0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n022.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 1440 0.12/0.33 % WCLimit : 180 0.12/0.33 % DateTime : Mon Jul 3 11:21:59 EDT 2023 0.12/0.33 % CPUTime : 1.31/1.60 ============================== Prover9 =============================== 1.31/1.60 Prover9 (32) version 2009-11A, November 2009. 1.31/1.60 Process 14701 was started by sandbox on n022.cluster.edu, 1.31/1.60 Mon Jul 3 11:22:00 2023 1.31/1.60 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1440 -f /tmp/Prover9_14548_n022.cluster.edu". 1.31/1.60 ============================== end of head =========================== 1.31/1.60 1.31/1.60 ============================== INPUT ================================= 1.31/1.60 1.31/1.60 % Reading from file /tmp/Prover9_14548_n022.cluster.edu 1.31/1.60 1.31/1.60 set(prolog_style_variables). 1.31/1.60 set(auto2). 1.31/1.60 % set(auto2) -> set(auto). 1.31/1.60 % set(auto) -> set(auto_inference). 1.31/1.60 % set(auto) -> set(auto_setup). 1.31/1.60 % set(auto_setup) -> set(predicate_elim). 1.31/1.60 % set(auto_setup) -> assign(eq_defs, unfold). 1.31/1.60 % set(auto) -> set(auto_limits). 1.31/1.60 % set(auto_limits) -> assign(max_weight, "100.000"). 1.31/1.60 % set(auto_limits) -> assign(sos_limit, 20000). 1.31/1.60 % set(auto) -> set(auto_denials). 1.31/1.60 % set(auto) -> set(auto_process). 1.31/1.60 % set(auto2) -> assign(new_constants, 1). 1.31/1.60 % set(auto2) -> assign(fold_denial_max, 3). 1.31/1.60 % set(auto2) -> assign(max_weight, "200.000"). 1.31/1.60 % set(auto2) -> assign(max_hours, 1). 1.31/1.60 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.31/1.60 % set(auto2) -> assign(max_seconds, 0). 1.31/1.60 % set(auto2) -> assign(max_minutes, 5). 1.31/1.60 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.31/1.60 % set(auto2) -> set(sort_initial_sos). 1.31/1.60 % set(auto2) -> assign(sos_limit, -1). 1.31/1.60 % set(auto2) -> assign(lrs_ticks, 3000). 1.31/1.60 % set(auto2) -> assign(max_megs, 400). 1.31/1.60 % set(auto2) -> assign(stats, some). 1.31/1.60 % set(auto2) -> clear(echo_input). 1.31/1.60 % set(auto2) -> set(quiet). 1.31/1.60 % set(auto2) -> clear(print_initial_clauses). 1.31/1.60 % set(auto2) -> clear(print_given). 1.31/1.60 assign(lrs_ticks,-1). 1.31/1.60 assign(sos_limit,10000). 1.31/1.60 assign(order,kbo). 1.31/1.60 set(lex_order_vars). 1.31/1.60 clear(print_given). 1.31/1.60 1.31/1.60 % formulas(sos). % not echoed (733 formulas) 1.31/1.60 1.31/1.60 ============================== end of input ========================== 1.31/1.60 1.31/1.60 % From the command line: assign(max_seconds, 1440). 1.31/1.60 1.31/1.60 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.31/1.60 1.31/1.60 % Formulas that are not ordinary clauses: 1.31/1.60 1 (all A all B (element(B,powerset(A)) -> element(subset_complement(A,B),powerset(A)))) # label(dt_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.60 2 (all A all B (-empty(B) & -empty(A) -> (all C (relation_of2(C,A,B) -> (quasi_total(C,A,B) & function(C) -> v1_partfun1(C,A,B) & quasi_total(C,A,B) & -empty(C) & function(C)))))) # label(cc6_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.60 3 (all A antisymmetric(inclusion_relation(A))) # label(t5_wellord2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.60 4 (all A all B (relation(B) -> relation_rng(relation_rng_restriction(A,B)) = set_intersection2(relation_rng(B),A))) # label(t119_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.60 5 (all A (one_sorted_str(A) -> (all B (element(B,powerset(powerset(the_carrier(A)))) -> (finite(B) <-> finite(complements_of_subsets(the_carrier(A),B))))))) # label(t13_tops_2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.60 6 (all A all B (-((all C -in(C,set_intersection2(A,B))) & -disjoint(A,B)) & -((exists C in(C,set_intersection2(A,B))) & disjoint(A,B)))) # label(t4_xboole_0) # label(lemma) # label(non_clause). [assumption]. 1.31/1.60 7 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.60 8 (all A (top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> (open_subset(B,A) <-> closed_subset(subset_complement(the_carrier(A),B),A)))))) # label(t30_tops_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.60 9 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.60 10 (all A (rel_str(A) -> (all B (subrelstr(B,A) & full_subrelstr(B,A) -> (all C (element(C,the_carrier(A)) -> (all D (element(D,the_carrier(A)) -> (all E (element(E,the_carrier(B)) -> (all F (element(F,the_carrier(B)) -> (F = D & in(F,the_carrier(B)) & in(E,the_carrier(B)) & related(A,C,D) & E = C -> related(B,E,F)))))))))))))) # label(t61_yellow_0) # label(lemma) # label(non_clause). [assumption]. 1.31/1.60 11 (all A (finite(A) <-> (exists B (relation(B) & in(relation_dom(B),omega) & A = relation_rng(B) & function(B))))) # label(d1_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 12 (exists A (being_limit_ordinal(A) & ordinal(A) & epsilon_connected(A) & epsilon_transitive(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 13 (all A (relation(A) -> (reflexive(A) & antisymmetric(A) & well_founded_relation(A) & connected(A) & transitive(A) <-> well_ordering(A)))) # label(d4_wellord1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 14 (all A (v2_membered(A) -> v1_membered(A))) # label(cc4_membered) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 15 (all A (top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> (closed_subset(B,A) <-> open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A)))))) # label(d6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 16 (all A all B all C all D (one_sorted_str(A) & one_sorted_str(B) & element(D,the_carrier(A)) & relation_of2(C,the_carrier(A),the_carrier(B)) & quasi_total(C,the_carrier(A),the_carrier(B)) & function(C) & -empty_carrier(B) & -empty_carrier(A) -> apply(C,D) = apply_on_structs(A,B,C,D))) # label(redefinition_k1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 17 (all A all B (element(B,the_carrier(boole_lattice(A))) -> (all C (element(C,the_carrier(boole_lattice(A))) -> join(boole_lattice(A),B,C) = set_union2(B,C) & meet(boole_lattice(A),B,C) = set_intersection2(B,C))))) # label(t1_lattice3) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 18 (all A all B all C (element(C,powerset(A)) -> -(in(B,subset_complement(A,C)) & in(B,C)))) # label(t54_subset_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 19 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 20 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & finite(B) & -empty(B))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 21 (all A all B (relation(B) -> ((all C all D (C = D & in(C,A) <-> in(ordered_pair(C,D),B))) <-> B = identity_relation(A)))) # label(d10_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 22 (all A (-empty_carrier(A) & one_sorted_str(A) -> (all B (element(B,the_carrier(A)) -> apply_as_element(the_carrier(A),the_carrier(A),identity_on_carrier(A),B) = B)))) # label(t91_tmap_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 23 (all A (ordinal(A) <-> epsilon_connected(A) & epsilon_transitive(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 24 (all A (rel_str(A) & antisymmetric_relstr(A) -> (all B (element(B,the_carrier(A)) -> (all C (((all D (element(D,the_carrier(A)) -> (relstr_set_smaller(A,C,D) -> related(A,B,D)))) & relstr_set_smaller(A,C,B) -> B = join_on_relstr(A,C) & ex_sup_of_relstr_set(A,C)) & (ex_sup_of_relstr_set(A,C) & join_on_relstr(A,C) = B -> (all D (element(D,the_carrier(A)) -> (relstr_set_smaller(A,C,D) -> related(A,B,D)))) & relstr_set_smaller(A,C,B)))))))) # label(t30_yellow_0) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 25 (all A all B all C all D -(unordered_pair(A,B) = unordered_pair(C,D) & D != A & A != C)) # label(t10_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 26 (all A (-empty_carrier(A) & latt_str(A) -> (all B meet_of_latt_set(A,B) = join_of_latt_set(A,a_2_2_lattice3(A,B))))) # label(d22_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 27 (all A all B (relation(A) & relation(B) -> relation(relation_composition(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 28 (all A exists B (in(A,B) & (all C all D (subset(D,C) & in(C,B) -> in(D,B))) & (all C -(subset(C,B) & -are_equipotent(C,B) & -in(C,B))) & (all C -(in(C,B) & (all D -((all E (subset(E,C) -> in(E,D))) & in(D,B))))))) # label(t9_tarski) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 29 (exists A (-empty(A) & epsilon_connected(A) & ordinal(A) & epsilon_transitive(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 30 (all A all B all C (unordered_pair(B,C) = singleton(A) -> B = A)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 31 (all A (relation(A) -> (all B (relation(B) -> (subset(A,B) <-> (all C all D (in(ordered_pair(C,D),A) -> in(ordered_pair(C,D),B)))))))) # label(d3_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 32 (all A (finite(singleton(A)) & -empty(singleton(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 33 (all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,D)) <-> in(A,C) & in(B,D))) # label(t106_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 34 (all A all B all C (element(C,powerset(A)) & element(B,powerset(A)) -> set_difference(B,C) = subset_difference(A,B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 35 (all A all B (element(B,powerset(the_carrier(A))) & top_str(A) & topological_space(A) -> (exists C all D ((exists E (subset(B,D) & closed_subset(E,A) & E = D & element(E,powerset(the_carrier(A))))) & in(D,powerset(the_carrier(A))) <-> in(D,C))))) # label(s1_xboole_0__e1_40__pre_topc__1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 36 (all A (-empty(A) -> (exists B (finite(B) & -empty(B) & element(B,powerset(A)))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 37 (all A all B all C all D (ordered_pair(A,B) = ordered_pair(C,D) -> C = A & D = B)) # label(t33_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 38 (all A exists B (relation_of2(B,A,A) & reflexive(B) & symmetric(B) & antisymmetric(B) & v1_partfun1(B,A,A) & transitive(B) & relation(B))) # label(rc3_partfun1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 39 (all A all B all C ((all D (in(D,B) | in(D,A) <-> in(D,C))) <-> set_union2(A,B) = C)) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 40 (exists A (-empty_carrier(A) & one_sorted_str(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 41 (all A all B (element(B,powerset(powerset(A))) -> -(complements_of_subsets(A,B) = empty_set & B != empty_set))) # label(t46_setfam_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 42 (all A (top_str(A) -> (all B (element(B,powerset(powerset(the_carrier(A)))) -> (open_subsets(complements_of_subsets(the_carrier(A),B),A) <-> closed_subsets(B,A)))))) # label(t16_tops_2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 43 (all A (rel_str(A) -> (all B (subrelstr(B,A) -> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A),the_carrier(B)) <-> full_subrelstr(B,A)))))) # label(d14_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 44 (all A (top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> (open_subset(subset_complement(the_carrier(A),B),A) <-> closed_subset(B,A)))))) # label(t29_tops_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 45 (all A all B all C (element(B,the_carrier(A)) & element(C,the_carrier(A)) & join_semilatt_str(A) & join_commutative(A) & -empty_carrier(A) -> join(A,B,C) = join_commut(A,B,C))) # label(redefinition_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 46 (all A all B (v5_membered(A) -> v1_membered(set_difference(A,B)) & v2_membered(set_difference(A,B)) & v4_membered(set_difference(A,B)) & v5_membered(set_difference(A,B)) & v3_membered(set_difference(A,B)))) # label(fc41_membered) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 47 (all A all B (relation_of2(B,A,A) -> strict_rel_str(rel_str_of(A,B)) & rel_str(rel_str_of(A,B)))) # label(dt_g1_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 48 (all A (-empty_carrier(A) & meet_semilatt_str(A) -> (lower_bounded_semilattstr(A) -> (all B (element(B,the_carrier(A)) -> (bottom_of_semilattstr(A) = B <-> (all C (element(C,the_carrier(A)) -> B = meet(A,B,C) & B = meet(A,C,B))))))))) # label(d16_lattices) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 49 (all A all B (relation(B) -> subset(relation_image(B,A),relation_rng(B)))) # label(t144_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 50 (all A all B (element(B,powerset(powerset(A))) -> element(meet_of_subsets(A,B),powerset(A)))) # label(dt_k6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 51 (all A (ordinal(A) -> ((all B all C all D (C = B & B = D & (exists I (ordinal(I) & (in(I,omega) -> (all J (element(J,powerset(powerset(I))) -> -(J != empty_set & (all K -(in(K,J) & (all L (in(L,J) & subset(K,L) -> L = K)))))))) & I = D)) & (exists E (ordinal(E) & (in(E,omega) -> (all F (element(F,powerset(powerset(E))) -> -(F != empty_set & (all G -(in(G,F) & (all H (in(H,F) & subset(G,H) -> G = H)))))))) & C = E)) -> D = C)) -> (exists B all C ((exists D (in(D,succ(A)) & C = D & (exists M ((in(M,omega) -> (all N (element(N,powerset(powerset(M))) -> -((all O -((all P (in(P,N) & subset(O,P) -> O = P)) & in(O,N))) & N != empty_set)))) & M = C & ordinal(M))))) <-> in(C,B)))))) # label(s1_tarski__e18_27__finset_1__1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 52 (exists A meet_semilatt_str(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 53 (all A all B (latt_str(A) & -empty_carrier(A) -> element(meet_of_latt_set(A,B),the_carrier(A)))) # label(dt_k16_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 54 (all A (one_sorted_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> B = subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A)))))) # label(t15_pre_topc) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 55 (all A all B all C (function(C) & relation(C) -> (in(B,A) -> apply(relation_dom_restriction(C,A),B) = apply(C,B)))) # label(t72_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 56 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 57 (all A all B (subset(A,B) <-> set_difference(A,B) = empty_set)) # label(t37_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 58 (all A all B all C all D all E all F (-empty(A) & -empty(B) & quasi_total(D,cartesian_product2(A,B),C) & element(F,B) & element(E,A) & relation_of2(D,cartesian_product2(A,B),C) & function(D) -> element(apply_binary_as_element(A,B,C,D,E,F),C))) # label(dt_k2_binop_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 59 (all A all B all C (element(C,powerset(A)) & element(B,powerset(A)) -> set_intersection2(B,C) = subset_intersection2(A,B,C))) # label(redefinition_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 60 $T # label(dt_k1_enumset1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 61 (all A (relation(A) -> (connected(A) <-> (all B all C -(-in(ordered_pair(C,B),A) & -in(ordered_pair(B,C),A) & B != C & in(C,relation_field(A)) & in(B,relation_field(A))))))) # label(l4_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 62 (all A all B all C all D (relation_of2_as_subset(D,C,A) -> (subset(A,B) -> relation_of2_as_subset(D,C,B)))) # label(t16_relset_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 63 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 64 (all A (relation(A) & function(A) -> relation(function_inverse(A)) & function(function_inverse(A)))) # label(dt_k2_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 65 (all A all B (element(B,powerset(powerset(A))) -> (empty_set != B -> subset_complement(A,union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B))))) # label(t11_tops_2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.61 66 (all A all B (v3_membered(A) -> v1_membered(set_difference(A,B)) & v2_membered(set_difference(A,B)) & v3_membered(set_difference(A,B)))) # label(fc39_membered) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 67 (all A all B all C (element(C,powerset(A)) & element(B,powerset(A)) -> set_union2(B,C) = subset_union2(A,B,C))) # label(redefinition_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 68 (all A (v3_membered(A) -> (all B (element(B,powerset(A)) -> v1_membered(B) & v2_membered(B) & v3_membered(B))))) # label(cc18_membered) # label(axiom) # label(non_clause). [assumption]. 