%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : REL008+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n015.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 : Mon Jul 18 19:14:08 EDT 2022 % Result : Theorem 3.60s 1.46s % Output : Proof 6.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : REL008+3 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n015.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Fri Jul 8 13:41:36 EDT 2022 % 0.13/0.33 % CPUTime : % 0.19/0.58 ____ _ % 0.19/0.58 ___ / __ \_____(_)___ ________ __________ % 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.58 % 0.19/0.58 A Theorem Prover for First-Order Logic % 0.19/0.58 (ePrincess v.1.0) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2015 % 0.19/0.58 (c) Peter Backeman, 2014-2015 % 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.58 Bug reports to peter@backeman.se % 0.19/0.58 % 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.58 % 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.55/0.94 Prover 0: Preprocessing ... % 2.56/1.22 Prover 0: Constructing countermodel ... % 3.60/1.46 Prover 0: proved (831ms) % 3.60/1.46 % 3.60/1.46 No countermodel exists, formula is valid % 3.60/1.46 % SZS status Theorem for theBenchmark % 3.60/1.46 % 3.60/1.46 Generating proof ... found it (size 53) % 6.19/2.10 % 6.19/2.10 % SZS output start Proof for theBenchmark % 6.19/2.10 Assumed formulas after preprocessing and simplification: % 6.19/2.10 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = v4) & composition(v0, v3) = v4 & composition(v0, v2) = v6 & composition(v0, v1) = v5 & join(v5, v6) = v7 & join(v1, v2) = v3 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v19 | ~ (converse(v9) = v13) | ~ (converse(v8) = v16) | ~ (composition(v16, v10) = v17) | ~ (composition(v15, v18) = v19) | ~ (composition(v10, v13) = v14) | ~ (composition(v8, v9) = v11) | ~ (meet(v11, v10) = v12) | ~ (meet(v9, v17) = v18) | ~ (meet(v8, v14) = v15) | ~ (join(v12, v19) = v20)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v17 | ~ (converse(v9) = v13) | ~ (composition(v15, v9) = v16) | ~ (composition(v10, v13) = v14) | ~ (composition(v8, v9) = v11) | ~ (meet(v16, v10) = v17) | ~ (meet(v11, v10) = v12) | ~ (meet(v8, v14) = v15) | ~ (join(v12, v17) = v18)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v17 | ~ (converse(v8) = v13) | ~ (composition(v13, v10) = v14) | ~ (composition(v8, v15) = v16) | ~ (composition(v8, v9) = v11) | ~ (meet(v16, v10) = v17) | ~ (meet(v11, v10) = v12) | ~ (meet(v9, v14) = v15) | ~ (join(v12, v17) = v18)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (converse(v9) = v11) | ~ (converse(v8) = v14) | ~ (composition(v14, v10) = v15) | ~ (composition(v13, v16) = v17) | ~ (composition(v10, v11) = v12) | ~ (meet(v9, v15) = v16) | ~ (meet(v8, v12) = v13) | ? [v18] : ? [v19] : (composition(v8, v9) = v18 & meet(v18, v10) = v19 & join(v19, v17) = v17)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v8 | ~ (complement(v14) = v15) | ~ (complement(v12) = v13) | ~ (complement(v9) = v11) | ~ (complement(v8) = v10) | ~ (join(v13, v15) = v16) | ~ (join(v10, v11) = v12) | ~ (join(v10, v9) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | ~ (converse(v8) = v10) | ~ (composition(v10, v12) = v13) | ~ (composition(v8, v9) = v11) | ~ (complement(v11) = v12) | ~ (complement(v9) = v14) | ~ (join(v13, v14) = v15)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (converse(v9) = v11) | ~ (composition(v13, v9) = v14) | ~ (composition(v10, v11) = v12) | ~ (meet(v14, v10) = v15) | ~ (meet(v8, v12) = v13) | ? [v16] : ? [v17] : (composition(v8, v9) = v16 & meet(v16, v10) = v17 & join(v17, v15) = v15)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (converse(v8) = v11) | ~ (composition(v11, v10) = v12) | ~ (composition(v8, v13) = v14) | ~ (meet(v14, v10) = v15) | ~ (meet(v9, v12) = v13) | ? [v16] : ? [v17] : (composition(v8, v9) = v16 & meet(v16, v10) = v17 & join(v17, v15) = v15)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (composition(v9, v10) = v12) | ~ (composition(v8, v10) = v11) | ~ (join(v11, v12) = v13) | ? [v14] : (composition(v14, v10) = v13 & join(v8, v9) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (converse(v9) = v11) | ~ (converse(v8) = v10) | ~ (join(v10, v11) = v12) | ? [v13] : (converse(v13) = v12 & join(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (converse(v9) = v10) | ~ (converse(v8) = v11) | ~ (composition(v10, v11) = v12) | ? [v13] : (converse(v13) = v12 & composition(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (composition(v11, v10) = v12) | ~ (composition(v8, v9) = v11) | ? [v13] : (composition(v9, v10) = v13 & composition(v8, v13) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (composition(v11, v10) = v12) | ~ (join(v8, v9) = v11) | ? [v13] : ? [v14] : (composition(v9, v10) = v14 & composition(v8, v10) = v13 & join(v13, v14) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (composition(v9, v10) = v11) | ~ (composition(v8, v11) = v12) | ? [v13] : (composition(v13, v10) = v12 & composition(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (complement(v9) = v11) | ~ (complement(v8) = v10) | ~ (join(v10, v11) = v12) | ? [v13] : (meet(v8, v9) = v13 & complement(v12) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (join(v11, v10) = v12) | ~ (join(v8, v9) = v11) | ? [v13] : (join(v9, v10) = v13 & join(v8, v13) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (join(v9, v10) = v11) | ~ (join(v8, v11) = v12) | ? [v13] : (join(v13, v10) = v12 & join(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (composition(v11, v10) = v9) | ~ (composition(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (meet(v11, v10) = v9) | ~ (meet(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (join(v11, v10) = v9) | ~ (join(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v10 = zero | ~ (meet(v8, v9) = v10) | ~ (complement(v8) = v9)) & ! [v8] : ! [v9] : ! [v10] : (v10 = top | ~ (complement(v8) = v9) | ~ (join(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (converse(v10) = v9) | ~ (converse(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (complement(v10) = v9) | ~ (complement(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (composition(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (converse(v10) = v11 & converse(v9) = v12 & converse(v8) = v13 & composition(v12, v13) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (meet(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (complement(v13) = v10 & complement(v9) = v12 & complement(v8) = v11 & join(v11, v12) = v13)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (join(v9, v8) = v10) | join(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (join(v8, v9) = v10) | join(v9, v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (join(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (converse(v10) = v11 & converse(v9) = v13 & converse(v8) = v12 & join(v12, v13) = v11)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (composition(v8, one) = v9)) & ! [v8] : ! [v9] : ( ~ (converse(v8) = v9) | converse(v9) = v8)) % 6.49/2.15 | 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 yields: % 6.49/2.15 | (1) ~ (all_0_0_0 = all_0_3_3) & composition(all_0_7_7, all_0_4_4) = all_0_3_3 & composition(all_0_7_7, all_0_5_5) = all_0_1_1 & composition(all_0_7_7, all_0_6_6) = all_0_2_2 & join(all_0_2_2, all_0_1_1) = all_0_0_0 & join(all_0_6_6, all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (converse(v1) = v5) | ~ (converse(v0) = v8) | ~ (composition(v8, v2) = v9) | ~ (composition(v7, v10) = v11) | ~ (composition(v2, v5) = v6) | ~ (composition(v0, v1) = v3) | ~ (meet(v3, v2) = v4) | ~ (meet(v1, v9) = v10) | ~ (meet(v0, v6) = v7) | ~ (join(v4, v11) = v12)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (converse(v1) = v5) | ~ (composition(v7, v1) = v8) | ~ (composition(v2, v5) = v6) | ~ (composition(v0, v1) = v3) | ~ (meet(v8, v2) = v9) | ~ (meet(v3, v2) = v4) | ~ (meet(v0, v6) = v7) | ~ (join(v4, v9) = v10)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (converse(v0) = v5) | ~ (composition(v5, v2) = v6) | ~ (composition(v0, v7) = v8) | ~ (composition(v0, v1) = v3) | ~ (meet(v8, v2) = v9) | ~ (meet(v3, v2) = v4) | ~ (meet(v1, v6) = v7) | ~ (join(v4, v9) = v10)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (converse(v1) = v3) | ~ (converse(v0) = v6) | ~ (composition(v6, v2) = v7) | ~ (composition(v5, v8) = v9) | ~ (composition(v2, v3) = v4) | ~ (meet(v1, v7) = v8) | ~ (meet(v0, v4) = v5) | ? [v10] : ? [v11] : (composition(v0, v1) = v10 & meet(v10, v2) = v11 & join(v11, v9) = v9)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v0 | ~ (complement(v6) = v7) | ~ (complement(v4) = v5) | ~ (complement(v1) = v3) | ~ (complement(v0) = v2) | ~ (join(v5, v7) = v8) | ~ (join(v2, v3) = v4) | ~ (join(v2, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (converse(v0) = v2) | ~ (composition(v2, v4) = v5) | ~ (composition(v0, v1) = v3) | ~ (complement(v3) = v4) | ~ (complement(v1) = v6) | ~ (join(v5, v6) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (converse(v1) = v3) | ~ (composition(v5, v1) = v6) | ~ (composition(v2, v3) = v4) | ~ (meet(v6, v2) = v7) | ~ (meet(v0, v4) = v5) | ? [v8] : ? [v9] : (composition(v0, v1) = v8 & meet(v8, v2) = v9 & join(v9, v7) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (converse(v0) = v3) | ~ (composition(v3, v2) = v4) | ~ (composition(v0, v5) = v6) | ~ (meet(v6, v2) = v7) | ~ (meet(v1, v4) = v5) | ? [v8] : ? [v9] : (composition(v0, v1) = v8 & meet(v8, v2) = v9 & join(v9, v7) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (composition(v1, v2) = v4) | ~ (composition(v0, v2) = v3) | ~ (join(v3, v4) = v5) | ? [v6] : (composition(v6, v2) = v5 & join(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (converse(v1) = v3) | ~ (converse(v0) = v2) | ~ (join(v2, v3) = v4) | ? [v5] : (converse(v5) = v4 & join(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (converse(v1) = v2) | ~ (converse(v0) = v3) | ~ (composition(v2, v3) = v4) | ? [v5] : (converse(v5) = v4 & composition(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (composition(v3, v2) = v4) | ~ (composition(v0, v1) = v3) | ? [v5] : (composition(v1, v2) = v5 & composition(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (composition(v3, v2) = v4) | ~ (join(v0, v1) = v3) | ? [v5] : ? [v6] : (composition(v1, v2) = v6 & composition(v0, v2) = v5 & join(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (composition(v1, v2) = v3) | ~ (composition(v0, v3) = v4) | ? [v5] : (composition(v5, v2) = v4 & composition(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (complement(v1) = v3) | ~ (complement(v0) = v2) | ~ (join(v2, v3) = v4) | ? [v5] : (meet(v0, v1) = v5 & complement(v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (join(v3, v2) = v4) | ~ (join(v0, v1) = v3) | ? [v5] : (join(v1, v2) = v5 & join(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (join(v1, v2) = v3) | ~ (join(v0, v3) = v4) | ? [v5] : (join(v5, v2) = v4 & join(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (composition(v3, v2) = v1) | ~ (composition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet(v3, v2) = v1) | ~ (meet(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (join(v3, v2) = v1) | ~ (join(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (meet(v0, v1) = v2) | ~ (complement(v0) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = top | ~ (complement(v0) = v1) | ~ (join(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (converse(v2) = v1) | ~ (converse(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (complement(v2) = v1) | ~ (complement(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (converse(v2) = v3 & converse(v1) = v4 & converse(v0) = v5 & composition(v4, v5) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (complement(v5) = v2 & complement(v1) = v4 & complement(v0) = v3 & join(v3, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (join(v1, v0) = v2) | join(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (join(v0, v1) = v2) | join(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (join(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (converse(v2) = v3 & converse(v1) = v5 & converse(v0) = v4 & join(v4, v5) = v3)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (composition(v0, one) = v1)) & ! [v0] : ! [v1] : ( ~ (converse(v0) = v1) | converse(v1) = v0) % 6.49/2.16 | % 6.49/2.16 | Applying alpha-rule on (1) yields: % 6.49/2.16 | (2) ! [v0] : ! [v1] : ( ~ (converse(v0) = v1) | converse(v1) = v0) % 6.49/2.16 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (join(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (converse(v2) = v3 & converse(v1) = v5 & converse(v0) = v4 & join(v4, v5) = v3)) % 6.49/2.16 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (composition(v3, v2) = v4) | ~ (composition(v0, v1) = v3) | ? [v5] : (composition(v1, v2) = v5 & composition(v0, v5) = v4)) % 6.49/2.16 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (converse(v1) = v2) | ~ (converse(v0) = v3) | ~ (composition(v2, v3) = v4) | ? [v5] : (converse(v5) = v4 & composition(v0, v1) = v5)) % 6.49/2.16 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (composition(v3, v2) = v1) | ~ (composition(v3, v2) = v0)) % 6.49/2.16 | (7) ! [v0] : ! [v1] : (v1 = v0 | ~ (composition(v0, one) = v1)) % 6.49/2.16 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (meet(v0, v1) = v2) | ~ (complement(v0) = v1)) % 6.49/2.16 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (composition(v1, v2) = v3) | ~ (composition(v0, v3) = v4) | ? [v5] : (composition(v5, v2) = v4 & composition(v0, v1) = v5)) % 6.49/2.17 | (10) ~ (all_0_0_0 = all_0_3_3) % 6.49/2.17 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (converse(v1) = v3) | ~ (converse(v0) = v6) | ~ (composition(v6, v2) = v7) | ~ (composition(v5, v8) = v9) | ~ (composition(v2, v3) = v4) | ~ (meet(v1, v7) = v8) | ~ (meet(v0, v4) = v5) | ? [v10] : ? [v11] : (composition(v0, v1) = v10 & meet(v10, v2) = v11 & join(v11, v9) = v9)) % 6.49/2.17 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (converse(v1) = v3) | ~ (converse(v0) = v2) | ~ (join(v2, v3) = v4) | ? [v5] : (converse(v5) = v4 & join(v0, v1) = v5)) % 6.49/2.17 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (complement(v2) = v1) | ~ (complement(v2) = v0)) % 6.49/2.17 | (14) composition(all_0_7_7, all_0_5_5) = all_0_1_1 % 6.49/2.17 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet(v3, v2) = v1) | ~ (meet(v3, v2) = v0)) % 6.49/2.17 | (16) join(all_0_6_6, all_0_5_5) = all_0_4_4 % 6.49/2.17 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (converse(v2) = v3 & converse(v1) = v4 & converse(v0) = v5 & composition(v4, v5) = v3)) % 6.49/2.17 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (composition(v3, v2) = v4) | ~ (join(v0, v1) = v3) | ? [v5] : ? [v6] : (composition(v1, v2) = v6 & composition(v0, v2) = v5 & join(v5, v6) = v4)) % 6.49/2.17 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (converse(v1) = v5) | ~ (converse(v0) = v8) | ~ (composition(v8, v2) = v9) | ~ (composition(v7, v10) = v11) | ~ (composition(v2, v5) = v6) | ~ (composition(v0, v1) = v3) | ~ (meet(v3, v2) = v4) | ~ (meet(v1, v9) = v10) | ~ (meet(v0, v6) = v7) | ~ (join(v4, v11) = v12)) % 6.49/2.17 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (converse(v0) = v3) | ~ (composition(v3, v2) = v4) | ~ (composition(v0, v5) = v6) | ~ (meet(v6, v2) = v7) | ~ (meet(v1, v4) = v5) | ? [v8] : ? [v9] : (composition(v0, v1) = v8 & meet(v8, v2) = v9 & join(v9, v7) = v7)) % 6.49/2.17 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (join(v0, v1) = v2) | join(v1, v0) = v2) % 6.49/2.17 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (join(v1, v0) = v2) | join(v0, v1) = v2) % 6.49/2.17 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (composition(v1, v2) = v4) | ~ (composition(v0, v2) = v3) | ~ (join(v3, v4) = v5) | ? [v6] : (composition(v6, v2) = v5 & join(v0, v1) = v6)) % 6.49/2.17 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v0 | ~ (complement(v6) = v7) | ~ (complement(v4) = v5) | ~ (complement(v1) = v3) | ~ (complement(v0) = v2) | ~ (join(v5, v7) = v8) | ~ (join(v2, v3) = v4) | ~ (join(v2, v1) = v6)) % 6.49/2.17 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = top | ~ (complement(v0) = v1) | ~ (join(v0, v1) = v2)) % 6.49/2.17 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (join(v3, v2) = v1) | ~ (join(v3, v2) = v0)) % 6.49/2.17 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (converse(v1) = v3) | ~ (composition(v5, v1) = v6) | ~ (composition(v2, v3) = v4) | ~ (meet(v6, v2) = v7) | ~ (meet(v0, v4) = v5) | ? [v8] : ? [v9] : (composition(v0, v1) = v8 & meet(v8, v2) = v9 & join(v9, v7) = v7)) % 6.49/2.17 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (converse(v2) = v1) | ~ (converse(v2) = v0)) % 6.49/2.17 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (complement(v5) = v2 & complement(v1) = v4 & complement(v0) = v3 & join(v3, v4) = v5)) % 6.49/2.18 | (30) join(all_0_2_2, all_0_1_1) = all_0_0_0 % 6.49/2.18 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (join(v3, v2) = v4) | ~ (join(v0, v1) = v3) | ? [v5] : (join(v1, v2) = v5 & join(v0, v5) = v4)) % 6.49/2.18 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (converse(v0) = v5) | ~ (composition(v5, v2) = v6) | ~ (composition(v0, v7) = v8) | ~ (composition(v0, v1) = v3) | ~ (meet(v8, v2) = v9) | ~ (meet(v3, v2) = v4) | ~ (meet(v1, v6) = v7) | ~ (join(v4, v9) = v10)) % 6.49/2.18 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (converse(v1) = v5) | ~ (composition(v7, v1) = v8) | ~ (composition(v2, v5) = v6) | ~ (composition(v0, v1) = v3) | ~ (meet(v8, v2) = v9) | ~ (meet(v3, v2) = v4) | ~ (meet(v0, v6) = v7) | ~ (join(v4, v9) = v10)) % 6.49/2.18 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (join(v1, v2) = v3) | ~ (join(v0, v3) = v4) | ? [v5] : (join(v5, v2) = v4 & join(v0, v1) = v5)) % 6.49/2.18 | (35) composition(all_0_7_7, all_0_4_4) = all_0_3_3 % 6.49/2.18 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (converse(v0) = v2) | ~ (composition(v2, v4) = v5) | ~ (composition(v0, v1) = v3) | ~ (complement(v3) = v4) | ~ (complement(v1) = v6) | ~ (join(v5, v6) = v7)) % 6.49/2.18 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (complement(v1) = v3) | ~ (complement(v0) = v2) | ~ (join(v2, v3) = v4) | ? [v5] : (meet(v0, v1) = v5 & complement(v4) = v5)) % 6.49/2.18 | (38) composition(all_0_7_7, all_0_6_6) = all_0_2_2 % 6.49/2.18 | % 6.49/2.18 | Instantiating formula (17) with all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms composition(all_0_7_7, all_0_4_4) = all_0_3_3, yields: % 6.49/2.18 | (39) ? [v0] : ? [v1] : ? [v2] : (converse(all_0_3_3) = v0 & converse(all_0_4_4) = v1 & converse(all_0_7_7) = v2 & composition(v1, v2) = v0) % 6.49/2.18 | % 6.49/2.18 | Instantiating formula (17) with all_0_1_1, all_0_5_5, all_0_7_7 and discharging atoms composition(all_0_7_7, all_0_5_5) = all_0_1_1, yields: % 6.49/2.18 | (40) ? [v0] : ? [v1] : ? [v2] : (converse(all_0_1_1) = v0 & converse(all_0_5_5) = v1 & converse(all_0_7_7) = v2 & composition(v1, v2) = v0) % 6.49/2.18 | % 6.49/2.18 | Instantiating formula (17) with