%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : NUM461+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n012.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 4.63s 1.75s % Output : Proof 7.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUM461+1 : TPTP v8.1.0. Released v4.0.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n012.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 14:22:45 EDT 2022 % 0.12/0.33 % CPUTime : % 0.60/0.60 ____ _ % 0.60/0.60 ___ / __ \_____(_)___ ________ __________ % 0.60/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.60/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.60/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.60/0.60 % 0.60/0.60 A Theorem Prover for First-Order Logic % 0.60/0.60 (ePrincess v.1.0) % 0.60/0.60 % 0.60/0.60 (c) Philipp Rümmer, 2009-2015 % 0.60/0.60 (c) Peter Backeman, 2014-2015 % 0.60/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.60/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.60/0.60 Bug reports to peter@backeman.se % 0.60/0.60 % 0.60/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.60/0.60 % 0.60/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.66/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.59/1.00 Prover 0: Preprocessing ... % 2.87/1.35 Prover 0: Constructing countermodel ... % 4.63/1.75 Prover 0: proved (1092ms) % 4.63/1.75 % 4.63/1.75 No countermodel exists, formula is valid % 4.63/1.75 % SZS status Theorem for theBenchmark % 4.63/1.75 % 4.63/1.75 Generating proof ... found it (size 90) % 7.32/2.35 % 7.32/2.35 % SZS output start Proof for theBenchmark % 7.32/2.35 Assumed formulas after preprocessing and simplification: % 7.32/2.35 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (xn = xl) & ~ (sz10 = sz00) & sdtpldt0(xm, xn) = v1 & sdtpldt0(xm, xl) = v0 & sdtpldt0(xn, xm) = v3 & sdtpldt0(xl, xm) = v2 & sdtlseqdt0(xl, xn) & aNaturalNumber0(xm) & aNaturalNumber0(xn) & aNaturalNumber0(xl) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v6, v4) = v8) | ~ (sdtasdt0(v5, v4) = v7) | ~ (sdtpldt0(v7, v8) = v9) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (sdtasdt0(v10, v4) = v9 & sdtasdt0(v4, v10) = v11 & sdtasdt0(v4, v6) = v13 & sdtasdt0(v4, v5) = v12 & sdtpldt0(v12, v13) = v11 & sdtpldt0(v5, v6) = v10)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v4, v6) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ (sdtpldt0(v7, v8) = v9) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (sdtasdt0(v10, v4) = v11 & sdtasdt0(v6, v4) = v13 & sdtasdt0(v5, v4) = v12 & sdtasdt0(v4, v10) = v9 & sdtpldt0(v12, v13) = v11 & sdtpldt0(v5, v6) = v10)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v8) | ~ (sdtasdt0(v5, v4) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtasdt0(v4, v6) = v10 & sdtasdt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtasdt0(v5, v4) = v10 & sdtasdt0(v4, v6) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v5, v4) = v8) | ~ (sdtasdt0(v4, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtasdt0(v6, v4) = v10 & sdtasdt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v4, v6) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtasdt0(v6, v4) = v10 & sdtasdt0(v5, v4) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v6, v4) = v8) | ~ (sdtpldt0(v5, v4) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtpldt0(v4, v6) = v10 & sdtpldt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v6, v4) = v8) | ~ (sdtpldt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtpldt0(v5, v4) = v10 & sdtpldt0(v4, v6) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v5, v4) = v8) | ~ (sdtpldt0(v4, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v8) & ~ (v9 = v7) & sdtpldt0(v6, v4) = v10 & sdtpldt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v4, v6) = v8) | ~ (sdtpldt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & sdtpldt0(v6, v4) = v10 & sdtpldt0(v5, v4) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v7, v6) = v8) | ~ (sdtasdt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : (sdtasdt0(v5, v6) = v9 & sdtasdt0(v4, v9) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v7, v4) = v8) | ~ (sdtpldt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (sdtasdt0(v6, v4) = v13 & sdtasdt0(v5, v4) = v12 & sdtasdt0(v4, v7) = v9 & sdtasdt0(v4, v6) = v11 & sdtasdt0(v4, v5) = v10 & sdtpldt0(v12, v13) = v8 & sdtpldt0(v10, v11) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v5, v6) = v7) | ~ (sdtasdt0(v4, v7) = v8) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : (sdtasdt0(v9, v6) = v8 & sdtasdt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v4, v7) = v8) | ~ (sdtpldt0(v5, v6) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (sdtasdt0(v7, v4) = v11 & sdtasdt0(v6, v4) = v13 & sdtasdt0(v5, v4) = v12 & sdtasdt0(v4, v6) = v10 & sdtasdt0(v4, v5) = v9 & sdtpldt0(v12, v13) = v11 & sdtpldt0(v9, v10) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v7, v6) = v8) | ~ (sdtpldt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : (sdtpldt0(v5, v6) = v9 & sdtpldt0(v4, v9) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ (sdtpldt0(v4, v7) = v8) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v9] : (sdtpldt0(v9, v6) = v8 & sdtpldt0(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (sdtmndt0(v5, v4) = v6) | ~ (sdtpldt0(v4, v7) = v5) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v7) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (sdtmndt0(v5, v4) = v6) | ~ (sdtpldt0(v4, v6) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v6, v4) = v7) | ~ (sdtasdt0(v5, v4) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | v4 = sz00 | ~ (sdtasdt0(v4, v6) = v7) | ~ (sdtasdt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (sdtpldt0(v6, v4) = v7) | ~ (sdtpldt0(v5, v4) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (sdtpldt0(v4, v6) = v7) | ~ (sdtpldt0(v4, v5) = v7) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtmndt0(v7, v6) = v5) | ~ (sdtmndt0(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtasdt0(v7, v6) = v5) | ~ (sdtasdt0(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (sdtpldt0(v7, v6) = v5) | ~ (sdtpldt0(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtmndt0(v5, v4) = v6) | ~ (sdtpldt0(v4, v6) = v7) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | aNaturalNumber0(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, v4) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtasdt0(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v4, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtasdt0(v5, v4) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v4, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | aNaturalNumber0(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v5, v4) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtpldt0(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v4, v6) = v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v4, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtpldt0(v5, v4) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v4, v5) = v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | aNaturalNumber0(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ sdtlseqdt0(v5, v6) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v6) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v4, v6)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtasdt0(v4, sz10) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtasdt0(sz10, v4) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtpldt0(v4, sz00) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtpldt0(sz00, v4) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ sdtlseqdt0(v5, v4) | ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = sz00 | v4 = sz00 | ~ (sdtasdt0(v4, v5) = sz00) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = sz00 | ~ (sdtasdt0(v4, sz00) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = sz00 | ~ (sdtasdt0(sz00, v4) = v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v5 = sz00 | ~ (sdtpldt0(v4, v5) = sz00) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : (v4 = sz00 | ~ (sdtpldt0(v4, v5) = sz00) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4)) & ! [v4] : ! [v5] : ( ~ (sdtasdt0(v4, sz10) = v5) | ~ aNaturalNumber0(v4) | sdtasdt0(sz10, v4) = v4) & ! [v4] : ! [v5] : ( ~ (sdtasdt0(v4, sz00) = v5) | ~ aNaturalNumber0(v4) | sdtasdt0(sz00, v4) = sz00) & ! [v4] : ! [v5] : ( ~ (sdtasdt0(sz10, v4) = v5) | ~ aNaturalNumber0(v4) | sdtasdt0(v4, sz10) = v4) & ! [v4] : ! [v5] : ( ~ (sdtasdt0(sz00, v4) = v5) | ~ aNaturalNumber0(v4) | sdtasdt0(v4, sz00) = sz00) & ! [v4] : ! [v5] : ( ~ (sdtpldt0(v4, sz00) = v5) | ~ aNaturalNumber0(v4) | sdtpldt0(sz00, v4) = v4) & ! [v4] : ! [v5] : ( ~ (sdtpldt0(sz00, v4) = v5) | ~ aNaturalNumber0(v4) | sdtpldt0(v4, sz00) = v4) & ! [v4] : ! [v5] : ( ~ sdtlseqdt0(v4, v5) | ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | ? [v6] : (sdtpldt0(v4, v6) = v5 & aNaturalNumber0(v6))) & ! [v4] : ! [v5] : ( ~ aNaturalNumber0(v5) | ~ aNaturalNumber0(v4) | sdtlseqdt0(v5, v4) | sdtlseqdt0(v4, v5)) & ! [v4] : ( ~ aNaturalNumber0(v4) | sdtlseqdt0(v4, v4)) & (v3 = v2 | v1 = v0 | ~ sdtlseqdt0(v2, v3) | ~ sdtlseqdt0(v0, v1))) % 7.75/2.40 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 7.75/2.40 | (1) ~ (xn = xl) & ~ (sz10 = sz00) & sdtpldt0(xm, xn) = all_0_2_2 & sdtpldt0(xm, xl) = all_0_3_3 & sdtpldt0(xn, xm) = all_0_0_0 & sdtpldt0(xl, xm) = all_0_1_1 & sdtlseqdt0(xl, xn) & 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_0_0 = all_0_1_1 | all_0_2_2 = all_0_3_3 | ~ sdtlseqdt0(all_0_1_1, all_0_0_0) | ~ sdtlseqdt0(all_0_3_3, all_0_2_2)) % 7.87/2.41 | % 7.87/2.41 | Applying alpha-rule on (1) yields: % 7.87/2.41 | (2) ! [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)) % 7.87/2.41 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 7.87/2.41 | (4) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) % 7.87/2.41 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) % 7.87/2.41 | (6) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 7.87/2.42 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 7.87/2.42 | (8) ! [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)) % 7.87/2.42 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0)) % 7.87/2.42 | (10) aNaturalNumber0(xm) % 7.87/2.42 | (11) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00) % 7.87/2.42 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 7.87/2.42 | (13) ! [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)) % 7.87/2.42 | (14) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 7.87/2.42 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 7.87/2.42 | (16) ! [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)) % 7.87/2.42 | (17) ! [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)) % 7.87/2.42 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 7.87/2.42 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2) % 7.87/2.42 | (20) sdtpldt0(xn, xm) = all_0_0_0 % 7.87/2.42 | (21) aNaturalNumber0(sz10) % 7.87/2.42 | (22) ! [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)) % 7.87/2.42 | (23) ! [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)) % 7.87/2.42 | (24) ! [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)) % 7.87/2.42 | (25) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) % 7.87/2.42 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 7.87/2.42 | (27) ! [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)) % 7.87/2.42 | (28) ~ (xn = xl) % 7.87/2.42 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v0, v2) = v6 & sdtpldt0(v0, v1) = v5)) % 7.87/2.42 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 7.87/2.42 | (31) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) % 7.87/2.42 | (32) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 7.87/2.42 | (33) ! [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)) % 7.87/2.43 | (34) sdtpldt0(xl, xm) = all_0_1_1 % 7.87/2.43 | (35) sdtlseqdt0(xl, xn) % 7.87/2.43 | (36) ! [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)) % 7.87/2.43 | (37) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) % 7.87/2.43 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 7.87/2.43 | (39) sdtpldt0(xm, xn) = all_0_2_2 % 7.87/2.43 | (40) ~ (sz10 = sz00) % 7.87/2.43 | (41) ! [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)) % 7.87/2.43 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, v1) = v2) % 7.87/2.43 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 7.87/2.43 | (44) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00) % 7.87/2.43 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 7.87/2.43 | (46) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(sz00, v0) = v0) % 7.87/2.43 | (47) aNaturalNumber0(xn) % 7.87/2.43 | (48) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 7.87/2.43 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) % 7.87/2.43 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2)) % 7.87/2.43 | (51) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2))) % 7.87/2.43 | (52) sdtpldt0(xm, xl) = all_0_3_3 % 7.87/2.43 | (53) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0)) % 7.87/2.43 | (54) ! [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)) % 7.87/2.43 | (55) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0) % 7.87/2.43 | (56) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) % 7.87/2.43 | (57) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aNaturalNumber0(v0)) % 7.87/2.43 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, v1) = v2) % 7.87/2.43 | (59) all_0_0_0 = all_0_1_1 | all_0_2_2 = all_0_3_3 | ~ sdtlseqdt0(all_0_1_1, all_0_0_0) | ~ sdtlseqdt0(all_0_3_3, all_0_2_2) % 7.87/2.43 | (60) ! [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)) % 7.87/2.43 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2) % 7.87/2.43 | (62) aNaturalNumber0(sz00) % 7.87/2.43 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 7.87/2.43 | (64) aNaturalNumber0(xl) % 7.87/2.43 | (65) ! [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)) % 7.87/2.43 | (66) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0) % 7.87/2.43 | (67) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0) % 7.87/2.43 | % 7.87/2.44 | Instantiating formula (58) with all_0_0_0, xn, xm and discharging atoms sdtpldt0(xn, xm) = all_0_0_0, aNaturalNumber0(xm), aNaturalNumber0(xn), yields: % 7.87/2.44 | (68) sdtpldt0(xm, xn) = all_0_0_0 % 7.87/2.44 | % 7.87/2.44 | Instantiating formula (7) with all_0_0_0, xm, xn and discharging atoms sdtpldt0(xn, xm) = all_0_0_0, aNaturalNumber0(xm), aNaturalNumber0(xn), yields: % 7.87/2.44 | (69) aNaturalNumber0(all_0_0_0) % 7.87/2.44 | % 7.87/2.44 | Instantiating formula (36) with all_0_2_2, all_0_3_3, xn, xl, xm and discharging atoms sdtpldt0(xm, xn) = all_0_2_2, sdtpldt0(xm, xl) = all_0_3_3, aNaturalNumber0(xm), aNaturalNumber0(xn), aNaturalNumber0(xl), yields: % 7.87/2.44 | (70) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xn, xm) = v1 & sdtpldt0(xl, xm) = v0) % 7.87/2.44 | % 7.87/2.44 | Instantiating formula (36) with all_0_3_3, all_0_2_2, xl, xn, xm and discharging atoms sdtpldt0(xm, xn) = all_0_2_2, sdtpldt0(xm, xl) = all_0_3_3, aNaturalNumber0(xm), aNaturalNumber0(xn), aNaturalNumber0(xl), yields: % 7.87/2.44 | (71) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xn, xm) = v0 & sdtpldt0(xl, xm) = v1) % 7.87/2.44 | % 7.87/2.44 | Instantiating formula (8) with all_0_0_0, all_0_3_3, xn, xl, xm and discharging atoms sdtpldt0(xm, xl) = all_0_3_3, sdtpldt0(xn, xm) = all_0_0_0, aNaturalNumber0(xm), aNaturalNumber0(xn), aNaturalNumber0(xl), yields: % 7.87/2.44 | (72) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = all_0_0_0) & ~ (v0 = all_0_3_3) & sdtpldt0(xm, xn) = v0 & sdtpldt0(xl, xm) = v1) % 7.87/2.44 | % 7.87/2.44 | Instantiating formula (29) with all_0_0_0, all_0_1_1, xn, xl, xm and discharging atoms sdtpldt0(xn, xm) = all_0_0_0, sdtpldt0(xl, xm) = all_0_1_1, aNaturalNumber0(xm), aNaturalNumber0(xn), aNaturalNumber0(xl), yields: % 7.87/2.44 | (73) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xm, xn) = v1 & sdtpldt0(xm, xl) = v0) % 7.87/2.44 | % 7.87/2.44 | Instantiating formula (8) with all_0_1_1, all_0_2_2, xl, xn, xm and discharging atoms sdtpldt0(xm, xn) = all_0_2_2, sdtpldt0(xl, xm) = all_0_1_1, aNaturalNumber0(xm), aNaturalNumber0(xn), aNaturalNumber0(xl), yields: % 7.87/2.44 | (74) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = all_0_1_1) & ~ (v0 = all_0_2_2) & sdtpldt0(xm, xl) = v0 & sdtpldt0(xn, xm) = v1) % 7.87/2.44 | % 7.87/2.44 | Instantiating formula (29) with all_0_1_1, all_0_0_0, xl, xn, xm and discharging atoms sdtpldt0(xn, xm) = all_0_0_0, sdtpldt0(xl, xm) = all_0_1_1, aNaturalNumber0(xm), aNaturalNumber0(xn), aNaturalNumber0(xl), yields: % 7.87/2.44 | (75) xn = xl | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xm, xn) = v0 & sdtpldt0(xm, xl) = v1) % 7.87/2.44 | % 7.87/2.44 | Instantiating formula (58) with all_0_1_1, xl, xm and discharging atoms sdtpldt0(xl, xm) = all_0_1_1, aNaturalNumber0(xm), aNaturalNumber0(xl), yields: % 7.87/2.44 | (76) sdtpldt0(xm, xl) = all_0_1_1 % 7.87/2.44 | % 7.87/2.44 | Instantiating formula (7) with all_0_1_1, xm, xl and discharging atoms sdtpldt0(xl, xm) = all_0_1_1, aNaturalNumber0(xm), aNaturalNumber0(xl), yields: % 7.87/2.44 | (77) aNaturalNumber0(all_0_1_1) % 7.87/2.44 | % 7.87/2.44 | Instantiating formula (51) with xn, xl and discharging atoms sdtlseqdt0(xl, xn), aNaturalNumber0(xn), aNaturalNumber0(xl), yields: % 7.87/2.44 | (78) ? [v0] : (sdtpldt0(xl, v0) = xn & aNaturalNumber0(v0)) % 7.87/2.44 | % 7.87/2.44 | Instantiating (78) with all_9_0_4 yields: % 7.87/2.44 | (79) sdtpldt0(xl, all_9_0_4) = xn & aNaturalNumber0(all_9_0_4) % 7.87/2.44 | % 7.87/2.44 | Applying alpha-rule on (79) yields: % 7.87/2.44 | (80) sdtpldt0(xl, all_9_0_4) = xn % 7.87/2.44 | (81) aNaturalNumber0(all_9_0_4) % 7.87/2.44 | % 7.87/2.44 +-Applying beta-rule and splitting (75), into two cases. % 7.87/2.44 |-Branch one: % 7.87/2.44 | (82) xn = xl % 7.87/2.44 | % 7.87/2.44 | Equations (82) can reduce 28 to: % 7.87/2.44 | (83) $false % 7.87/2.44 | % 7.87/2.44 |-The branch is then unsatisfiable % 7.87/2.44 |-Branch two: % 7.87/2.44 | (28) ~ (xn = xl) % 7.87/2.44 | (85) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xm, xn) = v0 & sdtpldt0(xm, xl) = v1) % 7.87/2.44 | % 7.87/2.44 | Instantiating (85) with all_15_0_5, all_15_1_6 yields: % 7.87/2.44 | (86) ~ (all_15_0_5 = all_15_1_6) & sdtpldt0(xm, xn) = all_15_1_6 & sdtpldt0(xm, xl) = all_15_0_5 % 7.87/2.44 | % 7.87/2.44 | Applying alpha-rule on (86) yields: % 7.87/2.44 | (87) ~ (all_15_0_5 = all_15_1_6) % 7.87/2.44 | (88) sdtpldt0(xm, xn) = all_15_1_6 % 7.87/2.44 | (89) sdtpldt0(xm, xl) = all_15_0_5 % 7.87/2.44 | % 7.87/2.44 +-Applying beta-rule