%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : ALG075+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 15:34:14 EDT 2022 % Result : Theorem 3.98s 1.50s % Output : Proof 7.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : ALG075+1 : TPTP v8.1.0. Released v2.7.0. % 0.03/0.12 % 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 18:11:36 EDT 2022 % 0.12/0.34 % CPUTime : % 0.54/0.57 ____ _ % 0.54/0.57 ___ / __ \_____(_)___ ________ __________ % 0.54/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.57 % 0.54/0.57 A Theorem Prover for First-Order Logic % 0.54/0.57 (ePrincess v.1.0) % 0.54/0.57 % 0.54/0.57 (c) Philipp Rümmer, 2009-2015 % 0.54/0.57 (c) Peter Backeman, 2014-2015 % 0.54/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.54/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.54/0.57 Bug reports to peter@backeman.se % 0.54/0.57 % 0.54/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.54/0.57 % 0.54/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.60/0.61 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.77/0.98 Prover 0: Preprocessing ... % 2.79/1.24 Prover 0: Constructing countermodel ... % 3.98/1.50 Prover 0: proved (885ms) % 3.98/1.50 % 3.98/1.50 No countermodel exists, formula is valid % 3.98/1.50 % SZS status Theorem for theBenchmark % 3.98/1.50 % 3.98/1.50 Generating proof ... found it (size 61) % 7.19/2.22 % 7.19/2.22 % SZS output start Proof for theBenchmark % 7.19/2.22 Assumed formulas after preprocessing and simplification: % 7.19/2.22 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (e24 = e23) & ~ (e24 = e22) & ~ (e24 = e20) & ~ (e24 = e21) & ~ (e24 = e14) & ~ (e24 = e13) & ~ (e24 = e12) & ~ (e24 = e10) & ~ (e24 = e11) & ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e23 = e14) & ~ (e23 = e13) & ~ (e23 = e12) & ~ (e23 = e10) & ~ (e23 = e11) & ~ (e22 = e20) & ~ (e22 = e21) & ~ (e22 = e14) & ~ (e22 = e13) & ~ (e22 = e12) & ~ (e22 = e10) & ~ (e22 = e11) & ~ (e20 = e21) & ~ (e20 = e14) & ~ (e20 = e13) & ~ (e20 = e12) & ~ (e20 = e10) & ~ (e20 = e11) & ~ (e21 = e14) & ~ (e21 = e13) & ~ (e21 = e12) & ~ (e21 = e10) & ~ (e21 = e11) & ~ (e14 = e13) & ~ (e14 = e12) & ~ (e14 = e10) & ~ (e14 = e11) & ~ (e13 = e12) & ~ (e13 = e10) & ~ (e13 = e11) & ~ (e12 = e10) & ~ (e12 = e11) & ~ (e10 = e11) & op2(v4, v4) = v2 & op2(v4, v3) = v0 & op2(v4, v2) = v1 & op2(v4, v1) = v3 & op2(v4, v0) = v4 & op2(v3, v4) = v0 & op2(v3, v3) = v1 & op2(v3, v2) = v4 & op2(v3, v1) = v2 & op2(v3, v0) = v3 & op2(v2, v4) = v1 & op2(v2, v3) = v4 & op2(v2, v2) = v3 & op2(v2, v1) = v0 & op2(v2, v0) = v2 & op2(v1, v4) = v3 & op2(v1, v3) = v2 & op2(v1, v2) = v0 & op2(v1, v1) = v4 & op2(v1, v0) = v1 & op2(v0, v4) = v4 & op2(v0, v3) = v3 & op2(v0, v2) = v2 & op2(v0, v1) = v1 & op2(v0, v0) = v0 & op2(e24, e24) = e20 & op2(e24, e23) = e22 & op2(e24, e22) = e21 & op2(e24, e20) = e24 & op2(e24, e21) = e23 & op2(e23, e24) = e21 & op2(e23, e23) = e20 & op2(e23, e22) = e24 & op2(e23, e20) = e23 & op2(e23, e21) = e22 & op2(e22, e24) = e23 & op2(e22, e23) = e21 & op2(e22, e22) = e20 & op2(e22, e20) = e22 & op2(e22, e21) = e24 & op2(e20, e24) = e24 & op2(e20, e23) = e23 & op2(e20, e22) = e22 & op2(e20, e20) = e20 & op2(e20, e21) = e21 & op2(e21, e24) = e22 & op2(e21, e23) = e24 & op2(e21, e22) = e23 & op2(e21, e20) = e21 & op2(e21, e21) = e20 & op1(v9, v9) = v5 & op1(v9, v8) = v7 & op1(v9, v7) = v6 & op1(v9, v6) = v8 & op1(v9, v5) = v9 & op1(v8, v9) = v6 & op1(v8, v8) = v5 & op1(v8, v7) = v9 & op1(v8, v6) = v7 & op1(v8, v5) = v8 & op1(v7, v9) = v8 & op1(v7, v8) = v6 & op1(v7, v7) = v5 & op1(v7, v6) = v9 & op1(v7, v5) = v7 & op1(v6, v9) = v7 & op1(v6, v8) = v9 & op1(v6, v7) = v8 & op1(v6, v6) = v5 & op1(v6, v5) = v6 & op1(v5, v9) = v9 & op1(v5, v8) = v8 & op1(v5, v7) = v7 & op1(v5, v6) = v6 & op1(v5, v5) = v5 & op1(e14, e14) = e12 & op1(e14, e13) = e10 & op1(e14, e12) = e11 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e14) = e10 & op1(e13, e13) = e11 & op1(e13, e12) = e14 & op1(e13, e10) = e13 & op1(e13, e11) = e12 & op1(e12, e14) = e11 & op1(e12, e13) = e14 & op1(e12, e12) = e13 & op1(e12, e10) = e12 & op1(e12, e11) = e10 & op1(e10, e14) = e14 & op1(e10, e13) = e13 & op1(e10, e12) = e12 & op1(e10, e10) = e10 & op1(e10, e11) = e11 & op1(e11, e14) = e13 & op1(e11, e13) = e12 & op1(e11, e12) = e10 & op1(e11, e10) = e11 & op1(e11, e11) = e14 & h(v9) = e24 & h(v8) = e23 & h(v7) = e22 & h(v6) = e21 & h(v5) = e20 & h(e14) = v4 & h(e13) = v3 & h(e12) = v2 & h(e10) = v0 & h(e11) = v1 & j(v4) = e14 & j(v3) = e13 & j(v2) = e12 & j(v1) = e11 & j(v0) = e10 & j(e24) = v9 & j(e23) = v8 & j(e22) = v7 & j(e20) = v5 & j(e21) = v6 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (op2(v13, v12) = v11) | ~ (op2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (op1(v13, v12) = v11) | ~ (op1(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (h(v12) = v11) | ~ (h(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (j(v12) = v11) | ~ (j(v12) = v10)) & (v9 = e14 | v9 = e13 | v9 = e12 | v9 = e10 | v9 = e11) & (v8 = e14 | v8 = e13 | v8 = e12 | v8 = e10 | v8 = e11) & (v7 = e14 | v7 = e13 | v7 = e12 | v7 = e10 | v7 = e11) & (v6 = e14 | v6 = e13 | v6 = e12 | v6 = e10 | v6 = e11) & (v5 = e14 | v5 = e13 | v5 = e12 | v5 = e10 | v5 = e11) & (v4 = e24 | v4 = e23 | v4 = e22 | v4 = e20 | v4 = e21) & (v3 = e24 | v3 = e23 | v3 = e22 | v3 = e20 | v3 = e21) & (v2 = e24 | v2 = e23 | v2 = e22 | v2 = e20 | v2 = e21) & (v1 = e24 | v1 = e23 | v1 = e22 | v1 = e20 | v1 = e21) & (v0 = e24 | v0 = e23 | v0 = e22 | v0 = e20 | v0 = e21)) % 7.19/2.26 | 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: % 7.19/2.26 | (1) ~ (e24 = e23) & ~ (e24 = e22) & ~ (e24 = e20) & ~ (e24 = e21) & ~ (e24 = e14) & ~ (e24 = e13) & ~ (e24 = e12) & ~ (e24 = e10) & ~ (e24 = e11) & ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e23 = e14) & ~ (e23 = e13) & ~ (e23 = e12) & ~ (e23 = e10) & ~ (e23 = e11) & ~ (e22 = e20) & ~ (e22 = e21) & ~ (e22 = e14) & ~ (e22 = e13) & ~ (e22 = e12) & ~ (e22 = e10) & ~ (e22 = e11) & ~ (e20 = e21) & ~ (e20 = e14) & ~ (e20 = e13) & ~ (e20 = e12) & ~ (e20 = e10) & ~ (e20 = e11) & ~ (e21 = e14) & ~ (e21 = e13) & ~ (e21 = e12) & ~ (e21 = e10) & ~ (e21 = e11) & ~ (e14 = e13) & ~ (e14 = e12) & ~ (e14 = e10) & ~ (e14 = e11) & ~ (e13 = e12) & ~ (e13 = e10) & ~ (e13 = e11) & ~ (e12 = e10) & ~ (e12 = e11) & ~ (e10 = e11) & op2(all_0_5_5, all_0_5_5) = all_0_7_7 & op2(all_0_5_5, all_0_6_6) = all_0_9_9 & op2(all_0_5_5, all_0_7_7) = all_0_8_8 & op2(all_0_5_5, all_0_8_8) = all_0_6_6 & op2(all_0_5_5, all_0_9_9) = all_0_5_5 & op2(all_0_6_6, all_0_5_5) = all_0_9_9 & op2(all_0_6_6, all_0_6_6) = all_0_8_8 & op2(all_0_6_6, all_0_7_7) = all_0_5_5 & op2(all_0_6_6, all_0_8_8) = all_0_7_7 & op2(all_0_6_6, all_0_9_9) = all_0_6_6 & op2(all_0_7_7, all_0_5_5) = all_0_8_8 & op2(all_0_7_7, all_0_6_6) = all_0_5_5 & op2(all_0_7_7, all_0_7_7) = all_0_6_6 & op2(all_0_7_7, all_0_8_8) = all_0_9_9 & op2(all_0_7_7, all_0_9_9) = all_0_7_7 & op2(all_0_8_8, all_0_5_5) = all_0_6_6 & op2(all_0_8_8, all_0_6_6) = all_0_7_7 & op2(all_0_8_8, all_0_7_7) = all_0_9_9 & op2(all_0_8_8, all_0_8_8) = all_0_5_5 & op2(all_0_8_8, all_0_9_9) = all_0_8_8 & op2(all_0_9_9, all_0_5_5) = all_0_5_5 & op2(all_0_9_9, all_0_6_6) = all_0_6_6 & op2(all_0_9_9, all_0_7_7) = all_0_7_7 & op2(all_0_9_9, all_0_8_8) = all_0_8_8 & op2(all_0_9_9, all_0_9_9) = all_0_9_9 & op2(e24, e24) = e20 & op2(e24, e23) = e22 & op2(e24, e22) = e21 & op2(e24, e20) = e24 & op2(e24, e21) = e23 & op2(e23, e24) = e21 & op2(e23, e23) = e20 & op2(e23, e22) = e24 & op2(e23, e20) = e23 & op2(e23, e21) = e22 & op2(e22, e24) = e23 & op2(e22, e23) = e21 & op2(e22, e22) = e20 & op2(e22, e20) = e22 & op2(e22, e21) = e24 & op2(e20, e24) = e24 & op2(e20, e23) = e23 & op2(e20, e22) = e22 & op2(e20, e20) = e20 & op2(e20, e21) = e21 & op2(e21, e24) = e22 & op2(e21, e23) = e24 & op2(e21, e22) = e23 & op2(e21, e20) = e21 & op2(e21, e21) = e20 & 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_3_3 & op1(all_0_1_1, all_0_1_1) = all_0_4_4 & op1(all_0_1_1, all_0_2_2) = all_0_0_0 & op1(all_0_1_1, all_0_3_3) = all_0_2_2 & op1(all_0_1_1, all_0_4_4) = all_0_1_1 & op1(all_0_2_2, all_0_0_0) = all_0_1_1 & op1(all_0_2_2, all_0_1_1) = all_0_3_3 & op1(all_0_2_2, all_0_2_2) = all_0_4_4 & op1(all_0_2_2, all_0_3_3) = all_0_0_0 & op1(all_0_2_2, all_0_4_4) = all_0_2_2 & op1(all_0_3_3, all_0_0_0) = all_0_2_2 & op1(all_0_3_3, all_0_1_1) = all_0_0_0 & op1(all_0_3_3, all_0_2_2) = all_0_1_1 & op1(all_0_3_3, all_0_3_3) = all_0_4_4 & op1(all_0_3_3, all_0_4_4) = all_0_3_3 & op1(all_0_4_4, all_0_0_0) = all_0_0_0 & op1(all_0_4_4, all_0_1_1) = all_0_1_1 & op1(all_0_4_4, all_0_2_2) = all_0_2_2 & op1(all_0_4_4, all_0_3_3) = all_0_3_3 & op1(all_0_4_4, all_0_4_4) = all_0_4_4 & op1(e14, e14) = e12 & op1(e14, e13) = e10 & op1(e14, e12) = e11 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e14) = e10 & op1(e13, e13) = e11 & op1(e13, e12) = e14 & op1(e13, e10) = e13 & op1(e13, e11) = e12 & op1(e12, e14) = e11 & op1(e12, e13) = e14 & op1(e12, e12) = e13 & op1(e12, e10) = e12 & op1(e12, e11) = e10 & op1(e10, e14) = e14 & op1(e10, e13) = e13 & op1(e10, e12) = e12 & op1(e10, e10) = e10 & op1(e10, e11) = e11 & op1(e11, e14) = e13 & op1(e11, e13) = e12 & op1(e11, e12) = e10 & op1(e11, e10) = e11 & op1(e11, e11) = e14 & h(all_0_0_0) = e24 & h(all_0_1_1) = e23 & h(all_0_2_2) = e22 & h(all_0_3_3) = e21 & h(all_0_4_4) = e20 & h(e14) = all_0_5_5 & h(e13) = all_0_6_6 & h(e12) = all_0_7_7 & h(e10) = all_0_9_9 & h(e11) = all_0_8_8 & j(all_0_5_5) = e14 & j(all_0_6_6) = e13 & j(all_0_7_7) = e12 & j(all_0_8_8) = e11 & j(all_0_9_9) = e10 & j(e24) = all_0_0_0 & j(e23) = all_0_1_1 & j(e22) = all_0_2_2 & j(e20) = all_0_4_4 & j(e21) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) & (all_0_0_0 = e14 | all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11) & (all_0_1_1 = e14 | all_0_1_1 = e13 | all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11) & (all_0_2_2 = e14 | all_0_2_2 = e13 | all_0_2_2 = e12 | all_0_2_2 = e10 | all_0_2_2 = e11) & (all_0_3_3 = e14 | all_0_3_3 = e13 | all_0_3_3 = e12 | all_0_3_3 = e10 | all_0_3_3 = e11) & (all_0_4_4 = e14 | all_0_4_4 = e13 | all_0_4_4 = e12 | all_0_4_4 = e10 | all_0_4_4 = e11) & (all_0_5_5 = e24 | all_0_5_5 = e23 | all_0_5_5 = e22 | all_0_5_5 = e20 | all_0_5_5 = e21) & (all_0_6_6 = e24 | all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21) & (all_0_7_7 = e24 | all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21) & (all_0_8_8 = e24 | all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21) & (all_0_9_9 = e24 | all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21) % 7.19/2.27 | % 7.19/2.27 | Applying alpha-rule on (1) yields: % 7.19/2.27 | (2) ~ (e21 = e12) % 7.19/2.27 | (3) op1(all_0_4_4, all_0_1_1) = all_0_1_1 % 7.19/2.27 | (4) op2(all_0_7_7, all_0_8_8) = all_0_9_9 % 7.19/2.27 | (5) op1(e13, e12) = e14 % 7.19/2.27 | (6) ~ (e20 = e21) % 7.19/2.28 | (7) ~ (e20 = e14) % 7.19/2.28 | (8) op1(e12, e12) = e13 % 7.19/2.28 | (9) op2(e20, e23) = e23 % 7.19/2.28 | (10) op1(all_0_4_4, all_0_2_2) = all_0_2_2 % 7.19/2.28 | (11) ~ (e24 = e11) % 7.19/2.28 | (12) ~ (e12 = e11) % 7.19/2.28 | (13) h(e12) = all_0_7_7 % 7.19/2.28 | (14) h(all_0_0_0) = e24 % 7.19/2.28 | (15) h(e13) = all_0_6_6 % 7.19/2.28 | (16) op2(all_0_5_5, all_0_8_8) = all_0_6_6 % 7.19/2.28 | (17) ~ (e14 = e12) % 7.19/2.28 | (18) op2(e23, e21) = e22 % 7.19/2.28 | (19) ~ (e24 = e12) % 7.19/2.28 | (20) op1(e10, e11) = e11 % 7.19/2.28 | (21) j(e22) = all_0_2_2 % 7.19/2.28 | (22) op1(all_0_2_2, all_0_1_1) = all_0_3_3 % 7.19/2.28 | (23) op2(all_0_9_9, all_0_8_8) = all_0_8_8 % 7.19/2.28 | (24) j(e21) = all_0_3_3 % 7.19/2.28 | (25) j(all_0_8_8) = e11 % 7.19/2.28 | (26) ~ (e22 = e13) % 7.19/2.28 | (27) op2(all_0_6_6, all_0_9_9) = all_0_6_6 % 7.19/2.28 | (28) op2(all_0_8_8, all_0_6_6) = all_0_7_7 % 7.19/2.28 | (29) op1(e12, e14) = e11 % 7.19/2.28 | (30) op2(e24, e21) = e23 % 7.19/2.28 | (31) op1(all_0_3_3, all_0_4_4) = all_0_3_3 % 7.19/2.28 | (32) j(all_0_6_6) = e13 % 7.19/2.28 | (33) op2(e24, e22) = e21 % 7.19/2.28 | (34) op2(all_0_5_5, all_0_7_7) = all_0_8_8 % 7.19/2.28 | (35) h(all_0_4_4) = e20 % 7.19/2.28 | (36) op1(all_0_2_2, all_0_0_0) = all_0_1_1 % 7.19/2.28 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) % 7.19/2.28 | (38) op2(all_0_5_5, all_0_5_5) = all_0_7_7 % 7.19/2.28 | (39) op1(e14, e14) = e12 % 7.19/2.28 | (40) op2(e21, e22) = e23 % 7.19/2.28 | (41) ~ (e23 = e13) % 7.19/2.28 | (42) op1(all_0_0_0, all_0_4_4) = all_0_0_0 % 7.19/2.28 | (43) op2(all_0_9_9, all_0_6_6) = all_0_6_6 % 7.19/2.28 | (44) op2(e22, e20) = e22 % 7.19/2.28 | (45) 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 % 7.19/2.28 | (46) ~ (e23 = e12) % 7.19/2.28 | (47) op1(e11, e10) = e11 % 7.19/2.28 | (48) ~ (e24 = e14) % 7.19/2.28 | (49) h(all_0_3_3) = e21 % 7.19/2.28 | (50) ~ (e23 = e21) % 7.19/2.28 | (51) op1(e13, e11) = e12 % 7.19/2.28 | (52) all_0_1_1 = e14 | all_0_1_1 = e13 | all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11 % 7.19/2.28 | (53) op2(e23, e24) = e21 % 7.19/2.28 | (54) ~ (e22 = e21) % 7.19/2.28 | (55) ~ (e20 = e11) % 7.19/2.28 | (56) j(all_0_9_9) = e10 % 7.19/2.28 | (57) ~ (e14 = e10) % 7.19/2.28 | (58) ~ (e22 = e10) % 7.19/2.28 | (59) op1(all_0_0_0, all_0_0_0) = all_0_4_4 % 7.19/2.28 | (60) op1(e14, e12) = e11 % 7.19/2.28 | (61) h(all_0_1_1) = e23 % 7.19/2.28 | (62) op2(all_0_9_9, all_0_9_9) = all_0_9_9 % 7.19/2.28 | (63) op2(all_0_9_9, all_0_7_7) = all_0_7_7 % 7.19/2.28 | (64) op1(e12, e10) = e12 % 7.19/2.28 | (65) ~ (e12 = e10) % 7.19/2.28 | (66) ~ (e24 = e22) % 7.19/2.28 | (67) op1(all_0_1_1, all_0_4_4) = all_0_1_1 % 7.19/2.28 | (68) 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 % 7.19/2.29 | (69) op2(e20, e24) = e24 % 7.19/2.29 | (70) op2(e22, e21) = e24 % 7.19/2.29 | (71) op2(e20, e20) = e20 % 7.19/2.29 | (72) op2(e21, e24) = e22 % 7.19/2.29 | (73) 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 % 7.19/2.29 | (74) op2(all_0_6_6, all_0_5_5) = all_0_9_9 % 7.19/2.29 | (75) op2(all_0_7_7, all_0_9_9) = all_0_7_7 % 7.19/2.29 | (76) op1(all_0_0_0, all_0_1_1) = all_0_2_2 % 7.19/2.29 | (77) j(all_0_7_7) = e12 % 7.19/2.29 | (78) op2(all_0_8_8, all_0_5_5) = all_0_6_6 % 7.19/2.29 | (79) op2(all_0_5_5, all_0_9_9) = all_0_5_5 % 7.19/2.29 | (80) h(all_0_2_2) = e22 % 7.19/2.29 | (81) op1(e12, e13) = e14 % 7.19/2.29 | (82) ~ (e14 = e13) % 7.19/2.29 | (83) op2(e22, e23) = e21 % 7.19/2.29 | (84) ~ (e21 = e11) % 7.19/2.29 | (85) h(e14) = all_0_5_5 % 7.19/2.29 | (86) ~ (e24 = e20) % 7.19/2.29 | (87) ~ (e13 = e12) % 7.19/2.29 | (88) op2(all_0_6_6, all_0_7_7) = all_0_5_5 % 7.19/2.29 | (89) 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 % 7.19/2.29 | (90) op2(all_0_8_8, all_0_8_8) = all_0_5_5 % 7.19/2.29 | (91) op1(e11, e12) = e10 % 7.19/2.29 | (92) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) % 7.19/2.29 | (93) ~ (e14 = e11) % 7.19/2.29 | (94) op2(e21, e21) = e20 % 7.19/2.29 | (95) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) % 7.19/2.29 | (96) op1(all_0_2_2, all_0_4_4) = all_0_2_2 % 7.19/2.29 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) % 7.19/2.29 | (98) 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 % 7.19/2.29 | (99) op2(all_0_6_6, all_0_8_8) = all_0_7_7 % 7.19/2.29 | (100) op1(e13, e10) = e13 % 7.19/2.29 | (101) op1(e10, e10) = e10 % 7.19/2.29 | (102) op1(all_0_0_0, all_0_3_3) = all_0_1_1 % 7.19/2.29 | (103) ~ (e23 = e10) % 7.19/2.29 | (104) op1(all_0_4_4, all_0_4_4) = all_0_4_4 % 7.19/2.29 | (105) ~ (e13 = e10) % 7.19/2.29 | (106) op1(e10, e12) = e12 % 7.19/2.29 | (107) 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 % 7.19/2.29 | (108) 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 % 7.19/2.29 | (109) ~ (e23 = e22) % 7.19/2.29 | (110) op2(all_0_5_5, all_0_6_6) = all_0_9_9 % 7.19/2.29 | (111) ~ (e20 = e10) % 7.19/2.29 | (112) ~ (e22 = e11) % 7.19/2.29 | (113) op1(all_0_3_3, all_0_0_0) = all_0_2_2 % 7.19/2.29 | (114) op1(e13, e14) = e10 % 7.56/2.29 | (115) ~ (e20 = e12) % 7.56/2.29 | (116) op2(all_0_7_7, all_0_5_5) = all_0_8_8 % 7.56/2.29 | (117) op1(all_0_0_0, all_0_2_2) = all_0_3_3 % 7.56/2.29 | (118) op2(e23, e22) = e24 % 7.56/2.29 | (119) op1(e14, e11) = e13 % 7.56/2.29 | (120) op2(e24, e20) = e24 % 7.56/2.30 | (121) op1(all_0_4_4, all_0_0_0) = all_0_0_0 % 7.56/2.30 | (122) 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 % 7.56/2.30 | (123) ~ (e10 = e11) % 7.56/2.30 | (124) op1(all_0_1_1, all_0_1_1) = all_0_4_4 % 7.56/2.30 | (125) op1(all_0_3_3, all_0_2_2) = all_0_1_1 % 7.56/2.30 | (126) ~ (e23 = e14) % 7.56/2.30 | (127) h(e11) = all_0_8_8 % 7.56/2.30 | (128) op2(e23, e23) = e20 % 7.56/2.30 | (129) op1(e10, e13) = e13 % 7.56/2.30 | (130) op1(e14, e10) = e14 % 7.56/2.30 | (131) j(e23) = all_0_1_1 % 7.56/2.30 | (132) ~ (e23 = e20) % 7.56/2.30 | (133) op2(e21, e20) = e21 % 7.56/2.30 | (134) ~ (e21 = e14) % 7.56/2.30 | (135) op1(all_0_1_1, all_0_0_0) = all_0_3_3 % 7.56/2.30 | (136) j(e24) = all_0_0_0 % 7.56/2.30 | (137) op2(all_0_7_7, all_0_6_6) = all_0_5_5 % 7.56/2.30 | (138) op2(e24, e24) = e20 % 7.56/2.30 | (139) op1(e12, e11) = e10 % 7.56/2.30 | (140) op1(all_0_3_3, all_0_1_1) = all_0_0_0 % 7.56/2.30 | (141) op1(e10, e14) = e14 % 7.56/2.30 | (142) ~ (e24 = e21) % 7.56/2.30 | (143) op1(e11, e14) = e13 % 7.56/2.30 | (144) op1(all_0_2_2, all_0_2_2) = all_0_4_4 % 7.56/2.30 | (145) op2(all_0_8_8, all_0_9_9) = all_0_8_8 % 7.56/2.30 | (146) j(all_0_5_5) = e14 % 7.56/2.30 | (147) op2(e23, e20) = e23 % 7.56/2.30 | (148) op1(all_0_1_1, all_0_2_2) = all_0_0_0 % 7.56/2.30 | (149) ~ (e22 = e20) % 7.56/2.30 | (150) ~ (e23 = e11) % 7.56/2.30 | (151) op2(all_0_6_6, all_0_6_6) = all_0_8_8 % 7.56/2.30 | (152) op1(all_0_1_1, all_0_3_3) = all_0_2_2 % 7.56/2.30 | (153) op2(all_0_7_7, all_0_7_7) = all_0_6_6 % 7.56/2.30 | (154) op2(e22, e22) = e20 % 7.56/2.30 | (155) op1(e11, e11) = e14 % 7.56/2.30 | (156) op2(e21, e23) = e24 % 7.56/2.30 | (157) op2(all_0_8_8, all_0_7_7) = all_0_9_9 % 7.56/2.30 | (158) op1(all_0_2_2, all_0_3_3) = all_0_0_0 % 7.56/2.30 | (159) ~ (e24 = e10) % 7.56/2.30 | (160) ~ (e24 = e23) % 7.56/2.30 | (161) op1(e11, e13) = e12 % 7.56/2.30 | (162) ~ (e20 = e13) % 7.56/2.30 | (163) ~ (e24 = e13) % 7.56/2.30 | (164) op1(all_0_4_4, all_0_3_3) = all_0_3_3 % 7.56/2.30 | (165) ~ (e21 = e10) % 7.56/2.30 | (166) ~ (e21 = e13) % 7.56/2.30 | (167) j(e20) = all_0_4_4 % 7.56/2.30 | (168) ~ (e22 = e12) % 7.56/2.30 | (169) op2(e24, e23) = e22 % 7.56/2.30 | (170) op1(all_0_3_3, all_0_3_3) = all_0_4_4 % 7.56/2.30 | (171) op2(e20, e22) = e22 % 7.56/2.31 | (172) op1(e13, e13) = e11 % 7.56/2.31 | (173) 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 % 7.56/2.31 | (174) op2(e22, e24) = e23 % 7.56/2.31 | (175) op1(e14, e13) = e10 % 7.56/2.31 | (176) h(e10) = all_0_9_9 % 7.56/2.31 | (177) ~ (e22 = e14) % 7.56/2.31 | (178) op2(e20, e21) = e21 % 7.56/2.31 | (179) op2(all_0_9_9, all_0_5_5) = all_0_5_5 % 7.56/2.31 | (180) ~ (e13 = e11) % 7.56/2.31 | % 7.56/2.31 +-Applying beta-rule and splitting (108), into two cases. % 7.56/2.31 |-Branch one: % 7.56/2.31 | (181) all_0_0_0 = e14 % 7.56/2.31 | % 7.56/2.31 | From (181)(181) and (59) follows: % 7.56/2.31 | (182) op1(e14, e14) = all_0_4_4 % 7.56/2.31 | % 7.56/2.31 | Instantiating formula (97) with e14, e14, all_0_4_4, e12 and discharging atoms op1(e14, e14) = all_0_4_4, op1(e14, e14) = e12, yields: % 7.56/2.31 | (183) all_0_4_4 = e12 % 7.56/2.31 | % 7.56/2.31 | From (183)(183)(183) and (104) follows: % 7.56/2.31 | (184) op1(e12, e12) = e12 % 7.56/2.31 | % 7.56/2.31 | Instantiating formula (97) with e12, e12, e12, e13 and discharging atoms op1(e12, e12) = e13, op1(e12, e12) = e12, yields: % 7.56/2.31 | (185) e13 = e12 % 7.56/2.31 | % 7.56/2.31 | Equations (185) can reduce 87 to: % 7.56/2.31 | (186) $false % 7.56/2.31 | % 7.56/2.31 |-The branch is then unsatisfiable % 7.56/2.31 |-Branch two: % 7.56/2.31 | (187) ~ (all_0_0_0 = e14) % 7.56/2.31 | (188) all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11 % 7.56/2.31 | % 7.56/2.31 +-Applying beta-rule and splitting (68), into two cases. % 7.56/2.31 |-Branch one: % 7.56/2.31 | (189) all_0_9_9 = e24 % 7.56/2.31 | % 7.56/2.31 | From (189)(189)(189) and (62) follows: % 7.56/2.31 | (190) op2(e24, e24) = e24 % 7.56/2.31 | % 7.56/2.31 | Instantiating formula (37) with e24, e24, e24, e20 and discharging atoms op2(e24, e24) = e24, op2(e24, e24) = e20, yields: % 7.56/2.31 | (191) e24 = e20 % 7.56/2.31 | % 7.56/2.31 | Equations (191) can reduce 86 to: % 7.56/2.31 | (186) $false % 7.56/2.31 | % 7.56/2.31 |-The branch