%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU114+1 : TPTP v8.1.0. Released v3.2.0. % 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 08:46:40 EDT 2022 % Result : Theorem 4.96s 1.93s % Output : Proof 7.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU114+1 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.13 % 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 : Mon Jun 20 07:27:09 EDT 2022 % 0.12/0.34 % CPUTime : % 0.63/0.63 ____ _ % 0.63/0.63 ___ / __ \_____(_)___ ________ __________ % 0.63/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.63/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.63/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.63/0.63 % 0.63/0.63 A Theorem Prover for First-Order Logic % 0.63/0.64 (ePrincess v.1.0) % 0.63/0.64 % 0.63/0.64 (c) Philipp Rümmer, 2009-2015 % 0.63/0.64 (c) Peter Backeman, 2014-2015 % 0.63/0.64 (contributions by Angelo Brillout, Peter Baumgartner) % 0.63/0.64 Free software under GNU Lesser General Public License (LGPL). % 0.63/0.64 Bug reports to peter@backeman.se % 0.63/0.64 % 0.63/0.64 For more information, visit http://user.uu.se/~petba168/breu/ % 0.63/0.64 % 0.63/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.63/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.67/1.02 Prover 0: Preprocessing ... % 2.30/1.25 Prover 0: Warning: ignoring some quantifiers % 2.45/1.28 Prover 0: Constructing countermodel ... % 4.96/1.93 Prover 0: proved (1250ms) % 4.96/1.93 % 4.96/1.93 No countermodel exists, formula is valid % 4.96/1.93 % SZS status Theorem for theBenchmark % 4.96/1.94 % 4.96/1.94 Generating proof ... Warning: ignoring some quantifiers % 6.94/2.31 found it (size 37) % 6.94/2.31 % 6.94/2.31 % SZS output start Proof for theBenchmark % 6.94/2.31 Assumed formulas after preprocessing and simplification: % 6.94/2.31 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v2 = v1) & finite_subsets(v0) = v1 & powerset(v0) = v2 & cap_closed(v5) & diff_closed(v5) & cup_closed(v5) & preboolean(v5) & finite(v6) & finite(v0) & empty(v4) & empty(empty_set) & ~ empty(v6) & ~ empty(v5) & ~ empty(v3) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ~ element(v8, v10) | ~ empty(v9) | ~ in(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ~ element(v8, v10) | ~ in(v7, v8) | element(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (finite_subsets(v7) = v9) | ~ preboolean(v8) | ? [v10] : (( ~ subset(v10, v7) | ~ finite(v10) | ~ in(v10, v8)) & (in(v10, v8) | (subset(v10, v7) & finite(v10))))) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (finite_subsets(v9) = v8) | ~ (finite_subsets(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (powerset(v9) = v8) | ~ (powerset(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (finite_subsets(v7) = v9) | ~ element(v8, v9) | finite(v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (finite_subsets(v7) = v8) | ~ subset(v9, v7) | ~ preboolean(v8) | ~ finite(v9) | in(v9, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (finite_subsets(v7) = v8) | ~ preboolean(v8) | ~ in(v9, v8) | subset(v9, v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (finite_subsets(v7) = v8) | ~ preboolean(v8) | ~ in(v9, v8) | finite(v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ~ subset(v7, v8) | element(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ~ element(v7, v9) | subset(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v7) = v8) | ~ element(v9, v8) | ~ finite(v7) | finite(v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ subset(v7, v8) | ~ in(v9, v7) | in(v9, v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ subset(v8, v7) | ~ subset(v7, v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ empty(v8) | ~ empty(v7)) & ! [v7] : ! [v8] : ( ~ (finite_subsets(v7) = v8) | ~ empty(v8)) & ! [v7] : ! [v8] : ( ~ (finite_subsets(v7) = v8) | diff_closed(v8)) & ! [v7] : ! [v8] : ( ~ (finite_subsets(v7) = v8) | cup_closed(v8)) & ! [v7] : ! [v8] : ( ~ (finite_subsets(v7) = v8) | preboolean(v8)) & ! [v7] : ! [v8] : ( ~ (finite_subsets(v7) = v8) | ? [v9] : (powerset(v7) = v9 & subset(v8, v9))) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ~ empty(v8)) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | diff_closed(v8)) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | cup_closed(v8)) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | preboolean(v8)) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | empty(v7) | ? [v9] : (element(v9, v8) & finite(v9) & ~ empty(v9))) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | empty(v7) | ? [v9] : (element(v9, v8) & ~ empty(v9))) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ? [v9] : (finite_subsets(v7) = v9 & subset(v9, v8))) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ? [v9] : (natural(v9) & ordinal(v9) & epsilon_connected(v9) & epsilon_transitive(v9) & one_to_one(v9) & function(v9) & relation(v9) & element(v9, v8) & finite(v9) & empty(v9))) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ? [v9] : (element(v9, v8) & empty(v9))) & ! [v7] : ! [v8] : ( ~ subset(v7, v8) | ~ finite(v8) | finite(v7)) & ! [v7] : ! [v8] : ( ~ element(v7, v8) | empty(v8) | in(v7, v8)) & ! [v7] : ! [v8] : ( ~ empty(v8) | ~ in(v7, v8)) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8)) & ! [v7] : ! [v8] : ( ~ in(v7, v8) | element(v7, v8)) & ! [v7] : (v7 = empty_set | ~ empty(v7)) & ! [v7] : ( ~ diff_closed(v7) | ~ cup_closed(v7) | preboolean(v7)) & ! [v7] : ( ~ preboolean(v7) | diff_closed(v7)) & ! [v7] : ( ~ preboolean(v7) | cup_closed(v7)) & ! [v7] : ( ~ empty(v7) | finite(v7)) & ? [v7] : ? [v8] : (subset(v7, v8) | ? [v9] : (in(v9, v7) & ~ in(v9, v8))) & ? [v7] : ? [v8] : element(v8, v7) & ? [v7] : subset(v7, v7)) % 7.10/2.36 | 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 yields: % 7.10/2.36 | (1) ~ (all_0_4_4 = all_0_5_5) & finite_subsets(all_0_6_6) = all_0_5_5 & powerset(all_0_6_6) = all_0_4_4 & cap_closed(all_0_1_1) & diff_closed(all_0_1_1) & cup_closed(all_0_1_1) & preboolean(all_0_1_1) & finite(all_0_0_0) & finite(all_0_6_6) & 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) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (finite_subsets(v0) = v2) | ~ preboolean(v1) | ? [v3] : (( ~ subset(v3, v0) | ~ finite(v3) | ~ in(v3, v1)) & (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) | ~ preboolean(v1) | ~ finite(v2) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v1) | ~ preboolean(v1) | ~ in(v2, v1) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v1) | ~ preboolean(v1) | ~ in(v2, 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] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [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] : ( ~ (finite_subsets(v0) = v1) | ? [v2] : (powerset(v0) = v2 & subset(v1, v2))) & ! [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] : (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] : (finite_subsets(v0) = v2 & subset(v2, v1))) & ! [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] : ( ~ subset(v0, v1) | ~ finite(v1) | finite(v0)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [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] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) % 