1.31/1.61 69 (all A (join_semilatt_str(A) & -empty_carrier(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> join(A,B,C) = apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_join(A),B,C))))))) # label(d1_lattices) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 70 (all A all B (rel_str(A) -> element(meet_on_relstr(A,B),the_carrier(A)))) # label(dt_k2_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 71 (all A (top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> (all C (in(C,the_carrier(A)) -> (in(C,topstr_closure(A,B)) <-> (all D (element(D,powerset(the_carrier(A))) -> (subset(B,D) & closed_subset(D,A) -> in(C,D))))))))))) # label(t45_pre_topc) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 72 (all A all B (element(B,powerset(powerset(the_carrier(A)))) & one_sorted_str(A) -> (all C exists D all E (in(E,cartesian_product2(B,C)) & (exists F exists G ((all H (element(H,powerset(the_carrier(A))) -> (H = F -> subset_complement(the_carrier(A),H) = G))) & in(F,B) & ordered_pair(F,G) = E)) <-> in(E,D))))) # label(s1_xboole_0__e4_7_2__tops_2__1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 73 (all A all B all C (relation_of2_as_subset(C,A,B) -> (relation_rng_as_subset(A,B,C) = B <-> (all D -(in(D,B) & (all E -in(ordered_pair(E,D),C))))))) # label(t23_relset_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 74 (all A all B (v2_membered(A) -> v2_membered(set_difference(A,B)) & v1_membered(set_difference(A,B)))) # label(fc38_membered) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 75 (all A all B all C (-empty_carrier(A) & transitive_relstr(A) & element(B,powerset(the_carrier(A))) & finite(C) & element(C,powerset(B)) & rel_str(A) -> (finite(C) & (exists D (in(D,B) & relstr_set_smaller(A,empty_set,D) & element(D,the_carrier(A)))) & (all E all F (in(E,C) & subset(F,C) & (exists G (element(G,the_carrier(A)) & in(G,B) & relstr_set_smaller(A,F,G))) -> (exists H (element(H,the_carrier(A)) & relstr_set_smaller(A,set_union2(F,singleton(E)),H) & in(H,B))))) -> (exists I (relstr_set_smaller(A,C,I) & in(I,B) & element(I,the_carrier(A))))))) # label(s2_finset_1__e11_2_1__waybel_0) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 76 (all A (relation(A) -> (all B (relation(B) -> (all C (relation(C) & function(C) -> (relation_isomorphism(A,B,C) -> (connected(A) -> connected(B)) & (antisymmetric(A) -> antisymmetric(B)) & (well_founded_relation(A) -> well_founded_relation(B)) & (transitive(A) -> transitive(B)) & (reflexive(A) -> reflexive(B))))))))) # label(t53_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 77 (all A (meet_absorbing(A) & latt_str(A) & meet_commutative(A) & -empty_carrier(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> below(A,meet_commut(A,B,C),B))))))) # label(t23_lattices) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 78 (exists A (latt_str(A) & strict_latt_str(A))) # label(rc3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 79 (all A all B (relation(A) -> relation_of2_as_subset(relation_restriction_as_relation_of(A,B),B,B))) # label(dt_k1_toler_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 80 (all A all B (equipotent(A,B) -> equipotent(B,A))) # label(symmetry_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 81 (all A (relation(A) -> (reflexive(A) <-> (all B (in(B,relation_field(A)) -> in(ordered_pair(B,B),A)))))) # label(l1_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 82 (all A relation(identity_relation(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 83 (all A (v4_membered(A) -> v3_membered(A))) # label(cc2_membered) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 84 (all A all B all C (subset(A,B) -> subset(set_difference(A,C),set_difference(B,C)))) # label(t33_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 85 (all A all B (latt_str(B) & lattice(B) & -empty_carrier(B) -> (all C (element(C,the_carrier(poset_of_lattice(B))) -> (relstr_set_smaller(poset_of_lattice(B),A,C) <-> latt_element_smaller(B,cast_to_el_of_lattice(B,C),A)))))) # label(t31_lattice3) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 86 (all A all B (element(B,powerset(powerset(A))) -> meet_of_subsets(A,B) = set_meet(B))) # label(redefinition_k6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 87 (all A all B all C (latt_str(B) & -empty_carrier(B) -> ((exists D (latt_set_smaller(B,D,C) & D = A & element(D,the_carrier(B)))) <-> in(A,a_2_2_lattice3(B,C))))) # label(fraenkel_a_2_2_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 88 (all A all B all C (element(B,the_carrier(A)) & element(C,the_carrier(A)) & latt_str(A) & join_absorbing(A) & meet_absorbing(A) & meet_commutative(A) & -empty_carrier(A) -> (below(A,B,C) <-> below_refl(A,B,C)))) # label(redefinition_r3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 89 (all A (rel_str(A) -> (antisymmetric_relstr(A) <-> is_antisymmetric_in(the_InternalRel(A),the_carrier(A))))) # label(d6_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 90 (all A (-empty_carrier(A) & rel_str(A) & transitive_relstr(A) -> (all B (element(B,powerset(the_carrier(A))) -> (-empty(B) & directed_subset(B,A) <-> (all C (element(C,powerset(B)) & finite(C) -> (exists D (element(D,the_carrier(A)) & relstr_set_smaller(A,C,D) & in(D,B)))))))))) # label(t1_waybel_0) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 91 (all A ((all B -((all C C != singleton(B)) & in(B,A))) & (all B all C all D (singleton(B) = C & D = singleton(B) & in(B,A) -> D = C)) -> (exists B (relation(B) & A = relation_dom(B) & (all C (in(C,A) -> singleton(C) = apply(B,C))) & function(B))))) # label(s2_funct_1__e16_22__wellord2__1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 92 (all A (-empty_carrier(A) & latt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (latt_element_smaller(A,B,C) <-> (all D (element(D,the_carrier(A)) -> (in(D,C) -> below(A,D,B)))))))))) # label(d17_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 93 (all A all B (relation(B) -> subset(relation_field(relation_restriction(B,A)),A) & subset(relation_field(relation_restriction(B,A)),relation_field(B)))) # label(t20_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 94 (all A all B (v5_membered(A) -> v1_membered(set_intersection2(B,A)) & v3_membered(set_intersection2(B,A)) & v5_membered(set_intersection2(B,A)) & v4_membered(set_intersection2(B,A)) & v2_membered(set_intersection2(B,A)))) # label(fc36_membered) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 95 (all A (latt_str(A) & complete_latt_str(A) & lattice(A) & -empty_carrier(A) -> (all B (element(B,the_carrier(A)) -> (all C ((all D (element(D,the_carrier(A)) -> (latt_set_smaller(A,D,C) -> below_refl(A,D,B)))) & latt_set_smaller(A,B,C) <-> meet_of_latt_set(A,C) = B)))))) # label(t34_lattice3) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 96 (all A (latt_str(A) -> (-empty_carrier(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A) & meet_commutative(A) & join_associative(A) & join_commutative(A) -> lattice(A) & -empty_carrier(A)))) # label(cc2_lattices) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 97 (all A all B all C (relation_of2(C,A,B) <-> relation_of2_as_subset(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 98 (all A all B -(empty(B) & A != B & empty(A))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 99 (all A all B all C all D (function(C) & quasi_total(C,A,B) & relation_of2(C,A,B) & element(D,A) & -empty(A) -> element(apply_as_element(A,B,C,D),B))) # label(dt_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 100 (all A all B (topological_space(A) & closed_subset(B,A) & element(B,powerset(the_carrier(A))) & top_str(A) -> open_subset(subset_complement(the_carrier(A),B),A))) # label(fc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 101 (all A (relation(A) -> (all B (relation(B) -> (subset(relation_rng(A),relation_dom(B)) -> relation_dom(A) = relation_dom(relation_composition(A,B))))))) # label(t46_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 102 (all A (relation(A) -> (all B all C ((all D ((exists E (in(ordered_pair(D,E),A) & in(E,B))) <-> in(D,C))) <-> C = relation_inverse_image(A,B))))) # label(d14_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 103 (all A all B (element(B,powerset(powerset(the_carrier(A)))) & one_sorted_str(A) -> ((all C all D all E ((all F (element(F,powerset(the_carrier(A))) -> (F = C -> subset_complement(the_carrier(A),F) = D))) & (all G (element(G,powerset(the_carrier(A))) -> (G = C -> E = subset_complement(the_carrier(A),G)))) & in(C,B) & in(C,B) -> D = E)) -> (exists C all D (in(D,C) <-> (exists E ((all H (element(H,powerset(the_carrier(A))) -> (E = H -> subset_complement(the_carrier(A),H) = D))) & in(E,B) & in(E,B)))))))) # label(s1_tarski__e4_7_2__tops_2__1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 104 (all A all B (relation(B) & function(B) -> (subset(A,relation_rng(B)) -> A = relation_image(B,relation_inverse_image(B,A))))) # label(t147_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 105 (all A all B all C (relation_of2(B,cartesian_product2(A,A),A) & function(C) & relation_of2(C,cartesian_product2(A,A),A) & quasi_total(C,cartesian_product2(A,A),A) & quasi_total(B,cartesian_product2(A,A),A) & function(B) -> strict_latt_str(latt_str_of(A,B,C)) & latt_str(latt_str_of(A,B,C)))) # label(dt_g3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 106 (all A (v1_membered(A) -> (all B (element(B,powerset(A)) -> v1_membered(B))))) # label(cc16_membered) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 107 (all A all B all C (element(C,powerset(A)) & element(B,powerset(A)) -> element(subset_intersection2(A,B,C),powerset(A)))) # label(dt_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 108 (all A (rel_str(A) & antisymmetric_relstr(A) -> (all B ((exists C ((all D (element(D,the_carrier(A)) -> (relstr_element_smaller(A,B,D) -> related(A,D,C)))) & relstr_element_smaller(A,B,C) & element(C,the_carrier(A)))) <-> ex_inf_of_relstr_set(A,B))))) # label(t16_yellow_0) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 109 (all A (empty(A) & ordinal(A) -> epsilon_transitive(A) & epsilon_connected(A) & ordinal(A) & natural(A))) # label(cc2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 110 (all A all B (relation(B) -> relation_rng_restriction(A,relation_dom_restriction(B,A)) = relation_restriction(B,A))) # label(t18_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 111 (all A all B (element(B,powerset(powerset(A))) -> (B != empty_set -> meet_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),union_of_subsets(A,B))))) # label(t47_setfam_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 112 (all A all B all C (-empty_carrier(A) & meet_semilatt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) & meet_commutative(A) -> meet_commut(A,B,C) = meet(A,B,C))) # label(redefinition_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 113 (all A (relation(A) -> (is_antisymmetric_in(A,relation_field(A)) <-> antisymmetric(A)))) # label(d12_relat_2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 114 (all A all B all C all D (-empty_carrier(A) & lattice(A) & -empty_carrier(B) & element(D,the_carrier(B)) & element(C,the_carrier(A)) & latt_str(B) & lattice(B) & latt_str(A) -> k10_filter_1(A,B,C,D) = ordered_pair(C,D))) # label(redefinition_k10_filter_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 115 (all A all B all C (relation_of2(C,A,B) -> relation_dom(C) = relation_dom_as_subset(A,B,C))) # label(redefinition_k4_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 116 (all A all B exists C (relation(C) & function(C) & relation_of2(C,A,B))) # label(rc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 117 (all A all B (subset(A,B) -> B = set_union2(A,set_difference(B,A)))) # label(t45_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 118 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 119 (all A (relation(A) -> (well_founded_relation(A) <-> (all B -(empty_set != B & (all C -(in(C,B) & disjoint(fiber(A,C),B))) & subset(B,relation_field(A))))))) # label(d2_wellord1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 120 (all A (top_str(A) -> (all B (element(B,powerset(powerset(the_carrier(A)))) -> (closed_subsets(complements_of_subsets(the_carrier(A),B),A) <-> open_subsets(B,A)))))) # label(t17_tops_2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 121 (all A all B (relation(A) & relation(B) -> relation(set_difference(A,B)))) # label(fc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 122 (all A (relation(A) & function(A) -> (one_to_one(A) -> (all B (relation(B) & function(B) -> ((all C all D ((in(C,relation_rng(A)) & apply(B,C) = D -> in(D,relation_dom(A)) & apply(A,D) = C) & (C = apply(A,D) & in(D,relation_dom(A)) -> apply(B,C) = D & in(C,relation_rng(A))))) & relation_rng(A) = relation_dom(B) <-> function_inverse(A) = B)))))) # label(t54_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 123 (all A (one_sorted_str(A) -> element(cast_as_carrier_subset(A),powerset(the_carrier(A))))) # label(dt_k2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 124 (all A (ordinal(A) -> (exists B all C (in(C,B) <-> in(C,succ(A)) & (exists D (ordinal(D) & (in(D,omega) -> (all E (element(E,powerset(powerset(D))) -> -((all F -(in(F,E) & (all G (in(G,E) & subset(F,G) -> F = G)))) & E != empty_set)))) & D = C)))))) # label(s1_xboole_0__e18_27__finset_1__1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 125 (all A all B (element(B,powerset(powerset(the_carrier(A)))) & one_sorted_str(A) -> ((all C -(in(C,complements_of_subsets(the_carrier(A),B)) & (all D -(all H (element(H,powerset(the_carrier(A))) -> (H = C -> subset_complement(the_carrier(A),H) = D)))))) & (all C all D all E ((all G (element(G,powerset(the_carrier(A))) -> (C = G -> subset_complement(the_carrier(A),G) = E))) & (all F (element(F,powerset(the_carrier(A))) -> (C = F -> subset_complement(the_carrier(A),F) = D))) & in(C,complements_of_subsets(the_carrier(A),B)) -> E = D)) -> (exists C (relation(C) & function(C) & relation_dom(C) = complements_of_subsets(the_carrier(A),B) & (all D (in(D,complements_of_subsets(the_carrier(A),B)) -> (all I (element(I,powerset(the_carrier(A))) -> (I = D -> subset_complement(the_carrier(A),I) = apply(C,D))))))))))) # label(s2_funct_1__e4_7_1__tops_2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 126 (exists A (rel_str(A) & strict_rel_str(A))) # label(rc1_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 127 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 128 (all A all B all C (relation(C) -> (in(A,C) & in(A,cartesian_product2(B,B)) <-> in(A,relation_restriction(C,B))))) # label(t16_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 129 (all A (A != empty_set & (all B -(empty_set != B & empty_set = set_meet(B) & finite(B) & subset(B,A))) <-> centered(A))) # label(d2_compts_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 130 (all A (-empty(powerset(A)) & cup_closed(powerset(A)) & preboolean(powerset(A)) & diff_closed(powerset(A)))) # label(fc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 131 (all A (relation(A) -> (all B (relation(B) -> subset(relation_rng(relation_composition(A,B)),relation_rng(B)))))) # label(t45_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 132 (all A all B all C (relation(C) & function(C) -> (in(B,relation_dom(relation_dom_restriction(C,A))) -> apply(relation_dom_restriction(C,A),B) = apply(C,B)))) # label(t70_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 133 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 134 (all A (relation(A) -> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)))) # label(d6_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 135 (all A (relation(A) & -empty(A) -> -empty(relation_rng(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 136 (all A all B (relation(A) & function(A) -> relation(relation_dom_restriction(A,B)) & function(relation_dom_restriction(A,B)))) # label(fc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 137 (all A exists B all C (in(C,A) & ordinal(C) <-> in(C,B))) # label(s1_xboole_0__e6_22__wellord2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 138 (all A (ordinal(A) -> well_founded_relation(inclusion_relation(A)))) # label(t6_wellord2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 139 (exists A (function(A) & one_to_one(A) & relation(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 140 (all A (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))) # label(dt_k1_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 141 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 142 (all A (epsilon_connected(A) & epsilon_transitive(A) -> ordinal(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 143 (all A all B all C all D (function(D) & relation_of2_as_subset(D,A,B) & quasi_total(D,A,B) -> (empty_set != B -> (all E (in(E,relation_inverse_image(D,C)) <-> in(E,A) & in(apply(D,E),C)))))) # label(t46_funct_2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 144 (all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,D)) <-> in(A,C) & in(B,D))) # label(l55_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 145 (all A all B ((exists C (function(C) & relation_dom(C) = A & relation_rng(C) = B & one_to_one(C) & relation(C))) <-> equipotent(A,B))) # label(d4_wellord2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 146 (all A reflexive(inclusion_relation(A))) # label(t2_wellord2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 147 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(cast_as_carrier_subset(A)))) # label(fc2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 148 (all A all B all C (relation_of2(C,A,B) -> relation_rng(C) = relation_rng_as_subset(A,B,C))) # label(redefinition_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 149 (all A all B (relation(B) -> (all C (relation(C) -> ((all D all E (in(ordered_pair(D,E),B) & in(E,A) <-> in(ordered_pair(D,E),C))) <-> C = relation_rng_restriction(A,B)))))) # label(d12_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 150 (all A (rel_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (related(A,B,C) <-> in(ordered_pair(B,C),the_InternalRel(A))))))))) # label(d9_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 151 (all A all B (B = pair_second(ordered_pair(A,B)) & pair_first(ordered_pair(A,B)) = A)) # label(t7_mcart_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 152 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 153 (all A (latt_str(A) & lattice(A) & -empty_carrier(A) -> relation(relation_of_lattice(A)))) # label(dt_k9_filter_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 154 (all A (top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> (closed_subset(B,A) -> B = topstr_closure(A,B)) & (topstr_closure(A,B) = B & topological_space(A) -> closed_subset(B,A)))))) # label(t52_pre_topc) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 155 (all A all B (subset(B,A) & subset(A,B) <-> B = A)) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 156 (all A (latt_str(A) -> (strict_latt_str(A) -> latt_str_of(the_carrier(A),the_L_join(A),the_L_meet(A)) = A))) # label(abstractness_v3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 157 (all A all B all C (subset(A,B) -> in(C,A) | subset(A,set_difference(B,singleton(C))))) # label(l3_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.62 158 (all A all B set_union2(B,A) = set_union2(A,B)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 159 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.62 160 (exists A (relation(A) & -empty(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 161 (all A all B (element(B,powerset(powerset(the_carrier(A)))) & one_sorted_str(A) -> (all C ((all D all E all F (D = E & (exists J exists K (F = ordered_pair(J,K) & in(J,complements_of_subsets(the_carrier(A),B)) & (all L (element(L,powerset(the_carrier(A))) -> (J = L -> K = subset_complement(the_carrier(A),L)))))) & F = D & (exists G exists H (ordered_pair(G,H) = E & (all I (element(I,powerset(the_carrier(A))) -> (I = G -> subset_complement(the_carrier(A),I) = H))) & in(G,complements_of_subsets(the_carrier(A),B)))) -> F = E)) -> (exists D all E ((exists F (in(F,cartesian_product2(complements_of_subsets(the_carrier(A),B),C)) & E = F & (exists M exists N (in(M,complements_of_subsets(the_carrier(A),B)) & (all O (element(O,powerset(the_carrier(A))) -> (M = O -> N = subset_complement(the_carrier(A),O)))) & ordered_pair(M,N) = E)))) <-> in(E,D))))))) # label(s1_tarski__e4_7_1__tops_2__2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 162 (all A succ(A) = set_union2(A,singleton(A))) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 163 (all A (meet_semilatt_str(A) & meet_commutative(A) & -empty_carrier(A) -> function(the_L_meet(A)) & v1_binop_1(the_L_meet(A),the_carrier(A)) & v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & relation(the_L_meet(A)))) # label(fc4_lattice2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 