%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : NUM461+2 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n021.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 4.09s 1.60s % Output : Proof 6.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM461+2 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n021.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 : Tue Jul 5 18:44:18 EDT 2022 % 0.12/0.33 % CPUTime : % 0.50/0.58 ____ _ % 0.50/0.58 ___ / __ \_____(_)___ ________ __________ % 0.50/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.50/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.50/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.50/0.58 % 0.50/0.58 A Theorem Prover for First-Order Logic % 0.50/0.58 (ePrincess v.1.0) % 0.50/0.58 % 0.50/0.58 (c) Philipp Rümmer, 2009-2015 % 0.50/0.58 (c) Peter Backeman, 2014-2015 % 0.50/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.50/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.50/0.58 Bug reports to peter@backeman.se % 0.50/0.58 % 0.50/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.50/0.58 % 0.50/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.50/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.70/0.95 Prover 0: Preprocessing ... % 3.17/1.35 Prover 0: Constructing countermodel ... % 4.09/1.60 Prover 0: proved (965ms) % 4.09/1.60 % 4.09/1.60 No countermodel exists, formula is valid % 4.09/1.60 % SZS status Theorem for theBenchmark % 4.09/1.60 % 4.09/1.60 Generating proof ... found it (size 97) % 6.58/2.12 % 6.58/2.12 % SZS output start Proof for theBenchmark % 6.58/2.12 Assumed formulas after preprocessing and simplification: % 6.58/2.12 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (xn = xl) & ~ (sz10 = sz00) & sdtpldt0(xm, xn) = v1 & sdtpldt0(xm, xl) = v0 & sdtpldt0(xn, xm) = v3 & sdtpldt0(xl, v4) = xn & sdtpldt0(xl, xm) = v2 & sdtlseqdt0(xl, xn) & aNaturalNumber0(v4) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(xl) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v7, v5) = v9) | ~ (sdtasdt0(v6, v5) = v8) | ~ (sdtpldt0(v8, v9) = v10) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v11, v5) = v10 & sdtasdt0(v5, v11) = v12 & sdtasdt0(v5, v7) = v14 & sdtasdt0(v5, v6) = v13 & sdtpldt0(v13, v14) = v12 & sdtpldt0(v6, v7) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v5, v7) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ (sdtpldt0(v8, v9) = v10) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v11, v5) = v12 & sdtasdt0(v7, v5) = v14 & sdtasdt0(v6, v5) = v13 & sdtasdt0(v5, v11) = v10 & sdtpldt0(v13, v14) = v12 & sdtpldt0(v6, v7) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v9) | ~ (sdtasdt0(v6, v5) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtasdt0(v5, v7) = v11 & sdtasdt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtasdt0(v6, v5) = v11 & sdtasdt0(v5, v7) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v6, v5) = v9) | ~ (sdtasdt0(v5, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtasdt0(v7, v5) = v11 & sdtasdt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v5, v7) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtasdt0(v7, v5) = v11 & sdtasdt0(v6, v5) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v7, v5) = v9) | ~ (sdtpldt0(v6, v5) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtpldt0(v5, v7) = v11 & sdtpldt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v7, v5) = v9) | ~ (sdtpldt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtpldt0(v6, v5) = v11 & sdtpldt0(v5, v7) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v6, v5) = v9) | ~ (sdtpldt0(v5, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v9) & ~ (v10 = v8) & sdtpldt0(v7, v5) = v11 & sdtpldt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (sdtpldt0(v5, v7) = v9) | ~ (sdtpldt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ( ~ (v11 = v10) & sdtpldt0(v7, v5) = v11 & sdtpldt0(v6, v5) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v8, v7) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : (sdtasdt0(v6, v7) = v10 & sdtasdt0(v5, v10) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v8, v5) = v9) | ~ (sdtpldt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v7, v5) = v14 & sdtasdt0(v6, v5) = v13 & sdtasdt0(v5, v8) = v10 & sdtasdt0(v5, v7) = v12 & sdtasdt0(v5, v6) = v11 & sdtpldt0(v13, v14) = v9 & sdtpldt0(v11, v12) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v6, v7) = v8) | ~ (sdtasdt0(v5, v8) = v9) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : (sdtasdt0(v10, v7) = v9 & sdtasdt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v5, v8) = v9) | ~ (sdtpldt0(v6, v7) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v8, v5) = v12 & sdtasdt0(v7, v5) = v14 & sdtasdt0(v6, v5) = v13 & sdtasdt0(v5, v7) = v11 & sdtasdt0(v5, v6) = v10 & sdtpldt0(v13, v14) = v12 & sdtpldt0(v10, v11) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v8, v7) = v9) | ~ (sdtpldt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : (sdtpldt0(v6, v7) = v10 & sdtpldt0(v5, v10) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v6, v7) = v8) | ~ (sdtpldt0(v5, v8) = v9) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v10] : (sdtpldt0(v10, v7) = v9 & sdtpldt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ (sdtmndt0(v6, v5) = v7) | ~ (sdtpldt0(v5, v8) = v6) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v8) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v6 | ~ (sdtmndt0(v6, v5) = v7) | ~ (sdtpldt0(v5, v7) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v7, v5) = v8) | ~ (sdtasdt0(v6, v5) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | v5 = sz00 | ~ (sdtasdt0(v5, v7) = v8) | ~ (sdtasdt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (sdtpldt0(v7, v5) = v8) | ~ (sdtpldt0(v6, v5) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (sdtpldt0(v5, v7) = v8) | ~ (sdtpldt0(v5, v6) = v8) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtmndt0(v8, v7) = v6) | ~ (sdtmndt0(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtasdt0(v8, v7) = v6) | ~ (sdtasdt0(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v8, v7) = v6) | ~ (sdtpldt0(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtmndt0(v6, v5) = v7) | ~ (sdtpldt0(v5, v7) = v8) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | aNaturalNumber0(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v6, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtasdt0(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtasdt0(v6, v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | aNaturalNumber0(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v6, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtpldt0(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v7) = v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtlseqdt0(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtpldt0(v6, v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | aNaturalNumber0(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ sdtlseqdt0(v6, v7) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtlseqdt0(v5, v7)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtasdt0(v5, sz10) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtasdt0(sz10, v5) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtpldt0(v5, sz00) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtpldt0(sz00, v5) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ sdtlseqdt0(v6, v5) | ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = sz00 | v5 = sz00 | ~ (sdtasdt0(v5, v6) = sz00) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = sz00 | ~ (sdtasdt0(v5, sz00) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = sz00 | ~ (sdtasdt0(sz00, v5) = v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v6 = sz00 | ~ (sdtpldt0(v5, v6) = sz00) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : (v5 = sz00 | ~ (sdtpldt0(v5, v6) = sz00) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5)) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, sz10) = v6) | ~ aNaturalNumber0(v5) | sdtasdt0(sz10, v5) = v5) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, sz00) = v6) | ~ aNaturalNumber0(v5) | sdtasdt0(sz00, v5) = sz00) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(sz10, v5) = v6) | ~ aNaturalNumber0(v5) | sdtasdt0(v5, sz10) = v5) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(sz00, v5) = v6) | ~ aNaturalNumber0(v5) | sdtasdt0(v5, sz00) = sz00) & ! [v5] : ! [v6] : ( ~ (sdtpldt0(v5, sz00) = v6) | ~ aNaturalNumber0(v5) | sdtpldt0(sz00, v5) = v5) & ! [v5] : ! [v6] : ( ~ (sdtpldt0(sz00, v5) = v6) | ~ aNaturalNumber0(v5) | sdtpldt0(v5, sz00) = v5) & ! [v5] : ! [v6] : ( ~ sdtlseqdt0(v5, v6) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ? [v7] : (sdtpldt0(v5, v7) = v6 & aNaturalNumber0(v7))) & ! [v5] : ! [v6] : ( ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | sdtlseqdt0(v6, v5) | sdtlseqdt0(v5, v6)) & ! [v5] : ( ~ aNaturalNumber0(v5) | sdtlseqdt0(v5, v5)) & (v3 = v2 | v1 = v0 | ( ~ sdtlseqdt0(v2, v3) & ! [v5] : ( ~ aNaturalNumber0(v5) | ? [v6] : ( ~ (v6 = v3) & sdtpldt0(v2, v5) = v6))) | ( ~ sdtlseqdt0(v0, v1) & ! [v5] : ( ~ aNaturalNumber0(v5) | ? [v6] : ( ~ (v6 = v1) & sdtpldt0(v0, v5) = v6))))) % 6.82/2.17 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 6.82/2.17 | (1) ~ (xn = xl) & ~ (sz10 = sz00) & sdtpldt0(xm, xn) = all_0_3_3 & sdtpldt0(xm, xl) = all_0_4_4 & sdtpldt0(xn, xm) = all_0_1_1 & sdtpldt0(xl, all_0_0_0) = xn & sdtpldt0(xl, xm) = all_0_2_2 & sdtlseqdt0(xl, xn) & aNaturalNumber0(all_0_0_0) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(xl) & 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] : ( ~ (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_1_1 = all_0_2_2 | all_0_3_3 = all_0_4_4 | ( ~ sdtlseqdt0(all_0_2_2, all_0_1_1) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_1_1) & sdtpldt0(all_0_2_2, v0) = v1))) | ( ~ sdtlseqdt0(all_0_4_4, all_0_3_3) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_3_3) & sdtpldt0(all_0_4_4, v0) = v1)))) % 6.82/2.19 | % 6.82/2.19 | Applying alpha-rule on (1) yields: % 6.82/2.19 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 6.82/2.19 | (3) ! [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)) % 6.82/2.19 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2) % 6.82/2.19 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 6.82/2.19 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 6.82/2.19 | (7) aNaturalNumber0(sz00) % 6.82/2.19 | (8) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0) % 6.82/2.19 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2) % 6.82/2.19 | (10) ! [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)) % 6.82/2.19 | (11) sdtpldt0(xm, xl) = all_0_4_4 % 6.82/2.19 | (12) aNaturalNumber0(all_0_0_0) % 6.82/2.19 | (13) sdtpldt0(xl, xm) = all_0_2_2 % 6.82/2.19 | (14) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 6.82/2.19 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 6.82/2.19 | (16) ! [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)) % 6.82/2.19 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2) % 6.82/2.19 | (18) sdtpldt0(xn, xm) = all_0_1_1 % 6.82/2.19 | (19) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00) % 6.82/2.20 | (20) sdtpldt0(xm, xn) = all_0_3_3 % 6.82/2.20 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2) % 6.82/2.20 | (22) aNaturalNumber0(xl) % 6.82/2.20 | (23) ! [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)) % 6.82/2.20 | (24) sdtpldt0(xl, all_0_0_0) = xn % 6.82/2.20 | (25) ! [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)) % 6.82/2.20 | (26) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0) % 6.82/2.20 | (27) all_0_1_1 = all_0_2_2 | all_0_3_3 = all_0_4_4 | ( ~ sdtlseqdt0(all_0_2_2, all_0_1_1) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_1_1) & sdtpldt0(all_0_2_2, v0) = v1))) | ( ~ sdtlseqdt0(all_0_4_4, all_0_3_3) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_3_3) & sdtpldt0(all_0_4_4, v0) = v1))) % 6.82/2.20 | (28) ! [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)) % 6.82/2.20 | (29) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) % 6.82/2.20 | (30) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 6.82/2.20 | (31) ! [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)) % 