is then unsatisfiable % 7.56/2.31 |-Branch two: % 7.56/2.31 | (193) ~ (all_0_9_9 = e24) % 7.56/2.31 | (194) all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21 % 7.56/2.31 | % 7.56/2.31 +-Applying beta-rule and splitting (89), into two cases. % 7.56/2.31 |-Branch one: % 7.56/2.31 | (195) all_0_7_7 = e24 % 7.56/2.31 | % 7.56/2.31 | From (195)(195) and (153) follows: % 7.56/2.31 | (196) op2(e24, e24) = all_0_6_6 % 7.56/2.31 | % 7.56/2.31 | Instantiating formula (37) with e24, e24, all_0_6_6, e20 and discharging atoms op2(e24, e24) = all_0_6_6, op2(e24, e24) = e20, yields: % 7.56/2.31 | (197) all_0_6_6 = e20 % 7.56/2.31 | % 7.56/2.31 | From (197)(197) and (151) follows: % 7.56/2.32 | (198) op2(e20, e20) = all_0_8_8 % 7.56/2.32 | % 7.56/2.32 | From (197) and (32) follows: % 7.56/2.32 | (199) j(e20) = e13 % 7.56/2.32 | % 7.56/2.32 | Instantiating formula (37) with e20, e20, all_0_8_8, e20 and discharging atoms op2(e20, e20) = all_0_8_8, op2(e20, e20) = e20, yields: % 7.56/2.32 | (200) all_0_8_8 = e20 % 7.56/2.32 | % 7.56/2.32 | Instantiating formula (95) with e20, e13, all_0_4_4 and discharging atoms j(e20) = all_0_4_4, j(e20) = e13, yields: % 7.56/2.32 | (201) all_0_4_4 = e13 % 7.56/2.32 | % 7.56/2.32 | From (200) and (25) follows: % 7.56/2.32 | (202) j(e20) = e11 % 7.56/2.32 | % 7.56/2.32 | From (201) and (167) follows: % 7.56/2.32 | (199) j(e20) = e13 % 7.56/2.32 | % 7.56/2.32 | Instantiating formula (95) with e20, e11, e13 and discharging atoms j(e20) = e13, j(e20) = e11, yields: % 7.56/2.32 | (204) e13 = e11 % 7.56/2.32 | % 7.56/2.32 | Equations (204) can reduce 180 to: % 7.56/2.32 | (186) $false % 7.56/2.32 | % 7.56/2.32 |-The branch is then unsatisfiable % 7.56/2.32 |-Branch two: % 7.56/2.32 | (206) ~ (all_0_7_7 = e24) % 7.56/2.32 | (207) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21 % 7.56/2.32 | % 7.56/2.32 +-Applying beta-rule and splitting (107), into two cases. % 7.56/2.32 |-Branch one: % 7.56/2.32 | (208) all_0_6_6 = e24 % 7.56/2.32 | % 7.56/2.32 | From (208)(208) and (151) follows: % 7.56/2.32 | (209) op2(e24, e24) = all_0_8_8 % 7.56/2.32 | % 7.56/2.32 | From (208) and (28) follows: % 7.56/2.32 | (210) op2(all_0_8_8, e24) = all_0_7_7 % 7.56/2.32 | % 7.56/2.32 | Instantiating formula (37) with e24, e24, all_0_8_8, e20 and discharging atoms op2(e24, e24) = all_0_8_8, op2(e24, e24) = e20, yields: % 7.56/2.32 | (200) all_0_8_8 = e20 % 7.56/2.32 | % 7.56/2.32 | From (200) and (210) follows: % 7.56/2.32 | (212) op2(e20, e24) = all_0_7_7 % 7.56/2.32 | % 7.56/2.32 | Instantiating formula (37) with e20, e24, all_0_7_7, e24 and discharging atoms op2(e20, e24) = all_0_7_7, op2(e20, e24) = e24, yields: % 7.56/2.32 | (195) all_0_7_7 = e24 % 7.56/2.32 | % 7.56/2.32 | Equations (195) can reduce 206 to: % 7.56/2.32 | (186) $false % 7.56/2.32 | % 7.56/2.32 |-The branch is then unsatisfiable % 7.56/2.32 |-Branch two: % 7.56/2.32 | (215) ~ (all_0_6_6 = e24) % 7.56/2.32 | (216) all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21 % 7.56/2.32 | % 7.56/2.32 +-Applying beta-rule and splitting (122), into two cases. % 7.56/2.32 |-Branch one: % 7.56/2.32 | (217) all_0_8_8 = e24 % 7.56/2.32 | % 7.56/2.32 | From (217) and (16) follows: % 7.56/2.32 | (218) op2(all_0_5_5, e24) = all_0_6_6 % 7.56/2.32 | % 7.56/2.32 | From (217)(217) and (90) follows: % 7.56/2.32 | (219) op2(e24, e24) = all_0_5_5 % 7.56/2.32 | % 7.56/2.32 | Instantiating