164 (all A (ordinal(A) -> connected(inclusion_relation(A)))) # label(t4_wellord2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.63 165 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 166 (all A (join_semilatt_str(A) -> relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & function(the_L_join(A)))) # label(dt_u2_lattices) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 167 (all A (relation(A) & function(A) -> (one_to_one(A) -> function_inverse(A) = relation_inverse(A)))) # label(d9_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 168 (all A all B -(disjoint(singleton(A),B) & in(A,B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.63 169 (all A (relation(identity_relation(A)) & function(identity_relation(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 170 (all A (relation(A) -> (all B (relation(B) -> (all C (function(C) & relation(C) -> (relation_isomorphism(A,B,C) -> relation_isomorphism(B,A,function_inverse(C))))))))) # label(t49_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.63 171 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 172 (all A all B (empty_set = A | A = singleton(B) <-> subset(A,singleton(B)))) # label(l4_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.63 173 (all A (relation(A) -> (well_orders(A,relation_field(A)) <-> well_ordering(A)))) # label(t8_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.63 174 (all A (top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> subset(interior(A,B),B))))) # label(t44_tops_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.63 175 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 176 (all A (relation(A) -> (is_connected_in(A,relation_field(A)) <-> connected(A)))) # label(d14_relat_2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 177 (all A all B all C (relation(C) -> (subset(A,B) -> subset(relation_inverse_image(C,A),relation_inverse_image(C,B))))) # label(t178_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.63 178 (all A all B (-empty(A) & relation(B) -> ((all C all D all E ((exists F (C = F & (all G (in(G,F) -> in(ordered_pair(D,G),B))) & in(D,F))) & (exists H ((all I (in(I,H) -> in(ordered_pair(E,I),B))) & in(E,H) & C = H)) & in(C,A) -> E = D)) & (all C -(in(C,A) & (all D -(exists J (C = J & (all K (in(K,J) -> in(ordered_pair(D,K),B))) & in(D,J)))))) -> (exists C ((all D (in(D,A) -> (exists L (D = L & in(apply(C,D),L) & (all M (in(M,L) -> in(ordered_pair(apply(C,D),M),B))))))) & A = relation_dom(C) & function(C) & relation(C)))))) # label(s2_funct_1__e10_24__wellord2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.63 179 (all A all B (ordinal(B) & ordinal(A) -> ordinal_subset(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 180 (all A all B all C (disjoint(B,C) & subset(A,B) -> disjoint(A,C))) # label(t63_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.63 181 (all A all B all C all D (-empty_carrier(A) & function(C) & quasi_total(C,the_carrier(A),the_carrier(B)) & relation_of2(C,the_carrier(A),the_carrier(B)) & element(D,the_carrier(A)) & one_sorted_str(B) & -empty_carrier(B) & one_sorted_str(A) -> element(apply_on_structs(A,B,C,D),the_carrier(B)))) # label(dt_k1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 182 (all A ((all B (in(B,A) -> ordinal(B) & subset(B,A))) -> ordinal(A))) # label(t31_ordinal1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.63 183 (all A (relation(A) -> (all B ((all C (in(C,B) <-> (exists D in(ordered_pair(D,C),A)))) <-> B = relation_rng(A))))) # label(d5_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 184 (all A all B (one_sorted_str(A) & net_str(B,A) -> function(the_mapping(A,B)) & quasi_total(the_mapping(A,B),the_carrier(B),the_carrier(A)) & relation_of2_as_subset(the_mapping(A,B),the_carrier(B),the_carrier(A)))) # label(dt_u1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 185 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 186 (all A (relation(A) -> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))))) # label(t21_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.63 187 (all A (join_associative(A) & join_semilatt_str(A) & -empty_carrier(A) -> relation(the_L_join(A)) & function(the_L_join(A)) & v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & v2_binop_1(the_L_join(A),the_carrier(A)) & quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))) # label(fc3_lattice2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 188 (all A all B (element(B,powerset(powerset(the_carrier(A)))) & one_sorted_str(A) -> ((all C all D all E (in(C,B) & (all F (element(F,powerset(the_carrier(A))) -> (F = C -> D = subset_complement(the_carrier(A),F)))) & (all G (element(G,powerset(the_carrier(A))) -> (G = C -> subset_complement(the_carrier(A),G) = E))) -> D = E)) & (all C -(in(C,B) & (all D -(all H (element(H,powerset(the_carrier(A))) -> (H = C -> subset_complement(the_carrier(A),H) = D)))))) -> (exists C (function(C) & (all D (in(D,B) -> (all I (element(I,powerset(the_carrier(A))) -> (I = D -> subset_complement(the_carrier(A),I) = apply(C,D)))))) & relation_dom(C) = B & relation(C)))))) # label(s2_funct_1__e4_7_2__tops_2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.63 189 (all A (one_sorted_str(A) -> (all B (net_str(B,A) -> rel_str(B))))) # label(dt_l1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 190 (all A all B (function(B) & relation(B) -> (one_to_one(B) & in(A,relation_rng(B)) -> apply(relation_composition(function_inverse(B),B),A) = A & apply(B,apply(function_inverse(B),A)) = A))) # label(t57_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.63 191 (all A all B (element(B,powerset(the_carrier(A))) & top_str(A) -> element(interior(A,B),powerset(the_carrier(A))))) # label(dt_k1_tops_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 192 (all A (relation(A) -> (all B all C (relation_image(A,B) = C <-> (all D ((exists E (in(E,B) & in(ordered_pair(E,D),A))) <-> in(D,C))))))) # label(d13_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 193 (all A (v5_membered(A) -> v4_membered(A))) # label(cc1_membered) # label(axiom) # label(non_clause). [assumption]. 1.31/1.63 194 (all A all B (element(B,powerset(A)) -> (B != A <-> proper_element(B,powerset(A))))) # label(t5_tex_2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 195 (all A all B all C all D all E all F (-empty(A) & relation_of2(D,cartesian_product2(A,B),C) & element(F,B) & element(E,A) & quasi_total(D,cartesian_product2(A,B),C) & function(D) & -empty(B) -> apply_binary(D,E,F) = apply_binary_as_element(A,B,C,D,E,F))) # label(redefinition_k2_binop_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 196 (all A (relation(A) -> ((all B all C -in(ordered_pair(B,C),A)) -> empty_set = A))) # label(t56_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 197 (all A all B (latt_str(B) & -empty_carrier(B) & latt_str(A) & -empty_carrier(A) -> strict_latt_str(k8_filter_1(A,B)) & latt_str(k8_filter_1(A,B)))) # label(dt_k8_filter_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 198 (all A all B all C (element(C,powerset(A)) & element(B,powerset(A)) -> B = subset_intersection2(A,B,B))) # label(idempotence_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 199 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 200 (all A element(cast_to_subset(A),powerset(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 201 (all A (-empty_carrier(boole_lattice(A)) & strict_latt_str(boole_lattice(A)))) # label(fc1_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 202 (all A identity_as_relation_of(A) = identity_relation(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 203 (all A all B (finite(B) & subset(A,B) -> finite(A))) # label(t13_finset_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 204 (all A all B (topological_space(A) & element(B,powerset(the_carrier(A))) & top_str(A) -> (exists C ((all D (element(D,powerset(the_carrier(A))) -> (in(D,C) <-> (exists E (element(E,powerset(the_carrier(A))) & E = D & closed_subset(E,A) & subset(B,D)))))) & element(C,powerset(powerset(the_carrier(A)))))))) # label(s3_subset_1__e1_40__pre_topc) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 205 (all A ((exists B (in(B,A) & ordinal(B))) -> (exists B (ordinal(B) & (all C (ordinal(C) -> (in(C,A) -> ordinal_subset(B,C)))) & in(B,A))))) # label(s1_ordinal1__e8_6__wellord2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 206 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 207 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 208 (all A all B all C (C = unordered_pair(A,B) <-> (all D (in(D,C) <-> D = B | A = D)))) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 209 (all A (relation(A) & function(A) -> (one_to_one(A) -> one_to_one(function_inverse(A))))) # label(t62_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 210 (exists A (-empty(A) & v1_membered(A) & v3_membered(A) & v5_membered(A) & v4_membered(A) & v2_membered(A))) # label(rc1_membered) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 211 (all A (rel_str(A) -> (all B (rel_str(B) -> (subset(the_InternalRel(B),the_InternalRel(A)) & subset(the_carrier(B),the_carrier(A)) <-> subrelstr(B,A)))))) # label(d13_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 212 (all A all B (-(-disjoint(A,B) & (all C -(in(C,B) & in(C,A)))) & -(disjoint(A,B) & (exists C (in(C,B) & in(C,A)))))) # label(t3_xboole_0) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 213 (all A all B all C (relation_of2(C,A,B) -> element(relation_rng_as_subset(A,B,C),powerset(B)))) # label(dt_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 214 $T # label(dt_k2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 215 (all A (rel_str(A) -> (all B all C (element(C,the_carrier(A)) -> (ex_inf_of_relstr_set(A,B) -> ((all D (element(D,the_carrier(A)) -> (relstr_element_smaller(A,B,D) -> related(A,D,C)))) & relstr_element_smaller(A,B,C) <-> C = meet_on_relstr(A,B))))))) # label(d10_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 216 (all A all B (top_str(A) & element(B,powerset(the_carrier(A))) & topological_space(A) -> ((all C all D all E (E = C & (exists G (element(G,powerset(the_carrier(A))) & G = E & closed_subset(G,A) & subset(B,E))) & (exists F (element(F,powerset(the_carrier(A))) & subset(B,D) & closed_subset(F,A) & F = D)) & D = C -> D = E)) -> (exists C all D ((exists E (E = D & (exists H (element(H,powerset(the_carrier(A))) & closed_subset(H,A) & subset(B,D) & H = D)) & in(E,powerset(the_carrier(A))))) <-> in(D,C)))))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 217 (all A all B (lattice(B) & latt_str(B) & -empty_carrier(B) -> (all C (element(C,the_carrier(B)) -> (relstr_set_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C)) <-> latt_element_smaller(B,C,A)))))) # label(t30_lattice3) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 218 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> element(subset_union2(A,B,C),powerset(A)))) # label(dt_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 219 (all A (relation(A) & function(A) -> (all B all C (C = relation_image(A,B) <-> (all D (in(D,C) <-> (exists E (in(E,B) & D = apply(A,E) & in(E,relation_dom(A)))))))))) # label(d12_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 220 (all A (one_sorted_str(A) -> cast_as_carrier_subset(A) = the_carrier(A))) # label(d3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 221 (all A all B all C (element(C,powerset(cartesian_product2(A,B))) -> relation(C))) # label(cc1_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 222 (all A (relation(A) -> (all B (relation(B) -> (all C (relation(C) & function(C) -> (relation_dom(C) = relation_field(A) & one_to_one(C) & (all D all E (in(ordered_pair(D,E),A) <-> in(D,relation_field(A)) & in(E,relation_field(A)) & in(ordered_pair(apply(C,D),apply(C,E)),B))) & relation_rng(C) = relation_field(B) <-> relation_isomorphism(A,B,C)))))))) # label(d7_wellord1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 223 (all A (empty(A) -> relation(relation_dom(A)) & empty(relation_dom(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 224 (all A all B all C (relation_of2(C,A,B) -> element(relation_dom_as_subset(A,B,C),powerset(A)))) # label(dt_k4_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 225 (all A all B all C (relation(C) -> subset(fiber(relation_restriction(C,A),B),fiber(C,B)))) # label(t21_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 226 (all A (relation(A) -> (relation_dom(A) = empty_set <-> relation_rng(A) = empty_set))) # label(t65_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 227 (all A all B (relation(B) -> subset(relation_dom_restriction(B,A),B))) # label(t88_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 228 (all A all B all C (subset(A,B) -> subset(cartesian_product2(A,C),cartesian_product2(B,C)) & subset(cartesian_product2(C,A),cartesian_product2(C,B)))) # label(t118_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 229 (all A all B all C -(in(A,B) & in(C,A) & in(B,C))) # label(t3_ordinal1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 230 (all A (-empty_carrier(A) & meet_semilatt_str(A) -> (lower_bounded_semilattstr(A) <-> (exists B (element(B,the_carrier(A)) & (all C (element(C,the_carrier(A)) -> B = meet(A,B,C) & meet(A,C,B) = B))))))) # label(d13_lattices) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 231 (all A (one_sorted_str(A) & -empty_carrier(A) -> (all B (element(B,powerset(the_carrier(A))) -> (all C (element(C,the_carrier(A)) -> (in(C,subset_complement(the_carrier(A),B)) <-> -in(C,B)))))))) # label(l40_tops_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 232 (all A (one_sorted_str(A) -> v1_membered(empty_carrier_subset(A)) & v2_membered(empty_carrier_subset(A)) & v3_membered(empty_carrier_subset(A)) & v5_membered(empty_carrier_subset(A)) & v4_membered(empty_carrier_subset(A)) & empty(empty_carrier_subset(A)))) # label(fc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 233 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> A = C)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 234 (all A all B all C all D (relation_of2_as_subset(D,C,A) -> (subset(relation_rng(D),B) -> relation_of2_as_subset(D,C,B)))) # label(t14_relset_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 235 (all A (ordinal(A) -> epsilon_transitive(union(A)) & epsilon_connected(union(A)) & ordinal(union(A)))) # label(fc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 236 (all A all B all C (-empty_carrier(A) & transitive_relstr(A) & rel_str(A) & finite(C) & element(C,powerset(B)) & element(B,powerset(the_carrier(A))) -> ((all D all E all F ((exists G (G = E & (exists H (in(H,B) & relstr_set_smaller(A,G,H) & element(H,the_carrier(A)))))) & D = F & (exists I ((exists J (relstr_set_smaller(A,I,J) & in(J,B) & element(J,the_carrier(A)))) & I = F)) & D = E -> E = F)) -> (exists D all E ((exists F ((exists K ((exists L (in(L,B) & relstr_set_smaller(A,K,L) & element(L,the_carrier(A)))) & E = K)) & F = E & in(F,powerset(C)))) <-> in(E,D)))))) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 237 (all A all B (topological_space(A) & top_str(A) & element(B,powerset(the_carrier(A))) & open_subset(B,A) -> closed_subset(subset_complement(the_carrier(A),B),A))) # label(fc4_tops_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 238 (all A all B all C (in(A,B) & element(B,powerset(C)) -> element(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 239 (all A all B (v2_membered(A) -> v1_membered(set_intersection2(A,B)) & v2_membered(set_intersection2(A,B)))) # label(fc29_membered) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 240 (exists A (empty(A) & one_to_one(A) & function(A) & relation(A))) # label(rc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 241 (all A all B (relation(A) -> relation(relation_dom_restriction(A,B)))) # label(dt_k7_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 242 (all A (finite(A) -> (all B (element(B,powerset(powerset(A))) -> -((all C -((all D (in(D,B) & subset(C,D) -> C = D)) & in(C,B))) & empty_set != B))))) # label(t18_finset_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 243 (all A all B (element(B,powerset(powerset(the_carrier(A)))) & one_sorted_str(A) -> (all C ((all D all E all F (E = D & D = F & (exists J exists K (ordered_pair(J,K) = F & (all L (element(L,powerset(the_carrier(A))) -> (J = L -> K = subset_complement(the_carrier(A),L)))) & in(J,B))) & (exists G exists H ((all I (element(I,powerset(the_carrier(A))) -> (I = G -> H = subset_complement(the_carrier(A),I)))) & in(G,B) & ordered_pair(G,H) = E)) -> F = E)) -> (exists D all E (in(E,D) <-> (exists F ((exists M exists N (E = ordered_pair(M,N) & (all O (element(O,powerset(the_carrier(A))) -> (O = M -> N = subset_complement(the_carrier(A),O)))) & in(M,B))) & E = F & in(F,cartesian_product2(B,C)))))))))) # label(s1_tarski__e4_7_2__tops_2__2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 244 (all A (rel_str(A) -> bottom_of_relstr(A) = join_on_relstr(A,empty_set))) # label(d11_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 245 (all A all B all C (one_sorted_str(A) & element(C,the_carrier(A)) & element(B,the_carrier(A)) & -empty_carrier(A) -> element(unordered_pair_as_carrier_subset(A,B,C),powerset(the_carrier(A))))) # label(dt_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 246 (all A (preboolean(A) -> cup_closed(A) & diff_closed(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 247 (all A all B (relation(B) & function(B) -> (all C (function(C) & relation(C) -> (in(apply(C,A),relation_dom(B)) & in(A,relation_dom(C)) <-> in(A,relation_dom(relation_composition(C,B)))))))) # label(t21_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 248 (all A (-empty_carrier(A) & meet_semilatt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> meet(A,B,C) = apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_meet(A),B,C))))))) # label(d2_lattices) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 249 $T # label(dt_k1_wellord1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 250 (all A all B all C (relation(C) -> (in(ordered_pair(A,B),C) -> in(B,relation_rng(C)) & in(A,relation_dom(C))))) # label(t20_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 251 (all A all B (v2_membered(A) -> v2_membered(set_intersection2(B,A)) & v1_membered(set_intersection2(B,A)))) # label(fc30_membered) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 252 (all A all B (ordinal(B) & ordinal(A) -> ordinal_subset(A,B) | ordinal_subset(B,A))) # label(connectedness_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 