6.82/2.20 | (32) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) % 6.82/2.20 | (33) ! [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)) % 6.82/2.20 | (34) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) % 6.82/2.20 | (35) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0) % 6.82/2.20 | (36) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0)) % 6.82/2.20 | (37) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2))) % 6.82/2.20 | (38) ~ (sz10 = sz00) % 6.82/2.20 | (39) aNaturalNumber0(xm) % 6.82/2.20 | (40) ! [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)) % 6.82/2.20 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) % 6.82/2.20 | (42) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) % 6.82/2.21 | (43) aNaturalNumber0(sz10) % 6.82/2.21 | (44) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) % 6.82/2.21 | (45) ! [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)) % 6.82/2.21 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 6.82/2.21 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) % 6.82/2.21 | (48) aNaturalNumber0(xn) % 6.82/2.21 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2)) % 6.82/2.21 | (50) ! [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)) % 6.82/2.21 | (51) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) % 6.82/2.21 | (52) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0) % 6.82/2.21 | (53) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 6.82/2.21 | (54) ~ (xn = xl) % 6.82/2.21 | (55) ! [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)) % 6.82/2.21 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 6.82/2.21 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 6.82/2.21 | (58) ! [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)) % 6.82/2.21 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 6.82/2.21 | (60) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00) % 6.82/2.21 | (61) ! [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)) % 6.82/2.21 | (62) ! [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)) % 6.82/2.21 | (63) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0)) % 6.82/2.21 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 6.82/2.21 | (65) sdtlseqdt0(xl, xn) % 6.82/2.21 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 6.82/2.21 | (67) ! [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)) % 6.82/2.22 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 6.82/2.22 | (69) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 6.82/2.22 | % 6.82/2.22 | Instantiating formula (9) with all_0_1_1, xn, xm and discharging atoms sdtpldt0(xn, xm) = all_0_1_1, aNaturalNumber0(xm), aNaturalNumber0(xn), yields: % 6.82/2.22 | (70) sdtpldt0(xm, xn) = all_0_1_1 % 6.82/2.22 | % 6.82/2.22 | Instantiating formula (61) with all_0_3_3, all_0_4_4, xn, xl, xm and discharging atoms sdtpldt0(xm, xn) = all_0_3_3, sdtpldt0(xm, xl) = all_0_4_4, aNaturalNumber0(xm), aNaturalNumber0(xn), aNaturalNumber0(xl), yields: % 6.82/2.22 | (71) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xn, xm) = v1 & sdtpldt0(xl, xm) = v0) % 6.82/2.22 | % 6.82/2.22 | Instantiating formula (61) with all_0_4_4, all_0_3_3, xl, xn, xm and discharging atoms sdtpldt0(xm, xn) = all_0_3_3, sdtpldt0(xm, xl) = all_0_4_4, aNaturalNumber0(xm), aNaturalNumber0(xn), aNaturalNumber0(xl), yields: % 6.82/2.22 | (72) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xn, xm) = v0 & sdtpldt0(xl, xm) = v1) % 6.82/2.22 | % 6.82/2.22 | Instantiating formula (28) with all_0_1_1, all_0_4_4, xn, xl, xm and discharging atoms sdtpldt0(xm, xl) = all_0_4_4, sdtpldt0(xn, xm) = all_0_1_1, aNaturalNumber0(xm), aNaturalNumber0(xn), aNaturalNumber0(xl), yields: % 6.82/2.22 | (73) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = all_0_1_1) & ~ (v0 = all_0_4_4) & sdtpldt0(xm, xn) = v0 & sdtpldt0(xl, xm) = v1) % 6.82/2.22 | % 6.82/2.22 | Instantiating formula (3) with all_0_1_1, all_0_2_2, xn, xl, xm and discharging atoms sdtpldt0(xn, xm) = all_0_1_1, sdtpldt0(xl, xm) = all_0_2_2, aNaturalNumber0(xm), aNaturalNumber0(xn), aNaturalNumber0(xl), yields: % 6.82/2.22 | (74) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xm, xn) = v1 & sdtpldt0(xm, xl) = v0) % 6.82/2.22 | % 6.82/2.22 | Instantiating formula (25) with all_0_3_3, xn, all_0_0_0, xl, xm and discharging atoms sdtpldt0(xm, xn) = all_0_3_3, sdtpldt0(xl, all_0_0_0) = xn, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xm), aNaturalNumber0(xl), yields: % 6.82/2.22 | (75) ? [v0] : (sdtpldt0(v0, all_0_0_0) = all_0_3_3 & sdtpldt0(xm, xl) = v0) % 6.82/2.22 | % 6.82/2.22 | Instantiating formula (28) with all_0_2_2, all_0_3_3, xl, xn, xm and discharging atoms sdtpldt0(xm, xn) = all_0_3_3, sdtpldt0(xl, xm) = all_0_2_2, aNaturalNumber0(xm), aNaturalNumber0(xn), aNaturalNumber0(xl), yields: % 6.82/2.22 | (76) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = all_0_2_2) & ~ (v0 = all_0_3_3) & sdtpldt0(xm, xl) = v0 & sdtpldt0(xn, xm) = v1) % 6.82/2.22 | % 6.82/2.22 | Instantiating formula (3) with all_0_2_2, all_0_1_1, xl, xn, xm and discharging atoms sdtpldt0(xn, xm) = all_0_1_1, sdtpldt0(xl, xm) = all_0_2_2, aNaturalNumber0(xm), aNaturalNumber0(xn), aNaturalNumber0(xl), yields: % 6.82/2.23 | (77) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xm, xn) = v0 & sdtpldt0(xm, xl) = v1) % 6.82/2.23 | % 6.82/2.23 | Instantiating formula (9) with all_0_2_2, xl, xm and discharging atoms sdtpldt0(xl, xm) = all_0_2_2, aNaturalNumber0(xm), aNaturalNumber0(xl), yields: % 6.82/2.23 | (78) sdtpldt0(xm, xl) = all_0_2_2 % 6.82/2.23 | % 6.82/2.23 | Instantiating formula (37) with xn, xl and discharging atoms sdtlseqdt0(xl, xn), aNaturalNumber0(xn), aNaturalNumber0(xl), yields: % 6.82/2.23 | (79) ? [v0] : (sdtpldt0(xl, v0) = xn & aNaturalNumber0(v0)) % 6.82/2.23 | % 6.82/2.23 | Instantiating (79) with all_9_0_5 yields: % 6.82/2.23 | (80) sdtpldt0(xl, all_9_0_5) = xn & aNaturalNumber0(all_9_0_5) % 6.82/2.23 | % 6.82/2.23 | Applying alpha-rule on (80) yields: % 6.82/2.23 | (81) sdtpldt0(xl, all_9_0_5) = xn % 6.82/2.23 | (82) aNaturalNumber0(all_9_0_5) % 6.82/2.23 | % 6.82/2.23 | Instantiating (75) with all_11_0_6 yields: % 6.82/2.23 | (83) sdtpldt0(all_11_0_6, all_0_0_0) = all_0_3_3 & sdtpldt0(xm, xl) = all_11_0_6 % 6.82/2.23 | % 6.82/2.23 | Applying alpha-rule on (83) yields: % 6.82/2.23 | (84) sdtpldt0(all_11_0_6, all_0_0_0) = all_0_3_3 % 6.82/2.23 | (85) sdtpldt0(xm, xl) = all_11_0_6 % 6.82/2.23 | % 6.82/2.23 +-Applying beta-rule and splitting (77), into two cases. % 6.82/2.23 |-Branch one: % 6.82/2.23 | (86) xn = xl % 6.82/2.23 | % 6.82/2.23 | Equations (86) can reduce 54 to: % 6.82/2.23 | (87) $false % 6.82/2.23 | % 6.82/2.23 |-The branch is then unsatisfiable % 6.82/2.23 |-Branch two: % 6.82/2.23 | (54) ~ (xn = xl) % 6.82/2.23 | (89) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xm, xn) = v0 & sdtpldt0(xm, xl) = v1) % 6.82/2.23 | % 6.82/2.23 | Instantiating (89) with all_19_0_8, all_19_1_9 yields: % 6.82/2.23 | (90) ~ (all_19_0_8 = all_19_1_9) & sdtpldt0(xm, xn) = all_19_1_9 & sdtpldt0(xm, xl) = all_19_0_8 % 6.82/2.23 | % 6.82/2.23 | Applying alpha-rule on (90) yields: % 6.82/2.23 | (91) ~ (all_19_0_8 = all_19_1_9) % 6.82/2.23 | (92) sdtpldt0(xm, xn) = all_19_1_9 % 6.82/2.23 | (93) sdtpldt0(xm, xl) = all_19_0_8 % 6.82/2.23 | % 6.82/2.23 +-Applying beta-rule and splitting (72), into two cases. % 6.82/2.23 |-Branch one: % 6.82/2.23 | (86) xn = xl % 6.82/2.23 | % 6.82/2.23 | Equations (86) can reduce 54 to: % 6.82/2.23 | (87) $false % 6.82/2.23 | % 6.82/2.23 |-The branch is then unsatisfiable % 6.82/2.23 |-Branch two: % 6.82/2.23 | (54) ~ (xn = xl) % 6.82/2.23 | (97) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xn, xm) = v0 & sdtpldt0(xl, xm) = v1) % 6.82/2.23 | % 6.82/2.23 +-Applying beta-rule and splitting (76), into two cases. % 6.82/2.23 |-Branch one: % 6.82/2.23 | (86) xn = xl % 6.82/2.23 | % 6.82/2.23 | Equations (86) can reduce 54 to: % 6.82/2.23 | (87) $false % 6.82/2.23 | % 6.82/2.23 |-The branch is then unsatisfiable % 6.82/2.23 |-Branch two: % 6.82/2.23 | (54) ~ (xn = xl) % 6.82/2.23 | (101) ? [v0] : ? [v1] : ( ~ (v1 = all_0_2_2) & ~ (v0 = all_0_3_3) & sdtpldt0(xm, xl) = v0 & sdtpldt0(xn, xm) = v1) % 6.82/2.23 | % 6.82/2.23 | Instantiating (101) with all_31_0_12, all_31_1_13 yields: % 6.82/2.23 | (102) ~ (all_31_0_12 = all_0_2_2) & ~ (all_31_1_13 = all_0_3_3) & sdtpldt0(xm, xl) = all_31_1_13 & sdtpldt0(xn, xm) = all_31_0_12 % 6.82/2.23 | % 6.82/2.23 | Applying alpha-rule on (102) yields: % 6.82/2.23 | (103) ~ (all_31_0_12 = all_0_2_2) % 6.82/2.23 | (104) ~ (all_31_1_13 = all_0_3_3) % 6.82/2.23 | (105) sdtpldt0(xm, xl) = all_31_1_13 % 6.82/2.23 | (106) sdtpldt0(xn, xm) = all_31_0_12 % 6.82/2.23 | % 6.82/2.23 +-Applying beta-rule and splitting (71), into two cases. % 6.82/2.23 |-Branch one: % 6.82/2.23 | (86) xn = xl % 6.82/2.23 | % 6.82/2.23 | Equations (86) can reduce 54 to: % 6.82/2.23 | (87) $false % 6.82/2.23 | % 6.82/2.23 |-The branch is then unsatisfiable % 6.82/2.23 |-Branch two: % 6.82/2.23 | (54) ~ (xn = xl) % 6.82/2.23 | (110) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xn, xm) = v1 & sdtpldt0(xl, xm) = v0) % 6.82/2.23 | % 6.82/2.23 +-Applying beta-rule and splitting (74), into two cases. % 6.82/2.23 |-Branch one: % 6.82/2.23 | (86) xn = xl % 6.82/2.23 | % 6.82/2.23 | Equations (86) can reduce 54 to: % 6.82/2.23 | (87) $false % 6.82/2.23 | % 6.82/2.23 |-The branch is then unsatisfiable % 6.82/2.23 |-Branch two: % 6.82/2.23 | (54) ~ (xn = xl) % 6.82/2.23 | (114) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xm, xn) = v1 & sdtpldt0(xm, xl) = v0) % 6.82/2.23 | % 6.82/2.23 | Instantiating (114) with all_43_0_16, all_43_1_17 yields: % 6.82/2.23 | (115) ~ (all_43_0_16 = all_43_1_17) & sdtpldt0(xm, xn) = all_43_0_16 & sdtpldt0(xm, xl) = all_43_1_17 % 6.82/2.23 | % 6.82/2.23 | Applying alpha-rule on (115) yields: % 6.82/2.23 | (116) ~ (all_43_0_16 = all_43_1_17) % 6.82/2.23 | (117) sdtpldt0(xm, xn) = all_43_0_16 % 6.82/2.23 | (118) sdtpldt0(xm, xl) = all_43_1_17 % 6.82/2.23 | % 6.82/2.23 +-Applying beta-rule and splitting (73), into two cases. % 6.82/2.23 |-Branch one: % 6.82/2.23 | (86) xn = xl % 6.82/2.23 | % 6.82/2.23 | Equations (86) can reduce 54 to: % 6.82/2.23 | (87) $false % 6.82/2.23 | % 6.82/2.23 |-The branch is then unsatisfiable % 6.82/2.23 |-Branch two: % 6.82/2.23 | (54) ~ (xn = xl) % 6.82/2.23 | (122) ? [v0] : ? [v1] : ( ~ (v1 = all_0_1_1) & ~ (v0 = all_0_4_4) & sdtpldt0(xm, xn) = v0 & sdtpldt0(xl, xm) = v1) % 6.82/2.23 | % 6.82/2.23 | Instantiating (122) with all_49_0_18, all_49_1_19 yields: % 6.82/2.23 | (123) ~ (all_49_0_18 = all_0_1_1) & ~ (all_49_1_19 = all_0_4_4) & sdtpldt0(xm, xn) = all_49_1_19 & sdtpldt0(xl, xm) = all_49_0_18 % 6.82/2.24 | % 6.82/2.24 | Applying alpha-rule on (123) yields: % 6.82/2.24 | (124) ~ (all_49_0_18 = all_0_1_1) % 6.82/2.24 | (125) ~ (all_49_1_19 = all_0_4_4) % 6.82/2.24 | (126) sdtpldt0(xm, xn) = all_49_1_19 % 6.82/2.24 | (127) sdtpldt0(xl, xm) = all_49_0_18 % 6.82/2.24 | % 6.82/2.24 | Instantiating formula (6) with xm, xn, all_43_0_16, all_49_1_19 and discharging atoms sdtpldt0(xm, xn) = all_49_1_19, sdtpldt0(xm, xn) = all_43_0_16, yields: % 6.82/2.24 | (128) all_49_1_19 = all_43_0_16 % 6.82/2.24 | % 6.82/2.24 | Instantiating formula (6) with xm, xn, all_19_1_9, all_0_3_3 and discharging atoms sdtpldt0(xm, xn) = all_19_1_9, sdtpldt0(xm, xn) = all_0_3_3, yields: % 6.82/2.24 | (129) all_19_1_9 = all_0_3_3 % 6.82/2.24 | % 6.82/2.24 | Instantiating formula (6) with xm, xn, all_19_1_9, all_43_0_16 and discharging atoms sdtpldt0(xm, xn) = all_43_0_16, sdtpldt0(xm, xn) = all_19_1_9, yields: % 6.82/2.24 | (130) all_43_0_16 = all_19_1_9 % 6.82/2.24 | % 6.82/2.24 | Instantiating formula (6) with xm, xn, all_0_1_1, all_49_1_19 and discharging atoms sdtpldt0(xm, xn) = all_49_1_19, sdtpldt0(xm, xn) = all_0_1_1, yields: % 6.82/2.24 | (131) all_49_1_19 = all_0_1_1 % 6.82/2.24 | % 6.82/2.24 | Instantiating formula (6) with xm, xl, all_43_1_17, all_0_4_4 and discharging atoms sdtpldt0(xm, xl) = all_43_1_17, sdtpldt0(xm, xl) = all_0_4_4, yields: % 6.82/2.24 | (132) all_43_1_17 = all_0_4_4 % 6.82/2.24 | % 6.82/2.24 | Instantiating formula (6) with xm, xl, all_31_1_13, all_43_1_17 and discharging atoms