05 | (156) all_79_1_69 = all_55_3_40 % 14.42/4.05 | % 14.42/4.05 | Instantiating formula (10) with xn, all_0_0_0, all_17_0_6, all_89_0_81 and discharging atoms sdtasdt0(xn, all_0_0_0) = all_89_0_81, sdtasdt0(xn, all_0_0_0) = all_17_0_6, yields: % 14.42/4.05 | (157) all_89_0_81 = all_17_0_6 % 14.42/4.05 | % 14.42/4.05 | Combining equations (152,153) yields a new equation: % 14.42/4.05 | (158) all_79_1_69 = all_79_2_70 % 14.42/4.05 | % 14.42/4.05 | Simplifying 158 yields: % 14.42/4.05 | (159) all_79_1_69 = all_79_2_70 % 14.42/4.05 | % 14.42/4.05 | Combining equations (157,153) yields a new equation: % 14.42/4.05 | (160) all_79_2_70 = all_17_0_6 % 14.42/4.05 | % 14.42/4.05 | Combining equations (154,151) yields a new equation: % 14.42/4.05 | (161) all_77_1_64 = all_17_3_9 % 14.42/4.05 | % 14.42/4.05 | Simplifying 161 yields: % 14.42/4.05 | (162) all_77_1_64 = all_17_3_9 % 14.42/4.05 | % 14.42/4.05 | Combining equations (155,156) yields a new equation: % 14.42/4.05 | (163) all_77_1_64 = all_55_3_40 % 14.42/4.05 | % 14.42/4.05 | Simplifying 163 yields: % 14.42/4.05 | (164) all_77_1_64 = all_55_3_40 % 14.42/4.05 | % 14.42/4.05 | Combining equations (159,156) yields a new equation: % 14.42/4.05 | (165) all_79_2_70 = all_55_3_40 % 14.42/4.05 | % 14.42/4.05 | Simplifying 165 yields: % 14.42/4.05 | (166) all_79_2_70 = all_55_3_40 % 14.42/4.05 | % 14.42/4.05 | Combining equations (166,160) yields a new equation: % 14.42/4.05 | (167) all_55_3_40 = all_17_0_6 % 14.42/4.05 | % 14.42/4.05 | Simplifying 167 yields: % 14.42/4.05 | (168) all_55_3_40 = all_17_0_6 % 14.42/4.05 | % 14.42/4.05 | Combining equations (164,162) yields a new equation: % 14.42/4.05 | (169) all_55_3_40 = all_17_3_9 % 14.42/4.05 | % 14.42/4.05 | Simplifying 169 yields: % 14.42/4.05 | (170) all_55_3_40 = all_17_3_9 % 14.42/4.05 | % 14.42/4.05 | Combining equations (168,170) yields a new equation: % 14.42/4.05 | (171) all_17_0_6 = all_17_3_9 % 14.42/4.05 | % 14.42/4.05 | Simplifying 171 yields: % 14.42/4.05 | (172) all_17_0_6 = all_17_3_9 % 14.42/4.05 | % 14.42/4.05 | From (172) and (106) follows: % 14.42/4.05 | (173) sdtpldt0(xn, all_17_3_9) = all_0_1_1 % 14.42/4.05 | % 14.42/4.05 | From (172) and (110) follows: % 14.42/4.05 | (174) aNaturalNumber0(all_17_3_9) % 14.42/4.06 | % 14.42/4.06 | Instantiating formula (23) with all_17_3_9, all_0_1_1, xn and discharging atoms sdtpldt0(xn, all_17_3_9) = all_0_1_1, aNaturalNumber0(all_17_3_9), aNaturalNumber0(all_0_1_1), aNaturalNumber0(xn), ~ sdtlseqdt0(xn, all_0_1_1), yields: % 14.42/4.06 | (175) $false % 14.42/4.06 | % 14.42/4.06 |-The branch is then unsatisfiable % 14.42/4.06 % SZS output end Proof for theBenchmark % 14.42/4.06 % 14.42/4.06 3469ms %------------------------------------------------------------------------------