%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU117+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n016.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 08:46:41 EDT 2022 % Result : Theorem 3.13s 1.36s % Output : Proof 4.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU117+1 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n016.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 : Sun Jun 19 05:30:23 EDT 2022 % 0.13/0.34 % CPUTime : % 0.56/0.59 ____ _ % 0.56/0.59 ___ / __ \_____(_)___ ________ __________ % 0.56/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.56/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.56/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.56/0.59 % 0.56/0.59 A Theorem Prover for First-Order Logic % 0.56/0.60 (ePrincess v.1.0) % 0.56/0.60 % 0.56/0.60 (c) Philipp Rümmer, 2009-2015 % 0.56/0.60 (c) Peter Backeman, 2014-2015 % 0.56/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.56/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.56/0.60 Bug reports to peter@backeman.se % 0.56/0.60 % 0.56/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.56/0.60 % 0.56/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.72/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.71/0.95 Prover 0: Preprocessing ... % 2.09/1.14 Prover 0: Warning: ignoring some quantifiers % 2.32/1.16 Prover 0: Constructing countermodel ... % 2.92/1.36 Prover 0: proved (713ms) % 3.13/1.36 % 3.13/1.36 No countermodel exists, formula is valid % 3.13/1.36 % SZS status Theorem for theBenchmark % 3.13/1.36 % 3.13/1.36 Generating proof ... Warning: ignoring some quantifiers % 4.27/1.64 found it (size 24) % 4.27/1.64 % 4.27/1.64 % SZS output start Proof for theBenchmark % 4.27/1.64 Assumed formulas after preprocessing and simplification: % 4.27/1.64 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (finite_subsets(v0) = v2 & powerset(v0) = v3 & cap_closed(v7) & element(v1, v2) & finite(v6) & preboolean(v7) & diff_closed(v7) & cup_closed(v7) & empty(v5) & empty(empty_set) & ~ element(v1, v3) & ~ empty(v7) & ~ empty(v6) & ~ empty(v4) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ~ in(v8, v9) | ~ element(v9, v11) | ~ empty(v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ~ in(v8, v9) | ~ element(v9, v11) | element(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (finite_subsets(v8) = v10) | ~ preboolean(v9) | ? [v11] : (( ~ subset(v11, v8) | ~ in(v11, v9) | ~ finite(v11)) & (in(v11, v9) | (subset(v11, v8) & finite(v11))))) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (finite_subsets(v10) = v9) | ~ (finite_subsets(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (powerset(v10) = v9) | ~ (powerset(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (finite_subsets(v8) = v10) | ~ element(v9, v10) | finite(v9)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (finite_subsets(v8) = v9) | ~ subset(v10, v8) | ~ finite(v10) | ~ preboolean(v9) | in(v10, v9)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (finite_subsets(v8) = v9) | ~ in(v10, v9) | ~ preboolean(v9) | subset(v10, v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (finite_subsets(v8) = v9) | ~ in(v10, v9) | ~ preboolean(v9) | finite(v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ~ subset(v8, v9) | element(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ~ element(v8, v10) | subset(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v8) = v9) | ~ element(v10, v9) | ~ finite(v8) | finite(v10)) & ! [v8] : ! [v9] : (v9 = v8 | ~ empty(v9) | ~ empty(v8)) & ! [v8] : ! [v9] : ( ~ (finite_subsets(v8) = v9) | ~ empty(v9)) & ! [v8] : ! [v9] : ( ~ (finite_subsets(v8) = v9) | preboolean(v9)) & ! [v8] : ! [v9] : ( ~ (finite_subsets(v8) = v9) | diff_closed(v9)) & ! [v8] : ! [v9] : ( ~ (finite_subsets(v8) = v9) | cup_closed(v9)) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ~ empty(v9)) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | preboolean(v9)) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | diff_closed(v9)) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | cup_closed(v9)) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | empty(v8) | ? [v10] : (element(v10, v9) & finite(v10) & ~ empty(v10))) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | empty(v8) | ? [v10] : (element(v10, v9) & ~ empty(v10))) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ? [v10] : (natural(v10) & ordinal(v10) & epsilon_connected(v10) & epsilon_transitive(v10) & one_to_one(v10) & function(v10) & relation(v10) & element(v10, v9) & finite(v10) & empty(v10))) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ? [v10] : (element(v10, v9) & empty(v10))) & ! [v8] : ! [v9] : ( ~ in(v9, v8) | ~ in(v8, v9)) & ! [v8] : ! [v9] : ( ~ in(v8, v9) | ~ empty(v9)) & ! [v8] : ! [v9] : ( ~ in(v8, v9) | element(v8, v9)) & ! [v8] : ! [v9] : ( ~ element(v8, v9) | in(v8, v9) | empty(v9)) & ! [v8] : (v8 = empty_set | ~ empty(v8)) & ! [v8] : ( ~ preboolean(v8) | diff_closed(v8)) & ! [v8] : ( ~ preboolean(v8) | cup_closed(v8)) & ! [v8] : ( ~ diff_closed(v8) | ~ cup_closed(v8) | preboolean(v8)) & ! [v8] : ( ~ empty(v8) | finite(v8)) & ? [v8] : ? [v9] : element(v9, v8) & ? [v8] : subset(v8, v8)) % 4.50/1.69 | 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: % 4.50/1.69 | (1) finite_subsets(all_0_7_7) = all_0_5_5 & powerset(all_0_7_7) = all_0_4_4 & cap_closed(all_0_0_0) & element(all_0_6_6, all_0_5_5) & finite(all_0_1_1) & preboolean(all_0_0_0) & diff_closed(all_0_0_0) & cup_closed(all_0_0_0) & empty(all_0_2_2) & empty(empty_set) & ~ element(all_0_6_6, all_0_4_4) & ~ empty(all_0_0_0) & ~ empty(all_0_1_1) & ~ empty(all_0_3_3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v0, v1) | ~ element(v1, v3) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v0, v1) | ~ element(v1, v3) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (finite_subsets(v0) = v2) | ~ preboolean(v1) | ? [v3] : (( ~ subset(v3, v0) | ~ in(v3, v1) | ~ finite(v3)) & (in(v3, v1) | (subset(v3, v0) & finite(v3))))) & ! [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] : ( ~ (finite_subsets(v0) = v1) | ~ subset(v2, v0) | ~ finite(v2) | ~ preboolean(v1) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v1) | ~ in(v2, v1) | ~ preboolean(v1) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v1) | ~ in(v2, v1) | ~ preboolean(v1) | finite(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ finite(v0) | finite(v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | preboolean(v1)) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | diff_closed(v1)) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | cup_closed(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & finite(v2) & ~ 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) & element(v2, v1) & finite(v2) & empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | in(v0, v1) | empty(v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ( ~ preboolean(v0) | diff_closed(v0)) & ! [v0] : ( ~ preboolean(v0) | cup_closed(v0)) & ! [v0] : ( ~ diff_closed(v0) | ~ cup_closed(v0) | preboolean(v0)) & ! [v0] : ( ~ empty(v0) | finite(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) % 4.50/1.70 | % 4.50/1.70 | Applying alpha-rule on (1) yields: % 4.50/1.70 | (2) ~ element(all_0_6_6, all_0_4_4) % 4.50/1.70 | (3) ! [v0] : ! [v1] : ( ~ in(v0, v1) | ~ empty(v1)) % 4.50/1.70 | (4) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 4.50/1.70 | (5) ! [v0] : ( ~ preboolean(v0) | diff_closed(v0)) % 4.50/1.70 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (finite_subsets(v0) = v2) | ~ preboolean(v1) | ? [v3] : (( ~ subset(v3, v0) | ~ in(v3, v1) | ~ finite(v3)) & (in(v3, v1) | (subset(v3, v0) & finite(v3))))) % 4.50/1.70 | (7) powerset(all_0_7_7) = all_0_4_4 % 4.50/1.70 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 4.50/1.70 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 