%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : ALG180+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n019.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 15:37:05 EDT 2022 % Result : Theorem 4.24s 1.58s % Output : Proof 8.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ALG180+1 : TPTP v8.1.0. Released v2.7.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n019.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Tue Jun 7 22:12:55 EDT 2022 % 0.12/0.33 % CPUTime : % 0.48/0.57 ____ _ % 0.48/0.57 ___ / __ \_____(_)___ ________ __________ % 0.48/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.48/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.48/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.48/0.57 % 0.48/0.57 A Theorem Prover for First-Order Logic % 0.48/0.57 (ePrincess v.1.0) % 0.48/0.57 % 0.48/0.57 (c) Philipp Rümmer, 2009-2015 % 0.48/0.57 (c) Peter Backeman, 2014-2015 % 0.48/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.48/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.48/0.57 Bug reports to peter@backeman.se % 0.48/0.57 % 0.48/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.48/0.57 % 0.48/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.48/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.78/1.00 Prover 0: Preprocessing ... % 2.96/1.29 Prover 0: Constructing countermodel ... % 4.24/1.58 Prover 0: proved (961ms) % 4.24/1.58 % 4.24/1.58 No countermodel exists, formula is valid % 4.24/1.58 % SZS status Theorem for theBenchmark % 4.24/1.58 % 4.24/1.58 Generating proof ... found it (size 125) % 7.86/2.39 % 7.86/2.39 % SZS output start Proof for theBenchmark % 7.86/2.39 Assumed formulas after preprocessing and simplification: % 7.86/2.39 | (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) = v1 & op2(v4, v3) = v3 & op2(v4, v2) = v4 & op2(v4, v1) = v0 & op2(v4, v0) = v2 & op2(v3, v4) = v2 & op2(v3, v3) = v0 & op2(v3, v2) = v3 & op2(v3, v1) = v1 & op2(v3, v0) = v4 & op2(v2, v4) = v0 & op2(v2, v3) = v4 & op2(v2, v2) = v2 & op2(v2, v1) = v3 & op2(v2, v0) = v1 & op2(v1, v4) = v3 & op2(v1, v3) = v2 & op2(v1, v2) = v1 & op2(v1, v1) = v4 & op2(v1, v0) = v0 & op2(v0, v4) = v4 & op2(v0, v3) = v1 & op2(v0, v2) = v0 & op2(v0, v1) = v2 & op2(v0, v0) = v3 & op2(e24, e24) = e20 & op2(e24, e23) = e24 & op2(e24, e22) = e21 & op2(e24, e20) = e22 & op2(e24, e21) = e23 & op2(e23, e24) = e21 & op2(e23, e23) = e22 & op2(e23, e22) = e24 & op2(e23, e20) = e23 & op2(e23, e21) = e20 & op2(e22, e24) = e22 & op2(e22, e23) = e20 & op2(e22, e22) = e23 & op2(e22, e20) = e21 & op2(e22, e21) = e24 & op2(e20, e24) = e23 & op2(e20, e23) = e21 & op2(e20, e22) = e20 & op2(e20, e20) = e24 & op2(e20, e21) = e22 & op2(e21, e24) = e24 & op2(e21, e23) = e23 & op2(e21, e22) = e22 & op2(e21, e20) = e20 & op2(e21, e21) = e21 & op1(v9, v9) = v5 & op1(v9, v8) = v9 & op1(v9, v7) = v6 & op1(v9, v6) = v8 & op1(v9, v5) = v7 & op1(v8, v9) = v6 & op1(v8, v8) = v7 & op1(v8, v7) = v9 & op1(v8, v6) = v5 & op1(v8, v5) = v8 & op1(v7, v9) = v7 & op1(v7, v8) = v5 & op1(v7, v7) = v8 & op1(v7, v6) = v9 & op1(v7, v5) = v6 & op1(v6, v9) = v9 & op1(v6, v8) = v8 & op1(v6, v7) = v7 & op1(v6, v6) = v6 & op1(v6, v5) = v5 & op1(v5, v9) = v8 & op1(v5, v8) = v6 & op1(v5, v7) = v5 & op1(v5, v6) = v7 & op1(v5, v5) = v9 & op1(e14, e14) = e11 & op1(e14, e13) = e13 & op1(e14, e12) = e14 & op1(e14, e10) = e12 & op1(e14, e11) = e10 & op1(e13, e14) = e12 & op1(e13, e13) = e10 & op1(e13, e12) = e13 & op1(e13, e10) = e14 & op1(e13, e11) = e11 & op1(e12, e14) = e10 & op1(e12, e13) = e14 & op1(e12, e12) = e12 & op1(e12, e10) = e11 & op1(e12, e11) = e13 & op1(e10, e14) = e14 & op1(e10, e13) = e11 & op1(e10, e12) = e10 & op1(e10, e10) = e13 & op1(e10, e11) = e12 & op1(e11, e14) = e13 & op1(e11, e13) = e12 & op1(e11, e12) = e11 & op1(e11, e10) = e10 & 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)) % 7.86/2.44 | 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: % 7.86/2.44 | (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_8_8 & op2(all_0_5_5, all_0_6_6) = all_0_6_6 & op2(all_0_5_5, all_0_7_7) = all_0_5_5 & op2(all_0_5_5, all_0_8_8) = all_0_9_9 & op2(all_0_5_5, all_0_9_9) = all_0_7_7 & op2(all_0_6_6, all_0_5_5) = all_0_7_7 & op2(all_0_6_6, all_0_6_6) = all_0_9_9 & op2(all_0_6_6, all_0_7_7) = all_0_6_6 & op2(all_0_6_6, all_0_8_8) = all_0_8_8 & op2(all_0_6_6, all_0_9_9) = all_0_5_5 & op2(all_0_7_7, all_0_5_5) = all_0_9_9 & op2(all_0_7_7, all_0_6_6) = all_0_5_5 & op2(all_0_7_7, all_0_7_7) = all_0_7_7 & op2(all_0_7_7, all_0_8_8) = all_0_6_6 & op2(all_0_7_7, all_0_9_9) = all_0_8_8 & 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_8_8 & op2(all_0_8_8, all_0_8_8) = all_0_5_5 & op2(all_0_8_8, all_0_9_9) = all_0_9_9 & op2(all_0_9_9, all_0_5_5) = all_0_5_5 & op2(all_0_9_9, all_0_6_6) = all_0_8_8 & op2(all_0_9_9, all_0_7_7) = all_0_9_9 & op2(all_0_9_9, all_0_8_8) = all_0_7_7 & op2(all_0_9_9, all_0_9_9) = all_0_6_6 & op2(e24, e24) = e20 & op2(e24, e23) = e24 & op2(e24, e22) = e21 & op2(e24, e20) = e22 & op2(e24, e21) = e23 & op2(e23, e24) = e21 & op2(e23, e23) = e22 & op2(e23, e22) = e24 & op2(e23, e20) = e23 & op2(e23, e21) = e20 & op2(e22, e24) = e22 & op2(e22, e23) = e20 & op2(e22, e22) = e23 & op2(e22, e20) = e21 & op2(e22, e21) = e24 & op2(e20, e24) = e23 & op2(e20, e23) = e21 & op2(e20, e22) = e20 & op2(e20, e20) = e24 & op2(e20, e21) = e22 & op2(e21, e24) = e24 & op2(e21, e23) = e23 & op2(e21, e22) = e22 & op2(e21, e20) = e20 & op2(e21, e21) = e21 & op1(all_0_0_0, all_0_0_0) = all_0_4_4 & op1(all_0_0_0, all_0_1_1) = all_0_0_0 & op1(all_0_0_0, all_0_2_2) = all_0_3_3 & op1(all_0_0_0, all_0_3_3) = all_0_1_1 & op1(all_0_0_0, all_0_4_4) = all_0_2_2 & op1(all_0_1_1, all_0_0_0) = all_0_3_3 & op1(all_0_1_1, all_0_1_1) = all_0_2_2 & 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_2_2 & 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_3_3 & op1(all_0_3_3, all_0_0_0) = all_0_0_0 & op1(all_0_3_3, all_0_1_1) = all_0_1_1 & op1(all_0_3_3, all_0_2_2) = all_0_2_2 & op1(all_0_3_3, all_0_3_3) = all_0_3_3 & op1(all_0_3_3, all_0_4_4) = all_0_4_4 & op1(all_0_4_4, all_0_0_0) = all_0_1_1 & op1(all_0_4_4, all_0_1_1) = all_0_3_3 & op1(all_0_4_4, all_0_2_2) = all_0_4_4 & op1(all_0_4_4, all_0_3_3) = all_0_2_2 & op1(all_0_4_4, all_0_4_4) = all_0_0_0 & op1(e14, e14) = e11 & op1(e14, e13) = e13 & op1(e14, e12) = e14 & op1(e14, e10) = e12 & op1(e14, e11) = e10 & op1(e13, e14) = e12 & op1(e13, e13) = e10 & op1(e13, e12) = e13 & op1(e13, e10) = e14 & op1(e13, e11) = e11 & op1(e12, e14) = e10 & op1(e12, e13) = e14 & op1(e12, e12) = e12 & op1(e12, e10) = e11 & op1(e12, e11) = e13 & op1(e10, e14) = e14 & op1(e10, e13) = e11 & op1(e10, e12) = e10 & op1(e10, e10) = e13 & op1(e10, e11) = e12 & op1(e11, e14) = e13 & op1(e11, e13) = e12 & op1(e11, e12) = e11 & op1(e11, e10) = e10 & 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) % 7.86/2.45 | % 7.86/2.45 | Applying alpha-rule on (1) yields: % 7.86/2.45 | (2) op2(all_0_6_6, all_0_9_9) = all_0_5_5 % 7.86/2.45 | (3) ~ (e21 = e12) % 7.86/2.45 | (4) op2(e21, e21) = e21 % 7.86/2.45 | (5) ~ (e20 = e21) % 7.86/2.45 | (6) ~ (e20 = e14) % 7.86/2.45 | (7) op1(e11, e10) = e10 % 7.86/2.45 | (8) op1(all_0_2_2, all_0_2_2) = all_0_1_1 % 7.86/2.45 | (9) op1(e14, e10) = e12 % 7.86/2.45 | (10) op2(all_0_5_5, all_0_5_5) = all_0_8_8 % 7.86/2.45 | (11) ~ (e24 = e11) % 7.86/2.45 | (12) op1(all_0_4_4, all_0_2_2) = all_0_4_4 % 7.86/2.45 | (13) op2(all_0_9_9, all_0_6_6) = all_0_8_8 % 7.86/2.45 | (14) ~ (e12 = e11) % 7.86/2.45 | (15) op1(e13, e14) = e12 % 7.86/2.45 | (16) h(e12) = all_0_7_7 % 7.86/2.45 | (17) op2(all_0_7_7, all_0_7_7) = all_0_7_7 % 7.86/2.45 | (18) op1(all_0_0_0, all_0_1_1) = all_0_0_0 % 7.86/2.45 | (19) h(all_0_0_0) = e24 % 7.86/2.45 | (20) h(e13) = all_0_6_6 % 7.86/2.45 | (21) ~ (e14 = e12) % 7.86/2.45 | (22) ~ (e24 = e12) % 7.86/2.45 | (23) op2(all_0_6_6, all_0_6_6) = all_0_9_9 % 7.86/2.45 | (24) op1(e13, e11) = e11 % 7.86/2.45 | (25) op2(e23, e23) = e22 % 7.86/2.45 | (26) j(e22) = all_0_2_2 % 7.86/2.45 | (27) op1(all_0_4_4, all_0_4_4) = all_0_0_0 % 7.86/2.45 | (28) op1(e14, e11) = e10 % 7.86/2.45 | (29) op2(all_0_5_5, all_0_6_6) = all_0_6_6 % 7.86/2.45 | (30) op2(e20, e24) = e23 % 7.86/2.45 | (31) j(e21) = all_0_3_3 % 7.86/2.45 | (32) j(all_0_8_8) = e11 % 7.86/2.45 | (33) ~ (e22 = e13) % 7.86/2.45 | (34) op2(all_0_5_5, all_0_7_7) = all_0_5_5 % 7.86/2.45 | (35) op1(e13, e13) = e10 % 7.86/2.45 | (36) op2(all_0_7_7, all_0_8_8) = all_0_6_6 % 7.86/2.45 | (37) op2(all_0_8_8, all_0_6_6) = all_0_7_7 % 7.86/2.45 | (38) op2(e20, e23) = e21 % 7.86/2.45 | (39) op2(e24, e21) = e23 % 7.86/2.46 | (40) j(all_0_6_6) = e13 % 7.86/2.46 | (41) op2(e24, e22) = e21 % 7.86/2.46 | (42) op1(all_0_0_0, all_0_4_4) = all_0_2_2 % 7.86/2.46 | (43) h(all_0_4_4) = e20 % 7.86/2.46 | (44) op1(all_0_4_4, all_0_0_0) = all_0_1_1 % 7.86/2.46 | (45) op2(e22, e20) = e21 % 7.86/2.46 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) % 7.86/2.46 | (47) op2(all_0_6_6, all_0_5_5) = all_0_7_7 % 7.86/2.46 | (48) ~ (e23 = e13) % 7.86/2.46 | (49) 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 % 7.86/2.46 | (50) op1(e13, e12) = e13 % 7.86/2.46 | (51) ~ (e23 = e12) % 7.86/2.46 | (52) ~ (e24 = e14) % 7.86/2.46 | (53) op1(e14, e13) = e13 % 7.86/2.46 | (54) h(all_0_3_3) = e21 % 7.86/2.46 | (55) ~ (e23 = e21) % 7.86/2.46 | (56) 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 % 7.86/2.46 | (57) op2(e23, e24) = e21 % 7.86/2.46 | (58) op1(all_0_2_2, all_0_0_0) = all_0_2_2 % 7.86/2.46 | (59) ~ (e22 = e21) % 7.86/2.46 | (60) ~ (e20 = e11) % 7.86/2.46 | (61) j(all_0_9_9) = e10 % 7.86/2.46 | (62) op2(all_0_9_9, all_0_8_8) = all_0_7_7 % 7.86/2.46 | (63) ~ (e14 = e10) % 7.86/2.46 | (64) op1(e14, e12) = e14 % 7.86/2.46 | (65) ~ (e22 = e10) % 7.86/2.46 | (66) op1(all_0_0_0, all_0_0_0) = all_0_4_4 % 7.86/2.46 | (67) h(all_0_1_1) = e23 % 7.86/2.46 | (68) op2(all_0_9_9, all_0_7_7) = all_0_9_9 % 7.86/2.46 | (69) ~ (e12 = e10) % 7.86/2.46 | (70) ~ (e24 = e22) % 7.86/2.46 | (71) op1(all_0_1_1, all_0_4_4) = all_0_1_1 % 7.86/2.46 | (72) op2(all_0_8_8, all_0_9_9) = all_0_9_9 % 7.86/2.46 | (73) 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 % 7.86/2.46 | (74) op1(e13, e10) = e14 % 7.86/2.46 | (75) op2(e22, e21) = e24 % 7.86/2.46 | (76) op2(all_0_5_5, all_0_9_9) = all_0_7_7 % 7.86/2.46 | (77) op1(e10, e12) = e10 % 7.86/2.46 | (78) op2(e21, e23) = e23 % 8.27/2.46 | (79) 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 % 8.27/2.46 | (80) j(all_0_7_7) = e12 % 8.27/2.46 | (81) op1(all_0_3_3, all_0_2_2) = all_0_2_2 % 8.27/2.46 | (82) op1(e12, e11) = e13 % 8.27/2.46 | (83) op1(e11, e12) = e11 % 8.27/2.46 | (84) op2(all_0_8_8, all_0_5_5) = all_0_6_6 % 8.27/2.46 | (85) op2(e20, e22) = e20 % 8.27/2.46 | (86) h(all_0_2_2) = e22 % 8.27/2.46 | (87) op1(e12, e13) = e14 % 8.27/2.46 | (88) ~ (e14 = e13) % 8.27/2.46 | (89) ~ (e21 = e11) % 8.27/2.46 | (90) h(e14) = all_0_5_5 % 8.27/2.46 | (91) ~ (e24 = e20) % 8.27/2.46 | (92) ~ (e13 = e12) % 8.27/2.46 | (93) op1(all_0_3_3, all_0_4_4) = all_0_4_4 % 8.27/2.46 | (94) 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 % 8.27/2.47 | (95) op2(all_0_8_8, all_0_8_8) = all_0_5_5 % 8.27/2.47 | (96) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) % 8.27/2.47 | (97) op1(all_0_2_2, all_0_4_4) = all_0_3_3 % 8.27/2.47 | (98) ~ (e14 = e11) % 8.27/2.47 | (99) op2(e22, e24) = e22 % 8.27/2.47 | (100) op2(e21, e20) = e20 % 8.27/2.47 | (101) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) % 8.27/2.47 | (102) op1(all_0_3_3, all_0_3_3) = all_0_3_3 % 8.27/2.47 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) % 8.27/2.47 | (104) 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 % 8.27/2.47 | (105) op2(all_0_5_5, all_0_8_8) = all_0_9_9 % 8.27/2.47 | (106) op2(all_0_9_9, all_0_9_9) = all_0_6_6 % 8.27/2.47 | (107) op1(all_0_0_0, all_0_3_3) = all_0_1_1 % 8.27/2.47 | (108) ~ (e23 = e10) % 8.27/2.47 | (109) op1(all_0_3_3, all_0_0_0) = all_0_0_0 % 8.27/2.47 | (110) op1(all_0_1_1, all_0_3_3) = all_0_4_4 % 8.27/2.47 | (111) ~ (e13 = e10) % 8.27/2.47 | (112) op1(all_0_1_1, all_0_1_1) = all_0_2_2 % 8.27/2.47 | (113) 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 % 8.27/2.47 | (114) 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 % 8.27/2.47 | (115) ~ (e23 = e22) % 8.27/2.47 | (116) ~ (e20 = e10) % 8.27/2.47 | (117) ~ (e22 = e11) % 8.27/2.47 | (118) op2(e22, e23) = e20 % 8.27/2.47 | (119) op2(e21, e22) = e22 % 8.27/2.47 | (120) op2(e21, e24) = e24 % 8.27/2.47 | (121) op2(e22, e22) = e23 % 8.27/2.47 | (122) op2(all_0_7_7, all_0_5_5) = all_0_9_9 % 8.27/2.47 | (123) ~ (e20 = e12) % 8.27/2.47 | (124) op2(all_0_6_6, all_0_7_7) = all_0_6_6 % 8.27/2.47 | (125) op1(all_0_0_0, all_0_2_2) = all_0_3_3 % 8.27/2.47 | (126) op2(e23, e22) = e24 % 8.27/2.47 | (127) op1(e10, e10) = e13 % 8.27/2.47 | (128) 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 % 8.27/2.47 | (129) ~ (e10 = e11) % 8.27/2.47 | (130) ~ (e23 = e14) % 8.27/2.47 | (131) h(e11) = all_0_8_8 % 8.27/2.47 | (132) op1(all_0_3_3, all_0_1_1) = all_0_1_1 % 8.27/2.47 | (133) op1(e10, e13) = e11 % 8.27/2.47 | (134) j(e23) = all_0_1_1 % 8.27/2.47 | (135) ~ (e23 = e20) % 8.27/2.47 | (136) ~ (e21 = e14) % 8.27/2.47 | (137) op1(e12, e12) = e12 % 8.27/2.47 | (138) op1(all_0_4_4, all_0_1_1) = all_0_3_3 % 8.27/2.47 | (139) op1(all_0_1_1, all_0_0_0) = all_0_3_3 % 8.27/2.47 | (140) j(e24) = all_0_0_0 % 8.27/2.47 | (141) op2(all_0_7_7, all_0_6_6) = all_0_5_5 % 8.27/2.47 | (142) op2(e24, e24) = e20 % 8.27/2.48 | (143) op1(e10, e14) = e14 % 8.27/2.48 | (144) op1(all_0_2_2, all_0_1_1) = all_0_4_4 % 8.27/2.48 | (145) ~ (e24 = e21) % 8.27/2.48 | (146) op1(e11, e14) = e13 % 8.27/2.48 | (147) op2(e20, e21) = e22 % 8.27/2.48 | (148) op2(e23, e21) = e20 % 8.27/2.48 | (149) j(all_0_5_5) = e14 % 8.27/2.48 | (150) op2(e23, e20) = e23 % 8.27/2.48 | (151) op1(all_0_1_1, all_0_2_2) = all_0_0_0 % 8.27/2.48 | (152) ~ (e22 = e20) % 8.27/2.48 | (153) ~ (e23 = e11) % 8.27/2.48 | (154) op1(e14, e14) = e11 % 8.27/2.48 | (155) op2(e20, e20) = e24 % 8.27/2.48 | (156) op1(e11, e11) = e14 % 8.27/2.48 | (157) op2(all_0_8_8, all_0_7_7) = all_0_8_8 % 8.27/2.48 | (158) op1(all_0_2_2, all_0_3_3) = all_0_0_0 % 8.27/2.48 | (159) ~ (e24 = e10) % 8.27/2.48 | (160) ~ (e24 = e23) % 8.27/2.48 | (161) op1(e11, e13) = e12 % 8.27/2.48 | (162) op1(all_0_4_4, all_0_3_3) = all_0_2_2 % 8.27/2.48 | (163) ~ (e20 = e13) % 8.27/2.48 | (164) op1(e10, e11) = e12 % 8.27/2.48 | (165) ~ (e24 = e13) % 8.27/2.48 | (166) op2(all_0_7_7, all_0_9_9) = all_0_8_8 % 8.27/2.48 | (167) ~ (e21 = e10) % 8.27/2.48 | (168) ~ (e21 = e13) % 8.27/2.48 | (169) j(e20) = all_0_4_4 % 8.27/2.48 | (170) ~ (e22 = e12) % 8.27/2.48 | (171) op2(all_0_6_6, all_0_8_8) = all_0_8_8 % 8.27/2.48 | (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 % 8.27/2.48 | (173) op2(e24, e20) = e22 % 8.27/2.48 | (174) op1(e12, e10) = e11 % 8.27/2.48 | (175) h(e10) = all_0_9_9 % 8.27/2.48 | (176) ~ (e22 = e14) % 8.27/2.48 | (177) op1(e12, e14) = e10 % 8.27/2.48 | (178) op2(all_0_9_9, all_0_5_5) = all_0_5_5 % 8.27/2.48 | (179) op2(e24, e23) = e24 % 8.27/2.48 | (180) ~ (e13 = e11) % 8.27/2.48 | % 8.27/2.48 +-Applying beta-rule and splitting (114), into two cases. % 8.27/2.48 |-Branch one: % 8.27/2.48 | (181) all_0_0_0 = e14 % 8.27/2.48 | % 8.27/2.48 | From (181)(181) and (66) follows: % 8.27/2.48 | (182) op1(e14, e14) = all_0_4_4 % 8.27/2.48 | % 8.27/2.48 | From (181)(181) and (18) follows: % 8.27/2.48 | (183) op1(e14, all_0_1_1) = e14 % 8.27/2.48 | % 8.27/2.48 | From (181) and (42) follows: % 8.27/2.49 | (184) op1(e14, all_0_4_4) = all_0_2_2 % 8.27/2.49 | % 8.27/2.49 | From (181) and (58) follows: % 8.27/2.49 | (185) op1(all_0_2_2, e14) = all_0_2_2 % 8.27/2.49 | % 8.27/2.49 | From (181) and (44) follows: % 8.27/2.49 | (186) op1(all_0_4_4, e14) = all_0_1_1 % 8.27/2.49 | % 8.27/2.49 | Instantiating formula (103) with e14, e14, all_0_4_4, e11 and