%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : REL009+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n018.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 19:14:10 EDT 2022 % Result : Theorem 3.16s 1.53s % Output : Proof 5.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : REL009+1 : TPTP v8.1.0. Released v4.0.0. % 0.08/0.15 % Command : ePrincess-casc -timeout=%d %s % 0.15/0.36 % Computer : n018.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 600 % 0.15/0.36 % DateTime : Fri Jul 8 10:57:55 EDT 2022 % 0.15/0.36 % CPUTime : % 0.63/0.66 ____ _ % 0.63/0.66 ___ / __ \_____(_)___ ________ __________ % 0.63/0.66 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.63/0.66 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.63/0.66 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.63/0.66 % 0.63/0.66 A Theorem Prover for First-Order Logic % 0.63/0.67 (ePrincess v.1.0) % 0.63/0.67 % 0.63/0.67 (c) Philipp Rümmer, 2009-2015 % 0.63/0.67 (c) Peter Backeman, 2014-2015 % 0.63/0.67 (contributions by Angelo Brillout, Peter Baumgartner) % 0.63/0.67 Free software under GNU Lesser General Public License (LGPL). % 0.63/0.67 Bug reports to peter@backeman.se % 0.63/0.67 % 0.63/0.67 For more information, visit http://user.uu.se/~petba168/breu/ % 0.63/0.67 % 0.63/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.77/0.72 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.66/1.00 Prover 0: Preprocessing ... % 2.26/1.26 Prover 0: Constructing countermodel ... % 3.16/1.52 Prover 0: proved (808ms) % 3.16/1.53 % 3.16/1.53 No countermodel exists, formula is valid % 3.16/1.53 % SZS status Theorem for theBenchmark % 3.16/1.53 % 3.16/1.53 Generating proof ... found it (size 73) % 5.42/1.98 % 5.42/1.98 % SZS output start Proof for theBenchmark % 5.42/1.98 Assumed formulas after preprocessing and simplification: % 5.42/1.98 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (composition(v2, v1) = v7 & composition(v2, v0) = v6 & composition(v1, v2) = v4 & composition(v0, v2) = v3 & join(v6, v7) = v8 & join(v3, v4) = v5 & join(v0, v1) = v1 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = v9 | ~ (complement(v15) = v16) | ~ (complement(v13) = v14) | ~ (complement(v10) = v12) | ~ (complement(v9) = v11) | ~ (join(v14, v16) = v17) | ~ (join(v11, v12) = v13) | ~ (join(v11, v10) = v15)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v15 | ~ (converse(v9) = v11) | ~ (composition(v11, v13) = v14) | ~ (composition(v9, v10) = v12) | ~ (complement(v12) = v13) | ~ (complement(v10) = v15) | ~ (join(v14, v15) = v16)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (composition(v10, v11) = v13) | ~ (composition(v9, v11) = v12) | ~ (join(v12, v13) = v14) | ? [v15] : (composition(v15, v11) = v14 & join(v9, v10) = v15)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (converse(v10) = v12) | ~ (converse(v9) = v11) | ~ (join(v11, v12) = v13) | ? [v14] : (converse(v14) = v13 & join(v9, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (converse(v10) = v11) | ~ (converse(v9) = v12) | ~ (composition(v11, v12) = v13) | ? [v14] : (converse(v14) = v13 & composition(v9, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (composition(v12, v11) = v13) | ~ (composition(v9, v10) = v12) | ? [v14] : (composition(v10, v11) = v14 & composition(v9, v14) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (composition(v12, v11) = v13) | ~ (join(v9, v10) = v12) | ? [v14] : ? [v15] : (composition(v10, v11) = v15 & composition(v9, v11) = v14 & join(v14, v15) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (composition(v10, v11) = v12) | ~ (composition(v9, v12) = v13) | ? [v14] : (composition(v14, v11) = v13 & composition(v9, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (complement(v10) = v12) | ~ (complement(v9) = v11) | ~ (join(v11, v12) = v13) | ? [v14] : (meet(v9, v10) = v14 & complement(v13) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (join(v12, v11) = v13) | ~ (join(v9, v10) = v12) | ? [v14] : (join(v10, v11) = v14 & join(v9, v14) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (join(v10, v11) = v12) | ~ (join(v9, v12) = v13) | ? [v14] : (join(v14, v11) = v13 & join(v9, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (composition(v12, v11) = v10) | ~ (composition(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (meet(v12, v11) = v10) | ~ (meet(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (join(v12, v11) = v10) | ~ (join(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v11 = zero | ~ (meet(v9, v10) = v11) | ~ (complement(v9) = v10)) & ! [v9] : ! [v10] : ! [v11] : (v11 = top | ~ (complement(v9) = v10) | ~ (join(v9, v10) = v11)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (converse(v11) = v10) | ~ (converse(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (complement(v11) = v10) | ~ (complement(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (composition(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (converse(v11) = v12 & converse(v10) = v13 & converse(v9) = v14 & composition(v13, v14) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (meet(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (complement(v14) = v11 & complement(v10) = v13 & complement(v9) = v12 & join(v12, v13) = v14)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (join(v10, v9) = v11) | join(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (join(v9, v10) = v11) | join(v10, v9) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (join(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (converse(v11) = v12 & converse(v10) = v14 & converse(v9) = v13 & join(v13, v14) = v12)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (composition(v9, one) = v10)) & ! [v9] : ! [v10] : ( ~ (converse(v9) = v10) | converse(v10) = v9) & ( ~ (v8 = v7) | ~ (v5 = v4))) % 5.42/2.02 | 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 yields: % 5.42/2.02 | (1) composition(all_0_6_6, all_0_7_7) = all_0_1_1 & composition(all_0_6_6, all_0_8_8) = all_0_2_2 & composition(all_0_7_7, all_0_6_6) = all_0_4_4 & composition(all_0_8_8, all_0_6_6) = all_0_5_5 & join(all_0_2_2, all_0_1_1) = all_0_0_0 & join(all_0_5_5, all_0_4_4) = all_0_3_3 & join(all_0_8_8, all_0_7_7) = all_0_7_7 & ! [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] : ( ~ (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) & ( ~ (all_0_0_0 = all_0_1_1) | ~ (all_0_3_3 = all_0_4_4)) % 5.42/2.03 | % 5.42/2.03 | Applying alpha-rule on (1) yields: % 5.42/2.03 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (join(v3, v2) = v4) | ~ (join(v0, v1) = v3) | ? [v5] : (join(v1, v2) = v5 & join(v0, v5) = v4)) % 5.42/2.03 | (3) join(all_0_5_5, all_0_4_4) = all_0_3_3 % 5.42/2.03 | (4) composition(all_0_8_8, all_0_6_6) = all_0_5_5 % 5.42/2.03 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (composition(v3, v2) = v1) | ~ (composition(v3, v2) = v0)) % 5.42/2.03 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (join(v1, v2) = v3) | ~ (join(v0, v3) = v4) | ? [v5] : (join(v5, v2) = v4 & join(v0, v1) = v5)) % 5.42/2.03 | (7) join(all_0_8_8, all_0_7_7) = all_0_7_7 % 5.42/2.03 | (8) composition(all_0_6_6, all_0_7_7) = all_0_1_1 % 5.42/2.03 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (converse(v1) = v3) | ~ (converse(v0) = v2) | ~ (join(v2, v3) = v4) | ? [v5] : (converse(v5) = v4 & join(v0, v1) = v5)) % 5.42/2.03 | (10) ~ (all_0_0_0 = all_0_1_1) | ~ (all_0_3_3 = all_0_4_4) % 5.42/2.03 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (converse(v2) = v1) | ~ (converse(v2) = v0)) % 5.42/2.03 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet(v3, v2) = v1) | ~ (meet(v3, v2) = v0)) % 5.42/2.03 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (converse(v1) = v2) | ~ (converse(v0) = v3) | ~ (composition(v2, v3) = v4) | ? [v5] : (converse(v5) = v4 & composition(v0, v1) = v5)) % 5.42/2.03 | (14) ! [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)) % 5.42/2.03 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (composition(v3, v2) = v4) | ~ (composition(v0, v1) = v3) | ? [v5] : (composition(v1, v2) = v5 & composition(v0, v5) = v4)) % 5.42/2.04 | (16) composition(all_0_7_7, all_0_6_6) = all_0_4_4 % 5.42/2.04 | (17) ! [v0] : ! [v1] : ( ~ (converse(v0) = v1) | converse(v1) = v0) % 5.42/2.04 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (join(v3, v2) = v1) | ~ (join(v3, v2) = v0)) % 5.72/2.04 | (19) ! [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)) % 5.72/2.04 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (meet(v0, v1) = v2) | ~ (complement(v0) = v1)) % 5.72/2.04 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (converse(v2) = v3 & converse(v1) = v4 & converse(v0) = v5 & composition(v4, v5) = v3)) % 5.72/2.04 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = top | ~ (complement(v0) = v1) | ~ (join(v0, v1) = v2)) % 5.72/2.04 | (23) composition(all_0_6_6, all_0_8_8) = all_0_2_2 % 5.72/2.04 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (complement(v2) = v1) | ~ (complement(v2) = v0)) % 5.72/2.04 | (25) ! [v0] : ! [v1] : (v1 = v0 | ~ (composition(v0, one) = v1)) % 5.72/2.04 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (join(v0, v1) = v2) | join(v1, v0) = v2) % 5.72/2.04 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (join(v1, v0) = v2) | join(v0, v1) = v2) % 5.72/2.04 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (complement(v5) = v2 & complement(v1) = v4 & complement(v0) = v3 & join(v3, v4) = v5)) % 5.72/2.04 | (29) ! [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)) % 5.72/2.04 | (30) join(all_0_2_2, all_0_1_1) = all_0_0_0 % 5.72/2.04 | (31) ! [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)) % 5.72/2.04 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (complement(v1) = v3) | ~ (complement(v0) = v2) | ~ (join(v2, v3) = v4) | ? [v5] : (meet(v0, v1) = v5 & complement(v4) = v5)) % 5.72/2.04 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (join(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (converse(v2) = v3 & converse(v1) = v5 & converse(v0) = v4 & join(v4, v5) = v3)) % 5.72/2.04 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (composition(v1, v2) = v3) | ~ (composition(v0, v3) = v4) | ? [v5] : (composition(v5, v2) = v4 & composition(v0, v1) = v5)) % 5.72/2.04 | % 5.72/2.04 | Instantiating formula (21) with all_0_1_1, all_0_7_7, all_0_6_6 and discharging atoms composition(all_0_6_6, all_0_7_7) = all_0_1_1, yields: % 5.72/2.04 | (35) ? [v0] : ? [v1] : ? [v2] : (converse(all_0_1_1) = v0 & converse(all_0_6_6) = v2 & converse(all_0_7_7) = v1 & composition(v1, v2) = v0) % 5.72/2.04 | % 5.72/2.04 | Instantiating formula (21) with all_0_2_2, all_0_8_8, all_0_6_6 and discharging atoms composition(all_0_6_6, all_0_8_8) = all_0_2_2, yields: % 5.72/2.04 | (36) ? [v0] : ? [v1] : ? [v2] : (converse(all_0_2_2) = v0 & converse(all_0_6_6) = v2 & converse(all_0_8_8) = v1 & composition(v1, v2) = v0) % 5.72/2.04 | % 5.72/2.04 | Instantiating formula (21) with all_0_4_4, all_0_6_6, all_0_7_7 and discharging atoms composition(all_0_7_7, all_0_6_6) = all_0_4_4, yields: % 5.72/2.04 | (37) ? [v0] : ? [v1] : ? [v2] : (converse(all_0_4_4) = v0 & converse(all_0_6_6) = v1 & converse(all_0_7_7) = v2 & composition(v1, v2) = v0) % 5.72/2.04 | % 5.72/2.04 | Instantiating formula (21) with all_0_5_5, all_0_6_6, all_0_8_8 and discharging atoms composition(all_0_8_8, all_0_6_6) = all_0_5_5, yields: % 5.72/2.05 | (38) ? [v0] : ? [v1] : ? [v2] : (converse(all_0_5_5) = v0 & converse(all_0_6_6) = v1 & converse(all_0_8_8) = v2 & composition(v1, v2) = v0) % 5.72/2.05 | % 5.72/2.05 | Instantiating formula (33) 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: % 5.72/2.05 | (39) ? [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) % 5.72/2.05 | % 5.72/2.05 | Instantiating formula (14) with all_0_4_4, all_0_7_7, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms composition(all_0_7_7, all_0_6_6) = all_0_4_4, join(all_0_8_8, all_0_7_7) = all_0_7_7, yields: % 5.72/2.05 | (40) ? [v0] : ? [v1] : (composition(all_0_7_7, all_0_6_6) = v1 & composition(all_0_8_8, all_0_6_6) = v0 & join(v0, v1) = all_0_4_4) % 5.72/2.05 | % 5.72/2.05 | Instantiating formula (33) with all_0_7_7, all_0_7_7, all_0_8_8 and discharging atoms join(all_0_8_8, all_0_7_7) = all_0_7_7, yields: % 5.72/2.05 | (41) ? [v0] : ? [v1] : ? [v2] : (converse(all_0_7_7) = v2 & converse(all_0_7_7) = v0 & converse(all_0_8_8) = v1 & join(v1, v2) = v0) % 5.72/2.05 | % 5.72/2.05 | Instantiating (41) with all_11_0_10, all_11_1_11, all_11_2_12 yields: % 5.72/2.05 | (42) converse(all_0_7_7) = all_11_0_10 & converse(all_0_7_7) = all_11_2_12 & converse(all_0_8_8) = all_11_1_11 & join(all_11_1_11, all_11_0_10) = all_11_2_12 % 5.72/2.05 | % 5.72/2.05 | Applying alpha-rule on (42) yields: % 5.72/2.05 | (43) converse(all_0_7_7) = all_11_0_10 % 5.72/2.05 | (44) converse(all_0_7_7) = all_11_2_12 % 5.72/2.05 | (45) converse(all_0_8_8) = all_11_1_11 % 5.72/2.05 | (46) join(all_11_1_11, all_11_0_10) = all_11_2_12 % 5.72/2.05 | % 5.72/2.05 | Instantiating (39) with all_15_0_14, all_15_1_15, all_15_2_16 yields: % 5.72/2.05 | (47) converse(all_0_0_0) = all_15_2_16 & converse(all_0_1_1) = all_15_0_14 & converse(all_0_2_2) = all_15_1_15 & join(all_15_1_15, all_15_0_14) = all_15_2_16 % 5.72/2.05 | % 5.72/2.05 | Applying alpha-rule on (47) yields: % 5.72/2.05 | (48) converse(all_0_0_0) = all_15_2_16 % 5.72/2.05 | (49) converse(all_0_1_1) = all_15_0_14 % 5.72/2.05 | (50) converse(all_0_2_2) = all_15_1_15 % 5.72/2.05 | (51) join(all_15_1_15, all_15_0_14) = all_15_2_16 % 5.72/2.05 | % 5.72/2.05 | Instantiating (40) with all_17_0_17, all_17_1_18 yields: % 5.72/2.05 | (52) composition(all_0_7_7, all_0_6_6) = all_17_0_17 & composition(all_0_8_8, all_0_6_6) = all_17_1_18 & join(all_17_1_18, all_17_0_17) = all_0_4_4 % 5.72/2.05 | % 5.72/2.05 | Applying alpha-rule on (52) yields: % 5.72/2.05 | (53) composition(all_0_7_7, all_0_6_6) = all_17_0_17 % 5.72/2.05 | (54) composition(all_0_8_8, all_0_6_6) = all_17_1_18 % 5.72/2.05 | (55) join(all_17_1_18, all_17_0_17) = all_0_4_4 % 5.72/2.05 | % 5.72/2.05 | Instantiating (38) with all_19_0_19, all_19_1_20, all_19_2_21 yields: % 5.72/2.05 | (56) converse(all_0_5_5) = all_19_2_21 & converse(all_0_6_6) = all_19_1_20 & converse(all_0_8_8) = all_19_0_19 & composition(all_19_1_20, all_19_0_19) = all_19_2_21 % 5.72/2.05 | % 5.72/2.05 | Applying alpha-rule on (56) yields: % 5.72/2.05 | (57) converse(all_0_5_5) = all_19_2_21 % 5.72/2.05 | (58) converse(all_0_6_6) = all_19_1_20 % 5.72/2.05 | (59) converse(all_0_8_8) = all_19_0_19 % 5.72/2.05 | (60) composition(all_19_1_20, all_19_0_19) = all_19_2_21 % 5.72/2.05 | % 5.72/2.05 | Instantiating (37) with all_21_0_22, all_21_1_23, all_21_2_24 yields: % 5.72/2.05 | (61) converse(all_0_4_4) = all_21_2_24 & converse(all_0_6_6) = all_21_1_23 & converse(all_0_7_7) = all_21_0_22 & composition(all_21_1_23, all_21_0_22) = all_21_2_24 % 5.72/2.05 | % 5.72/2.05 | Applying alpha-rule on (61) yields: % 5.72/2.05 | (62) converse(all_0_4_4) = all_21_2_24 % 5.72/2.05 | (63) converse(all_0_6_6) = all_21_1_23 % 5.72/2.05 | (64) converse(all_0_7_7) = all_21_0_22 % 5.72/2.05 | (65) composition(all_21_1_23, all_21_0_22) = all_21_2_24 % 5.72/2.05 | % 5.72/2.05 | Instantiating (36) with all_23_0_25, all_23_1_26, all_23_2_27 yields: % 5.72/2.05 | (66) converse(all_0_2_2) = all_23_2_27 & converse(all_0_6_6) = all_23_0_25 & converse(all_0_8_8) = all_23_1_26 & composition(all_23_1_26, all_23_0_25) = all_23_2_27 % 5.72/2.05 | % 5.72/2.05 | Applying alpha-rule on (66) yields: % 5.72/2.05 | (67) converse(all_0_2_2) = all_23_2_27 % 5.72/2.05 | (68) converse(all_0_6_6) = all_23_0_25 % 5.72/2.05 | (69) converse(all_0_8_8) = all_23_1_26 % 5.72/2.05 | (70) composition(all_23_1_26, all_23_0_25) = all_23_2_27 % 5.72/2.05 | % 5.72/2.05 | Instantiating (35) with all_25_0_28, all_25_1_29, all_25_2_30 yields: % 5.72/2.05 | (71) converse(all_0_1_1) = all_25_2_30 & converse(all_0_6_6) = all_25_0_28 & converse(all_0_7_7) = all_25_1_29 & composition(all_25_1_29, all_25_0_28) = all_25_2_30 % 5.72/2.05 | % 5.72/2.05 | Applying alpha-rule on (71) yields: % 5.72/2.05 | (72) converse(all_0_1_1) = all_25_2_30 % 5.72/2.05 | (73) converse(all_0_6_6) = all_25_0_28 % 5.72/2.05 | (74) converse(all_0_7_7) = all_25_1_29 % 5.72/2.05 | (75) composition(all_25_1_29, all_25_0_28) = all_25_2_30 % 5.72/2.05 | % 5.72/2.05 | Instantiating formula (11) with all_0_1_1, all_15_0_14, all_25_2_30 and discharging atoms converse(all_0_1_1) = all_25_2_30, converse(all_0_1_1) = all_15_0_14, yields: % 5.72/2.05 | (76) all_25_2_30 = all_15_0_14 % 5.72/2.05 | % 5.72/2.05 | Instantiating formula (11) with all_0_2_2, all_15_1_15, all_23_2_27 and discharging