253 (all A all B (one_sorted_str(A) & element(B,powerset(powerset(the_carrier(A)))) -> (all C exists D all E ((exists F exists G (ordered_pair(F,G) = E & (all H (element(H,powerset(the_carrier(A))) -> (F = H -> G = subset_complement(the_carrier(A),H)))) & in(F,complements_of_subsets(the_carrier(A),B)))) & in(E,cartesian_product2(complements_of_subsets(the_carrier(A),B),C)) <-> in(E,D))))) # label(s1_xboole_0__e4_7_1__tops_2__1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 254 (all A all B (v4_membered(A) -> v4_membered(set_difference(A,B)) & v3_membered(set_difference(A,B)) & v2_membered(set_difference(A,B)) & v1_membered(set_difference(A,B)))) # label(fc40_membered) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 255 (all A all B all C (relation(C) & function(C) & relation(B) -> (exists D ((all E all F (in(ordered_pair(apply(C,E),apply(C,F)),B) & in(F,A) & in(E,A) <-> in(ordered_pair(E,F),D))) & relation(D))))) # label(s1_relat_1__e6_21__wellord2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 256 (all A all B (relation(B) -> -(A != empty_set & relation_inverse_image(B,A) = empty_set & subset(A,relation_rng(B))))) # label(t174_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 257 (all A all B all C (relation(C) -> (in(A,relation_inverse_image(C,B)) <-> (exists D (in(D,relation_rng(C)) & in(ordered_pair(A,D),C) & in(D,B)))))) # label(t166_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 258 (all A all B (relation_of2(B,A,A) -> (function(B) & v1_partfun1(B,A,A) & reflexive(B) & quasi_total(B,A,A) -> function(B) & quasi_total(B,A,A) & onto(B,A,A) & bijective(B,A,A) & one_to_one(B)))) # label(cc4_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 259 (all A all B (relation(B) -> (well_founded_relation(B) -> well_founded_relation(relation_restriction(B,A))))) # label(t31_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 260 (all A all B (-empty_carrier(B) & lattice(B) & latt_str(B) -> (in(A,a_1_0_filter_1(B)) <-> (exists C exists D (element(C,the_carrier(B)) & element(D,the_carrier(B)) & ordered_pair_as_product_element(the_carrier(B),the_carrier(B),C,D) = A & below_refl(B,C,D)))))) # label(fraenkel_a_1_0_filter_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 261 (all A all B all C (-empty_carrier(A) & element(C,the_carrier(A)) & element(B,the_carrier(A)) & meet_semilatt_str(A) -> element(meet(A,B,C),the_carrier(A)))) # label(dt_k2_lattices) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 262 (all A all B (relation(A) & relation(B) -> relation(set_union2(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.64 263 (all A (transitive_relstr(A) & rel_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (all D (element(D,the_carrier(A)) -> (related(A,B,C) & related(A,C,D) -> related(A,B,D)))))))))) # label(t26_orders_2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 264 (all A all B all C all D (function(D) & relation_of2_as_subset(D,A,B) & quasi_total(D,A,B) -> (subset(B,C) -> function(D) & relation_of2_as_subset(D,A,C) & quasi_total(D,A,C) | empty_set != A & empty_set = B))) # label(t9_funct_2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.64 265 (all A (ordinal(A) & natural(A) -> -empty(succ(A)) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A)) & natural(succ(A)))) # label(fc2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 266 (all A transitive(inclusion_relation(A))) # label(t3_wellord2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 267 (all A (v4_membered(A) -> (all B (element(B,A) -> v1_xcmplx_0(B) & v1_rat_1(B) & v1_int_1(B) & v1_xreal_0(B))))) # label(cc13_membered) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 268 (all A all B all C (subset(A,B) -> subset(set_intersection2(A,C),set_intersection2(B,C)))) # label(t26_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 269 (all A (lattice(A) & latt_str(A) & -empty_carrier(A) -> (all B (element(B,the_carrier(poset_of_lattice(A))) -> cast_to_el_of_lattice(A,B) = B)))) # label(d4_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 270 (all A (relation(A) -> (antisymmetric(A) <-> (all B all C (in(ordered_pair(B,C),A) & in(ordered_pair(C,B),A) -> C = B))))) # label(l3_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 271 (all A (ordinal(A) -> well_ordering(inclusion_relation(A)))) # label(t7_wellord2) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 272 (all A all B all C (-empty_carrier(A) & element(C,the_carrier(B)) & net_str(B,A) & -empty_carrier(B) & one_sorted_str(A) -> element(apply_netmap(A,B,C),the_carrier(A)))) # label(dt_k3_waybel_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 273 (all A all B set_difference(A,set_difference(A,B)) = set_intersection2(A,B)) # label(t48_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 274 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 275 (all A all B all C (cartesian_product2(A,B) = C <-> (all D (in(D,C) <-> (exists E exists F (in(F,B) & D = ordered_pair(E,F) & in(E,A))))))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 276 (all A (diff_closed(A) & cup_closed(A) -> preboolean(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 277 (all A (join_semilatt_str(A) & -empty_carrier(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (below(A,B,C) <-> join(A,B,C) = C))))))) # label(d3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 278 (all A all B all C (C = set_intersection2(A,B) <-> (all D (in(D,B) & in(D,A) <-> in(D,C))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 279 (all A (top_str(A) & topological_space(A) -> (exists B (element(B,powerset(the_carrier(A))) & open_subset(B,A))))) # label(rc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 280 (all A (v4_membered(A) -> (all B (element(B,powerset(A)) -> v2_membered(B) & v4_membered(B) & v3_membered(B) & v1_membered(B))))) # label(cc19_membered) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 281 (all A all B (relation(B) & empty(A) -> empty(relation_composition(A,B)) & relation(relation_composition(A,B)))) # label(fc9_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 282 (all A all B (-empty(B) & -empty(A) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 283 (all A all B (relation(B) -> (inclusion_relation(A) = B <-> relation_field(B) = A & (all C all D (in(C,A) & in(D,A) -> (in(ordered_pair(C,D),B) <-> subset(C,D))))))) # label(d1_wellord2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 284 (all A all B ((all C all D all E (C = E & (exists H exists I (singleton(H) = I & in(H,A) & E = ordered_pair(H,I))) & (exists F exists G (ordered_pair(F,G) = D & G = singleton(F) & in(F,A))) & C = D -> E = D)) -> (exists C all D (in(D,C) <-> (exists E (E = D & (exists J exists K (D = ordered_pair(J,K) & K = singleton(J) & in(J,A))) & in(E,cartesian_product2(A,B)))))))) # label(s1_tarski__e16_22__wellord2__2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 285 (all A (-empty_carrier(A) & rel_str(A) & lower_bounded_relstr(A) & antisymmetric_relstr(A) -> ex_inf_of_relstr_set(A,the_carrier(A)) & ex_sup_of_relstr_set(A,empty_set))) # label(t42_yellow_0) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 286 (all A (meet_semilatt_str(A) -> quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & function(the_L_meet(A)))) # label(dt_u1_lattices) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 287 (all A all B (finite(A) -> finite(set_intersection2(A,B)))) # label(t15_finset_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 288 (all A all B (relation(B) -> set_intersection2(relation_dom(B),A) = relation_dom(relation_dom_restriction(B,A)))) # label(t90_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 289 (all A (-empty_carrier(A) & topological_space(A) & top_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,powerset(the_carrier(A))) -> (point_neighbourhood(C,A,B) <-> in(B,interior(A,C))))))))) # label(d1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 290 (all A all B all C (relation(C) -> (in(A,relation_field(relation_restriction(C,B))) -> in(A,relation_field(C)) & in(A,B)))) # label(t19_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 291 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 292 (all A (empty(A) & function(A) & relation(A) -> one_to_one(A) & function(A) & relation(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 293 (exists A rel_str(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 294 (all A all B (element(B,powerset(powerset(the_carrier(A)))) & top_str(A) & topological_space(A) -> (exists C ((all D (element(D,powerset(the_carrier(A))) -> (in(set_difference(cast_as_carrier_subset(A),D),B) <-> in(D,C)))) & element(C,powerset(powerset(the_carrier(A)))))))) # label(s3_subset_1__e2_37_1_1__pre_topc) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 295 (all A all B (relation(B) & empty(A) -> relation(relation_composition(B,A)) & empty(relation_composition(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 296 (all A (join_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 297 (all A all B all C (rel_str(A) & element(C,powerset(B)) & finite(C) & element(B,powerset(the_carrier(A))) & transitive_relstr(A) & -empty_carrier(A) -> (exists D all E (in(E,D) <-> (exists F (F = E & (exists G (relstr_set_smaller(A,F,G) & in(G,B) & element(G,the_carrier(A)))))) & in(E,powerset(C)))))) # label(s1_xboole_0__e11_2_1__waybel_0__1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 298 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 299 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 300 $T # label(dt_k1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 301 (all A (top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))))))) # label(d1_tops_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 302 (all A all B (relation(B) -> (subset(A,relation_dom(B)) -> subset(A,relation_inverse_image(B,relation_image(B,A)))))) # label(t146_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 303 (all A (relation(A) -> (all B ((all C (in(C,B) <-> (exists D in(ordered_pair(C,D),A)))) <-> relation_dom(A) = B)))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 304 (all A (empty(A) -> ordinal(A) & epsilon_connected(A) & epsilon_transitive(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 305 (all A all B (-empty(A) & relation_of2(B,A,A) -> -empty_carrier(rel_str_of(A,B)) & strict_rel_str(rel_str_of(A,B)))) # label(fc1_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 306 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 307 (all A all B (in(A,B) -> subset(A,union(B)))) # label(t92_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 308 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 309 (all A (one_sorted_str(A) & -empty_carrier(A) -> (all B (-empty_carrier(B) & net_str(B,A) -> (all C (is_eventually_in(A,B,C) <-> (exists D ((all E (element(E,the_carrier(B)) -> (related(B,D,E) -> in(apply_netmap(A,B,E),C)))) & element(D,the_carrier(B)))))))))) # label(d11_waybel_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 310 (all A (top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> subset(B,topstr_closure(A,B)))))) # label(t48_pre_topc) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 311 (all A all B set_union2(A,B) = set_union2(A,set_difference(B,A))) # label(t39_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 312 (all A (rel_str(A) -> (all B (element(B,the_carrier(A)) -> relstr_element_smaller(A,empty_set,B) & relstr_set_smaller(A,empty_set,B))))) # label(t6_yellow_0) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 313 (all A (one_sorted_str(A) -> (empty(the_carrier(A)) <-> empty_carrier(A)))) # label(d1_struct_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 314 (all A (ordinal(A) -> (being_limit_ordinal(A) <-> (all B (ordinal(B) -> (in(B,A) -> in(succ(B),A))))))) # label(t41_ordinal1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 315 (all A all B (ordinal(B) -> (in(A,B) -> ordinal(A)))) # label(t23_ordinal1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 316 (all A all B ((all C (in(C,A) -> in(C,B))) <-> subset(A,B))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 317 (all A all B (-empty_carrier(A) & latt_str(A) -> element(join_of_latt_set(A,B),the_carrier(A)))) # label(dt_k15_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 318 (all A all B all C (in(B,C) & in(A,C) <-> subset(unordered_pair(A,B),C))) # label(t38_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 319 (all A all B all C all D (relation(D) -> (in(ordered_pair(A,B),D) & in(A,C) <-> in(ordered_pair(A,B),relation_composition(identity_relation(C),D))))) # label(t74_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 320 (all A (relation(A) -> (all B (relation(B) -> (subset(A,B) -> subset(relation_dom(A),relation_dom(B)) & subset(relation_rng(A),relation_rng(B))))))) # label(t25_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 321 (all A all B equipotent(A,A)) # label(reflexivity_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 322 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 323 (all A -empty(succ(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 324 (all A (-empty_carrier(A) & latt_str(A) & complete_latt_str(A) & lattice(A) -> (all B (join_of_latt_set(A,B) = join_on_relstr(poset_of_lattice(A),B) & meet_of_latt_set(A,B) = meet_on_relstr(poset_of_lattice(A),B))))) # label(t29_yellow_0) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 325 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 326 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 327 (all A all B (element(B,powerset(powerset(A))) -> (empty_set != B -> subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B)) = union_of_subsets(A,complements_of_subsets(A,B))))) # label(t48_setfam_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 328 (all A (v3_membered(A) -> v2_membered(A))) # label(cc3_membered) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 329 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.31/1.65 330 (all A (rel_str(A) -> (all B all C (element(C,the_carrier(A)) -> ((all D (element(D,the_carrier(A)) -> (in(D,B) -> related(A,D,C)))) <-> relstr_set_smaller(A,B,C)))))) # label(d9_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.31/1.65 331 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 332 (all A all B (element(B,powerset(powerset(A))) -> (all C (element(C,powerset(powerset(A))) -> (complements_of_subsets(A,B) = C <-> (all D (element(D,powerset(A)) -> (in(subset_complement(A,D),B) <-> in(D,C))))))))) # label(d8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 333 (all A all B (element(B,powerset(powerset(succ(A)))) & ordinal(A) -> (exists C all D (in(D,powerset(A)) & (exists E (in(E,B) & D = set_difference(E,singleton(A)))) <-> in(D,C))))) # label(s1_xboole_0__e4_27_3_1__finset_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.65 334 (all A (one_sorted_str(A) -> function(identity_on_carrier(A)) & relation_of2_as_subset(identity_on_carrier(A),the_carrier(A),the_carrier(A)) & quasi_total(identity_on_carrier(A),the_carrier(A),the_carrier(A)))) # label(dt_k7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 335 (exists A (function(A) & epsilon_transitive(A) & ordinal(A) & epsilon_connected(A) & empty(A) & one_to_one(A) & relation(A))) # label(rc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 336 (all A all B (relation(B) & -empty(A) -> (all C ((all D all E all F (D = E & (exists G exists H (E = ordered_pair(G,H) & (exists I (I = G & in(H,I) & (all J (in(J,I) -> in(ordered_pair(H,J),B))))) & in(G,A))) & (exists K exists L (ordered_pair(K,L) = F & in(K,A) & (exists M ((all N (in(N,M) -> in(ordered_pair(L,N),B))) & in(L,M) & M = K)))) & F = D -> F = E)) -> (exists D all E (in(E,D) <-> (exists F ((exists O exists P (E = ordered_pair(O,P) & in(O,A) & (exists Q (O = Q & (all R (in(R,Q) -> in(ordered_pair(P,R),B))) & in(P,Q))))) & E = F & in(F,cartesian_product2(A,C)))))))))) # label(s1_tarski__e10_24__wellord2__2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 337 (all A (rel_str(A) -> (all B (ex_inf_of_relstr_set(A,B) <-> (exists C (element(C,the_carrier(A)) & relstr_element_smaller(A,B,C) & (all D (element(D,the_carrier(A)) -> (relstr_element_smaller(A,B,D) -> related(A,D,C)))) & (all D (element(D,the_carrier(A)) -> (relstr_element_smaller(A,B,D) & (all E (element(E,the_carrier(A)) -> (relstr_element_smaller(A,B,E) -> related(A,E,D)))) -> D = C))))))))) # label(d8_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 338 (all A (-empty_carrier(A) & latt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C ((all D (element(D,the_carrier(A)) -> (in(D,C) -> below(A,B,D)))) <-> latt_set_smaller(A,B,C))))))) # label(d16_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 339 (all A (one_sorted_str(A) -> (all B (element(B,powerset(powerset(the_carrier(A)))) -> (cast_as_carrier_subset(A) = union_of_subsets(the_carrier(A),B) <-> is_a_cover_of_carrier(A,B)))))) # label(d8_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 340 (all A all B (relation(B) -> (transitive(B) -> transitive(relation_restriction(B,A))))) # label(t24_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.65 341 (all A all B (subset(A,B) <-> element(A,powerset(B)))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 342 (all A (empty(A) -> function(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 343 (all A all B (element(B,powerset(powerset(A))) -> -(empty_set = complements_of_subsets(A,B) & empty_set != B) & -(empty_set != complements_of_subsets(A,B) & empty_set = B))) # label(t10_tops_2) # label(lemma) # label(non_clause). [assumption]. 