discharging atoms op1(e14, e14) = all_0_4_4, op1(e14, e14) = e11, yields: % 8.27/2.49 | (187) all_0_4_4 = e11 % 8.27/2.49 | % 8.27/2.49 | From (187) and (71) follows: % 8.27/2.49 | (188) op1(all_0_1_1, e11) = all_0_1_1 % 8.27/2.49 | % 8.27/2.49 | From (187) and (186) follows: % 8.27/2.49 | (189) op1(e11, e14) = all_0_1_1 % 8.27/2.49 | % 8.27/2.49 | From (187) and (184) follows: % 8.27/2.49 | (190) op1(e14, e11) = all_0_2_2 % 8.27/2.49 | % 8.27/2.49 | Instantiating formula (103) with e14, e11, all_0_2_2, e10 and discharging atoms op1(e14, e11) = all_0_2_2, op1(e14, e11) = e10, yields: % 8.27/2.49 | (191) all_0_2_2 = e10 % 8.27/2.49 | % 8.27/2.49 | Instantiating formula (103) with e11, e14, all_0_1_1, e13 and discharging atoms op1(e11, e14) = all_0_1_1, op1(e11, e14) = e13, yields: % 8.27/2.49 | (192) all_0_1_1 = e13 % 8.27/2.49 | % 8.27/2.49 | From (192)(192) and (188) follows: % 8.27/2.49 | (193) op1(e13, e11) = e13 % 8.27/2.49 | % 8.27/2.49 | From (191)(191) and (185) follows: % 8.27/2.49 | (194) op1(e10, e14) = e10 % 8.27/2.49 | % 8.27/2.49 | From (192) and (183) follows: % 8.27/2.49 | (195) op1(e14, e13) = e14 % 8.27/2.49 | % 8.27/2.49 | Instantiating formula (103) with e14, e13, e14, e13 and discharging atoms op1(e14, e13) = e14, op1(e14, e13) = e13, yields: % 8.27/2.49 | (196) e14 = e13 % 8.27/2.49 | % 8.27/2.49 | Instantiating formula (103) with e13, e11, e13, e11 and discharging atoms op1(e13, e11) = e13, op1(e13, e11) = e11, yields: % 8.27/2.49 | (197) e13 = e11 % 8.27/2.49 | % 8.27/2.49 | Instantiating formula (103) with e10, e14, e10, e14 and discharging atoms op1(e10, e14) = e14, op1(e10, e14) = e10, yields: % 8.27/2.49 | (198) e14 = e10 % 8.27/2.49 | % 8.27/2.49 | Combining equations (198,196) yields a new equation: % 8.27/2.49 | (199) e13 = e10 % 8.27/2.49 | % 8.27/2.49 | Combining equations (199,197) yields a new equation: % 8.27/2.49 | (200) e10 = e11 % 8.27/2.49 | % 8.27/2.49 | Simplifying 200 yields: % 8.27/2.49 | (201) e10 = e11 % 8.27/2.49 | % 8.27/2.49 | Equations (201) can reduce 129 to: % 8.27/2.49 | (202) $false % 8.27/2.49 | % 8.27/2.49 |-The branch is then unsatisfiable % 8.27/2.49 |-Branch two: % 8.27/2.50 | (203) ~ (all_0_0_0 = e14) % 8.27/2.50 | (204) all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11 % 8.27/2.50 | % 8.27/2.50 +-Applying beta-rule and splitting (73), into two cases. % 8.27/2.50 |-Branch one: % 8.27/2.50 | (205) all_0_9_9 = e24 % 8.27/2.50 | % 8.27/2.50 | From (205) and (2) follows: % 8.27/2.50 | (206) op2(all_0_6_6, e24) = all_0_5_5 % 8.27/2.50 | % 8.27/2.50 | From (205)(205) and (72) follows: % 8.27/2.50 | (207) op2(all_0_8_8, e24) = e24 % 8.27/2.50 | % 8.27/2.50 | From (205) and (178) follows: % 8.44/2.50 | (208) op2(e24, all_0_5_5) = all_0_5_5 % 8.44/2.50 | % 8.44/2.50 | From (205) and (13) follows: % 8.44/2.50 | (209) op2(e24, all_0_6_6) = all_0_8_8 % 8.44/2.50 | % 8.44/2.50 | From (205)(205) and (106) follows: % 8.44/2.50 | (210) op2(e24, e24) = all_0_6_6 % 8.44/2.50 | % 8.44/2.50 | Instantiating formula (46) with e24, e24, all_0_6_6, e20 and discharging atoms op2(e24, e24) = all_0_6_6, op2(e24, e24) = e20, yields: % 8.44/2.50 | (211) all_0_6_6 = e20 % 8.44/2.50 | % 8.44/2.50 | From (211)(211) and (29) follows: % 8.44/2.50 | (212) op2(all_0_5_5, e20) = e20 % 8.44/2.50 | % 8.44/2.50 | From (211) and (206) follows: % 8.44/2.50 | (213) op2(e20, e24) = all_0_5_5 % 8.44/2.50 | % 8.44/2.50 | From (211) and (209) follows: % 8.44/2.50 | (214) op2(e24, e20) = all_0_8_8 % 8.44/2.50 | % 8.44/2.50 | Instantiating formula (46) with e24, e20, all_0_8_8, e22 and discharging atoms op2(e24, e20) = all_0_8_8, op2(e24, e20) = e22, yields: % 8.44/2.50 | (215) all_0_8_8 = e22 % 8.44/2.50 | % 8.44/2.50 | Instantiating formula (46) with e20, e24, all_0_5_5, e23 and discharging atoms op2(e20, e24) = all_0_5_5, op2(e20, e24) = e23, yields: % 8.44/2.50 | (216) all_0_5_5 = e23 % 8.44/2.50 | % 8.44/2.50 | From (216) and (212) follows: % 8.44/2.50 | (217) op2(e23, e20) = e20 % 8.44/2.50 | % 8.44/2.50 | From (215) and (207) follows: % 8.44/2.50 | (218) op2(e22, e24) = e24 % 8.44/2.50 | % 8.44/2.50 | From (216)(216) and (208) follows: % 8.44/2.50 | (219) op2(e24, e23) = e23 % 8.44/2.50 | % 8.44/2.50 | Instantiating formula (46) with e24, e23, e23, e24 and discharging atoms op2(e24, e23) = e24, op2(e24, e23) = e23, yields: % 8.44/2.50 | (220) e24 = e23 % 8.44/2.50 | % 8.44/2.50 | Instantiating formula (46) with e23, e20, e20, e23 and discharging atoms op2(e23, e20) = e23, op2(e23, e20) = e20, yields: % 8.44/2.50 | (221) e23 = e20 % 8.44/2.50 | % 8.44/2.50 | Instantiating formula (46) with e22, e24, e24, e22 and discharging atoms op2(e22, e24) = e24, op2(e22, e24) = e22, yields: % 8.44/2.50 | (222) e24 = e22 % 8.44/2.50 | % 8.44/2.50 | Combining equations (222,220) yields a new equation: % 8.44/2.50 | (223) e23 = e22 % 8.44/2.50 | % 8.44/2.51 | Combining equations (223,221) yields a new equation: % 8.44/2.51 | (224) e22 = e20 % 8.44/2.51 | % 8.44/2.51 | Simplifying 224 yields: % 8.44/2.51 | (225) e22 = e20 % 8.44/2.51 | % 8.44/2.51 | Equations (225) can reduce 152 to: % 8.44/2.51 | (202) $false % 8.44/2.51 | % 8.44/2.51 |-The branch is then unsatisfiable % 8.44/2.51 |-Branch two: % 8.44/2.51 | (227) ~ (all_0_9_9 = e24) % 8.44/2.51 | (228) all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21 % 8.44/2.51 | % 8.44/2.51 +-Applying beta-rule and splitting (94), into two cases. % 8.44/2.51 |-Branch one: % 8.44/2.51 | (229) all_0_7_7 = e24 % 8.44/2.51 | % 8.44/2.51 | From (229)(229)(229) and (17) follows: % 8.44/2.51 | (230) op2(e24, e24) = e24 % 8.44/2.51 | % 8.44/2.51 | Instantiating formula (46) with e24, e24, e24, e20 and discharging atoms op2(e24, e24) = e24, op2(e24, e24) = e20, yields: % 8.44/2.51 | (231) e24 = e20 % 8.44/2.51 | % 8.44/2.51 | Equations (231) can reduce 91 to: % 8.44/2.51 | (202) $false % 8.44/2.51 | % 8.44/2.51 |-The branch is then unsatisfiable % 8.44/2.51 |-Branch two: % 8.44/2.51 | (233) ~ (all_0_7_7 = e24) % 8.44/2.51 | (234) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21 % 8.44/2.51 | % 8.44/2.51 +-Applying beta-rule and splitting (104), into two cases. % 8.44/2.51 |-Branch one: % 8.44/2.51 | (235) all_0_4_4 = e14 % 8.44/2.51 | % 8.44/2.51 | From (235) and (42) follows: % 8.44/2.51 | (236) op1(all_0_0_0, e14) = all_0_2_2 % 8.44/2.51 | % 8.44/2.51 | From (235) and (71) follows: % 8.44/2.51 | (237) op1(all_0_1_1, e14) = all_0_1_1 % 8.44/2.51 | % 8.44/2.51 | From (235) and (44) follows: % 8.44/2.51 | (238) op1(e14, all_0_0_0) = all_0_1_1 % 8.44/2.51 | % 8.44/2.51 | From (235)(235) and (12) follows: % 8.44/2.51 | (239) op1(e14, all_0_2_2) = e14 % 8.44/2.51 | % 8.44/2.51 | From (235)(235) and (27) follows: % 8.44/2.51 | (240) op1(e14, e14) = all_0_0_0 % 8.44/2.51 | % 8.44/2.51 | Instantiating formula (103) with e14, e14, all_0_0_0, e11 and discharging atoms op1(e14, e14) = all_0_0_0, op1(e14, e14) = e11, yields: % 8.44/2.51 | (241) all_0_0_0 = e11 % 8.44/2.51 | % 8.44/2.51 | From (241) and (236) follows: % 8.44/2.51 | (242) op1(e11, e14) = all_0_2_2 % 8.44/2.51 | % 8.44/2.51 | From (241) and (58) follows: % 8.44/2.51 | (243) op1(all_0_2_2, e11) = all_0_2_2 % 8.44/2.51 | % 8.44/2.51 | From (241) and (238) follows: % 8.44/2.51 | (244) op1(e14, e11) = all_0_1_1 % 8.44/2.51 | % 8.44/2.51 | Instantiating formula (103) with e14, e11, all_0_1_1, e10 and discharging atoms op1(e14, e11) = all_0_1_1, op1(e14, e11) = e10, yields: % 8.44/2.51 | (245) all_0_1_1 = e10 % 8.44/2.51 | % 8.44/2.51 | Instantiating formula (103) with e11, e14, all_0_2_2, e13 and discharging atoms op1(e11, e14) = all_0_2_2, op1(e11, e14) = e13, yields: % 8.44/2.51 | (246) all_0_2_2 = e13 % 8.44/2.51 | % 8.44/2.51 | From (245)(245) and (237) follows: % 8.44/2.51 | (194) op1(e10, e14) = e10 % 8.44/2.51 | % 8.44/2.51 | From (246)(246) and (243) follows: % 8.44/2.51 | (193) op1(e13, e11) = e13 % 8.44/2.51 | % 8.44/2.51 | From (246) and (239) follows: % 8.44/2.51 | (195) op1(e14, e13) = e14 % 8.44/2.51 | % 8.44/2.51 | Instantiating formula (103) with e14, e13, e14, e13 and discharging atoms op1(e14, e13) = e14, op1(e14, e13) = e13, yields: % 8.44/2.51 | (196) e14 = e13 % 8.44/2.51 | % 8.44/2.51 | Instantiating formula (103) with e13, e11, e13, e11 and discharging atoms op1(e13, e11) = e13, op1(e13, e11) = e11, yields: % 8.44/2.51 | (197) e13 = e11 % 8.44/2.51 | % 8.44/2.51 | Instantiating formula (103) with e10, e14, e10, e14 and discharging atoms op1(e10, e14) = e14, op1(e10, e14) = e10, yields: % 8.44/2.52 | (198) e14 = e10 % 8.44/2.52 | % 8.44/2.52 | Combining equations (198,196) yields a new equation: % 8.44/2.52 | (199) e13 = e10 % 8.44/2.52 | % 8.44/2.52 | Combining equations (199,197) yields a new equation: % 8.44/2.52 | (200) e10 = e11 % 8.44/2.52 | % 8.44/2.52 | Simplifying 200 yields: % 8.44/2.52 | (201) e10 = e11 % 8.44/2.52 | % 8.44/2.52 | Equations (201) can reduce 129 to: % 8.44/2.52 | (202) $false % 8.44/2.52 | % 8.44/2.52 |-The branch is then unsatisfiable % 8.44/2.52 |-Branch two: % 8.44/2.52 | (257) ~ (all_0_4_4 = e14) % 8.44/2.52 | (258) all_0_4_4 = e13 | all_0_4_4 = e12 | all_0_4_4 = e10 | all_0_4_4 = e11 % 8.44/2.52 | % 8.44/2.52 +-Applying beta-rule and splitting (113), into two cases. % 8.44/2.52 |-Branch one: % 8.44/2.52 | (259) all_0_6_6 = e24 % 8.44/2.52 | % 8.44/2.52 | From (259)(259) and (29) follows: % 8.44/2.52 | (260) op2(all_0_5_5, e24) = e24 % 8.44/2.52 | % 8.44/2.52 | From (259)(259) and (23) follows: % 8.44/2.52 | (261) op2(e24, e24) = all_0_9_9 % 8.44/2.52 | % 8.44/2.52 | From (259) and (171) follows: % 8.44/2.52 | (262) op2(e24, all_0_8_8) = all_0_8_8 % 8.44/2.52 | % 8.44/2.52 | From (259) and (2) follows: % 8.44/2.52 | (263) op2(e24, all_0_9_9) = all_0_5_5 % 8.44/2.52 | % 8.44/2.52 | From (259) and (13) follows: % 8.44/2.52 | (264) op2(all_0_9_9, e24) = all_0_8_8 % 8.44/2.52 | % 8.44/2.52 | Instantiating formula (46) with e24, e24, all_0_9_9, e20 and discharging atoms op2(e24, e24) = all_0_9_9, op2(e24, e24) = e20, yields: % 8.44/2.52 | (265) all_0_9_9 = e20 % 8.44/2.52 | % 8.44/2.52 | From (265)(265) and (72) follows: % 8.44/2.52 | (266) op2(all_0_8_8, e20) = e20 % 8.44/2.52 | % 8.44/2.52 | From (265) and (264) follows: % 8.44/2.52 | (267) op2(e20, e24) = all_0_8_8 % 8.44/2.52 | % 8.44/2.52 | From (265) and (263) follows: % 8.44/2.52 | (268) op2(e24, e20) = all_0_5_5 % 8.44/2.52 | % 8.44/2.52 | Instantiating formula (46) with e24, e20, all_0_5_5, e22 and discharging atoms op2(e24, e20) = all_0_5_5, op2(e24, e20) = e22, yields: % 8.44/2.52 | (269) all_0_5_5 = e22 % 8.44/2.52 | % 8.44/2.52 | Instantiating formula (46) with e20, e24, all_0_8_8, e23 and discharging atoms op2(e20, e24) = all_0_8_8, op2(e20, e24) = e23, yields: % 8.44/2.52 | (270) all_0_8_8 = e23 % 8.44/2.52 | % 8.44/2.52 | From (269) and (260) follows: % 8.44/2.52 | (218) op2(e22, e24) = e24 % 8.44/2.52 | % 8.44/2.52 | From (270) and (266) follows: % 8.44/2.52 | (217) op2(e23, e20) = e20 % 8.44/2.52 | % 8.44/2.52 | From (270)(270) and (262) follows: % 8.44/2.52 | (219) op2(e24, e23) = e23 % 8.44/2.52 | % 8.44/2.52 | Instantiating formula (46) with e24, e23, e23, e24 and discharging atoms op2(e24, e23) = e24, op2(e24, e23) = e23, yields: % 8.44/2.52 | (220) e24 = e23 % 8.44/2.52 | % 8.44/2.52 | Instantiating formula (46) with e23, e20, e20, e23 and discharging atoms op2(e23, e20) = e23, op2(e23, e20) = e20, yields: % 8.44/2.52 | (221) e23 = e20 % 8.44/2.52 | % 8.44/2.52 | Instantiating formula (46) with e22, e24, e24, e22 and discharging atoms op2(e22, e24) = e24, op2(e22, e24) = e22, yields: % 8.44/2.52 | (222) e24 = e22 % 8.44/2.52 | % 8.44/2.52 | Combining equations (222,220) yields a new equation: % 8.44/2.52 | (223) e23 = e22 % 8.44/2.52 | % 8.44/2.52 | Combining equations (223,221) yields a new equation: % 8.44/2.52 | (224) e22 = e20 % 8.44/2.52 | % 8.44/2.52 | Simplifying 224 yields: % 8.44/2.52 | (225) e22 = e20 % 