and splitting (71), into two cases. % 7.87/2.44 |-Branch one: % 7.87/2.44 | (82) xn = xl % 7.87/2.44 | % 7.87/2.44 | Equations (82) can reduce 28 to: % 7.87/2.44 | (83) $false % 7.87/2.44 | % 7.87/2.44 |-The branch is then unsatisfiable % 7.87/2.44 |-Branch two: % 7.87/2.44 | (28) ~ (xn = xl) % 7.87/2.44 | (93) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xn, xm) = v0 & sdtpldt0(xl, xm) = v1) % 7.87/2.44 | % 7.87/2.44 +-Applying beta-rule and splitting (74), into two cases. % 7.87/2.44 |-Branch one: % 7.87/2.44 | (82) xn = xl % 7.87/2.44 | % 7.87/2.44 | Equations (82) can reduce 28 to: % 7.87/2.44 | (83) $false % 7.87/2.44 | % 7.87/2.44 |-The branch is then unsatisfiable % 7.87/2.44 |-Branch two: % 7.87/2.44 | (28) ~ (xn = xl) % 7.87/2.44 | (97) ? [v0] : ? [v1] : ( ~ (v1 = all_0_1_1) & ~ (v0 = all_0_2_2) & sdtpldt0(xm, xl) = v0 & sdtpldt0(xn, xm) = v1) % 7.87/2.44 | % 7.87/2.44 | Instantiating (97) with all_27_0_9, all_27_1_10 yields: % 7.87/2.44 | (98) ~ (all_27_0_9 = all_0_1_1) & ~ (all_27_1_10 = all_0_2_2) & sdtpldt0(xm, xl) = all_27_1_10 & sdtpldt0(xn, xm) = all_27_0_9 % 7.87/2.44 | % 7.87/2.44 | Applying alpha-rule on (98) yields: % 7.87/2.44 | (99) ~ (all_27_0_9 = all_0_1_1) % 7.87/2.44 | (100) ~ (all_27_1_10 = all_0_2_2) % 7.87/2.44 | (101) sdtpldt0(xm, xl) = all_27_1_10 % 7.87/2.44 | (102) sdtpldt0(xn, xm) = all_27_0_9 % 7.87/2.44 | % 7.87/2.44 +-Applying beta-rule and splitting (73), into two cases. % 7.87/2.44 |-Branch one: % 7.87/2.44 | (82) xn = xl % 7.87/2.44 | % 7.87/2.44 | Equations (82) can reduce 28 to: % 7.87/2.44 | (83) $false % 7.87/2.44 | % 7.87/2.44 |-The branch is then unsatisfiable % 7.87/2.44 |-Branch two: % 7.87/2.44 | (28) ~ (xn = xl) % 7.87/2.44 | (106) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xm, xn) = v1 & sdtpldt0(xm, xl) = v0) % 7.87/2.44 | % 7.87/2.44 | Instantiating (106) with all_33_0_11, all_33_1_12 yields: % 7.87/2.44 | (107) ~ (all_33_0_11 = all_33_1_12) & sdtpldt0(xm, xn) = all_33_0_11 & sdtpldt0(xm, xl) = all_33_1_12 % 7.87/2.44 | % 7.87/2.44 | Applying alpha-rule on (107) yields: % 7.87/2.44 | (108) ~ (all_33_0_11 = all_33_1_12) % 7.87/2.45 | (109) sdtpldt0(xm, xn) = all_33_0_11 % 7.87/2.45 | (110) sdtpldt0(xm, xl) = all_33_1_12 % 7.87/2.45 | % 7.87/2.45 +-Applying beta-rule and splitting (70), into two cases. % 7.87/2.45 |-Branch one: % 7.87/2.45 | (82) xn = xl % 7.87/2.45 | % 7.87/2.45 | Equations (82) can reduce 28 to: % 7.87/2.45 | (83) $false % 7.87/2.45 | % 7.87/2.45 |-The branch is then unsatisfiable % 7.87/2.45 |-Branch two: % 7.87/2.45 | (28) ~ (xn = xl) % 7.87/2.45 | (114) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(xn, xm) = v1 & sdtpldt0(xl, xm) = v0) % 7.87/2.45 | % 7.87/2.45 +-Applying beta-rule and splitting (72), into two cases. % 7.87/2.45 |-Branch one: % 7.87/2.45 | (82) xn = xl % 7.87/2.45 | % 7.87/2.45 | Equations (82) can reduce 28 to: % 7.87/2.45 | (83) $false % 7.87/2.45 | % 7.87/2.45 |-The branch is then unsatisfiable % 7.87/2.45 |-Branch two: % 7.87/2.45 | (28) ~ (xn = xl) % 7.87/2.45 | (118) ? [v0] : ? [v1] : ( ~ (v1 = all_0_0_0) & ~ (v0 = all_0_3_3) & sdtpldt0(xm, xn) = v0 & sdtpldt0(xl, xm) = v1) % 7.87/2.45 | % 7.87/2.45 | Instantiating (118) with all_45_0_15, all_45_1_16 yields: % 7.87/2.45 | (119) ~ (all_45_0_15 = all_0_0_0) & ~ (all_45_1_16 = all_0_3_3) & sdtpldt0(xm, xn) = all_45_1_16 & sdtpldt0(xl, xm) = all_45_0_15 % 7.87/2.45 | % 7.87/2.45 | Applying alpha-rule on (119) yields: % 7.87/2.45 | (120) ~ (all_45_0_15 = all_0_0_0) % 7.87/2.45 | (121) ~ (all_45_1_16 = all_0_3_3) % 7.87/2.45 | (122) sdtpldt0(xm, xn) = all_45_1_16 % 7.87/2.45 | (123) sdtpldt0(xl, xm) = all_45_0_15 % 7.87/2.45 | % 7.87/2.45 | Instantiating formula (45) with xm, xn, all_45_1_16, all_0_2_2 and discharging