%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET635+3 : TPTP v8.1.0. Released v2.2.0. % 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 : Tue Jul 19 00:21:03 EDT 2022 % Result : Theorem 2.72s 1.35s % Output : Proof 4.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SET635+3 : TPTP v8.1.0. Released v2.2.0. % 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n019.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sun Jul 10 13:36:23 EDT 2022 % 0.12/0.34 % CPUTime : % 0.48/0.59 ____ _ % 0.48/0.59 ___ / __ \_____(_)___ ________ __________ % 0.48/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.48/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.48/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.48/0.59 % 0.48/0.59 A Theorem Prover for First-Order Logic % 0.48/0.60 (ePrincess v.1.0) % 0.48/0.60 % 0.48/0.60 (c) Philipp Rümmer, 2009-2015 % 0.48/0.60 (c) Peter Backeman, 2014-2015 % 0.48/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.48/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.48/0.60 Bug reports to peter@backeman.se % 0.48/0.60 % 0.48/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.48/0.60 % 0.48/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.66/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.43/0.93 Prover 0: Preprocessing ... % 1.97/1.14 Prover 0: Warning: ignoring some quantifiers % 2.03/1.16 Prover 0: Constructing countermodel ... % 2.72/1.34 Prover 0: proved (695ms) % 2.72/1.35 % 2.72/1.35 No countermodel exists, formula is valid % 2.72/1.35 % SZS status Theorem for theBenchmark % 2.72/1.35 % 2.72/1.35 Generating proof ... Warning: ignoring some quantifiers % 3.99/1.67 found it (size 19) % 3.99/1.67 % 3.99/1.67 % SZS output start Proof for theBenchmark % 3.99/1.67 Assumed formulas after preprocessing and simplification: % 3.99/1.67 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = v4) & difference(v5, v6) = v7 & difference(v1, v2) = v3 & intersection(v0, v3) = v4 & intersection(v0, v2) = v6 & intersection(v0, v1) = v5 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (union(v11, v12) = v13) | ~ (difference(v8, v10) = v12) | ~ (difference(v8, v9) = v11) | ? [v14] : (difference(v8, v14) = v13 & intersection(v9, v10) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (difference(v11, v10) = v12) | ~ (intersection(v8, v9) = v11) | ? [v13] : (difference(v9, v10) = v13 & intersection(v8, v13) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (difference(v9, v10) = v11) | ~ (intersection(v8, v11) = v12) | ? [v13] : (difference(v13, v10) = v12 & intersection(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (difference(v8, v11) = v12) | ~ (intersection(v9, v10) = v11) | ? [v13] : ? [v14] : (union(v13, v14) = v12 & difference(v8, v10) = v14 & difference(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (union(v11, v10) = v9) | ~ (union(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (difference(v11, v10) = v9) | ~ (difference(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (intersection(v11, v10) = v9) | ~ (intersection(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (difference(v8, v9) = v11) | ~ member(v10, v11) | ~ member(v10, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (difference(v8, v9) = v11) | ~ member(v10, v11) | member(v10, v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (difference(v8, v9) = v11) | ~ member(v10, v8) | member(v10, v11) | member(v10, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (intersection(v8, v9) = v11) | ~ member(v10, v11) | member(v10, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (intersection(v8, v9) = v11) | ~ member(v10, v11) | member(v10, v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (intersection(v8, v9) = v11) | ~ member(v10, v9) | ~ member(v10, v8) | member(v10, v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = empty_set | ~ (difference(v8, v9) = v10) | ~ subset(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v9, v8) = v10) | union(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v8, v9) = v10) | union(v9, v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection(v9, v8) = v10) | intersection(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection(v8, v9) = v10) | intersection(v9, v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection(v8, v9) = v10) | subset(v10, v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ member(v10, v8) | ~ subset(v8, v9) | member(v10, v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (union(v8, empty_set) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ subset(v9, v8) | ~ subset(v8, v9)) & ! [v8] : ! [v9] : ( ~ (difference(v8, v9) = empty_set) | subset(v8, v9)) & ! [v8] : ! [v9] : ( ~ empty(v8) | ~ member(v9, v8)) & ! [v8] : ~ member(v8, empty_set) & ? [v8] : ? [v9] : (v9 = v8 | ? [v10] : (( ~ member(v10, v9) | ~ member(v10, v8)) & (member(v10, v9) | member(v10, v8)))) & ? [v8] : ? [v9] : (subset(v8, v9) | ? [v10] : (member(v10, v8) & ~ member(v10, v9))) & ? [v8] : (empty(v8) | ? [v9] : member(v9, v8)) & ? [v8] : subset(v8, v8)) % 4.08/1.74 | 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: % 4.08/1.74 | (1) ~ (all_0_0_0 = all_0_3_3) & difference(all_0_2_2, all_0_1_1) = all_0_0_0 & difference(all_0_6_6, all_0_5_5) = all_0_4_4 & intersection(all_0_7_7, all_0_4_4) = all_0_3_3 & intersection(all_0_7_7, all_0_5_5) = all_0_1_1 & intersection(all_0_7_7, all_0_6_6) = all_0_2_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (union(v3, v4) = v5) | ~ (difference(v0, v2) = v4) | ~ (difference(v0, v1) = v3) | ? [v6] : (difference(v0, v6) = v5 & intersection(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v3, v2) = v4) | ~ (intersection(v0, v1) = v3) | ? [v5] : (difference(v1, v2) = v5 & intersection(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v2) = v3) | ~ (intersection(v0, v3) = v4) | ? [v5] : (difference(v5, v2) = v4 & intersection(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v0, v3) = v4) | ~ (intersection(v1, v2) = v3) | ? [v5] : ? [v6] : (union(v5, v6) = v4 & difference(v0, v2) = v6 & difference(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | ~ member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (difference(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (union(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ (difference(v0, v1) = empty_set) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v0) | ~ member(v1, v0)) & ! [v0] : ~ member(v0, empty_set) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) & ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) & ? [v0] : (empty(v0) | ? [v1] : member(v1, v0)) & ? [v0] : subset(v0, v0) % 4.22/1.76 | % 4.22/1.76 | Applying alpha-rule on (1) yields: % 4.22/1.76 | (2) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (difference(v0, v1) = v2) | ~ subset(v0, v1)) % 4.22/1.76 | (3) difference(all_0_2_2, all_0_1_1) = all_0_0_0 % 4.22/1.76 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) % 4.22/1.76 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 4.22/1.76 | (6) ~ (all_0_0_0 = all_0_3_3) % 4.22/1.76 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1)) % 4.22/1.76 | (8) difference(all_0_6_6, all_0_5_5) = all_0_4_4 % 4.28/1.76 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 4.28/1.76 | (10) ? [v0] : subset(v0, v0) % 4.28/1.76 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v2) = v3) | ~ (intersection(v0, v3) = v4) | ? [v5] : (difference(v5, v2) = v4 & intersection(v0, v1) = v5)) % 4.28/1.76 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 4.28/1.76 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) % 4.28/1.76 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) % 4.28/1.76 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) % 4.28/1.76 | (16) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) % 4.28/1.77 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3)) % 4.28/1.77 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1)) % 4.28/1.77 | (19) ! [v0] : ! [v1] : ( ~ empty(v0) | ~ member(v1, v0)) % 4.28/1.77 | (20) ! [v0] : ~ member(v0, empty_set) % 4.28/1.77 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) % 4.28/1.77 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (union(v3, v4) = v5) | ~ (difference(v0, v2) = v4) | ~ (difference(v0, v1) = v3) | ? [v6] : (difference(v0, v6) = v5 & intersection(v1, v2) = v6)) % 4.28/1.77 | (23) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 4.28/1.77 | (24) intersection(all_0_7_7, all_0_4_4) = all_0_3_3 % 4.28/1.77 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v3, v2) = v4) | ~ (intersection(v0, v1) = v3) | ? [v5] : (difference(v1, v2) = v5 & intersection(v0, v5) = v4)) % 4.28/1.77 | (26) intersection(all_0_7_7, all_0_6_6) = all_0_2_2 % 4.28/1.77 | (27) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) % 4.28/1.77 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | subset(v2, v0)) % 