%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU115+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n028.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 08:46:40 EDT 2022 % Result : Theorem 2.78s 1.40s % Output : Proof 4.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU115+1 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n028.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 : Sun Jun 19 09:06:00 EDT 2022 % 0.13/0.34 % CPUTime : % 0.54/0.62 ____ _ % 0.54/0.62 ___ / __ \_____(_)___ ________ __________ % 0.54/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.62 % 0.54/0.62 A Theorem Prover for First-Order Logic % 0.54/0.62 (ePrincess v.1.0) % 0.54/0.62 % 0.54/0.62 (c) Philipp Rümmer, 2009-2015 % 0.54/0.62 (c) Peter Backeman, 2014-2015 % 0.54/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.54/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.54/0.62 Bug reports to peter@backeman.se % 0.54/0.62 % 0.54/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.54/0.62 % 0.54/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.69/1.03 Prover 0: Preprocessing ... % 2.26/1.25 Prover 0: Warning: ignoring some quantifiers % 2.26/1.27 Prover 0: Constructing countermodel ... % 2.78/1.40 Prover 0: proved (709ms) % 2.78/1.40 % 2.78/1.40 No countermodel exists, formula is valid % 2.78/1.40 % SZS status Theorem for theBenchmark % 2.78/1.40 % 2.78/1.40 Generating proof ... Warning: ignoring some quantifiers % 4.00/1.71 found it (size 17) % 4.00/1.71 % 4.00/1.71 % SZS output start Proof for theBenchmark % 4.00/1.71 Assumed formulas after preprocessing and simplification: % 4.00/1.71 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v1 = v0) & singleton(empty_set) = v0 & finite_subsets(empty_set) = v1 & powerset(empty_set) = v0 & cap_closed(v5) & finite(v4) & diff_closed(v5) & cup_closed(v5) & preboolean(v5) & empty(v3) & empty(empty_set) & ~ empty(v5) & ~ empty(v4) & ~ empty(v2) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ~ empty(v8) | ~ element(v7, v9) | ~ in(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ~ element(v7, v9) | ~ in(v6, v7) | element(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (singleton(v8) = v7) | ~ (singleton(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (finite_subsets(v8) = v7) | ~ (finite_subsets(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (powerset(v8) = v7) | ~ (powerset(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (finite_subsets(v6) = v8) | ~ element(v7, v8) | finite(v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ~ element(v6, v8) | subset(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ~ subset(v6, v7) | element(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (powerset(v6) = v7) | ~ finite(v6) | ~ element(v8, v7) | finite(v8)) & ! [v6] : ! [v7] : (v7 = v6 | ~ empty(v7) | ~ empty(v6)) & ! [v6] : ! [v7] : ( ~ (singleton(v6) = v7) | ~ empty(v7)) & ! [v6] : ! [v7] : ( ~ (singleton(v6) = v7) | finite(v7)) & ! [v6] : ! [v7] : ( ~ (finite_subsets(v6) = v7) | ~ finite(v6) | powerset(v6) = v7) & ! [v6] : ! [v7] : ( ~ (finite_subsets(v6) = v7) | ~ empty(v7)) & ! [v6] : ! [v7] : ( ~ (finite_subsets(v6) = v7) | diff_closed(v7)) & ! [v6] : ! [v7] : ( ~ (finite_subsets(v6) = v7) | cup_closed(v7)) & ! [v6] : ! [v7] : ( ~ (finite_subsets(v6) = v7) | preboolean(v7)) & ! [v6] : ! [v7] : ( ~ (powerset(v6) = v7) | ~ finite(v6) | finite_subsets(v6) = v7) & ! [v6] : ! [v7] : ( ~ (powerset(v6) = v7) | ~ empty(v7)) & ! [v6] : ! [v7] : ( ~ (powerset(v6) = v7) | diff_closed(v7)) & ! [v6] : ! [v7] : ( ~ (powerset(v6) = v7) | cup_closed(v7)) & ! [v6] : ! [v7] : ( ~ (powerset(v6) = v7) | preboolean(v7)) & ! [v6] : ! [v7] : ( ~ (powerset(v6) = v7) | empty(v6) | ? [v8] : (finite(v8) & element(v8, v7) & ~ empty(v8))) & ! [v6] : ! [v7] : ( ~ (powerset(v6) = v7) | empty(v6) | ? [v8] : (element(v8, v7) & ~ empty(v8))) & ! [v6] : ! [v7] : ( ~ (powerset(v6) = v7) | ? [v8] : (natural(v8) & ordinal(v8) & epsilon_connected(v8) & epsilon_transitive(v8) & one_to_one(v8) & function(v8) & relation(v8) & finite(v8) & empty(v8) & element(v8, v7))) & ! [v6] : ! [v7] : ( ~ (powerset(v6) = v7) | ? [v8] : (empty(v8) & element(v8, v7))) & ! [v6] : ! [v7] : ( ~ empty(v7) | ~ in(v6, v7)) & ! [v6] : ! [v7] : ( ~ element(v6, v7) | empty(v7) | in(v6, v7)) & ! [v6] : ! [v7] : ( ~ in(v7, v6) | ~ in(v6, v7)) & ! [v6] : ! [v7] : ( ~ in(v6, v7) | element(v6, v7)) & ! [v6] : (v6 = empty_set | ~ empty(v6)) & ! [v6] : ( ~ diff_closed(v6) | ~ cup_closed(v6) | preboolean(v6)) & ! [v6] : ( ~ preboolean(v6) | diff_closed(v6)) & ! [v6] : ( ~ preboolean(v6) | cup_closed(v6)) & ! [v6] : ( ~ empty(v6) | finite(v6)) & ? [v6] : ? [v7] : element(v7, v6) & ? [v6] : subset(v6, v6)) % 4.00/1.75 | 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: % 4.00/1.75 | (1) ~ (all_0_4_4 = all_0_5_5) & singleton(empty_set) = all_0_5_5 & finite_subsets(empty_set) = all_0_4_4 & powerset(empty_set) = all_0_5_5 & cap_closed(all_0_0_0) & finite(all_0_1_1) & diff_closed(all_0_0_0) & cup_closed(all_0_0_0) & preboolean(all_0_0_0) & empty(all_0_2_2) & empty(empty_set) & ~ empty(all_0_0_0) & ~ empty(all_0_1_1) & ~ empty(all_0_3_3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ empty(v2) | ~ element(v1, v3) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite_subsets(v2) = v1) | ~ (finite_subsets(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v2) | ~ element(v1, v2) | finite(v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ finite(v0) | ~ element(v2, v1) | finite(v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | finite(v1)) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | ~ finite(v0) | powerset(v0) = v1) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | diff_closed(v1)) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | cup_closed(v1)) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | preboolean(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ finite(v0) | finite_subsets(v0) = v1) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (finite(v2) & element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (natural(v2) & ordinal(v2) & epsilon_connected(v2) & epsilon_transitive(v2) & one_to_one(v2) & function(v2) & relation(v2) & finite(v2) & empty(v2) & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ( ~ diff_closed(v0) | ~ cup_closed(v0) | preboolean(v0)) & ! [v0] : ( ~ preboolean(v0) | diff_closed(v0)) & ! [v0] : ( ~ preboolean(v0) | cup_closed(v0)) & ! [v0] : ( ~ empty(v0) | finite(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) % 4.00/1.76 | % 4.00/1.76 | Applying alpha-rule on (1) yields: % 4.00/1.76 | (2) ~ empty(all_0_1_1) % 4.00/1.76 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 4.00/1.76 | (4) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 4.00/1.76 | (5) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 4.00/1.76 | (6) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 4.00/1.76 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 4.00/1.76 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 4.00/1.76 | (9) ~ (all_0_4_4 = all_0_5_5) % 4.00/1.76 | (10) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | ~ empty(v1)) % 4.00/1.76 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v2) | ~ element(v1, v2) | finite(v1)) % 4.00/1.76 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 4.00/1.76 | (13) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | diff_closed(v1)) % 4.00/1.76 | (14) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ finite(v0) | finite_subsets(v0) = v1) % 4.00/1.76 | (15) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 4.00/1.76 | (16) powerset(empty_set) = all_0_5_5 % 4.00/1.76 | (17) ~ empty(all_0_0_0) % 4.00/1.76 | (18) empty(all_0_2_2) % 4.00/1.76 | (19) ! [v0] : ( ~ diff_closed(v0) | ~ cup_closed(v0) | preboolean(v0)) % 4.00/1.76 | (20) empty(empty_set) % 4.00/1.76 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ empty(v2) | ~ element(v1, v3) | ~ in(v0, v1)) % 4.00/1.76 | (22) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | ~ finite(v0) | powerset(v0) = v1) % 4.00/1.77 | (23) finite_subsets(empty_set) = all_0_4_4 % 4.00/1.77 | (24) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (finite(v2) & element(v2, v1) & ~ empty(v2))) % 4.00/1.77 | (25) diff_closed(all_0_0_0) % 4.00/1.77 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 4.00/1.77 | (27) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 4.00/1.77 | (28) ~ empty(all_0_3_3) % 4.00/1.77 | (29) ! [v0] : ( ~ preboolean(v0) | cup_closed(v0)) % 4.00/1.77 | (30) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1))) % 4.00/1.77 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite_subsets(v2) = v1) | ~ (finite_subsets(v2) = v0)) % 4.00/1.77 | (32) singleton(empty_set) = all_0_5_5 % 4.00/1.77 | (33) preboolean(all_0_0_0) % 4.00/1.77 | (34) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | preboolean(v1)) % 4.00/1.77 | (35) ? [v0] : ? [v1] : element(v1, v0) % 4.00/1.77 | (36) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) % 4.00/1.77 | (37) cup_closed(all_0_0_0) % 4.00/1.77 | (38) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1)) % 4.00/1.77 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ finite(v0) | ~ element(v2, v1) | finite(v2)) % 4.00/1.77 | (40) ? [v0] : subset(v0, v0) % 4.00/1.77 | (41) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 4.00/1.77 | (42) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1)) % 4.00/1.77 | (43) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | finite(v1)) % 4.00/1.77 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 4.00/1.77 | (45) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(v1)) % 4.00/1.77 | (46) ! [v0] : ( ~ empty(v0) | finite(v0)) % 4.00/1.77 | (47) finite(all_0_1_1) % 4.00/1.77 | (48) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (natural(v2) & ordinal(v2) & epsilon_connected(v2) & epsilon_transitive(v2) & one_to_one(v2) & function(v2) & relation(v2) & finite(v2) & empty(v2) & element(v2, v1))) % 4.00/1.77 | (49) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 