%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : REL003+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n019.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 19:14:01 EDT 2022 % Result : Theorem 2.42s 1.29s % Output : Proof 4.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.12 % Problem : REL003+1 : TPTP v8.1.0. Released v4.0.0. % 0.13/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n019.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Fri Jul 8 13:21:08 EDT 2022 % 0.13/0.34 % CPUTime : % 0.58/0.59 ____ _ % 0.58/0.59 ___ / __ \_____(_)___ ________ __________ % 0.58/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.59 % 0.58/0.59 A Theorem Prover for First-Order Logic % 0.58/0.59 (ePrincess v.1.0) % 0.58/0.59 % 0.58/0.59 (c) Philipp Rümmer, 2009-2015 % 0.58/0.59 (c) Peter Backeman, 2014-2015 % 0.58/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.59 Bug reports to peter@backeman.se % 0.58/0.59 % 0.58/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.59 % 0.58/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.75/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.50/0.92 Prover 0: Preprocessing ... % 1.94/1.16 Prover 0: Constructing countermodel ... % 2.42/1.29 Prover 0: proved (652ms) % 2.42/1.29 % 2.42/1.29 No countermodel exists, formula is valid % 2.42/1.29 % SZS status Theorem for theBenchmark % 2.42/1.29 % 2.42/1.29 Generating proof ... found it (size 38) % 3.68/1.57 % 3.68/1.57 % SZS output start Proof for theBenchmark % 3.68/1.57 Assumed formulas after preprocessing and simplification: % 3.68/1.57 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (converse(v1) = v4 & converse(v0) = v3 & join(v3, v4) = v5 & join(v0, v1) = v2 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v6 | ~ (complement(v12) = v13) | ~ (complement(v10) = v11) | ~ (complement(v7) = v9) | ~ (complement(v6) = v8) | ~ (join(v11, v13) = v14) | ~ (join(v8, v9) = v10) | ~ (join(v8, v7) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (converse(v6) = v8) | ~ (composition(v8, v10) = v11) | ~ (composition(v6, v7) = v9) | ~ (complement(v9) = v10) | ~ (complement(v7) = v12) | ~ (join(v11, v12) = v13)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (composition(v7, v8) = v10) | ~ (composition(v6, v8) = v9) | ~ (join(v9, v10) = v11) | ? [v12] : (composition(v12, v8) = v11 & join(v6, v7) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (converse(v7) = v9) | ~ (converse(v6) = v8) | ~ (join(v8, v9) = v10) | ? [v11] : (converse(v11) = v10 & join(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (converse(v7) = v8) | ~ (converse(v6) = v9) | ~ (composition(v8, v9) = v10) | ? [v11] : (converse(v11) = v10 & composition(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (composition(v9, v8) = v10) | ~ (composition(v6, v7) = v9) | ? [v11] : (composition(v7, v8) = v11 & composition(v6, v11) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (composition(v9, v8) = v10) | ~ (join(v6, v7) = v9) | ? [v11] : ? [v12] : (composition(v7, v8) = v12 & composition(v6, v8) = v11 & join(v11, v12) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (composition(v7, v8) = v9) | ~ (composition(v6, v9) = v10) | ? [v11] : (composition(v11, v8) = v10 & composition(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (complement(v7) = v9) | ~ (complement(v6) = v8) | ~ (join(v8, v9) = v10) | ? [v11] : (meet(v6, v7) = v11 & complement(v10) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (join(v9, v8) = v10) | ~ (join(v6, v7) = v9) | ? [v11] : (join(v7, v8) = v11 & join(v6, v11) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (join(v7, v8) = v9) | ~ (join(v6, v9) = v10) | ? [v11] : (join(v11, v8) = v10 & join(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (composition(v9, v8) = v7) | ~ (composition(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (meet(v9, v8) = v7) | ~ (meet(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (join(v9, v8) = v7) | ~ (join(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = zero | ~ (meet(v6, v7) = v8) | ~ (complement(v6) = v7)) & ! [v6] : ! [v7] : ! [v8] : (v8 = top | ~ (complement(v6) = v7) | ~ (join(v6, v7) = v8)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (converse(v8) = v7) | ~ (converse(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (complement(v8) = v7) | ~ (complement(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (composition(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (converse(v8) = v9 & converse(v7) = v10 & converse(v6) = v11 & composition(v10, v11) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (meet(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (complement(v11) = v8 & complement(v7) = v10 & complement(v6) = v9 & join(v9, v10) = v11)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (join(v7, v6) = v8) | join(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (join(v6, v7) = v8) | join(v7, v6) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (join(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (converse(v8) = v9 & converse(v7) = v11 & converse(v6) = v10 & join(v10, v11) = v9)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (composition(v6, one) = v7)) & ! [v6] : ! [v7] : ( ~ (converse(v6) = v7) | converse(v7) = v6) & ((v5 = v4 & ~ (v2 = v1)) | (v2 = v1 & ~ (v5 = v4)))) % 3.68/1.62 | 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 yields: % 3.68/1.62 | (1) converse(all_0_4_4) = all_0_1_1 & converse(all_0_5_5) = all_0_2_2 & 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 & ! [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)) | (all_0_3_3 = all_0_4_4 & ~ (all_0_0_0 = all_0_1_1))) % 4.00/1.63 | % 4.00/1.63 | Applying alpha-rule on (1) yields: % 4.00/1.63 | (2) ! [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)) % 4.00/1.63 | (3) ! [v0] : ! [v1] : ( ~ (converse(v0) = v1) | converse(v1) = v0) % 4.00/1.63 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (composition(v3, v2) = v4) | ~ (composition(v0, v1) = v3) | ? [v5] : (composition(v1, v2) = v5 & composition(v0, v5) = v4)) % 4.00/1.63 | (5) ! [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)) % 4.00/1.63 | (6) converse(all_0_5_5) = all_0_2_2 % 4.00/1.63 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = top | ~ (complement(v0) = v1) | ~ (join(v0, v1) = v2)) % 4.00/1.63 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (complement(v5) = v2 & complement(v1) = v4 & complement(v0) = v3 & join(v3, v4) = v5)) % 4.00/1.63 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (converse(v1) = v3) | ~ (converse(v0) = v2) | ~ (join(v2, v3) = v4) | ? [v5] : (converse(v5) = v4 & join(v0, v1) = v5)) % 4.00/1.63 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (join(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (converse(v2) = v3 & converse(v1) = v5 & converse(v0) = v4 & join(v4, v5) = v3)) % 4.00/1.63 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (join(v0, v1) = v2) | join(v1, v0) = v2) % 4.00/1.63 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (join(v1, v0) = v2) | join(v0, v1) = v2) % 4.00/1.63 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (join(v3, v2) = v1) | ~ (join(v3, v2) = v0)) % 4.00/1.63 | (14) (all_0_0_0 = all_0_1_1 & ~ (all_0_3_3 = all_0_4_4)) | (all_0_3_3 = all_0_4_4 & ~ (all_0_0_0 = all_0_1_1)) % 4.00/1.63 | (15) ! [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)) % 4.00/1.63 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (meet(v0, v1) = v2) | ~ (complement(v0) = v1)) % 4.00/1.63 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (converse(v1) = v2) | ~ (converse(v0) = v3) | ~ (composition(v2, v3) = v4) | ? [v5] : (converse(v5) = v4 & composition(v0, v1) = v5)) % 4.00/1.64 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet(v3, v2) = v1) | ~ (meet(v3, v2) = v0)) % 4.00/1.64 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (converse(v2) = v1) | ~ (converse(v2) = v0)) % 4.00/1.64 | (20) converse(all_0_4_4) = all_0_1_1 % 4.00/1.64 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (composition(v3, v2) = v1) | ~ (composition(v3, v2) = v0)) % 4.00/1.64 