%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : ALG077+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n022.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 : Thu Jul 14 15:34:15 EDT 2022 % Result : Theorem 4.01s 1.63s % Output : Proof 8.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ALG077+1 : TPTP v8.1.0. Released v2.7.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n022.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Wed Jun 8 00:08:50 EDT 2022 % 0.13/0.34 % CPUTime : % 0.20/0.60 ____ _ % 0.20/0.60 ___ / __ \_____(_)___ ________ __________ % 0.20/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.20/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.20/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic % 0.20/0.60 (ePrincess v.1.0) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2015 % 0.20/0.60 (c) Peter Backeman, 2014-2015 % 0.20/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.20/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.20/0.60 Bug reports to peter@backeman.se % 0.20/0.60 % 0.20/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.93/1.03 Prover 0: Preprocessing ... % 3.11/1.34 Prover 0: Constructing countermodel ... % 4.01/1.63 Prover 0: proved (974ms) % 4.01/1.63 % 4.01/1.63 No countermodel exists, formula is valid % 4.01/1.63 % SZS status Theorem for theBenchmark % 4.01/1.63 % 4.01/1.63 Generating proof ... found it (size 129) % 7.35/2.31 % 7.35/2.31 % SZS output start Proof for theBenchmark % 7.35/2.32 Assumed formulas after preprocessing and simplification: % 7.35/2.32 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (e24 = e23) & ~ (e24 = e22) & ~ (e24 = e20) & ~ (e24 = e21) & ~ (e24 = e14) & ~ (e24 = e13) & ~ (e24 = e12) & ~ (e24 = e10) & ~ (e24 = e11) & ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e23 = e14) & ~ (e23 = e13) & ~ (e23 = e12) & ~ (e23 = e10) & ~ (e23 = e11) & ~ (e22 = e20) & ~ (e22 = e21) & ~ (e22 = e14) & ~ (e22 = e13) & ~ (e22 = e12) & ~ (e22 = e10) & ~ (e22 = e11) & ~ (e20 = e21) & ~ (e20 = e14) & ~ (e20 = e13) & ~ (e20 = e12) & ~ (e20 = e10) & ~ (e20 = e11) & ~ (e21 = e14) & ~ (e21 = e13) & ~ (e21 = e12) & ~ (e21 = e10) & ~ (e21 = e11) & ~ (e14 = e13) & ~ (e14 = e12) & ~ (e14 = e10) & ~ (e14 = e11) & ~ (e13 = e12) & ~ (e13 = e10) & ~ (e13 = e11) & ~ (e12 = e10) & ~ (e12 = e11) & ~ (e10 = e11) & op2(v4, v4) = v0 & op2(v4, v3) = v2 & op2(v4, v2) = v1 & op2(v4, v1) = v3 & op2(v4, v0) = v4 & op2(v3, v4) = v1 & op2(v3, v3) = v4 & op2(v3, v2) = v0 & op2(v3, v1) = v2 & op2(v3, v0) = v3 & op2(v2, v4) = v3 & op2(v2, v3) = v1 & op2(v2, v2) = v4 & op2(v2, v1) = v0 & op2(v2, v0) = v2 & op2(v1, v4) = v2 & op2(v1, v3) = v0 & op2(v1, v2) = v3 & op2(v1, v1) = v4 & op2(v1, v0) = v1 & op2(v0, v4) = v4 & op2(v0, v3) = v3 & op2(v0, v2) = v2 & op2(v0, v1) = v1 & op2(v0, v0) = v0 & op2(e24, e24) = e21 & op2(e24, e23) = e22 & op2(e24, e22) = e20 & op2(e24, e20) = e24 & op2(e24, e21) = e23 & op2(e23, e24) = e22 & op2(e23, e23) = e21 & op2(e23, e22) = e24 & op2(e23, e20) = e23 & op2(e23, e21) = e20 & op2(e22, e24) = e23 & op2(e22, e23) = e20 & op2(e22, e22) = e21 & op2(e22, e20) = e22 & op2(e22, e21) = e24 & op2(e20, e24) = e24 & op2(e20, e23) = e23 & op2(e20, e22) = e22 & op2(e20, e20) = e20 & op2(e20, e21) = e21 & op2(e21, e24) = e20 & op2(e21, e23) = e24 & op2(e21, e22) = e23 & op2(e21, e20) = e21 & op2(e21, e21) = e22 & op1(v9, v9) = v6 & op1(v9, v8) = v7 & op1(v9, v7) = v5 & op1(v9, v6) = v8 & op1(v9, v5) = v9 & op1(v8, v9) = v7 & op1(v8, v8) = v6 & op1(v8, v7) = v9 & op1(v8, v6) = v5 & op1(v8, v5) = v8 & op1(v7, v9) = v8 & op1(v7, v8) = v5 & op1(v7, v7) = v6 & op1(v7, v6) = v9 & op1(v7, v5) = v7 & op1(v6, v9) = v5 & op1(v6, v8) = v9 & op1(v6, v7) = v8 & op1(v6, v6) = v7 & op1(v6, v5) = v6 & op1(v5, v9) = v9 & op1(v5, v8) = v8 & op1(v5, v7) = v7 & op1(v5, v6) = v6 & op1(v5, v5) = v5 & op1(e14, e14) = e10 & op1(e14, e13) = e12 & op1(e14, e12) = e11 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e14) = e11 & op1(e13, e13) = e14 & op1(e13, e12) = e10 & op1(e13, e10) = e13 & op1(e13, e11) = e12 & op1(e12, e14) = e13 & op1(e12, e13) = e11 & op1(e12, e12) = e14 & op1(e12, e10) = e12 & op1(e12, e11) = e10 & op1(e10, e14) = e14 & op1(e10, e13) = e13 & op1(e10, e12) = e12 & op1(e10, e10) = e10 & op1(e10, e11) = e11 & op1(e11, e14) = e12 & op1(e11, e13) = e10 & op1(e11, e12) = e13 & op1(e11, e10) = e11 & op1(e11, e11) = e14 & h(v9) = e24 & h(v8) = e23 & h(v7) = e22 & h(v6) = e21 & h(v5) = e20 & h(e14) = v4 & h(e13) = v3 & h(e12) = v2 & h(e10) = v0 & h(e11) = v1 & j(v4) = e14 & j(v3) = e13 & j(v2) = e12 & j(v1) = e11 & j(v0) = e10 & j(e24) = v9 & j(e23) = v8 & j(e22) = v7 & j(e20) = v5 & j(e21) = v6 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (op2(v13, v12) = v11) | ~ (op2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (op1(v13, v12) = v11) | ~ (op1(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (h(v12) = v11) | ~ (h(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (j(v12) = v11) | ~ (j(v12) = v10)) & (v9 = e14 | v9 = e13 | v9 = e12 | v9 = e10 | v9 = e11) & (v8 = e14 | v8 = e13 | v8 = e12 | v8 = e10 | v8 = e11) & (v7 = e14 | v7 = e13 | v7 = e12 | v7 = e10 | v7 = e11) & (v6 = e14 | v6 = e13 | v6 = e12 | v6 = e10 | v6 = e11) & (v5 = e14 | v5 = e13 | v5 = e12 | v5 = e10 | v5 = e11) & (v4 = e24 | v4 = e23 | v4 = e22 | v4 = e20 | v4 = e21) & (v3 = e24 | v3 = e23 | v3 = e22 | v3 = e20 | v3 = e21) & (v2 = e24 | v2 = e23 | v2 = e22 | v2 = e20 | v2 = e21) & (v1 = e24 | v1 = e23 | v1 = e22 | v1 = e20 | v1 = e21) & (v0 = e24 | v0 = e23 | v0 = e22 | v0 = e20 | v0 = e21)) % 7.35/2.37 | 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 yields: % 7.35/2.37 | (1) ~ (e24 = e23) & ~ (e24 = e22) & ~ (e24 = e20) & ~ (e24 = e21) & ~ (e24 = e14) & ~ (e24 = e13) & ~ (e24 = e12) & ~ (e24 = e10) & ~ (e24 = e11) & ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e23 = e14) & ~ (e23 = e13) & ~ (e23 = e12) & ~ (e23 = e10) & ~ (e23 = e11) & ~ (e22 = e20) & ~ (e22 = e21) & ~ (e22 = e14) & ~ (e22 = e13) & ~ (e22 = e12) & ~ (e22 = e10) & ~ (e22 = e11) & ~ (e20 = e21) & ~ (e20 = e14) & ~ (e20 = e13) & ~ (e20 = e12) & ~ (e20 = e10) & ~ (e20 = e11) & ~ (e21 = e14) & ~ (e21 = e13) & ~ (e21 = e12) & ~ (e21 = e10) & ~ (e21 = e11) & ~ (e14 = e13) & ~ (e14 = e12) & ~ (e14 = e10) & ~ (e14 = e11) & ~ (e13 = e12) & ~ (e13 = e10) & ~ (e13 = e11) & ~ (e12 = e10) & ~ (e12 = e11) & ~ (e10 = e11) & op2(all_0_5_5, all_0_5_5) = all_0_9_9 & op2(all_0_5_5, all_0_6_6) = all_0_7_7 & op2(all_0_5_5, all_0_7_7) = all_0_8_8 & op2(all_0_5_5, all_0_8_8) = all_0_6_6 & op2(all_0_5_5, all_0_9_9) = all_0_5_5 & op2(all_0_6_6, all_0_5_5) = all_0_8_8 & op2(all_0_6_6, all_0_6_6) = all_0_5_5 & op2(all_0_6_6, all_0_7_7) = all_0_9_9 & op2(all_0_6_6, all_0_8_8) = all_0_7_7 & op2(all_0_6_6, all_0_9_9) = all_0_6_6 & op2(all_0_7_7, all_0_5_5) = all_0_6_6 & op2(all_0_7_7, all_0_6_6) = all_0_8_8 & op2(all_0_7_7, all_0_7_7) = all_0_5_5 & op2(all_0_7_7, all_0_8_8) = all_0_9_9 & op2(all_0_7_7, all_0_9_9) = all_0_7_7 & op2(all_0_8_8, all_0_5_5) = all_0_7_7 & op2(all_0_8_8, all_0_6_6) = all_0_9_9 & op2(all_0_8_8, all_0_7_7) = all_0_6_6 & op2(all_0_8_8, all_0_8_8) = all_0_5_5 & op2(all_0_8_8, all_0_9_9) = all_0_8_8 & op2(all_0_9_9, all_0_5_5) = all_0_5_5 & op2(all_0_9_9, all_0_6_6) = all_0_6_6 & op2(all_0_9_9, all_0_7_7) = all_0_7_7 & op2(all_0_9_9, all_0_8_8) = all_0_8_8 & op2(all_0_9_9, all_0_9_9) = all_0_9_9 & op2(e24, e24) = e21 & op2(e24, e23) = e22 & op2(e24, e22) = e20 & op2(e24, e20) = e24 & op2(e24, e21) = e23 & op2(e23, e24) = e22 & op2(e23, e23) = e21 & op2(e23, e22) = e24 & op2(e23, e20) = e23 & op2(e23, e21) = e20 & op2(e22, e24) = e23 & op2(e22, e23) = e20 & op2(e22, e22) = e21 & op2(e22, e20) = e22 & op2(e22, e21) = e24 & op2(e20, e24) = e24 & op2(e20, e23) = e23 & op2(e20, e22) = e22 & op2(e20, e20) = e20 & op2(e20, e21) = e21 & op2(e21, e24) = e20 & op2(e21, e23) = e24 & op2(e21, e22) = e23 & op2(e21, e20) = e21 & op2(e21, e21) = e22 & op1(all_0_0_0, all_0_0_0) = all_0_3_3 & op1(all_0_0_0, all_0_1_1) = all_0_2_2 & op1(all_0_0_0, all_0_2_2) = all_0_4_4 & op1(all_0_0_0, all_0_3_3) = all_0_1_1 & op1(all_0_0_0, all_0_4_4) = all_0_0_0 & op1(all_0_1_1, all_0_0_0) = all_0_2_2 & op1(all_0_1_1, all_0_1_1) = all_0_3_3 & op1(all_0_1_1, all_0_2_2) = all_0_0_0 & op1(all_0_1_1, all_0_3_3) = all_0_4_4 & op1(all_0_1_1, all_0_4_4) = all_0_1_1 & op1(all_0_2_2, all_0_0_0) = all_0_1_1 & op1(all_0_2_2, all_0_1_1) = all_0_4_4 & op1(all_0_2_2, all_0_2_2) = all_0_3_3 & op1(all_0_2_2, all_0_3_3) = all_0_0_0 & op1(all_0_2_2, all_0_4_4) = all_0_2_2 & op1(all_0_3_3, all_0_0_0) = all_0_4_4 & op1(all_0_3_3, all_0_1_1) = all_0_0_0 & op1(all_0_3_3, all_0_2_2) = all_0_1_1 & op1(all_0_3_3, all_0_3_3) = all_0_2_2 & op1(all_0_3_3, all_0_4_4) = all_0_3_3 & op1(all_0_4_4, all_0_0_0) = all_0_0_0 & op1(all_0_4_4, all_0_1_1) = all_0_1_1 & op1(all_0_4_4, all_0_2_2) = all_0_2_2 & op1(all_0_4_4, all_0_3_3) = all_0_3_3 & op1(all_0_4_4, all_0_4_4) = all_0_4_4 & op1(e14, e14) = e10 & op1(e14, e13) = e12 & op1(e14, e12) = e11 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e14) = e11 & op1(e13, e13) = e14 & op1(e13, e12) = e10 & op1(e13, e10) = e13 & op1(e13, e11) = e12 & op1(e12, e14) = e13 & op1(e12, e13) = e11 & op1(e12, e12) = e14 & op1(e12, e10) = e12 & op1(e12, e11) = e10 & op1(e10, e14) = e14 & op1(e10, e13) = e13 & op1(e10, e12) = e12 & op1(e10, e10) = e10 & op1(e10, e11) = e11 & op1(e11, e14) = e12 & op1(e11, e13) = e10 & op1(e11, e12) = e13 & op1(e11, e10) = e11 & op1(e11, e11) = e14 & h(all_0_0_0) = e24 & h(all_0_1_1) = e23 & h(all_0_2_2) = e22 & h(all_0_3_3) = e21 & h(all_0_4_4) = e20 & h(e14) = all_0_5_5 & h(e13) = all_0_6_6 & h(e12) = all_0_7_7 & h(e10) = all_0_9_9 & h(e11) = all_0_8_8 & j(all_0_5_5) = e14 & j(all_0_6_6) = e13 & j(all_0_7_7) = e12 & j(all_0_8_8) = e11 & j(all_0_9_9) = e10 & j(e24) = all_0_0_0 & j(e23) = all_0_1_1 & j(e22) = all_0_2_2 & j(e20) = all_0_4_4 & j(e21) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) & (all_0_0_0 = e14 | all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11) & (all_0_1_1 = e14 | all_0_1_1 = e13 | all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11) & (all_0_2_2 = e14 | all_0_2_2 = e13 | all_0_2_2 = e12 | all_0_2_2 = e10 | all_0_2_2 = e11) & (all_0_3_3 = e14 | all_0_3_3 = e13 | all_0_3_3 = e12 | all_0_3_3 = e10 | all_0_3_3 = e11) & (all_0_4_4 = e14 | all_0_4_4 = e13 | all_0_4_4 = e12 | all_0_4_4 = e10 | all_0_4_4 = e11) & (all_0_5_5 = e24 | all_0_5_5 = e23 | all_0_5_5 = e22 | all_0_5_5 = e20 | all_0_5_5 = e21) & (all_0_6_6 = e24 | all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21) & (all_0_7_7 = e24 | all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21) & (all_0_8_8 = e24 | all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21) & (all_0_9_9 = e24 | all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21) % 7.74/2.38 | % 7.74/2.38 | Applying alpha-rule on (1) yields: % 7.74/2.38 | (2) ~ (e21 = e12) % 7.74/2.38 | (3) op1(all_0_4_4, all_0_1_1) = all_0_1_1 % 7.74/2.38 | (4) op1(e13, e14) = e11 % 7.74/2.38 | (5) op2(all_0_7_7, all_0_8_8) = all_0_9_9 % 7.74/2.38 | (6) ~ (e20 = e21) % 7.74/2.38 | (7) ~ (e20 = e14) % 7.74/2.38 | (8) op2(e20, e23) = e23 % 7.74/2.38 | (9) op1(all_0_4_4, all_0_2_2) = all_0_2_2 % 7.74/2.38 | (10) ~ (e24 = e11) % 7.74/2.38 | (11) ~ (e12 = e11) % 7.74/2.38 | (12) op2(all_0_6_6, all_0_7_7) = all_0_9_9 % 7.74/2.38 | (13) h(e12) = all_0_7_7 % 7.74/2.38 | (14) h(all_0_0_0) = e24 % 7.74/2.38 | (15) h(e13) = all_0_6_6 % 7.74/2.38 | (16) op2(all_0_5_5, all_0_8_8) = all_0_6_6 % 7.74/2.38 | (17) ~ (e14 = e12) % 7.74/2.38 | (18) ~ (e24 = e12) % 7.74/2.38 | (19) op1(all_0_0_0, all_0_0_0) = all_0_3_3 % 7.74/2.38 | (20) op2(all_0_7_7, all_0_7_7) = all_0_5_5 % 7.74/2.38 | (21) op1(e12, e14) = e13 % 7.74/2.38 | (22) op1(e10, e11) = e11 % 7.74/2.38 | (23) j(e22) = all_0_2_2 % 7.74/2.38 | (24) op2(all_0_9_9, all_0_8_8) = all_0_8_8 % 7.74/2.38 | (25) j(e21) = all_0_3_3 % 7.74/2.38 | (26) j(all_0_8_8) = e11 % 7.74/2.38 | (27) ~ (e22 = e13) % 7.74/2.38 | (28) op2(all_0_6_6, all_0_9_9) = all_0_6_6 % 7.74/2.38 | (29) op2(all_0_8_8, all_0_7_7) = all_0_6_6 % 7.74/2.38 | (30) op2(e24, e21) = e23 % 7.74/2.38 | (31) op1(all_0_3_3, all_0_4_4) = all_0_3_3 % 7.74/2.38 | (32) op1(e11, e12) = e13 % 7.74/2.38 | (33) j(all_0_6_6) = e13 % 7.74/2.38 | (34) op2(all_0_5_5, all_0_7_7) = all_0_8_8 % 7.74/2.38 | (35) h(all_0_4_4) = e20 % 7.74/2.38 | (36) op1(all_0_2_2, all_0_0_0) = all_0_1_1 % 7.74/2.38 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) % 7.74/2.38 | (38) op2(e21, e22) = e23 % 7.74/2.38 | (39) ~ (e23 = e13) % 7.74/2.38 | (40) op1(all_0_0_0, all_0_4_4) = all_0_0_0 % 7.74/2.38 | (41) op2(all_0_9_9, all_0_6_6) = all_0_6_6 % 7.74/2.39 | (42) op2(e24, e22) = e20 % 7.74/2.39 | (43) op2(e22, e20) = e22 % 7.74/2.39 | (44) all_0_5_5 = e24 | all_0_5_5 = e23 | all_0_5_5 = e22 | all_0_5_5 = e20 | all_0_5_5 = e21 % 7.74/2.39 | (45) ~ (e23 = e12) % 7.74/2.39 | (46) op1(e11, e10) = e11 % 7.74/2.39 | (47) op2(e21, e21) = e22 % 7.74/2.39 | (48) ~ (e24 = e14) % 7.74/2.39 | (49) h(all_0_3_3) = e21 % 7.74/2.39 | (50) ~ (e23 = e21) % 7.74/2.39 | (51) op1(e13, e11) = e12 % 7.74/2.39 | (52) all_0_1_1 = e14 | all_0_1_1 = e13 | all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11 % 7.74/2.39 | (53) ~ (e22 = e21) % 7.74/2.39 | (54) ~ (e20 = e11) % 7.74/2.39 | (55) j(all_0_9_9) = e10 % 7.74/2.39 | (56) op1(all_0_3_3, all_0_3_3) = all_0_2_2 % 7.74/2.39 | (57) op1(all_0_2_2, all_0_2_2) = all_0_3_3 % 7.74/2.39 | (58) ~ (e14 = e10) % 7.74/2.39 | (59) ~ (e22 = e10) % 7.74/2.39 | (60) op1(e14, e12) = e11 % 7.74/2.39 | (61) h(all_0_1_1) = e23 % 7.74/2.39 | (62) op2(all_0_9_9, all_0_9_9) = all_0_9_9 % 7.74/2.39 | (63) op2(all_0_9_9, all_0_7_7) = all_0_7_7 % 7.74/2.39 | (64) op1(e12, e10) = e12 % 7.74/2.39 | (65) ~ (e12 = e10) % 7.74/2.39 | (66) ~ (e24 = e22) % 7.74/2.39 | (67) op1(all_0_1_1, all_0_4_4) = all_0_1_1 % 7.74/2.39 | (68) op1(e14, e14) = e10 % 7.74/2.39 | (69) op2(e21, e24) = e20 % 7.74/2.39 | (70) op1(all_0_3_3, all_0_0_0) = all_0_4_4 % 7.74/2.39 | (71) all_0_9_9 = e24 | all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21 % 7.74/2.39 | (72) op2(e20, e24) = e24 % 7.74/2.39 | (73) op2(e22, e21) = e24 % 7.74/2.39 | (74) op2(e20, e20) = e20 % 7.74/2.39 | (75) all_0_2_2 = e14 | all_0_2_2 = e13 | all_0_2_2 = e12 | all_0_2_2 = e10 | all_0_2_2 = e11 % 7.74/2.39 | (76) op1(all_0_1_1, all_0_0_0) = all_0_2_2 % 7.74/2.39 | (77) op2(all_0_7_7, all_0_9_9) = all_0_7_7 % 7.74/2.39 | (78) op1(all_0_0_0, all_0_1_1) = all_0_2_2 % 7.74/2.39 | (79) j(all_0_7_7) = e12 % 7.74/2.39 | (80) op1(e12, e13) = e11 % 7.74/2.39 | (81) op2(all_0_7_7, all_0_5_5) = all_0_6_6 % 7.74/2.39 | (82) op2(all_0_5_5, all_0_9_9) = all_0_5_5 % 7.74/2.39 | (83) h(all_0_2_2) = e22 % 7.74/2.39 | (84) ~ (e14 = e13) % 7.86/2.39 | (85) ~ (e21 = e11) % 7.86/2.39 | (86) h(e14) = all_0_5_5 % 7.86/2.39 | (87) ~ (e24 = e20) % 7.86/2.39 | (88) op2(e23, e23) = e21 % 7.86/2.40 | (89) ~ (e13 = e12) % 7.86/2.40 | (90) all_0_7_7 = e24 | all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21 % 7.86/2.40 | (91) op2(all_0_8_8, all_0_8_8) = all_0_5_5 % 7.86/2.40 | (92) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) % 7.86/2.40 | (93) ~ (e14 = e11) % 7.86/2.40 | (94) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) % 7.86/2.40 | (95) op1(all_0_2_2, all_0_4_4) = all_0_2_2 % 7.86/2.40 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) % 7.86/2.40 | (97) all_0_4_4 = e14 | all_0_4_4 = e13 | all_0_4_4 = e12 | all_0_4_4 = e10 | all_0_4_4 = e11 % 7.86/2.40 | (98) op1(all_0_1_1, all_0_1_1) = all_0_3_3 % 7.86/2.40 | (99) op2(all_0_6_6, all_0_8_8) = all_0_7_7 % 7.86/2.40 | (100) op1(e13, e10) = e13 % 7.86/2.40 | (101) op2(all_0_6_6, all_0_6_6) = all_0_5_5 % 7.86/2.40 | (102) op1(e10, e10) = e10 % 7.86/2.40 | (103) op1(all_0_0_0, all_0_3_3) = all_0_1_1 % 7.86/2.40 | (104) ~ (e23 = e10) % 7.86/2.40 | (105) op1(all_0_4_4, all_0_4_4) = all_0_4_4 % 7.86/2.40 | (106) op1(all_0_1_1, all_0_3_3) = all_0_4_4 % 7.86/2.40 | (107) ~ (e13 = e10) % 7.86/2.40 | (108) op1(e14, e13) = e12 % 7.86/2.40 | (109) op1(e10, e12) = e12 % 7.86/2.40 | (110) all_0_6_6 = e24 | all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21 % 7.86/2.40 | (111) op2(all_0_7_7, all_0_6_6) = all_0_8_8 % 7.86/2.40 | (112) all_0_0_0 = e14 | all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11 % 7.86/2.40 | (113) ~ (e23 = e22) % 7.86/2.40 | (114) ~ (e20 = e10) % 7.86/2.40 | (115) ~ (e22 = e11) % 7.86/2.40 | (116) op2(e22, e23) = e20 % 7.86/2.40 | (117) ~ (e20 = e12) % 7.86/2.40 | (118) op2(e24, e24) = e21 % 7.86/2.40 | (119) op1(all_0_0_0, all_0_2_2) = all_0_4_4 % 7.86/2.40 | (120) op2(e23, e22) = e24 % 7.86/2.40 | (121) op1(e14, e11) = e13 % 7.86/2.40 | (122) op2(e24, e20) = e24 % 7.86/2.40 | (123) op1(all_0_4_4, all_0_0_0) = all_0_0_0 % 7.86/2.40 | (124) all_0_8_8 = e24 | all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21 % 7.86/2.40 | (125) ~ (e10 = e11) % 7.86/2.40 | (126) op1(all_0_3_3, all_0_2_2) = all_0_1_1 % 7.86/2.41 | (127) ~ (e23 = e14) % 7.86/2.41 | (128) h(e11) = all_0_8_8 % 7.86/2.41 | (129) op1(e10, e13) = e13 % 7.86/2.41 | (130) op1(e14, e10) = e14 % 7.86/2.41 | (131) op2(e23, e24) = e22 % 7.86/2.41 | (132) j(e23) = all_0_1_1 % 7.86/2.41 | (133) ~ (e23 = e20) % 7.86/2.41 | (134) op2(e21, e20) = e21 % 7.86/2.41 | (135) ~ (e21 = e14) % 7.86/2.41 | (136) j(e24) = all_0_0_0 % 7.86/2.41 | (137) op2(all_0_5_5, all_0_6_6) = all_0_7_7 % 7.86/2.41 | (138) op1(e12, e11) = e10 % 7.86/2.41 | (139) op1(all_0_3_3, all_0_1_1) = all_0_0_0 % 7.86/2.41 | (140) op1(e10, e14) = e14 % 7.86/2.41 | (141) op1(all_0_2_2, all_0_1_1) = all_0_4_4 % 7.86/2.41 | (142) ~ (e24 = e21) % 7.86/2.41 | (143) op1(e11, e13) = e10 % 7.86/2.41 | (144) op2(e23, e21) = e20 % 7.86/2.41 | (145) op2(all_0_8_8, all_0_9_9) = all_0_8_8 % 7.86/2.41 | (146) j(all_0_5_5) = e14 % 7.86/2.41 | (147) op2(all_0_8_8, all_0_5_5) = all_0_7_7 % 7.86/2.41 | (148) op1(e11, e14) = e12 % 7.86/2.41 | (149) op2(e23, e20) = e23 % 7.86/2.41 | (150) op1(all_0_1_1, all_0_2_2) = all_0_0_0 % 7.86/2.41 | (151) ~ (e22 = e20) % 7.86/2.41 | (152) ~ (e23 = e11) % 7.86/2.41 | (153) op2(all_0_8_8, all_0_6_6) = all_0_9_9 % 7.86/2.41 | (154) op1(e11, e11) = e14 % 7.86/2.41 | (155) op2(e21, e23) = e24 % 7.86/2.41 | (156) op1(all_0_2_2, all_0_3_3) = all_0_0_0 % 7.86/2.41 | (157) ~ (e24 = e10) % 7.86/2.41 | (158) ~ (e24 = e23) % 7.86/2.41 | (159) ~ (e20 = e13) % 7.86/2.41 | (160) ~ (e24 = e13) % 7.86/2.41 | (161) op1(all_0_4_4, all_0_3_3) = all_0_3_3 % 7.86/2.41 | (162) ~ (e21 = e10) % 7.86/2.41 | (163) op1(e13, e13) = e14 % 7.86/2.41 | (164) ~ (e21 = e13) % 7.86/2.42 | (165) op1(e12, e12) = e14 % 7.86/2.42 | (166) j(e20) = all_0_4_4 % 7.86/2.42 | (167) op2(all_0_5_5, all_0_5_5) = all_0_9_9 % 7.86/2.42 | (168) ~ (e22 = e12) % 7.86/2.42 | (169) op1(e13, e12) = e10 % 7.86/2.42 | (170) op2(e24, e23) = e22 % 7.86/2.42 | (171) op2(e20, e22) = e22 % 7.86/2.42 | (172) all_0_3_3 = e14 | all_0_3_3 = e13 | all_0_3_3 = e12 | all_0_3_3 = e10 | all_0_3_3 = e11 % 7.86/2.42 | (173) op2(e22, e24) = e23 % 7.86/2.42 | (174) op2(all_0_6_6, all_0_5_5) = all_0_8_8 % 7.86/2.42 | (175) h(e10) = all_0_9_9 % 7.86/2.42 | (176) op2(e22, e22) = e21 % 7.86/2.42 | (177) ~ (e22 = e14) % 7.86/2.42 | (178) op2(e20, e21) = e21 % 7.86/2.42 | (179) op2(all_0_9_9, all_0_5_5) = all_0_5_5 % 7.86/2.42 | (180) ~ (e13 = e11) % 7.86/2.42 | % 7.86/2.42 +-Applying beta-rule and splitting (112), into two cases. % 7.86/2.42 |-Branch one: % 7.86/2.42 | (181) all_0_0_0 = e14 % 7.86/2.42 | % 7.86/2.42 | From (181)(181) and (19) follows: % 7.86/2.42 | (182) op1(e14, e14) = all_0_3_3 % 7.86/2.42 | % 7.86/2.42 | From (181) and (103) follows: % 7.86/2.42 | (183) op1(e14, all_0_3_3) = all_0_1_1 % 7.86/2.42 | % 7.86/2.42 | Instantiating formula (96) with e14, e14, all_0_3_3, e10 and discharging atoms op1(e14, e14) = all_0_3_3, op1(e14, e14) = e10, yields: % 7.86/2.42 | (184) all_0_3_3 = e10 % 7.86/2.42 | % 7.86/2.42 | From (184) and (126) follows: % 7.86/2.42 | (185) op1(e10, all_0_2_2) = all_0_1_1 % 7.86/2.42 | % 7.86/2.42 | From (184)(184) and (56) follows: % 7.99/2.42 | (186) op1(e10, e10) = all_0_2_2 % 7.99/2.42 | % 7.99/2.42 | From (184) and (183) follows: % 7.99/2.42 | (187) op1(e14, e10) = all_0_1_1 % 7.99/2.42 | % 7.99/2.42 | Instantiating formula (96) with e14, e10, all_0_1_1, e14 and discharging atoms op1(e14, e10) = all_0_1_1, op1(e14, e10) = e14, yields: % 7.99/2.42 | (188) all_0_1_1 = e14 % 7.99/2.42 | % 7.99/2.42 | Instantiating formula (96) with e10, e10, all_0_2_2, e10 and discharging atoms op1(e10, e10) = all_0_2_2, op1(e10, e10) = e10, yields: % 7.99/2.42 | (189) all_0_2_2 = e10 % 7.99/2.42 | % 7.99/2.42 | From (189)(188) and (185) follows: % 7.99/2.42 | (190) op1(e10, e10) = e14 % 7.99/2.42 | % 7.99/2.42 | From (189) and (186) follows: % 7.99/2.42 | (102) op1(e10, e10) = e10 % 7.99/2.42 | % 7.99/2.42 | Instantiating formula (96) with e10, e10, e14, e10 and discharging atoms op1(e10, e10) = e14, op1(e10, e10) = e10, yields: % 7.99/2.42 | (192) e14 = e10 % 7.99/2.42 | % 8.00/2.42 | Equations (192) can reduce 58 to: % 8.00/2.42 | (193) $false % 8.00/2.42 | % 8.00/2.42 |-The branch is then unsatisfiable % 8.00/2.42 |-Branch two: % 8.00/2.42 | (194) ~ (all_0_0_0 = e14) % 8.00/2.43 | (195) all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11 % 8.00/2.43 | % 8.00/2.43 +-Applying beta-rule and splitting (71), into two cases. % 8.00/2.43 |-Branch one: % 8.00/2.43 | (196) all_0_9_9 = e24 % 8.00/2.43 | % 8.00/2.43 | From (196)(196)(196) and (62) follows: % 8.00/2.43 | (197) op2(e24, e24) = e24 % 8.00/2.43 | % 8.00/2.43 | Instantiating formula (37) with e24, e24, e24, e21 and discharging atoms op2(e24, e24) = e24, op2(e24, e24) = e21, yields: % 8.00/2.43 | (198) e24 = e21 % 8.00/2.43 | % 8.00/2.43 | Equations (198) can reduce 142 to: % 8.00/2.43 | (193) $false % 8.00/2.43 | % 8.00/2.43 |-The branch is then unsatisfiable % 8.00/2.43 |-Branch two: % 8.00/2.43 | (200) ~ (all_0_9_9 = e24) % 8.00/2.43 | (201) all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21 % 8.00/2.43 | % 8.00/2.43 +-Applying beta-rule and splitting (90), into two cases. % 8.00/2.43 |-Branch one: % 8.00/2.43 | (202) all_0_7_7 = e24 % 8.00/2.43 | % 8.00/2.43 | From (202) and (34) follows: % 8.00/2.43 | (203) op2(all_0_5_5, e24) = all_0_8_8 % 8.00/2.43 | % 8.00/2.43 | From (202) and (81) follows: % 8.00/2.43 | (204) op2(e24, all_0_5_5) = all_0_6_6 % 8.00/2.43 | % 8.00/2.43 | From (202)(202) and (20) follows: % 8.00/2.43 | (205) op2(e24, e24) = all_0_5_5 % 8.00/2.43 | % 8.00/2.43 | From (202) and (5) follows: % 8.00/2.43 | (206) op2(e24, all_0_8_8) = all_0_9_9 % 8.00/2.43 | % 8.00/2.43 | From (202)(202) and (77) follows: % 8.00/2.43 | (207) op2(e24, all_0_9_9) = e24 % 8.00/2.43 | % 8.00/2.43 | From (202) and (147) follows: % 8.00/2.43 | (208) op2(all_0_8_8, all_0_5_5) = e24 % 8.00/2.43 | % 8.00/2.43 | From (202) and (29) follows: % 