%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : ALG081+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n032.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Thu Jul 14 15:34:16 EDT 2022 % Result : Theorem 3.69s 1.40s % Output : Proof 7.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.10 % Problem : ALG081+1 : TPTP v8.1.0. Released v2.7.0. % 0.05/0.10 % Command : ePrincess-casc -timeout=%d %s % 0.08/0.29 % Computer : n032.cluster.edu % 0.08/0.29 % Model : x86_64 x86_64 % 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.29 % Memory : 8042.1875MB % 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.29 % CPULimit : 300 % 0.08/0.29 % WCLimit : 600 % 0.08/0.29 % DateTime : Tue Jun 7 22:57:51 EDT 2022 % 0.08/0.29 % CPUTime : % 0.14/0.48 ____ _ % 0.14/0.48 ___ / __ \_____(_)___ ________ __________ % 0.14/0.48 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.14/0.48 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.14/0.48 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.14/0.48 % 0.14/0.48 A Theorem Prover for First-Order Logic % 0.14/0.48 (ePrincess v.1.0) % 0.14/0.48 % 0.14/0.48 (c) Philipp Rümmer, 2009-2015 % 0.14/0.48 (c) Peter Backeman, 2014-2015 % 0.14/0.48 (contributions by Angelo Brillout, Peter Baumgartner) % 0.14/0.48 Free software under GNU Lesser General Public License (LGPL). % 0.14/0.48 Bug reports to peter@backeman.se % 0.14/0.48 % 0.14/0.48 For more information, visit http://user.uu.se/~petba168/breu/ % 0.14/0.48 % 0.14/0.48 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.14/0.53 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.51/0.84 Prover 0: Preprocessing ... % 2.41/1.12 Prover 0: Constructing countermodel ... % 3.69/1.40 Prover 0: proved (872ms) % 3.69/1.40 % 3.69/1.40 No countermodel exists, formula is valid % 3.69/1.40 % SZS status Theorem for theBenchmark % 3.69/1.40 % 3.69/1.40 Generating proof ... found it (size 59) % 6.70/2.06 % 6.70/2.06 % SZS output start Proof for theBenchmark % 6.70/2.06 Assumed formulas after preprocessing and simplification: % 6.70/2.06 | (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) = v2 & op2(v4, v2) = v0 & op2(v4, v1) = v3 & op2(v4, v0) = v4 & op2(v3, v4) = v2 & op2(v3, v3) = v1 & op2(v3, v2) = v4 & op2(v3, v1) = v0 & op2(v3, v0) = v3 & op2(v2, v4) = v3 & op2(v2, v3) = v0 & op2(v2, v2) = v1 & op2(v2, v1) = v4 & op2(v2, v0) = v2 & op2(v1, v4) = v0 & op2(v1, v3) = v4 & op2(v1, v2) = v3 & op2(v1, v1) = v2 & op2(v1, v0) = v1 & op2(v0, v4) = v4 & op2(v0, v3) = v3 & op2(v0, v2) = v2 & op2(v0, v1) = v1 & op2(v0, v0) = v0 & op2(e24, e24) = e20 & op2(e24, e23) = e22 & op2(e24, e22) = e21 & op2(e24, e20) = e24 & op2(e24, e21) = e23 & op2(e23, e24) = e22 & op2(e23, e23) = e21 & op2(e23, e22) = e20 & op2(e23, e20) = e23 & op2(e23, e21) = e24 & op2(e22, e24) = e21 & op2(e22, e23) = e24 & op2(e22, e22) = e23 & op2(e22, e20) = e22 & op2(e22, e21) = e20 & op2(e20, e24) = e24 & op2(e20, e23) = e23 & op2(e20, e22) = e22 & op2(e20, e20) = e20 & op2(e20, e21) = e21 & op2(e21, e24) = e23 & op2(e21, e23) = e20 & op2(e21, e22) = e24 & op2(e21, e20) = e21 & op2(e21, e21) = e22 & op1(v9, v9) = v5 & op1(v9, v8) = v7 & op1(v9, v7) = v6 & op1(v9, v6) = v8 & op1(v9, v5) = v9 & op1(v8, v9) = v7 & op1(v8, v8) = v6 & op1(v8, v7) = v5 & op1(v8, v6) = v9 & op1(v8, v5) = v8 & op1(v7, v9) = v6 & op1(v7, v8) = v9 & op1(v7, v7) = v8 & op1(v7, v6) = v5 & op1(v7, v5) = v7 & op1(v6, v9) = v8 & op1(v6, v8) = v5 & op1(v6, v7) = v9 & op1(v6, v6) = v7 & op1(v6, v5) = v6 & op1(v5, v9) = v9 & op1(v5, v8) = v8 & op1(v5, v7) = v7 & op1(v5, v6) = v6 & op1(v5, v5) = v5 & op1(e14, e14) = e11 & op1(e14, e13) = e12 & op1(e14, e12) = e10 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e14) = e12 & op1(e13, e13) = e11 & op1(e13, e12) = e14 & op1(e13, e10) = e13 & op1(e13, e11) = e10 & op1(e12, e14) = e13 & op1(e12, e13) = e10 & op1(e12, e12) = e11 & op1(e12, e10) = e12 & op1(e12, e11) = e14 & op1(e10, e14) = e14 & op1(e10, e13) = e13 & op1(e10, e12) = e12 & op1(e10, e10) = e10 & op1(e10, e11) = e11 & op1(e11, e14) = e10 & op1(e11, e13) = e14 & op1(e11, e12) = e13 & op1(e11, e10) = e11 & op1(e11, e11) = e12 & 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)) % 6.76/2.10 | 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: % 6.76/2.10 | (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_7_7 & op2(all_0_5_5, all_0_7_7) = all_0_9_9 & op2(all_0_5_5, all_0_8_8) = all_0_6_6 & op2(all_0_5_5, all_0_9_9) = all_0_5_5 & op2(all_0_6_6, all_0_5_5) = all_0_7_7 & op2(all_0_6_6, all_0_6_6) = all_0_8_8 & op2(all_0_6_6, all_0_7_7) = all_0_5_5 & op2(all_0_6_6, all_0_8_8) = all_0_9_9 & op2(all_0_6_6, all_0_9_9) = all_0_6_6 & op2(all_0_7_7, all_0_5_5) = all_0_6_6 & op2(all_0_7_7, all_0_6_6) = all_0_9_9 & op2(all_0_7_7, all_0_7_7) = all_0_8_8 & op2(all_0_7_7, all_0_8_8) = all_0_5_5 & op2(all_0_7_7, all_0_9_9) = all_0_7_7 & op2(all_0_8_8, all_0_5_5) = all_0_9_9 & op2(all_0_8_8, all_0_6_6) = all_0_5_5 & op2(all_0_8_8, all_0_7_7) = all_0_6_6 & op2(all_0_8_8, all_0_8_8) = all_0_7_7 & op2(all_0_8_8, all_0_9_9) = all_0_8_8 & op2(all_0_9_9, all_0_5_5) = all_0_5_5 & op2(all_0_9_9, all_0_6_6) = all_0_6_6 & op2(all_0_9_9, all_0_7_7) = all_0_7_7 & op2(all_0_9_9, all_0_8_8) = all_0_8_8 & op2(all_0_9_9, all_0_9_9) = all_0_9_9 & op2(e24, e24) = e20 & op2(e24, e23) = e22 & op2(e24, e22) = e21 & op2(e24, e20) = e24 & op2(e24, e21) = e23 & op2(e23, e24) = e22 & op2(e23, e23) = e21 & op2(e23, e22) = e20 & op2(e23, e20) = e23 & op2(e23, e21) = e24 & op2(e22, e24) = e21 & op2(e22, e23) = e24 & op2(e22, e22) = e23 & op2(e22, e20) = e22 & op2(e22, e21) = e20 & op2(e20, e24) = e24 & op2(e20, e23) = e23 & op2(e20, e22) = e22 & op2(e20, e20) = e20 & op2(e20, e21) = e21 & op2(e21, e24) = e23 & op2(e21, e23) = e20 & op2(e21, e22) = e24 & op2(e21, e20) = e21 & op2(e21, e21) = e22 & op1(all_0_0_0, all_0_0_0) = all_0_4_4 & op1(all_0_0_0, all_0_1_1) = all_0_2_2 & 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_0_0 & op1(all_0_1_1, all_0_0_0) = all_0_2_2 & op1(all_0_1_1, all_0_1_1) = all_0_3_3 & op1(all_0_1_1, all_0_2_2) = all_0_4_4 & op1(all_0_1_1, all_0_3_3) = all_0_0_0 & op1(all_0_1_1, all_0_4_4) = all_0_1_1 & op1(all_0_2_2, all_0_0_0) = all_0_3_3 & op1(all_0_2_2, all_0_1_1) = all_0_0_0 & op1(all_0_2_2, all_0_2_2) = all_0_1_1 & op1(all_0_2_2, all_0_3_3) = all_0_4_4 & op1(all_0_2_2, all_0_4_4) = all_0_2_2 & op1(all_0_3_3, all_0_0_0) = all_0_1_1 & op1(all_0_3_3, all_0_1_1) = all_0_4_4 & op1(all_0_3_3, all_0_2_2) = all_0_0_0 & op1(all_0_3_3, all_0_3_3) = all_0_2_2 & op1(all_0_3_3, all_0_4_4) = all_0_3_3 & op1(all_0_4_4, all_0_0_0) = all_0_0_0 & op1(all_0_4_4, all_0_1_1) = all_0_1_1 & op1(all_0_4_4, all_0_2_2) = all_0_2_2 & op1(all_0_4_4, all_0_3_3) = all_0_3_3 & op1(all_0_4_4, all_0_4_4) = all_0_4_4 & op1(e14, e14) = e11 & op1(e14, e13) = e12 & op1(e14, e12) = e10 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e14) = e12 & op1(e13, e13) = e11 & op1(e13, e12) = e14 & op1(e13, e10) = e13 & op1(e13, e11) = e10 & op1(e12, e14) = e13 & op1(e12, e13) = e10 & op1(e12, e12) = e11 & op1(e12, e10) = e12 & op1(e12, e11) = e14 & op1(e10, e14) = e14 & op1(e10, e13) = e13 & op1(e10, e12) = e12 & op1(e10, e10) = e10 & op1(e10, e11) = e11 & op1(e11, e14) = e10 & op1(e11, e13) = e14 & op1(e11, e12) = e13 & op1(e11, e10) = e11 & op1(e11, e11) = e12 & 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) % 6.76/2.11 | % 6.76/2.11 | Applying alpha-rule on (1) yields: % 6.76/2.11 | (2) op1(all_0_1_1, all_0_0_0) = all_0_2_2 % 6.76/2.11 | (3) op1(all_0_3_3, all_0_0_0) = all_0_1_1 % 6.76/2.11 | (4) ~ (e22 = e13) % 6.76/2.11 | (5) ~ (e24 = e23) % 6.76/2.11 | (6) op1(e14, e14) = e11 % 6.76/2.11 | (7) op2(e22, e23) = e24 % 6.76/2.11 | (8) j(e21) = all_0_3_3 % 6.76/2.11 | (9) h(all_0_2_2) = e22 % 6.76/2.11 | (10) ~ (e22 = e11) % 6.76/2.11 | (11) ~ (e24 = e10) % 6.76/2.11 | (12) op2(e20, e24) = e24 % 6.76/2.11 | (13) ~ (e21 = e11) % 6.76/2.11 | (14) op1(e12, e12) = e11 % 7.00/2.11 | (15) op1(e11, e12) = e13 % 7.00/2.11 | (16) op2(e20, e23) = e23 % 7.00/2.11 | (17) op2(all_0_5_5, all_0_8_8) = all_0_6_6 % 7.00/2.11 | (18) ~ (e21 = e12) % 7.00/2.11 | (19) ~ (e24 = e12) % 7.00/2.11 | (20) op2(all_0_8_8, all_0_8_8) = all_0_7_7 % 7.00/2.11 | (21) ~ (e24 = e21) % 7.00/2.11 | (22) op1(all_0_4_4, all_0_2_2) = all_0_2_2 % 7.00/2.11 | (23) j(e20) = all_0_4_4 % 7.00/2.11 | (24) op2(e22, e20) = e22 % 7.00/2.11 | (25) ~ (e14 = e11) % 7.00/2.11 | (26) op2(all_0_5_5, all_0_7_7) = all_0_9_9 % 7.00/2.11 | (27) op2(e21, e22) = e24 % 7.00/2.11 | (28) ~ (e20 = e10) % 7.00/2.11 | (29) op2(all_0_6_6, all_0_5_5) = all_0_7_7 % 7.00/2.11 | (30) op1(all_0_1_1, all_0_2_2) = all_0_4_4 % 7.00/2.11 | (31) op2(all_0_8_8, all_0_9_9) = all_0_8_8 % 7.00/2.11 | (32) op2(e23, e24) = e22 % 7.00/2.11 | (33) op1(all_0_3_3, all_0_2_2) = all_0_0_0 % 7.00/2.11 | (34) op2(all_0_9_9, all_0_6_6) = all_0_6_6 % 7.00/2.11 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) % 7.00/2.11 | (36) op1(all_0_2_2, all_0_2_2) = all_0_1_1 % 7.00/2.11 | (37) ~ (e23 = e10) % 7.00/2.11 | (38) op1(all_0_3_3, all_0_4_4) = all_0_3_3 % 7.00/2.11 | (39) op1(e10, e11) = e11 % 7.00/2.11 | (40) op1(all_0_2_2, all_0_4_4) = all_0_2_2 % 7.00/2.11 | (41) ~ (e23 = e22) % 7.00/2.11 | (42) op2(all_0_9_9, all_0_8_8) = all_0_8_8 % 7.00/2.11 | (43) op2(e22, e21) = e20 % 7.00/2.11 | (44) ~ (e22 = e12) % 7.00/2.11 | (45) op2(e23, e23) = e21 % 7.00/2.11 | (46) op2(e22, e24) = e21 % 7.00/2.11 | (47) ~ (e23 = e20) % 7.00/2.11 | (48) h(e14) = all_0_5_5 % 7.00/2.12 | (49) op1(e13, e13) = e11 % 7.00/2.12 | (50) ~ (e22 = e10) % 7.00/2.12 | (51) op2(all_0_7_7, all_0_9_9) = all_0_7_7 % 7.00/2.12 | (52) op2(e20, e22) = e22 % 7.00/2.12 | (53) op1(e13, e14) = e12 % 7.00/2.12 | (54) ~ (e14 = e10) % 7.00/2.12 | (55) op2(e23, e20) = e23 % 7.00/2.12 | (56) op1(all_0_0_0, all_0_0_0) = all_0_4_4 % 7.00/2.12 | (57) ~ (e14 = e12) % 7.00/2.12 | (58) ~ (e13 = e11) % 7.00/2.12 | (59) op2(all_0_7_7, all_0_7_7) = all_0_8_8 % 7.00/2.12 | (60) j(all_0_6_6) = e13 % 7.00/2.12 | (61) ~ (e20 = e13) % 7.00/2.12 | (62) j(e23) = all_0_1_1 % 7.00/2.12 | (63) j(all_0_5_5) = e14 % 7.00/2.12 | (64) op2(e24, e21) = e23 % 7.00/2.12 | (65) op1(e11, e10) = e11 % 7.00/2.12 | (66) op1(all_0_2_2, all_0_3_3) = all_0_4_4 % 7.00/2.12 | (67) ~ (e12 = e10) % 7.00/2.12 | (68) op2(all_0_5_5, all_0_9_9) = all_0_5_5 % 7.00/2.12 | (69) op1(all_0_0_0, all_0_1_1) = all_0_2_2 % 7.00/2.12 | (70) ~ (e20 = e11) % 7.00/2.12 | (71) h(all_0_1_1) = e23 % 7.00/2.12 | (72) op1(all_0_0_0, all_0_3_3) = all_0_1_1 % 7.00/2.12 | (73) op2(all_0_6_6, all_0_8_8) = all_0_9_9 % 7.00/2.12 | (74) op2(e23, e21) = e24 % 7.00/2.12 | (75) op2(e24, e23) = e22 % 7.00/2.12 | (76) j(e24) = all_0_0_0 % 7.00/2.12 | (77) op1(e13, e11) = e10 % 7.00/2.12 | (78) op2(all_0_5_5, all_0_5_5) = all_0_8_8 % 7.00/2.12 | (79) op2(all_0_6_6, all_0_7_7) = all_0_5_5 % 7.00/2.12 | (80) op2(all_0_8_8, all_0_6_6) = all_0_5_5 % 7.00/2.12 | (81) op2(all_0_7_7, all_0_5_5) = all_0_6_6 % 7.00/2.12 | (82) ~ (e23 = e13) % 7.00/2.12 | (83) ~ (e13 = e10) % 7.00/2.12 | (84) op2(all_0_7_7, all_0_8_8) = all_0_5_5 % 7.00/2.12 | (85) h(e12) = all_0_7_7 % 7.00/2.12 | (86) op1(all_0_1_1, all_0_1_1) = all_0_3_3 % 7.00/2.12 | (87) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) % 7.00/2.12 | (88) op1(e10, e10) = e10 % 7.00/2.12 | (89) ~ (e20 = e21) % 7.00/2.12 | (90) op2(e24, e20) = e24 % 7.00/2.12 | (91) j(e22) = all_0_2_2 % 7.00/2.12 | (92) ~ (e22 = e14) % 7.00/2.12 | (93) ~ (e24 = e13) % 7.00/2.12 | (94) j(all_0_8_8) = e11 % 7.00/2.12 | (95) op2(e20, e20) = e20 % 7.00/2.12 | (96) ~ (e24 = e14) % 7.00/2.12 | (97) op2(all_0_9_9, all_0_5_5) = all_0_5_5 % 7.00/2.12 | (98) op1(e10, e12) = e12 % 7.00/2.12 | (99) op1(all_0_0_0, all_0_2_2) = all_0_3_3 % 7.00/2.12 | (100) op1(e14, e11) = e13 % 7.00/2.12 | (101) ~ (e24 = e11) % 7.00/2.12 | (102) op1(e14, e12) = e10 % 7.00/2.12 | (103) op1(e12, e13) = e10 % 7.00/2.12 | (104) op1(all_0_4_4, all_0_0_0) = all_0_0_0 % 7.00/2.12 | (105) ~ (e20 = e12) % 7.00/2.12 | (106) ~ (e12 = e11) % 7.00/2.12 | (107) op1(e11, e11) = e12 % 7.00/2.12 | (108) all_0_4_4 = e14 | all_0_4_4 = e13 | all_0_4_4 = e12 | all_0_4_4 = e10 | all_0_4_4 = e11 % 7.00/2.12 | (109) op2(e21, e23) = e20 % 7.00/2.12 | (110) op1(all_0_1_1, all_0_3_3) = all_0_0_0 % 7.00/2.12 | (111) all_0_2_2 = e14 | all_0_2_2 = e13 | all_0_2_2 = e12 | all_0_2_2 = e10 | all_0_2_2 = e11 % 7.00/2.12 | (112) ~ (e21 = e10) % 7.00/2.12 | (113) all_0_0_0 = e14 | all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11 % 7.00/2.12 | (114) h(all_0_4_4) = e20 % 7.00/2.12 | (115) h(all_0_3_3) = e21 % 7.00/2.13 | (116) ~ (e24 = e20) % 7.00/2.13 | (117) ~ (e13 = e12) % 7.00/2.13 | (118) op2(all_0_8_8, all_0_5_5) = all_0_9_9 % 7.00/2.13 | (119) op1(all_0_2_2, all_0_0_0) = all_0_3_3 % 7.00/2.13 | (120) 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 % 7.00/2.13 | (121) all_0_6_6 = e24 | all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21 % 7.00/2.13 | (122) op1(all_0_4_4, all_0_4_4) = all_0_4_4 % 7.00/2.13 | (123) ~ (e22 = e20) % 7.00/2.13 | (124) op2(all_0_5_5, all_0_6_6) = all_0_7_7 % 7.00/2.13 | (125) op1(all_0_2_2, all_0_1_1) = all_0_0_0 % 7.00/2.13 | (126) op1(all_0_4_4, all_0_3_3) = all_0_3_3 % 7.00/2.13 | (127) ~ (e22 = e21) % 7.00/2.13 | (128) op1(e13, e12) = e14 % 7.00/2.13 | (129) op1(e11, e13) = e14 % 7.00/2.13 | (130) op1(e10, e13) = e13 % 7.00/2.13 | (131) op1(e11, e14) = e10 % 7.00/2.13 | (132) ~ (e23 = e12) % 7.00/2.13 | (133) all_0_8_8 = e24 | all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21 % 7.00/2.13 | (134) op1(e10, e14) = e14 % 7.00/2.13 | (135) op2(all_0_6_6, all_0_9_9) = all_0_6_6 % 7.00/2.13 | (136) op1(all_0_1_1, all_0_4_4) = all_0_1_1 % 7.00/2.13 | (137) ~ (e23 = e11) % 7.00/2.13 | (138) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) % 7.00/2.13 | (139) ~ (e23 = e21) % 7.00/2.13 | (140) h(e10) = all_0_9_9 % 7.00/2.13 | (141) op2(all_0_6_6, all_0_6_6) = all_0_8_8 % 7.00/2.13 | (142) h(e13) = all_0_6_6 % 7.00/2.13 | (143) op1(e14, e13) = e12 % 7.00/2.13 | (144) ~ (e14 = e13) % 7.00/2.13 | (145) ~ (e23 = e14) % 7.00/2.13 | (146) op2(all_0_7_7, all_0_6_6) = all_0_9_9 % 7.00/2.13 | (147) op2(e21, e24) = e23 % 7.00/2.13 | (148) 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 % 7.00/2.13 | (149) ~ (e21 = e13) % 7.00/2.13 | (150) ~ (e21 = e14) % 7.00/2.13 | (151) op1(e14, e10) = e14 % 7.00/2.13 | (152) h(all_0_0_0) = e24 % 7.00/2.13 | (153) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) % 7.00/2.13 | (154) op2(e23, e22) = e20 % 7.00/2.13 | (155) all_0_3_3 = e14 | all_0_3_3 = e13 | all_0_3_3 = e12 | all_0_3_3 = e10 | all_0_3_3 = e11 % 7.00/2.13 | (156) op1(all_0_4_4, all_0_1_1) = all_0_1_1 % 7.00/2.13 | (157) op1(e12, e14) = e13 % 7.00/2.13 | (158) op2(all_0_8_8, all_0_7_7) = all_0_6_6 % 7.00/2.13 | (159) op2(e21, e20) = e21 % 7.00/2.13 | (160) op1(e13, e10) = e13 % 7.00/2.13 | (161) op1(e12, e10) = e12 % 7.00/2.13 | (162) op2(e24, e24) = e20 % 7.00/2.13 | (163) op1(all_0_3_3, all_0_1_1) = all_0_4_4 % 7.00/2.13 | (164) ~ (e10 = e11) % 7.00/2.13 | (165) 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 % 7.00/2.13 | (166) op2(e24, e22) = e21 % 7.00/2.13 | (167) op1(all_0_0_0, all_0_4_4) = all_0_0_0 % 7.00/2.13 | (168) op2(all_0_9_9, all_0_9_9) = all_0_9_9 % 7.00/2.13 | (169) ~ (e20 = e14) % 7.00/2.14 | (170) ~ (e24 = e22) % 7.00/2.14 | (171) op2(all_0_9_9, all_0_7_7) = all_0_7_7 % 7.00/2.14 | (172) op1(all_0_3_3, all_0_3_3) = all_0_2_2 % 7.00/2.14 | (173) op2(e20, e21) = e21 % 7.00/2.14 | (174) op2(e22, e22) = e23 % 7.00/2.14 | (175) all_0_7_7 = e24 | all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21 % 7.00/2.14 | (176) j(all_0_9_9) = e10 % 7.00/2.14 | (177) op1(e12, e11) = e14 % 7.00/2.14 | (178) h(e11) = all_0_8_8 % 7.00/2.14 | (179) op2(e21, e21) = e22 % 7.00/2.14 | (180) j(all_0_7_7) = e12 % 7.00/2.14 | % 7.00/2.14 +-Applying beta-rule and splitting (113), into two cases. % 7.00/2.14 |-Branch one: % 7.00/2.14 | (181) all_0_0_0 = e14 % 7.00/2.14 | % 7.00/2.14 | From (181)(181) and (56) follows: % 7.00/2.14 | (182) op1(e14, e14) = all_0_4_4 % 7.00/2.14 | % 7.00/2.14 | Instantiating formula (35) with e14, e14, all_0_4_4, e11 and discharging atoms op1(e14, e14) = all_0_4_4, op1(e14, e14) = e11, yields: % 7.00/2.14 | (183) all_0_4_4 = e11 % 7.00/2.14 | % 7.00/2.14 | From (183)(183)(183) and (122) follows: % 7.00/2.14 | (184) op1(e11, e11) = e11 % 7.00/2.14 | % 7.00/2.14 | Instantiating formula (35) with e11, e11, e11, e12 and discharging atoms op1(e11, e11) = e12, op1(e11, e11) = e11, yields: % 7.00/2.14 | (185) e12 = e11 % 7.00/2.14 | % 7.00/2.14 | Equations (185) can reduce 106 to: % 7.00/2.14 | (186) $false % 7.00/2.14 | % 7.00/2.14 |-The branch is then unsatisfiable % 7.00/2.14 |-Branch two: % 7.00/2.14 | (187) ~ (all_0_0_0 = e14) % 7.00/2.14 | (188) all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11 % 7.00/2.14 | % 7.00/2.14 +-Applying beta-rule and splitting (165), into two cases. % 7.00/2.14 |-Branch one: % 7.00/2.14 | (189) all_0_9_9 = e24 % 7.00/2.14 | % 7.00/2.14 | From (189)(189)(189) and (168) follows: % 7.00/2.14 | (190) op2(e24, e24) = e24 % 7.00/2.14 | % 7.00/2.14 | Instantiating formula (138) with e24, e24, e24, e20 and discharging atoms op2(e24, e24) = e24, op2(e24, e24) = e20, yields: % 7.00/2.14 | (191) e24 = e20 % 7.00/2.14 | % 7.00/2.14 | Equations (191) can reduce 116 to: % 7.00/2.14 | (186) $false % 7.00/2.14 | % 7.00/2.14 |-The branch is then unsatisfiable % 7.00/2.14 |-Branch two: % 7.00/2.14 | (193) ~ (all_0_9_9 = e24) % 7.00/2.14 | (194) all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21 % 7.00/2.14 | % 7.00/2.14 +-Applying beta-rule and splitting (175), into two cases. % 7.00/2.14 |-Branch one: % 7.00/2.14 | (195) all_0_7_7 = e24 % 7.00/2.14 | % 7.00/2.14 | From (195)(195) and (59) follows: % 7.00/2.14 | (196) op2(e24, e24) = all_0_8_8 % 7.00/2.14 | % 7.00/2.14 | From (195) and (20) follows: % 7.00/2.14 | (197) op2(all_0_8_8, all_0_8_8) = e24 % 7.00/2.14 | % 7.00/2.14 | Instantiating formula (138) with e24, e24, all_0_8_8, e20 and discharging atoms op2(e24, e24) = all_0_8_8, op2(e24, e24) = e20, yields: % 7.00/2.14 | (198) all_0_8_8 = e20 % 7.00/2.14 | % 7.00/2.14 | From (198)(198) and (197) follows: % 7.00/2.14 | (199) op2(e20, e20) = e24 % 7.00/2.14 | % 7.00/2.14 | Instantiating formula (138) with e20, e20, e24, e20 and discharging atoms op2(e20, e20) = e24, op2(e20, e20) = e20, yields: % 7.00/2.14 | (191) e24 = e20 % 7.00/2.14 | % 7.00/2.14 | Equations (191) can reduce 116 to: % 7.00/2.14 | (186) $false % 7.00/2.14 | % 7.00/2.14 |-The branch is then unsatisfiable % 7.00/2.14 |-Branch two: % 7.00/2.14 | (202) ~ (all_0_7_7 = e24) % 7.00/2.14 | (203) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21 % 7.00/2.14 | % 7.00/2.14 +-Applying beta-rule and splitting (121), into two cases. % 7.00/2.14 |-Branch one: % 7.00/2.14 | (204) all_0_6_6 = e24 % 7.00/2.14 | % 7.00/2.14 | From (204)(204) and (141) follows: % 7.00/2.14 | (196) op2(e24, e24) = all_0_8_8 % 7.00/2.14 | % 7.00/2.14 | From (204) and (73) follows: % 7.00/2.14 | (206) op2(e24, all_0_8_8) = all_0_9_9 % 7.00/2.14 | % 7.00/2.14 | Instantiating formula (138) with e24, e24, all_0_8_8, e20 and discharging atoms op2(e24, e24) = all_0_8_8, op2(e24, e24) = e20, yields: % 7.00/2.14 | (198) all_0_8_8 = e20 % 7.00/2.14 | % 7.00/2.14 | From (198) and (206) follows: % 7.00/2.14 | (208) op2(e24, e20) = all_0_9_9 % 7.00/2.14 | % 7.00/2.14 | Instantiating formula (138) with e24, e20, all_0_9_9, e24 and discharging atoms op2(e24, e20) = all_0_9_9, op2(e24, e20) = e24, yields: % 7.00/2.14 | (189) all_0_9_9 = e24 % 7.00/2.14 | % 7.00/2.14 | Equations (189) can reduce 193 to: % 7.00/2.14 | (186) $false % 7.00/2.14 | % 7.00/2.14 |-The branch is then unsatisfiable % 7.00/2.14 |-Branch two: % 7.00/2.14 | (211) ~ (all_0_6_6 = e24) % 7.00/2.14 | (212) all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21 % 7.00/2.14 | % 7.00/2.14 +-Applying beta-rule and splitting (133), into two cases. % 7.00/2.14 |-Branch one: % 7.00/2.14 | (213) all_0_8_8 = e24 % 7.00/2.14 | % 7.00/2.14 | From (213) and (59) follows: % 7.00/2.14 | (214) op2(all_0_7_7, all_0_7_7) = e24 % 7.00/2.14 | % 7.00/2.14 | From (213)(213) and (20) follows: % 7.00/2.14 | (215) op2(e24, e24) = all_0_7_7 % 7.00/2.14 | % 7.00/2.14 | Instantiating formula (138) with e24, e24, all_0_7_7, e20 and discharging atoms op2(e24, e24) = all_0_7_7, op2(e24, e24) = e20, yields: % 7.00/2.14 | (216) all_0_7_7 = e20 % 7.00/2.14 | % 7.00/2.14 | Equations (216) can reduce 202 to: % 7.00/2.14 | (217) ~ (e24 = e20) % 7.00/2.14 | % 7.00/2.14 | Simplifying 217 yields: % 7.00/2.14 | (116) ~ (e24 = e20) % 7.00/2.14 | % 7.00/2.14 | From (216)(216) and (214) follows: % 7.00/2.14 | (199) op2(e20, e20) = e24 % 7.00/2.14 | % 7.00/2.14 | Instantiating formula (138) with e20, e20, e24, e20 and discharging atoms op2(e20, e20) = e24, op2(e20, e20) = e20, yields: % 