4.50/1.70 | (10) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 4.50/1.70 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v1) | ~ in(v2, v1) | ~ preboolean(v1) | finite(v2)) % 4.50/1.70 | (12) element(all_0_6_6, all_0_5_5) % 4.50/1.70 | (13) preboolean(all_0_0_0) % 4.50/1.70 | (14) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | ~ empty(v1)) % 4.50/1.70 | (15) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 4.50/1.70 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v2) | ~ element(v1, v2) | finite(v1)) % 4.50/1.70 | (17) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (natural(v2) & ordinal(v2) & epsilon_connected(v2) & epsilon_transitive(v2) & one_to_one(v2) & function(v2) & relation(v2) & element(v2, v1) & finite(v2) & empty(v2))) % 4.50/1.70 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 4.50/1.70 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v1) | ~ subset(v2, v0) | ~ finite(v2) | ~ preboolean(v1) | in(v2, v1)) % 4.50/1.71 | (20) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 4.50/1.71 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v0, v1) | ~ element(v1, v3) | element(v0, v2)) % 4.50/1.71 | (22) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | diff_closed(v1)) % 4.50/1.71 | (23) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(v1)) % 4.50/1.71 | (24) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1)) % 4.50/1.71 | (25) finite(all_0_1_1) % 4.50/1.71 | (26) ~ empty(all_0_0_0) % 4.50/1.71 | (27) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 4.50/1.71 | (28) ! [v0] : ( ~ preboolean(v0) | cup_closed(v0)) % 4.50/1.71 | (29) ! [v0] : ! [v1] : ( ~ element(v0, v1) | in(v0, v1) | empty(v1)) % 4.50/1.71 | (30) ! [v0] : ( ~ diff_closed(v0) | ~ cup_closed(v0) | preboolean(v0)) % 4.50/1.71 | (31) cup_closed(all_0_0_0) % 4.50/1.71 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v0, v1) | ~ element(v1, v3) | ~ empty(v2)) % 4.50/1.71 | (33) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | preboolean(v1)) % 4.50/1.71 | (34) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & finite(v2) & ~ empty(v2))) % 4.50/1.71 | (35) ~ empty(all_0_1_1) % 4.50/1.71 | (36) ! [v0] : ( ~ empty(v0) | finite(v0)) % 4.50/1.71 | (37) finite_subsets(all_0_7_7) = all_0_5_5 % 4.50/1.71 | (38) empty(empty_set) % 4.50/1.71 | (39) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) % 4.50/1.71 | (40) diff_closed(all_0_0_0) % 4.50/1.71 | (41) cap_closed(all_0_0_0) % 4.50/1.71 | (42) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 4.50/1.71 | (43) ~ empty(all_0_3_3) % 4.50/1.71 | (44) ? [v0] : subset(v0, v0) % 4.50/1.71 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ finite(v0) | finite(v2)) % 4.50/1.71 | (46) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite_subsets(v2) = v1) | ~ (finite_subsets(v2) = v0)) % 4.50/1.71 | (47) empty(all_0_2_2) % 4.50/1.71 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v1) | ~ in(v2, v1) | ~ preboolean(v1) | subset(v2, v0)) % 4.50/1.71 | (49) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | cup_closed(v1)) % 4.50/1.71 | (50) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1)) % 4.50/1.71 | (51) ? [v0] : ? [v1] : element(v1, v0) % 4.50/1.71 | % 4.50/1.71 | Instantiating formula (33) with all_0_5_5, all_0_7_7 and discharging atoms finite_subsets(all_0_7_7) = all_0_5_5, yields: % 4.50/1.71 | (52) preboolean(all_0_5_5) % 4.50/1.71 | % 4.50/1.71 | Instantiating formula (17) with all_0_4_4, all_0_7_7 and discharging atoms powerset(all_0_7_7) = all_0_4_4, yields: % 4.50/1.71 | (53) ? [v0] : (natural(v0) & ordinal(v0) & epsilon_connected(v0) & epsilon_transitive(v0) & one_to_one(v0) & function(v0) & relation(v0) & element(v0, all_0_4_4) & finite(v0) & empty(v0)) % 4.50/1.71 | % 4.50/1.72 | Instantiating formula (39) with all_0_4_4, all_0_7_7 and discharging atoms powerset(all_0_7_7) = all_0_4_4, yields: % 4.50/1.72 | (54) ? [v0] : (element(v0, all_0_4_4) & empty(v0)) % 4.50/1.72 | % 4.50/1.72 | Instantiating formula (29) with all_0_5_5, all_0_6_6 and discharging atoms element(all_0_6_6, all_0_5_5), yields: % 4.50/1.72 | (55) in(all_0_6_6, all_0_5_5) | empty(all_0_5_5) % 4.50/1.72 | % 4.50/1.72 | Instantiating (54) with all_17_0_11 yields: % 4.50/1.72 | (56) element(all_17_0_11, all_0_4_4) & empty(all_17_0_11) % 4.50/1.72 | % 4.50/1.72 | Applying alpha-rule on (56) yields: % 4.50/1.72 | (57) element(all_17_0_11, all_0_4_4) % 4.50/1.72 | (58) empty(all_17_0_11) % 4.50/1.72 | % 4.50/1.72 | Instantiating (53) with all_19_0_12 yields: % 4.50/1.72 | (59) natural(all_19_0_12) & ordinal(all_19_0_12) & epsilon_connected(all_19_0_12) & epsilon_transitive(all_19_0_12) & one_to_one(all_19_0_12) & function(all_19_0_12) & relation(all_19_0_12) & element(all_19_0_12, all_0_4_4) & finite(all_19_0_12) & empty(all_19_0_12) % 4.50/1.72 | % 4.50/1.72 | Applying alpha-rule on (59) yields: % 4.50/1.72 | (60) ordinal(all_19_0_12) % 4.50/1.72 | (61) function(all_19_0_12) % 4.50/1.72 | (62) one_to_one(all_19_0_12) % 4.50/1.72 | (63) element(all_19_0_12, all_0_4_4) % 4.50/1.72 | (64) epsilon_transitive(all_19_0_12) % 4.50/1.72 | (65) empty(all_19_0_12) % 4.50/1.72 | (66) finite(all_19_0_12) % 4.50/1.72 | (67) epsilon_connected(all_19_0_12) % 4.50/1.72 | (68) relation(all_19_0_12) % 4.50/1.72 | (69) natural(all_19_0_12) % 4.50/1.72 | % 4.50/1.72 | Instantiating formula (10) with all_19_0_12 and discharging atoms empty(all_19_0_12), yields: % 4.50/1.72 | (70) all_19_0_12 = empty_set % 4.50/1.72 | % 4.50/1.72 | Instantiating formula (4) with all_17_0_11, all_19_0_12 and discharging atoms empty(all_19_0_12), empty(all_17_0_11), yields: % 4.50/1.72 | (71) all_19_0_12 = all_17_0_11 % 4.50/1.72 | % 4.50/1.72 | Combining equations (70,71) yields a new equation: % 4.50/1.72 | (72) all_17_0_11 = empty_set % 4.50/1.72 | % 4.50/1.72 | Combining equations (72,71) yields a new equation: % 4.50/1.72 | (70) all_19_0_12 = empty_set % 4.50/1.72 | % 4.50/1.72 | From (72) and (57) follows: % 4.50/1.72 | (74) element(empty_set, all_0_4_4) % 4.50/1.72 | % 4.50/1.72 | From (70) and (66) follows: % 4.50/1.72 | (75) finite(empty_set) % 4.50/1.72 | % 4.50/1.72 | Instantiating formula (8) with all_0_4_4, all_0_7_7, empty_set and discharging atoms powerset(all_0_7_7) = all_0_4_4, element(empty_set, all_0_4_4), yields: % 4.50/1.72 | (76) subset(empty_set, all_0_7_7) % 4.50/1.72 | % 4.50/1.72 | Instantiating formula (19) with empty_set, all_0_5_5, all_0_7_7 and discharging atoms finite_subsets(all_0_7_7) = all_0_5_5, subset(empty_set, all_0_7_7), finite(empty_set), preboolean(all_0_5_5), yields: % 4.50/1.72 | (77) in(empty_set, all_0_5_5) % 4.50/1.72 | % 4.50/1.72 +-Applying beta-rule and splitting (55), into two cases. % 4.50/1.72 |-Branch one: % 4.50/1.72 | (78) empty(all_0_5_5) % 4.50/1.72 | % 4.50/1.72 | Instantiating formula (3) with all_0_5_5, empty_set and discharging atoms in(empty_set, all_0_5_5), empty(all_0_5_5), yields: % 4.50/1.72 | (79) $false % 4.50/1.72 | % 4.50/1.72 |-The branch is then unsatisfiable % 4.50/1.72 |-Branch two: % 4.50/1.72 | (80) ~ empty(all_0_5_5) % 4.50/1.72 | (81) in(all_0_6_6, all_0_5_5) % 4.50/1.73 | % 4.50/1.73 | Instantiating formula (48) with all_0_6_6, all_0_5_5, all_0_7_7 and discharging atoms finite_subsets(all_0_7_7) = all_0_5_5, in(all_0_6_6, all_0_5_5), preboolean(all_0_5_5), yields: % 4.50/1.73 | (82) subset(all_0_6_6, all_0_7_7) % 4.50/1.73 | % 4.50/1.73 | Instantiating formula (9) with all_0_4_4, all_0_7_7, all_0_6_6 and discharging atoms powerset(all_0_7_7) = all_0_4_4, subset(all_0_6_6, all_0_7_7), ~ element(all_0_6_6, all_0_4_4), yields: % 4.50/1.73 | (79) $false % 4.50/1.73 | % 4.50/1.73 |-The branch is then unsatisfiable % 4.50/1.73 % SZS output end Proof for theBenchmark % 4.50/1.73 % 4.50/1.73 1119ms %------------------------------------------------------------------------------