all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms composition(all_0_7_7, all_0_6_6) = all_0_2_2, yields: % 6.49/2.18 | (41) ? [v0] : ? [v1] : ? [v2] : (converse(all_0_2_2) = v0 & converse(all_0_6_6) = v1 & converse(all_0_7_7) = v2 & composition(v1, v2) = v0) % 6.49/2.18 | % 6.49/2.18 | Instantiating formula (3) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms join(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 6.49/2.18 | (42) ? [v0] : ? [v1] : ? [v2] : (converse(all_0_0_0) = v0 & converse(all_0_1_1) = v2 & converse(all_0_2_2) = v1 & join(v1, v2) = v0) % 6.49/2.18 | % 6.49/2.18 | Instantiating formula (3) with all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms join(all_0_6_6, all_0_5_5) = all_0_4_4, yields: % 6.49/2.18 | (43) ? [v0] : ? [v1] : ? [v2] : (converse(all_0_4_4) = v0 & converse(all_0_5_5) = v2 & converse(all_0_6_6) = v1 & join(v1, v2) = v0) % 6.49/2.18 | % 6.49/2.18 | Instantiating (40) with all_9_0_8, all_9_1_9, all_9_2_10 yields: % 6.49/2.18 | (44) converse(all_0_1_1) = all_9_2_10 & converse(all_0_5_5) = all_9_1_9 & converse(all_0_7_7) = all_9_0_8 & composition(all_9_1_9, all_9_0_8) = all_9_2_10 % 6.49/2.18 | % 6.49/2.18 | Applying alpha-rule on (44) yields: % 6.49/2.18 | (45) converse(all_0_1_1) = all_9_2_10 % 6.49/2.18 | (46) converse(all_0_5_5) = all_9_1_9 % 6.49/2.18 | (47) converse(all_0_7_7) = all_9_0_8 % 6.49/2.18 | (48) composition(all_9_1_9, all_9_0_8) = all_9_2_10 % 6.49/2.18 | % 6.49/2.18 | Instantiating (43) with all_11_0_11, all_11_1_12, all_11_2_13 yields: % 6.49/2.18 | (49) converse(all_0_4_4) = all_11_2_13 & converse(all_0_5_5) = all_11_0_11 & converse(all_0_6_6) = all_11_1_12 & join(all_11_1_12, all_11_0_11) = all_11_2_13 % 6.49/2.18 | % 6.49/2.18 | Applying alpha-rule on (49) yields: % 6.49/2.18 | (50) converse(all_0_4_4) = all_11_2_13 % 6.49/2.18 | (51) converse(all_0_5_5) = all_11_0_11 % 6.49/2.18 | (52) converse(all_0_6_6) = all_11_1_12 % 6.49/2.18 | (53) join(all_11_1_12, all_11_0_11) = all_11_2_13 % 6.49/2.18 | % 6.49/2.18 | Instantiating (39) with all_13_0_14, all_13_1_15, all_13_2_16 yields: % 6.49/2.18 | (54) converse(all_0_3_3) = all_13_2_16 & converse(all_0_4_4) = all_13_1_15 & converse(all_0_7_7) = all_13_0_14 & composition(all_13_1_15, all_13_0_14) = all_13_2_16 % 6.49/2.19 | % 6.49/2.19 | Applying alpha-rule on (54) yields: % 6.49/2.19 | (55) converse(all_0_3_3) = all_13_2_16 % 6.49/2.19 | (56) converse(all_0_4_4) = all_13_1_15 % 6.49/2.19 | (57) converse(all_0_7_7) = all_13_0_14 % 6.49/2.19 | (58) composition(all_13_1_15, all_13_0_14) = all_13_2_16 % 6.49/2.19 | % 6.49/2.19 | Instantiating (42) with all_15_0_17, all_15_1_18, all_15_2_19 yields: % 6.49/2.19 | (59) converse(all_0_0_0) = all_15_2_19 & converse(all_0_1_1) = all_15_0_17 & converse(all_0_2_2) = all_15_1_18 & join(all_15_1_18, all_15_0_17) = all_15_2_19 % 6.49/2.19 | % 6.49/2.19 | Applying alpha-rule on (59) yields: % 6.49/2.19 | (60) converse(all_0_0_0) = all_15_2_19 % 6.49/2.19 | (61) converse(all_0_1_1) = all_15_0_17 % 6.49/2.19 | (62) converse(all_0_2_2) = all_15_1_18 % 6.49/2.19 | (63) join(all_15_1_18, all_15_0_17) = all_15_2_19 % 6.49/2.19 | % 6.49/2.19 | Instantiating (41) with all_17_0_20, all_17_1_21, all_17_2_22 yields: % 6.49/2.19 | (64) converse(all_0_2_2) = all_17_2_22 & converse(all_0_6_6) = all_17_1_21 & converse(all_0_7_7) = all_17_0_20 & composition(all_17_1_21, all_17_0_20) = all_17_2_22 % 6.49/2.19 | % 6.49/2.19 | Applying alpha-rule on (64) yields: % 6.49/2.19 | (65) converse(all_0_2_2) = all_17_2_22 % 6.49/2.19 | (66) converse(all_0_6_6) = all_17_1_21 % 6.49/2.19 | (67) converse(all_0_7_7) = all_17_0_20 % 6.49/2.19 | (68) composition(all_17_1_21, all_17_0_20) = all_17_2_22 % 6.49/2.19 | % 6.49/2.19 | Instantiating formula (28) with all_0_1_1, all_9_2_10, all_15_0_17 and discharging atoms converse(all_0_1_1) = all_15_0_17, converse(all_0_1_1) = all_9_2_10, yields: % 6.49/2.19 | (69) all_15_0_17 = all_9_2_10 % 6.49/2.19 | % 6.49/2.19 | Instantiating formula (28) with all_0_2_2, all_15_1_18, all_17_2_22 and discharging atoms converse(all_0_2_2) = all_17_2_22, converse(all_0_2_2) = all_15_1_18, yields: % 6.49/2.19 | (70) all_17_2_22 = all_15_1_18 % 6.49/2.19 | % 6.49/2.19 | Instantiating formula (28) with all_0_4_4, all_11_2_13, all_13_1_15 and discharging atoms converse(all_0_4_4) = all_13_1_15, converse(all_0_4_4) = all_11_2_13, yields: % 6.49/2.19 | (71) all_13_1_15 = all_11_2_13 % 6.49/2.19 | % 6.49/2.19 | Instantiating formula (28) with all_0_5_5, all_9_1_9, all_11_0_11 and discharging atoms converse(all_0_5_5) = all_11_0_11, converse(all_0_5_5) = all_9_1_9, yields: % 6.49/2.19 | (72) all_11_0_11 = all_9_1_9 % 6.49/2.19 | % 6.49/2.19 | Instantiating formula (28) with all_0_6_6, all_11_1_12, all_17_1_21 and discharging atoms converse(all_0_6_6) = all_17_1_21, converse(all_0_6_6) = all_11_1_12, yields: % 6.49/2.19 | (73) all_17_1_21 = all_11_1_12 % 6.49/2.19 | % 6.49/2.19 | Instantiating formula (28) with all_0_7_7, all_13_0_14, all_17_0_20 and discharging atoms converse(all_0_7_7) = all_17_0_20, converse(all_0_7_7) = all_13_0_14, yields: % 6.49/2.19 | (74) all_17_0_20 = all_13_0_14 % 6.49/2.19 | % 6.49/2.19 | Instantiating formula (28) with all_0_7_7, all_9_0_8, all_17_0_20 and discharging atoms converse(all_0_7_7) = all_17_0_20, converse(all_0_7_7) = all_9_0_8, yields: % 6.49/2.19 | (75) all_17_0_20 = all_9_0_8 % 6.49/2.19 | % 6.49/2.19 | Combining equations (74,75) yields a new equation: % 6.49/2.19 | (76) all_13_0_14 = all_9_0_8 % 6.49/2.19 | % 6.49/2.19 | Simplifying 76 yields: % 6.49/2.19 | (77) all_13_0_14 = all_9_0_8 % 6.49/2.19 | % 6.49/2.19 | From (73)(75)(70) and (68) follows: % 6.49/2.19 | (78) composition(all_11_1_12, all_9_0_8) = all_15_1_18 % 6.49/2.19 | % 6.49/2.19 | From (71)(77) and (58) follows: % 6.49/2.19 | (79) composition(all_11_2_13, all_9_0_8) = all_13_2_16 % 6.49/2.19 | % 6.49/2.19 | From (69) and (63) follows: % 6.49/2.19 | (80) join(all_15_1_18, all_9_2_10) = all_15_2_19 % 6.49/2.19 | % 6.49/2.19 | From (72) and (53) follows: % 6.49/2.19 | (81) join(all_11_1_12, all_9_1_9) = all_11_2_13 % 6.49/2.19 | % 6.49/2.19 | Instantiating formula (2) with all_15_2_19, all_0_0_0 and discharging atoms converse(all_0_0_0) = all_15_2_19, yields: % 6.49/2.19 | (82) converse(all_15_2_19) = all_0_0_0 % 6.49/2.19 | % 6.49/2.19 | Instantiating formula (2) with all_13_2_16, all_0_3_3 and discharging atoms converse(all_0_3_3) = all_13_2_16, yields: % 6.49/2.19 | (83) converse(all_13_2_16) = all_0_3_3 % 6.49/2.19 | % 6.49/2.19 | Instantiating formula (17) with all_13_2_16, all_9_0_8, all_11_2_13 and discharging atoms composition(all_11_2_13, all_9_0_8) = all_13_2_16, yields: % 6.49/2.19 | (84) ? [v0] : ? [v1] : ? [v2] : (converse(all_13_2_16) = v0 & converse(all_11_2_13) = v2 & converse(all_9_0_8) = v1 & composition(v1, v2) = v0) % 6.49/2.19 | % 6.49/2.19 | Instantiating formula (3) with all_15_2_19, all_9_2_10, all_15_1_18 and discharging atoms join(all_15_1_18, all_9_2_10) = all_15_2_19, yields: % 6.49/2.19 | (85) ? [v0] : ? [v1] : ? [v2] : (converse(all_15_1_18) = v1 & converse(all_15_2_19) = v0 & converse(all_9_2_10) = v2 & join(v1, v2) = v0) % 6.49/2.20 | % 6.49/2.20 | Instantiating formula (18) with all_13_2_16, all_11_2_13, all_9_0_8, all_9_1_9, all_11_1_12 and discharging atoms composition(all_11_2_13, all_9_0_8) = all_13_2_16, join(all_11_1_12, all_9_1_9) = all_11_2_13, yields: % 6.49/2.20 | (86) ? [v0] : ? [v1] : (composition(all_11_1_12, all_9_0_8) = v0 & composition(all_9_1_9, all_9_0_8) = v1 & join(v0, v1) = all_13_2_16) % 6.49/2.20 | % 6.49/2.20 | Instantiating (86) with all_31_0_26, all_31_1_27 yields: % 6.49/2.20 | (87) composition(all_11_1_12, all_9_0_8) = all_31_1_27 & composition(all_9_1_9, all_9_0_8) = all_31_0_26 & join(all_31_1_27, all_31_0_26) = all_13_2_16 % 6.49/2.20 | % 6.49/2.20 | Applying alpha-rule on (87) yields: % 6.49/2.20 | (88) composition(all_11_1_12, all_9_0_8) = all_31_1_27 % 6.49/2.20 | (89) composition(all_9_1_9, all_9_0_8) = all_31_0_26 % 6.49/2.20 | (90) join(all_31_1_27, all_31_0_26) = all_13_2_16 % 6.49/2.20 | % 6.49/2.20 | Instantiating (85) with all_35_0_31, all_35_1_32, all_35_2_33 yields: % 6.49/2.20 | (91) converse(all_15_1_18) = all_35_1_32 & converse(all_15_2_19) = all_35_2_33 & converse(all_9_2_10) = all_35_0_31 & join(all_35_1_32, all_35_0_31) = all_35_2_33 % 6.49/2.20 | % 6.49/2.20 | Applying alpha-rule on (91) yields: % 6.49/2.20 | (92) converse(all_15_1_18) = all_35_1_32 % 6.49/2.20 | (93) converse(all_15_2_19) = all_35_2_33 % 6.49/2.20 | (94) converse(all_9_2_10) = all_35_0_31 % 6.49/2.20 | (95) join(all_35_1_32, all_35_0_31) = all_35_2_33 % 6.49/2.20 | % 6.49/2.20 | Instantiating (84) with all_41_0_38, all_41_1_39, all_41_2_40 yields: % 6.49/2.20 | (96) converse(all_13_2_16) = all_41_2_40 & converse(all_11_2_13) = all_41_0_38 & converse(all_9_0_8) = all_41_1_39 & composition(all_41_1_39, all_41_0_38) = all_41_2_40 % 6.49/2.20 | % 6.49/2.20 | Applying alpha-rule on (96) yields: % 6.49/2.20 | (97) converse(all_13_2_16) = all_41_2_40 % 6.49/2.20 | (98) converse(all_11_2_13) = all_41_0_38 % 6.49/2.20 | (99) converse(all_9_0_8) = all_41_1_39 % 6.49/2.20 | (100) composition(all_41_1_39, all_41_0_38) = all_41_2_40 % 6.49/2.20 | % 6.49/2.20 | Instantiating formula (28) with all_15_2_19, all_0_0_0, all_35_2_33 and discharging atoms converse(all_15_2_19) = all_35_2_33, converse(all_15_2_19) = all_0_0_0, yields: % 6.49/2.20 | (101) all_35_2_33 = all_0_0_0 % 6.49/2.20 | % 6.49/2.20 | Instantiating formula (28) with all_13_2_16, all_0_3_3, all_41_2_40 and discharging atoms converse(all_13_2_16) = all_41_2_40, converse(all_13_2_16) = all_0_3_3, yields: % 6.49/2.20 | (102) all_41_2_40 = all_0_3_3 % 6.49/2.20 | % 6.49/2.20 | Instantiating formula (6) with all_11_1_12, all_9_0_8, all_31_1_27, all_15_1_18 and discharging atoms composition(all_11_1_12, all_9_0_8) = all_31_1_27, composition(all_11_1_12, all_9_0_8) = all_15_1_18, yields: % 6.49/2.20 | (103) all_31_1_27 = all_15_1_18 % 6.49/2.20 | % 6.49/2.20 | Instantiating formula (6) with all_9_1_9, all_9_0_8, all_31_0_26, all_9_2_10 and discharging atoms composition(all_9_1_9, all_9_0_8) = all_31_0_26, composition(all_9_1_9, all_9_0_8) = all_9_2_10, yields: % 6.49/2.20 | (104) all_31_0_26 = all_9_2_10 % 6.49/2.20 | % 6.49/2.20 | From (101) and (93) follows: % 6.49/2.20 | (82) converse(all_15_2_19) = all_0_0_0 % 6.49/2.20 | % 6.49/2.20 | From (102) and (97) follows: % 6.49/2.20 | (83) converse(all_13_2_16) = all_0_3_3 % 6.49/2.20 | % 6.49/2.20 | From (103)(104) and (90) follows: % 6.49/2.20 | (107) join(all_15_1_18, all_9_2_10) = all_13_2_16 % 6.49/2.20 | % 6.49/2.20 | Instantiating formula (26) with all_15_1_18, all_9_2_10, all_13_2_16, all_15_2_19 and discharging atoms join(all_15_1_18, all_9_2_10) = all_15_2_19, join(all_15_1_18, all_9_2_10) = all_13_2_16, yields: % 6.49/2.20 | (108) all_15_2_19 = all_13_2_16 % 6.49/2.20 | % 6.49/2.20 | From (108) and (82) follows: % 6.49/2.20 | (109) converse(all_13_2_16) = all_0_0_0 % 6.49/2.20 | % 6.49/2.20 | Instantiating formula (28) with all_13_2_16, all_0_0_0, all_0_3_3 and discharging atoms converse(all_13_2_16) = all_0_0_0, converse(all_13_2_16) = all_0_3_3, yields: % 6.49/2.20 | (110) all_0_0_0 = all_0_3_3 % 6.49/2.20 | % 6.49/2.20 | Equations (110) can reduce 10 to: % 6.49/2.20 | (111) $false % 6.49/2.20 | % 6.49/2.20 |-The branch is then unsatisfiable % 6.49/2.20 % SZS output end Proof for theBenchmark % 6.49/2.20 % 6.49/2.20 1617ms %------------------------------------------------------------------------------