1.43/1.65 344 (all A (topological_space(A) & top_str(A) -> (exists B (element(B,powerset(the_carrier(A))) & open_subset(B,A) & closed_subset(B,A))))) # label(rc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 345 (all A (-empty_carrier(A) & one_sorted_str(A) -> (all B (-empty_carrier(B) & net_str(B,A) -> (all C (is_often_in(A,B,C) <-> (all D (element(D,the_carrier(B)) -> (exists E (element(E,the_carrier(B)) & related(B,D,E) & in(apply_netmap(A,B,E),C))))))))))) # label(d12_waybel_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 346 (all A all B (relation(B) & -empty(A) -> (all C exists D all E (in(E,D) <-> (exists F exists G (E = ordered_pair(F,G) & (exists H (in(G,H) & (all I (in(I,H) -> in(ordered_pair(G,I),B))) & H = F)) & in(F,A))) & in(E,cartesian_product2(A,C)))))) # label(s1_xboole_0__e10_24__wellord2__1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.65 347 (all A (relation(A) & function(A) -> ((all B all C (in(C,relation_dom(A)) & apply(A,B) = apply(A,C) & in(B,relation_dom(A)) -> C = B)) <-> one_to_one(A)))) # label(d8_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 348 (all A (latt_str(A) -> join_semilatt_str(A) & meet_semilatt_str(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 349 (all A all B all C (relation(C) -> (in(A,B) & in(A,relation_rng(C)) <-> in(A,relation_rng(relation_rng_restriction(B,C)))))) # label(t115_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.65 350 (all A all B (relation(B) & function(B) -> subset(relation_image(B,relation_inverse_image(B,A)),A))) # label(t145_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.65 351 (all A all B all C (function(C) & relation(C) & element(B,powerset(powerset(A))) -> ((all D all E all F (D = E & in(relation_image(C,F),B) & F = D & in(relation_image(C,E),B) -> E = F)) -> (exists D all E ((exists F (in(F,powerset(relation_dom(C))) & in(relation_image(C,E),B) & E = F)) <-> in(E,D)))))) # label(s1_tarski__e6_27__finset_1__1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 352 (all A (relation(A) -> (all B (is_reflexive_in(A,B) <-> (all C (in(C,B) -> in(ordered_pair(C,C),A))))))) # label(d1_relat_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 353 (all A all B (relation(B) -> relation(relation_rng_restriction(A,B)))) # label(dt_k8_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 354 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 355 (all A (relation(A) & function(A) -> (all B all C ((in(B,relation_dom(A)) -> (in(ordered_pair(B,C),A) <-> apply(A,B) = C)) & (-in(B,relation_dom(A)) -> (C = apply(A,B) <-> C = empty_set)))))) # label(d4_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 356 (all A (relation(A) -> (all B ((all C all D (in(C,B) & in(ordered_pair(C,D),A) & in(ordered_pair(D,C),A) & in(D,B) -> C = D)) <-> is_antisymmetric_in(A,B))))) # label(d4_relat_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 357 (all A all B all C (relation(C) -> (in(A,relation_dom(C)) & in(A,B) <-> in(A,relation_dom(relation_dom_restriction(C,B)))))) # label(t86_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.65 358 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 359 (all A all B (finite(A) -> finite(set_difference(A,B)))) # label(fc12_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 360 (all A all B (element(B,powerset(powerset(succ(A)))) & ordinal(A) -> ((all C all D all E (D = C & E = C & (exists G (in(G,B) & E = set_difference(G,singleton(A)))) & (exists F (D = set_difference(F,singleton(A)) & in(F,B))) -> E = D)) -> (exists C all D ((exists E (in(E,powerset(A)) & E = D & (exists H (set_difference(H,singleton(A)) = D & in(H,B))))) <-> in(D,C)))))) # label(s1_tarski__e4_27_3_1__finset_1__1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 361 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> subset_union2(A,B,B) = B)) # label(idempotence_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 362 (all A (top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> (in(B,the_topology(A)) <-> open_subset(B,A)))))) # label(d5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 363 (all A (one_sorted_str(A) -> identity_as_relation_of(the_carrier(A)) = identity_on_carrier(A))) # label(d11_grcat_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 364 (all A all B (-empty(A) & relation(B) -> ((all C all D all E (in(C,A) & (exists F ((all G (in(G,F) -> in(ordered_pair(D,G),B))) & in(D,F) & F = C)) & in(C,A) & (exists H (C = H & in(E,H) & (all I (in(I,H) -> in(ordered_pair(E,I),B))))) -> D = E)) -> (exists C ((all D all E (in(ordered_pair(D,E),C) <-> in(D,A) & in(D,A) & (exists J (in(E,J) & (all K (in(K,J) -> in(ordered_pair(E,K),B))) & D = J)))) & function(C) & relation(C)))))) # label(s1_funct_1__e10_24__wellord2__1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.65 365 (all A all B all C (subset(A,B) & subset(B,C) -> subset(A,C))) # label(t1_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.65 366 (all A all B (in(A,B) -> B = set_union2(singleton(A),B))) # label(t46_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.65 367 (all A all B all C (element(C,the_carrier(A)) & element(B,the_carrier(A)) & rel_str(A) & reflexive_relstr(A) & -empty_carrier(A) -> (related_reflexive(A,B,C) <-> related(A,B,C)))) # label(redefinition_r3_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 368 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(t37_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.65 369 (exists A (empty(A) & relation(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 370 (exists A (reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & strict_rel_str(A) & -empty_carrier(A) & rel_str(A))) # label(rc2_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 371 (all A all B (element(B,the_carrier(boole_lattice(A))) -> (all C (element(C,the_carrier(boole_lattice(A))) -> (subset(B,C) <-> below(boole_lattice(A),B,C)))))) # label(t2_lattice3) # label(lemma) # label(non_clause). [assumption]. 1.43/1.65 372 (all A all B (element(A,B) -> in(A,B) | empty(B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 373 (all A all B (relation(B) -> (antisymmetric(B) -> antisymmetric(relation_restriction(B,A))))) # label(t25_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.65 374 (all A all B all C (singleton(A) = unordered_pair(B,C) -> C = B)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.65 375 (all A all B all C (meet_commutative(A) & meet_semilatt_str(A) & element(C,the_carrier(A)) & element(B,the_carrier(A)) & -empty_carrier(A) -> meet_commut(A,B,C) = meet_commut(A,C,B))) # label(commutativity_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 376 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 377 (all A all B (element(B,powerset(powerset(A))) -> element(union_of_subsets(A,B),powerset(A)))) # label(dt_k5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 378 (all A all B (element(B,powerset(A)) -> B = subset_complement(A,subset_complement(A,B)))) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 379 (all A all B (relation(B) -> (reflexive(B) -> reflexive(relation_restriction(B,A))))) # label(t22_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.65 380 (all A all B (element(B,powerset(A)) -> (all C (in(C,B) -> in(C,A))))) # label(l3_subset_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.65 381 (all A all B (A = empty_set | singleton(B) = A <-> subset(A,singleton(B)))) # label(t39_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.65 382 (all A all B set_difference(set_union2(A,B),B) = set_difference(A,B)) # label(t40_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.65 383 (all A (meet_commutative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & meet_associative(boole_lattice(A)) & join_associative(boole_lattice(A)) & join_commutative(boole_lattice(A)) & strict_latt_str(boole_lattice(A)) & -empty_carrier(boole_lattice(A)))) # label(fc2_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 384 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 385 (all A all B all C (-empty_carrier(A) & join_semilatt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> element(join(A,B,C),the_carrier(A)))) # label(dt_k1_lattices) # label(axiom) # label(non_clause). [assumption]. 1.43/1.65 386 (all A singleton(A) != empty_set) # label(l1_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 387 (all A all B set_intersection2(B,A) = set_intersection2(A,B)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 388 (all A (topological_space(A) & top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> open_subset(interior(A,B),A))))) # label(t51_tops_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 389 (all A (relation(A) -> (all B (relation(B) -> relation_image(B,relation_rng(A)) = relation_rng(relation_composition(A,B)))))) # label(t160_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 390 (exists A (relation(A) & relation_empty_yielding(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 391 (all A all B ((all C ((exists D (in(C,D) & in(D,A))) <-> in(C,B))) <-> B = union(A))) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 392 (all A (relation(A) -> (all B (relation(B) -> ((all C all D (in(ordered_pair(D,C),A) <-> in(ordered_pair(C,D),B))) <-> relation_inverse(A) = B))))) # label(d7_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 393 (all A all B (element(B,powerset(powerset(A))) -> union(B) = union_of_subsets(A,B))) # label(redefinition_k5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 394 (all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 395 (all A (A = omega <-> in(empty_set,A) & ordinal(A) & (all B (ordinal(B) -> (in(empty_set,B) & being_limit_ordinal(B) -> subset(A,B)))) & being_limit_ordinal(A))) # label(d5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 396 (all A (finite(A) -> (all B (element(B,powerset(A)) -> finite(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 397 (all A (top_str(A) -> (compact_top_space(A) <-> (all B (element(B,powerset(powerset(the_carrier(A)))) -> -((all C (element(C,powerset(powerset(the_carrier(A)))) -> -(is_a_cover_of_carrier(A,C) & finite(C) & subset(C,B)))) & open_subsets(B,A) & is_a_cover_of_carrier(A,B))))))) # label(d3_compts_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 398 (all A ((all B all C all D (in(ordered_pair(B,C),A) & in(ordered_pair(B,D),A) -> C = D)) <-> function(A))) # label(d1_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 399 (all A ((all B -in(B,A)) <-> A = empty_set)) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 400 (all A (lattice(A) & latt_str(A) & -empty_carrier(A) -> strict_rel_str(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & -empty_carrier(poset_of_lattice(A)))) # label(fc4_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 401 (all A all B (relation(B) -> subset(relation_inverse_image(B,A),relation_dom(B)))) # label(t167_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 402 (all A (rel_str(A) -> (all B (subrelstr(B,A) -> rel_str(B))))) # label(dt_m1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 403 (all A relation(inclusion_relation(A))) # label(dt_k1_wellord2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 404 (all A all B (v5_membered(A) -> v3_membered(set_intersection2(A,B)) & v5_membered(set_intersection2(A,B)) & v4_membered(set_intersection2(A,B)) & v2_membered(set_intersection2(A,B)) & v1_membered(set_intersection2(A,B)))) # label(fc35_membered) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 405 (all A all B (v1_membered(A) -> v1_membered(set_intersection2(A,B)))) # label(fc27_membered) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 406 (all A (latt_str(A) & lattice(A) & -empty_carrier(A) -> reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & rel_str(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & strict_rel_str(poset_of_lattice(A)))) # label(dt_k3_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 407 (all A all B (top_str(A) & element(B,powerset(powerset(the_carrier(A)))) & topological_space(A) -> (exists C all D (in(set_difference(cast_as_carrier_subset(A),D),B) & in(D,powerset(the_carrier(A))) <-> in(D,C))))) # label(s1_xboole_0__e2_37_1_1__pre_topc__1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 408 (all A (relation(A) -> relation(relation_inverse(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 409 (all A all B all C (relation(B) & function(C) & relation(C) -> ((all D all E all F ((exists G exists H (in(ordered_pair(apply(C,G),apply(C,H)),B) & E = ordered_pair(G,H))) & (exists I exists J (in(ordered_pair(apply(C,I),apply(C,J)),B) & F = ordered_pair(I,J))) & D = F & E = D -> F = E)) -> (exists D all E (in(E,D) <-> (exists F (in(F,cartesian_product2(A,A)) & (exists K exists L (in(ordered_pair(apply(C,K),apply(C,L)),B) & E = ordered_pair(K,L))) & E = F))))))) # label(s1_tarski__e6_21__wellord2__1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 410 (all A ((all B -(in(B,A) & (all C all D B != ordered_pair(C,D)))) <-> relation(A))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 411 (all A all B all C (relation(C) -> (in(A,relation_image(C,B)) <-> (exists D (in(ordered_pair(D,A),C) & in(D,B) & in(D,relation_dom(C))))))) # label(t143_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 412 (all A (ordinal(A) -> (all B (element(B,A) -> epsilon_connected(B) & ordinal(B) & epsilon_transitive(B))))) # label(cc1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 413 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 414 (all A (empty_set = bottom_of_semilattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)))) # label(t3_lattice3) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 415 (all A (join_semilatt_str(A) & join_commutative(A) & -empty_carrier(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (below(A,C,B) & below(A,B,C) -> C = B))))))) # label(t26_lattices) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 416 (all A (relation(A) & transitive(A) & symmetric(A) -> relation(A) & reflexive(A))) # label(cc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 417 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 418 (all A (empty(A) -> relation(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 419 (all A all B (proper_subset(A,B) <-> subset(A,B) & B != A)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 420 (all A (relation(A) -> (all B (is_reflexive_in(A,B) & is_transitive_in(A,B) & is_antisymmetric_in(A,B) & is_connected_in(A,B) & is_well_founded_in(A,B) <-> well_orders(A,B))))) # label(d5_wellord1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 421 (all A (relation(A) -> (transitive(A) <-> (all B all C all D (in(ordered_pair(C,D),A) & in(ordered_pair(B,C),A) -> in(ordered_pair(B,D),A)))))) # label(l2_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 422 (all A all B (element(B,powerset(powerset(A))) -> complements_of_subsets(A,complements_of_subsets(A,B)) = B)) # label(involutiveness_k7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 423 (all A all B all C (relation_of2_as_subset(C,B,A) -> (B = relation_dom_as_subset(B,A,C) <-> (all D -(in(D,B) & (all E -in(ordered_pair(D,E),C))))))) # label(t22_relset_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 424 (all A (rel_str(A) -> (exists B subrelstr(B,A)))) # label(existence_m1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 425 (all A (rel_str(A) -> relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)))) # label(dt_u1_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 426 (all A all B (-empty_carrier(A) & topological_space(A) & top_str(A) & element(B,the_carrier(A)) -> (all C (point_neighbourhood(C,A,B) -> element(C,powerset(the_carrier(A))))))) # label(dt_m1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 427 (all A (v5_membered(A) -> (all B (element(B,powerset(A)) -> v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_membered(B) & v1_membered(B))))) # label(cc20_membered) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 428 (all A (top_str(A) & topological_space(A) -> (all B (element(B,powerset(the_carrier(A))) -> (exists C (element(C,powerset(powerset(the_carrier(A)))) & topstr_closure(A,B) = meet_of_subsets(the_carrier(A),C) & (all D (element(D,powerset(the_carrier(A))) -> (subset(B,D) & closed_subset(D,A) <-> in(D,C)))))))))) # label(t46_pre_topc) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 429 (exists A top_str(A)) # label(existence_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 430 (all A all B (function(B) & relation(B) -> (finite(A) -> finite(relation_image(B,A))))) # label(t17_finset_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 431 (all A exists B (relation_of2(B,A,A) & quasi_total(B,A,A) & bijective(B,A,A) & onto(B,A,A) & one_to_one(B) & function(B) & relation(B))) # label(rc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 432 (all A all B ((all C (subset(C,A) <-> in(C,B))) <-> powerset(A) = B)) # label(d1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 433 (all A all B all C (relation(C) & function(C) -> (in(B,relation_dom(relation_dom_restriction(C,A))) <-> in(B,relation_dom(C)) & in(B,A)))) # label(l82_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 434 (all A all B (element(B,powerset(A)) -> subset_complement(A,B) = set_difference(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 435 (all A (top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> (all C (element(C,powerset(the_carrier(A))) -> ((all D (in(D,the_carrier(A)) -> ((all E (element(E,powerset(the_carrier(A))) -> -(open_subset(E,A) & disjoint(B,E) & in(D,E)))) <-> in(D,C)))) <-> topstr_closure(A,B) = C))))))) # label(d13_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 436 (all A ((all B all C all D (C = B & ordinal(C) & ordinal(D) & B = D -> C = D)) -> (exists B all C (in(C,B) <-> (exists D (ordinal(C) & C = D & in(D,A))))))) # label(s1_tarski__e6_22__wellord2__1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 437 (all A all B (relation_of2(B,A,A) -> (all C all D (rel_str_of(A,B) = rel_str_of(C,D) -> A = C & B = D)))) # label(free_g1_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 438 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> relation_of2_as_subset(k2_lattice3(A),the_carrier(A),the_carrier(A)) & v1_partfun1(k2_lattice3(A),the_carrier(A),the_carrier(A)) & transitive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & reflexive(k2_lattice3(A)))) # label(dt_k2_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 439 (all A all B (finite(A) & finite(B) -> finite(cartesian_product2(A,B)))) # label(fc14_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 440 (all A (antisymmetric_relstr(A) & rel_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (related(A,C,B) & related(A,B,C) -> B = C))))))) # label(t25_orders_2) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 441 (all A all B (relation(B) -> (well_orders(B,A) -> well_ordering(relation_restriction(B,A)) & relation_field(relation_restriction(B,A)) = A))) # label(t25_wellord2) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 442 (all A (antisymmetric_relstr(A) & rel_str(A) & transitive_relstr(A) & reflexive_relstr(A) -> relation(the_InternalRel(A)) & reflexive(the_InternalRel(A)) & antisymmetric(the_InternalRel(A)) & transitive(the_InternalRel(A)) & v1_partfun1(the_InternalRel(A),the_carrier(A),the_carrier(A)))) # label(fc2_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 443 (all A all B all C (subset(A,B) & subset(A,C) -> subset(A,set_intersection2(B,C)))) # label(t19_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 444 (all A all B all C (relation_of2_as_subset(C,A,B) -> subset(relation_dom(C),A) & subset(relation_rng(C),B))) # label(t12_relset_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 445 (all A (ordinal(A) -> (all B (ordinal(B) -> (in(A,B) <-> ordinal_subset(succ(A),B)))))) # label(t33_ordinal1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 446 (all A all B all C (relation_of2(C,A,B) -> (quasi_total(C,A,B) & bijective(C,A,B) & function(C) -> function(C) & one_to_one(C) & quasi_total(C,A,B) & onto(C,A,B)))) # label(cc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 447 (exists A (relation_empty_yielding(A) & function(A) & relation(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 448 (all A all B all C (meet_commutative(A) & meet_absorbing(A) & element(C,the_carrier(A)) & element(B,the_carrier(A)) & latt_str(A) & join_absorbing(A) & -empty_carrier(A) -> below_refl(A,B,B))) # label(reflexivity_r3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 449 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 450 (all A cast_to_subset(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 451 (exists A (epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 452 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> relation_of_lattice(A) = a_1_0_filter_1(A))) # label(d8_filter_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 453 (all A (relation(A) -> (is_reflexive_in(A,relation_field(A)) <-> reflexive(A)))) # label(d9_relat_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 454 (all A (latt_str(A) & lattice(A) & -empty_carrier(A) -> relation_of_lattice(A) = k2_lattice3(A))) # label(redefinition_k2_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 455 (all A all B all C (quasi_total(B,cartesian_product2(A,A),A) & relation_of2(B,cartesian_product2(A,A),A) & function(C) & relation_of2(C,cartesian_product2(A,A),A) & quasi_total(C,cartesian_product2(A,A),A) & function(B) -> (all D all E all F (latt_str_of(A,B,C) = latt_str_of(D,E,F) -> A = D & E = B & C = F)))) # label(free_g3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 456 (all A all B (subset(A,B) -> A = set_intersection2(A,B))) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 457 (all A (one_sorted_str(A) & -empty_carrier(A) -> (all B (element(B,powerset(powerset(the_carrier(A)))) -> -(is_a_cover_of_carrier(A,B) & B = empty_set))))) # label(t5_tops_2) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 458 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 459 (all A (rel_str(A) -> element(bottom_of_relstr(A),the_carrier(A)))) # label(dt_k3_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 460 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> subset_intersection2(A,C,B) = subset_intersection2(A,B,C))) # label(commutativity_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 461 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 462 (all A all B (relation(B) -> relation_dom_restriction(relation_rng_restriction(A,B),A) = relation_restriction(B,A))) # label(t17_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 463 (all A (relation(A) & function(A) -> (one_to_one(A) -> relation_dom(A) = relation_rng(function_inverse(A)) & relation_rng(A) = relation_dom(function_inverse(A))))) # label(t55_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 464 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 465 (all A all B (relation(A) -> relation_restriction(A,B) = relation_restriction_as_relation_of(A,B))) # label(redefinition_k1_toler_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 466 (all A exists B (element(B,powerset(A)) & relation(B) & epsilon_connected(B) & finite(B) & natural(B) & ordinal(B) & epsilon_transitive(B) & one_to_one(B) & function(B) & empty(B))) # label(rc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 467 (all A all B (relation(A) & function(A) & finite(B) -> finite(relation_image(A,B)))) # label(fc13_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 468 (all A (empty(A) -> empty(relation_rng(A)) & relation(relation_rng(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 469 (all A ((all B all C all D (in(B,A) & singleton(B) = C & in(B,A) & D = singleton(B) -> D = C)) -> (exists B all C (in(C,B) <-> (exists D (C = singleton(D) & in(D,A) & in(D,A))))))) # label(s1_tarski__e16_22__wellord2__1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 470 (all A (rel_str(A) -> (all B all C (element(C,the_carrier(A)) -> (relstr_element_smaller(A,B,C) <-> (all D (element(D,the_carrier(A)) -> (in(D,B) -> related(A,C,D))))))))) # label(d8_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 471 (all A in(A,succ(A))) # label(t10_ordinal1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 472 (all A all B (finite(B) -> finite(set_intersection2(A,B)))) # label(fc10_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 473 (all A all B (element(B,powerset(A)) -> (all C (element(C,powerset(A)) -> (disjoint(B,C) <-> subset(B,subset_complement(A,C))))))) # label(t43_subset_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 474 (all A all B (v3_membered(A) -> v1_membered(set_intersection2(B,A)) & v3_membered(set_intersection2(B,A)) & v2_membered(set_intersection2(B,A)))) # label(fc32_membered) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 475 (all A k1_pcomps_1(A) = powerset(A)) # label(redefinition_k1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 476 (all A (rel_str(A) -> (all B all C (element(C,the_carrier(A)) -> (ex_sup_of_relstr_set(A,B) -> (relstr_set_smaller(A,B,C) & (all D (element(D,the_carrier(A)) -> (relstr_set_smaller(A,B,D) -> related(A,C,D)))) <-> join_on_relstr(A,B) = C)))))) # label(d9_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 477 (all A all B (ordinal(A) & ordinal(B) -> (subset(A,B) <-> ordinal_subset(A,B)))) # label(redefinition_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 478 (all A (antisymmetric_relstr(A) & rel_str(A) -> (all B ((exists C (element(C,the_carrier(A)) & (all D (element(D,the_carrier(A)) -> (relstr_set_smaller(A,B,D) -> related(A,C,D)))) & relstr_set_smaller(A,B,C))) <-> ex_sup_of_relstr_set(A,B))))) # label(t15_yellow_0) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 479 (exists A (-empty(A) & finite(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 480 (all A (relation(A) & function(A) & one_to_one(A) -> relation(relation_inverse(A)) & function(relation_inverse(A)))) # label(fc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 481 (all A all B all C (element(C,powerset(A)) & element(B,powerset(A)) -> element(subset_difference(A,B,C),powerset(A)))) # label(dt_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 482 (all A (-empty_carrier(A) & topological_space(A) & top_str(A) -> (compact_top_space(A) <-> (all B (element(B,powerset(powerset(the_carrier(A)))) -> -(empty_set = meet_of_subsets(the_carrier(A),B) & closed_subsets(B,A) & centered(B))))))) # label(t13_compts_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 483 (all A all B (relation(B) & function(B) -> (all C (relation(C) & function(C) -> (in(A,relation_dom(relation_composition(C,B))) -> apply(B,apply(C,A)) = apply(relation_composition(C,B),A)))))) # label(t22_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 484 (all A exists B (element(B,powerset(A)) & -proper_element(B,powerset(A)))) # label(rc2_tex_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 485 (all A (one_sorted_str(A) & -empty_carrier(A) -> (exists B (-empty(B) & element(B,powerset(the_carrier(A))))))) # label(rc5_struct_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 486 (all A all B (topological_space(A) & top_str(A) & element(B,powerset(the_carrier(A))) -> open_subset(interior(A,B),A))) # label(fc6_tops_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 487 (all A (epsilon_transitive(A) <-> (all B (in(B,A) -> subset(B,A))))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 488 (all A all B (v4_membered(A) -> v2_membered(set_intersection2(A,B)) & v3_membered(set_intersection2(A,B)) & v4_membered(set_intersection2(A,B)) & v1_membered(set_intersection2(A,B)))) # label(fc33_membered) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 489 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 490 (all A all B all C (relation_of2_as_subset(C,A,B) -> ((empty_set = B -> empty_set = A) -> (quasi_total(C,A,B) <-> A = relation_dom_as_subset(A,B,C))) & (B = empty_set -> (quasi_total(C,A,B) <-> empty_set = C) | empty_set = A))) # label(d1_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 491 (all A all B (one_sorted_str(A) & element(B,powerset(powerset(the_carrier(A)))) -> ((all C all D all E ((all G (element(G,powerset(the_carrier(A))) -> (G = C -> subset_complement(the_carrier(A),G) = E))) & in(C,complements_of_subsets(the_carrier(A),B)) & (all F (element(F,powerset(the_carrier(A))) -> (C = F -> subset_complement(the_carrier(A),F) = D))) & in(C,complements_of_subsets(the_carrier(A),B)) -> D = E)) -> (exists C all D (in(D,C) <-> (exists E (in(E,complements_of_subsets(the_carrier(A),B)) & (all H (element(H,powerset(the_carrier(A))) -> (H = E -> D = subset_complement(the_carrier(A),H)))) & in(E,complements_of_subsets(the_carrier(A),B))))))))) # label(s1_tarski__e4_7_1__tops_2__1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 492 (all A all B all C (join_commutative(A) & element(C,the_carrier(A)) & element(B,the_carrier(A)) & join_semilatt_str(A) & -empty_carrier(A) -> join_commut(A,C,B) = join_commut(A,B,C))) # label(commutativity_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 493 (all A all B (-empty(B) -> (all C (relation_of2(C,A,B) -> (quasi_total(C,A,B) & function(C) -> function(C) & v1_partfun1(C,A,B) & quasi_total(C,A,B)))))) # label(cc5_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 494 (all A (-empty_carrier(A) & latt_str(A) -> ((all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> join(A,meet(A,B,C),C) = C)))) <-> meet_absorbing(A)))) # label(d8_lattices) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 495 (all A all B (equipotent(A,B) <-> are_equipotent(A,B))) # label(redefinition_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 496 (all A (v3_membered(A) -> (all B (element(B,A) -> v1_xreal_0(B) & v1_rat_1(B) & v1_xcmplx_0(B))))) # label(cc12_membered) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 497 (all A (-empty_carrier(A) & latt_str(A) & lattice(A) -> (all B (element(B,the_carrier(A)) -> cast_to_el_of_LattPOSet(A,B) = B)))) # label(d3_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 498 (all A (relation_of2_as_subset(identity_as_relation_of(A),A,A) & v1_partfun1(identity_as_relation_of(A),A,A))) # label(dt_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 499 (all A all B all C all D (-empty(A) & -empty(B) & element(C,A) & element(D,B) -> element(ordered_pair_as_product_element(A,B,C,D),cartesian_product2(A,B)))) # label(dt_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 500 (all A all B (lattice(B) & latt_str(B) & -empty_carrier(B) -> (all C (element(C,the_carrier(B)) -> (relstr_element_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C)) <-> latt_set_smaller(B,C,A)))))) # label(t28_lattice3) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 501 (all A (one_sorted_str(A) -> the_carrier(A) = cast_as_carrier_subset(A))) # label(t12_pre_topc) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 502 (all A ((all B all C all D (in(B,A) & singleton(B) = C & singleton(B) = D & in(B,A) -> D = C)) -> (exists B ((all C all D (in(C,A) & singleton(C) = D & in(C,A) <-> in(ordered_pair(C,D),B))) & function(B) & relation(B))))) # label(s1_funct_1__e16_22__wellord2__1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 503 (all A all B all C all D (subset(A,B) & subset(C,D) -> subset(cartesian_product2(A,C),cartesian_product2(B,D)))) # label(t119_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 504 (all A all B (relation(A) & relation_empty_yielding(A) -> relation(relation_dom_restriction(A,B)) & relation_empty_yielding(relation_dom_restriction(A,B)))) # label(fc13_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 505 (all A (subset(A,empty_set) -> empty_set = A)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 506 (all A all B (element(B,powerset(the_carrier(A))) & top_str(A) -> element(topstr_closure(A,B),powerset(the_carrier(A))))) # label(dt_k6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 507 (all A (relation(A) -> (all B (relation(B) -> (all C (relation(C) -> (relation_composition(A,B) = C <-> (all D all E (in(ordered_pair(D,E),C) <-> (exists F (in(ordered_pair(F,E),B) & in(ordered_pair(D,F),A)))))))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 508 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 509 (all A all B (relation(B) -> subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)))) # label(t118_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 510 (all A (top_str(A) & topological_space(A) -> (exists B (closed_subset(B,A) & element(B,powerset(the_carrier(A))))))) # label(rc6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 511 (all A all B (rel_str(A) -> element(join_on_relstr(A,B),the_carrier(A)))) # label(dt_k1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 512 (all A (relation(A) -> (well_founded_relation(A) <-> is_well_founded_in(A,relation_field(A))))) # label(t5_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 513 (all A (v5_membered(A) -> (all B (element(B,A) -> v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) & natural(B) & v1_xcmplx_0(B))))) # label(cc14_membered) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 514 (all A (topological_space(A) & top_str(A) -> (all B (element(B,powerset(powerset(the_carrier(A)))) -> ((all C (element(C,powerset(the_carrier(A))) -> (in(C,B) -> closed_subset(C,A)))) -> closed_subset(meet_of_subsets(the_carrier(A),B),A)))))) # label(t44_pre_topc) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 515 (all A (latt_str(A) & lattice(A) & -empty_carrier(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (below_refl(A,B,C) <-> related_reflexive(poset_of_lattice(A),cast_to_el_of_LattPOSet(A,B),cast_to_el_of_LattPOSet(A,C))))))))) # label(t7_lattice3) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 516 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 517 (all A (-empty_carrier(A) & top_str(A) & topological_space(A) -> (all B (element(B,powerset(the_carrier(A))) -> (all C (element(C,the_carrier(A)) -> (open_subset(B,A) & in(C,B) -> point_neighbourhood(B,A,C)))))))) # label(t5_connsp_2) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 518 (all A all B all C all D (function(D) & quasi_total(D,A,B) & relation_of2_as_subset(D,A,B) -> (all E (relation(E) & function(E) -> (in(C,A) -> empty_set = B | apply(relation_composition(D,E),C) = apply(E,apply(D,C))))))) # label(t21_funct_2) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 519 (all A exists B (relation(B) & function(B) & (all C (in(C,A) -> apply(B,C) = singleton(C))) & relation_dom(B) = A)) # label(s3_funct_1__e16_22__wellord2) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 520 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) & complete_latt_str(A) -> lower_bounded_semilattstr(A) & join_of_latt_set(A,empty_set) = bottom_of_semilattstr(A) & latt_str(A) & lattice(A) & -empty_carrier(A))) # label(t50_lattice3) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 521 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 522 (all A all B (relation(A) -> relation(relation_restriction(A,B)))) # label(dt_k2_wellord1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 523 (all A all B (relation(B) -> subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)))) # label(t99_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 524 (all A all B all C (function(B) & relation_of2(B,cartesian_product2(A,A),A) & relation_of2(C,cartesian_product2(A,A),A) & quasi_total(C,cartesian_product2(A,A),A) & function(C) & quasi_total(B,cartesian_product2(A,A),A) & -empty(A) -> strict_latt_str(latt_str_of(A,B,C)) & -empty_carrier(latt_str_of(A,B,C)))) # label(fc3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 525 (all A (relation(A) & function(A) -> (all B ((all C ((exists D (in(D,relation_dom(A)) & apply(A,D) = C)) <-> in(C,B))) <-> B = relation_rng(A))))) # label(d5_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 526 (all A all B (element(B,the_carrier(A)) & top_str(A) & topological_space(A) & -empty_carrier(A) -> (exists C point_neighbourhood(C,A,B)))) # label(existence_m1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 527 (all A (top_str(A) & topological_space(A) & -empty_carrier(A) -> (exists B (closed_subset(B,A) & -empty(B) & element(B,powerset(the_carrier(A))))))) # label(rc7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 528 (all A (being_limit_ordinal(A) <-> A = union(A))) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 529 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 530 (all A (rel_str(A) -> (is_transitive_in(the_InternalRel(A),the_carrier(A)) <-> transitive_relstr(A)))) # label(d5_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 531 (all A all B (relation(B) & function(B) -> relation(relation_rng_restriction(A,B)) & function(relation_rng_restriction(A,B)))) # label(fc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 532 (all A all B exists C all D (in(D,C) <-> (exists E exists F (singleton(E) = F & in(E,A) & D = ordered_pair(E,F))) & in(D,cartesian_product2(A,B)))) # label(s1_xboole_0__e16_22__wellord2__1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 533 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 534 (all A (-empty(A) & relation(A) -> -empty(relation_dom(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 535 (all A (relation(A) & function(A) -> (finite(relation_dom(A)) -> finite(relation_rng(A))))) # label(t26_finset_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 536 (all A (latt_str(A) -> (-empty_carrier(A) & lattice(A) -> -empty_carrier(A) & join_commutative(A) & join_absorbing(A) & meet_absorbing(A) & meet_associative(A) & meet_commutative(A) & join_associative(A)))) # label(cc1_lattices) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 537 (all A all B (v4_membered(A) -> v2_membered(set_intersection2(B,A)) & v4_membered(set_intersection2(B,A)) & v3_membered(set_intersection2(B,A)) & v1_membered(set_intersection2(B,A)))) # label(fc34_membered) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 538 (all A (lower_bounded_relstr(A) & rel_str(A) & antisymmetric_relstr(A) & -empty_carrier(A) -> (all B (element(B,the_carrier(A)) -> related(A,bottom_of_relstr(A),B))))) # label(t44_yellow_0) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 