4.28/1.77 | (29) ! [v0] : ! [v1] : (v1 = v0 | ~ (union(v0, empty_set) = v1)) % 4.28/1.77 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | ~ member(v2, v1)) % 4.28/1.77 | (31) ? [v0] : (empty(v0) | ? [v1] : member(v1, v0)) % 4.28/1.77 | (32) ! [v0] : ! [v1] : ( ~ (difference(v0, v1) = empty_set) | subset(v0, v1)) % 4.28/1.77 | (33) intersection(all_0_7_7, all_0_5_5) = all_0_1_1 % 4.28/1.77 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) % 4.28/1.77 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2) % 4.28/1.77 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v0, v3) = v4) | ~ (intersection(v1, v2) = v3) | ? [v5] : ? [v6] : (union(v5, v6) = v4 & difference(v0, v2) = v6 & difference(v0, v1) = v5)) % 4.28/1.78 | % 4.28/1.78 | Instantiating formula (11) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms difference(all_0_6_6, all_0_5_5) = all_0_4_4, intersection(all_0_7_7, all_0_4_4) = all_0_3_3, yields: % 4.28/1.78 | (37) ? [v0] : (difference(v0, all_0_5_5) = all_0_3_3 & intersection(all_0_7_7, all_0_6_6) = v0) % 4.28/1.78 | % 4.28/1.78 | Instantiating formula (36) with all_0_0_0, all_0_1_1, all_0_5_5, all_0_7_7, all_0_2_2 and discharging atoms difference(all_0_2_2, all_0_1_1) = all_0_0_0, intersection(all_0_7_7, all_0_5_5) = all_0_1_1, yields: % 4.28/1.78 | (38) ? [v0] : ? [v1] : (union(v0, v1) = all_0_0_0 & difference(all_0_2_2, all_0_5_5) = v1 & difference(all_0_2_2, all_0_7_7) = v0) % 4.28/1.78 | % 4.28/1.78 | Instantiating formula (28) with all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms intersection(all_0_7_7, all_0_6_6) = all_0_2_2, yields: % 4.28/1.78 | (39) subset(all_0_2_2, all_0_7_7) % 4.28/1.78 | % 4.28/1.78 | Instantiating (37) with all_16_0_15 yields: % 4.28/1.78 | (40) difference(all_16_0_15, all_0_5_5) = all_0_3_3 & intersection(all_0_7_7, all_0_6_6) = all_16_0_15 % 4.28/1.78 | % 4.28/1.78 | Applying alpha-rule on (40) yields: % 4.28/1.78 | (41) difference(all_16_0_15, all_0_5_5) = all_0_3_3 % 4.28/1.78 | (42) intersection(all_0_7_7, all_0_6_6) = all_16_0_15 % 4.28/1.78 | % 4.28/1.78 | Instantiating (38) with all_18_0_16, all_18_1_17 yields: % 4.28/1.78 | (43) union(all_18_1_17, all_18_0_16) = all_0_0_0 & difference(all_0_2_2, all_0_5_5) = all_18_0_16 & difference(all_0_2_2, all_0_7_7) = all_18_1_17 % 4.28/1.78 | % 4.28/1.78 | Applying alpha-rule on (43) yields: % 4.28/1.78 | (44) union(all_18_1_17, all_18_0_16) = all_0_0_0 % 4.28/1.78 | (45) difference(all_0_2_2, all_0_5_5) = all_18_0_16 % 4.28/1.78 | (46) difference(all_0_2_2, all_0_7_7) = all_18_1_17 % 4.28/1.78 | % 4.28/1.78 | Instantiating formula (9) with all_0_7_7, all_0_6_6, all_16_0_15, all_0_2_2 and discharging atoms intersection(all_0_7_7, all_0_6_6) = all_16_0_15, intersection(all_0_7_7, all_0_6_6) = all_0_2_2, yields: % 4.28/1.78 | (47) all_16_0_15 = all_0_2_2 % 4.28/1.78 | % 4.28/1.78 | Instantiating formula (2) with all_18_1_17, all_0_7_7, all_0_2_2 and discharging atoms difference(all_0_2_2, all_0_7_7) = all_18_1_17, subset(all_0_2_2, all_0_7_7), yields: % 4.28/1.78 | (48) all_18_1_17 = empty_set % 4.28/1.78 | % 4.28/1.78 | From (48) and (44) follows: % 4.28/1.78 | (49) union(empty_set, all_18_0_16) = all_0_0_0 % 4.28/1.78 | % 4.28/1.78 | From (47) and (41) follows: % 4.28/1.78 | (50) difference(all_0_2_2, all_0_5_5) = all_0_3_3 % 4.28/1.78 | % 4.28/1.78 | Instantiating formula (5) with all_0_2_2, all_0_5_5, all_0_3_3, all_18_0_16 and discharging atoms difference(all_0_2_2, all_0_5_5) = all_18_0_16, difference(all_0_2_2, all_0_5_5) = all_0_3_3, yields: % 4.28/1.78 | (51) all_18_0_16 = all_0_3_3 % 4.28/1.78 | % 4.28/1.78 | From (51) and (49) follows: % 4.28/1.78 | (52) union(empty_set, all_0_3_3) = all_0_0_0 % 4.28/1.78 | % 4.28/1.78 | Instantiating formula (14) with all_0_0_0, empty_set, all_0_3_3 and discharging atoms union(empty_set, all_0_3_3) = all_0_0_0, yields: % 4.28/1.78 | (53) union(all_0_3_3, empty_set) = all_0_0_0 % 4.28/1.78 | % 4.28/1.78 | Instantiating formula (29) with all_0_0_0, all_0_3_3 and discharging atoms union(all_0_3_3, empty_set) = all_0_0_0, yields: % 4.28/1.78 | (54) all_0_0_0 = all_0_3_3 % 4.28/1.78 | % 4.28/1.78 | Equations (54) can reduce 6 to: % 4.28/1.78 | (55) $false % 4.28/1.78 | % 4.28/1.78 |-The branch is then unsatisfiable % 4.28/1.79 % SZS output end Proof for theBenchmark % 4.28/1.79 % 4.28/1.79 1180ms %------------------------------------------------------------------------------