4.00/1.77 | (50) ! [v0] : ( ~ preboolean(v0) | diff_closed(v0)) % 4.00/1.77 | (51) cap_closed(all_0_0_0) % 4.00/1.77 | (52) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | cup_closed(v1)) % 4.00/1.77 | % 4.00/1.77 | Instantiating formula (48) with all_0_5_5, empty_set and discharging atoms powerset(empty_set) = all_0_5_5, yields: % 4.00/1.77 | (53) ? [v0] : (natural(v0) & ordinal(v0) & epsilon_connected(v0) & epsilon_transitive(v0) & one_to_one(v0) & function(v0) & relation(v0) & finite(v0) & empty(v0) & element(v0, all_0_5_5)) % 4.00/1.77 | % 4.00/1.77 | Instantiating formula (30) with all_0_5_5, empty_set and discharging atoms powerset(empty_set) = all_0_5_5, yields: % 4.00/1.77 | (54) ? [v0] : (empty(v0) & element(v0, all_0_5_5)) % 4.00/1.77 | % 4.00/1.78 | Instantiating (54) with all_17_0_9 yields: % 4.00/1.78 | (55) empty(all_17_0_9) & element(all_17_0_9, all_0_5_5) % 4.00/1.78 | % 4.00/1.78 | Applying alpha-rule on (55) yields: % 4.00/1.78 | (56) empty(all_17_0_9) % 4.00/1.78 | (57) element(all_17_0_9, all_0_5_5) % 4.00/1.78 | % 4.00/1.78 | Instantiating (53) with all_19_0_10 yields: % 4.00/1.78 | (58) natural(all_19_0_10) & ordinal(all_19_0_10) & epsilon_connected(all_19_0_10) & epsilon_transitive(all_19_0_10) & one_to_one(all_19_0_10) & function(all_19_0_10) & relation(all_19_0_10) & finite(all_19_0_10) & empty(all_19_0_10) & element(all_19_0_10, all_0_5_5) % 4.00/1.78 | % 4.00/1.78 | Applying alpha-rule on (58) yields: % 4.00/1.78 | (59) element(all_19_0_10, all_0_5_5) % 4.00/1.78 | (60) epsilon_connected(all_19_0_10) % 4.00/1.78 | (61) ordinal(all_19_0_10) % 4.00/1.78 | (62) empty(all_19_0_10) % 4.00/1.78 | (63) one_to_one(all_19_0_10) % 4.00/1.78 | (64) epsilon_transitive(all_19_0_10) % 4.00/1.78 | (65) natural(all_19_0_10) % 4.00/1.78 | (66) relation(all_19_0_10) % 4.00/1.78 | (67) finite(all_19_0_10) % 4.00/1.78 | (68) function(all_19_0_10) % 4.00/1.78 | % 4.00/1.78 | Instantiating formula (27) with all_19_0_10 and discharging atoms empty(all_19_0_10), yields: % 4.00/1.78 | (69) all_19_0_10 = empty_set % 4.38/1.78 | % 4.38/1.78 | Instantiating formula (12) with all_17_0_9, all_19_0_10 and discharging atoms empty(all_19_0_10), empty(all_17_0_9), yields: % 4.38/1.78 | (70) all_19_0_10 = all_17_0_9 % 4.38/1.78 | % 4.38/1.78 | Combining equations (69,70) yields a new equation: % 4.38/1.78 | (71) all_17_0_9 = empty_set % 4.38/1.78 | % 4.38/1.78 | Combining equations (71,70) yields a new equation: % 4.38/1.78 | (69) all_19_0_10 = empty_set % 4.38/1.78 | % 4.38/1.78 | From (69) and (67) follows: % 4.38/1.78 | (73) finite(empty_set) % 4.38/1.78 | % 4.38/1.78 | Instantiating formula (22) with all_0_4_4, empty_set and discharging atoms finite_subsets(empty_set) = all_0_4_4, finite(empty_set), yields: % 4.38/1.78 | (74) powerset(empty_set) = all_0_4_4 % 4.38/1.78 | % 4.38/1.78 | Instantiating formula (44) with empty_set, all_0_4_4, all_0_5_5 and discharging atoms powerset(empty_set) = all_0_4_4, powerset(empty_set) = all_0_5_5, yields: % 4.38/1.78 | (75) all_0_4_4 = all_0_5_5 % 4.38/1.78 | % 4.38/1.78 | Equations (75) can reduce 9 to: % 4.38/1.78 | (76) $false % 4.38/1.78 | % 4.38/1.78 |-The branch is then unsatisfiable % 4.38/1.78 % SZS output end Proof for theBenchmark % 4.38/1.78 % 4.38/1.78 1148ms %------------------------------------------------------------------------------