%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : ALG205+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n020.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 15:37:31 EDT 2022 % Result : Theorem 5.78s 1.94s % Output : Proof 13.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ALG205+1 : TPTP v8.1.0. Released v2.7.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n020.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 19:21:21 EDT 2022 % 0.12/0.33 % CPUTime : % 0.48/0.62 ____ _ % 0.48/0.62 ___ / __ \_____(_)___ ________ __________ % 0.48/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.48/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.48/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.48/0.62 % 0.48/0.62 A Theorem Prover for First-Order Logic % 0.65/0.63 (ePrincess v.1.0) % 0.65/0.63 % 0.65/0.63 (c) Philipp Rümmer, 2009-2015 % 0.65/0.63 (c) Peter Backeman, 2014-2015 % 0.65/0.63 (contributions by Angelo Brillout, Peter Baumgartner) % 0.65/0.63 Free software under GNU Lesser General Public License (LGPL). % 0.65/0.63 Bug reports to peter@backeman.se % 0.65/0.63 % 0.65/0.63 For more information, visit http://user.uu.se/~petba168/breu/ % 0.65/0.63 % 0.65/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.65/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.36/1.14 Prover 0: Preprocessing ... % 3.76/1.49 Prover 0: Constructing countermodel ... % 5.78/1.94 Prover 0: proved (1264ms) % 5.78/1.94 % 5.78/1.94 No countermodel exists, formula is valid % 5.78/1.94 % SZS status Theorem for theBenchmark % 5.78/1.94 % 5.78/1.94 Generating proof ... found it (size 112) % 12.17/3.45 % 12.17/3.45 % SZS output start Proof for theBenchmark % 12.17/3.45 Assumed formulas after preprocessing and simplification: % 12.17/3.45 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ( ~ (e26 = e25) & ~ (e26 = e24) & ~ (e26 = e23) & ~ (e26 = e22) & ~ (e26 = e20) & ~ (e26 = e21) & ~ (e26 = e16) & ~ (e26 = e15) & ~ (e26 = e14) & ~ (e26 = e13) & ~ (e26 = e12) & ~ (e26 = e10) & ~ (e26 = e11) & ~ (e25 = e24) & ~ (e25 = e23) & ~ (e25 = e22) & ~ (e25 = e20) & ~ (e25 = e21) & ~ (e25 = e16) & ~ (e25 = e15) & ~ (e25 = e14) & ~ (e25 = e13) & ~ (e25 = e12) & ~ (e25 = e10) & ~ (e25 = e11) & ~ (e24 = e23) & ~ (e24 = e22) & ~ (e24 = e20) & ~ (e24 = e21) & ~ (e24 = e16) & ~ (e24 = e15) & ~ (e24 = e14) & ~ (e24 = e13) & ~ (e24 = e12) & ~ (e24 = e10) & ~ (e24 = e11) & ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e23 = e16) & ~ (e23 = e15) & ~ (e23 = e14) & ~ (e23 = e13) & ~ (e23 = e12) & ~ (e23 = e10) & ~ (e23 = e11) & ~ (e22 = e20) & ~ (e22 = e21) & ~ (e22 = e16) & ~ (e22 = e15) & ~ (e22 = e14) & ~ (e22 = e13) & ~ (e22 = e12) & ~ (e22 = e10) & ~ (e22 = e11) & ~ (e20 = e21) & ~ (e20 = e16) & ~ (e20 = e15) & ~ (e20 = e14) & ~ (e20 = e13) & ~ (e20 = e12) & ~ (e20 = e10) & ~ (e20 = e11) & ~ (e21 = e16) & ~ (e21 = e15) & ~ (e21 = e14) & ~ (e21 = e13) & ~ (e21 = e12) & ~ (e21 = e10) & ~ (e21 = e11) & ~ (e16 = e15) & ~ (e16 = e14) & ~ (e16 = e13) & ~ (e16 = e12) & ~ (e16 = e10) & ~ (e16 = e11) & ~ (e15 = e14) & ~ (e15 = e13) & ~ (e15 = e12) & ~ (e15 = e10) & ~ (e15 = e11) & ~ (e14 = e13) & ~ (e14 = e12) & ~ (e14 = e10) & ~ (e14 = e11) & ~ (e13 = e12) & ~ (e13 = e10) & ~ (e13 = e11) & ~ (e12 = e10) & ~ (e12 = e11) & ~ (e10 = e11) & op2(v6, v6) = v0 & op2(v6, v5) = v6 & op2(v6, v4) = v1 & op2(v6, v3) = v3 & op2(v6, v2) = v4 & op2(v6, v1) = v2 & op2(v6, v0) = v5 & op2(v5, v6) = v6 & op2(v5, v5) = v1 & op2(v5, v4) = v5 & op2(v5, v3) = v0 & op2(v5, v2) = v3 & op2(v5, v1) = v4 & op2(v5, v0) = v2 & op2(v4, v6) = v1 & op2(v4, v5) = v5 & op2(v4, v4) = v2 & op2(v4, v3) = v6 & op2(v4, v2) = v0 & op2(v4, v1) = v3 & op2(v4, v0) = v4 & op2(v3, v6) = v3 & op2(v3, v5) = v0 & op2(v3, v4) = v6 & op2(v3, v3) = v4 & op2(v3, v2) = v2 & op2(v3, v1) = v5 & op2(v3, v0) = v1 & op2(v2, v6) = v4 & op2(v2, v5) = v3 & op2(v2, v4) = v0 & op2(v2, v3) = v2 & op2(v2, v2) = v5 & op2(v2, v1) = v1 & op2(v2, v0) = v6 & op2(v1, v6) = v2 & op2(v1, v5) = v4 & op2(v1, v4) = v3 & op2(v1, v3) = v5 & op2(v1, v2) = v1 & op2(v1, v1) = v6 & op2(v1, v0) = v0 & op2(v0, v6) = v5 & op2(v0, v5) = v2 & op2(v0, v4) = v4 & op2(v0, v3) = v1 & op2(v0, v2) = v6 & op2(v0, v1) = v0 & op2(v0, v0) = v3 & op2(e26, e26) = e25 & op2(e26, e25) = e20 & op2(e26, e24) = e21 & op2(e26, e23) = e24 & op2(e26, e22) = e22 & op2(e26, e20) = e26 & op2(e26, e21) = e23 & op2(e25, e26) = e20 & op2(e25, e25) = e21 & op2(e25, e24) = e26 & op2(e25, e23) = e23 & op2(e25, e22) = e25 & op2(e25, e20) = e24 & op2(e25, e21) = e22 & op2(e24, e26) = e21 & op2(e24, e25) = e26 & op2(e24, e24) = e24 & op2(e24, e23) = e22 & op2(e24, e22) = e20 & op2(e24, e20) = e23 & op2(e24, e21) = e25 & op2(e23, e26) = e24 & op2(e23, e25) = e23 & op2(e23, e24) = e22 & op2(e23, e23) = e20 & op2(e23, e22) = e26 & op2(e23, e20) = e25 & op2(e23, e21) = e21 & op2(e22, e26) = e22 & op2(e22, e25) = e25 & op2(e22, e24) = e20 & op2(e22, e23) = e26 & op2(e22, e22) = e23 & op2(e22, e20) = e21 & op2(e22, e21) = e24 & op2(e20, e26) = e26 & op2(e20, e25) = e24 & op2(e20, e24) = e23 & op2(e20, e23) = e25 & op2(e20, e22) = e21 & op2(e20, e20) = e22 & op2(e20, e21) = e20 & op2(e21, e26) = e23 & op2(e21, e25) = e22 & op2(e21, e24) = e25 & op2(e21, e23) = e21 & op2(e21, e22) = e24 & op2(e21, e20) = e20 & op2(e21, e21) = e26 & op1(v13, v13) = v12 & op1(v13, v12) = v7 & op1(v13, v11) = v8 & op1(v13, v10) = v11 & op1(v13, v9) = v9 & op1(v13, v8) = v10 & op1(v13, v7) = v13 & op1(v12, v13) = v7 & op1(v12, v12) = v8 & op1(v12, v11) = v13 & op1(v12, v10) = v10 & op1(v12, v9) = v12 & op1(v12, v8) = v9 & op1(v12, v7) = v11 & op1(v11, v13) = v8 & op1(v11, v12) = v13 & op1(v11, v11) = v11 & op1(v11, v10) = v9 & op1(v11, v9) = v7 & op1(v11, v8) = v12 & op1(v11, v7) = v10 & op1(v10, v13) = v11 & op1(v10, v12) = v10 & op1(v10, v11) = v9 & op1(v10, v10) = v7 & op1(v10, v9) = v13 & op1(v10, v8) = v8 & op1(v10, v7) = v12 & op1(v9, v13) = v9 & op1(v9, v12) = v12 & op1(v9, v11) = v7 & op1(v9, v10) = v13 & op1(v9, v9) = v10 & op1(v9, v8) = v11 & op1(v9, v7) = v8 & op1(v8, v13) = v10 & op1(v8, v12) = v9 & op1(v8, v11) = v12 & op1(v8, v10) = v8 & op1(v8, v9) = v11 & op1(v8, v8) = v13 & op1(v8, v7) = v7 & op1(v7, v13) = v13 & op1(v7, v12) = v11 & op1(v7, v11) = v10 & op1(v7, v10) = v12 & op1(v7, v9) = v8 & op1(v7, v8) = v7 & op1(v7, v7) = v9 & op1(e16, e16) = e10 & op1(e16, e15) = e16 & op1(e16, e14) = e11 & op1(e16, e13) = e13 & op1(e16, e12) = e14 & op1(e16, e10) = e15 & op1(e16, e11) = e12 & op1(e15, e16) = e16 & op1(e15, e15) = e11 & op1(e15, e14) = e15 & op1(e15, e13) = e10 & op1(e15, e12) = e13 & op1(e15, e10) = e12 & op1(e15, e11) = e14 & op1(e14, e16) = e11 & op1(e14, e15) = e15 & op1(e14, e14) = e12 & op1(e14, e13) = e16 & op1(e14, e12) = e10 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e16) = e13 & op1(e13, e15) = e10 & op1(e13, e14) = e16 & op1(e13, e13) = e14 & op1(e13, e12) = e12 & op1(e13, e10) = e11 & op1(e13, e11) = e15 & op1(e12, e16) = e14 & op1(e12, e15) = e13 & op1(e12, e14) = e10 & op1(e12, e13) = e12 & op1(e12, e12) = e15 & op1(e12, e10) = e16 & op1(e12, e11) = e11 & op1(e10, e16) = e15 & op1(e10, e15) = e12 & op1(e10, e14) = e14 & op1(e10, e13) = e11 & op1(e10, e12) = e16 & op1(e10, e10) = e13 & op1(e10, e11) = e10 & op1(e11, e16) = e12 & op1(e11, e15) = e14 & op1(e11, e14) = e13 & op1(e11, e13) = e15 & op1(e11, e12) = e11 & op1(e11, e10) = e10 & op1(e11, e11) = e16 & h(v13) = e26 & h(v12) = e25 & h(v11) = e24 & h(v10) = e23 & h(v9) = e22 & h(v8) = e21 & h(v7) = e20 & h(e16) = v6 & h(e15) = v5 & h(e14) = v4 & h(e13) = v3 & h(e12) = v2 & h(e10) = v0 & h(e11) = v1 & j(v6) = e16 & j(v5) = e15 & j(v4) = e14 & j(v3) = e13 & j(v2) = e12 & j(v1) = e11 & j(v0) = e10 & j(e26) = v13 & j(e25) = v12 & j(e24) = v11 & j(e23) = v10 & j(e22) = v9 & j(e20) = v7 & j(e21) = v8 & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (op2(v17, v16) = v15) | ~ (op2(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (op1(v17, v16) = v15) | ~ (op1(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (h(v16) = v15) | ~ (h(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (j(v16) = v15) | ~ (j(v16) = v14)) & (v13 = e16 | v13 = e15 | v13 = e14 | v13 = e13 | v13 = e12 | v13 = e10 | v13 = e11) & (v12 = e16 | v12 = e15 | v12 = e14 | v12 = e13 | v12 = e12 | v12 = e10 | v12 = e11) & (v11 = e16 | v11 = e15 | v11 = e14 | v11 = e13 | v11 = e12 | v11 = e10 | v11 = e11) & (v10 = e16 | v10 = e15 | v10 = e14 | v10 = e13 | v10 = e12 | v10 = e10 | v10 = e11) & (v9 = e16 | v9 = e15 | v9 = e14 | v9 = e13 | v9 = e12 | v9 = e10 | v9 = e11) & (v8 = e16 | v8 = e15 | v8 = e14 | v8 = e13 | v8 = e12 | v8 = e10 | v8 = e11) & (v7 = e16 | v7 = e15 | v7 = e14 | v7 = e13 | v7 = e12 | v7 = e10 | v7 = e11) & (v6 = e26 | v6 = e25 | v6 = e24 | v6 = e23 | v6 = e22 | v6 = e20 | v6 = e21) & (v5 = e26 | v5 = e25 | v5 = e24 | v5 = e23 | v5 = e22 | v5 = e20 | v5 = e21) & (v4 = e26 | v4 = e25 | v4 = e24 | v4 = e23 | v4 = e22 | v4 = e20 | v4 = e21) & (v3 = e26 | v3 = e25 | v3 = e24 | v3 = e23 | v3 = e22 | v3 = e20 | v3 = e21) & (v2 = e26 | v2 = e25 | v2 = e24 | v2 = e23 | v2 = e22 | v2 = e20 | v2 = e21) & (v1 = e26 | v1 = e25 | v1 = e24 | v1 = e23 | v1 = e22 | v1 = e20 | v1 = e21) & (v0 = e26 | v0 = e25 | v0 = e24 | v0 = e23 | v0 = e22 | v0 = e20 | v0 = e21)) % 12.50/3.51 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13 yields: % 12.50/3.51 | (1) ~ (e26 = e25) & ~ (e26 = e24) & ~ (e26 = e23) & ~ (e26 = e22) & ~ (e26 = e20) & ~ (e26 = e21) & ~ (e26 = e16) & ~ (e26 = e15) & ~ (e26 = e14) & ~ (e26 = e13) & ~ (e26 = e12) & ~ (e26 = e10) & ~ (e26 = e11) & ~ (e25 = e24) & ~ (e25 = e23) & ~ (e25 = e22) & ~ (e25 = e20) & ~ (e25 = e21) & ~ (e25 = e16) & ~ (e25 = e15) & ~ (e25 = e14) & ~ (e25 = e13) & ~ (e25 = e12) & ~ (e25 = e10) & ~ (e25 = e11) & ~ (e24 = e23) & ~ (e24 = e22) & ~ (e24 = e20) & ~ (e24 = e21) & ~ (e24 = e16) & ~ (e24 = e15) & ~ (e24 = e14) & ~ (e24 = e13) & ~ (e24 = e12) & ~ (e24 = e10) & ~ (e24 = e11) & ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e23 = e16) & ~ (e23 = e15) & ~ (e23 = e14) & ~ (e23 = e13) & ~ (e23 = e12) & ~ (e23 = e10) & ~ (e23 = e11) & ~ (e22 = e20) & ~ (e22 = e21) & ~ (e22 = e16) & ~ (e22 = e15) & ~ (e22 = e14) & ~ (e22 = e13) & ~ (e22 = e12) & ~ (e22 = e10) & ~ (e22 = e11) & ~ (e20 = e21) & ~ (e20 = e16) & ~ (e20 = e15) & ~ (e20 = e14) & ~ (e20 = e13) & ~ (e20 = e12) & ~ (e20 = e10) & ~ (e20 = e11) & ~ (e21 = e16) & ~ (e21 = e15) & ~ (e21 = e14) & ~ (e21 = e13) & ~ (e21 = e12) & ~ (e21 = e10) & ~ (e21 = e11) & ~ (e16 = e15) & ~ (e16 = e14) & ~ (e16 = e13) & ~ (e16 = e12) & ~ (e16 = e10) & ~ (e16 = e11) & ~ (e15 = e14) & ~ (e15 = e13) & ~ (e15 = e12) & ~ (e15 = e10) & ~ (e15 = e11) & ~ (e14 = e13) & ~ (e14 = e12) & ~ (e14 = e10) & ~ (e14 = e11) & ~ (e13 = e12) & ~ (e13 = e10) & ~ (e13 = e11) & ~ (e12 = e10) & ~ (e12 = e11) & ~ (e10 = e11) & op2(all_0_7_7, all_0_7_7) = all_0_13_13 & op2(all_0_7_7, all_0_8_8) = all_0_7_7 & op2(all_0_7_7, all_0_9_9) = all_0_12_12 & op2(all_0_7_7, all_0_10_10) = all_0_10_10 & op2(all_0_7_7, all_0_11_11) = all_0_9_9 & op2(all_0_7_7, all_0_12_12) = all_0_11_11 & op2(all_0_7_7, all_0_13_13) = all_0_8_8 & op2(all_0_8_8, all_0_7_7) = all_0_7_7 & op2(all_0_8_8, all_0_8_8) = all_0_12_12 & op2(all_0_8_8, all_0_9_9) = all_0_8_8 & op2(all_0_8_8, all_0_10_10) = all_0_13_13 & op2(all_0_8_8, all_0_11_11) = all_0_10_10 & op2(all_0_8_8, all_0_12_12) = all_0_9_9 & op2(all_0_8_8, all_0_13_13) = all_0_11_11 & op2(all_0_9_9, all_0_7_7) = all_0_12_12 & op2(all_0_9_9, all_0_8_8) = all_0_8_8 & op2(all_0_9_9, all_0_9_9) = all_0_11_11 & op2(all_0_9_9, all_0_10_10) = all_0_7_7 & op2(all_0_9_9, all_0_11_11) = all_0_13_13 & op2(all_0_9_9, all_0_12_12) = all_0_10_10 & op2(all_0_9_9, all_0_13_13) = all_0_9_9 & op2(all_0_10_10, all_0_7_7) = all_0_10_10 & op2(all_0_10_10, all_0_8_8) = all_0_13_13 & op2(all_0_10_10, all_0_9_9) = all_0_7_7 & op2(all_0_10_10, all_0_10_10) = all_0_9_9 & op2(all_0_10_10, all_0_11_11) = all_0_11_11 & op2(all_0_10_10, all_0_12_12) = all_0_8_8 & op2(all_0_10_10, all_0_13_13) = all_0_12_12 & op2(all_0_11_11, all_0_7_7) = all_0_9_9 & op2(all_0_11_11, all_0_8_8) = all_0_10_10 & op2(all_0_11_11, all_0_9_9) = all_0_13_13 & op2(all_0_11_11, all_0_10_10) = all_0_11_11 & op2(all_0_11_11, all_0_11_11) = all_0_8_8 & op2(all_0_11_11, all_0_12_12) = all_0_12_12 & op2(all_0_11_11, all_0_13_13) = all_0_7_7 & op2(all_0_12_12, all_0_7_7) = all_0_11_11 & op2(all_0_12_12, all_0_8_8) = all_0_9_9 & op2(all_0_12_12, all_0_9_9) = all_0_10_10 & op2(all_0_12_12, all_0_10_10) = all_0_8_8 & op2(all_0_12_12, all_0_11_11) = all_0_12_12 & op2(all_0_12_12, all_0_12_12) = all_0_7_7 & op2(all_0_12_12, all_0_13_13) = all_0_13_13 & op2(all_0_13_13, all_0_7_7) = all_0_8_8 & op2(all_0_13_13, all_0_8_8) = all_0_11_11 & op2(all_0_13_13, all_0_9_9) = all_0_9_9 & op2(all_0_13_13, all_0_10_10) = all_0_12_12 & op2(all_0_13_13, all_0_11_11) = all_0_7_7 & op2(all_0_13_13, all_0_12_12) = all_0_13_13 & op2(all_0_13_13, all_0_13_13) = all_0_10_10 & op2(e26, e26) = e25 & op2(e26, e25) = e20 & op2(e26, e24) = e21 & op2(e26, e23) = e24 & op2(e26, e22) = e22 & op2(e26, e20) = e26 & op2(e26, e21) = e23 & op2(e25, e26) = e20 & op2(e25, e25) = e21 & op2(e25, e24) = e26 & op2(e25, e23) = e23 & op2(e25, e22) = e25 & op2(e25, e20) = e24 & op2(e25, e21) = e22 & op2(e24, e26) = e21 & op2(e24, e25) = e26 & op2(e24, e24) = e24 & op2(e24, e23) = e22 & op2(e24, e22) = e20 & op2(e24, e20) = e23 & op2(e24, e21) = e25 & op2(e23, e26) = e24 & op2(e23, e25) = e23 & op2(e23, e24) = e22 & op2(e23, e23) = e20 & op2(e23, e22) = e26 & op2(e23, e20) = e25 & op2(e23, e21) = e21 & op2(e22, e26) = e22 & op2(e22, e25) = e25 & op2(e22, e24) = e20 & op2(e22, e23) = e26 & op2(e22, e22) = e23 & op2(e22, e20) = e21 & op2(e22, e21) = e24 & op2(e20, e26) = e26 & op2(e20, e25) = e24 & op2(e20, e24) = e23 & op2(e20, e23) = e25 & op2(e20, e22) = e21 & op2(e20, e20) = e22 & op2(e20, e21) = e20 & op2(e21, e26) = e23 & op2(e21, e25) = e22 & op2(e21, e24) = e25 & op2(e21, e23) = e21 & op2(e21, e22) = e24 & op2(e21, e20) = e20 & op2(e21, e21) = e26 & op1(all_0_0_0, all_0_0_0) = all_0_1_1 & op1(all_0_0_0, all_0_1_1) = all_0_6_6 & op1(all_0_0_0, all_0_2_2) = all_0_5_5 & op1(all_0_0_0, all_0_3_3) = all_0_2_2 & op1(all_0_0_0, all_0_4_4) = all_0_4_4 & op1(all_0_0_0, all_0_5_5) = all_0_3_3 & op1(all_0_0_0, all_0_6_6) = all_0_0_0 & op1(all_0_1_1, all_0_0_0) = all_0_6_6 & op1(all_0_1_1, all_0_1_1) = all_0_5_5 & op1(all_0_1_1, all_0_2_2) = all_0_0_0 & op1(all_0_1_1, all_0_3_3) = all_0_3_3 & op1(all_0_1_1, all_0_4_4) = all_0_1_1 & op1(all_0_1_1, all_0_5_5) = all_0_4_4 & op1(all_0_1_1, all_0_6_6) = all_0_2_2 & op1(all_0_2_2, all_0_0_0) = all_0_5_5 & op1(all_0_2_2, all_0_1_1) = all_0_0_0 & op1(all_0_2_2, all_0_2_2) = all_0_2_2 & op1(all_0_2_2, all_0_3_3) = all_0_4_4 & op1(all_0_2_2, all_0_4_4) = all_0_6_6 & op1(all_0_2_2, all_0_5_5) = all_0_1_1 & op1(all_0_2_2, all_0_6_6) = all_0_3_3 & op1(all_0_3_3, all_0_0_0) = all_0_2_2 & op1(all_0_3_3, all_0_1_1) = all_0_3_3 & op1(all_0_3_3, all_0_2_2) = all_0_4_4 & op1(all_0_3_3, all_0_3_3) = all_0_6_6 & op1(all_0_3_3, all_0_4_4) = all_0_0_0 & op1(all_0_3_3, all_0_5_5) = all_0_5_5 & op1(all_0_3_3, all_0_6_6) = all_0_1_1 & op1(all_0_4_4, all_0_0_0) = all_0_4_4 & op1(all_0_4_4, all_0_1_1) = all_0_1_1 & op1(all_0_4_4, all_0_2_2) = all_0_6_6 & op1(all_0_4_4, all_0_3_3) = all_0_0_0 & op1(all_0_4_4, all_0_4_4) = all_0_3_3 & op1(all_0_4_4, all_0_5_5) = all_0_2_2 & op1(all_0_4_4, all_0_6_6) = all_0_5_5 & op1(all_0_5_5, all_0_0_0) = all_0_3_3 & op1(all_0_5_5, all_0_1_1) = all_0_4_4 & op1(all_0_5_5, all_0_2_2) = all_0_1_1 & op1(all_0_5_5, all_0_3_3) = all_0_5_5 & op1(all_0_5_5, all_0_4_4) = all_0_2_2 & op1(all_0_5_5, all_0_5_5) = all_0_0_0 & op1(all_0_5_5, all_0_6_6) = all_0_6_6 & op1(all_0_6_6, all_0_0_0) = all_0_0_0 & op1(all_0_6_6, all_0_1_1) = all_0_2_2 & op1(all_0_6_6, all_0_2_2) = all_0_3_3 & op1(all_0_6_6, all_0_3_3) = all_0_1_1 & op1(all_0_6_6, all_0_4_4) = all_0_5_5 & op1(all_0_6_6, all_0_5_5) = all_0_6_6 & op1(all_0_6_6, all_0_6_6) = all_0_4_4 & op1(e16, e16) = e10 & op1(e16, e15) = e16 & op1(e16, e14) = e11 & op1(e16, e13) = e13 & op1(e16, e12) = e14 & op1(e16, e10) = e15 & op1(e16, e11) = e12 & op1(e15, e16) = e16 & op1(e15, e15) = e11 & op1(e15, e14) = e15 & op1(e15, e13) = e10 & op1(e15, e12) = e13 & op1(e15, e10) = e12 & op1(e15, e11) = e14 & op1(e14, e16) = e11 & op1(e14, e15) = e15 & op1(e14, e14) = e12 & op1(e14, e13) = e16 & op1(e14, e12) = e10 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e16) = e13 & op1(e13, e15) = e10 & op1(e13, e14) = e16 & op1(e13, e13) = e14 & op1(e13, e12) = e12 & op1(e13, e10) = e11 & op1(e13, e11) = e15 & op1(e12, e16) = e14 & op1(e12, e15) = e13 & op1(e12, e14) = e10 & op1(e12, e13) = e12 & op1(e12, e12) = e15 & op1(e12, e10) = e16 & op1(e12, e11) = e11 & op1(e10, e16) = e15 & op1(e10, e15) = e12 & op1(e10, e14) = e14 & op1(e10, e13) = e11 & op1(e10, e12) = e16 & op1(e10, e10) = e13 & op1(e10, e11) = e10 & op1(e11, e16) = e12 & op1(e11, e15) = e14 & op1(e11, e14) = e13 & op1(e11, e13) = e15 & op1(e11, e12) = e11 & op1(e11, e10) = e10 & op1(e11, e11) = e16 & h(all_0_0_0) = e26 & h(all_0_1_1) = e25 & h(all_0_2_2) = e24 & h(all_0_3_3) = e23 & h(all_0_4_4) = e22 & h(all_0_5_5) = e21 & h(all_0_6_6) = e20 & h(e16) = all_0_7_7 & h(e15) = all_0_8_8 & h(e14) = all_0_9_9 & h(e13) = all_0_10_10 & h(e12) = all_0_11_11 & h(e10) = all_0_13_13 & h(e11) = all_0_12_12 & j(all_0_7_7) = e16 & j(all_0_8_8) = e15 & j(all_0_9_9) = e14 & j(all_0_10_10) = e13 & j(all_0_11_11) = e12 & j(all_0_12_12) = e11 & j(all_0_13_13) = e10 & j(e26) = all_0_0_0 & j(e25) = all_0_1_1 & j(e24) = all_0_2_2 & j(e23) = all_0_3_3 & j(e22) = all_0_4_4 & j(e20) = all_0_6_6 & j(e21) = all_0_5_5 & ! [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 = e16 | all_0_0_0 = e15 | 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 = e16 | all_0_1_1 = e15 | 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 = e16 | all_0_2_2 = e15 | 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 = e16 | all_0_3_3 = e15 | 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 = e16 | all_0_4_4 = e15 | 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 = e16 | all_0_5_5 = e15 | all_0_5_5 = e14 | all_0_5_5 = e13 | all_0_5_5 = e12 | all_0_5_5 = e10 | all_0_5_5 = e11) & (all_0_6_6 = e16 | all_0_6_6 = e15 | all_0_6_6 = e14 | all_0_6_6 = e13 | all_0_6_6 = e12 | all_0_6_6 = e10 | all_0_6_6 = e11) & (all_0_7_7 = e26 | all_0_7_7 = e25 | 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 = e26 | all_0_8_8 = e25 | 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 = e26 | all_0_9_9 = e25 | 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) & (all_0_10_10 = e26 | all_0_10_10 = e25 | all_0_10_10 = e24 | all_0_10_10 = e23 | all_0_10_10 = e22 | all_0_10_10 = e20 | all_0_10_10 = e21) & (all_0_11_11 = e26 | all_0_11_11 = e25 | all_0_11_11 = e24 | all_0_11_11 = e23 | all_0_11_11 = e22 | all_0_11_11 = e20 | all_0_11_11 = e21) & (all_0_12_12 = e26 | all_0_12_12 = e25 | all_0_12_12 = e24 | all_0_12_12 = e23 | all_0_12_12 = e22 | all_0_12_12 = e20 | all_0_12_12 = e21) & (all_0_13_13 = e26 | all_0_13_13 = e25 | all_0_13_13 = e24 | all_0_13_13 = e23 | all_0_13_13 = e22 | all_0_13_13 = e20 | all_0_13_13 = e21) % 12.50/3.53 | % 12.50/3.53 | Applying alpha-rule on (1) yields: % 12.50/3.53 | (2) ~ (e21 = e13) % 12.50/3.53 | (3) ~ (e24 = e10) % 12.50/3.53 | (4) op1(e10, e12) = e16 % 12.50/3.53 | (5) op1(all_0_5_5, all_0_3_3) = all_0_5_5 % 12.50/3.53 | (6) ~ (e21 = e16) % 12.50/3.53 | (7) ~ (e16 = e14) % 12.50/3.53 | (8) j(all_0_10_10) = e13 % 12.50/3.53 | (9) op2(all_0_11_11, all_0_13_13) = all_0_7_7 % 12.50/3.53 | (10) op1(e15, e14) = e15 % 12.50/3.53 | (11) op2(all_0_10_10, all_0_12_12) = all_0_8_8 % 12.50/3.53 | (12) op1(e11, e15) = e14 % 12.50/3.53 | (13) j(e26) = all_0_0_0 % 12.50/3.54 | (14) all_0_3_3 = e16 | all_0_3_3 = e15 | 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 % 12.50/3.54 | (15) op1(e10, e13) = e11 % 12.50/3.54 | (16) ~ (e25 = e24) % 12.50/3.54 | (17) op1(e13, e14) = e16 % 12.50/3.54 | (18) j(e22) = all_0_4_4 % 12.50/3.54 | (19) all_0_0_0 = e16 | all_0_0_0 = e15 | 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 % 12.50/3.54 | (20) ~ (e23 = e16) % 12.50/3.54 | (21) op1(all_0_2_2, all_0_3_3) = all_0_4_4 % 12.50/3.54 | (22) op1(all_0_3_3, all_0_1_1) = all_0_3_3 % 12.50/3.54 | (23) op2(all_0_9_9, all_0_11_11) = all_0_13_13 % 12.50/3.54 | (24) ~ (e12 = e11) % 12.50/3.54 | (25) op1(e14, e10) = e14 % 12.50/3.54 | (26) ~ (e20 = e21) % 12.50/3.54 | (27) op1(all_0_1_1, all_0_0_0) = all_0_6_6 % 12.50/3.54 | (28) ~ (e21 = e12) % 12.50/3.54 | (29) op2(all_0_7_7, all_0_8_8) = all_0_7_7 % 12.50/3.54 | (30) all_0_13_13 = e26 | all_0_13_13 = e25 | all_0_13_13 = e24 | all_0_13_13 = e23 | all_0_13_13 = e22 | all_0_13_13 = e20 | all_0_13_13 = e21 % 12.50/3.54 | (31) op2(e26, e25) = e20 % 12.50/3.54 | (32) op1(all_0_5_5, all_0_0_0) = all_0_3_3 % 12.50/3.54 | (33) ~ (e14 = e12) % 12.50/3.54 | (34) ~ (e25 = e14) % 12.50/3.54 | (35) ~ (e24 = e20) % 12.50/3.54 | (36) h(e16) = all_0_7_7 % 12.50/3.54 | (37) op2(all_0_12_12, all_0_12_12) = all_0_7_7 % 12.50/3.54 | (38) ~ (e26 = e10) % 12.50/3.54 | (39) ~ (e26 = e25) % 12.50/3.54 | (40) op1(e13, e11) = e15 % 12.50/3.54 | (41) op2(e23, e22) = e26 % 12.50/3.54 | (42) ~ (e16 = e13) % 12.50/3.54 | (43) op1(all_0_6_6, all_0_1_1) = all_0_2_2 % 12.50/3.54 | (44) op2(all_0_7_7, all_0_12_12) = all_0_11_11 % 12.50/3.54 | (45) j(all_0_11_11) = e12 % 12.50/3.54 | (46) ~ (e24 = e23) % 12.50/3.54 | (47) op2(all_0_13_13, all_0_7_7) = all_0_8_8 % 12.50/3.54 | (48) op1(all_0_4_4, all_0_2_2) = all_0_6_6 % 12.50/3.54 | (49) op1(e15, e15) = e11 % 12.50/3.54 | (50) op1(e11, e11) = e16 % 12.50/3.54 | (51) op1(all_0_0_0, all_0_0_0) = all_0_1_1 % 12.50/3.54 | (52) op2(e26, e20) = e26 % 12.50/3.54 | (53) op2(all_0_11_11, all_0_11_11) = all_0_8_8 % 12.50/3.54 | (54) ~ (e26 = e14) % 12.50/3.54 | (55) op2(e20, e26) = e26 % 12.50/3.54 | (56) op1(e10, e11) = e10 % 12.50/3.54 | (57) ~ (e22 = e21) % 12.50/3.54 | (58) ~ (e24 = e22) % 12.50/3.54 | (59) op2(e20, e20) = e22 % 12.50/3.54 | (60) op2(e22, e23) = e26 % 12.50/3.54 | (61) op1(e10, e16) = e15 % 12.50/3.54 | (62) op1(all_0_5_5, all_0_4_4) = all_0_2_2 % 12.50/3.54 | (63) op2(e20, e24) = e23 % 12.50/3.54 | (64) ~ (e20 = e14) % 12.50/3.54 | (65) ~ (e16 = e10) % 12.50/3.54 | (66) op2(e20, e22) = e21 % 12.50/3.54 | (67) ~ (e25 = e20) % 12.50/3.54 | (68) op1(all_0_6_6, all_0_2_2) = all_0_3_3 % 12.50/3.54 | (69) op1(all_0_0_0, all_0_5_5) = all_0_3_3 % 12.50/3.54 | (70) op2(e23, e21) = e21 % 12.50/3.54 | (71) h(all_0_4_4) = e22 % 12.50/3.54 | (72) op2(all_0_9_9, all_0_9_9) = all_0_11_11 % 12.50/3.54 | (73) h(all_0_2_2) = e24 % 12.50/3.54 | (74) op1(e14, e14) = e12 % 12.50/3.54 | (75) op2(all_0_13_13, all_0_12_12) = all_0_13_13 % 12.50/3.54 | (76) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) % 12.50/3.54 | (77) ~ (e24 = e14) % 12.50/3.54 | (78) h(e15) = all_0_8_8 % 12.50/3.54 | (79) op1(e15, e11) = e14 % 12.50/3.54 | (80) ~ (e20 = e10) % 12.50/3.54 | (81) op1(all_0_1_1, all_0_5_5) = all_0_4_4 % 12.50/3.54 | (82) op2(e21, e25) = e22 % 12.50/3.54 | (83) j(all_0_9_9) = e14 % 12.50/3.54 | (84) op1(e12, e14) = e10 % 12.50/3.54 | (85) ~ (e26 = e24) % 12.50/3.54 | (86) op2(all_0_13_13, all_0_13_13) = all_0_10_10 % 12.50/3.55 | (87) op2(e23, e24) = e22 % 12.50/3.55 | (88) h(all_0_6_6) = e20 % 12.50/3.55 | (89) op1(e12, e16) = e14 % 12.50/3.55 | (90) op2(e25, e21) = e22 % 12.50/3.55 | (91) op1(all_0_6_6, all_0_6_6) = all_0_4_4 % 12.50/3.55 | (92) ~ (e22 = e14) % 12.50/3.55 | (93) op2(all_0_12_12, all_0_9_9) = all_0_10_10 % 12.50/3.55 | (94) op2(all_0_12_12, all_0_7_7) = all_0_11_11 % 12.50/3.55 | (95) op2(all_0_10_10, all_0_13_13) = all_0_12_12 % 12.50/3.55 | (96) op1(all_0_4_4, all_0_4_4) = all_0_3_3 % 12.50/3.55 | (97) ~ (e25 = e13) % 12.50/3.55 | (98) h(all_0_0_0) = e26 % 12.50/3.55 | (99) ~ (e15 = e14) % 12.50/3.55 | (100) op1(e15, e10) = e12 % 12.50/3.55 | (101) ~ (e20 = e16) % 12.50/3.55 | (102) ~ (e22 = e20) % 12.50/3.55 | (103) ~ (e25 = e11) % 12.50/3.55 | (104) ~ (e16 = e12) % 12.50/3.55 | (105) op1(all_0_2_2, all_0_4_4) = all_0_6_6 % 12.50/3.55 | (106) op2(e26, e22) = e22 % 12.50/3.55 | (107) ~ (e24 = e15) % 12.50/3.55 | (108) op1(all_0_2_2, all_0_1_1) = all_0_0_0 % 12.50/3.55 | (109) ~ (e15 = e12) % 12.50/3.55 | (110) op2(all_0_10_10, all_0_8_8) = all_0_13_13 % 12.50/3.55 | (111) ~ (e26 = e20) % 12.50/3.55 | (112) j(all_0_8_8) = e15 % 12.50/3.55 | (113) op2(all_0_13_13, all_0_9_9) = all_0_9_9 % 12.50/3.55 | (114) j(e23) = all_0_3_3 % 12.50/3.55 | (115) op2(all_0_13_13, all_0_8_8) = all_0_11_11 % 12.50/3.55 | (116) op2(all_0_9_9, all_0_8_8) = all_0_8_8 % 12.50/3.55 | (117) j(e25) = all_0_1_1 % 12.50/3.55 | (118) op1(all_0_3_3, all_0_0_0) = all_0_2_2 % 12.50/3.55 | (119) op1(all_0_4_4, all_0_6_6) = all_0_5_5 % 12.50/3.55 | (120) op1(all_0_2_2, all_0_5_5) = all_0_1_1 % 12.50/3.55 | (121) ~ (e25 = e22) % 12.50/3.55 | (122) ~ (e24 = e13) % 12.50/3.55 | (123) ~ (e22 = e10) % 12.50/3.55 | (124) op1(all_0_2_2, all_0_2_2) = all_0_2_2 % 12.50/3.55 | (125) ~ (e14 = e10) % 12.50/3.55 | (126) op1(e15, e12) = e13 % 12.50/3.55 | (127) op1(all_0_5_5, all_0_6_6) = all_0_6_6 % 12.50/3.55 | (128) all_0_9_9 = e26 | all_0_9_9 = e25 | 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 % 12.50/3.55 | (129) op1(e10, e15) = e12 % 12.50/3.55 | (130) ~ (e25 = e10) % 12.50/3.55 | (131) op2(all_0_8_8, all_0_10_10) = all_0_13_13 % 12.50/3.55 | (132) ~ (e12 = e10) % 12.50/3.55 | (133) op2(e22, e26) = e22 % 12.50/3.55 | (134) op2(e25, e24) = e26 % 12.50/3.55 | (135) ~ (e15 = e10) % 12.50/3.55 | (136) op2(all_0_11_11, all_0_9_9) = all_0_13_13 % 12.50/3.55 | (137) all_0_5_5 = e16 | all_0_5_5 = e15 | all_0_5_5 = e14 | all_0_5_5 = e13 | all_0_5_5 = e12 | all_0_5_5 = e10 | all_0_5_5 = e11 % 12.50/3.55 | (138) h(e13) = all_0_10_10 % 12.50/3.55 | (139) op2(e25, e23) = e23 % 12.50/3.55 | (140) op2(all_0_8_8, all_0_12_12) = all_0_9_9 % 12.50/3.55 | (141) op2(e24, e24) = e24 % 12.50/3.55 | (142) op1(all_0_4_4, all_0_5_5) = all_0_2_2 % 12.50/3.55 | (143) op2(e21, e20) = e20 % 12.50/3.55 | (144) op1(e14, e11) = e13 % 12.50/3.55 | (145) op1(e11, e13) = e15 % 12.50/3.55 | (146) op1(all_0_4_4, all_0_0_0) = all_0_4_4 % 12.50/3.55 | (147) h(e14) = all_0_9_9 % 12.50/3.55 | (148) op2(all_0_8_8, all_0_8_8) = all_0_12_12 % 12.50/3.55 | (149) op2(e24, e26) = e21 % 12.50/3.56 | (150) ~ (e23 = e12) % 12.50/3.56 | (151) op2(e25, e26) = e20 % 12.50/3.56 | (152) all_0_11_11 = e26 | all_0_11_11 = e25 | all_0_11_11 = e24 | all_0_11_11 = e23 | all_0_11_11 = e22 | all_0_11_11 = e20 | all_0_11_11 = e21 % 12.50/3.56 | (153) op2(e26, e24) = e21 % 12.50/3.56 | (154) ~ (e23 = e20) % 12.50/3.56 | (155) op2(all_0_9_9, all_0_13_13) = all_0_9_9 % 12.50/3.56 | (156) op1(e11, e16) = e12 % 12.50/3.56 | (157) ~ (e20 = e11) % 12.50/3.56 | (158) op1(all_0_3_3, all_0_5_5) = all_0_5_5 % 12.50/3.56 | (159) op1(all_0_3_3, all_0_4_4) = all_0_0_0 % 12.50/3.56 | (160) op2(e24, e21) = e25 % 12.50/3.56 | (161) op1(e12, e15) = e13 % 12.50/3.56 | (162) op1(e10, e10) = e13 % 12.50/3.56 | (163) op2(e24, e23) = e22 % 12.50/3.56 | (164) ~ (e15 = e11) % 12.50/3.56 | (165) ~ (e16 = e11) % 12.50/3.56 | (166) j(e21) = all_0_5_5 % 12.50/3.56 | (167) op1(e16, e16) = e10 % 12.50/3.56 | (168) op2(all_0_13_13, all_0_11_11) = all_0_7_7 % 12.50/3.56 | (169) op2(e22, e25) = e25 % 12.50/3.56 | (170) op1(all_0_1_1, all_0_6_6) = all_0_2_2 % 12.50/3.56 | (171) ~ (e14 = e13) % 12.50/3.56 | (172) op1(e12, e13) = e12 % 12.50/3.56 | (173) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) % 12.50/3.56 | (174) ~ (e25 = e15) % 12.50/3.56 | (175) op2(e26, e23) = e24 % 12.50/3.56 | (176) h(all_0_3_3) = e23 % 12.50/3.56 | (177) op2(all_0_13_13, all_0_10_10) = all_0_12_12 % 12.50/3.56 | (178) op1(e13, e10) = e11 % 12.50/3.56 | (179) op2(all_0_12_12, all_0_11_11) = all_0_12_12 % 12.50/3.56 | (180) op1(all_0_5_5, all_0_2_2) = all_0_1_1 % 12.50/3.56 | (181) op2(e21, e22) = e24 % 12.50/3.56 | (182) ~ (e13 = e12) % 12.50/3.56 | (183) op2(all_0_7_7, all_0_7_7) = all_0_13_13 % 12.50/3.56 | (184) op1(all_0_1_1, all_0_2_2) = all_0_0_0 % 12.50/3.56 | (185) op2(all_0_8_8, all_0_11_11) = all_0_10_10 % 12.50/3.56 | (186) op2(e25, e25) = e21 % 12.50/3.56 | (187) j(e20) = all_0_6_6 % 12.50/3.56 | (188) h(all_0_5_5) = e21 % 12.50/3.56 | (189) ~ (e14 = e11) % 12.50/3.56 | (190) ~ (e23 = e15) % 12.50/3.56 | (191) op1(e12, e10) = e16 % 12.50/3.56 | (192) ~ (e26 = e11) % 12.50/3.56 | (193) op1(all_0_6_6, all_0_4_4) = all_0_5_5 % 12.50/3.56 | (194) op2(all_0_7_7, all_0_11_11) = all_0_9_9 % 12.50/3.56 | (195) op2(e22, e20) = e21 % 12.50/3.56 | (196) ~ (e24 = e11) % 12.50/3.56 | (197) op1(all_0_5_5, all_0_1_1) = all_0_4_4 % 12.50/3.56 | (198) op2(e23, e26) = e24 % 12.50/3.56 | (199) ~ (e26 = e23) % 12.50/3.56 | (200) op1(all_0_1_1, all_0_4_4) = all_0_1_1 % 12.50/3.56 | (201) op1(e12, e12) = e15 % 12.50/3.56 | (202) op2(all_0_9_9, all_0_12_12) = all_0_10_10 % 12.50/3.56 | (203) op1(e16, e15) = e16 % 12.50/3.57 | (204) op2(all_0_11_11, all_0_12_12) = all_0_12_12 % 12.50/3.57 | (205) op1(all_0_3_3, all_0_3_3) = all_0_6_6 % 12.50/3.57 | (206) h(e12) = all_0_11_11 % 12.50/3.57 | (207) op2(e24, e22) = e20 % 12.50/3.57 | (208) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) % 12.50/3.57 | (209) op2(e20, e21) = e20 % 12.50/3.57 | (210) op2(all_0_10_10, all_0_9_9) = all_0_7_7 % 12.50/3.57 | (211) op2(all_0_9_9, all_0_7_7) = all_0_12_12 % 12.50/3.57 | (212) ~ (e23 = e14) % 12.50/3.57 | (213) ~ (e21 = e15) % 12.50/3.57 | (214) op2(e22, e22) = e23 % 12.50/3.57 | (215) op1(all_0_0_0, all_0_6_6) = all_0_0_0 % 12.94/3.57 | (216) h(all_0_1_1) = e25 % 12.94/3.57 | (217) ~ (e23 = e13) % 12.94/3.57 | (218) op2(all_0_11_11, all_0_7_7) = all_0_9_9 % 12.94/3.57 | (219) j(e24) = all_0_2_2 % 12.94/3.57 | (220) op2(all_0_8_8, all_0_7_7) = all_0_7_7 % 12.94/3.57 | (221) ~ (e13 = e10) % 12.94/3.57 | (222) ~ (e21 = e10) % 12.94/3.57 | (223) all_0_4_4 = e16 | all_0_4_4 = e15 | 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 % 12.94/3.57 | (224) ~ (e22 = e13) % 12.94/3.57 | (225) op2(all_0_10_10, all_0_10_10) = all_0_9_9 % 12.94/3.57 | (226) op1(all_0_6_6, all_0_3_3) = all_0_1_1 % 12.94/3.57 | (227) ~ (e20 = e12) % 12.94/3.57 | (228) ~ (e22 = e15) % 12.94/3.57 | (229) ~ (e25 = e21) % 12.94/3.57 | (230) op2(all_0_12_12, all_0_13_13) = all_0_13_13 % 12.94/3.57 | (231) all_0_10_10 = e26 | all_0_10_10 = e25 | all_0_10_10 = e24 | all_0_10_10 = e23 | all_0_10_10 = e22 | all_0_10_10 = e20 | all_0_10_10 = e21 % 12.94/3.57 | (232) op2(all_0_12_12, all_0_8_8) = all_0_9_9 % 12.94/3.57 | (233) ~ (e26 = e21) % 12.94/3.57 | (234) op1(e10, e14) = e14 % 12.94/3.57 | (235) op2(e25, e22) = e25 % 12.94/3.57 | (236) op1(all_0_1_1, all_0_3_3) = all_0_3_3 % 12.94/3.57 | (237) ~ (e16 = e15) % 12.94/3.57 | (238) op2(all_0_11_11, all_0_8_8) = all_0_10_10 % 12.94/3.57 | (239) op2(e20, e25) = e24 % 12.94/3.57 | (240) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) % 12.94/3.57 | (241) op1(e14, e12) = e10 % 12.94/3.57 | (242) ~ (e21 = e11) % 12.94/3.57 | (243) op2(e23, e20) = e25 % 12.94/3.57 | (244) ~ (e22 = e16) % 12.94/3.57 | (245) op1(e16, e11) = e12 % 12.94/3.57 | (246) op2(e21, e23) = e21 % 12.94/3.57 | (247) j(all_0_12_12) = e11 % 12.94/3.57 | (248) ~ (e10 = e11) % 12.94/3.57 | (249) op1(all_0_3_3, all_0_6_6) = all_0_1_1 % 12.94/3.58 | (250) op1(all_0_6_6, all_0_5_5) = all_0_6_6 % 12.94/3.58 | (251) ~ (e25 = e16) % 12.94/3.58 | (252) op1(all_0_6_6, all_0_0_0) = all_0_0_0 % 12.94/3.58 | (253) op2(all_0_8_8, all_0_13_13) = all_0_11_11 % 12.94/3.58 | (254) ~ (e26 = e13) % 12.94/3.58 | (255) op2(all_0_7_7, all_0_10_10) = all_0_10_10 % 12.94/3.58 | (256) op2(e22, e21) = e24 % 12.94/3.58 | (257) all_0_6_6 = e16 | all_0_6_6 = e15 | all_0_6_6 = e14 | all_0_6_6 = e13 | all_0_6_6 = e12 | all_0_6_6 = e10 | all_0_6_6 = e11 % 12.94/3.58 | (258) h(e10) = all_0_13_13 % 12.94/3.58 | (259) op1(all_0_5_5, all_0_5_5) = all_0_0_0 % 12.94/3.58 | (260) ~ (e25 = e23) % 12.94/3.58 | (261) ~ (e22 = e12) % 12.94/3.58 | (262) op1(e14, e13) = e16 % 12.94/3.58 | (263) ~ (e24 = e16) % 12.94/3.58 | (264) op2(all_0_12_12, all_0_10_10) = all_0_8_8 % 12.94/3.58 | (265) j(all_0_7_7) = e16 % 12.94/3.58 | (266) op2(e24, e25) = e26 % 12.94/3.58 | (267) op1(e11, e14) = e13 % 12.94/3.58 | (268) all_0_12_12 = e26 | all_0_12_12 = e25 | all_0_12_12 = e24 | all_0_12_12 = e23 | all_0_12_12 = e22 | all_0_12_12 = e20 | all_0_12_12 = e21 % 12.94/3.58 | (269) ~ (e23 = e22) % 12.94/3.58 | (270) op1(all_0_1_1, all_0_1_1) = all_0_5_5 % 12.94/3.58 | (271) op2(e21, e24) = e25 % 12.94/3.58 | (272) all_0_8_8 = e26 | all_0_8_8 = e25 | 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 % 12.94/3.58 | (273) op1(all_0_0_0, all_0_1_1) = all_0_6_6 % 12.94/3.58 | (274) op1(e11, e12) = e11 % 12.94/3.58 | (275) all_0_7_7 = e26 | all_0_7_7 = e25 | 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 % 12.94/3.58 | (276) op2(all_0_7_7, all_0_9_9) = all_0_12_12 % 12.94/3.58 | (277) op1(all_0_3_3, all_0_2_2) = all_0_4_4 % 12.94/3.58 | (278) op2(all_0_7_7, all_0_13_13) = all_0_8_8 % 12.94/3.58 | (279) op1(e14, e15) = e15 % 12.94/3.58 | (280) op1(e16, e14) = e11 % 12.94/3.58 | (281) ~ (e23 = e21) % 12.94/3.58 | (282) ~ (e21 = e14) % 12.94/3.58 | (283) op1(e15, e16) = e16 % 12.94/3.58 | (284) op1(e13, e12) = e12 % 12.94/3.58 | (285) ~ (e22 = e11) % 12.94/3.58 | (286) ~ (e23 = e11) % 12.94/3.58 | (287) op2(e21, e26) = e23 % 12.94/3.58 | (288) j(all_0_13_13) = e10 % 12.94/3.58 | (289) op2(all_0_11_11, all_0_10_10) = all_0_11_11 % 12.94/3.58 | (290) op2(e26, e21) = e23 % 12.94/3.58 | (291) op2(e24, e20) = e23 % 12.94/3.58 | (292) op2(e26, e26) = e25 % 12.94/3.58 | (293) op1(e16, e13) = e13 % 12.94/3.58 | (294) ~ (e26 = e15) % 12.94/3.58 | (295) op1(all_0_2_2, all_0_0_0) = all_0_5_5 % 12.94/3.59 | (296) op2(all_0_8_8, all_0_9_9) = all_0_8_8 % 12.94/3.59 | (297) ~ (e26 = e22) % 12.94/3.59 | (298) ~ (e15 = e13) % 12.94/3.59 | (299) op2(e20, e23) = e25 % 12.94/3.59 | (300) op1(e16, e12) = e14 % 12.94/3.59 | (301) all_0_1_1 = e16 | all_0_1_1 = e15 | 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 % 13.03/3.59 | (302) op2(e25, e20) = e24 % 13.03/3.59 | (303) ~ (e20 = e13) % 13.03/3.59 | (304) op2(all_0_9_9, all_0_10_10) = all_0_7_7 % 13.03/3.59 | (305) op1(all_0_0_0, all_0_4_4) = all_0_4_4 % 13.03/3.59 | (306) ~ (e25 = e12) % 13.03/3.59 | (307) h(e11) = all_0_12_12 % 13.03/3.59 | (308) op1(e12, e11) = e11 % 13.03/3.59 | (309) op1(all_0_2_2, all_0_6_6) = all_0_3_3 % 13.03/3.59 | (310) op1(e14, e16) = e11 % 13.03/3.59 | (311) op2(e23, e23) = e20 % 13.03/3.59 | (312) op1(e13, e13) = e14 % 13.03/3.59 | (313) ~ (e20 = e15) % 13.03/3.59 | (314) op2(e22, e24) = e20 % 13.03/3.59 | (315) op1(e16, e10) = e15 % 13.03/3.59 | (316) op1(e11, e10) = e10 % 13.03/3.59 | (317) op2(e21, e21) = e26 % 13.03/3.59 | (318) op1(e15, e13) = e10 % 13.03/3.59 | (319) op2(all_0_10_10, all_0_11_11) = all_0_11_11 % 13.03/3.59 | (320) op1(e13, e15) = e10 % 13.03/3.59 | (321) ~ (e26 = e12) % 13.03/3.59 | (322) op2(e23, e25) = e23 % 13.03/3.59 | (323) op2(all_0_10_10, all_0_7_7) = all_0_10_10 % 13.03/3.59 | (324) ~ (e24 = e12) % 13.03/3.59 | (325) op1(all_0_4_4, all_0_3_3) = all_0_0_0 % 13.03/3.59 | (326) ~ (e26 = e16) % 13.03/3.59 | (327) ~ (e24 = e21) % 13.03/3.59 | (328) op1(all_0_4_4, all_0_1_1) = all_0_1_1 % 13.03/3.59 | (329) op1(all_0_0_0, all_0_3_3) = all_0_2_2 % 13.03/3.59 | (330) op1(all_0_0_0, all_0_2_2) = all_0_5_5 % 13.03/3.59 | (331) op1(e13, e16) = e13 % 13.03/3.59 | (332) ~ (e23 = e10) % 13.03/3.60 | (333) ~ (e13 = e11) % 13.03/3.60 | (334) all_0_2_2 = e16 | all_0_2_2 = e15 | 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 % 13.03/3.60 | % 13.03/3.60 +-Applying beta-rule and splitting (19), into two cases. % 13.03/3.60 |-Branch one: % 13.03/3.60 | (335) all_0_0_0 = e16 % 13.03/3.60 | % 13.03/3.60 | From (335)(335) and (51) follows: % 13.03/3.60 | (336) op1(e16, e16) = all_0_1_1 % 13.03/3.60 | % 13.03/3.60 | From (335) and (27) follows: % 13.03/3.60 | (337) op1(all_0_1_1, e16) = all_0_6_6 % 13.03/3.60 | % 13.03/3.60 | Instantiating formula (208) with e16, e16, all_0_1_1, e10 and discharging atoms op1(e16, e16) = all_0_1_1, op1(e16, e16) = e10, yields: % 13.03/3.60 | (338) all_0_1_1 = e10 % 13.03/3.60 | % 13.03/3.60 | From (338)(338) and (270) follows: % 13.03/3.60 | (339) op1(e10, e10) = all_0_5_5 % 13.03/3.60 | % 13.03/3.60 | From (338) and (337) follows: % 13.03/3.60 | (340) op1(e10, e16) = all_0_6_6 % 13.03/3.60 | % 13.03/3.60 | Instantiating formula (208) with e10, e16, all_0_6_6, e15 and discharging atoms op1(e10, e16) = all_0_6_6, op1(e10, e16) = e15, yields: % 13.03/3.60 | (341) all_0_6_6 = e15 % 13.03/3.60 | % 13.03/3.60 | Instantiating formula (208) with e10, e10, all_0_5_5, e13 and discharging atoms op1(e10, e10) = all_0_5_5, op1(e10, e10) = e13, yields: % 13.03/3.60 | (342) all_0_5_5 = e13 % 13.03/3.60 | % 13.03/3.60 | From (342)(341)(341) and (127) follows: % 13.03/3.60 | (343) op1(e13, e15) = e15 % 13.03/3.60 | % 13.03/3.60 | Instantiating formula (208) with e13, e15, e15, e10 and discharging atoms op1(e13, e15) = e15, op1(e13, e15) = e10, yields: % 13.03/3.60 | (344) e15 = e10 % 13.03/3.60 | % 13.03/3.60 | Equations (344) can reduce 135 to: % 13.03/3.60 | (345) $false % 13.03/3.60 | % 13.03/3.60 |-The branch is then unsatisfiable % 13.03/3.60 |-Branch two: % 13.03/3.60 | (346) ~ (all_0_0_0 = e16) % 13.03/3.60 | (347) all_0_0_0 = e15 | 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 % 13.03/3.60 | % 13.03/3.60 +-Applying beta-rule and splitting (152), into two cases. % 13.03/3.60 |-Branch one: % 13.03/3.60 | (348) all_0_11_11 = e26 % 13.03/3.60 | % 13.03/3.60 | From (348)(348) and (53) follows: % 13.03/3.60 | (349) op2(e26, e26) = all_0_8_8 % 13.03/3.60 | % 13.03/3.60 | From (348) and (179) follows: % 13.03/3.60 | (350) op2(all_0_12_12, e26) = all_0_12_12 % 13.03/3.60 | % 13.03/3.60 | Instantiating formula (240) with e26, e26, all_0_8_8, e25 and discharging atoms op2(e26, e26) = all_0_8_8, op2(e26, e26) = e25, yields: % 13.03/3.60 | (351) all_0_8_8 = e25 % 13.03/3.60 | % 13.03/3.60 | From (351)(351) and (148) follows: % 13.03/3.60 | (352) op2(e25, e25) = all_0_12_12 % 13.03/3.60 | % 13.03/3.60 | Instantiating formula (240) with e25, e25, all_0_12_12, e21 and discharging atoms op2(e25, e25) = all_0_12_12, op2(e25, e25) = e21, yields: % 13.03/3.61 | (353) all_0_12_12 = e21 % 13.03/3.61 | % 13.03/3.61 | From (353)(353) and (350) follows: % 13.03/3.61 | (354) op2(e21, e26) = e21 % 13.03/3.61 | % 13.03/3.61 | Instantiating formula (240) with e21, e26, e21, e23 and discharging atoms op2(e21, e26) = e23, op2(e21, e26) = e21, yields: % 13.03/3.61 | (355) e23 = e21 % 13.03/3.61 | % 13.03/3.61 | Equations (355) can reduce 281 to: % 13.03/3.61 | (345) $false % 13.03/3.61 | % 13.03/3.61 |-The branch is then unsatisfiable % 13.03/3.61 |-Branch two: % 13.03/3.61 | (357) ~ (all_0_11_11 = e26) % 13.03/3.61 | (358) all_0_11_11 = e25 | all_0_11_11 = e24 | all_0_11_11 = e23 | all_0_11_11 = e22 | all_0_11_11 = e20 | all_0_11_11 = e21 % 13.03/3.61 | % 13.03/3.61 +-Applying beta-rule and splitting (301), into two cases. % 13.03/3.61 |-Branch one: % 13.03/3.61 | (359) all_0_1_1 = e16 % 13.03/3.61 | % 13.03/3.61 | From (359)(359) and (270) follows: % 13.03/3.61 | (360) op1(e16, e16) = all_0_5_5 % 13.03/3.61 | % 13.03/3.61 | From (359) and (197) follows: % 13.03/3.61 | (361) op1(all_0_5_5, e16) = all_0_4_4 % 13.03/3.61 | % 13.03/3.61 | Instantiating formula (208) with e16, e16, all_0_5_5, e10 and discharging atoms op1(e16, e16) = all_0_5_5, op1(e16, e16) = e10, yields: % 13.03/3.61 | (362) all_0_5_5 = e10 % 13.03/3.61 | % 13.03/3.61 | From (362)(362) and (259) follows: % 13.03/3.61 | (363) op1(e10, e10) = all_0_0_0 % 13.03/3.61 | % 13.03/3.61 | From (362) and (361) follows: % 13.03/3.61 | (364) op1(e10, e16) = all_0_4_4 % 13.03/3.61 | % 13.03/3.61 | Instantiating formula (208) with e10, e16, all_0_4_4, e15 and discharging atoms op1(e10, e16) = all_0_4_4, op1(e10, e16) = e15, yields: % 13.03/3.61 | (365) all_0_4_4 = e15 % 13.03/3.61 | % 13.03/3.61 | Instantiating formula (208) with e10, e10, all_0_0_0, e13 and discharging atoms op1(e10, e10) = all_0_0_0, op1(e10, e10) = e13, yields: % 13.03/3.61 | (366) all_0_0_0 = e13 % 13.03/3.61 | % 13.03/3.61 | From (366)(365)(365) and (305) follows: % 13.03/3.61 | (343) op1(e13, e15) = e15 % 13.03/3.61 | % 13.03/3.61 | Instantiating formula (208) with e13, e15, e15, e10 and discharging atoms op1(e13, e15) = e15, op1(e13, e15) = e10, yields: % 13.03/3.61 | (344) e15 = e10 % 13.03/3.61 | % 13.03/3.61 | Equations (344) can reduce 135 to: % 13.03/3.61 | (345) $false % 13.03/3.61 | % 13.03/3.61 |-The branch is then unsatisfiable % 13.03/3.61 |-Branch two: % 13.03/3.61 | (370) ~ (all_0_1_1 = e16) % 13.03/3.61 | (371) all_0_1_1 = e15 | 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 % 13.03/3.61 | % 13.03/3.61 +-Applying beta-rule and splitting (128), into two cases. % 13.03/3.61 |-Branch one: % 13.03/3.61 | (372) all_0_9_9 = e26 % 13.03/3.61 | % 13.03/3.61 | From (372) and (296) follows: % 13.03/3.61 | (373) op2(all_0_8_8, e26) = all_0_8_8 % 13.03/3.61 | % 13.03/3.61 | From (372)(372) and (72) follows: % 13.03/3.61 | (374) op2(e26, e26) = all_0_11_11 % 13.03/3.61 | % 13.03/3.61 | Instantiating formula (240) with e26, e26, all_0_11_11, e25 and discharging atoms op2(e26, e26) = all_0_11_11, op2(e26, e26) = e25, yields: % 13.03/3.61 | (375) all_0_11_11 = e25 % 13.03/3.61 | % 13.03/3.61 | From (375)(375) and (53) follows: % 13.03/3.61 | (376) op2(e25, e25) = all_0_8_8 % 13.03/3.61 | % 13.03/3.61 | Instantiating formula (240) with e25, e25, all_0_8_8, e21 and discharging atoms op2(e25, e25) = all_0_8_8, op2(e25, e25) = e21, yields: % 13.03/3.61 | (377) all_0_8_8 = e21 % 13.03/3.61 | % 13.03/3.61 | From (377)(377) and (373) follows: % 13.03/3.61 | (354) op2(e21, e26) = e21 % 13.03/3.61 | % 13.03/3.61 | Instantiating formula (240) with e21, e26, e21, e23 and discharging atoms op2(e21, e26) = e23, op2(e21, e26) = e21, yields: % 13.03/3.61 | (355) e23 = e21 % 13.03/3.61 | % 13.03/3.61 | Equations (355) can reduce 281 to: % 13.03/3.61 | (345) $false % 13.03/3.61 | % 13.03/3.61 |-The branch is then unsatisfiable % 13.03/3.61 |-Branch two: % 13.03/3.61 | (381) ~ (all_0_9_9 = e26) % 13.03/3.61 | (382) all_0_9_9 = e25 | 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 % 13.03/3.61 | % 13.03/3.61 +-Applying beta-rule and splitting (30), into two cases. % 13.03/3.61 |-Branch one: % 13.03/3.61 | (383) all_0_13_13 = e26 % 13.03/3.61 | % 13.03/3.61 | From (383) and (155) follows: % 13.03/3.61 | (384) op2(all_0_9_9, e26) = all_0_9_9 % 13.03/3.61 | % 13.03/3.61 | From (383)(383) and (86) follows: % 13.03/3.61 | (385) op2(e26, e26) = all_0_10_10 % 13.03/3.61 | % 13.03/3.61 | Instantiating formula (240) with e26, e26, all_0_10_10, e25 and discharging atoms op2(e26, e26) = all_0_10_10, op2(e26, e26) = e25, yields: % 13.03/3.61 | (386) all_0_10_10 = e25 % 13.03/3.61 | % 13.03/3.61 | From (386)(386) and (225) follows: % 13.03/3.61 | (387) op2(e25, e25) = all_0_9_9 % 13.03/3.61 | % 13.03/3.61 | Instantiating formula (240) with e25, e25, all_0_9_9, e21 and discharging atoms op2(e25, e25) = all_0_9_9, op2(e25, e25) = e21, yields: % 13.03/3.61 | (388) all_0_9_9 = e21 % 13.03/3.61 | % 13.03/3.61 | From (388)(388) and (384) follows: % 13.03/3.61 | (354) op2(e21, e26) = e21 % 13.03/3.61 | % 13.03/3.61 | Instantiating formula (240) with e21, e26, e21, e23 and discharging atoms op2(e21, e26) = e23, op2(e21, e26) = e21, yields: % 13.03/3.61 | (355) e23 = e21 % 13.03/3.61 | % 13.03/3.61 | Equations (355) can reduce 281 to: % 13.03/3.61 | (345) $false % 13.03/3.61 | % 13.03/3.61 |-The branch is then unsatisfiable % 13.03/3.61 |-Branch two: % 13.03/3.61 | (392) ~ (all_0_13_13 = e26) % 13.03/3.61 | (393) all_0_13_13 = e25 | all_0_13_13 = e24 | all_0_13_13 = e23 | all_0_13_13 = e22 | all_0_13_13 = e20 | all_0_13_13 = e21 % 13.03/3.61 | % 13.03/3.61 +-Applying beta-rule and splitting (268), into two cases. % 13.03/3.61 |-Branch one: % 13.03/3.61 | (394) all_0_12_12 = e26 % 13.03/3.61 | % 13.03/3.61 | From (394)(394) and (37) follows: % 13.03/3.61 | (395) op2(e26, e26) = all_0_7_7 % 13.03/3.61 | % 13.03/3.61 | Instantiating formula (240) with e26, e26, all_0_7_7, e25 and discharging atoms op2(e26, e26) = all_0_7_7, op2(e26, e26) = e25, yields: % 13.03/3.61 | (396) all_0_7_7 = e25 % 13.03/3.61 | % 13.03/3.61 | From (396) and (265) follows: % 13.03/3.61 | (397) j(e25) = e16 % 13.03/3.61 | % 13.03/3.61 | Instantiating formula (76) with e25, e16, all_0_1_1 and discharging atoms j(e25) = all_0_1_1, j(e25) = e16, yields: % 13.03/3.61 | (359) all_0_1_1 = e16 % 13.03/3.61 | % 13.03/3.61 | Equations (359) can reduce 370 to: % 13.03/3.61 | (345) $false % 13.03/3.61 | % 13.03/3.61 |-The branch is then unsatisfiable % 13.03/3.61 |-Branch two: % 13.03/3.61 | (400) ~ (all_0_12_12 = e26) % 13.03/3.61 | (401) all_0_12_12 = e25 | all_0_12_12 = e24 | all_0_12_12 = e23 | all_0_12_12 = e22 | all_0_12_12 = e20 | all_0_12_12 = e21 % 13.03/3.61 | % 13.03/3.61 +-Applying beta-rule and splitting (272), into two cases. % 13.03/3.61 |-Branch one: % 13.03/3.61 | (402) all_0_8_8 = e26 % 13.03/3.61 | % 13.03/3.61 | From (402) and (29) follows: % 13.03/3.61 | (403) op2(all_0_7_7, e26) = all_0_7_7 % 13.03/3.61 | % 13.03/3.61 | From (402)(402) and (148) follows: % 13.03/3.61 | (404) op2(e26, e26) = all_0_12_12 % 13.03/3.61 | % 13.03/3.61 | Instantiating formula (240) with e26, e26, all_0_12_12, e25 and discharging atoms op2(e26, e26) = all_0_12_12, op2(e26, e26) = e25, yields: % 13.03/3.61 | (405) all_0_12_12 = e25 % 13.03/3.61 | % 13.03/3.61 | From (405)(405) and (37) follows: % 13.03/3.62 | (406) op2(e25, e25) = all_0_7_7 % 13.03/3.62 | % 13.03/3.62 | Instantiating formula (240) with e25, e25, all_0_7_7, e21 and discharging atoms op2(e25, e25) = all_0_7_7, op2(e25, e25) = e21, yields: % 13.03/3.62 | (407) all_0_7_7 = e21 % 13.03/3.62 | % 13.03/3.62 | From (407)(407) and (403) follows: % 13.03/3.62 | (354) op2(e21, e26) = e21 % 13.03/3.62 | % 13.03/3.62 | Instantiating formula (240) with e21, e26, e21, e23 and discharging atoms op2(e21, e26) = e23, op2(e21, e26) = e21, yields: % 13.03/3.62 | (355) e23 = e21 % 13.03/3.62 | % 13.03/3.62 | Equations (355) can reduce 281 to: % 13.03/3.62 | (345) $false % 13.03/3.62 | % 13.03/3.62 |-The branch is then unsatisfiable % 13.03/3.62 |-Branch two: % 13.03/3.62 | (411) ~ (all_0_8_8 = e26) % 13.03/3.62 | (412) all_0_8_8 = e25 | 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 % 13.03/3.62 | % 13.03/3.62 +-Applying beta-rule and splitting (231), into two cases. % 13.03/3.62 |-Branch one: % 13.03/3.62 | (413) all_0_10_10 = e26 % 13.03/3.62 | % 13.03/3.62 | From (413)(413) and (225) follows: % 13.03/3.62 | (414) op2(e26, e26) = all_0_9_9 % 13.03/3.62 | % 13.03/3.62 | From (413) and (289) follows: % 13.03/3.62 | (415) op2(all_0_11_11, e26) = all_0_11_11 % 13.18/3.62 | % 13.18/3.62 | Instantiating formula (240) with e26, e26, all_0_9_9, e25 and discharging atoms op2(e26, e26) = all_0_9_9, op2(e26, e26) = e25, yields: % 13.18/3.62 | (416) all_0_9_9 = e25 % 13.18/3.62 | % 13.18/3.62 | From (416)(416) and (72) follows: % 13.18/3.62 | (417) op2(e25, e25) = all_0_11_11 % 13.18/3.62 | % 13.18/3.62 | Instantiating formula (240) with e25, e25, all_0_11_11, e21 and discharging atoms op2(e25, e25) = all_0_11_11, op2(e25, e25) = e21, yields: % 13.18/3.62 | (418) all_0_11_11 = e21 % 13.18/3.62 | % 13.18/3.62 | From (418)(418) and (415) follows: % 13.18/3.62 | (354) op2(e21, e26) = e21 % 13.18/3.62 | % 13.18/3.62 | Instantiating formula (240) with e21, e26, e21, e23 and discharging atoms op2(e21, e26) = e23, op2(e21, e26) = e21, yields: % 13.18/3.62 | (355) e23 = e21 % 13.18/3.62 | % 13.18/3.62 | Equations (355) can reduce 281 to: % 13.18/3.62 | (345) $false % 13.18/3.62 | % 13.18/3.62 |-The branch is then unsatisfiable % 13.18/3.62 |-Branch two: % 13.18/3.62 | (422) ~ (all_0_10_10 = e26) % 13.18/3.62 | (423) all_0_10_10 = e25 | all_0_10_10 = e24 | all_0_10_10 = e23 | all_0_10_10 = e22 | all_0_10_10 = e20 | all_0_10_10 = e21 % 13.18/3.62 | % 13.18/3.62 +-Applying beta-rule and splitting (347), into two cases. % 13.18/3.62 |-Branch one: % 13.18/3.62 | (424) all_0_0_0 = e15 % 13.18/3.62 | % 13.18/3.62 | From (424) and (98) follows: % 13.18/3.62 | (425) h(e15) = e26 % 13.18/3.62 | % 13.18/3.62 | Instantiating formula (173) with e15, e26, all_0_8_8 and discharging atoms h(e15) = all_0_8_8, h(e15) = e26, yields: % 13.18/3.62 | (402) all_0_8_8 = e26 % 13.18/3.62 | % 13.18/3.62 | Equations (402) can reduce 411 to: % 13.18/3.62 | (345) $false % 13.18/3.62 | % 13.18/3.62 |-The branch is then unsatisfiable % 13.18/3.62 |-Branch two: % 13.18/3.62 | (428) ~ (all_0_0_0 = e15) % 13.18/3.62 | (429) 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 % 13.18/3.62 | % 13.18/3.62 +-Applying beta-rule and splitting (429), into two cases. % 13.18/3.62 |-Branch one: % 13.18/3.62 | (430) all_0_0_0 = e14 % 13.18/3.62 | % 13.18/3.62 | From (430) and (98) follows: % 13.18/3.62 | (431) h(e14) = e26 % 13.18/3.62 | % 13.18/3.62 | Instantiating formula (173) with e14, e26, all_0_9_9 and discharging atoms h(e14) = all_0_9_9, h(e14) = e26, yields: % 13.18/3.62 | (372) all_0_9_9 = e26 % 13.18/3.62 | % 13.18/3.62 | Equations (372) can reduce 381 to: % 13.18/3.62 | (345) $false % 13.18/3.62 | % 13.18/3.62 |-The branch is then unsatisfiable % 13.18/3.62 |-Branch two: % 13.18/3.62 | (434) ~ (all_0_0_0 = e14) % 13.18/3.62 | (435) all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11 % 13.18/3.62 | % 13.18/3.62 +-Applying beta-rule and splitting (435), into two cases. % 13.18/3.62 |-Branch one: % 13.18/3.62 | (366) all_0_0_0 = e13 % 13.18/3.62 | % 13.18/3.62 | From (366) and (98) follows: % 13.18/3.62 | (437) h(e13) = e26 % 13.18/3.62 | % 13.18/3.62 | Instantiating formula (173) with e13, e26, all_0_10_10 and discharging atoms h(e13) = all_0_10_10, h(e13) = e26, yields: % 13.18/3.62 | (413) all_0_10_10 = e26 % 13.18/3.62 | % 13.18/3.62 | Equations (413) can reduce 422 to: % 13.18/3.62 | (345) $false % 13.18/3.62 | % 13.18/3.62 |-The branch is then unsatisfiable % 13.18/3.62 |-Branch two: % 13.18/3.62 | (440) ~ (all_0_0_0 = e13) % 13.18/3.62 | (441) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11 % 13.18/3.62 | % 13.18/3.62 +-Applying beta-rule and splitting (441), into two cases. % 13.18/3.62 |-Branch one: % 13.18/3.62 | (442) all_0_0_0 = e12 % 13.18/3.62 | % 13.18/3.62 | From (442) and (98) follows: % 13.18/3.62 | (443) h(e12) = e26 % 13.18/3.62 | % 13.18/3.62 | Instantiating formula (173) with e12, e26, all_0_11_11 and discharging atoms h(e12) = all_0_11_11, h(e12) = e26, yields: % 13.18/3.62 | (348) all_0_11_11 = e26 % 13.18/3.62 | % 13.18/3.62 | Equations (348) can reduce 357 to: % 13.18/3.62 | (345) $false % 13.18/3.62 | % 13.18/3.62 |-The branch is then unsatisfiable % 13.18/3.62 |-Branch two: % 13.18/3.62 | (446) ~ (all_0_0_0 = e12) % 13.18/3.62 | (447) all_0_0_0 = e10 | all_0_0_0 = e11 % 13.18/3.62 | % 13.18/3.62 +-Applying beta-rule and splitting (447), into two cases. % 13.18/3.62 |-Branch one: % 13.18/3.62 | (448) all_0_0_0 = e10 % 13.18/3.62 | % 13.18/3.62 | From (448) and (98) follows: % 13.18/3.62 | (449) h(e10) = e26 % 13.18/3.62 | % 13.18/3.62 | Instantiating formula (173) with e10, e26, all_0_13_13 and discharging atoms h(e10) = all_0_13_13, h(e10) = e26, yields: % 13.18/3.62 | (383) all_0_13_13 = e26 % 13.18/3.62 | % 13.18/3.62 | Equations (383) can reduce 392 to: % 13.18/3.62 | (345) $false % 13.18/3.62 | % 13.18/3.62 |-The branch is then unsatisfiable % 13.18/3.62 |-Branch two: % 13.18/3.62 | (452) ~ (all_0_0_0 = e10) % 13.18/3.62 | (453) all_0_0_0 = e11 % 13.18/3.62 | % 13.18/3.62 | From (453) and (98) follows: % 13.18/3.62 | (454) h(e11) = e26 % 13.18/3.62 | % 13.18/3.62 | Instantiating formula (173) with e11, e26, all_0_12_12 and discharging atoms h(e11) = all_0_12_12, h(e11) = e26, yields: % 13.18/3.62 | (394) all_0_12_12 = e26 % 13.18/3.62 | % 13.18/3.62 | Equations (394) can reduce 400 to: % 13.18/3.62 | (345) $false % 13.18/3.62 | % 13.18/3.62 |-The branch is then unsatisfiable % 13.18/3.62 % SZS output end Proof for theBenchmark % 13.18/3.62 % 13.18/3.62 2986ms %------------------------------------------------------------------------------