8.00/2.43 | (209) op2(all_0_8_8, e24) = all_0_6_6 % 8.00/2.43 | % 8.00/2.43 | Instantiating formula (37) with e24, e24, all_0_5_5, e21 and discharging atoms op2(e24, e24) = all_0_5_5, op2(e24, e24) = e21, yields: % 8.00/2.43 | (210) all_0_5_5 = e21 % 8.00/2.43 | % 8.00/2.43 | From (210)(210) and (167) follows: % 8.00/2.43 | (211) op2(e21, e21) = all_0_9_9 % 8.00/2.43 | % 8.00/2.43 | From (210) and (203) follows: % 8.00/2.43 | (212) op2(e21, e24) = all_0_8_8 % 8.00/2.43 | % 8.00/2.43 | From (210) and (208) follows: % 8.00/2.43 | (213) op2(all_0_8_8, e21) = e24 % 8.00/2.43 | % 8.00/2.43 | From (210) and (204) follows: % 8.00/2.43 | (214) op2(e24, e21) = all_0_6_6 % 8.00/2.43 | % 8.00/2.43 | Instantiating formula (37) with e24, e21, all_0_6_6, e23 and discharging atoms op2(e24, e21) = all_0_6_6, op2(e24, e21) = e23, yields: % 8.00/2.43 | (215) all_0_6_6 = e23 % 8.00/2.43 | % 8.00/2.43 | Instantiating formula (37) with e21, e24, all_0_8_8, e20 and discharging atoms op2(e21, e24) = all_0_8_8, op2(e21, e24) = e20, yields: % 8.00/2.43 | (216) all_0_8_8 = e20 % 8.00/2.43 | % 8.00/2.43 | Instantiating formula (37) with e21, e21, all_0_9_9, e22 and discharging atoms op2(e21, e21) = all_0_9_9, op2(e21, e21) = e22, yields: % 8.00/2.43 | (217) all_0_9_9 = e22 % 8.00/2.43 | % 8.00/2.43 | From (216)(215) and (209) follows: % 8.00/2.43 | (218) op2(e20, e24) = e23 % 8.00/2.43 | % 8.00/2.43 | From (216) and (213) follows: % 8.00/2.43 | (219) op2(e20, e21) = e24 % 8.00/2.43 | % 8.00/2.43 | From (216)(217) and (206) follows: % 8.00/2.43 | (220) op2(e24, e20) = e22 % 8.00/2.43 | % 8.00/2.43 | From (217) and (207) follows: % 8.00/2.43 | (221) op2(e24, e22) = e24 % 8.00/2.43 | % 8.00/2.43 | Instantiating formula (37) with e24, e22, e24, e20 and discharging atoms op2(e24, e22) = e24, op2(e24, e22) = e20, yields: % 8.00/2.43 | (222) e24 = e20 % 8.00/2.43 | % 8.00/2.43 | Instantiating formula (37) with e24, e20, e22, e24 and discharging atoms op2(e24, e20) = e24, op2(e24, e20) = e22, yields: % 8.00/2.43 | (223) e24 = e22 % 8.00/2.43 | % 8.00/2.43 | Instantiating formula (37) with e20, e24, e23, e24 and discharging atoms op2(e20, e24) = e24, op2(e20, e24) = e23, yields: % 8.00/2.43 | (224) e24 = e23 % 8.00/2.43 | % 8.00/2.43 | Instantiating formula (37) with e20, e21, e24, e21 and discharging atoms op2(e20, e21) = e24, op2(e20, e21) = e21, yields: % 8.00/2.43 | (198) e24 = e21 % 8.00/2.43 | % 8.00/2.43 | Combining equations (198,224) yields a new equation: % 8.00/2.43 | (226) e23 = e21 % 8.00/2.43 | % 8.00/2.43 | Combining equations (223,224) yields a new equation: % 8.00/2.43 | (227) e23 = e22 % 8.00/2.43 | % 8.00/2.43 | Combining equations (222,224) yields a new equation: % 8.00/2.43 | (228) e23 = e20 % 8.00/2.43 | % 8.00/2.43 | Combining equations (228,227) yields a new equation: % 8.00/2.43 | (229) e22 = e20 % 8.00/2.43 | % 8.00/2.43 | Combining equations (226,227) yields a new equation: % 8.00/2.43 | (230) e22 = e21 % 8.00/2.43 | % 8.00/2.43 | Combining equations (230,229) yields a new equation: % 8.00/2.43 | (231) e20 = e21 % 8.00/2.43 | % 8.00/2.43 | Equations (231) can reduce 6 to: % 8.00/2.43 | (193) $false % 8.00/2.43 | % 8.00/2.43 |-The branch is then unsatisfiable % 8.00/2.43 |-Branch two: % 8.00/2.43 | (233) ~ (all_0_7_7 = e24) % 8.00/2.44 | (234) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21 % 8.00/2.44 | % 8.00/2.44 +-Applying beta-rule and splitting (75), into two cases. % 8.00/2.44 |-Branch one: % 8.00/2.44 | (235) all_0_2_2 = e14 % 8.00/2.44 | % 8.00/2.44 | From (235)(235) and (57) follows: % 8.00/2.44 | (182) op1(e14, e14) = all_0_3_3 % 8.00/2.44 | % 8.00/2.44 | From (235) and (56) follows: % 8.00/2.44 | (237) op1(all_0_3_3, all_0_3_3) = e14 % 8.00/2.44 | % 8.00/2.44 | Instantiating formula (96) with e14, e14, all_0_3_3, e10 and discharging atoms op1(e14, e14) = all_0_3_3, op1(e14, e14) = e10, yields: % 8.00/2.44 | (184) all_0_3_3 = e10 % 8.00/2.44 | % 8.00/2.44 | From (184)(184) and (237) follows: % 8.00/2.44 | (190) op1(e10, e10) = e14 % 8.00/2.44 | % 8.00/2.44 | Instantiating formula (96) with e10, e10, e14, e10 and discharging atoms op1(e10, e10) = e14, op1(e10, e10) = e10, yields: % 8.00/2.44 | (192) e14 = e10 % 8.00/2.44 | % 8.00/2.44 | Equations (192) can reduce 58 to: % 8.00/2.44 | (193) $false % 8.00/2.44 | % 8.00/2.44 |-The branch is then unsatisfiable % 8.00/2.44 |-Branch two: % 8.00/2.44 | (242) ~ (all_0_2_2 = e14) % 8.00/2.44 | (243) all_0_2_2 = e13 | all_0_2_2 = e12 | all_0_2_2 = e10 | all_0_2_2 = e11 % 8.00/2.44 | % 8.00/2.44 +-Applying beta-rule and splitting (110), into