539 (all A (-empty_carrier(A) & latt_str(A) & lattice(A) -> rel_str_of(the_carrier(A),k2_lattice3(A)) = poset_of_lattice(A))) # label(d2_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 540 (all A (relation(A) -> relation_dom(A) = relation_rng(relation_inverse(A)) & relation_dom(relation_inverse(A)) = relation_rng(A))) # label(t37_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.66 541 (all A all B (ordinal(B) -> ((all C all D all E ((exists G (E = G & in(G,A) & ordinal(G))) & C = E & (exists F (D = F & in(F,A) & ordinal(F))) & C = D -> D = E)) -> (exists C all D (in(D,C) <-> (exists E (in(E,succ(B)) & (exists H (H = D & in(H,A) & ordinal(H))) & E = D))))))) # label(s1_tarski__e8_6__wellord2__1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 542 (all A all B (finite(A) -> finite(set_intersection2(A,B)))) # label(fc11_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.66 543 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 544 (all A (rel_str(A) -> (strict_rel_str(A) -> rel_str_of(the_carrier(A),the_InternalRel(A)) = A))) # label(abstractness_v1_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 545 (all A (rel_str(A) -> (all B (subrelstr(B,A) -> (all C (element(C,the_carrier(A)) -> (all D (element(D,the_carrier(A)) -> (all E (element(E,the_carrier(B)) -> (all F (element(F,the_carrier(B)) -> (C = E & related(B,E,F) & F = D -> related(A,C,D)))))))))))))) # label(t60_yellow_0) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 546 (all A ((exists B exists C ordered_pair(B,C) = A) -> (all B (pair_first(A) = B <-> (all C all D (A = ordered_pair(C,D) -> B = C)))))) # label(d1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 547 (all A all B all C (function(C) & relation(C) & relation(B) -> (exists D all E (in(E,cartesian_product2(A,A)) & (exists F exists G (E = ordered_pair(F,G) & in(ordered_pair(apply(C,F),apply(C,G)),B))) <-> in(E,D))))) # label(s1_xboole_0__e6_21__wellord2__1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 548 (all A (relation(A) & function(A) -> (all B all C apply(A,ordered_pair(B,C)) = apply_binary(A,B,C)))) # label(d1_binop_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 549 (all A all B (relation(B) & -empty(A) -> ((all C all D all E ((exists H (H = C & (all I (in(I,H) -> in(ordered_pair(E,I),B))) & in(E,H))) & in(C,A) & (exists F (in(D,F) & (all G (in(G,F) -> in(ordered_pair(D,G),B))) & C = F)) & in(C,A) -> D = E)) -> (exists C all D ((exists E (in(E,A) & (exists J (E = J & (all K (in(K,J) -> in(ordered_pair(D,K),B))) & in(D,J))) & in(E,A))) <-> in(D,C)))))) # label(s1_tarski__e10_24__wellord2__1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 550 (all A all B all C all D (-empty(A) & element(D,A) & relation_of2(C,A,B) & quasi_total(C,A,B) & function(C) -> apply_as_element(A,B,C,D) = apply(C,D))) # label(redefinition_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 551 (all A all B all C (subset(A,B) & subset(C,B) -> subset(set_union2(A,C),B))) # label(t8_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 552 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 553 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 554 (all A all B (ordinal(B) -> (exists C all D (in(D,succ(B)) & (exists E (E = D & in(E,A) & ordinal(E))) <-> in(D,C))))) # label(s1_xboole_0__e8_6__wellord2__1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 555 (all A (relation(A) -> (all B relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B))))) # label(d6_wellord1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 556 (all A union(powerset(A)) = A) # label(t99_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 557 (all A all B (relation(B) -> (well_ordering(B) & subset(A,relation_field(B)) -> relation_field(relation_restriction(B,A)) = A))) # label(t39_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 558 (all A (top_str(A) -> one_sorted_str(A))) # label(dt_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 559 (all A all B (relation(B) & relation(A) -> relation(set_intersection2(A,B)))) # label(fc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 560 (all A all B ((empty(A) -> (element(B,A) <-> empty(B))) & (-empty(A) -> (in(B,A) <-> element(B,A))))) # label(d2_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 561 (all A (ordinal(A) -> epsilon_transitive(succ(A)) & ordinal(succ(A)) & epsilon_connected(succ(A)) & -empty(succ(A)))) # label(fc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 562 (all A all B all C (C = set_difference(A,B) <-> (all D (in(D,C) <-> in(D,A) & -in(D,B))))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 563 (all A all B all C (-empty_carrier(A) & join_semilatt_str(A) & element(C,the_carrier(A)) & element(B,the_carrier(A)) & join_commutative(A) -> element(join_commut(A,B,C),the_carrier(A)))) # label(dt_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 564 (all A (v2_membered(A) -> (all B (element(B,A) -> v1_xreal_0(B) & v1_xcmplx_0(B))))) # label(cc11_membered) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 565 (all A all B (function(A) & relation(B) & function(B) & relation(A) -> relation(relation_composition(A,B)) & function(relation_composition(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 566 (all A (topological_space(A) & top_str(A) -> closed_subset(cast_as_carrier_subset(A),A))) # label(fc5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 567 (all A (one_sorted_str(A) & -empty_carrier(A) -> (all B (net_str(B,A) & -empty_carrier(B) -> (all C (element(C,the_carrier(B)) -> apply_on_structs(B,A,the_mapping(A,B),C) = apply_netmap(A,B,C))))))) # label(d8_waybel_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 568 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 569 (all A (one_sorted_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> subset_difference(the_carrier(A),cast_as_carrier_subset(A),subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)) = B)))) # label(t22_pre_topc) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 570 (all A all B (finite(unordered_pair(A,B)) & -empty(unordered_pair(A,B)))) # label(fc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 571 (all A all B (in(A,B) <-> subset(singleton(A),B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 572 (all A all B all C (relation_of2_as_subset(C,A,B) -> element(C,powerset(cartesian_product2(A,B))))) # label(dt_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 573 (all A all B ((all C (in(C,A) -> in(C,B))) -> element(A,powerset(B)))) # label(l71_subset_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 574 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 575 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 576 (all A all B (element(B,powerset(powerset(the_carrier(A)))) & one_sorted_str(A) -> ((all C all D all E (in(C,B) & (all G (element(G,powerset(the_carrier(A))) -> (C = G -> subset_complement(the_carrier(A),G) = E))) & (all F (element(F,powerset(the_carrier(A))) -> (C = F -> subset_complement(the_carrier(A),F) = D))) & in(C,B) -> D = E)) -> (exists C (relation(C) & function(C) & (all D all E (in(D,B) & (all H (element(H,powerset(the_carrier(A))) -> (H = D -> E = subset_complement(the_carrier(A),H)))) & in(D,B) <-> in(ordered_pair(D,E),C)))))))) # label(s1_funct_1__e4_7_2__tops_2__1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 577 (all A all B all C (element(B,powerset(powerset(A))) & relation(C) & function(C) -> (exists D all E (in(relation_image(C,E),B) & in(E,powerset(relation_dom(C))) <-> in(E,D))))) # label(s1_xboole_0__e6_27__finset_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 578 (all A all B (finite(B) & finite(A) -> finite(set_union2(A,B)))) # label(fc9_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 579 (all A (v2_membered(A) -> (all B (element(B,powerset(A)) -> v1_membered(B) & v2_membered(B))))) # label(cc17_membered) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 580 (all A all B all C (relation_of2(C,A,B) -> (quasi_total(C,A,B) & onto(C,A,B) & one_to_one(C) & function(C) -> quasi_total(C,A,B) & bijective(C,A,B) & function(C)))) # label(cc3_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 581 (all A all B (relation(B) & function(B) -> (all C (function(C) & relation(C) -> (in(A,relation_dom(B)) -> apply(C,apply(B,A)) = apply(relation_composition(B,C),A)))))) # label(t23_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 582 (all A (one_sorted_str(A) & -empty_carrier(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 583 (all A (ordinal(A) -> ((all B (ordinal(B) -> (in(B,A) -> (in(B,omega) -> (all C (element(C,powerset(powerset(B))) -> -((all D -(in(D,C) & (all E (in(E,C) & subset(D,E) -> D = E)))) & empty_set != C))))))) -> (in(A,omega) -> (all F (element(F,powerset(powerset(A))) -> -((all G -((all H (subset(G,H) & in(H,F) -> G = H)) & in(G,F))) & F != empty_set))))))) -> (all A (ordinal(A) -> (in(A,omega) -> (all I (element(I,powerset(powerset(A))) -> -((all J -((all K (in(K,I) & subset(J,K) -> K = J)) & in(J,I))) & I != empty_set)))))) # label(s2_ordinal1__e18_27__finset_1__1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 584 (all A (meet_associative(A) & meet_semilatt_str(A) & -empty_carrier(A) -> function(the_L_meet(A)) & v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & v2_binop_1(the_L_meet(A),the_carrier(A)) & quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & relation(the_L_meet(A)))) # label(fc5_lattice2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 585 (all A all B (relation(B) -> -(well_ordering(B) & (all C (relation(C) -> -well_orders(C,A))) & equipotent(A,relation_field(B))))) # label(l30_wellord2) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 586 (all A singleton(A) = unordered_pair(A,A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 587 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 588 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 589 (all A all B ((all C (in(C,B) <-> in(C,A))) -> B = A)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 590 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 591 (all A all B (element(B,powerset(powerset(A))) -> (B != empty_set -> union_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,meet_of_subsets(A,B))))) # label(t12_tops_2) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 592 (all A all B (topological_space(A) & top_str(A) & element(B,powerset(powerset(the_carrier(A)))) -> ((all C all D all E (C = D & E = C & in(set_difference(cast_as_carrier_subset(A),E),B) & in(set_difference(cast_as_carrier_subset(A),D),B) -> D = E)) -> (exists C all D ((exists E (in(set_difference(cast_as_carrier_subset(A),D),B) & E = D & in(E,powerset(the_carrier(A))))) <-> in(D,C)))))) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 593 (all A (relation(A) -> (all B (is_connected_in(A,B) <-> (all C all D -(C != D & -in(ordered_pair(D,C),A) & -in(ordered_pair(C,D),A) & in(D,B) & in(C,B))))))) # label(d6_relat_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 594 (all A (rel_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> ((all C (element(C,the_carrier(A)) -> (all D (element(D,the_carrier(A)) -> -(in(D,B) & (all E (element(E,the_carrier(A)) -> -(related(A,D,E) & related(A,C,E) & in(E,B)))) & in(C,B)))))) <-> directed_subset(B,A)))))) # label(d1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 595 (exists A (relation(A) & function(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 596 (all A (empty(A) -> empty(relation_inverse(A)) & relation(relation_inverse(A)))) # label(fc11_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 597 (all A all B all C (meet_commutative(A) & meet_semilatt_str(A) & element(C,the_carrier(A)) & element(B,the_carrier(A)) & -empty_carrier(A) -> element(meet_commut(A,B,C),the_carrier(A)))) # label(dt_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 598 (all A all B (relation(B) -> relation_image(B,set_intersection2(relation_dom(B),A)) = relation_image(B,A))) # label(t145_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 599 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 600 (all A (top_str(A) -> (all B (element(B,powerset(powerset(the_carrier(A)))) -> (closed_subsets(B,A) <-> (all C (element(C,powerset(the_carrier(A))) -> (in(C,B) -> closed_subset(C,A))))))))) # label(d2_tops_2) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 601 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 602 (all A all B all C all D (-empty(B) & element(C,A) & element(D,B) & -empty(A) -> ordered_pair_as_product_element(A,B,C,D) = ordered_pair(C,D))) # label(redefinition_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 603 (all A (relation(A) -> (all B all C (relation(C) -> (C = relation_dom_restriction(A,B) <-> (all D all E (in(ordered_pair(D,E),A) & in(D,B) <-> in(ordered_pair(D,E),C)))))))) # label(d11_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 604 (all A all B (-empty_carrier(A) & lattice(A) & latt_str(A) & element(B,the_carrier(poset_of_lattice(A))) -> element(cast_to_el_of_lattice(A,B),the_carrier(A)))) # label(dt_k5_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 605 (all A all B (element(B,powerset(powerset(A))) -> element(complements_of_subsets(A,B),powerset(powerset(A))))) # label(dt_k7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 606 (all A (one_sorted_str(A) -> element(empty_carrier_subset(A),powerset(the_carrier(A))))) # label(dt_k1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 607 (all A (empty_set != A -> (all B (element(B,powerset(A)) -> (all C (element(C,A) -> (-in(C,B) -> in(C,subset_complement(A,B))))))))) # label(t50_subset_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 608 (all A all B -(in(A,B) & (all C -((all D -(in(D,B) & in(D,C))) & in(C,B))))) # label(t7_tarski) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 609 (all A exists B (relation(B) & well_orders(B,A))) # label(t26_wellord2) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 610 (all A (ordinal(A) -> -(-being_limit_ordinal(A) & (all B (ordinal(B) -> succ(B) != A))) & -((exists B (ordinal(B) & A = succ(B))) & being_limit_ordinal(A)))) # label(t42_ordinal1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 611 (all A all B (relation(B) -> subset(relation_rng(relation_rng_restriction(A,B)),A))) # label(t116_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 612 (all A all B all C all D ((all E (-(C != E & E != B & A != E) <-> in(E,D))) <-> unordered_triple(A,B,C) = D)) # label(d1_enumset1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 613 (all A all B (subset(A,B) -> B = set_union2(A,B))) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 614 (all A (rel_str(A) -> (all B ((exists C ((all D (element(D,the_carrier(A)) -> (relstr_set_smaller(A,B,D) & (all E (element(E,the_carrier(A)) -> (relstr_set_smaller(A,B,E) -> related(A,D,E)))) -> C = D))) & (all D (element(D,the_carrier(A)) -> (relstr_set_smaller(A,B,D) -> related(A,C,D)))) & relstr_set_smaller(A,B,C) & element(C,the_carrier(A)))) <-> ex_sup_of_relstr_set(A,B))))) # label(d7_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 615 (all A all B all C all D (-empty_carrier(A) & lattice(A) & latt_str(A) & -empty_carrier(B) & latt_str(B) & element(C,the_carrier(A)) & element(D,the_carrier(B)) & lattice(B) -> element(k10_filter_1(A,B,C,D),the_carrier(k8_filter_1(A,B))))) # label(dt_k10_filter_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 616 (all A all B all C (element(C,powerset(A)) & element(B,powerset(A)) -> subset_union2(A,C,B) = subset_union2(A,B,C))) # label(commutativity_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 617 (exists A (-empty_carrier(A) & join_associative(A) & meet_associative(A) & join_absorbing(A) & lattice(A) & meet_absorbing(A) & meet_commutative(A) & join_commutative(A) & strict_latt_str(A) & latt_str(A))) # label(rc9_lattices) # label(axiom) # label(non_clause). [assumption]. 1.43/1.67 618 (all A all B (subset(singleton(A),singleton(B)) -> B = A)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 619 (all A all B (relation(B) -> subset(relation_rng_restriction(A,B),B))) # label(t117_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 620 (all A all B (set_difference(A,singleton(B)) = A <-> -in(B,A))) # label(t65_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.43/1.67 621 (all A (ordinal(A) -> epsilon_connected(A) & epsilon_transitive(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 622 (all A all B (v3_membered(A) -> v1_membered(set_intersection2(A,B)) & v3_membered(set_intersection2(A,B)) & v2_membered(set_intersection2(A,B)))) # label(fc31_membered) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 623 (all A all B (relation(B) & function(B) -> (all C (relation(C) & function(C) -> (relation_dom(B) = set_intersection2(relation_dom(C),A) & (all D (in(D,relation_dom(B)) -> apply(C,D) = apply(B,D))) <-> B = relation_dom_restriction(C,A)))))) # label(t68_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.63/1.86 624 (all A all B exists C (relation_of2(C,A,B) & function(C) & quasi_total(C,A,B) & relation(C))) # label(rc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 625 (all A (-empty(A) -> -((all B -(empty_set = B & in(B,A))) & (all B (function(B) & relation(B) -> -(relation_dom(B) = A & (all C (in(C,A) -> in(apply(B,C),C))))))))) # label(t28_wellord2) # label(lemma) # label(non_clause). [assumption]. 1.63/1.86 626 (all A all B all C (relation(C) -> relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B)))) # label(t140_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.63/1.86 627 (all A empty_set = set_intersection2(A,empty_set)) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 628 (all A (relation(A) -> (transitive(A) <-> is_transitive_in(A,relation_field(A))))) # label(d16_relat_2) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 629 (all A (rel_str(A) -> one_sorted_str(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 630 (all A (ordinal(A) -> (all B (ordinal(B) -> -(-in(B,A) & B != A & -in(A,B)))))) # label(t24_ordinal1) # label(lemma) # label(non_clause). [assumption]. 1.63/1.86 631 (all A all B (element(B,A) -> (proper_element(B,A) <-> union(A) != B))) # label(d2_tex_2) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 632 (all A (epsilon_transitive(A) -> (all B (ordinal(B) -> (proper_subset(A,B) -> in(A,B)))))) # label(t21_ordinal1) # label(lemma) # label(non_clause). [assumption]. 