formula (37) with e24, e24, all_0_5_5, e20 and discharging atoms op2(e24, e24) = all_0_5_5, op2(e24, e24) = e20, yields: % 7.56/2.32 | (220) all_0_5_5 = e20 % 7.56/2.32 | % 7.56/2.32 | From (220) and (218) follows: % 7.56/2.32 | (221) op2(e20, e24) = all_0_6_6 % 7.56/2.32 | % 7.56/2.32 | Instantiating formula (37) with e20, e24, all_0_6_6, e24 and discharging atoms op2(e20, e24) = all_0_6_6, op2(e20, e24) = e24, yields: % 7.56/2.32 | (208) all_0_6_6 = e24 % 7.56/2.32 | % 7.56/2.32 | Equations (208) can reduce 215 to: % 7.56/2.32 | (186) $false % 7.56/2.32 | % 7.56/2.32 |-The branch is then unsatisfiable % 7.56/2.32 |-Branch two: % 7.56/2.32 | (224) ~ (all_0_8_8 = e24) % 7.56/2.33 | (225) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21 % 7.56/2.33 | % 7.56/2.33 +-Applying beta-rule and splitting (188), into two cases. % 7.56/2.33 |-Branch one: % 7.56/2.33 | (226) all_0_0_0 = e13 % 7.56/2.33 | % 7.56/2.33 | From (226) and (14) follows: % 7.56/2.33 | (227) h(e13) = e24 % 7.56/2.33 | % 7.56/2.33 | Instantiating formula (92) with e13, e24, all_0_6_6 and discharging atoms h(e13) = all_0_6_6, h(e13) = e24, yields: % 7.56/2.33 | (208) all_0_6_6 = e24 % 7.56/2.33 | % 7.56/2.33 | Equations (208) can reduce 215 to: % 7.56/2.33 | (186) $false % 7.56/2.33 | % 7.56/2.33 |-The branch is then unsatisfiable % 7.56/2.33 |-Branch two: % 7.56/2.33 | (230) ~ (all_0_0_0 = e13) % 7.56/2.33 | (231) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11 % 7.56/2.33 | % 7.56/2.33 +-Applying beta-rule and splitting (231), into two cases. % 7.56/2.33 |-Branch one: % 7.56/2.33 | (232) all_0_0_0 = e12 % 7.56/2.33 | % 7.56/2.33 | From (232) and (14) follows: % 7.56/2.33 | (233) h(e12) = e24 % 7.56/2.33 | % 7.56/2.33 | Instantiating formula (92) with e12, e24, all_0_7_7 and discharging atoms h(e12) = all_0_7_7, h(e12) = e24, yields: % 7.56/2.33 | (195) all_0_7_7 = e24 % 7.56/2.33 | % 7.56/2.33 | Equations (195) can reduce 206 to: % 7.56/2.33 | (186) $false % 7.56/2.33 | % 7.56/2.33 |-The branch is then unsatisfiable % 7.56/2.33 |-Branch two: % 7.56/2.33 | (236) ~ (all_0_0_0 = e12) % 7.56/2.33 | (237) all_0_0_0 = e10 | all_0_0_0 = e11 % 7.56/2.33 | % 7.56/2.33 +-Applying beta-rule and splitting (237), into two cases. % 7.56/2.33 |-Branch one: % 7.56/2.33 | (238) all_0_0_0 = e10 % 7.56/2.33 | % 7.56/2.33 | From (238) and (14) follows: % 7.56/2.33 | (239) h(e10) = e24 % 7.56/2.33 | % 7.56/2.33 | Instantiating formula (92) with e10, e24, all_0_9_9 and discharging atoms h(e10) = all_0_9_9, h(e10) = e24, yields: % 7.56/2.33 | (189) all_0_9_9 = e24 % 7.56/2.33 | % 7.56/2.33 | Equations (189) can reduce 193 to: % 7.56/2.33 | (186) $false % 7.56/2.33 | % 7.56/2.33 |-The branch is then unsatisfiable % 7.56/2.33 |-Branch two: % 7.56/2.33 | (242) ~ (all_0_0_0 = e10) % 7.56/2.33 | (243) all_0_0_0 = e11 % 7.56/2.33 | % 7.56/2.33 | From (243) and (14) follows: % 7.56/2.33 | (244) h(e11) = e24 % 7.56/2.33 | % 7.56/2.33 | Instantiating formula (92) with e11, e24, all_0_8_8 and discharging atoms h(e11) = all_0_8_8, h(e11) = e24, yields: % 7.56/2.33 | (217) all_0_8_8 = e24 % 7.56/2.33 | % 7.56/2.33 | Equations (217) can reduce 224 to: % 7.56/2.33 | (186) $false % 7.56/2.33 | % 7.56/2.33 |-The branch is then unsatisfiable % 7.56/2.33 % SZS output end Proof for theBenchmark % 7.56/2.33 % 7.56/2.33 1754ms %------------------------------------------------------------------------------