7.00/2.14 | (191) e24 = e20 % 7.00/2.14 | % 7.00/2.14 | Equations (191) can reduce 116 to: % 7.00/2.14 | (186) $false % 7.00/2.14 | % 7.00/2.14 |-The branch is then unsatisfiable % 7.00/2.14 |-Branch two: % 7.00/2.14 | (222) ~ (all_0_8_8 = e24) % 7.00/2.15 | (223) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21 % 7.00/2.15 | % 7.00/2.15 +-Applying beta-rule and splitting (188), into two cases. % 7.00/2.15 |-Branch one: % 7.00/2.15 | (224) all_0_0_0 = e13 % 7.00/2.15 | % 7.00/2.15 | From (224) and (152) follows: % 7.00/2.15 | (225) h(e13) = e24 % 7.00/2.15 | % 7.00/2.15 | Instantiating formula (153) with e13, e24, all_0_6_6 and discharging atoms h(e13) = all_0_6_6, h(e13) = e24, yields: % 7.00/2.15 | (204) all_0_6_6 = e24 % 7.00/2.15 | % 7.00/2.15 | Equations (204) can reduce 211 to: % 7.00/2.15 | (186) $false % 7.00/2.15 | % 7.00/2.15 |-The branch is then unsatisfiable % 7.00/2.15 |-Branch two: % 7.00/2.15 | (228) ~ (all_0_0_0 = e13) % 7.00/2.15 | (229) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11 % 7.00/2.15 | % 7.00/2.15 +-Applying beta-rule and splitting (229), into two cases. % 7.00/2.15 |-Branch one: % 7.00/2.15 | (230) all_0_0_0 = e12 % 7.00/2.15 | % 7.00/2.15 | From (230) and (152) follows: % 7.00/2.15 | (231) h(e12) = e24 % 7.00/2.15 | % 7.00/2.15 | Instantiating formula (153) with e12, e24, all_0_7_7 and discharging atoms h(e12) = all_0_7_7, h(e12) = e24, yields: % 7.00/2.15 | (195) all_0_7_7 = e24 % 7.00/2.15 | % 7.00/2.15 | Equations (195) can reduce 202 to: % 7.00/2.15 | (186) $false % 7.00/2.15 | % 7.00/2.15 |-The branch is then unsatisfiable % 7.00/2.15 |-Branch two: % 7.00/2.15 | (234) ~ (all_0_0_0 = e12) % 7.00/2.15 | (235) all_0_0_0 = e10 | all_0_0_0 = e11 % 7.00/2.15 | % 7.00/2.15 +-Applying beta-rule and splitting (235), into two cases. % 7.00/2.15 |-Branch one: % 7.00/2.15 | (236) all_0_0_0 = e10 % 7.00/2.15 | % 7.00/2.15 | From (236) and (152) follows: % 7.00/2.15 | (237) h(e10) = e24 % 7.00/2.15 | % 7.00/2.15 | Instantiating formula (153) with e10, e24, all_0_9_9 and discharging atoms h(e10) = all_0_9_9, h(e10) = e24, yields: % 7.00/2.15 | (189) all_0_9_9 = e24 % 7.00/2.15 | % 7.00/2.15 | Equations (189) can reduce 193 to: % 7.00/2.15 | (186) $false % 7.00/2.15 | % 7.00/2.15 |-The branch is then unsatisfiable % 7.00/2.15 |-Branch two: % 7.00/2.15 | (240) ~ (all_0_0_0 = e10) % 7.00/2.15 | (241) all_0_0_0 = e11 % 7.00/2.15 | % 7.00/2.15 | From (241) and (152) follows: % 7.00/2.15 | (242) h(e11) = e24 % 7.00/2.15 | % 7.00/2.15 | Instantiating formula (153) with e11, e24, all_0_8_8 and discharging atoms h(e11) = all_0_8_8, h(e11) = e24, yields: % 7.00/2.15 | (213) all_0_8_8 = e24 % 7.00/2.15 | % 7.00/2.15 | Equations (213) can reduce 222 to: % 7.00/2.15 | (186) $false % 7.00/2.15 | % 7.00/2.15 |-The branch is then unsatisfiable % 7.00/2.15 % SZS output end Proof for theBenchmark % 7.00/2.15 % 7.00/2.15 1654ms %------------------------------------------------------------------------------