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ (composition(v0, one) = v1)) % 4.00/1.64 | (23) join(all_0_2_2, all_0_1_1) = all_0_0_0 % 4.00/1.64 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (composition(v1, v2) = v3) | ~ (composition(v0, v3) = v4) | ? [v5] : (composition(v5, v2) = v4 & composition(v0, v1) = v5)) % 4.00/1.64 | (25) join(all_0_5_5, all_0_4_4) = all_0_3_3 % 4.00/1.64 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (complement(v2) = v1) | ~ (complement(v2) = v0)) % 4.00/1.64 | (27) ! [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)) % 4.00/1.64 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (converse(v2) = v3 & converse(v1) = v4 & converse(v0) = v5 & composition(v4, v5) = v3)) % 4.00/1.64 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (complement(v1) = v3) | ~ (complement(v0) = v2) | ~ (join(v2, v3) = v4) | ? [v5] : (meet(v0, v1) = v5 & complement(v4) = v5)) % 4.00/1.64 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (join(v1, v2) = v3) | ~ (join(v0, v3) = v4) | ? [v5] : (join(v5, v2) = v4 & join(v0, v1) = v5)) % 4.00/1.64 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (join(v3, v2) = v4) | ~ (join(v0, v1) = v3) | ? [v5] : (join(v1, v2) = v5 & join(v0, v5) = v4)) % 4.00/1.64 | % 4.00/1.64 | Instantiating formula (3) with all_0_1_1, all_0_4_4 and discharging atoms converse(all_0_4_4) = all_0_1_1, yields: % 4.00/1.64 | (32) converse(all_0_1_1) = all_0_4_4 % 4.00/1.64 | % 4.00/1.64 | Instantiating formula (3) with all_0_2_2, all_0_5_5 and discharging atoms converse(all_0_5_5) = all_0_2_2, yields: % 4.00/1.64 | (33) converse(all_0_2_2) = all_0_5_5 % 4.00/1.64 | % 4.00/1.64 | Instantiating formula (9) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms converse(all_0_4_4) = all_0_1_1, converse(all_0_5_5) = all_0_2_2, join(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 4.00/1.64 | (34) ? [v0] : (converse(v0) = all_0_0_0 & join(all_0_5_5, all_0_4_4) = v0) % 4.00/1.64 | % 4.00/1.64 | Instantiating formula (10) 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: % 4.00/1.64 | (35) ? [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) % 4.00/1.64 | % 4.00/1.64 | Instantiating formula (10) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms join(all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 4.00/1.64 | (36) ? [v0] : ? [v1] : ? [v2] : (converse(all_0_3_3) = v0 & converse(all_0_4_4) = v2 & converse(all_0_5_5) = v1 & join(v1, v2) = v0) % 4.00/1.65 | % 4.00/1.65 | Instantiating (36) with all_9_0_6, all_9_1_7, all_9_2_8 yields: % 4.00/1.65 | (37) converse(all_0_3_3) = all_9_2_8 & converse(all_0_4_4) = all_9_0_6 & converse(all_0_5_5) = all_9_1_7 & join(all_9_1_7, all_9_0_6) = all_9_2_8 % 4.00/1.65 | % 4.00/1.65 | Applying alpha-rule on (37) yields: % 4.00/1.65 | (38) converse(all_0_3_3) = all_9_2_8 % 4.00/1.65 | (39) converse(all_0_4_4) = all_9_0_6 % 4.00/1.65 | (40) converse(all_0_5_5) = all_9_1_7 % 4.00/1.65 | (41) join(all_9_1_7, all_9_0_6) = all_9_2_8 % 4.00/1.65 | % 4.00/1.65 | Instantiating (34) with all_11_0_9 yields: % 4.00/1.65 | (42) converse(all_11_0_9) = all_0_0_0 & join(all_0_5_5, all_0_4_4) = all_11_0_9 % 4.00/1.65 | % 4.00/1.65 | Applying alpha-rule on (42) yields: % 4.00/1.65 | (43) converse(all_11_0_9) = all_0_0_0 % 4.00/1.65 | (44) join(all_0_5_5, all_0_4_4) = all_11_0_9 % 4.00/1.65 | % 4.00/1.65 | Instantiating (35) with all_13_0_10, all_13_1_11, all_13_2_12 yields: % 4.00/1.65 | (45) converse(all_0_0_0) = all_13_2_12 & converse(all_0_1_1) = all_13_0_10 & converse(all_0_2_2) = all_13_1_11 & join(all_13_1_11, all_13_0_10) = all_13_2_12 % 4.00/1.65 | % 4.00/1.65 | Applying alpha-rule on (45) yields: % 4.00/1.65 | (46) converse(all_0_0_0) = all_13_2_12 % 4.00/1.65 | (47) converse(all_0_1_1) = all_13_0_10 % 4.00/1.65 | (48) converse(all_0_2_2) = all_13_1_11 % 4.00/1.65 | (49) join(all_13_1_11, all_13_0_10) = all_13_2_12 % 4.00/1.65 | % 4.00/1.65 | Instantiating formula (19) with all_0_1_1, all_0_4_4, all_13_0_10 and discharging atoms converse(all_0_1_1) = all_13_0_10, converse(all_0_1_1) = all_0_4_4, yields: % 4.00/1.65 | (50) all_13_0_10 = all_0_4_4 % 4.00/1.65 | % 4.00/1.65 | Instantiating formula (19) with all_0_2_2, all_0_5_5, all_13_1_11 and discharging atoms converse(all_0_2_2) = all_13_1_11, converse(all_0_2_2) = all_0_5_5, yields: % 4.00/1.65 | (51) all_13_1_11 = all_0_5_5 % 4.00/1.65 | % 4.00/1.65 | Instantiating formula (19) with all_0_4_4, all_9_0_6, all_0_1_1 and discharging atoms converse(all_0_4_4) = all_9_0_6, converse(all_0_4_4) = all_0_1_1, yields: % 4.00/1.65 | (52) all_9_0_6 = all_0_1_1 % 4.00/1.65 | % 4.00/1.65 | Instantiating formula (19) with all_0_5_5, all_9_1_7, all_0_2_2 and discharging atoms converse(all_0_5_5) = all_9_1_7, converse(all_0_5_5) = all_0_2_2, yields: % 4.00/1.65 | (53) all_9_1_7 = all_0_2_2 % 4.00/1.65 | % 4.00/1.65 | Instantiating formula (13) with all_0_5_5, all_0_4_4, all_11_0_9, all_0_3_3 and discharging atoms join(all_0_5_5, all_0_4_4) = all_11_0_9, join(all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 4.00/1.65 | (54) all_11_0_9 = all_0_3_3 % 4.00/1.65 | % 4.00/1.65 | From (50) and (47) follows: % 4.00/1.65 | (32) converse(all_0_1_1) = all_0_4_4 % 4.00/1.65 | % 4.00/1.65 | From (52) and (39) follows: % 4.00/1.65 | (20) converse(all_0_4_4) = all_0_1_1 % 4.00/1.65 | % 4.00/1.65 | From (51)(50) and (49) follows: % 4.00/1.65 | (57) join(all_0_5_5, all_0_4_4) = all_13_2_12 % 4.00/1.65 | % 4.00/1.65 | From (53)(52) and (41) follows: % 4.00/1.65 | (58) join(all_0_2_2, all_0_1_1) = all_9_2_8 % 4.00/1.65 | % 4.00/1.65 | From (54) and (44) follows: % 4.00/1.65 | (25) join(all_0_5_5, all_0_4_4) = all_0_3_3 % 4.00/1.65 | % 4.00/1.65 | Instantiating formula (13) with all_0_2_2, all_0_1_1, all_9_2_8, all_0_0_0 and discharging atoms join(all_0_2_2, all_0_1_1) = all_9_2_8, join(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 4.00/1.65 | (60) all_9_2_8 = all_0_0_0 % 4.00/1.65 | % 4.00/1.65 | Instantiating formula (13) with all_0_5_5, all_0_4_4, all_13_2_12, all_0_3_3 and discharging atoms join(all_0_5_5, all_0_4_4) = all_13_2_12, join(all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 4.00/1.65 | (61) all_13_2_12 = all_0_3_3 % 4.00/1.65 | % 4.00/1.65 | From (61) and (46) follows: % 4.00/1.65 | (62) converse(all_0_0_0) = all_0_3_3 % 4.00/1.65 | % 4.00/1.65 | From (60) and (38) follows: % 4.00/1.66 | (63) converse(all_0_3_3) = all_0_0_0 % 4.00/1.66 | % 4.00/1.66 +-Applying beta-rule and splitting (14), into two cases. % 4.00/1.66 |-Branch one: % 4.00/1.66 | (64) all_0_0_0 = all_0_1_1 & ~ (all_0_3_3 = all_0_4_4) % 4.00/1.66 | % 4.00/1.66 | Applying alpha-rule on (64) yields: % 4.00/1.66 | (65) all_0_0_0 = all_0_1_1 % 4.00/1.66 | (66) ~ (all_0_3_3 = all_0_4_4) % 4.00/1.66 | % 4.00/1.66 | From (65) and (62) follows: % 4.00/1.66 | (67) converse(all_0_1_1) = all_0_3_3 % 4.00/1.66 | % 4.00/1.66 | Instantiating formula (19) with all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms converse(all_0_1_1) = all_0_3_3, converse(all_0_1_1) = all_0_4_4, yields: % 4.00/1.66 | (68) all_0_3_3 = all_0_4_4 % 4.00/1.66 | % 4.00/1.66 | Equations (68) can reduce 66 to: % 4.00/1.66 | (69) $false % 4.00/1.66 | % 4.00/1.66 |-The branch is then unsatisfiable % 4.00/1.66 |-Branch two: % 4.00/1.66 | (70) all_0_3_3 = all_0_4_4 & ~ (all_0_0_0 = all_0_1_1) % 4.00/1.66 | % 4.00/1.66 | Applying alpha-rule on (70) yields: % 4.00/1.66 | (68) all_0_3_3 = all_0_4_4 % 4.00/1.66 | (72) ~ (all_0_0_0 = all_0_1_1) % 4.00/1.66 | % 4.00/1.66 | From (68) and (63) follows: % 4.00/1.66 | (73) converse(all_0_4_4) = all_0_0_0 % 4.00/1.66 | % 4.00/1.66 | Instantiating formula (19) with all_0_4_4, all_0_0_0, all_0_1_1 and discharging atoms converse(all_0_4_4) = all_0_0_0, converse(all_0_4_4) = all_0_1_1, yields: % 4.00/1.66 | (65) all_0_0_0 = all_0_1_1 % 4.00/1.66 | % 4.00/1.66 | Equations (65) can reduce 72 to: % 4.00/1.66 | (69) $false % 4.00/1.66 | % 4.00/1.66 |-The branch is then unsatisfiable % 4.00/1.66 % SZS output end Proof for theBenchmark % 4.00/1.66 % 4.00/1.66 1059ms %------------------------------------------------------------------------------