%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : ALG083+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n017.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 15:34:16 EDT 2022 % Result : Theorem 4.22s 1.53s % Output : Proof 7.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : ALG083+1 : TPTP v8.1.0. Released v2.7.0. % 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n017.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Wed Jun 8 08:42:18 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.57 ____ _ % 0.18/0.57 ___ / __ \_____(_)___ ________ __________ % 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.57 % 0.18/0.57 A Theorem Prover for First-Order Logic % 0.18/0.57 (ePrincess v.1.0) % 0.18/0.57 % 0.18/0.57 (c) Philipp Rümmer, 2009-2015 % 0.18/0.57 (c) Peter Backeman, 2014-2015 % 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.57 Bug reports to peter@backeman.se % 0.18/0.57 % 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.57 % 0.18/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.78/0.99 Prover 0: Preprocessing ... % 2.85/1.26 Prover 0: Constructing countermodel ... % 4.22/1.53 Prover 0: proved (907ms) % 4.22/1.53 % 4.22/1.53 No countermodel exists, formula is valid % 4.22/1.53 % SZS status Theorem for theBenchmark % 4.22/1.53 % 4.22/1.53 Generating proof ... found it (size 86) % 7.30/2.24 % 7.30/2.24 % SZS output start Proof for theBenchmark % 7.30/2.24 Assumed formulas after preprocessing and simplification: % 7.30/2.24 | (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) = v2 & op2(v4, v3) = v0 & op2(v4, v2) = v1 & op2(v4, v1) = v3 & op2(v4, v0) = v4 & op2(v3, v4) = v0 & op2(v3, v3) = v1 & op2(v3, v2) = v4 & op2(v3, v1) = v2 & op2(v3, v0) = v3 & op2(v2, v4) = v1 & op2(v2, v3) = v4 & op2(v2, v2) = v3 & op2(v2, v1) = v0 & op2(v2, v0) = v2 & op2(v1, v4) = v3 & op2(v1, v3) = v2 & op2(v1, v2) = v0 & 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) = e22 & op2(e24, e23) = e21 & op2(e24, e22) = e20 & op2(e24, e20) = e24 & op2(e24, e21) = e23 & op2(e23, e24) = e20 & op2(e23, e23) = e24 & op2(e23, e22) = e21 & op2(e23, e20) = e23 & op2(e23, e21) = e22 & op2(e22, e24) = e21 & op2(e22, e23) = e20 & op2(e22, e22) = e23 & 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) = e23 & op2(e21, e23) = e22 & op2(e21, e22) = e24 & op2(e21, e20) = e21 & op2(e21, e21) = e20 & op1(v9, v9) = v7 & op1(v9, v8) = v6 & op1(v9, v7) = v5 & op1(v9, v6) = v8 & op1(v9, v5) = v9 & op1(v8, v9) = v5 & op1(v8, v8) = v9 & op1(v8, v7) = v6 & op1(v8, v6) = v7 & op1(v8, v5) = v8 & op1(v7, v9) = v6 & op1(v7, v8) = v5 & op1(v7, v7) = v8 & op1(v7, v6) = v9 & op1(v7, v5) = v7 & op1(v6, v9) = v8 & op1(v6, v8) = v7 & op1(v6, v7) = v9 & op1(v6, v6) = v5 & 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) = e12 & op1(e14, e13) = e10 & op1(e14, e12) = e11 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e14) = e10 & op1(e13, e13) = e11 & op1(e13, e12) = e14 & op1(e13, e10) = e13 & op1(e13, e11) = e12 & op1(e12, e14) = e11 & op1(e12, e13) = e14 & op1(e12, e12) = e13 & 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) = e13 & op1(e11, e13) = e12 & op1(e11, e12) = e10 & 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)) % 7.30/2.29 | 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: % 7.30/2.29 | (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_7_7 & op2(all_0_5_5, all_0_6_6) = all_0_9_9 & 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_9_9 & op2(all_0_6_6, all_0_6_6) = all_0_8_8 & op2(all_0_6_6, all_0_7_7) = all_0_5_5 & 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_8_8 & op2(all_0_7_7, all_0_6_6) = all_0_5_5 & op2(all_0_7_7, all_0_7_7) = all_0_6_6 & 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_6_6 & op2(all_0_8_8, all_0_6_6) = all_0_7_7 & op2(all_0_8_8, all_0_7_7) = all_0_9_9 & 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) = e22 & op2(e24, e23) = e21 & op2(e24, e22) = e20 & op2(e24, e20) = e24 & op2(e24, e21) = e23 & op2(e23, e24) = e20 & op2(e23, e23) = e24 & op2(e23, e22) = e21 & op2(e23, e20) = e23 & op2(e23, e21) = e22 & op2(e22, e24) = e21 & op2(e22, e23) = e20 & op2(e22, e22) = e23 & 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) = e23 & op2(e21, e23) = e22 & op2(e21, e22) = e24 & op2(e21, e20) = e21 & op2(e21, e21) = e20 & op1(all_0_0_0, all_0_0_0) = all_0_2_2 & op1(all_0_0_0, all_0_1_1) = all_0_3_3 & 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_4_4 & op1(all_0_1_1, all_0_1_1) = all_0_0_0 & op1(all_0_1_1, all_0_2_2) = all_0_3_3 & op1(all_0_1_1, all_0_3_3) = all_0_2_2 & op1(all_0_1_1, all_0_4_4) = all_0_1_1 & op1(all_0_2_2, all_0_0_0) = all_0_3_3 & op1(all_0_2_2, all_0_1_1) = all_0_4_4 & op1(all_0_2_2, all_0_2_2) = all_0_1_1 & 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_1_1 & op1(all_0_3_3, all_0_1_1) = all_0_2_2 & op1(all_0_3_3, all_0_2_2) = all_0_0_0 & op1(all_0_3_3, all_0_3_3) = all_0_4_4 & 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) = e12 & op1(e14, e13) = e10 & op1(e14, e12) = e11 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e14) = e10 & op1(e13, e13) = e11 & op1(e13, e12) = e14 & op1(e13, e10) = e13 & op1(e13, e11) = e12 & op1(e12, e14) = e11 & op1(e12, e13) = e14 & op1(e12, e12) = e13 & 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) = e13 & op1(e11, e13) = e12 & op1(e11, e12) = e10 & 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) % 7.73/2.31 | % 7.73/2.31 | Applying alpha-rule on (1) yields: % 7.73/2.31 | (2) ~ (e21 = e12) % 7.73/2.31 | (3) op1(all_0_4_4, all_0_1_1) = all_0_1_1 % 7.73/2.31 | (4) op2(all_0_7_7, all_0_8_8) = all_0_9_9 % 7.73/2.31 | (5) op1(e13, e12) = e14 % 7.73/2.31 | (6) ~ (e20 = e21) % 7.73/2.31 | (7) ~ (e20 = e14) % 7.73/2.31 | (8) op1(all_0_2_2, all_0_2_2) = all_0_1_1 % 7.73/2.31 | (9) op1(e12, e12) = e13 % 7.73/2.31 | (10) op2(e20, e23) = e23 % 7.73/2.31 | (11) op1(all_0_4_4, all_0_2_2) = all_0_2_2 % 7.73/2.31 | (12) ~ (e24 = e11) % 7.73/2.31 | (13) ~ (e12 = e11) % 7.73/2.31 | (14) h(e12) = all_0_7_7 % 7.73/2.31 | (15) h(all_0_0_0) = e24 % 7.73/2.31 | (16) h(e13) = all_0_6_6 % 7.73/2.31 | (17) op2(e24, e24) = e22 % 7.73/2.31 | (18) op2(all_0_5_5, all_0_8_8) = all_0_6_6 % 7.73/2.31 | (19) ~ (e14 = e12) % 7.73/2.31 | (20) op2(e23, e21) = e22 % 7.73/2.31 | (21) ~ (e24 = e12) % 7.73/2.31 | (22) op1(all_0_1_1, all_0_0_0) = all_0_4_4 % 7.73/2.31 | (23) op1(e10, e11) = e11 % 7.73/2.31 | (24) j(e22) = all_0_2_2 % 7.73/2.31 | (25) op2(all_0_9_9, all_0_8_8) = all_0_8_8 % 7.73/2.31 | (26) j(e21) = all_0_3_3 % 7.73/2.31 | (27) op1(all_0_1_1, all_0_2_2) = all_0_3_3 % 7.73/2.31 | (28) j(all_0_8_8) = e11 % 7.73/2.31 | (29) ~ (e22 = e13) % 7.73/2.31 | (30) op2(all_0_6_6, all_0_9_9) = all_0_6_6 % 7.73/2.31 | (31) op2(all_0_8_8, all_0_6_6) = all_0_7_7 % 7.73/2.32 | (32) op1(e12, e14) = e11 % 7.73/2.32 | (33) op2(e24, e21) = e23 % 7.73/2.32 | (34) op1(all_0_3_3, all_0_4_4) = all_0_3_3 % 7.73/2.32 | (35) j(all_0_6_6) = e13 % 7.73/2.32 | (36) op2(all_0_5_5, all_0_7_7) = all_0_8_8 % 7.73/2.32 | (37) h(all_0_4_4) = e20 % 7.73/2.32 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) % 7.73/2.32 | (39) op1(all_0_3_3, all_0_2_2) = all_0_0_0 % 7.73/2.32 | (40) op2(all_0_5_5, all_0_5_5) = all_0_7_7 % 7.73/2.32 | (41) op1(e14, e14) = e12 % 7.73/2.32 | (42) op2(e23, e23) = e24 % 7.73/2.32 | (43) ~ (e23 = e13) % 7.73/2.32 | (44) op1(all_0_0_0, all_0_4_4) = all_0_0_0 % 7.73/2.32 | (45) op2(all_0_9_9, all_0_6_6) = all_0_6_6 % 7.73/2.32 | (46) op2(e24, e22) = e20 % 7.73/2.32 | (47) op2(e22, e20) = e22 % 7.73/2.32 | (48) 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 % 7.73/2.32 | (49) op2(e23, e22) = e21 % 7.73/2.32 | (50) ~ (e23 = e12) % 7.73/2.32 | (51) op1(e11, e10) = e11 % 7.73/2.32 | (52) op2(e21, e24) = e23 % 7.73/2.32 | (53) ~ (e24 = e14) % 7.73/2.32 | (54) h(all_0_3_3) = e21 % 7.73/2.32 | (55) ~ (e23 = e21) % 7.73/2.32 | (56) op1(e13, e11) = e12 % 7.73/2.32 | (57) 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 % 7.73/2.32 | (58) ~ (e22 = e21) % 7.73/2.32 | (59) ~ (e20 = e11) % 7.73/2.32 | (60) j(all_0_9_9) = e10 % 7.73/2.32 | (61) op1(all_0_0_0, all_0_0_0) = all_0_2_2 % 7.73/2.32 | (62) ~ (e14 = e10) % 7.73/2.32 | (63) ~ (e22 = e10) % 7.73/2.32 | (64) op1(e14, e12) = e11 % 7.73/2.32 | (65) h(all_0_1_1) = e23 % 7.73/2.32 | (66) op2(all_0_9_9, all_0_9_9) = all_0_9_9 % 7.73/2.32 | (67) op2(all_0_9_9, all_0_7_7) = all_0_7_7 % 7.73/2.32 | (68) op1(e12, e10) = e12 % 7.73/2.32 | (69) ~ (e12 = e10) % 7.73/2.32 | (70) ~ (e24 = e22) % 7.73/2.32 | (71) op1(all_0_1_1, all_0_4_4) = all_0_1_1 % 7.73/2.32 | (72) 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 % 7.73/2.32 | (73) op2(e20, e24) = e24 % 7.73/2.32 | (74) op2(e22, e21) = e24 % 7.73/2.32 | (75) op2(e20, e20) = e20 % 7.73/2.32 | (76) 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 % 7.73/2.32 | (77) op2(all_0_6_6, all_0_5_5) = all_0_9_9 % 7.73/2.33 | (78) op2(all_0_7_7, all_0_9_9) = all_0_7_7 % 7.73/2.33 | (79) j(all_0_7_7) = e12 % 7.73/2.33 | (80) op2(all_0_8_8, all_0_5_5) = all_0_6_6 % 7.73/2.33 | (81) op2(all_0_5_5, all_0_9_9) = all_0_5_5 % 7.73/2.33 | (82) h(all_0_2_2) = e22 % 7.73/2.33 | (83) op1(e12, e13) = e14 % 7.73/2.33 | (84) ~ (e14 = e13) % 7.73/2.33 | (85) ~ (e21 = e11) % 7.73/2.33 | (86) h(e14) = all_0_5_5 % 7.73/2.33 | (87) ~ (e24 = e20) % 7.73/2.33 | (88) ~ (e13 = e12) % 7.73/2.33 | (89) op2(all_0_6_6, all_0_7_7) = all_0_5_5 % 7.73/2.33 | (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 % 7.73/2.33 | (91) op2(all_0_8_8, all_0_8_8) = all_0_5_5 % 7.73/2.33 | (92) op1(e11, e12) = e10 % 7.73/2.33 | (93) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) % 7.73/2.33 | (94) ~ (e14 = e11) % 7.73/2.33 | (95) op2(e22, e24) = e21 % 7.73/2.33 | (96) op2(e21, e21) = e20 % 7.73/2.33 | (97) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) % 7.73/2.33 | (98) op1(all_0_2_2, all_0_4_4) = all_0_2_2 % 7.73/2.33 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) % 7.73/2.33 | (100) 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 % 7.73/2.33 | (101) op2(all_0_6_6, all_0_8_8) = all_0_7_7 % 7.73/2.33 | (102) op1(e13, e10) = e13 % 7.73/2.33 | (103) op1(e10, e10) = e10 % 7.73/2.33 | (104) op1(all_0_0_0, all_0_3_3) = all_0_1_1 % 7.73/2.33 | (105) ~ (e23 = e10) % 7.73/2.33 | (106) op1(all_0_4_4, all_0_4_4) = all_0_4_4 % 7.73/2.33 | (107) ~ (e13 = e10) % 7.73/2.33 | (108) op1(e10, e12) = e12 % 7.73/2.33 | (109) 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 % 7.73/2.33 | (110) 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 % 7.73/2.33 | (111) ~ (e23 = e22) % 7.73/2.33 | (112) op2(all_0_5_5, all_0_6_6) = all_0_9_9 % 7.73/2.33 | (113) ~ (e20 = e10) % 7.73/2.33 | (114) ~ (e22 = e11) % 7.73/2.33 | (115) op2(e22, e23) = e20 % 7.73/2.33 | (116) op1(e13, e14) = e10 % 7.73/2.33 | (117) op2(e22, e22) = e23 % 7.73/2.34 | (118) ~ (e20 = e12) % 7.73/2.34 | (119) op2(all_0_7_7, all_0_5_5) = all_0_8_8 % 7.73/2.34 | (120) op1(all_0_0_0, all_0_2_2) = all_0_4_4 % 7.73/2.34 | (121) op1(all_0_3_3, all_0_0_0) = all_0_1_1 % 7.73/2.34 | (122) op1(e14, e11) = e13 % 7.73/2.34 | (123) op2(e24, e20) = e24 % 7.73/2.34 | (124) op1(all_0_4_4, all_0_0_0) = all_0_0_0 % 7.73/2.34 | (125) 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 % 7.73/2.34 | (126) ~ (e10 = e11) % 7.73/2.34 | (127) op1(all_0_2_2, all_0_0_0) = all_0_3_3 % 7.73/2.34 | (128) ~ (e23 = e14) % 7.73/2.34 | (129) h(e11) = all_0_8_8 % 7.73/2.34 | (130) op1(e10, e13) = e13 % 7.73/2.34 | (131) op2(e23, e24) = e20 % 7.73/2.34 | (132) op1(e14, e10) = e14 % 7.73/2.34 | (133) j(e23) = all_0_1_1 % 7.73/2.34 | (134) ~ (e23 = e20) % 7.73/2.34 | (135) op2(e21, e20) = e21 % 7.73/2.34 | (136) ~ (e21 = e14) % 7.73/2.34 | (137) j(e24) = all_0_0_0 % 7.73/2.34 | (138) op2(all_0_7_7, all_0_6_6) = all_0_5_5 % 7.73/2.34 | (139) op1(e12, e11) = e10 % 7.73/2.34 | (140) op1(e10, e14) = e14 % 7.73/2.34 | (141) op1(all_0_2_2, all_0_1_1) = all_0_4_4 % 7.73/2.34 | (142) ~ (e24 = e21) % 7.73/2.34 | (143) op1(e11, e14) = e13 % 7.73/2.34 | (144) op2(all_0_8_8, all_0_9_9) = all_0_8_8 % 7.73/2.34 | (145) j(all_0_5_5) = e14 % 7.73/2.34 | (146) op2(e23, e20) = e23 % 7.73/2.34 | (147) ~ (e22 = e20) % 7.73/2.34 | (148) ~ (e23 = e11) % 7.73/2.34 | (149) op2(all_0_6_6, all_0_6_6) = all_0_8_8 % 7.73/2.34 | (150) op2(e21, e23) = e22 % 7.73/2.34 | (151) op1(all_0_1_1, all_0_3_3) = all_0_2_2 % 7.73/2.34 | (152) op1(all_0_3_3, all_0_1_1) = all_0_2_2 % 7.73/2.34 | (153) op2(all_0_7_7, all_0_7_7) = all_0_6_6 % 7.73/2.34 | (154) op1(e11, e11) = e14 % 7.73/2.34 | (155) op2(all_0_8_8, all_0_7_7) = all_0_9_9 % 7.73/2.34 | (156) op1(all_0_1_1, all_0_1_1) = all_0_0_0 % 7.73/2.34 | (157) op1(all_0_2_2, all_0_3_3) = all_0_0_0 % 7.73/2.34 | (158) ~ (e24 = e10) % 7.73/2.34 | (159) ~ (e24 = e23) % 7.73/2.34 | (160) op1(e11, e13) = e12 % 7.73/2.35 | (161) ~ (e20 = e13) % 7.73/2.35 | (162) ~ (e24 = e13) % 7.73/2.35 | (163) op1(all_0_4_4, all_0_3_3) = all_0_3_3 % 7.73/2.35 | (164) ~ (e21 = e10) % 7.73/2.35 | (165) ~ (e21 = e13) % 7.73/2.35 | (166) j(e20) = all_0_4_4 % 7.73/2.35 | (167) ~ (e22 = e12) % 7.73/2.35 | (168) op1(all_0_0_0, all_0_1_1) = all_0_3_3 % 7.73/2.35 | (169) op1(all_0_3_3, all_0_3_3) = all_0_4_4 % 7.73/2.35 | (170) op2(e20, e22) = e22 % 7.73/2.35 | (171) op1(e13, e13) = e11 % 7.73/2.35 | (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 % 7.73/2.35 | (173) op1(e14, e13) = e10 % 7.73/2.35 | (174) h(e10) = all_0_9_9 % 7.73/2.35 | (175) ~ (e22 = e14) % 7.73/2.35 | (176) op2(e24, e23) = e21 % 7.73/2.35 | (177) op2(e20, e21) = e21 % 7.73/2.35 | (178) op2(all_0_9_9, all_0_5_5) = all_0_5_5 % 7.73/2.35 | (179) op2(e21, e22) = e24 % 7.73/2.35 | (180) ~ (e13 = e11) % 7.73/2.35 | % 7.73/2.35 +-Applying beta-rule and splitting (110), into two cases. % 7.73/2.35 |-Branch one: % 7.73/2.35 | (181) all_0_0_0 = e14 % 7.73/2.35 | % 7.73/2.35 | From (181)(181) and (61) follows: % 7.73/2.35 | (182) op1(e14, e14) = all_0_2_2 % 7.73/2.35 | % 7.73/2.35 | From (181) and (120) follows: % 7.73/2.35 | (183) op1(e14, all_0_2_2) = all_0_4_4 % 7.73/2.35 | % 7.73/2.35 | From (181) and (127) follows: % 7.73/2.35 | (184) op1(all_0_2_2, e14) = all_0_3_3 % 7.73/2.35 | % 7.73/2.35 | From (181) and (39) follows: % 7.73/2.35 | (185) op1(all_0_3_3, all_0_2_2) = e14 % 7.73/2.35 | % 7.73/2.35 | Instantiating formula (99) with e14, e14, all_0_2_2, e12 and discharging atoms op1(e14, e14) = all_0_2_2, op1(e14, e14) = e12, yields: % 7.73/2.35 | (186) all_0_2_2 = e12 % 7.73/2.35 | % 7.73/2.35 | From (186) and (184) follows: % 7.73/2.35 | (187) op1(e12, e14) = all_0_3_3 % 7.73/2.35 | % 7.73/2.35 | From (186) and (185) follows: % 7.73/2.35 | (188) op1(all_0_3_3, e12) = e14 % 7.73/2.35 | % 7.73/2.35 | From (186)(186) and (11) follows: % 7.73/2.35 | (189) op1(all_0_4_4, e12) = e12 % 7.73/2.35 | % 7.73/2.35 | From (186) and (183) follows: % 7.73/2.35 | (190) op1(e14, e12) = all_0_4_4 % 7.73/2.35 | % 7.73/2.35 | Instantiating formula (99) with e14, e12, all_0_4_4, e11 and discharging atoms op1(e14, e12) = all_0_4_4, op1(e14, e12) = e11, yields: % 7.73/2.35 | (191) all_0_4_4 = e11 % 7.73/2.35 | % 7.73/2.35 | Instantiating formula (99) with e12, e14, all_0_3_3, e11 and discharging atoms op1(e12, e14) = all_0_3_3, op1(e12, e14) = e11, yields: % 7.73/2.35 | (192) all_0_3_3 = e11 % 7.73/2.35 | % 7.73/2.35 | From (192) and (188) follows: % 7.73/2.35 | (193) op1(e11, e12) = e14 % 7.73/2.35 | % 7.73/2.35 | From (191)(191)(191) and (106) follows: % 7.73/2.35 | (194) op1(e11, e11) = e11 % 7.73/2.35 | % 7.73/2.35 | From (191) and (189) follows: % 7.73/2.35 | (195) op1(e11, e12) = e12 % 7.73/2.35 | % 7.73/2.35 | Instantiating formula (99) with e11, e12, e14, e10 and discharging atoms op1(e11, e12) = e14, op1(e11, e12) = e10, yields: % 7.73/2.35 | (196) e14 = e10 % 7.73/2.35 | % 7.73/2.35 | Instantiating formula (99) with