8.44/2.52 | % 8.44/2.52 | Equations (225) can reduce 152 to: % 8.44/2.52 | (202) $false % 8.44/2.52 | % 8.44/2.52 |-The branch is then unsatisfiable % 8.44/2.52 |-Branch two: % 8.44/2.52 | (281) ~ (all_0_6_6 = e24) % 8.44/2.52 | (282) all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21 % 8.44/2.52 | % 8.44/2.52 +-Applying beta-rule and splitting (128), into two cases. % 8.44/2.52 |-Branch one: % 8.44/2.52 | (283) all_0_8_8 = e24 % 8.44/2.52 | % 8.44/2.52 | From (283)(283) and (95) follows: % 8.44/2.52 | (284) op2(e24, e24) = all_0_5_5 % 8.44/2.52 | % 8.44/2.52 | Instantiating formula (46) with e24, e24, all_0_5_5, e20 and discharging atoms op2(e24, e24) = all_0_5_5, op2(e24, e24) = e20, yields: % 8.44/2.52 | (285) all_0_5_5 = e20 % 8.44/2.52 | % 8.44/2.52 | From (285) and (149) follows: % 8.44/2.52 | (286) j(e20) = e14 % 8.44/2.52 | % 8.44/2.52 | Instantiating formula (101) with e20, e14, all_0_4_4 and discharging atoms j(e20) = all_0_4_4, j(e20) = e14, yields: % 8.44/2.52 | (235) all_0_4_4 = e14 % 8.44/2.52 | % 8.44/2.52 | Equations (235) can reduce 257 to: % 8.44/2.52 | (202) $false % 8.44/2.52 | % 8.44/2.52 |-The branch is then unsatisfiable % 8.44/2.52 |-Branch two: % 8.44/2.52 | (289) ~ (all_0_8_8 = e24) % 8.44/2.52 | (290) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21 % 8.44/2.52 | % 8.44/2.52 +-Applying beta-rule and splitting (204), into two cases. % 8.44/2.52 |-Branch one: % 8.44/2.52 | (291) all_0_0_0 = e13 % 8.44/2.52 | % 8.44/2.52 | From (291) and (19) follows: % 8.44/2.52 | (292) h(e13) = e24 % 8.44/2.52 | % 8.44/2.52 | Instantiating formula (96) with e13, e24, all_0_6_6 and discharging atoms h(e13) = all_0_6_6, h(e13) = e24, yields: % 8.44/2.52 | (259) all_0_6_6 = e24 % 8.44/2.52 | % 8.44/2.52 | Equations (259) can reduce 281 to: % 8.44/2.52 | (202) $false % 8.44/2.52 | % 8.44/2.52 |-The branch is then unsatisfiable % 8.44/2.52 |-Branch two: % 8.44/2.52 | (295) ~ (all_0_0_0 = e13) % 8.44/2.52 | (296) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11 % 8.44/2.52 | % 8.44/2.52 +-Applying beta-rule and splitting (296), into two cases. % 8.44/2.52 |-Branch one: % 8.44/2.52 | (297) all_0_0_0 = e12 % 8.44/2.52 | % 8.44/2.52 | From (297) and (19) follows: % 8.44/2.52 | (298) h(e12) = e24 % 8.44/2.52 | % 8.44/2.52 | Instantiating formula (96) with e12, e24, all_0_7_7 and discharging atoms h(e12) = all_0_7_7, h(e12) = e24, yields: % 8.44/2.52 | (229) all_0_7_7 = e24 % 8.44/2.52 | % 8.44/2.52 | Equations (229) can reduce 233 to: % 8.44/2.52 | (202) $false % 8.44/2.52 | % 8.44/2.52 |-The branch is then unsatisfiable % 8.44/2.52 |-Branch two: % 8.44/2.52 | (301) ~ (all_0_0_0 = e12) % 8.44/2.52 | (302) all_0_0_0 = e10 | all_0_0_0 = e11 % 8.44/2.52 | % 8.44/2.52 +-Applying beta-rule and splitting (302), into two cases. % 8.44/2.52 |-Branch one: % 8.44/2.52 | (303) all_0_0_0 = e10 % 8.44/2.52 | % 8.44/2.52 | From (303) and (19) follows: % 8.44/2.52 | (304) h(e10) = e24 % 8.44/2.52 | % 8.44/2.52 | Instantiating formula (96) with e10, e24, all_0_9_9 and discharging atoms h(e10) = all_0_9_9, h(e10) = e24, yields: % 8.44/2.52 | (205) all_0_9_9 = e24 % 8.44/2.52 | % 8.44/2.52 | Equations (205) can reduce 227 to: % 8.44/2.52 | (202) $false % 8.44/2.52 | % 8.44/2.52 |-The branch is then unsatisfiable % 8.44/2.52 |-Branch two: % 8.44/2.52 | (307) ~ (all_0_0_0 = e10) % 8.44/2.52 | (241) all_0_0_0 = e11 % 8.44/2.53 | % 8.44/2.53 | From (241) and (19) follows: % 8.44/2.53 | (309) h(e11) = e24 % 8.44/2.53 | % 8.44/2.53 | Instantiating formula (96) with e11, e24, all_0_8_8 and discharging atoms h(e11) = all_0_8_8, h(e11) = e24, yields: % 8.44/2.53 | (283) all_0_8_8 = e24 % 8.44/2.53 | % 8.44/2.53 | Equations (283) can reduce 289 to: % 8.44/2.53 | (202) $false % 8.44/2.53 | % 8.44/2.53 |-The branch is then unsatisfiable % 8.44/2.53 % SZS output end Proof for theBenchmark % 8.44/2.53 % 8.44/2.53 1949ms %------------------------------------------------------------------------------