two cases. % 8.00/2.44 |-Branch one: % 8.00/2.44 | (244) all_0_6_6 = e24 % 8.00/2.44 | % 8.00/2.44 | From (244) and (137) follows: % 8.00/2.44 | (245) op2(all_0_5_5, e24) = all_0_7_7 % 8.00/2.44 | % 8.00/2.44 | From (244) and (174) follows: % 8.00/2.44 | (246) op2(e24, all_0_5_5) = all_0_8_8 % 8.00/2.44 | % 8.00/2.44 | From (244)(244) and (101) follows: % 8.00/2.44 | (205) op2(e24, e24) = all_0_5_5 % 8.00/2.44 | % 8.00/2.44 | From (244) and (12) follows: % 8.00/2.44 | (248) op2(e24, all_0_7_7) = all_0_9_9 % 8.00/2.44 | % 8.00/2.44 | From (244)(244) and (28) follows: % 8.00/2.44 | (207) op2(e24, all_0_9_9) = e24 % 8.00/2.44 | % 8.00/2.44 | From (244) and (81) follows: % 8.00/2.44 | (250) op2(all_0_7_7, all_0_5_5) = e24 % 8.00/2.44 | % 8.00/2.44 | From (244) and (111) follows: % 8.00/2.44 | (251) op2(all_0_7_7, e24) = all_0_8_8 % 8.00/2.44 | % 8.00/2.44 | Instantiating formula (37) with e24, e24, all_0_5_5, e21 and discharging atoms op2(e24, e24) = all_0_5_5, op2(e24, e24) = e21, yields: % 8.00/2.44 | (210) all_0_5_5 = e21 % 8.00/2.44 | % 8.00/2.44 | From (210)(210) and (167) follows: % 8.00/2.44 | (211) op2(e21, e21) = all_0_9_9 % 8.00/2.44 | % 8.00/2.44 | From (210) and (245) follows: % 8.00/2.44 | (254) op2(e21, e24) = all_0_7_7 % 8.00/2.44 | % 8.00/2.44 | From (210) and (250) follows: % 8.00/2.44 | (255) op2(all_0_7_7, e21) = e24 % 8.00/2.44 | % 8.00/2.44 | From (210) and (246) follows: % 8.00/2.44 | (256) op2(e24, e21) = all_0_8_8 % 8.00/2.44 | % 8.00/2.44 | Instantiating formula (37) with e24, e21, all_0_8_8, e23 and discharging atoms op2(e24, e21) = all_0_8_8, op2(e24, e21) = e23, yields: % 8.00/2.44 | (257) all_0_8_8 = e23 % 8.00/2.44 | % 8.00/2.44 | Instantiating formula (37) with e21, e24, all_0_7_7, e20 and discharging atoms op2(e21, e24) = all_0_7_7, op2(e21, e24) = e20, yields: % 8.00/2.44 | (258) all_0_7_7 = e20 % 8.00/2.44 | % 8.00/2.44 | Instantiating formula (37) with e21, e21, all_0_9_9, e22 and discharging atoms op2(e21, e21) = all_0_9_9, op2(e21, e21) = e22, yields: % 8.00/2.44 | (217) all_0_9_9 = e22 % 8.00/2.44 | % 8.00/2.44 | From (258)(257) and (251) follows: % 8.00/2.44 | (218) op2(e20, e24) = e23 % 8.00/2.44 | % 8.00/2.44 | From (258) and (255) follows: % 8.00/2.44 | (219) op2(e20, e21) = e24 % 8.00/2.44 | % 8.00/2.44 | From (258)(217) and (248) follows: % 8.00/2.44 | (220) op2(e24, e20) = e22 % 8.00/2.44 | % 8.00/2.44 | From (217) and (207) follows: % 8.00/2.44 | (221) op2(e24, e22) = e24 % 8.00/2.44 | % 8.00/2.44 | Instantiating formula (37) with e24, e22, e24, e20 and discharging atoms op2(e24, e22) = e24, op2(e24, e22) = e20, yields: % 8.00/2.44 | (222) e24 = e20 % 8.00/2.44 | % 8.00/2.44 | Instantiating formula (37) with e24, e20, e22, e24 and discharging atoms op2(e24, e20) = e24, op2(e24, e20) = e22, yields: % 8.00/2.44 | (223) e24 = e22 % 8.00/2.44 | % 8.00/2.44 | Instantiating formula (37) with e20, e24, e23, e24 and discharging atoms op2(e20, e24) = e24, op2(e20, e24) = e23, yields: % 8.00/2.44 | (224) e24 = e23 % 8.00/2.44 | % 8.00/2.44 | Instantiating formula (37) with e20, e21, e24, e21 and discharging atoms op2(e20, e21) = e24, op2(e20, e21) = e21, yields: % 8.00/2.44 | (198) e24 = e21 % 8.00/2.44 | % 8.00/2.44 | Combining equations (198,224) yields a new equation: % 8.00/2.44 | (226) e23 = e21 % 8.00/2.44 | % 8.00/2.44 | Combining equations (223,224) yields a new equation: % 8.00/2.44 | (227) e23 = e22 % 8.00/2.44 | % 8.00/2.44 | Combining equations (222,224) yields a new equation: % 8.00/2.44 | (228) e23 = e20 % 8.00/2.44 | % 8.00/2.44 | Combining equations (228,227) yields a new equation: % 8.00/2.44 | (229) e22 = e20 % 8.00/2.44 | % 8.00/2.44 | Combining equations (226,227) yields a new equation: % 8.00/2.44 | (230) e22 = e21 % 8.00/2.44 | % 8.00/2.44 | Combining equations (230,229) yields a new equation: % 8.00/2.44 | (231) e20 = e21 % 8.00/2.44 | % 8.00/2.44 | Equations (231) can reduce 6 to: % 8.00/2.44 | (193) $false % 8.00/2.44 | % 8.00/2.44 |-The branch is then unsatisfiable % 8.00/2.44 |-Branch two: % 8.00/2.44 | (275) ~ (all_0_6_6 = e24) % 8.00/2.44 | (276) all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21 % 8.00/2.44 | % 8.00/2.44 +-Applying beta-rule and splitting (172), into two cases. % 8.00/2.44 |-Branch one: % 8.00/2.44 | (277) all_0_3_3 = e14 % 8.00/2.44 | % 8.00/2.44 | From (277) and (57) follows: % 8.00/2.44 | (278) op1(all_0_2_2, all_0_2_2) = e14 % 8.00/2.44 | % 8.00/2.44 | From (277)(277) and (56) follows: % 8.00/2.44 | (279) op1(e14, e14) = all_0_2_2 % 8.00/2.44 | % 8.00/2.44 | Instantiating formula (96) with