sdtpldt0(xm, xl) = all_43_1_17, sdtpldt0(xm, xl) = all_31_1_13, yields: % 6.82/2.24 | (133) all_43_1_17 = all_31_1_13 % 6.82/2.24 | % 6.82/2.24 | Instantiating formula (6) with xm, xl, all_19_0_8, all_43_1_17 and discharging atoms sdtpldt0(xm, xl) = all_43_1_17, sdtpldt0(xm, xl) = all_19_0_8, yields: % 6.82/2.24 | (134) all_43_1_17 = all_19_0_8 % 6.82/2.24 | % 6.82/2.24 | Instantiating formula (6) with xm, xl, all_11_0_6, all_19_0_8 and discharging atoms sdtpldt0(xm, xl) = all_19_0_8, sdtpldt0(xm, xl) = all_11_0_6, yields: % 6.82/2.24 | (135) all_19_0_8 = all_11_0_6 % 6.82/2.24 | % 6.82/2.24 | Instantiating formula (6) with xm, xl, all_0_2_2, all_11_0_6 and discharging atoms sdtpldt0(xm, xl) = all_11_0_6, sdtpldt0(xm, xl) = all_0_2_2, yields: % 6.82/2.24 | (136) all_11_0_6 = all_0_2_2 % 6.82/2.24 | % 6.82/2.24 | Instantiating formula (59) with xn, all_0_0_0, all_9_0_5, xl and discharging atoms sdtpldt0(xl, all_9_0_5) = xn, sdtpldt0(xl, all_0_0_0) = xn, aNaturalNumber0(all_9_0_5), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), yields: % 6.82/2.24 | (137) all_9_0_5 = all_0_0_0 % 6.82/2.24 | % 6.82/2.24 | Combining equations (128,131) yields a new equation: % 6.82/2.24 | (138) all_43_0_16 = all_0_1_1 % 6.82/2.24 | % 6.82/2.24 | Simplifying 138 yields: % 6.82/2.24 | (139) all_43_0_16 = all_0_1_1 % 6.82/2.24 | % 6.82/2.24 | Combining equations (130,139) yields a new equation: % 6.82/2.24 | (140) all_19_1_9 = all_0_1_1 % 6.82/2.24 | % 6.82/2.24 | Simplifying 140 yields: % 6.82/2.24 | (141) all_19_1_9 = all_0_1_1 % 6.82/2.24 | % 6.82/2.24 | Combining equations (132,133) yields a new equation: % 6.82/2.24 | (142) all_31_1_13 = all_0_4_4 % 6.82/2.24 | % 6.82/2.24 | Combining equations (134,133) yields a new equation: % 6.82/2.24 | (143) all_31_1_13 = all_19_0_8 % 6.82/2.24 | % 6.82/2.24 | Combining equations (143,142) yields a new equation: % 6.82/2.24 | (144) all_19_0_8 = all_0_4_4 % 6.82/2.24 | % 6.82/2.24 | Simplifying 144 yields: % 6.82/2.24 | (145) all_19_0_8 = all_0_4_4 % 6.82/2.24 | % 6.82/2.24 | Combining equations (135,145) yields a new equation: % 6.82/2.24 | (146) all_11_0_6 = all_0_4_4 % 6.82/2.24 | % 6.82/2.24 | Simplifying 146 yields: % 6.82/2.24 | (147) all_11_0_6 = all_0_4_4 % 6.82/2.24 | % 6.82/2.24 | Combining equations (129,141) yields a new equation: % 6.82/2.24 | (148) all_0_1_1 = all_0_3_3 % 6.82/2.24 | % 6.82/2.24 | Combining equations (136,147) yields a new equation: % 6.82/2.24 | (149) all_0_2_2 = all_0_4_4 % 6.82/2.24 | % 6.82/2.24 | Simplifying 149 yields: % 6.82/2.24 | (150) all_0_2_2 = all_0_4_4 % 6.82/2.24 | % 6.82/2.24 | Combining equations (148,141) yields a new equation: % 6.82/2.24 | (129) all_19_1_9 = all_0_3_3 % 6.82/2.24 | % 6.82/2.24 | Equations (145,129) can reduce 91 to: % 6.82/2.24 | (152) ~ (all_0_3_3 = all_0_4_4) % 6.82/2.24 | % 6.82/2.24 | Simplifying 152 yields: % 6.82/2.24 | (153) ~ (all_0_3_3 = all_0_4_4) % 6.82/2.24 | % 6.82/2.24 | From (147) and (84) follows: % 6.82/2.24 | (154) sdtpldt0(all_0_4_4, all_0_0_0) = all_0_3_3 % 6.82/2.24 | % 6.82/2.24 | From (137) and (82) follows: % 6.82/2.24 | (12) aNaturalNumber0(all_0_0_0) % 6.82/2.24 | % 6.82/2.24 +-Applying beta-rule and splitting (27), into two cases. % 6.82/2.24 |-Branch one: % 6.82/2.24 | (156) all_0_1_1 = all_0_2_2 % 6.82/2.24 | % 6.82/2.24 | Combining equations (148,156) yields a new equation: % 6.82/2.24 | (157) all_0_2_2 = all_0_3_3 % 6.82/2.24 | % 6.82/2.24 | Combining equations (157,150) yields a new equation: % 6.82/2.24 | (158) all_0_3_3 = all_0_4_4 % 6.82/2.24 | % 6.82/2.24 | Simplifying 158 yields: % 6.82/2.24 | (159) all_0_3_3 = all_0_4_4 % 6.82/2.24 | % 6.82/2.24 | Equations (159) can reduce 153 to: % 6.82/2.24 | (87) $false % 6.82/2.24 | % 6.82/2.24 |-The branch is then unsatisfiable % 6.82/2.24 |-Branch two: % 6.82/2.24 | (161) ~ (all_0_1_1 = all_0_2_2) % 6.82/2.24 | (162) all_0_3_3 = all_0_4_4 | ( ~ sdtlseqdt0(all_0_2_2, all_0_1_1) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_1_1) & sdtpldt0(all_0_2_2, v0) = v1))) | ( ~ sdtlseqdt0(all_0_4_4, all_0_3_3) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_3_3) & sdtpldt0(all_0_4_4, v0) = v1))) % 