e11, e12, e12, e14 and discharging atoms op1(e11, e12) = e14, op1(e11, e12) = e12, yields: % 7.73/2.36 | (197) e14 = e12 % 7.73/2.36 | % 7.73/2.36 | Instantiating formula (99) with e11, e11, e11, e14 and discharging atoms op1(e11, e11) = e14, op1(e11, e11) = e11, yields: % 7.73/2.36 | (198) e14 = e11 % 7.73/2.36 | % 7.73/2.36 | Combining equations (196,197) yields a new equation: % 7.73/2.36 | (199) e12 = e10 % 7.73/2.36 | % 7.73/2.36 | Combining equations (198,197) yields a new equation: % 7.73/2.36 | (200) e12 = e11 % 7.73/2.36 | % 7.73/2.36 | Combining equations (199,200) yields a new equation: % 7.73/2.36 | (201) e10 = e11 % 7.73/2.36 | % 7.73/2.36 | Simplifying 201 yields: % 7.73/2.36 | (202) e10 = e11 % 7.73/2.36 | % 7.73/2.36 | Equations (202) can reduce 126 to: % 7.73/2.36 | (203) $false % 7.73/2.36 | % 7.73/2.36 |-The branch is then unsatisfiable % 7.73/2.36 |-Branch two: % 7.73/2.36 | (204) ~ (all_0_0_0 = e14) % 7.73/2.36 | (205) all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11 % 7.73/2.36 | % 7.73/2.36 +-Applying beta-rule and splitting (72), into two cases. % 7.73/2.36 |-Branch one: % 7.73/2.36 | (206) all_0_9_9 = e24 % 7.73/2.36 | % 7.73/2.36 | From (206)(206)(206) and (66) follows: % 7.73/2.36 | (207) op2(e24, e24) = e24 % 7.73/2.36 | % 7.73/2.36 | Instantiating formula (38) with e24, e24, e24, e22 and discharging atoms op2(e24, e24) = e24, op2(e24, e24) = e22, yields: % 7.73/2.36 | (208) e24 = e22 % 7.73/2.36 | % 7.73/2.36 | Equations (208) can reduce 70 to: % 7.73/2.36 | (203) $false % 7.73/2.36 | % 7.73/2.36 |-The branch is then unsatisfiable % 7.73/2.36 |-Branch two: % 7.73/2.36 | (210) ~ (all_0_9_9 = e24) % 7.73/2.36 | (211) all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21 % 7.73/2.36 | % 7.73/2.36 +-Applying beta-rule and splitting (90), into two cases. % 7.73/2.36 |-Branch one: % 7.73/2.36 | (212) all_0_7_7 = e24 % 7.73/2.36 | % 7.73/2.36 | From (212) and (89) follows: % 7.73/2.36 | (213) op2(all_0_6_6, e24) = all_0_5_5 % 7.73/2.36 | % 7.73/2.36 | From (212) and (138) follows: % 7.73/2.36 | (214) op2(e24, all_0_6_6) = all_0_5_5 % 7.73/2.36 | % 7.73/2.36 | From (212)(212) and (153) follows: % 7.73/2.36 | (215) op2(e24, e24) = all_0_6_6 % 7.73/2.36 | % 7.73/2.36 | Instantiating formula (38) with e24, e24, all_0_6_6, e22 and discharging atoms op2(e24, e24) = all_0_6_6, op2(e24, e24) = e22, yields: % 7.73/2.36 | (216) all_0_6_6 = e22 % 7.73/2.36 | % 7.73/2.36 | From (216) and (213) follows: % 7.73/2.36 | (217) op2(e22, e24) = all_0_5_5 % 7.73/2.36 | % 7.73/2.36 | From (216) and (214) follows: % 7.73/2.36 | (218) op2(e24, e22) = all_0_5_5 % 7.73/2.36 | % 7.73/2.36 | Instantiating formula (38) with e24, e22, all_0_5_5, e20 and discharging atoms op2(e24, e22) = all_0_5_5, op2(e24, e22) = e20, yields: % 7.73/2.36 | (219) all_0_5_5 = e20 % 7.73/2.36 | % 7.73/2.36 | Instantiating formula (38) with e22, e24, all_0_5_5, e21 and discharging atoms op2(e22, e24) = all_0_5_5, op2(e22, e24) = e21, yields: % 7.73/2.36 | (220) all_0_5_5 = e21 % 7.73/2.36 | % 7.73/2.36 | Combining equations (220,219) yields a new equation: % 7.73/2.36 | (221) e20 = e21 % 7.73/2.36 | % 7.73/2.36 | Equations (221) can reduce 6 to: % 7.73/2.36 | (203) $false % 7.73/2.36 | % 7.73/2.36 |-The branch is then unsatisfiable % 7.73/2.36 |-Branch two: % 7.73/2.36 | (223) ~ (all_0_7_7 = e24) % 7.73/2.36 | (224) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21 % 7.73/2.36 | % 7.73/2.36 +-Applying beta-rule and splitting (109), into two cases. % 7.73/2.36 |-Branch one: % 7.73/2.36 | (225) all_0_6_6 = e24 % 7.73/2.36 | % 7.73/2.36 | From (225)(225) and (149) follows: % 7.73/2.36 | (226) op2(e24, e24) = all_0_8_8 % 7.73/2.36 | % 7.73/2.36 | From (225) and (101) follows: % 7.73/2.36 | (227) op2(e24, all_0_8_8) = all_0_7_7 % 7.73/2.36 | % 7.73/2.36 | From (225) and (31) follows: % 7.73/2.36 | (228) op2(all_0_8_8, e24) = all_0_7_7 % 7.73/2.36 | % 7.73/2.36 | Instantiating formula (38) with e24, e24, all_0_8_8, e22 and discharging atoms op2(e24, e24) = all_0_8_8, op2(e24, e24) = e22, yields: % 7.73/2.36 | (229) all_0_8_8 = e22 % 7.73/2.36 | % 7.73/2.36 | From (229) and (228) follows: % 7.73/2.36 | (230) op2(e22, e24) = all_0_7_7 % 7.73/2.36 | % 7.73/2.36 | From (229) and (227) follows: % 7.73/2.36 | (231) op2(e24, e22) = all_0_7_7 % 7.73/2.36 | % 7.73/2.36 | Instantiating formula (38) with e24, e22, all_0_7_7, e20 and discharging atoms op2(e24, e22) = all_0_7_7, op2(e24, e22) = e20, yields: % 7.73/2.36 | (232) all_0_7_7 = e20 % 7.73/2.36 | % 7.73/2.36 | Instantiating formula (38) with e22, e24, all_0_7_7, e21 and discharging atoms op2(e22, e24) = all_0_7_7, op2(e22, e24) = e21, yields: % 7.73/2.36 | (233) all_0_7_7 = e21 % 7.73/2.36 | % 7.73/2.36 | Combining equations (233,232) yields a new equation: % 7.73/2.36 | (221) e20 = e21 % 7.73/2.36 | % 7.73/2.36 | Equations (221) can reduce 6 to: % 7.73/2.36 | (203) $false % 7.73/2.36 | % 7.73/2.36 |-The branch is then unsatisfiable % 7.73/2.36 |-Branch two: % 7.73/2.36 | (236) ~ (all_0_6_6 = e24) % 7.73/2.36 | (237) all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21 % 7.73/2.36 | % 7.73/2.36 +-Applying beta-rule and splitting (125), into two cases. % 7.73/2.36 |-Branch one: % 7.73/2.36 | (238) all_0_8_8 = e24 % 7.73/2.36 | % 7.73/2.36 | From (238) and (18) follows: % 7.73/2.36 | (239) op2(all_0_5_5, e24) = all_0_6_6 % 7.73/2.36 | % 7.73/2.36 | From (238) and (80) follows: % 7.73/2.36 | (240) op2(e24, all_0_5_5) = all_0_6_6 % 7.73/2.36 | % 7.73/2.36 | From (238)(238) and (91) follows: % 7.73/2.36 | (241) op2(e24, e24) = all_0_5_5 % 7.73/2.36 | % 7.73/2.36 | Instantiating formula (38) with e24, e24, all_0_5_5, e22 and discharging atoms op2(e24, e24) = all_0_5_5, op2(e24, e24) = e22, yields: % 7.73/2.36 | (242) all_0_5_5 = e22 % 7.73/2.36 | % 7.73/2.36 | From (242) and (239) follows: % 7.73/2.36 | (243) op2(e22, e24) = all_0_6_6 % 7.73/2.36 | % 7.73/2.36 | From (242) and (240) follows: % 7.73/2.36 | (244) op2(e24, e22) = all_0_6_6 % 7.73/2.36 | % 7.73/2.36 | Instantiating formula (38) with e24, e22, all_0_6_6, e20 and discharging atoms op2(e24, e22) = all_0_6_6, op2(e24, e22) = e20, yields: % 7.73/2.36 | (245) all_0_6_6 = e20 % 7.73/2.36 | % 7.73/2.36 | Instantiating formula (38) with e22, e24, all_0_6_6, e21 and discharging atoms