7.10/2.37 | % 7.10/2.37 | Applying alpha-rule on (1) yields: % 7.10/2.37 | (2) cup_closed(all_0_1_1) % 7.10/2.37 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) % 7.10/2.37 | (4) empty(all_0_2_2) % 7.10/2.37 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (finite_subsets(v0) = v2) | ~ preboolean(v1) | ? [v3] : (( ~ subset(v3, v0) | ~ finite(v3) | ~ in(v3, v1)) & (in(v3, v1) | (subset(v3, v0) & finite(v3))))) % 7.10/2.37 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 7.10/2.37 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v1) | ~ preboolean(v1) | ~ in(v2, v1) | finite(v2)) % 7.10/2.37 | (8) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ finite(v1) | finite(v0)) % 7.10/2.37 | (9) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1)) % 7.10/2.37 | (10) ! [v0] : ( ~ empty(v0) | finite(v0)) % 7.10/2.37 | (11) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | diff_closed(v1)) % 7.10/2.37 | (12) finite(all_0_0_0) % 7.10/2.37 | (13) ! [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))) % 7.10/2.37 | (14) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 7.10/2.37 | (15) cap_closed(all_0_1_1) % 7.10/2.37 | (16) ! [v0] : ( ~ preboolean(v0) | cup_closed(v0)) % 7.10/2.37 | (17) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) % 7.10/2.38 | (18) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | preboolean(v1)) % 7.10/2.38 | (19) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 7.10/2.38 | (20) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 7.10/2.38 | (21) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 7.10/2.38 | (22) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 7.10/2.38 | (23) ? [v0] : ? [v1] : element(v1, v0) % 7.10/2.38 | (24) preboolean(all_0_1_1) % 7.10/2.38 | (25) ~ (all_0_4_4 = all_0_5_5) % 7.10/2.38 | (26) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 7.10/2.38 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 7.10/2.38 | (28) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | ~ empty(v1)) % 7.10/2.38 | (29) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 7.10/2.38 | (30) ~ empty(all_0_3_3) % 7.10/2.38 | (31) ! [v0] : ( ~ preboolean(v0) | diff_closed(v0)) % 7.10/2.38 | (32) finite_subsets(all_0_6_6) = all_0_5_5 % 7.10/2.38 | (33) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 7.10/2.38 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v1) | ~ preboolean(v1) | ~ in(v2, v1) | subset(v2, v0)) % 7.10/2.38 | (35) empty(empty_set) % 7.10/2.38 | (36) ~ empty(all_0_0_0) % 7.10/2.38 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) % 7.10/2.38 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite_subsets(v2) = v1) | ~ (finite_subsets(v2) = v0)) % 7.10/2.38 | (39) ? [v0] : subset(v0, v0) % 7.10/2.38 | (40) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 7.10/2.38 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v2) | ~ element(v1, v2) | finite(v1)) % 7.10/2.38 | (42) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 7.10/2.38 | (43) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | ? [v2] : (powerset(v0) = v2 & subset(v1, v2))) % 7.10/2.38 | (44) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1)) % 7.10/2.38 | (45) ! [v0] : ( ~ diff_closed(v0) | ~ cup_closed(v0) | preboolean(v0)) % 7.10/2.38 | (46) powerset(all_0_6_6) = all_0_4_4 % 7.10/2.38 | (47) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | cup_closed(v1)) % 7.10/2.38 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v1) | ~ subset(v2, v0) | ~ preboolean(v1) | ~ finite(v2) | in(v2, v1)) % 7.10/2.38 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ finite(v0) | finite(v2)) % 7.10/2.38 | (50) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & finite(v2) & ~ empty(v2))) % 7.10/2.39 | (51) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(v1)) % 7.10/2.39 | (52) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (finite_subsets(v0) = v2 & subset(v2, v1))) % 7.10/2.39 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 7.10/2.39 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 7.10/2.39 | (55) finite(all_0_6_6) % 7.10/2.39 | (56) diff_closed(all_0_1_1) % 7.10/2.39 | (57) ~ empty(all_0_1_1) % 7.10/2.39 | % 7.10/2.39 | Instantiating formula (18) with all_0_5_5, all_0_6_6 and discharging atoms finite_subsets(all_0_6_6) = all_0_5_5, yields: % 7.10/2.39 | (58) preboolean(all_0_5_5) % 7.10/2.39 | % 7.10/2.39 | Instantiating formula (43) with all_0_5_5, all_0_6_6 and discharging atoms finite_subsets(all_0_6_6) = all_0_5_5, yields: % 7.10/2.39 | (59) ? [v0] : (powerset(all_0_6_6) = v0 & subset(all_0_5_5, v0)) % 7.10/2.39 | % 7.10/2.39 | Instantiating formula (51) with all_0_4_4, all_0_6_6 and discharging atoms powerset(all_0_6_6) = all_0_4_4, yields: % 7.10/2.39 | (60) preboolean(all_0_4_4) % 7.10/2.39 | % 7.10/2.39 | Instantiating formula (52) with all_0_4_4, all_0_6_6 and discharging atoms powerset(all_0_6_6) = all_0_4_4, yields: % 7.10/2.39 | (61) ? [v0] : (finite_subsets(all_0_6_6) = v0 & subset(v0, all_0_4_4)) % 7.10/2.39 | % 7.10/2.39 | Instantiating (61) with all_20_0_13 yields: % 7.10/2.39 | (62) finite_subsets(all_0_6_6) = all_20_0_13 & subset(all_20_0_13, all_0_4_4) % 7.10/2.39 | % 7.10/2.39 | Applying alpha-rule on (62) yields: % 7.10/2.39 | (63) finite_subsets(all_0_6_6) = all_20_0_13 % 7.10/2.39 | (64) subset(all_20_0_13, all_0_4_4) % 7.10/2.39 | % 7.10/2.39 | Instantiating (59) with all_22_0_14 yields: % 7.10/2.39 | (65) powerset(all_0_6_6) = all_22_0_14 & subset(all_0_5_5, all_22_0_14) % 7.10/2.39 | % 7.10/2.39 | Applying alpha-rule on (65) yields: % 7.10/2.39 | (66) powerset(all_0_6_6) = all_22_0_14 % 7.10/2.39 | (67) subset(all_0_5_5, all_22_0_14) % 7.10/2.39 | % 7.10/2.39 | Instantiating formula (38) with all_0_6_6, all_20_0_13, all_0_5_5 and discharging atoms finite_subsets(all_0_6_6) = all_20_0_13, finite_subsets(all_0_6_6) = all_0_5_5, yields: % 7.10/2.39 | (68) all_20_0_13 = all_0_5_5 % 7.10/2.39 | % 7.10/2.39 | Instantiating formula (27) with all_0_6_6, all_22_0_14, all_0_4_4 and discharging atoms powerset(all_0_6_6) = all_22_0_14, powerset(all_0_6_6) = all_0_4_4, yields: % 7.10/2.39 | (69) all_22_0_14 = all_0_4_4 % 7.10/2.39 | % 7.10/2.39 | From (68) and (63) follows: % 7.10/2.39 | (32) finite_subsets(all_0_6_6) = all_0_5_5 % 7.10/2.39 | % 7.10/2.39 | From (69) and (66) follows: % 7.10/2.39 | (46) powerset(all_0_6_6) = all_0_4_4 % 7.10/2.39 | % 7.10/2.39 | From (69) and (67) follows: % 7.10/2.39 | (72) subset(all_0_5_5, all_0_4_4) % 7.10/2.39 | % 7.10/2.39 | Instantiating formula (5) with all_0_5_5, all_0_4_4, all_0_6_6 and discharging atoms finite_subsets(all_0_6_6) = all_0_5_5, preboolean(all_0_4_4), yields: % 7.10/2.39 | (73) all_0_4_4 = all_0_5_5 | ? [v0] : (( ~ subset(v0, all_0_6_6) | ~ finite(v0) | ~ in(v0, all_0_4_4)) & (in(v0, all_0_4_4) | (subset(v0, all_0_6_6) & finite(v0)))) % 7.10/2.39 | % 7.10/2.40 +-Applying beta-rule and splitting (73), into two cases. % 7.10/2.40 |-Branch one: % 7.10/2.40 | (74) all_0_4_4 = all_0_5_5 % 7.10/2.40 | % 7.10/2.40 | Equations (74) can reduce 25 to: % 7.10/2.40 | (75) $false % 7.10/2.40 | % 7.10/2.40 |-The branch is then unsatisfiable % 7.10/2.40 |-Branch two: % 7.10/2.40 | (25) ~ (all_0_4_4 = all_0_5_5) % 7.10/2.40 | (77) ? [v0] : (( ~ subset(v0, all_0_6_6) | ~ finite(v0) | ~ in(v0, all_0_4_4)) & (in(v0, all_0_4_4) | (subset(v0, all_0_6_6) & finite(v0)))) % 7.10/2.40 | % 7.10/2.40 | Instantiating (77) with all_40_0_16 yields: % 7.10/2.40 | (78) ( ~ subset(all_40_0_16, all_0_6_6) | ~ finite(all_40_0_16) | ~ in(all_40_0_16, all_0_4_4)) & (in(all_40_0_16, all_0_4_4) | (subset(all_40_0_16, all_0_6_6) & finite(all_40_0_16))) % 7.10/2.40 | % 7.10/2.40 | Applying alpha-rule on (78) yields: % 7.10/2.40 | (79) ~ subset(all_40_0_16, all_0_6_6) | ~ finite(all_40_0_16) | ~ in(all_40_0_16, all_0_4_4) % 7.10/2.40 | (80) in(all_40_0_16, all_0_4_4) | (subset(all_40_0_16, all_0_6_6) & finite(all_40_0_16)) % 7.10/2.40 | % 7.10/2.40 +-Applying beta-rule and splitting (79), into two cases. % 7.10/2.40 |-Branch one: % 7.10/2.40 | (81) ~ in(all_40_0_16, all_0_4_4) % 7.10/2.40 | % 7.10/2.40 +-Applying beta-rule and splitting (80), into two cases. % 7.10/2.40 |-Branch one: % 7.10/2.40 | (82) in(all_40_0_16, all_0_4_4) % 7.10/2.40 | % 7.10/2.40 | Using (82) and (81) yields: % 7.10/2.40 | (83) $false % 7.10/2.40 | % 7.10/2.40 |-The branch is then unsatisfiable % 7.10/2.40 |-Branch two: % 7.10/2.40 | (81) ~ in(all_40_0_16, all_0_4_4) % 7.10/2.40 | (85) subset(all_40_0_16, all_0_6_6) & finite(all_40_0_16) % 7.10/2.40 | % 7.10/2.40 | Applying alpha-rule on (85) yields: % 7.10/2.40 | (86) subset(all_40_0_16, all_0_6_6) % 7.10/2.40 | (87) finite(all_40_0_16) % 7.10/2.40 | % 7.10/2.40 | Instantiating formula (48) with all_40_0_16, all_0_5_5, all_0_6_6 and discharging atoms finite_subsets(all_0_6_6) = all_0_5_5, subset(all_40_0_16, all_0_6_6), preboolean(all_0_5_5), finite(all_40_0_16), yields: % 7.10/2.40 | (88) in(all_40_0_16, all_0_5_5) % 7.10/2.40 | % 7.10/2.40 | Instantiating formula (3) with all_40_0_16, all_0_4_4, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_4_4), in(all_40_0_16, all_0_5_5), ~ in(all_40_0_16, all_0_4_4), yields: % 7.10/2.40 | (83) $false % 7.10/2.40 | % 7.10/2.40 |-The branch is then unsatisfiable % 7.10/2.40 |-Branch two: % 7.10/2.40 | (82) in(all_40_0_16, all_0_4_4) % 7.10/2.40 | (91) ~ subset(all_40_0_16, all_0_6_6) | ~ finite(all_40_0_16) % 7.10/2.40 | % 7.10/2.40 | Instantiating formula (19) with all_0_4_4, all_40_0_16 and discharging atoms in(all_40_0_16, all_0_4_4), yields: % 7.10/2.40 | (92) element(all_40_0_16, all_0_4_4) % 7.10/2.40 | % 7.10/2.40 | Instantiating formula (49) with all_40_0_16, all_0_4_4, all_0_6_6 and discharging atoms powerset(all_0_6_6) = all_0_4_4, element(all_40_0_16, all_0_4_4), finite(all_0_6_6), yields: % 7.10/2.40 | (87) finite(all_40_0_16) % 7.10/2.40 | % 7.10/2.40 | Instantiating formula (53) with all_0_4_4, all_0_6_6, all_40_0_16 and discharging atoms powerset(all_0_6_6) = all_0_4_4, element(all_40_0_16, all_0_4_4), yields: % 7.10/2.40 | (86) subset(all_40_0_16, all_0_6_6) % 7.10/2.40 | % 7.10/2.40 +-Applying beta-rule and splitting (91), into two cases. % 7.10/2.40 |-Branch one: % 7.10/2.40 | (95) ~ subset(all_40_0_16, all_0_6_6) % 7.10/2.40 | % 7.10/2.40 | Using (86) and (95) yields: % 7.10/2.40 | (83) $false % 7.10/2.40 | % 7.10/2.40 |-The branch is then unsatisfiable % 7.10/2.40 |-Branch two: % 7.10/2.40 | (86) subset(all_40_0_16, all_0_6_6) % 7.10/2.40 | (98) ~ finite(all_40_0_16) % 7.10/2.40 | % 7.10/2.40 | Using (87) and (98) yields: % 7.10/2.40 | (83) $false % 7.10/2.40 | % 7.10/2.40 |-The branch is then unsatisfiable % 7.10/2.40 % SZS output end Proof for theBenchmark % 7.10/2.40 % 7.10/2.40 1759ms %------------------------------------------------------------------------------