atoms converse(all_0_2_2) = all_23_2_27, converse(all_0_2_2) = all_15_1_15, yields: % 5.72/2.05 | (77) all_23_2_27 = all_15_1_15 % 5.72/2.05 | % 5.72/2.05 | Instantiating formula (11) with all_0_6_6, all_23_0_25, all_25_0_28 and discharging atoms converse(all_0_6_6) = all_25_0_28, converse(all_0_6_6) = all_23_0_25, yields: % 5.72/2.06 | (78) all_25_0_28 = all_23_0_25 % 5.72/2.06 | % 5.72/2.06 | Instantiating formula (11) with all_0_6_6, all_19_1_20, all_25_0_28 and discharging atoms converse(all_0_6_6) = all_25_0_28, converse(all_0_6_6) = all_19_1_20, yields: % 5.72/2.06 | (79) all_25_0_28 = all_19_1_20 % 5.72/2.06 | % 5.72/2.06 | Instantiating formula (11) with all_0_7_7, all_21_0_22, all_25_1_29 and discharging atoms converse(all_0_7_7) = all_25_1_29, converse(all_0_7_7) = all_21_0_22, yields: % 5.72/2.06 | (80) all_25_1_29 = all_21_0_22 % 5.72/2.06 | % 5.72/2.06 | Instantiating formula (11) with all_0_7_7, all_11_0_10, all_21_0_22 and discharging atoms converse(all_0_7_7) = all_21_0_22, converse(all_0_7_7) = all_11_0_10, yields: % 5.72/2.06 | (81) all_21_0_22 = all_11_0_10 % 5.72/2.06 | % 5.72/2.06 | Instantiating formula (11) with all_0_7_7, all_11_2_12, all_25_1_29 and discharging atoms converse(all_0_7_7) = all_25_1_29, converse(all_0_7_7) = all_11_2_12, yields: % 5.72/2.06 | (82) all_25_1_29 = all_11_2_12 % 5.72/2.06 | % 5.72/2.06 | Instantiating formula (11) with all_0_8_8, all_11_1_11, all_23_1_26 and discharging atoms converse(all_0_8_8) = all_23_1_26, converse(all_0_8_8) = all_11_1_11, yields: % 5.72/2.06 | (83) all_23_1_26 = all_11_1_11 % 5.72/2.06 | % 5.72/2.06 | Instantiating formula (5) with all_0_7_7, all_0_6_6, all_17_0_17, all_0_4_4 and discharging atoms composition(all_0_7_7, all_0_6_6) = all_17_0_17, composition(all_0_7_7, all_0_6_6) = all_0_4_4, yields: % 5.72/2.06 | (84) all_17_0_17 = all_0_4_4 % 5.72/2.06 | % 5.72/2.06 | Instantiating formula (5) with all_0_8_8, all_0_6_6, all_17_1_18, all_0_5_5 and discharging atoms composition(all_0_8_8, all_0_6_6) = all_17_1_18, composition(all_0_8_8, all_0_6_6) = all_0_5_5, yields: % 5.72/2.06 | (85) all_17_1_18 = all_0_5_5 % 5.72/2.06 | % 5.72/2.06 | Combining equations (78,79) yields a new equation: % 5.72/2.06 | (86) all_23_0_25 = all_19_1_20 % 5.72/2.06 | % 5.72/2.06 | Simplifying 86 yields: % 5.72/2.06 | (87) all_23_0_25 = all_19_1_20 % 5.72/2.06 | % 5.72/2.06 | Combining equations (80,82) yields a new equation: % 5.72/2.06 | (88) all_21_0_22 = all_11_2_12 % 5.72/2.06 | % 5.72/2.06 | Simplifying 88 yields: % 5.72/2.06 | (89) all_21_0_22 = all_11_2_12 % 5.72/2.06 | % 5.72/2.06 | Combining equations (81,89) yields a new equation: % 5.72/2.06 | (90) all_11_0_10 = all_11_2_12 % 5.72/2.06 | % 5.72/2.06 | Simplifying 90 yields: % 5.72/2.06 | (91) all_11_0_10 = all_11_2_12 % 5.72/2.06 | % 5.72/2.06 | From (76) and (72) follows: % 5.84/2.06 | (49) converse(all_0_1_1) = all_15_0_14 % 5.84/2.06 | % 5.84/2.06 | From (82)(79)(76) and (75) follows: % 5.84/2.06 | (93) composition(all_11_2_12, all_19_1_20) = all_15_0_14 % 5.84/2.06 | % 5.84/2.06 | From (83)(87)(77) and (70) follows: % 5.84/2.06 | (94) composition(all_11_1_11, all_19_1_20) = all_15_1_15 % 5.84/2.06 | % 5.84/2.06 | From (85)(84) and (55) follows: % 5.84/2.06 | (95) join(all_0_5_5, all_0_4_4) = all_0_4_4 % 5.84/2.06 | % 5.84/2.06 | From (91) and (46) follows: % 5.84/2.06 | (96) join(all_11_1_11, all_11_2_12) = all_11_2_12 % 5.84/2.06 | % 5.84/2.06 | Instantiating formula (18) with all_0_5_5, all_0_4_4, all_0_4_4, all_0_3_3 and discharging atoms join(all_0_5_5, all_0_4_4) = all_0_3_3, join(all_0_5_5, all_0_4_4) = all_0_4_4, yields: % 5.84/2.06 | (97) all_0_3_3 = all_0_4_4 % 5.84/2.06 | % 5.84/2.06 +-Applying beta-rule and splitting (10), into two cases. % 5.84/2.06 |-Branch one: % 5.84/2.06 | (98) ~ (all_0_0_0 = all_0_1_1) % 5.84/2.06 | % 5.84/2.06 | Instantiating formula (17) with all_15_2_16, all_0_0_0 and discharging atoms converse(all_0_0_0) = all_15_2_16, yields: % 5.84/2.06 | (99) converse(all_15_2_16) = all_0_0_0 % 5.84/2.06 | % 5.84/2.06 | Instantiating formula (17) with all_15_0_14, all_0_1_1 and discharging atoms converse(all_0_1_1) = all_15_0_14, yields: % 5.84/2.06 | (100) converse(all_15_0_14) = all_0_1_1 % 5.84/2.06 | % 5.84/2.06 | Instantiating formula (21) with all_15_0_14, all_19_1_20, all_11_2_12 and discharging atoms composition(all_11_2_12, all_19_1_20) = all_15_0_14, yields: % 5.84/2.06 | (101) ? [v0] : ? [v1] : ? [v2] : (converse(all_19_1_20) = v1 & converse(all_15_0_14) = v0 & converse(all_11_2_12) = v2 & composition(v1, v2) = v0) % 5.84/2.06 | % 5.84/2.06 | Instantiating formula (33) with all_15_2_16, all_15_0_14, all_15_1_15 and discharging atoms join(all_15_1_15, all_15_0_14) = all_15_2_16, yields: % 5.84/2.06 | (102) ? [v0] : ? [v1] : ? [v2] : (converse(all_15_0_14) = v2 & converse(all_15_1_15) = v1 & converse(all_15_2_16) = v0 & join(v1, v2) = v0) % 5.84/2.07 | % 5.84/2.07 | Instantiating formula (14) with all_15_0_14, all_11_2_12, all_19_1_20, all_11_2_12, all_11_1_11 and discharging atoms composition(all_11_2_12, all_19_1_20) = all_15_0_14, join(all_11_1_11, all_11_2_12) = all_11_2_12, yields: % 5.84/2.07 | (103) ? [v0] : ? [v1] : (composition(all_11_1_11, all_19_1_20) = v0 & composition(all_11_2_12, all_19_1_20) = v1 & join(v0, v1) = all_15_0_14) % 5.84/2.07 | % 5.84/2.07 | Instantiating (101) with all_65_0_45, all_65_1_46, all_65_2_47 yields: % 5.84/2.07 | (104) converse(all_19_1_20) = all_65_1_46 & converse(all_15_0_14) = all_65_2_47 & converse(all_11_2_12) = all_65_0_45 & composition(all_65_1_46, all_65_0_45) = all_65_2_47 % 5.84/2.07 | % 5.84/2.07 | Applying alpha-rule on (104) yields: % 5.84/2.07 | (105) converse(all_19_1_20) = all_65_1_46 % 5.84/2.07 | (106) converse(all_15_0_14) = all_65_2_47 % 5.84/2.07 | (107) converse(all_11_2_12) = all_65_0_45 % 5.84/2.07 | (108) composition(all_65_1_46, all_65_0_45) = all_65_2_47 % 5.84/2.07 | % 5.84/2.07 | Instantiating (102) with all_77_0_63, all_77_1_64, all_77_2_65 yields: % 5.84/2.07 | (109) converse(all_15_0_14) = all_77_0_63 & converse(all_15_1_15) = all_77_1_64 & converse(all_15_2_16) = all_77_2_65 & join(all_77_1_64, all_77_0_63) = all_77_2_65 % 5.84/2.07 | % 5.84/2.07 | Applying alpha-rule on (109) yields: % 5.84/2.07 | (110) converse(all_15_0_14) = all_77_0_63 % 5.84/2.07 | (111) converse(all_15_1_15) = all_77_1_64 % 5.84/2.07 | (112) converse(all_15_2_16) = all_77_2_65 % 5.84/2.07 | (113) join(all_77_1_64, all_77_0_63) = all_77_2_65 % 5.84/2.07 | % 5.84/2.07 | Instantiating (103) with all_93_0_79, all_93_1_80 yields: % 5.84/2.07 | (114) composition(all_11_1_11, all_19_1_20) = all_93_1_80 & composition(all_11_2_12, all_19_1_20) = all_93_0_79 & join(all_93_1_80, all_93_0_79) = all_15_0_14 % 5.84/2.07 | % 5.84/2.07 | Applying alpha-rule on (114) yields: % 5.84/2.07 | (115) composition(all_11_1_11, all_19_1_20) = all_93_1_80 % 5.84/2.07 | (116) composition(all_11_2_12, all_19_1_20) = all_93_0_79 % 5.84/2.07 | (117) join(all_93_1_80, all_93_0_79) = all_15_0_14 % 5.84/2.07 | % 5.84/2.07 | Instantiating formula (11) with all_15_0_14, all_65_2_47, all_77_0_63 and discharging atoms converse(all_15_0_14) = all_77_0_63, converse(all_15_0_14) = all_65_2_47, yields: % 5.84/2.07 | (118) all_77_0_63 = all_65_2_47 % 5.84/2.07 | % 5.84/2.07 | Instantiating formula (11) with all_15_0_14, all_0_1_1, all_77_0_63 and discharging atoms converse(all_15_0_14) = all_77_0_63, converse(all_15_0_14) = all_0_1_1, yields: % 5.84/2.07 | (119) all_77_0_63 = all_0_1_1 % 5.84/2.07 | % 5.84/2.07 | Instantiating formula (11) with all_15_2_16, all_0_0_0, all_77_2_65 and discharging atoms converse(all_15_2_16) = all_77_2_65, converse(all_15_2_16) = all_0_0_0, yields: % 5.84/2.07 | (120) all_77_2_65 = all_0_0_0 % 5.84/2.07 | % 5.84/2.07 | Instantiating formula (5) with all_11_1_11, all_19_1_20, all_93_1_80, all_15_1_15 and discharging atoms composition(all_11_1_11, all_19_1_20) = all_93_1_80, composition(all_11_1_11, all_19_1_20) = all_15_1_15, yields: % 5.84/2.07 | (121) all_93_1_80 = all_15_1_15 % 5.84/2.07 | % 5.84/2.07 | Instantiating formula (5) with all_11_2_12, all_19_1_20, all_93_0_79, all_15_0_14 and discharging atoms composition(all_11_2_12, all_19_1_20) = all_93_0_79, composition(all_11_2_12, all_19_1_20) = all_15_0_14, yields: % 5.84/2.07 | (122) all_93_0_79 = all_15_0_14 % 5.84/2.07 | % 5.84/2.07 | Combining equations (119,118) yields a new equation: % 5.84/2.07 | (123) all_65_2_47 = all_0_1_1 % 5.84/2.07 | % 5.84/2.07 | From (123) and (106) follows: % 5.84/2.07 | (100) converse(all_15_0_14) = all_0_1_1 % 5.84/2.07 | % 5.84/2.07 | From (120) and (112) follows: % 5.84/2.07 | (99) converse(all_15_2_16) = all_0_0_0 % 5.84/2.07 | % 5.84/2.07 | From (121)(122) and (117) follows: % 5.84/2.07 | (126) join(all_15_1_15, all_15_0_14) = all_15_0_14 % 5.84/2.07 | % 5.84/2.07 | Instantiating formula (18) with all_15_1_15, all_15_0_14, all_15_0_14, all_15_2_16 and discharging atoms join(all_15_1_15, all_15_0_14) = all_15_0_14, join(all_15_1_15, all_15_0_14) = all_15_2_16, yields: % 5.84/2.07 | (127) all_15_0_14 = all_15_2_16 % 5.84/2.07 | % 5.84/2.07 | From (127) and (100) follows: % 5.84/2.07 | (128) converse(all_15_2_16) = all_0_1_1 % 5.84/2.07 | % 5.84/2.07 | Instantiating formula (11) with all_15_2_16, all_0_1_1, all_0_0_0 and discharging atoms converse(all_15_2_16) = all_0_0_0, converse(all_15_2_16) = all_0_1_1, yields: % 5.84/2.07 | (129) all_0_0_0 = all_0_1_1 % 5.84/2.07 | % 5.84/2.07 | Equations (129) can reduce 98 to: % 5.84/2.07 | (130) $false % 5.84/2.07 | % 5.84/2.07 |-The branch is then unsatisfiable % 5.84/2.07 |-Branch two: % 5.84/2.07 | (129) all_0_0_0 = all_0_1_1 % 5.84/2.07 | (132) ~ (all_0_3_3 = all_0_4_4) % 5.84/2.07 | % 5.84/2.07 | Equations (97) can reduce 132 to: % 5.84/2.07 | (130) $false % 5.84/2.07 | % 5.84/2.07 |-The branch is then unsatisfiable % 5.84/2.07 % SZS output end Proof for theBenchmark % 5.84/2.07 % 5.84/2.07 1395ms %------------------------------------------------------------------------------