op2(e22, e24) = all_0_6_6, op2(e22, e24) = e21, yields: % 7.73/2.37 | (246) all_0_6_6 = e21 % 7.73/2.37 | % 7.73/2.37 | Combining equations (246,245) yields a new equation: % 7.73/2.37 | (221) e20 = e21 % 7.73/2.37 | % 7.73/2.37 | Equations (221) can reduce 6 to: % 7.73/2.37 | (203) $false % 7.73/2.37 | % 7.73/2.37 |-The branch is then unsatisfiable % 7.73/2.37 |-Branch two: % 7.73/2.37 | (249) ~ (all_0_8_8 = e24) % 7.73/2.37 | (250) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21 % 7.73/2.37 | % 7.73/2.37 +-Applying beta-rule and splitting (205), into two cases. % 7.73/2.37 |-Branch one: % 7.73/2.37 | (251) all_0_0_0 = e13 % 7.73/2.37 | % 7.73/2.37 | From (251) and (15) follows: % 7.73/2.37 | (252) h(e13) = e24 % 7.73/2.37 | % 7.73/2.37 | Instantiating formula (93) with e13, e24, all_0_6_6 and discharging atoms h(e13) = all_0_6_6, h(e13) = e24, yields: % 7.73/2.37 | (225) all_0_6_6 = e24 % 7.73/2.37 | % 7.73/2.37 | Equations (225) can reduce 236 to: % 7.73/2.37 | (203) $false % 7.73/2.37 | % 7.73/2.37 |-The branch is then unsatisfiable % 7.73/2.37 |-Branch two: % 7.73/2.37 | (255) ~ (all_0_0_0 = e13) % 7.73/2.37 | (256) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11 % 7.73/2.37 | % 7.73/2.37 +-Applying beta-rule and splitting (256), into two cases. % 7.73/2.37 |-Branch one: % 7.73/2.37 | (257) all_0_0_0 = e12 % 7.73/2.37 | % 7.73/2.37 | From (257) and (15) follows: % 7.73/2.37 | (258) h(e12) = e24 % 7.73/2.37 | % 7.73/2.37 | Instantiating formula (93) with e12, e24, all_0_7_7 and discharging atoms h(e12) = all_0_7_7, h(e12) = e24, yields: % 7.73/2.37 | (212) all_0_7_7 = e24 % 7.73/2.37 | % 7.73/2.37 | Equations (212) can reduce 223 to: % 7.73/2.37 | (203) $false % 7.73/2.37 | % 7.73/2.37 |-The branch is then unsatisfiable % 7.73/2.37 |-Branch two: % 7.73/2.37 | (261) ~ (all_0_0_0 = e12) % 7.73/2.37 | (262) all_0_0_0 = e10 | all_0_0_0 = e11 % 7.73/2.37 | % 7.73/2.37 +-Applying beta-rule and splitting (262), into two cases. % 7.73/2.37 |-Branch one: % 7.73/2.37 | (263) all_0_0_0 = e10 % 7.73/2.37 | % 7.73/2.37 | From (263) and (15) follows: % 7.73/2.37 | (264) h(e10) = e24 % 7.73/2.37 | % 7.73/2.37 | Instantiating formula (93) with e10, e24, all_0_9_9 and discharging atoms h(e10) = all_0_9_9, h(e10) = e24, yields: % 7.73/2.37 | (206) all_0_9_9 = e24 % 7.73/2.37 | % 7.73/2.37 | Equations (206) can reduce 210 to: % 7.73/2.37 | (203) $false % 7.73/2.37 | % 7.73/2.37 |-The branch is then unsatisfiable % 7.73/2.37 |-Branch two: % 7.73/2.37 | (267) ~ (all_0_0_0 = e10) % 7.73/2.37 | (268) all_0_0_0 = e11 % 7.73/2.37 | % 7.73/2.37 | From (268) and (15) follows: % 7.73/2.37 | (269) h(e11) = e24 % 7.73/2.37 | % 7.73/2.37 | Instantiating formula (93) with e11, e24, all_0_8_8 and discharging atoms h(e11) = all_0_8_8, h(e11) = e24, yields: % 7.73/2.37 | (238) all_0_8_8 = e24 % 7.73/2.37 | % 7.73/2.37 | Equations (238) can reduce 249 to: % 7.73/2.37 | (203) $false % 7.73/2.37 | % 7.73/2.37 |-The branch is then unsatisfiable % 7.73/2.37 % SZS output end Proof for theBenchmark % 7.73/2.37 % 7.73/2.37 1790ms %------------------------------------------------------------------------------