e14, e14, all_0_2_2, e10 and discharging atoms op1(e14, e14) = all_0_2_2, op1(e14, e14) = e10, yields: % 8.00/2.44 | (189) all_0_2_2 = e10 % 8.00/2.44 | % 8.00/2.44 | Equations (189) can reduce 242 to: % 8.00/2.44 | (281) ~ (e14 = e10) % 8.00/2.44 | % 8.00/2.44 | Simplifying 281 yields: % 8.00/2.44 | (58) ~ (e14 = e10) % 8.00/2.44 | % 8.00/2.44 | From (189)(189) and (278) follows: % 8.00/2.44 | (190) op1(e10, e10) = e14 % 8.00/2.44 | % 8.00/2.44 | Instantiating formula (96) with e10, e10, e14, e10 and discharging atoms op1(e10, e10) = e14, op1(e10, e10) = e10, yields: % 8.00/2.44 | (192) e14 = e10 % 8.00/2.44 | % 8.00/2.44 | Equations (192) can reduce 58 to: % 8.00/2.44 | (193) $false % 8.00/2.44 | % 8.00/2.44 |-The branch is then unsatisfiable % 8.00/2.44 |-Branch two: % 8.00/2.44 | (286) ~ (all_0_3_3 = e14) % 8.00/2.44 | (287) all_0_3_3 = e13 | all_0_3_3 = e12 | all_0_3_3 = e10 | all_0_3_3 = e11 % 8.00/2.44 | % 8.00/2.44 +-Applying beta-rule and splitting (124), into two cases. % 8.00/2.44 |-Branch one: % 8.00/2.44 | (288) all_0_8_8 = e24 % 8.00/2.44 | % 8.00/2.44 | From (288)(288) and (91) follows: % 8.00/2.44 | (205) op2(e24, e24) = all_0_5_5 % 8.00/2.45 | % 8.00/2.45 | Instantiating formula (37) with e24, e24, all_0_5_5, e21 and discharging atoms op2(e24, e24) = all_0_5_5, op2(e24, e24) = e21, yields: % 8.00/2.45 | (210) all_0_5_5 = e21 % 8.00/2.45 | % 8.00/2.45 | From (210) and (146) follows: % 8.00/2.45 | (291) j(e21) = e14 % 8.00/2.45 | % 8.00/2.45 | Instantiating formula (94) with e21, e14, all_0_3_3 and discharging atoms j(e21) = all_0_3_3, j(e21) = e14, yields: % 8.00/2.45 | (277) all_0_3_3 = e14 % 8.00/2.45 | % 8.00/2.45 | Equations (277) can reduce 286 to: % 8.00/2.45 | (193) $false % 8.00/2.45 | % 8.00/2.45 |-The branch is then unsatisfiable % 8.00/2.45 |-Branch two: % 8.00/2.45 | (294) ~ (all_0_8_8 = e24) % 8.00/2.45 | (295) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21 % 8.00/2.45 | % 8.00/2.45 +-Applying beta-rule and splitting (195), into two cases. % 8.00/2.45 |-Branch one: % 8.00/2.45 | (296) all_0_0_0 = e13 % 8.00/2.45 | % 8.00/2.45 | From (296) and (14) follows: % 8.00/2.45 | (297) h(e13) = e24 % 8.00/2.45 | % 8.00/2.45 | Instantiating formula (92) with e13, e24, all_0_6_6 and discharging atoms h(e13) = all_0_6_6, h(e13) = e24, yields: % 8.00/2.45 | (244) all_0_6_6 = e24 % 8.00/2.45 | % 8.00/2.45 | Equations (244) can reduce 275 to: % 8.00/2.45 | (193) $false % 8.00/2.45 | % 8.00/2.45 |-The branch is then unsatisfiable % 8.00/2.45 |-Branch two: % 8.00/2.45 | (300) ~ (all_0_0_0 = e13) % 8.00/2.45 | (301) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11 % 8.00/2.45 | % 8.00/2.45 +-Applying beta-rule and splitting (301), into two cases. % 8.00/2.45 |-Branch one: % 8.00/2.45 | (302) all_0_0_0 = e12 % 8.00/2.45 | % 8.00/2.45 | From (302) and (14) follows: % 8.00/2.45 | (303) h(e12) = e24 % 8.00/2.45 | % 8.00/2.45 | Instantiating formula (92) with e12, e24, all_0_7_7 and discharging atoms h(e12) = all_0_7_7, h(e12) = e24, yields: % 8.00/2.45 | (202) all_0_7_7 = e24 % 8.00/2.45 | % 8.00/2.45 | Equations (202) can reduce 233 to: % 8.00/2.45 | (193) $false % 8.00/2.45 | % 8.00/2.45 |-The branch is then unsatisfiable % 8.00/2.45 |-Branch two: % 8.00/2.45 | (306) ~ (all_0_0_0 = e12) % 8.00/2.45 | (307) all_0_0_0 = e10 | all_0_0_0 = e11 % 8.00/2.45 | % 8.00/2.45 +-Applying beta-rule and splitting (307), into two cases. % 8.00/2.45 |-Branch one: % 8.00/2.45 | (308) all_0_0_0 = e10 % 8.00/2.45 | % 8.00/2.45 | From (308) and (14) follows: % 8.00/2.45 | (309) h(e10) = e24 % 8.00/2.45 | % 8.00/2.45 | Instantiating formula (92) with e10, e24, all_0_9_9 and discharging atoms h(e10) = all_0_9_9, h(e10) = e24, yields: % 8.00/2.45 | (196) all_0_9_9 = e24 % 8.00/2.45 | % 8.00/2.45 | Equations (196) can reduce 200 to: % 8.00/2.45 | (193) $false % 8.00/2.45 | % 8.00/2.45 |-The branch is then unsatisfiable % 8.00/2.45 |-Branch two: % 8.00/2.45 | (312) ~ (all_0_0_0 = e10) % 8.00/2.45 | (313) all_0_0_0 = e11 % 8.00/2.45 | % 8.00/2.45 | From (313) and (14) follows: % 8.00/2.45 | (314) h(e11) = e24 % 8.00/2.45 | % 8.00/2.45 | Instantiating formula (92) with e11, e24, all_0_8_8 and discharging atoms h(e11) = all_0_8_8, h(e11) = e24, yields: % 8.00/2.45 | (288) all_0_8_8 = e24 % 8.00/2.45 | % 8.00/2.45 | Equations (288) can reduce 294 to: % 8.00/2.45 | (193) $false % 8.00/2.45 | % 8.00/2.45 |-The branch is then unsatisfiable % 8.00/2.45 % SZS output end Proof for theBenchmark % 8.00/2.45 % 8.00/2.45 1836ms %------------------------------------------------------------------------------