atoms sdtpldt0(xm, xn) = all_45_1_16, sdtpldt0(xm, xn) = all_0_2_2, yields: % 7.87/2.45 | (124) all_45_1_16 = all_0_2_2 % 7.87/2.45 | % 7.87/2.45 | Instantiating formula (45) with xm, xn, all_33_0_11, all_45_1_16 and discharging atoms sdtpldt0(xm, xn) = all_45_1_16, sdtpldt0(xm, xn) = all_33_0_11, yields: % 7.87/2.45 | (125) all_45_1_16 = all_33_0_11 % 7.87/2.45 | % 7.87/2.45 | Instantiating formula (45) with xm, xn, all_15_1_6, all_45_1_16 and discharging atoms sdtpldt0(xm, xn) = all_45_1_16, sdtpldt0(xm, xn) = all_15_1_6, yields: % 7.87/2.45 | (126) all_45_1_16 = all_15_1_6 % 7.87/2.45 | % 7.87/2.45 | Instantiating formula (45) with xm, xn, all_0_0_0, all_45_1_16 and discharging atoms sdtpldt0(xm, xn) = all_45_1_16, sdtpldt0(xm, xn) = all_0_0_0, yields: % 7.87/2.45 | (127) all_45_1_16 = all_0_0_0 % 7.87/2.45 | % 7.87/2.45 | Instantiating formula (45) with xm, xl, all_27_1_10, all_0_3_3 and discharging atoms sdtpldt0(xm, xl) = all_27_1_10, sdtpldt0(xm, xl) = all_0_3_3, yields: % 7.87/2.45 | (128) all_27_1_10 = all_0_3_3 % 7.87/2.45 | % 7.87/2.45 | Instantiating formula (45) with xm, xl, all_27_1_10, all_33_1_12 and discharging atoms sdtpldt0(xm, xl) = all_33_1_12, sdtpldt0(xm, xl) = all_27_1_10, yields: % 7.87/2.45 | (129) all_33_1_12 = all_27_1_10 % 7.87/2.45 | % 7.87/2.45 | Instantiating formula (45) with xm, xl, all_15_0_5, all_33_1_12 and discharging atoms sdtpldt0(xm, xl) = all_33_1_12, sdtpldt0(xm, xl) = all_15_0_5, yields: % 7.87/2.45 | (130) all_33_1_12 = all_15_0_5 % 7.87/2.45 | % 7.87/2.45 | Instantiating formula (45) with xm, xl, all_0_1_1, all_33_1_12 and discharging atoms sdtpldt0(xm, xl) = all_33_1_12, sdtpldt0(xm, xl) = all_0_1_1, yields: % 7.87/2.45 | (131) all_33_1_12 = all_0_1_1 % 7.87/2.45 | % 7.87/2.45 | Combining equations (124,125) yields a new equation: % 7.87/2.45 | (132) all_33_0_11 = all_0_2_2 % 7.87/2.45 | % 7.87/2.45 | Combining equations (127,125) yields a new equation: % 7.87/2.45 | (133) all_33_0_11 = all_0_0_0 % 7.87/2.45 | % 7.87/2.45 | Combining equations (126,125) yields a new equation: % 7.87/2.45 | (134) all_33_0_11 = all_15_1_6 % 7.87/2.45 | % 7.87/2.45 | Combining equations (133,134) yields a new equation: % 7.87/2.45 | (135) all_15_1_6 = all_0_0_0 % 7.87/2.45 | % 7.87/2.45 | Combining equations (132,134) yields a new equation: % 7.87/2.45 | (136) all_15_1_6 = all_0_2_2 % 7.87/2.45 | % 7.87/2.45 | Combining equations (129,130) yields a new equation: % 7.87/2.45 | (137) all_27_1_10 = all_15_0_5 % 7.87/2.45 | % 7.87/2.45 | Simplifying 137 yields: % 7.87/2.45 | (138) all_27_1_10 = all_15_0_5 % 7.87/2.45 | % 7.87/2.45 | Combining equations (131,130) yields a new equation: % 7.87/2.45 | (139) all_15_0_5 = all_0_1_1 % 7.87/2.45 | % 7.87/2.45 | Combining equations (138,128) yields a new equation: % 7.87/2.45 | (140) all_15_0_5 = all_0_3_3 % 7.87/2.45 | % 7.87/2.45 | Simplifying 140 yields: % 7.87/2.45 | (141) all_15_0_5 = all_0_3_3 % 7.87/2.45 | % 7.87/2.45 | Combining equations (139,141) yields a new equation: % 7.87/2.45 | (142) all_0_1_1 = all_0_3_3 % 7.87/2.45 | % 7.87/2.45 | Simplifying 142 yields: % 7.87/2.45 | (143) all_0_1_1 = all_0_3_3 % 7.87/2.45 | % 7.87/2.45 | Combining equations (135,136) yields a new equation: % 7.87/2.45 | (144) all_0_0_0 = all_0_2_2 % 7.87/2.45 | % 7.87/2.45 | Simplifying 144 yields: % 7.87/2.45 | (145) all_0_0_0 = all_0_2_2 % 7.87/2.45 | % 7.87/2.45 | Equations (141,136) can reduce 87 to: % 7.87/2.45 | (146) ~ (all_0_2_2 = all_0_3_3) % 7.87/2.45 | % 7.87/2.45 | Simplifying 146 yields: % 7.87/2.45 | (147) ~ (all_0_2_2 = all_0_3_3) % 7.87/2.45 | % 7.87/2.45 | From (145) and (68) follows: % 7.87/2.45 | (39) sdtpldt0(xm, xn) = all_0_2_2 % 7.87/2.45 | % 7.87/2.45 | From (143) and (76) follows: % 7.87/2.45 | (52) sdtpldt0(xm, xl) = all_0_3_3 % 7.87/2.45 | % 7.87/2.45 | From (145) and (69) follows: % 7.87/2.45 | (150) aNaturalNumber0(all_0_2_2) % 7.87/2.45 | % 7.87/2.45 | From (143) and (77) follows: % 7.87/2.45 | (151) aNaturalNumber0(all_0_3_3) % 7.87/2.45 | % 7.87/2.45 +-Applying beta-rule and splitting (59), into two cases. % 7.87/2.45 |-Branch one: % 7.87/2.45 | (152) ~ sdtlseqdt0(all_0_1_1, all_0_0_0) % 7.87/2.45 | % 7.87/2.45 | From (143)(145) and (152) follows: % 7.87/2.45 | (153) ~ sdtlseqdt0(all_0_3_3, all_0_2_2) % 7.87/2.45 | % 7.87/2.45 | Instantiating formula (13) with all_0_2_2, xn, all_9_0_4, xl, xm and discharging atoms sdtpldt0(xm, xn) = all_0_2_2, sdtpldt0(xl, all_9_0_4) = xn, aNaturalNumber0(all_9_0_4), aNaturalNumber0(xm), aNaturalNumber0(xl), yields: % 7.87/2.45 | (154) ? [v0] : (sdtpldt0(v0, all_9_0_4) = all_0_2_2 & sdtpldt0(xm, xl) = v0) % 7.87/2.45 | % 7.87/2.45 | Instantiating (154) with all_61_0_17 yields: % 7.87/2.45 | (155) sdtpldt0(all_61_0_17, all_9_0_4) = all_0_2_2 & sdtpldt0(xm, xl) = all_61_0_17 % 7.87/2.45 | % 7.87/2.45 | Applying alpha-rule on (155) yields: % 7.87/2.45 | (156) sdtpldt0(all_61_0_17, all_9_0_4) = all_0_2_2 % 7.87/2.45 | (157) sdtpldt0(xm, xl) = all_61_0_17 % 7.87/2.45 | % 7.87/2.45 | Instantiating formula (45) with xm, xl, all_61_0_17, all_0_3_3 and discharging atoms sdtpldt0(xm, xl) = all_61_0_17, sdtpldt0(xm, xl) = all_0_3_3, yields: % 7.87/2.45 | (158) all_61_0_17 = all_0_3_3 % 7.87/2.45 | % 7.87/2.45 | From (158) and (156) follows: % 7.87/2.45 | (159) sdtpldt0(all_0_3_3, all_9_0_4) = all_0_2_2 % 7.87/2.45 | % 7.87/2.45 | Instantiating formula (49) with all_9_0_4, all_0_2_2, all_0_3_3 and discharging atoms sdtpldt0(all_0_3_3, all_9_0_4) = all_0_2_2, aNaturalNumber0(all_9_0_4), aNaturalNumber0(all_0_2_2), aNaturalNumber0(all_0_3_3), ~ sdtlseqdt0(all_0_3_3, all_0_2_2), yields: % 7.87/2.45 | (160) $false % 7.87/2.45 | % 7.87/2.45 |-The branch is then unsatisfiable % 7.87/2.45 |-Branch two: % 7.87/2.45 | (161) sdtlseqdt0(all_0_1_1, all_0_0_0) % 7.87/2.45 | (162) all_0_0_0 = all_0_1_1 | all_0_2_2 = all_0_3_3 | ~ sdtlseqdt0(all_0_3_3, all_0_2_2) % 7.87/2.45 | % 7.87/2.45 | From (143)(145) and (161) follows: % 7.87/2.45 | (163) sdtlseqdt0(all_0_3_3, all_0_2_2) % 7.87/2.45 | % 7.87/2.45 +-Applying beta-rule and splitting (162), into two cases. % 7.87/2.45 |-Branch one: % 7.87/2.45 | (153) ~ sdtlseqdt0(all_0_3_3, all_0_2_2) % 7.87/2.45 | % 7.87/2.45 | Using (163) and (153) yields: % 7.87/2.45 | (160) $false % 7.87/2.45 | % 7.87/2.45 |-The branch is then unsatisfiable % 7.87/2.45 |-Branch two: % 7.87/2.45 | (163) sdtlseqdt0(all_0_3_3, all_0_2_2) % 7.87/2.45 | (167) all_0_0_0 = all_0_1_1 | all_0_2_2 = all_0_3_3 % 7.87/2.45 | % 7.87/2.45 +-Applying beta-rule and splitting (167), into two cases. % 7.87/2.45 |-Branch one: % 7.87/2.45 | (168) all_0_0_0 = all_0_1_1 % 7.87/2.45 | % 7.87/2.45 | Combining equations (145,168) yields a new equation: % 7.87/2.45 | (169) all_0_1_1 = all_0_2_2 % 7.87/2.45 | % 7.87/2.45 | Combining equations (169,143) yields a new equation: % 7.87/2.45 | (170) all_0_2_2 = all_0_3_3 % 7.87/2.45 | % 7.87/2.45 | Simplifying 170 yields: % 7.87/2.45 | (171) all_0_2_2 = all_0_3_3 % 7.87/2.45 | % 7.87/2.45 | Equations (171) can reduce 147 to: % 7.87/2.45 | (83) $false % 7.87/2.45 | % 7.87/2.45 |-The branch is then unsatisfiable % 7.87/2.45 |-Branch two: % 7.87/2.45 | (173) ~ (all_0_0_0 = all_0_1_1) % 7.87/2.45 | (171) all_0_2_2 = all_0_3_3 % 7.87/2.45 | % 7.87/2.45 | Equations (171) can reduce 147 to: % 7.87/2.45 | (83) $false % 7.87/2.45 | % 7.87/2.45 |-The branch is then unsatisfiable % 7.87/2.45 % SZS output end Proof for theBenchmark % 7.87/2.45 % 7.87/2.45 1838ms %------------------------------------------------------------------------------