%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : RNG062+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n018.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 20:25:14 EDT 2022 % Result : Theorem 58.09s 33.14s % Output : Proof 93.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : RNG062+1 : TPTP v8.1.0. Released v4.0.0. % 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.35 % Computer : n018.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Mon May 30 05:34:56 EDT 2022 % 0.13/0.35 % CPUTime : % 0.51/0.61 ____ _ % 0.51/0.61 ___ / __ \_____(_)___ ________ __________ % 0.51/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.51/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.51/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.51/0.61 % 0.51/0.61 A Theorem Prover for First-Order Logic % 0.51/0.62 (ePrincess v.1.0) % 0.51/0.62 % 0.51/0.62 (c) Philipp Rümmer, 2009-2015 % 0.51/0.62 (c) Peter Backeman, 2014-2015 % 0.51/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.51/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.51/0.62 Bug reports to peter@backeman.se % 0.51/0.62 % 0.51/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.51/0.62 % 0.51/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.79/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.88/1.03 Prover 0: Preprocessing ... % 4.09/1.55 Prover 0: Constructing countermodel ... % 15.37/5.96 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 15.61/6.05 Prover 1: Preprocessing ... % 16.61/6.21 Prover 1: Constructing countermodel ... % 24.61/8.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 25.07/8.63 Prover 2: Preprocessing ... % 25.79/8.81 Prover 2: Warning: ignoring some quantifiers % 25.79/8.82 Prover 2: Constructing countermodel ... % 32.91/11.56 Prover 0: stopped % 33.56/11.76 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 33.85/11.82 Prover 3: Preprocessing ... % 34.10/11.90 Prover 3: Constructing countermodel ... % 58.09/33.14 Prover 3: proved (21372ms) % 58.09/33.14 Prover 1: stopped % 58.09/33.14 Prover 2: stopped % 58.09/33.14 % 58.09/33.14 No countermodel exists, formula is valid % 58.09/33.14 % SZS status Theorem for theBenchmark % 58.09/33.14 % 58.09/33.14 Generating proof ... found it (size 73) % 92.90/59.79 % 92.90/59.79 % SZS output start Proof for theBenchmark % 92.90/59.79 Assumed formulas after preprocessing and simplification: % 92.90/59.79 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ( ~ (v16 = v9) & ~ (v1 = sz00) & sdtasasdt0(xq, xq) = xD & sdtasasdt0(xp, xq) = xE & sdtasasdt0(xp, xp) = xC & sziznziztdt0(xt) = xq & sziznziztdt0(xs) = xp & sdtlbdtrb0(xt, v1) = xB & sdtlbdtrb0(xs, v1) = xA & aDimensionOf0(xt) = v1 & aDimensionOf0(xs) = v1 & smndt0(xN) = v6 & smndt0(xS) = v5 & smndt0(sz0z00) = v0 & sdtasdt0(v8, v8) = v9 & sdtasdt0(v5, v5) = v7 & sdtasdt0(v5, xR) = v6 & sdtasdt0(xS, xS) = v7 & sdtasdt0(xP, xP) = v4 & sdtasdt0(xR, v5) = v6 & sdtasdt0(xR, xS) = xN & sdtasdt0(xR, xR) = v10 & sdtasdt0(xF, xD) = xS & sdtasdt0(xE, xH) = xP & sdtasdt0(xE, xE) = v2 & sdtasdt0(xC, xG) = xR & sdtasdt0(xC, xD) = v3 & sdtasdt0(xB, xB) = xG & sdtasdt0(xA, xB) = xH & sdtasdt0(xA, xA) = xF & sdtpldt0(v15, v6) = v16 & sdtpldt0(v14, v6) = v15 & sdtpldt0(v11, v13) = v9 & sdtpldt0(v11, v12) = v9 & sdtpldt0(v10, v7) = v14 & sdtpldt0(v10, v6) = v11 & sdtpldt0(v7, v6) = v13 & sdtpldt0(v6, v7) = v12 & sdtpldt0(xR, v5) = v8 & aVector0(xq) & aVector0(xp) & aVector0(xt) & aVector0(xs) & sdtlseqdt0(v4, xN) & sdtlseqdt0(v2, v3) & aScalar0(xN) & aScalar0(xS) & aScalar0(xP) & aScalar0(xR) & aScalar0(xH) & aScalar0(xG) & aScalar0(xF) & aScalar0(xE) & aScalar0(xD) & aScalar0(xC) & aScalar0(xB) & aScalar0(xA) & aScalar0(sz0z00) & aNaturalNumber0(sz00) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (sdtasdt0(v18, v20) = v25) | ~ (sdtasdt0(v18, v19) = v24) | ~ (sdtasdt0(v17, v20) = v22) | ~ (sdtasdt0(v17, v19) = v21) | ~ (sdtpldt0(v24, v25) = v26) | ~ (sdtpldt0(v23, v26) = v27) | ~ (sdtpldt0(v21, v22) = v23) | ~ aScalar0(v20) | ~ aScalar0(v19) | ~ aScalar0(v18) | ~ aScalar0(v17) | ? [v28] : ? [v29] : (sdtasdt0(v28, v29) = v27 & sdtpldt0(v19, v20) = v29 & sdtpldt0(v17, v18) = v28)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v19 = sz00 | ~ (sdtasasdt0(v20, v21) = v22) | ~ (sziznziztdt0(v18) = v21) | ~ (sziznziztdt0(v17) = v20) | ~ (sdtlbdtrb0(v18, v19) = v24) | ~ (sdtlbdtrb0(v17, v19) = v23) | ~ (aDimensionOf0(v18) = v19) | ~ (aDimensionOf0(v17) = v19) | ~ (sdtasdt0(v23, v24) = v25) | ~ (sdtpldt0(v22, v25) = v26) | ~ aVector0(v18) | ~ aVector0(v17) | sdtasasdt0(v17, v18) = v26) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (sdtasdt0(v18, v20) = v22) | ~ (sdtasdt0(v17, v19) = v21) | ~ sdtlseqdt0(v19, v20) | ~ sdtlseqdt0(v17, v18) | ~ sdtlseqdt0(sz0z00, v19) | ~ aScalar0(v20) | ~ aScalar0(v19) | ~ aScalar0(v18) | ~ aScalar0(v17) | sdtlseqdt0(v21, v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (sdtasdt0(v17, v19) = v21) | ~ (sdtasdt0(v17, v18) = v20) | ~ (sdtpldt0(v20, v21) = v22) | ~ aScalar0(v19) | ~ aScalar0(v18) | ~ aScalar0(v17) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (sdtasdt0(v24, v19) = v25 & sdtasdt0(v18, v19) = v26 & sdtasdt0(v17, v23) = v22 & sdtpldt0(v21, v26) = v25 & sdtpldt0(v18, v19) = v23 & sdtpldt0(v17, v18) = v24)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (sdtpldt0(v18, v20) = v22) | ~ (sdtpldt0(v17, v19) = v21) | ~ sdtlseqdt0(v19, v20) | ~ sdtlseqdt0(v17, v18) | ~ aScalar0(v20) | ~ aScalar0(v19) | ~ aScalar0(v18) | ~ aScalar0(v17) | sdtlseqdt0(v21, v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (sdtasasdt0(v18, v18) = v20) | ~ (sdtasasdt0(v17, v17) = v19) | ~ (sdtasdt0(v19, v20) = v21) | ~ aVector0(v18) | ~ aVector0(v17) | ? [v22] : ? [v23] : ((sdtasasdt0(v17, v18) = v22 & sdtasdt0(v22, v22) = v23 & sdtlseqdt0(v23, v21)) | (aDimensionOf0(v17) = v22 & ( ~ iLess0(v22, v1) | ( ~ (v23 = v22) & aDimensionOf0(v18) = v23))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (smndt0(v18) = v20) | ~ (smndt0(v17) = v19) | ~ (sdtasdt0(v19, v20) = v21) | ~ aScalar0(v18) | ~ aScalar0(v17) | sdtasdt0(v17, v18) = v21) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (sdtpldt0(v20, v19) = v21) | ~ (sdtpldt0(v17, v18) = v20) | ~ aScalar0(v19) | ~ aScalar0(v18) | ~ aScalar0(v17) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (sdtasdt0(v23, v19) = v24 & sdtasdt0(v18, v19) = v25 & sdtasdt0(v18, v17) = v23 & sdtasdt0(v17, v25) = v24 & sdtasdt0(v17, v18) = v23 & sdtpldt0(v18, v19) = v22 & sdtpldt0(v18, v17) = v20 & sdtpldt0(v17, v22) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (sdtasasdt0(v20, v19) = v18) | ~ (sdtasasdt0(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (sdtlbdtrb0(v20, v19) = v18) | ~ (sdtlbdtrb0(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (sdtasdt0(v20, v19) = v18) | ~ (sdtasdt0(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (sdtpldt0(v20, v19) = v18) | ~ (sdtpldt0(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (sziznziztdt0(v18) = v20) | ~ (sziznziztdt0(v17) = v19) | ~ aVector0(v18) | ~ aVector0(v17) | ? [v21] : ? [v22] : ((v22 = v21 & aDimensionOf0(v20) = v21 & aDimensionOf0(v19) = v21) | (aDimensionOf0(v18) = v22 & (v22 = sz00 | ( ~ (v22 = v21) & aDimensionOf0(v17) = v21))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (smndt0(v17) = v19) | ~ (sdtasdt0(v19, v18) = v20) | ~ aScalar0(v18) | ~ aScalar0(v17) | ? [v21] : ? [v22] : (smndt0(v22) = v20 & smndt0(v18) = v21 & sdtasdt0(v17, v21) = v20 & sdtasdt0(v17, v18) = v22)) & ! [v17] : ! [v18] : ! [v19] : (v19 = sz0z00 | ~ (sdtasasdt0(v17, v18) = v19) | ~ aVector0(v18) | ~ aVector0(v17) | ? [v20] : ? [v21] : (aDimensionOf0(v18) = v21 & ( ~ (v21 = sz00) | ( ~ (v20 = sz00) & aDimensionOf0(v17) = v20)))) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (sziznziztdt0(v19) = v18) | ~ (sziznziztdt0(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (aDimensionOf0(v19) = v18) | ~ (aDimensionOf0(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (smndt0(v19) = v18) | ~ (smndt0(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (sdtasdt0(v18, v18) = v19) | ~ (sdtasdt0(v17, v17) = v19) | ~ sdtlseqdt0(sz0z00, v18) | ~ sdtlseqdt0(sz0z00, v17) | ~ aScalar0(v18) | ~ aScalar0(v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (szszuzczcdt0(v19) = v18) | ~ (szszuzczcdt0(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (szszuzczcdt0(v18) = v19) | ~ (szszuzczcdt0(v17) = v19) | ~ aNaturalNumber0(v18) | ~ aNaturalNumber0(v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (sdtasasdt0(v17, v18) = v19) | ~ aVector0(v18) | ~ aVector0(v17) | aScalar0(v19) | ? [v20] : ? [v21] : ( ~ (v21 = v20) & aDimensionOf0(v18) = v21 & aDimensionOf0(v17) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (sdtlbdtrb0(v17, v18) = v19) | ~ aVector0(v17) | ~ aNaturalNumber0(v18) | aScalar0(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (sdtasdt0(v17, v18) = v19) | ~ aScalar0(v18) | ~ aScalar0(v17) | aScalar0(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (sdtpldt0(v17, v18) = v19) | ~ sdtlseqdt0(sz0z00, v18) | ~ sdtlseqdt0(sz0z00, v17) | ~ aScalar0(v18) | ~ aScalar0(v17) | sdtlseqdt0(sz0z00, v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (sdtpldt0(v17, v18) = v19) | ~ sdtlseqdt0(sz0z00, v18) | ~ sdtlseqdt0(sz0z00, v17) | ~ aScalar0(v18) | ~ aScalar0(v17) | ? [v20] : (sdtasdt0(v17, v18) = v20 & sdtlseqdt0(sz0z00, v20))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (sdtpldt0(v17, v18) = v19) | ~ aScalar0(v18) | ~ aScalar0(v17) | aScalar0(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ sdtlseqdt0(v18, v19) | ~ sdtlseqdt0(v17, v18) | ~ aScalar0(v19) | ~ aScalar0(v18) | ~ aScalar0(v17) | sdtlseqdt0(v17, v19)) & ! [v17] : ! [v18] : (v18 = v17 | ~ (sdtpldt0(sz0z00, v17) = v18) | ~ aScalar0(v17)) & ! [v17] : ! [v18] : (v18 = v17 | ~ sdtlseqdt0(v18, v17) | ~ sdtlseqdt0(v17, v18) | ~ aScalar0(v18) | ~ aScalar0(v17)) & ! [v17] : ! [v18] : (v0 = sz0z00 | ~ (sdtpldt0(sz0z00, v17) = v18) | ~ aScalar0(v17)) & ! [v17] : ! [v18] : ( ~ (sdtasasdt0(v17, v17) = v18) | ~ aVector0(v17) | sdtlseqdt0(sz0z00, v18)) & ! [v17] : ! [v18] : ( ~ (sziznziztdt0(v17) = v18) | ~ aVector0(v17) | ? [v19] : (aDimensionOf0(v17) = v19 & (v19 = sz00 | ( ! [v20] : ! [v21] : ! [v22] : ( ~ (sdtlbdtrb0(v17, v21) = v22) | ~ (aDimensionOf0(v18) = v20) | ~ aNaturalNumber0(v21) | sdtlbdtrb0(v18, v21) = v22) & ! [v20] : ! [v21] : (v20 = v18 | ~ (aDimensionOf0(v20) = v21) | ~ aVector0(v20) | ? [v22] : ? [v23] : ? [v24] : (( ~ (v24 = v23) & sdtlbdtrb0(v20, v22) = v23 & sdtlbdtrb0(v17, v22) = v24 & aNaturalNumber0(v22)) | ( ~ (v22 = v19) & szszuzczcdt0(v21) = v22))) & ! [v20] : ( ~ (aDimensionOf0(v18) = v20) | szszuzczcdt0(v20) = v19) & ! [v20] : ( ~ (aDimensionOf0(v18) = v20) | aVector0(v18)))))) & ! [v17] : ! [v18] : ( ~ (aDimensionOf0(v17) = v18) | ~ aVector0(v17) | aNaturalNumber0(v18)) & ! [v17] : ! [v18] : ( ~ (smndt0(v17) = v18) | ~ aScalar0(v17) | aScalar0(v18)) & ! [v17] : ! [v18] : ( ~ (sdtasdt0(v17, v17) = v18) | ~ aScalar0(v17) | sdtlseqdt0(sz0z00, v18)) & ! [v17] : ! [v18] : ( ~ (sdtpldt0(sz0z00, v17) = v18) | ~ aScalar0(v17) | ? [v19] : (smndt0(v19) = v17 & smndt0(v17) = v19 & sdtasdt0(v17, sz0z00) = sz0z00 & sdtasdt0(sz0z00, v17) = sz0z00 & sdtpldt0(v19, v17) = sz0z00 & sdtpldt0(v17, v19) = sz0z00 & sdtpldt0(v17, sz0z00) = v17)) & ! [v17] : ! [v18] : ( ~ (szszuzczcdt0(v17) = v18) | ~ aNaturalNumber0(v17) | iLess0(v17, v18)) & ! [v17] : ! [v18] : ( ~ (szszuzczcdt0(v17) = v18) | ~ aNaturalNumber0(v17) | aNaturalNumber0(v18)) & ! [v17] : ! [v18] : ( ~ aScalar0(v18) | ~ aScalar0(v17) | sdtlseqdt0(v18, v17) | sdtlseqdt0(v17, v18)) & ! [v17] : (v17 = sz00 | ~ aNaturalNumber0(v17) | ? [v18] : (szszuzczcdt0(v18) = v17 & aNaturalNumber0(v18))) & ! [v17] : ( ~ (szszuzczcdt0(v17) = sz00) | ~ aNaturalNumber0(v17)) & ! [v17] : ( ~ aScalar0(v17) | sdtlseqdt0(v17, v17))) % 93.20/59.85 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16 yields: % 93.20/59.85 | (1) ~ (all_0_0_0 = all_0_7_7) & ~ (all_0_15_15 = sz00) & sdtasasdt0(xq, xq) = xD & sdtasasdt0(xp, xq) = xE & sdtasasdt0(xp, xp) = xC & sziznziztdt0(xt) = xq & sziznziztdt0(xs) = xp & sdtlbdtrb0(xt, all_0_15_15) = xB & sdtlbdtrb0(xs, all_0_15_15) = xA & aDimensionOf0(xt) = all_0_15_15 & aDimensionOf0(xs) = all_0_15_15 & smndt0(xN) = all_0_10_10 & smndt0(xS) = all_0_11_11 & smndt0(sz0z00) = all_0_16_16 & sdtasdt0(all_0_8_8, all_0_8_8) = all_0_7_7 & sdtasdt0(all_0_11_11, all_0_11_11) = all_0_9_9 & sdtasdt0(all_0_11_11, xR) = all_0_10_10 & sdtasdt0(xS, xS) = all_0_9_9 & sdtasdt0(xP, xP) = all_0_12_12 & sdtasdt0(xR, all_0_11_11) = all_0_10_10 & sdtasdt0(xR, xS) = xN & sdtasdt0(xR, xR) = all_0_6_6 & sdtasdt0(xF, xD) = xS & sdtasdt0(xE, xH) = xP & sdtasdt0(xE, xE) = all_0_14_14 & sdtasdt0(xC, xG) = xR & sdtasdt0(xC, xD) = all_0_13_13 & sdtasdt0(xB, xB) = xG & sdtasdt0(xA, xB) = xH & sdtasdt0(xA, xA) = xF & sdtpldt0(all_0_1_1, all_0_10_10) = all_0_0_0 & sdtpldt0(all_0_2_2, all_0_10_10) = all_0_1_1 & sdtpldt0(all_0_5_5, all_0_3_3) = all_0_7_7 & sdtpldt0(all_0_5_5, all_0_4_4) = all_0_7_7 & sdtpldt0(all_0_6_6, all_0_9_9) = all_0_2_2 & sdtpldt0(all_0_6_6, all_0_10_10) = all_0_5_5 & sdtpldt0(all_0_9_9, all_0_10_10) = all_0_3_3 & sdtpldt0(all_0_10_10, all_0_9_9) = all_0_4_4 & sdtpldt0(xR, all_0_11_11) = all_0_8_8 & aVector0(xq) & aVector0(xp) & aVector0(xt) & aVector0(xs) & sdtlseqdt0(all_0_12_12, xN) & sdtlseqdt0(all_0_14_14, all_0_13_13) & aScalar0(xN) & aScalar0(xS) & aScalar0(xP) & aScalar0(xR) & aScalar0(xH) & aScalar0(xG) & aScalar0(xF) & aScalar0(xE) & aScalar0(xD) & aScalar0(xC) & aScalar0(xB) & aScalar0(xA) & aScalar0(sz0z00) & aNaturalNumber0(sz00) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v1, v3) = v8) | ~ (sdtasdt0(v1, v2) = v7) | ~ (sdtasdt0(v0, v3) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtpldt0(v7, v8) = v9) | ~ (sdtpldt0(v6, v9) = v10) | ~ (sdtpldt0(v4, v5) = v6) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v11] : ? [v12] : (sdtasdt0(v11, v12) = v10 & sdtpldt0(v2, v3) = v12 & sdtpldt0(v0, v1) = v11)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v2 = sz00 | ~ (sdtasasdt0(v3, v4) = v5) | ~ (sziznziztdt0(v1) = v4) | ~ (sziznziztdt0(v0) = v3) | ~ (sdtlbdtrb0(v1, v2) = v7) | ~ (sdtlbdtrb0(v0, v2) = v6) | ~ (aDimensionOf0(v1) = v2) | ~ (aDimensionOf0(v0) = v2) | ~ (sdtasdt0(v6, v7) = v8) | ~ (sdtpldt0(v5, v8) = v9) | ~ aVector0(v1) | ~ aVector0(v0) | sdtasasdt0(v0, v1) = v9) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v1, v3) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ sdtlseqdt0(v2, v3) | ~ sdtlseqdt0(v0, v1) | ~ sdtlseqdt0(sz0z00, v2) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | sdtlseqdt0(v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v4, v9) = v8 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtpldt0(v1, v3) = v5) | ~ (sdtpldt0(v0, v2) = v4) | ~ sdtlseqdt0(v2, v3) | ~ sdtlseqdt0(v0, v1) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | sdtlseqdt0(v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3) = v4) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v5] : ? [v6] : ((sdtasasdt0(v0, v1) = v5 & sdtasdt0(v5, v5) = v6 & sdtlseqdt0(v6, v4)) | (aDimensionOf0(v0) = v5 & ( ~ iLess0(v5, all_0_15_15) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (smndt0(v1) = v3) | ~ (smndt0(v0) = v2) | ~ (sdtasdt0(v2, v3) = v4) | ~ aScalar0(v1) | ~ aScalar0(v0) | sdtasdt0(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (sdtasdt0(v6, v2) = v7 & sdtasdt0(v1, v2) = v8 & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v8) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v1, v2) = v5 & sdtpldt0(v1, v0) = v3 & sdtpldt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(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] : ( ~ (sziznziztdt0(v1) = v3) | ~ (sziznziztdt0(v0) = v2) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v4] : ? [v5] : ((v5 = v4 & aDimensionOf0(v3) = v4 & aDimensionOf0(v2) = v4) | (aDimensionOf0(v1) = v5 & (v5 = sz00 | ( ~ (v5 = v4) & aDimensionOf0(v0) = v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (smndt0(v0) = v2) | ~ (sdtasdt0(v2, v1) = v3) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v4] : ? [v5] : (smndt0(v5) = v3 & smndt0(v1) = v4 & sdtasdt0(v0, v4) = v3 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : (v2 = sz0z00 | ~ (sdtasasdt0(v0, v1) = v2) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v3] : ? [v4] : (aDimensionOf0(v1) = v4 & ( ~ (v4 = sz00) | ( ~ (v3 = sz00) & aDimensionOf0(v0) = v3)))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~ (sziznziztdt0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sdtasdt0(v1, v1) = v2) | ~ (sdtasdt0(v0, v0) = v2) | ~ sdtlseqdt0(sz0z00, v1) | ~ sdtlseqdt0(sz0z00, v0) | ~ aScalar0(v1) | ~ aScalar0(v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (szszuzczcdt0(v1) = v2) | ~ (szszuzczcdt0(v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ aVector0(v1) | ~ aVector0(v0) | aScalar0(v2) | ? [v3] : ? [v4] : ( ~ (v4 = v3) & aDimensionOf0(v1) = v4 & aDimensionOf0(v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~ aVector0(v0) | ~ aNaturalNumber0(v1) | aScalar0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ sdtlseqdt0(sz0z00, v1) | ~ sdtlseqdt0(sz0z00, v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | sdtlseqdt0(sz0z00, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ sdtlseqdt0(sz0z00, v1) | ~ sdtlseqdt0(sz0z00, v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v3] : (sdtasdt0(v0, v1) = v3 & sdtlseqdt0(sz0z00, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | sdtlseqdt0(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz0z00, v0) = v1) | ~ aScalar0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aScalar0(v1) | ~ aScalar0(v0)) & ! [v0] : ! [v1] : (all_0_16_16 = sz0z00 | ~ (sdtpldt0(sz0z00, v0) = v1) | ~ aScalar0(v0)) & ! [v0] : ! [v1] : ( ~ (sdtasasdt0(v0, v0) = v1) | ~ aVector0(v0) | sdtlseqdt0(sz0z00, v1)) & ! [v0] : ! [v1] : ( ~ (sziznziztdt0(v0) = v1) | ~ aVector0(v0) | ? [v2] : (aDimensionOf0(v0) = v2 & (v2 = sz00 | ( ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ aNaturalNumber0(v4) | sdtlbdtrb0(v1, v4) = v5) & ! [v3] : ! [v4] : (v3 = v1 | ~ (aDimensionOf0(v3) = v4) | ~ aVector0(v3) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v7 = v6) & sdtlbdtrb0(v3, v5) = v6 & sdtlbdtrb0(v0, v5) = v7 & aNaturalNumber0(v5)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) = v5))) & ! [v3] : ( ~ (aDimensionOf0(v1) = v3) | szszuzczcdt0(v3) = v2) & ! [v3] : ( ~ (aDimensionOf0(v1) = v3) | aVector0(v1)))))) & ! [v0] : ! [v1] : ( ~ (aDimensionOf0(v0) = v1) | ~ aVector0(v0) | aNaturalNumber0(v1)) & ! [v0] : ! [v1] : ( ~ (smndt0(v0) = v1) | ~ aScalar0(v0) | aScalar0(v1)) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, v0) = v1) | ~ aScalar0(v0) | sdtlseqdt0(sz0z00, v1)) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz0z00, v0) = v1) | ~ aScalar0(v0) | ? [v2] : (smndt0(v2) = v0 & smndt0(v0) = v2 & sdtasdt0(v0, sz0z00) = sz0z00 & sdtasdt0(sz0z00, v0) = sz0z00 & sdtpldt0(v2, v0) = sz0z00 & sdtpldt0(v0, v2) = sz0z00 & sdtpldt0(v0, sz0z00) = v0)) & ! [v0] : ! [v1] : ( ~ (szszuzczcdt0(v0) = v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1)) & ! [v0] : ! [v1] : ( ~ (szszuzczcdt0(v0) = v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v1)) & ! [v0] : ! [v1] : ( ~ aScalar0(v1) | ~ aScalar0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) & ! [v0] : (v0 = sz00 | ~ aNaturalNumber0(v0) | ? [v1] : (szszuzczcdt0(v1) = v0 & aNaturalNumber0(v1))) & ! [v0] : ( ~ (szszuzczcdt0(v0) = sz00) | ~ aNaturalNumber0(v0)) & ! [v0] : ( ~ aScalar0(v0) | sdtlseqdt0(v0, v0)) % 93.20/59.87 | % 93.20/59.87 | Applying alpha-rule on (1) yields: % 93.20/59.87 | (2) sdtasdt0(xB, xB) = xG % 93.20/59.87 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) % 93.20/59.87 | (4) aScalar0(xS) % 93.20/59.87 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (sdtasdt0(v6, v2) = v7 & sdtasdt0(v1, v2) = v8 & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v8) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v1, v2) = v5 & sdtpldt0(v1, v0) = v3 & sdtpldt0(v0, v5) = v4)) % 93.20/59.87 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = sz0z00 | ~ (sdtasasdt0(v0, v1) = v2) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v3] : ? [v4] : (aDimensionOf0(v1) = v4 & ( ~ (v4 = sz00) | ( ~ (v3 = sz00) & aDimensionOf0(v0) = v3)))) % 93.20/59.87 | (7) sdtasdt0(xS, xS) = all_0_9_9 % 93.20/59.87 | (8) aScalar0(xF) % 93.20/59.87 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~ aVector0(v0) | ~ aNaturalNumber0(v1) | aScalar0(v2)) % 93.20/59.87 | (10) sziznziztdt0(xs) = xp % 93.20/59.87 | (11) sdtasdt0(xC, xD) = all_0_13_13 % 93.20/59.87 | (12) smndt0(xS) = all_0_11_11 % 93.20/59.87 | (13) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aScalar0(v1) | ~ aScalar0(v0)) % 93.20/59.87 | (14) aDimensionOf0(xt) = all_0_15_15 % 93.20/59.87 | (15) sdtasdt0(all_0_11_11, xR) = all_0_10_10 % 93.20/59.87 | (16) sdtpldt0(all_0_5_5, all_0_4_4) = all_0_7_7 % 93.20/59.87 | (17) aScalar0(xD) % 93.20/59.87 | (18) aScalar0(xP) % 93.20/59.87 | (19) aVector0(xt) % 93.20/59.87 | (20) sdtpldt0(all_0_6_6, all_0_9_9) = all_0_2_2 % 93.20/59.87 | (21) sdtlbdtrb0(xs, all_0_15_15) = xA % 93.20/59.87 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v1, v3) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ sdtlseqdt0(v2, v3) | ~ sdtlseqdt0(v0, v1) | ~ sdtlseqdt0(sz0z00, v2) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | sdtlseqdt0(v4, v5)) % 93.20/59.87 | (23) ~ (all_0_0_0 = all_0_7_7) % 93.20/59.87 | (24) aDimensionOf0(xs) = all_0_15_15 % 93.20/59.87 | (25) sdtasdt0(xP, xP) = all_0_12_12 % 93.20/59.87 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v4, v9) = v8 & sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v1) = v7)) % 93.20/59.88 | (27) aScalar0(xN) % 93.20/59.88 | (28) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz0z00, v0) = v1) | ~ aScalar0(v0)) % 93.20/59.88 | (29) sdtpldt0(all_0_5_5, all_0_3_3) = all_0_7_7 % 93.20/59.88 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (smndt0(v1) = v3) | ~ (smndt0(v0) = v2) | ~ (sdtasdt0(v2, v3) = v4) | ~ aScalar0(v1) | ~ aScalar0(v0) | sdtasdt0(v0, v1) = v4) % 93.20/59.88 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (smndt0(v0) = v2) | ~ (sdtasdt0(v2, v1) = v3) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v4] : ? [v5] : (smndt0(v5) = v3 & smndt0(v1) = v4 & sdtasdt0(v0, v4) = v3 & sdtasdt0(v0, v1) = v5)) % 93.20/59.88 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | sdtlseqdt0(v0, v2)) % 93.20/59.88 | (33) sdtlbdtrb0(xt, all_0_15_15) = xB % 93.20/59.88 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) % 93.20/59.88 | (35) sdtasdt0(xE, xE) = all_0_14_14 % 93.20/59.88 | (36) aVector0(xp) % 93.20/59.88 | (37) sdtpldt0(all_0_1_1, all_0_10_10) = all_0_0_0 % 93.20/59.88 | (38) aScalar0(xG) % 93.20/59.88 | (39) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz0z00, v0) = v1) | ~ aScalar0(v0) | ? [v2] : (smndt0(v2) = v0 & smndt0(v0) = v2 & sdtasdt0(v0, sz0z00) = sz0z00 & sdtasdt0(sz0z00, v0) = sz0z00 & sdtpldt0(v2, v0) = sz0z00 & sdtpldt0(v0, v2) = sz0z00 & sdtpldt0(v0, sz0z00) = v0)) % 93.20/59.88 | (40) sdtlseqdt0(all_0_14_14, all_0_13_13) % 93.20/59.88 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2)) % 93.20/59.88 | (42) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, v0) = v1) | ~ aScalar0(v0) | sdtlseqdt0(sz0z00, v1)) % 93.20/59.88 | (43) ~ (all_0_15_15 = sz00) % 93.20/59.88 | (44) aScalar0(xE) % 93.20/59.88 | (45) ! [v0] : (v0 = sz00 | ~ aNaturalNumber0(v0) | ? [v1] : (szszuzczcdt0(v1) = v0 & aNaturalNumber0(v1))) % 93.20/59.88 | (46) smndt0(sz0z00) = all_0_16_16 % 93.20/59.88 | (47) sdtasdt0(xC, xG) = xR % 93.20/59.88 | (48) aScalar0(xB) % 93.20/59.88 | (49) ! [v0] : ! [v1] : ( ~ (smndt0(v0) = v1) | ~ aScalar0(v0) | aScalar0(v1)) % 93.20/59.88 | (50) sdtasdt0(xR, xS) = xN % 93.20/59.88 | (51) ! [v0] : ( ~ (szszuzczcdt0(v0) = sz00) | ~ aNaturalNumber0(v0)) % 93.20/59.88 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (szszuzczcdt0(v1) = v2) | ~ (szszuzczcdt0(v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 93.20/59.88 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sziznziztdt0(v1) = v3) | ~ (sziznziztdt0(v0) = v2) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v4] : ? [v5] : ((v5 = v4 & aDimensionOf0(v3) = v4 & aDimensionOf0(v2) = v4) | (aDimensionOf0(v1) = v5 & (v5 = sz00 | ( ~ (v5 = v4) & aDimensionOf0(v0) = v4))))) % 93.20/59.88 | (54) sdtasdt0(xA, xA) = xF % 93.20/59.88 | (55) ! [v0] : ! [v1] : ( ~ (szszuzczcdt0(v0) = v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1)) % 93.20/59.88 | (56) aScalar0(xH) % 93.20/59.88 | (57) aVector0(xs) % 93.20/59.88 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 93.20/59.88 | (59) ! [v0] : ( ~ aScalar0(v0) | sdtlseqdt0(v0, v0)) % 93.20/59.88 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtpldt0(v1, v3) = v5) | ~ (sdtpldt0(v0, v2) = v4) | ~ sdtlseqdt0(v2, v3) | ~ sdtlseqdt0(v0, v1) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | sdtlseqdt0(v4, v5)) % 93.20/59.88 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) % 93.20/59.88 | (62) aScalar0(xC) % 93.20/59.88 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v1, v3) = v8) | ~ (sdtasdt0(v1, v2) = v7) | ~ (sdtasdt0(v0, v3) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtpldt0(v7, v8) = v9) | ~ (sdtpldt0(v6, v9) = v10) | ~ (sdtpldt0(v4, v5) = v6) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v11] : ? [v12] : (sdtasdt0(v11, v12) = v10 & sdtpldt0(v2, v3) = v12 & sdtpldt0(v0, v1) = v11)) % 93.20/59.88 | (64) aScalar0(sz0z00) % 93.20/59.88 | (65) sziznziztdt0(xt) = xq % 93.20/59.88 | (66) ! [v0] : ! [v1] : ( ~ (sziznziztdt0(v0) = v1) | ~ aVector0(v0) | ? [v2] : (aDimensionOf0(v0) = v2 & (v2 = sz00 | ( ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ aNaturalNumber0(v4) | sdtlbdtrb0(v1, v4) = v5) & ! [v3] : ! [v4] : (v3 = v1 | ~ (aDimensionOf0(v3) = v4) | ~ aVector0(v3) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v7 = v6) & sdtlbdtrb0(v3, v5) = v6 & sdtlbdtrb0(v0, v5) = v7 & aNaturalNumber0(v5)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) = v5))) & ! [v3] : ( ~ (aDimensionOf0(v1) = v3) | szszuzczcdt0(v3) = v2) & ! [v3] : ( ~ (aDimensionOf0(v1) = v3) | aVector0(v1)))))) % 93.20/59.89 | (67) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~ (sziznziztdt0(v2) = v0)) % 93.20/59.89 | (68) smndt0(xN) = all_0_10_10 % 93.20/59.89 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v2 = sz00 | ~ (sdtasasdt0(v3, v4) = v5) | ~ (sziznziztdt0(v1) = v4) | ~ (sziznziztdt0(v0) = v3) | ~ (sdtlbdtrb0(v1, v2) = v7) | ~ (sdtlbdtrb0(v0, v2) = v6) | ~ (aDimensionOf0(v1) = v2) | ~ (aDimensionOf0(v0) = v2) | ~ (sdtasdt0(v6, v7) = v8) | ~ (sdtpldt0(v5, v8) = v9) | ~ aVector0(v1) | ~ aVector0(v0) | sdtasasdt0(v0, v1) = v9) % 93.20/59.89 | (70) ! [v0] : ! [v1] : ( ~ (szszuzczcdt0(v0) = v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v1)) % 93.20/59.89 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ sdtlseqdt0(sz0z00, v1) | ~ sdtlseqdt0(sz0z00, v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v3] : (sdtasdt0(v0, v1) = v3 & sdtlseqdt0(sz0z00, v3))) % 93.20/59.89 | (72) sdtasasdt0(xp, xq) = xE % 93.20/59.89 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 93.20/59.89 | (74) sdtpldt0(all_0_9_9, all_0_10_10) = all_0_3_3 % 93.20/59.89 | (75) sdtasdt0(xR, all_0_11_11) = all_0_10_10 % 93.20/59.89 | (76) sdtasdt0(xA, xB) = xH % 93.20/59.89 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ sdtlseqdt0(sz0z00, v1) | ~ sdtlseqdt0(sz0z00, v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | sdtlseqdt0(sz0z00, v2)) % 93.20/59.89 | (78) ! [v0] : ! [v1] : (all_0_16_16 = sz0z00 | ~ (sdtpldt0(sz0z00, v0) = v1) | ~ aScalar0(v0)) % 93.20/59.89 | (79) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 93.20/59.89 | (80) aNaturalNumber0(sz00) % 93.20/59.89 | (81) sdtasasdt0(xq, xq) = xD % 93.20/59.89 | (82) sdtpldt0(all_0_2_2, all_0_10_10) = all_0_1_1 % 93.20/59.89 | (83) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sdtasdt0(v1, v1) = v2) | ~ (sdtasdt0(v0, v0) = v2) | ~ sdtlseqdt0(sz0z00, v1) | ~ sdtlseqdt0(sz0z00, v0) | ~ aScalar0(v1) | ~ aScalar0(v0)) % 93.20/59.89 | (84) sdtpldt0(all_0_10_10, all_0_9_9) = all_0_4_4 % 93.20/59.89 | (85) sdtasdt0(xR, xR) = all_0_6_6 % 93.20/59.89 | (86) sdtasdt0(all_0_11_11, all_0_11_11) = all_0_9_9 % 93.20/59.89 | (87) sdtpldt0(all_0_6_6, all_0_10_10) = all_0_5_5 % 93.20/59.89 | (88) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ aVector0(v1) | ~ aVector0(v0) | aScalar0(v2) | ? [v3] : ? [v4] : ( ~ (v4 = v3) & aDimensionOf0(v1) = v4 & aDimensionOf0(v0) = v3)) % 93.20/59.89 | (89) aScalar0(xA) % 93.20/59.89 | (90) sdtpldt0(xR, all_0_11_11) = all_0_8_8 % 93.20/59.89 | (91) sdtasdt0(xE, xH) = xP % 93.20/59.89 | (92) sdtasdt0(all_0_8_8, all_0_8_8) = all_0_7_7 % 93.20/59.89 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3) = v4) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v5] : ? [v6] : ((sdtasasdt0(v0, v1) = v5 & sdtasdt0(v5, v5) = v6 & sdtlseqdt0(v6, v4)) | (aDimensionOf0(v0) = v5 & ( ~ iLess0(v5, all_0_15_15) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6))))) % 93.20/59.89 | (94) aVector0(xq) % 93.20/59.89 | (95) aScalar0(xR) % 93.20/59.89 | (96) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2)) % 93.20/59.89 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0)) % 93.20/59.89 | (98) ! [v0] : ! [v1] : ( ~ (aDimensionOf0(v0) = v1) | ~ aVector0(v0) | aNaturalNumber0(v1)) % 93.20/59.89 | (99) ! [v0] : ! [v1] : ( ~ (sdtasasdt0(v0, v0) = v1) | ~ aVector0(v0) | sdtlseqdt0(sz0z00, v1)) % 93.20/59.89 | (100) ! [v0] : ! [v1] : ( ~ aScalar0(v1) | ~ aScalar0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) % 93.20/59.89 | (101) sdtlseqdt0(all_0_12_12, xN) % 93.20/59.89 | (102) sdtasasdt0(xp, xp) = xC % 93.20/59.89 | (103) sdtasdt0(xF, xD) = xS % 93.20/59.89 | % 93.20/59.89 | Instantiating formula (49) with all_0_10_10, xN and discharging atoms smndt0(xN) = all_0_10_10, aScalar0(xN), yields: % 93.20/59.89 | (104) aScalar0(all_0_10_10) % 93.20/59.89 | % 93.20/59.89 | Instantiating formula (49) with all_0_11_11, xS and discharging atoms smndt0(xS) = all_0_11_11, aScalar0(xS), yields: % 93.20/59.89 | (105) aScalar0(all_0_11_11) % 93.20/59.89 | % 93.20/59.89 | Instantiating formula (96) with all_0_9_9, xS, xS and discharging atoms sdtasdt0(xS, xS) = all_0_9_9, aScalar0(xS), yields: % 93.20/59.89 | (106) aScalar0(all_0_9_9) % 93.20/59.89 | % 93.20/59.89 | Instantiating formula (96) with all_0_6_6, xR, xR and discharging atoms sdtasdt0(xR, xR) = all_0_6_6, aScalar0(xR), yields: % 93.20/59.90 | (107) aScalar0(all_0_6_6) % 93.20/59.90 | % 93.20/59.90 | Instantiating formula (26) with all_0_5_5, all_0_10_10, all_0_6_6, all_0_11_11, xR, xR and discharging atoms sdtasdt0(xR, all_0_11_11) = all_0_10_10, sdtasdt0(xR, xR) = all_0_6_6, sdtpldt0(all_0_6_6, all_0_10_10) = all_0_5_5, aScalar0(all_0_11_11), aScalar0(xR), yields: % 93.20/59.90 | (108) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v1, all_0_11_11) = v2 & sdtasdt0(xR, v0) = all_0_5_5 & sdtasdt0(xR, all_0_11_11) = v3 & sdtpldt0(all_0_10_10, v3) = v2 & sdtpldt0(xR, all_0_11_11) = v0 & sdtpldt0(xR, xR) = v1) % 93.20/59.90 | % 93.20/59.90 | Instantiating formula (41) with all_0_2_2, all_0_9_9, all_0_6_6 and discharging atoms sdtpldt0(all_0_6_6, all_0_9_9) = all_0_2_2, aScalar0(all_0_6_6), aScalar0(all_0_9_9), yields: % 93.20/59.90 | (109) aScalar0(all_0_2_2) % 93.20/59.90 | % 93.20/59.90 | Instantiating formula (41) with all_0_3_3, all_0_10_10, all_0_9_9 and discharging atoms sdtpldt0(all_0_9_9, all_0_10_10) = all_0_3_3, aScalar0(all_0_9_9), aScalar0(all_0_10_10), yields: % 93.20/59.90 | (110) aScalar0(all_0_3_3) % 93.20/59.90 | % 93.20/59.90 | Instantiating formula (5) with all_0_1_1, all_0_2_2, all_0_10_10, all_0_9_9, all_0_6_6 and discharging atoms sdtpldt0(all_0_2_2, all_0_10_10) = all_0_1_1, sdtpldt0(all_0_6_6, all_0_9_9) = all_0_2_2, aScalar0(all_0_6_6), aScalar0(all_0_9_9), aScalar0(all_0_10_10), yields: % 93.20/59.90 | (111) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v1, all_0_10_10) = v2 & sdtasdt0(all_0_6_6, v3) = v2 & sdtasdt0(all_0_6_6, all_0_9_9) = v1 & sdtasdt0(all_0_9_9, all_0_6_6) = v1 & sdtasdt0(all_0_9_9, all_0_10_10) = v3 & sdtpldt0(all_0_6_6, v0) = all_0_1_1 & sdtpldt0(all_0_9_9, all_0_6_6) = all_0_2_2 & sdtpldt0(all_0_9_9, all_0_10_10) = v0) % 93.20/59.90 | % 93.20/59.90 | Instantiating formula (26) with all_0_4_4, all_0_9_9, all_0_10_10, all_0_11_11, xR, all_0_11_11 and discharging atoms sdtasdt0(all_0_11_11, all_0_11_11) = all_0_9_9, sdtasdt0(all_0_11_11, xR) = all_0_10_10, sdtpldt0(all_0_10_10, all_0_9_9) = all_0_4_4, aScalar0(all_0_11_11), aScalar0(xR), yields: % 93.20/59.90 | (112) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v1, all_0_11_11) = v2 & sdtasdt0(all_0_11_11, v0) = all_0_4_4 & sdtasdt0(xR, all_0_11_11) = v3 & sdtpldt0(all_0_9_9, v3) = v2 & sdtpldt0(all_0_11_11, xR) = v1 & sdtpldt0(xR, all_0_11_11) = v0) % 93.20/59.90 | % 93.20/59.90 | Instantiating formula (26) with all_0_3_3, all_0_10_10, all_0_9_9, xR, all_0_11_11, all_0_11_11 and discharging atoms sdtasdt0(all_0_11_11, all_0_11_11) = all_0_9_9, sdtasdt0(all_0_11_11, xR) = all_0_10_10, sdtpldt0(all_0_9_9, all_0_10_10) = all_0_3_3, aScalar0(all_0_11_11), aScalar0(xR), yields: % 93.20/59.90 | (113) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v1, xR) = v2 & sdtasdt0(all_0_11_11, v0) = all_0_3_3 & sdtasdt0(all_0_11_11, xR) = v3 & sdtpldt0(all_0_10_10, v3) = v2 & sdtpldt0(all_0_11_11, all_0_11_11) = v1 & sdtpldt0(all_0_11_11, xR) = v0) % 93.20/59.90 | % 93.20/59.90 | Instantiating (113) with all_60_0_31, all_60_1_32, all_60_2_33, all_60_3_34 yields: % 93.20/59.90 | (114) sdtasdt0(all_60_2_33, xR) = all_60_1_32 & sdtasdt0(all_0_11_11, all_60_3_34) = all_0_3_3 & sdtasdt0(all_0_11_11, xR) = all_60_0_31 & sdtpldt0(all_0_10_10, all_60_0_31) = all_60_1_32 & sdtpldt0(all_0_11_11, all_0_11_11) = all_60_2_33 & sdtpldt0(all_0_11_11, xR) = all_60_3_34 % 93.20/59.90 | % 93.20/59.90 | Applying alpha-rule on (114) yields: % 93.20/59.90 | (115) sdtasdt0(all_0_11_11, xR) = all_60_0_31 % 93.20/59.90 | (116) sdtpldt0(all_0_10_10, all_60_0_31) = all_60_1_32 % 93.20/59.90 | (117) sdtpldt0(all_0_11_11, all_0_11_11) = all_60_2_33 % 93.20/59.90 | (118) sdtasdt0(all_0_11_11, all_60_3_34) = all_0_3_3 % 93.20/59.90 | (119) sdtasdt0(all_60_2_33, xR) = all_60_1_32 % 93.20/59.90 | (120) sdtpldt0(all_0_11_11, xR) = all_60_3_34 % 93.20/59.90 | % 93.20/59.90 | Instantiating (111) with all_62_0_35, all_62_1_36, all_62_2_37, all_62_3_38 yields: % 93.20/59.90 | (121) sdtasdt0(all_62_2_37, all_0_10_10) = all_62_1_36 & sdtasdt0(all_0_6_6, all_62_0_35) = all_62_1_36 & sdtasdt0(all_0_6_6, all_0_9_9) = all_62_2_37 & sdtasdt0(all_0_9_9, all_0_6_6) = all_62_2_37 & sdtasdt0(all_0_9_9, all_0_10_10) = all_62_0_35 & sdtpldt0(all_0_6_6, all_62_3_38) = all_0_1_1 & sdtpldt0(all_0_9_9, all_0_6_6) = all_0_2_2 & sdtpldt0(all_0_9_9, all_0_10_10) = all_62_3_38 % 93.20/59.90 | % 93.20/59.90 | Applying alpha-rule on (121) yields: % 93.20/59.90 | (122) sdtpldt0(all_0_9_9, all_0_6_6) = all_0_2_2 % 93.20/59.90 | (123) sdtasdt0(all_0_6_6, all_62_0_35) = all_62_1_36 % 93.20/59.90 | (124) sdtasdt0(all_0_9_9, all_0_10_10) = all_62_0_35 % 93.20/59.90 | (125) sdtasdt0(all_0_6_6, all_0_9_9) = all_62_2_37 % 93.20/59.90 | (126) sdtpldt0(all_0_9_9, all_0_10_10) = all_62_3_38 % 93.20/59.90 | (127) sdtpldt0(all_0_6_6, all_62_3_38) = all_0_1_1 % 93.20/59.90 | (128) sdtasdt0(all_0_9_9, all_0_6_6) = all_62_2_37 % 93.20/59.90 | (129) sdtasdt0(all_62_2_37, all_0_10_10) = all_62_1_36 % 93.20/59.90 | % 93.20/59.90 | Instantiating (112) with all_64_0_39, all_64_1_40, all_64_2_41, all_64_3_42 yields: % 93.20/59.90 | (130) sdtasdt0(all_64_2_41, all_0_11_11) = all_64_1_40 & sdtasdt0(all_0_11_11, all_64_3_42) = all_0_4_4 & sdtasdt0(xR, all_0_11_11) = all_64_0_39 & sdtpldt0(all_0_9_9, all_64_0_39) = all_64_1_40 & sdtpldt0(all_0_11_11, xR) = all_64_2_41 & sdtpldt0(xR, all_0_11_11) = all_64_3_42 % 93.20/59.90 | % 93.20/59.90 | Applying alpha-rule on (130) yields: % 93.20/59.90 | (131) sdtasdt0(xR, all_0_11_11) = all_64_0_39 % 93.20/59.90 | (132) sdtpldt0(all_0_9_9, all_64_0_39) = all_64_1_40 % 93.20/59.90 | (133) sdtpldt0(all_0_11_11, xR) = all_64_2_41 % 93.20/59.90 | (134) sdtasdt0(all_64_2_41, all_0_11_11) = all_64_1_40 % 93.20/59.90 | (135) sdtpldt0(xR, all_0_11_11) = all_64_3_42 % 93.20/59.90 | (136) sdtasdt0(all_0_11_11, all_64_3_42) = all_0_4_4 % 93.20/59.90 | % 93.20/59.90 | Instantiating (108) with all_66_0_43, all_66_1_44, all_66_2_45, all_66_3_46 yields: % 93.20/59.90 | (137) sdtasdt0(all_66_2_45, all_0_11_11) = all_66_1_44 & sdtasdt0(xR, all_66_3_46) = all_0_5_5 & sdtasdt0(xR, all_0_11_11) = all_66_0_43 & sdtpldt0(all_0_10_10, all_66_0_43) = all_66_1_44 & sdtpldt0(xR, all_0_11_11) = all_66_3_46 & sdtpldt0(xR, xR) = all_66_2_45 % 93.20/59.90 | % 93.20/59.90 | Applying alpha-rule on (137) yields: % 93.20/59.90 | (138) sdtasdt0(xR, all_66_3_46) = all_0_5_5 % 93.20/59.90 | (139) sdtpldt0(xR, xR) = all_66_2_45 % 93.20/59.90 | (140) sdtpldt0(xR, all_0_11_11) = all_66_3_46 % 93.20/59.90 | (141) sdtpldt0(all_0_10_10, all_66_0_43) = all_66_1_44 % 93.20/59.90 | (142) sdtasdt0(all_66_2_45, all_0_11_11) = all_66_1_44 % 93.20/59.90 | (143) sdtasdt0(xR, all_0_11_11) = all_66_0_43 % 93.20/59.90 | % 93.20/59.90 | Instantiating formula (58) with all_0_11_11, xR, all_60_0_31, all_0_10_10 and discharging atoms sdtasdt0(all_0_11_11, xR) = all_60_0_31, sdtasdt0(all_0_11_11, xR) = all_0_10_10, yields: % 93.20/59.90 | (144) all_60_0_31 = all_0_10_10 % 93.20/59.90 | % 93.20/59.90 | Instantiating formula (58) with xR, all_0_11_11, all_66_0_43, all_0_10_10 and discharging atoms sdtasdt0(xR, all_0_11_11) = all_66_0_43, sdtasdt0(xR, all_0_11_11) = all_0_10_10, yields: % 93.20/59.90 | (145) all_66_0_43 = all_0_10_10 % 93.20/59.90 | % 93.20/59.90 | Instantiating formula (58) with xR, all_0_11_11, all_64_0_39, all_66_0_43 and discharging atoms sdtasdt0(xR, all_0_11_11) = all_66_0_43, sdtasdt0(xR, all_0_11_11) = all_64_0_39, yields: % 93.20/59.90 | (146) all_66_0_43 = all_64_0_39 % 93.20/59.90 | % 93.20/59.91 | Instantiating formula (73) with all_0_9_9, all_0_10_10, all_62_3_38, all_0_3_3 and discharging atoms sdtpldt0(all_0_9_9, all_0_10_10) = all_62_3_38, sdtpldt0(all_0_9_9, all_0_10_10) = all_0_3_3, yields: % 93.20/59.91 | (147) all_62_3_38 = all_0_3_3 % 93.20/59.91 | % 93.20/59.91 | Instantiating formula (73) with all_0_10_10, all_60_0_31, all_60_1_32, all_66_1_44 and discharging atoms sdtpldt0(all_0_10_10, all_60_0_31) = all_60_1_32, yields: % 93.20/59.91 | (148) all_66_1_44 = all_60_1_32 | ~ (sdtpldt0(all_0_10_10, all_60_0_31) = all_66_1_44) % 93.20/59.91 | % 93.20/59.91 | Combining equations (145,146) yields a new equation: % 93.20/59.91 | (149) all_64_0_39 = all_0_10_10 % 93.20/59.91 | % 93.20/59.91 | Combining equations (149,146) yields a new equation: % 93.20/59.91 | (145) all_66_0_43 = all_0_10_10 % 93.20/59.91 | % 93.20/59.91 | From (144) and (115) follows: % 93.20/59.91 | (15) sdtasdt0(all_0_11_11, xR) = all_0_10_10 % 93.20/59.91 | % 93.20/59.91 | From (147) and (127) follows: % 93.20/59.91 | (152) sdtpldt0(all_0_6_6, all_0_3_3) = all_0_1_1 % 93.20/59.91 | % 93.20/59.91 | From (145) and (141) follows: % 93.20/59.91 | (153) sdtpldt0(all_0_10_10, all_0_10_10) = all_66_1_44 % 93.20/59.91 | % 93.20/59.91 +-Applying beta-rule and splitting (148), into two cases. % 93.20/59.91 |-Branch one: % 93.20/59.91 | (154) ~ (sdtpldt0(all_0_10_10, all_60_0_31) = all_66_1_44) % 93.20/59.91 | % 93.20/59.91 | From (144) and (154) follows: % 93.20/59.91 | (155) ~ (sdtpldt0(all_0_10_10, all_0_10_10) = all_66_1_44) % 93.20/59.91 | % 93.20/59.91 | Using (153) and (155) yields: % 93.20/59.91 | (156) $false % 93.20/59.91 | % 93.20/59.91 |-The branch is then unsatisfiable % 93.20/59.91 |-Branch two: % 93.20/59.91 | (157) sdtpldt0(all_0_10_10, all_60_0_31) = all_66_1_44 % 93.20/59.91 | (158) all_66_1_44 = all_60_1_32 % 93.20/59.91 | % 93.20/59.91 | From (158) and (153) follows: % 93.20/59.91 | (159) sdtpldt0(all_0_10_10, all_0_10_10) = all_60_1_32 % 93.20/59.91 | % 93.20/59.91 | Instantiating formula (26) with all_60_1_32, all_0_10_10, all_0_10_10, xR, xR, all_0_11_11 and discharging atoms sdtasdt0(all_0_11_11, xR) = all_0_10_10, sdtpldt0(all_0_10_10, all_0_10_10) = all_60_1_32, aScalar0(all_0_11_11), aScalar0(xR), yields: % 93.20/59.91 | (160) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v1, xR) = v2 & sdtasdt0(all_0_11_11, v0) = all_60_1_32 & sdtasdt0(xR, xR) = v3 & sdtpldt0(all_0_10_10, v3) = v2 & sdtpldt0(all_0_11_11, xR) = v1 & sdtpldt0(xR, xR) = v0) % 93.20/59.91 | % 93.20/59.91 | Instantiating formula (5) with all_0_0_0, all_0_1_1, all_0_10_10, all_0_10_10, all_0_2_2 and discharging atoms sdtpldt0(all_0_1_1, all_0_10_10) = all_0_0_0, sdtpldt0(all_0_2_2, all_0_10_10) = all_0_1_1, aScalar0(all_0_2_2), aScalar0(all_0_10_10), yields: % 93.20/59.91 | (161) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v1, all_0_10_10) = v2 & sdtasdt0(all_0_2_2, v3) = v2 & sdtasdt0(all_0_2_2, all_0_10_10) = v1 & sdtasdt0(all_0_10_10, all_0_2_2) = v1 & sdtasdt0(all_0_10_10, all_0_10_10) = v3 & sdtpldt0(all_0_2_2, v0) = all_0_0_0 & sdtpldt0(all_0_10_10, all_0_2_2) = all_0_1_1 & sdtpldt0(all_0_10_10, all_0_10_10) = v0) % 93.20/59.91 | % 93.20/59.91 | Instantiating formula (5) with all_0_0_0, all_0_1_1, all_0_10_10, all_0_3_3, all_0_6_6 and discharging atoms sdtpldt0(all_0_1_1, all_0_10_10) = all_0_0_0, sdtpldt0(all_0_6_6, all_0_3_3) = all_0_1_1, aScalar0(all_0_3_3), aScalar0(all_0_6_6), aScalar0(all_0_10_10), yields: % 93.20/59.91 | (162) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v1, all_0_10_10) = v2 & sdtasdt0(all_0_3_3, all_0_6_6) = v1 & sdtasdt0(all_0_3_3, all_0_10_10) = v3 & sdtasdt0(all_0_6_6, v3) = v2 & sdtasdt0(all_0_6_6, all_0_3_3) = v1 & sdtpldt0(all_0_3_3, all_0_6_6) = all_0_1_1 & sdtpldt0(all_0_3_3, all_0_10_10) = v0 & sdtpldt0(all_0_6_6, v0) = all_0_0_0) % 93.20/59.91 | % 93.20/59.91 | Instantiating formula (5) with all_0_7_7, all_0_5_5, all_0_3_3, all_0_10_10, all_0_6_6 and discharging atoms sdtpldt0(all_0_5_5, all_0_3_3) = all_0_7_7, sdtpldt0(all_0_6_6, all_0_10_10) = all_0_5_5, aScalar0(all_0_3_3), aScalar0(all_0_6_6), aScalar0(all_0_10_10), yields: % 93.20/59.91 | (163) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v1, all_0_3_3) = v2 & sdtasdt0(all_0_6_6, v3) = v2 & sdtasdt0(all_0_6_6, all_0_10_10) = v1 & sdtasdt0(all_0_10_10, all_0_3_3) = v3 & sdtasdt0(all_0_10_10, all_0_6_6) = v1 & sdtpldt0(all_0_6_6, v0) = all_0_7_7 & sdtpldt0(all_0_10_10, all_0_3_3) = v0 & sdtpldt0(all_0_10_10, all_0_6_6) = all_0_5_5) % 93.20/59.91 | % 93.20/59.91 | Instantiating (163) with all_100_0_59, all_100_1_60, all_100_2_61, all_100_3_62 yields: % 93.20/59.91 | (164) sdtasdt0(all_100_2_61, all_0_3_3) = all_100_1_60 & sdtasdt0(all_0_6_6, all_100_0_59) = all_100_1_60 & sdtasdt0(all_0_6_6, all_0_10_10) = all_100_2_61 & sdtasdt0(all_0_10_10, all_0_3_3) = all_100_0_59 & sdtasdt0(all_0_10_10, all_0_6_6) = all_100_2_61 & sdtpldt0(all_0_6_6, all_100_3_62) = all_0_7_7 & sdtpldt0(all_0_10_10, all_0_3_3) = all_100_3_62 & sdtpldt0(all_0_10_10, all_0_6_6) = all_0_5_5 % 93.20/59.91 | % 93.20/59.91 | Applying alpha-rule on (164) yields: % 93.20/59.91 | (165) sdtpldt0(all_0_10_10, all_0_6_6) = all_0_5_5 % 93.20/59.91 | (166) sdtpldt0(all_0_10_10, all_0_3_3) = all_100_3_62 % 93.20/59.91 | (167) sdtasdt0(all_0_6_6, all_0_10_10) = all_100_2_61 % 93.20/59.91 | (168) sdtasdt0(all_0_10_10, all_0_6_6) = all_100_2_61 % 93.20/59.91 | (169) sdtasdt0(all_0_6_6, all_100_0_59) = all_100_1_60 % 93.20/59.91 | (170) sdtasdt0(all_100_2_61, all_0_3_3) = all_100_1_60 % 93.20/59.91 | (171) sdtpldt0(all_0_6_6, all_100_3_62) = all_0_7_7 % 93.20/59.91 | (172) sdtasdt0(all_0_10_10, all_0_3_3) = all_100_0_59 % 93.20/59.91 | % 93.20/59.91 | Instantiating (162) with all_104_0_67, all_104_1_68, all_104_2_69, all_104_3_70 yields: % 93.20/59.91 | (173) sdtasdt0(all_104_2_69, all_0_10_10) = all_104_1_68 & sdtasdt0(all_0_3_3, all_0_6_6) = all_104_2_69 & sdtasdt0(all_0_3_3, all_0_10_10) = all_104_0_67 & sdtasdt0(all_0_6_6, all_104_0_67) = all_104_1_68 & sdtasdt0(all_0_6_6, all_0_3_3) = all_104_2_69 & sdtpldt0(all_0_3_3, all_0_6_6) = all_0_1_1 & sdtpldt0(all_0_3_3, all_0_10_10) = all_104_3_70 & sdtpldt0(all_0_6_6, all_104_3_70) = all_0_0_0 % 93.20/59.91 | % 93.20/59.91 | Applying alpha-rule on (173) yields: % 93.20/59.91 | (174) sdtasdt0(all_0_3_3, all_0_10_10) = all_104_0_67 % 93.20/59.92 | (175) sdtasdt0(all_104_2_69, all_0_10_10) = all_104_1_68 % 93.20/59.92 | (176) sdtpldt0(all_0_3_3, all_0_10_10) = all_104_3_70 % 93.20/59.92 | (177) sdtasdt0(all_0_3_3, all_0_6_6) = all_104_2_69 % 93.20/59.92 | (178) sdtasdt0(all_0_6_6, all_0_3_3) = all_104_2_69 % 93.20/59.92 | (179) sdtasdt0(all_0_6_6, all_104_0_67) = all_104_1_68 % 93.20/59.92 | (180) sdtpldt0(all_0_3_3, all_0_6_6) = all_0_1_1 % 93.20/59.92 | (181) sdtpldt0(all_0_6_6, all_104_3_70) = all_0_0_0 % 93.20/59.92 | % 93.20/59.92 | Instantiating (161) with all_108_0_75, all_108_1_76, all_108_2_77, all_108_3_78 yields: % 93.20/59.92 | (182) sdtasdt0(all_108_2_77, all_0_10_10) = all_108_1_76 & sdtasdt0(all_0_2_2, all_108_0_75) = all_108_1_76 & sdtasdt0(all_0_2_2, all_0_10_10) = all_108_2_77 & sdtasdt0(all_0_10_10, all_0_2_2) = all_108_2_77 & sdtasdt0(all_0_10_10, all_0_10_10) = all_108_0_75 & sdtpldt0(all_0_2_2, all_108_3_78) = all_0_0_0 & sdtpldt0(all_0_10_10, all_0_2_2) = all_0_1_1 & sdtpldt0(all_0_10_10, all_0_10_10) = all_108_3_78 % 93.20/59.92 | % 93.20/59.92 | Applying alpha-rule on (182) yields: % 93.20/59.92 | (183) sdtasdt0(all_108_2_77, all_0_10_10) = all_108_1_76 % 93.20/59.92 | (184) sdtasdt0(all_0_2_2, all_108_0_75) = all_108_1_76 % 93.20/59.92 | (185) sdtasdt0(all_0_10_10, all_0_10_10) = all_108_0_75 % 93.20/59.92 | (186) sdtpldt0(all_0_10_10, all_0_2_2) = all_0_1_1 % 93.20/59.92 | (187) sdtpldt0(all_0_10_10, all_0_10_10) = all_108_3_78 % 93.20/59.92 | (188) sdtasdt0(all_0_10_10, all_0_2_2) = all_108_2_77 % 93.20/59.92 | (189) sdtasdt0(all_0_2_2, all_0_10_10) = all_108_2_77 % 93.20/59.92 | (190) sdtpldt0(all_0_2_2, all_108_3_78) = all_0_0_0 % 93.20/59.92 | % 93.20/59.92 | Instantiating (160) with all_116_0_89, all_116_1_90, all_116_2_91, all_116_3_92 yields: % 93.20/59.92 | (191) sdtasdt0(all_116_2_91, xR) = all_116_1_90 & sdtasdt0(all_0_11_11, all_116_3_92) = all_60_1_32 & sdtasdt0(xR, xR) = all_116_0_89 & sdtpldt0(all_0_10_10, all_116_0_89) = all_116_1_90 & sdtpldt0(all_0_11_11, xR) = all_116_2_91 & sdtpldt0(xR, xR) = all_116_3_92 % 93.20/59.92 | % 93.20/59.92 | Applying alpha-rule on (191) yields: % 93.20/59.92 | (192) sdtasdt0(xR, xR) = all_116_0_89 % 93.20/59.92 | (193) sdtasdt0(all_0_11_11, all_116_3_92) = all_60_1_32 % 93.20/59.92 | (194) sdtasdt0(all_116_2_91, xR) = all_116_1_90 % 93.20/59.92 | (195) sdtpldt0(xR, xR) = all_116_3_92 % 93.20/59.92 | (196) sdtpldt0(all_0_10_10, all_116_0_89) = all_116_1_90 % 93.20/59.92 | (197) sdtpldt0(all_0_11_11, xR) = all_116_2_91 % 93.20/59.92 | % 93.20/59.92 | Instantiating formula (58) with xR, xR, all_116_0_89, all_0_6_6 and discharging atoms sdtasdt0(xR, xR) = all_116_0_89, sdtasdt0(xR, xR) = all_0_6_6, yields: % 93.20/59.92 | (198) all_116_0_89 = all_0_6_6 % 93.20/59.92 | % 93.20/59.92 | Instantiating formula (73) with all_0_10_10, all_0_6_6, all_0_5_5, all_116_1_90 and discharging atoms sdtpldt0(all_0_10_10, all_0_6_6) = all_0_5_5, yields: % 93.20/59.92 | (199) all_116_1_90 = all_0_5_5 | ~ (sdtpldt0(all_0_10_10, all_0_6_6) = all_116_1_90) % 93.20/59.92 | % 93.20/59.92 | From (198) and (196) follows: % 93.20/59.92 | (200) sdtpldt0(all_0_10_10, all_0_6_6) = all_116_1_90 % 93.20/59.92 | % 93.20/59.92 +-Applying beta-rule and splitting (199), into two cases. % 93.20/59.92 |-Branch one: % 93.20/59.92 | (201) ~ (sdtpldt0(all_0_10_10, all_0_6_6) = all_116_1_90) % 93.20/59.92 | % 93.20/59.92 | Using (200) and (201) yields: % 93.20/59.92 | (156) $false % 93.20/59.92 | % 93.20/59.92 |-The branch is then unsatisfiable % 93.20/59.92 |-Branch two: % 93.20/59.92 | (200) sdtpldt0(all_0_10_10, all_0_6_6) = all_116_1_90 % 93.20/59.92 | (204) all_116_1_90 = all_0_5_5 % 93.20/59.92 | % 93.20/59.92 | From (204) and (200) follows: % 93.20/59.92 | (165) sdtpldt0(all_0_10_10, all_0_6_6) = all_0_5_5 % 93.20/59.92 | % 93.20/59.92 | Instantiating formula (5) with all_0_0_0, all_0_1_1, all_0_10_10, all_0_6_6, all_0_3_3 and discharging atoms sdtpldt0(all_0_1_1, all_0_10_10) = all_0_0_0, sdtpldt0(all_0_3_3, all_0_6_6) = all_0_1_1, aScalar0(all_0_3_3), aScalar0(all_0_6_6), aScalar0(all_0_10_10), yields: % 93.20/59.92 | (206) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v1, all_0_10_10) = v2 & sdtasdt0(all_0_3_3, v3) = v2 & sdtasdt0(all_0_3_3, all_0_6_6) = v1 & sdtasdt0(all_0_6_6, all_0_3_3) = v1 & sdtasdt0(all_0_6_6, all_0_10_10) = v3 & sdtpldt0(all_0_3_3, v0) = all_0_0_0 & sdtpldt0(all_0_6_6, all_0_3_3) = all_0_1_1 & sdtpldt0(all_0_6_6, all_0_10_10) = v0) % 93.20/59.92 | % 93.20/59.92 | Instantiating formula (5) with all_0_0_0, all_0_1_1, all_0_10_10, all_0_2_2, all_0_10_10 and discharging atoms sdtpldt0(all_0_1_1, all_0_10_10) = all_0_0_0, sdtpldt0(all_0_10_10, all_0_2_2) = all_0_1_1, aScalar0(all_0_2_2), aScalar0(all_0_10_10), yields: % 93.20/59.92 | (207) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v1, all_0_10_10) = v2 & sdtasdt0(all_0_2_2, all_0_10_10) = v3 & sdtasdt0(all_0_2_2, all_0_10_10) = v1 & sdtasdt0(all_0_10_10, v3) = v2 & sdtasdt0(all_0_10_10, all_0_2_2) = v1 & sdtpldt0(all_0_2_2, all_0_10_10) = v0 & sdtpldt0(all_0_2_2, all_0_10_10) = all_0_1_1 & sdtpldt0(all_0_10_10, v0) = all_0_0_0) % 93.20/59.92 | % 93.20/59.92 | Instantiating formula (5) with all_0_7_7, all_0_5_5, all_0_3_3, all_0_6_6, all_0_10_10 and discharging atoms sdtpldt0(all_0_5_5, all_0_3_3) = all_0_7_7, sdtpldt0(all_0_10_10, all_0_6_6) = all_0_5_5, aScalar0(all_0_3_3), aScalar0(all_0_6_6), aScalar0(all_0_10_10), yields: % 93.20/59.92 | (208) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (sdtasdt0(v1, all_0_3_3) = v2 & sdtasdt0(all_0_6_6, all_0_3_3) = v3 & sdtasdt0(all_0_6_6, all_0_10_10) = v1 & sdtasdt0(all_0_10_10, v3) = v2 & sdtasdt0(all_0_10_10, all_0_6_6) = v1 & sdtpldt0(all_0_6_6, all_0_3_3) = v0 & sdtpldt0(all_0_6_6, all_0_10_10) = all_0_5_5 & sdtpldt0(all_0_10_10, v0) = all_0_7_7) % 93.20/59.92 | % 93.20/59.92 | Instantiating (208) with all_156_0_105, all_156_1_106, all_156_2_107, all_156_3_108 yields: % 93.20/59.92 | (209) sdtasdt0(all_156_2_107, all_0_3_3) = all_156_1_106 & sdtasdt0(all_0_6_6, all_0_3_3) = all_156_0_105 & sdtasdt0(all_0_6_6, all_0_10_10) = all_156_2_107 & sdtasdt0(all_0_10_10, all_156_0_105) = all_156_1_106 & sdtasdt0(all_0_10_10, all_0_6_6) = all_156_2_107 & sdtpldt0(all_0_6_6, all_0_3_3) = all_156_3_108 & sdtpldt0(all_0_6_6, all_0_10_10) = all_0_5_5 & sdtpldt0(all_0_10_10, all_156_3_108) = all_0_7_7 % 93.20/59.92 | % 93.20/59.92 | Applying alpha-rule on (209) yields: % 93.20/59.92 | (210) sdtpldt0(all_0_6_6, all_0_3_3) = all_156_3_108 % 93.20/59.92 | (211) sdtasdt0(all_0_10_10, all_0_6_6) = all_156_2_107 % 93.20/59.92 | (212) sdtasdt0(all_0_10_10, all_156_0_105) = all_156_1_106 % 93.20/59.92 | (213) sdtasdt0(all_156_2_107, all_0_3_3) = all_156_1_106 % 93.20/59.92 | (214) sdtasdt0(all_0_6_6, all_0_3_3) = all_156_0_105 % 93.20/59.93 | (215) sdtasdt0(all_0_6_6, all_0_10_10) = all_156_2_107 % 93.20/59.93 | (87) sdtpldt0(all_0_6_6, all_0_10_10) = all_0_5_5 % 93.20/59.93 | (217) sdtpldt0(all_0_10_10, all_156_3_108) = all_0_7_7 % 93.20/59.93 | % 93.20/59.93 | Instantiating (206) with all_190_0_160, all_190_1_161, all_190_2_162, all_190_3_163 yields: % 93.20/59.93 | (218) sdtasdt0(all_190_2_162, all_0_10_10) = all_190_1_161 & sdtasdt0(all_0_3_3, all_190_0_160) = all_190_1_161 & sdtasdt0(all_0_3_3, all_0_6_6) = all_190_2_162 & sdtasdt0(all_0_6_6, all_0_3_3) = all_190_2_162 & sdtasdt0(all_0_6_6, all_0_10_10) = all_190_0_160 & sdtpldt0(all_0_3_3, all_190_3_163) = all_0_0_0 & sdtpldt0(all_0_6_6, all_0_3_3) = all_0_1_1 & sdtpldt0(all_0_6_6, all_0_10_10) = all_190_3_163 % 93.20/59.93 | % 93.20/59.93 | Applying alpha-rule on (218) yields: % 93.20/59.93 | (219) sdtasdt0(all_190_2_162, all_0_10_10) = all_190_1_161 % 93.20/59.93 | (220) sdtasdt0(all_0_3_3, all_0_6_6) = all_190_2_162 % 93.20/59.93 | (152) sdtpldt0(all_0_6_6, all_0_3_3) = all_0_1_1 % 93.20/59.93 | (222) sdtpldt0(all_0_3_3, all_190_3_163) = all_0_0_0 % 93.20/59.93 | (223) sdtasdt0(all_0_3_3, all_190_0_160) = all_190_1_161 % 93.20/59.93 | (224) sdtasdt0(all_0_6_6, all_0_3_3) = all_190_2_162 % 93.20/59.93 | (225) sdtpldt0(all_0_6_6, all_0_10_10) = all_190_3_163 % 93.20/59.93 | (226) sdtasdt0(all_0_6_6, all_0_10_10) = all_190_0_160 % 93.20/59.93 | % 93.20/59.93 | Instantiating (207) with all_222_0_201, all_222_1_202, all_222_2_203, all_222_3_204 yields: % 93.20/59.93 | (227) sdtasdt0(all_222_2_203, all_0_10_10) = all_222_1_202 & sdtasdt0(all_0_2_2, all_0_10_10) = all_222_0_201 & sdtasdt0(all_0_2_2, all_0_10_10) = all_222_2_203 & sdtasdt0(all_0_10_10, all_222_0_201) = all_222_1_202 & sdtasdt0(all_0_10_10, all_0_2_2) = all_222_2_203 & sdtpldt0(all_0_2_2, all_0_10_10) = all_222_3_204 & sdtpldt0(all_0_2_2, all_0_10_10) = all_0_1_1 & sdtpldt0(all_0_10_10, all_222_3_204) = all_0_0_0 % 93.20/59.93 | % 93.20/59.93 | Applying alpha-rule on (227) yields: % 93.20/59.93 | (228) sdtpldt0(all_0_10_10, all_222_3_204) = all_0_0_0 % 93.20/59.93 | (229) sdtpldt0(all_0_2_2, all_0_10_10) = all_222_3_204 % 93.20/59.93 | (230) sdtasdt0(all_0_10_10, all_0_2_2) = all_222_2_203 % 93.20/59.93 | (231) sdtasdt0(all_0_2_2, all_0_10_10) = all_222_2_203 % 93.20/59.93 | (82) sdtpldt0(all_0_2_2, all_0_10_10) = all_0_1_1 % 93.20/59.93 | (233) sdtasdt0(all_0_10_10, all_222_0_201) = all_222_1_202 % 93.20/59.93 | (234) sdtasdt0(all_222_2_203, all_0_10_10) = all_222_1_202 % 93.20/59.93 | (235) sdtasdt0(all_0_2_2, all_0_10_10) = all_222_0_201 % 93.20/59.93 | % 93.20/59.93 | Instantiating formula (73) with all_0_2_2, all_0_10_10, all_222_3_204, all_0_1_1 and discharging atoms sdtpldt0(all_0_2_2, all_0_10_10) = all_222_3_204, sdtpldt0(all_0_2_2, all_0_10_10) = all_0_1_1, yields: % 93.20/59.93 | (236) all_222_3_204 = all_0_1_1 % 93.20/59.93 | % 93.20/59.93 | Instantiating formula (73) with all_0_6_6, all_0_3_3, all_156_3_108, all_0_1_1 and discharging atoms sdtpldt0(all_0_6_6, all_0_3_3) = all_156_3_108, sdtpldt0(all_0_6_6, all_0_3_3) = all_0_1_1, yields: % 93.20/59.93 | (237) all_156_3_108 = all_0_1_1 % 93.20/59.93 | % 93.20/59.93 | Instantiating formula (73) with all_0_10_10, all_156_3_108, all_0_7_7, all_0_0_0 and discharging atoms sdtpldt0(all_0_10_10, all_156_3_108) = all_0_7_7, yields: % 93.20/59.93 | (238) all_0_0_0 = all_0_7_7 | ~ (sdtpldt0(all_0_10_10, all_156_3_108) = all_0_0_0) % 93.20/59.93 | % 93.20/59.93 | From (236) and (228) follows: % 93.20/59.93 | (239) sdtpldt0(all_0_10_10, all_0_1_1) = all_0_0_0 % 93.20/59.93 | % 93.20/59.93 +-Applying beta-rule and splitting (238), into two cases. % 93.20/59.93 |-Branch one: % 93.20/59.93 | (240) ~ (sdtpldt0(all_0_10_10, all_156_3_108) = all_0_0_0) % 93.20/59.93 | % 93.20/59.93 | From (237) and (240) follows: % 93.20/59.93 | (241) ~ (sdtpldt0(all_0_10_10, all_0_1_1) = all_0_0_0) % 93.20/59.93 | % 93.20/59.93 | Using (239) and (241) yields: % 93.20/59.93 | (156) $false % 93.20/59.93 | % 93.20/59.93 |-The branch is then unsatisfiable % 93.20/59.93 |-Branch two: % 93.20/59.93 | (243) sdtpldt0(all_0_10_10, all_156_3_108) = all_0_0_0 % 93.20/59.93 | (244) all_0_0_0 = all_0_7_7 % 93.20/59.93 | % 93.20/59.93 | Equations (244) can reduce 23 to: % 93.20/59.93 | (245) $false % 93.20/59.93 | % 93.20/59.93 |-The branch is then unsatisfiable % 93.20/59.93 % SZS output end Proof for theBenchmark % 93.20/59.93 % 93.20/59.93 59305ms %------------------------------------------------------------------------------