6.82/2.24 | % 6.82/2.24 | Equations (148,150) can reduce 161 to: % 6.82/2.24 | (153) ~ (all_0_3_3 = all_0_4_4) % 6.82/2.24 | % 6.82/2.24 +-Applying beta-rule and splitting (162), into two cases. % 6.82/2.24 |-Branch one: % 6.82/2.24 | (159) all_0_3_3 = all_0_4_4 % 6.82/2.24 | % 6.82/2.24 | Equations (159) can reduce 153 to: % 6.82/2.24 | (87) $false % 6.82/2.24 | % 6.82/2.24 |-The branch is then unsatisfiable % 6.82/2.24 |-Branch two: % 6.82/2.24 | (153) ~ (all_0_3_3 = all_0_4_4) % 6.82/2.24 | (167) ( ~ sdtlseqdt0(all_0_2_2, all_0_1_1) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_1_1) & sdtpldt0(all_0_2_2, v0) = v1))) | ( ~ sdtlseqdt0(all_0_4_4, all_0_3_3) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_3_3) & sdtpldt0(all_0_4_4, v0) = v1))) % 6.82/2.24 | % 6.82/2.24 +-Applying beta-rule and splitting (167), into two cases. % 6.82/2.24 |-Branch one: % 6.82/2.24 | (168) ~ sdtlseqdt0(all_0_2_2, all_0_1_1) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_1_1) & sdtpldt0(all_0_2_2, v0) = v1)) % 6.82/2.24 | % 6.82/2.24 | Applying alpha-rule on (168) yields: % 6.82/2.24 | (169) ~ sdtlseqdt0(all_0_2_2, all_0_1_1) % 6.82/2.24 | (170) ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_1_1) & sdtpldt0(all_0_2_2, v0) = v1)) % 6.82/2.24 | % 6.82/2.24 | Instantiating formula (170) with all_0_0_0 and discharging atoms aNaturalNumber0(all_0_0_0), yields: % 6.82/2.24 | (171) ? [v0] : ( ~ (v0 = all_0_1_1) & sdtpldt0(all_0_2_2, all_0_0_0) = v0) % 6.82/2.24 | % 6.82/2.24 | Instantiating (171) with all_78_0_25 yields: % 6.82/2.24 | (172) ~ (all_78_0_25 = all_0_1_1) & sdtpldt0(all_0_2_2, all_0_0_0) = all_78_0_25 % 6.82/2.24 | % 6.82/2.24 | Applying alpha-rule on (172) yields: % 6.82/2.24 | (173) ~ (all_78_0_25 = all_0_1_1) % 6.82/2.24 | (174) sdtpldt0(all_0_2_2, all_0_0_0) = all_78_0_25 % 6.82/2.24 | % 6.82/2.24 | Equations (148) can reduce 173 to: % 6.82/2.24 | (175) ~ (all_78_0_25 = all_0_3_3) % 6.82/2.24 | % 6.82/2.24 | From (150) and (174) follows: % 6.82/2.24 | (176) sdtpldt0(all_0_4_4, all_0_0_0) = all_78_0_25 % 6.82/2.25 | % 6.82/2.25 | Instantiating formula (6) with all_0_4_4, all_0_0_0, all_0_3_3, all_78_0_25 and discharging atoms sdtpldt0(all_0_4_4, all_0_0_0) = all_78_0_25, sdtpldt0(all_0_4_4, all_0_0_0) = all_0_3_3, yields: % 6.82/2.25 | (177) all_78_0_25 = all_0_3_3 % 6.82/2.25 | % 6.82/2.25 | Equations (177) can reduce 175 to: % 6.82/2.25 | (87) $false % 6.82/2.25 | % 6.82/2.25 |-The branch is then unsatisfiable % 6.82/2.25 |-Branch two: % 6.82/2.25 | (179) ~ sdtlseqdt0(all_0_4_4, all_0_3_3) & ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_3_3) & sdtpldt0(all_0_4_4, v0) = v1)) % 6.82/2.25 | % 6.82/2.25 | Applying alpha-rule on (179) yields: % 6.82/2.25 | (180) ~ sdtlseqdt0(all_0_4_4, all_0_3_3) % 6.82/2.25 | (181) ! [v0] : ( ~ aNaturalNumber0(v0) | ? [v1] : ( ~ (v1 = all_0_3_3) & sdtpldt0(all_0_4_4, v0) = v1)) % 6.82/2.25 | % 6.82/2.25 | Instantiating formula (181) with all_0_0_0 and discharging atoms aNaturalNumber0(all_0_0_0), yields: % 6.82/2.25 | (182) ? [v0] : ( ~ (v0 = all_0_3_3) & sdtpldt0(all_0_4_4, all_0_0_0) = v0) % 6.82/2.25 | % 6.82/2.25 | Instantiating (182) with all_78_0_31 yields: % 6.82/2.25 | (183) ~ (all_78_0_31 = all_0_3_3) & sdtpldt0(all_0_4_4, all_0_0_0) = all_78_0_31 % 6.82/2.25 | % 6.82/2.25 | Applying alpha-rule on (183) yields: % 6.82/2.25 | (184) ~ (all_78_0_31 = all_0_3_3) % 6.82/2.25 | (185) sdtpldt0(all_0_4_4, all_0_0_0) = all_78_0_31 % 6.82/2.25 | % 6.82/2.25 | Instantiating formula (6) with all_0_4_4, all_0_0_0, all_0_3_3, all_78_0_31 and discharging atoms sdtpldt0(all_0_4_4, all_0_0_0) = all_78_0_31, sdtpldt0(all_0_4_4, all_0_0_0) = all_0_3_3, yields: % 6.82/2.25 | (186) all_78_0_31 = all_0_3_3 % 6.82/2.25 | % 6.82/2.25 | Equations (186) can reduce 184 to: % 6.82/2.25 | (87) $false % 6.82/2.25 | % 6.82/2.25 |-The branch is then unsatisfiable % 6.82/2.25 % SZS output end Proof for theBenchmark % 6.82/2.25 % 6.82/2.25 1655ms %------------------------------------------------------------------------------