1.63/1.86 633 (all D (ordinal(D) -> ((in(D,omega) -> (all E (element(E,powerset(powerset(D))) -> -((all F -((all G (subset(F,G) & in(G,E) -> F = G)) & in(F,E))) & empty_set != E)))) -> (in(succ(D),omega) -> (all H (element(H,powerset(powerset(succ(D)))) -> -(H != empty_set & (all I -((all J (in(J,H) & subset(I,J) -> I = J)) & in(I,H)))))))))) & (all D (ordinal(D) -> ((all K (ordinal(K) -> (in(K,D) -> (in(K,omega) -> (all L (element(L,powerset(powerset(K))) -> -(empty_set != L & (all M -((all N (in(N,L) & subset(M,N) -> N = M)) & in(M,L)))))))))) & being_limit_ordinal(D) -> (in(D,omega) -> (all O (element(O,powerset(powerset(D))) -> -(empty_set != O & (all P -(in(P,O) & (all Q (in(Q,O) & subset(P,Q) -> P = Q)))))))) | D = empty_set))) & (in(empty_set,omega) -> (all A (element(A,powerset(powerset(empty_set))) -> -((all B -((all C (subset(B,C) & in(C,A) -> C = B)) & in(B,A))) & A != empty_set)))) -> (all D (ordinal(D) -> (in(D,omega) -> (all R (element(R,powerset(powerset(D))) -> -((all S -((all T (in(T,R) & subset(S,T) -> S = T)) & in(S,R))) & R != empty_set)))))) # label(s1_ordinal2__e18_27__finset_1) # label(lemma) # label(non_clause). [assumption]. 1.63/1.86 634 (all A (v1_membered(A) -> (all B (element(B,A) -> v1_xcmplx_0(B))))) # label(cc10_membered) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 635 (all A (element(A,omega) -> epsilon_connected(A) & natural(A) & ordinal(A) & epsilon_transitive(A))) # label(cc3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 636 (all A all B (-empty_carrier(B) & latt_str(B) & lattice(B) -> (all C (element(C,the_carrier(poset_of_lattice(B))) -> (latt_set_smaller(B,cast_to_el_of_lattice(B,C),A) <-> relstr_element_smaller(poset_of_lattice(B),A,C)))))) # label(t29_lattice3) # label(lemma) # label(non_clause). [assumption]. 1.63/1.86 637 (all A (relation(A) -> (all B all C ((all D (in(D,C) <-> D != B & in(ordered_pair(D,B),A))) <-> C = fiber(A,B))))) # label(d1_wellord1) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 638 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 639 (all A (one_sorted_str(A) -> empty_set = empty_carrier_subset(A))) # label(d2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 640 (all A (relation(A) -> relation_rng(A) = relation_image(A,relation_dom(A)))) # label(t146_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.63/1.86 641 (all A all B (v1_membered(A) -> v1_membered(set_difference(A,B)))) # label(fc37_membered) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 642 (exists A join_semilatt_str(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 643 (all A all B A = set_intersection2(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 644 (all A all B (strict_latt_str(B) & latt_str(B) -> ((all C (element(C,powerset(A)) -> (all D (element(D,powerset(A)) -> subset_union2(A,C,D) = apply_binary(the_L_join(B),C,D) & apply_binary(the_L_meet(B),C,D) = subset_intersection2(A,C,D))))) & the_carrier(B) = powerset(A) <-> boole_lattice(A) = B))) # label(d1_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 645 (all A all B (empty_set = set_intersection2(A,B) <-> disjoint(A,B))) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 646 (all A ((exists B exists C A = ordered_pair(B,C)) -> (all B (pair_second(A) = B <-> (all C all D (ordered_pair(C,D) = A -> D = B)))))) # label(d2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 647 (all A (rel_str(A) -> (lower_bounded_relstr(A) <-> (exists B (relstr_element_smaller(A,the_carrier(A),B) & element(B,the_carrier(A))))))) # label(d4_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 648 (all A all B (relation(B) -> (connected(B) -> connected(relation_restriction(B,A))))) # label(t23_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.63/1.86 649 (all A (relation(A) -> (all B ((all C all D all E (in(C,B) & in(D,B) & in(E,B) & in(ordered_pair(D,E),A) & in(ordered_pair(C,D),A) -> in(ordered_pair(C,E),A))) <-> is_transitive_in(A,B))))) # label(d8_relat_2) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 650 (all A all B ((empty_set = A -> (B = empty_set <-> set_meet(A) = B)) & (A != empty_set -> (B = set_meet(A) <-> (all C (in(C,B) <-> (all D (in(D,A) -> in(C,D))))))))) # label(d1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 651 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 652 (all A (meet_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 653 (all A all B all C (relation_of2(C,A,B) -> (v1_partfun1(C,A,B) & function(C) -> function(C) & quasi_total(C,A,B)))) # label(cc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 654 (all A element(k1_pcomps_1(A),powerset(powerset(A)))) # label(dt_k1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 655 (all A all B all C (-empty_carrier(A) & one_sorted_str(A) & element(C,the_carrier(A)) & element(B,the_carrier(A)) -> unordered_pair(B,C) = unordered_pair_as_carrier_subset(A,B,C))) # label(redefinition_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 656 (all A (relation(A) -> (all B (relation(B) -> (all C (relation(C) & function(C) -> (relation_isomorphism(A,B,C) & well_ordering(A) -> well_ordering(B)))))))) # label(t54_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.63/1.86 657 (all A all B (one_sorted_str(A) & element(B,powerset(powerset(the_carrier(A)))) -> ((all C all D all E ((all F (element(F,powerset(the_carrier(A))) -> (C = F -> D = subset_complement(the_carrier(A),F)))) & in(C,complements_of_subsets(the_carrier(A),B)) & (all G (element(G,powerset(the_carrier(A))) -> (C = G -> subset_complement(the_carrier(A),G) = E))) & in(C,complements_of_subsets(the_carrier(A),B)) -> E = D)) -> (exists C (relation(C) & (all D all E (in(ordered_pair(D,E),C) <-> in(D,complements_of_subsets(the_carrier(A),B)) & in(D,complements_of_subsets(the_carrier(A),B)) & (all H (element(H,powerset(the_carrier(A))) -> (H = D -> E = subset_complement(the_carrier(A),H)))))) & function(C)))))) # label(s1_funct_1__e4_7_1__tops_2__1) # label(lemma) # label(non_clause). [assumption]. 1.63/1.86 658 (all A (top_str(A) -> ((all B (element(B,powerset(the_carrier(A))) -> (all C (element(C,powerset(the_carrier(A))) -> (in(B,the_topology(A)) & in(C,the_topology(A)) -> in(subset_intersection2(the_carrier(A),B,C),the_topology(A))))))) & (all B (element(B,powerset(powerset(the_carrier(A)))) -> (subset(B,the_topology(A)) -> in(union_of_subsets(the_carrier(A),B),the_topology(A))))) & in(the_carrier(A),the_topology(A)) <-> topological_space(A)))) # label(d1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 659 (all A (relation(A) -> (all B ((all C -((all D -(disjoint(fiber(A,D),C) & in(D,C))) & C != empty_set & subset(C,B))) <-> is_well_founded_in(A,B))))) # label(d3_wellord1) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 660 (all A (function(A) & relation(A) -> (all B all C ((all D (in(D,relation_dom(A)) & in(apply(A,D),B) <-> in(D,C))) <-> C = relation_inverse_image(A,B))))) # label(d13_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 661 (all A (latt_str(A) & -empty_carrier(A) -> (-empty_carrier(A) & lattice(A) & complete_latt_str(A) & latt_str(A) -> (all B all C (element(C,the_carrier(A)) -> ((all D (element(D,the_carrier(A)) -> (latt_element_smaller(A,D,B) -> below(A,C,D)))) & latt_element_smaller(A,C,B) <-> C = join_of_latt_set(A,B))))))) # label(d21_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 662 (all A all B (ordinal(B) -> -(subset(A,B) & empty_set != A & (all C (ordinal(C) -> -(in(C,A) & (all D (ordinal(D) -> (in(D,A) -> ordinal_subset(C,D)))))))))) # label(t32_ordinal1) # label(lemma) # label(non_clause). [assumption]. 1.63/1.86 663 (all A all B (antisymmetric(B) & relation_of2(B,A,A) & v1_partfun1(B,A,A) & transitive(B) & reflexive(B) -> transitive_relstr(rel_str_of(A,B)) & antisymmetric_relstr(rel_str_of(A,B)) & reflexive_relstr(rel_str_of(A,B)) & strict_rel_str(rel_str_of(A,B)))) # label(fc3_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 664 (all A (relation(A) -> (relation_dom(A) = empty_set | relation_rng(A) = empty_set -> A = empty_set))) # label(t64_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.63/1.86 665 (all A all B (relation(B) -> relation_dom_restriction(B,A) = relation_composition(identity_relation(A),B))) # label(t94_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.63/1.86 666 (all A (-empty_carrier(A) & join_commutative(A) & join_semilatt_str(A) -> relation(the_L_join(A)) & function(the_L_join(A)) & quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & v1_binop_1(the_L_join(A),the_carrier(A)) & v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))) # label(fc2_lattice2) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 667 (all A all B (relation(B) -> subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)))) # label(l29_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.63/1.86 668 (exists A latt_str(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 669 (all A all B (latt_str(A) & element(B,the_carrier(A)) & lattice(A) & -empty_carrier(A) -> element(cast_to_el_of_LattPOSet(A,B),the_carrier(poset_of_lattice(A))))) # label(dt_k4_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 670 (all A all B unordered_pair(unordered_pair(A,B),singleton(A)) = ordered_pair(A,B)) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 671 (all A (empty(A) -> finite(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 672 (all A (relation(A) -> relation_inverse(relation_inverse(A)) = A)) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.63/1.86 673 (all A all B all C (-empty_carrier(A) & one_sorted_str(A) & element(C,the_carrier(A)) & element(B,the_carrier(A)) -> unordered_pair_as_carrier_subset(A,B,C) = unordered_pair_as_carrier_subset(A,C,B))) # label(commutativity_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 1.63/1.87 674 (all A all B (v1_membered(A) -> v1_membered(set_intersection2(B,A)))) # label(fc28_membered) # label(axiom) # label(non_clause). [assumption]. 1.63/1.87 675 (all A (-empty_carrier(A) & meet_semilatt_str(A) -> element(bottom_of_semilattstr(A),the_carrier(A)))) # label(dt_k5_lattices) # label(axiom) # label(non_clause). [assumption]. 1.63/1.87 676 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 1.63/1.87 677 (all A all B all C (complete_latt_str(B) & latt_str(B) & lattice(B) & -empty_carrier(B) -> ((exists D (A = D & latt_set_smaller(B,D,C) & element(D,the_carrier(B)))) <-> in(A,a_2_3_lattice3(B,C))))) # label(fraenkel_a_2_3_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.63/1.87 678 (exists A (-empty_carrier(A) & strict_latt_str(A) & latt_str(A))) # label(rc6_lattices) # label(axiom) # label(non_clause). [assumption]. 1.63/1.87 679 (all A (empty(A) -> v1_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) & v2_membered(A))) # label(cc15_membered) # label(axiom) # label(non_clause). [assumption]. 1.63/1.87 680 (all A (function(identity_relation(A)) & reflexive(identity_relation(A)) & transitive(identity_relation(A)) & antisymmetric(identity_relation(A)) & symmetric(identity_relation(A)) & relation(identity_relation(A)))) # label(fc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 1.63/1.87 681 (exists A (-empty(A) & epsilon_transitive(A) & epsilon_connected(A) & ordinal(A) & natural(A))) # label(rc1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 1.63/1.87 682 (exists A (relation(A) & empty(A) & function(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.63/1.87 683 (all A (top_str(A) -> element(the_topology(A),powerset(powerset(the_carrier(A)))))) # label(dt_u1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.63/1.87 684 (all A all B (relation(B) -> (well_ordering(B) -> well_ordering(relation_restriction(B,A))))) # label(t32_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.63/1.87 685 (all A (one_sorted_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B))))) # label(t17_pre_topc) # label(lemma) # label(non_clause). [assumption]. 1.63/1.87 686 (all A (relation(A) -> (all B (relation(B) -> (subset(relation_dom(A),relation_rng(B)) -> relation_rng(A) = relation_rng(relation_composition(B,A))))))) # label(t47_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.63/1.87 687 (all A all B all C all D (relation_of2_as_subset(D,A,B) & quasi_total(D,A,B) & function(D) -> (in(C,A) -> in(apply(D,C),relation_rng(D)) | B = empty_set))) # label(t6_funct_2) # label(lemma) # label(non_clause). [assumption]. 1.63/1.87 688 (all A all B (function(B) & relation(B) -> (A = relation_dom(B) & (all C (in(C,A) -> apply(B,C) = C)) <-> identity_relation(A) = B))) # label(t34_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.63/1.87 689 (all A (one_sorted_str(A) -> (exists B net_str(B,A)))) # label(existence_l1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 1.63/1.87 690 (all A (top_str(A) -> (all B (element(B,powerset(powerset(the_carrier(A)))) -> ((all C (element(C,powerset(the_carrier(A))) -> (in(C,B) -> open_subset(C,A)))) <-> open_subsets(B,A)))))) # label(d1_tops_2) # label(axiom) # label(non_clause). [assumption]. 1.63/1.87 691 (all A (relation(A) -> (all B (relation(B) -> ((all C all D (in(ordered_pair(C,D),B) <-> in(ordered_pair(C,D),A))) <-> B = A))))) # label(d2_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.63/1.87 692 (all A (relation(A) -> (all B (relation(B) -> subset(relation_dom(relation_composition(A,B)),relation_dom(A)))))) # label(t44_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.63/1.87 693 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.63/1.87 694 (all A all B (in(B,A) -> B = apply(identity_relation(A),B))) # label(t35_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.63/1.87 695 (all A (epsilon_connected(A) <-> (all B all C -(-in(C,B) & B != C & -in(B,C) & in(C,A) & in(B,A))))) # label(d3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.76/2.04 696 (all A all B all C (-empty_carrier(A) & reflexive_relstr(A) & element(C,the_carrier(A)) & element(B,the_carrier(A)) & rel_str(A) -> related_reflexive(A,B,B))) # label(reflexivity_r3_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.76/2.04 697 (all A (topological_space(A) & top_str(A) -> (all B (top_str(B) -> (all C (element(C,powerset(the_carrier(A))) -> (all D (element(D,powerset(the_carrier(B))) -> (open_subset(D,B) -> interior(B,D) = D) & (C = interior(A,C) -> open_subset(C,A)))))))))) # label(t55_tops_1) # label(lemma) # label(non_clause). [assumption]. 1.76/2.04 698 (all A (relation_dom(identity_relation(A)) = A & A = relation_rng(identity_relation(A)))) # label(t71_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.76/2.04 699 (all A all B (topological_space(A) & element(B,powerset(the_carrier(A))) & top_str(A) -> closed_subset(topstr_closure(A,B),A))) # label(fc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 1.76/2.04 700 (all A (latt_str(A) & lattice(A) & -empty_carrier(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (below_refl(A,B,C) <-> in(ordered_pair_as_product_element(the_carrier(A),the_carrier(A),B,C),relation_of_lattice(A))))))))) # label(t32_filter_1) # label(lemma) # label(non_clause). [assumption]. 1.76/2.04 701 (all A all B all C (relation(C) -> (in(ordered_pair(A,B),C) -> in(B,relation_field(C)) & in(A,relation_field(C))))) # label(t30_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.76/2.04 702 (all A all B all C (relation_of2(C,A,B) <-> subset(C,cartesian_product2(A,B)))) # label(d1_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.76/2.04 703 (all A all B all C (relation(C) & function(C) -> (in(A,relation_dom(C)) & apply(C,A) = B <-> in(ordered_pair(A,B),C)))) # label(t8_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.76/2.04 704 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.76/2.04 705 (all A exists B (in(A,B) & (all C -(subset(C,B) & -are_equipotent(C,B) & -in(C,B))) & (all C (in(C,B) -> in(powerset(C),B))) & (all C all D (in(C,B) & subset(D,C) -> in(D,B))))) # label(t136_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.76/2.04 706 -(all A (-empty_carrier(A) & one_sorted_str(A) -> (all B (net_str(B,A) & -empty_carrier(B) -> (all C all D (subset(C,D) -> (is_eventually_in(A,B,C) -> is_eventually_in(A,B,D)) & (is_often_in(A,B,C) -> is_often_in(A,B,D)))))))) # label(t8_waybel_0) # label(negated_conjecture) # label(non_clause). [assumption]. 1.76/2.04 1.76/2.04 ============================== end of process non-clausal formulas === 1.76/2.04 1.76/2.04 ============================== PROCESS INITIAL CLAUSES =============== 1.76/2.04 1.76/2.04 ============================== PREDICATE ELIMINATION ================= 1.76/2.04 707 -rel_str(A) | -rel_str(B) | -subset(the_InternalRel(B),the_InternalRel(A)) | -subset(the_carrier(B),the_carrier(A)) | subrelstr(B,A) # label(d13_yellow_0) # label(axiom). [clausify(211)]. 1.76/2.04 708 -rel_str(A) | -subrelstr(B,A) | -full_subrelstr(B,A) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -element(E,the_carrier(B)) | -element(F,the_carrier(B)) | F != D | -in(F,the_carrier(B)) | -in(E,the_carrier(B)) | -related(A,C,D) | E != C | related(B,E,F) # label(t61_yellow_0) # label(lemma). [clausify(10)]. 1.76/2.04 709 -rel_str(A) | -subrelstr(B,A) | relation_restriction_as_relation_of(the_InternalRel(A),the_carrier(B)) != the_InternalRel(B) | full_subrelstr(B,A) # label(d14_yellow_0) # label(axiom). [clausify(43)]. 1.76/2.04 710 -rel_str(A) | -subrelstr(B,A) | relation_restriction_as_relation_of(the_InternalRel(A),the_carrier(B)) = the_InternalRel(B) | -full_subrelstr(B,A) # label(d14_yellow_0) # label(axiom). [clausify(43)]. 1.76/2.04 Derived: -rel_str(A) | -rel_str(B) | -subset(the_InternalRel(B),the_InternalRel(A)) | -subset(the_carrier(B),the_carrier(A)) | -rel_str(A) | -full_subrelstr(B,A) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -element(E,the_carrier(B)) | -element(F,the_carrier(B)) | F != D | -in(F,the_carrier(B)) | -in(E,the_carrier(B)) | -related(A,C,D) | E != C | related(B,E,F). [resolve(707,e,708,b)]. 3.71/3.94 Derived: -rel_str(A) | -rel_str(B) | -subset(the_InternalRel(B),the_InternalRel(A)) | -subset(the_carrier(B),the_carrier(A)) | -rel_str(A) | relation_restriction_as_relation_of(the_InternalRel(A),the_carrier(B)) != the_InternalRel(B) | full_subrelstr(B,A). [resolve(707,e,709,b)]. 3.71/3.94 Derived: -rel_str(A) | -rel_str(B) | -subset(the_InternalRel(B),the_InternalRel(A)) | -subset(the_carrier(B),the_carrier(A)) | -rel_str(A) | relation_restriction_as_relation_of(the_InternalRel(A),the_carrier(B)) = the_InternalRel(B) | -full_subrelstr(B,A). [resolve(707,e,710,b)]. 3.71/3.94 711 -rel_str(A) | -rel_str(B) | subset(the_InternalRel(B),the_InternalRel(A)) | -subrelstr(B,A) # label(d13_yellow_0) # label(axiom). [clausify(211)]. 3.71/3.94 712 -rel_str(A) | -rel_str(B) | subset(the_carrier(B),the_carrier(A)) | -subrelstr(B,A) # label(d13_yellow_0) # label(axiom). [clausify(211)]. 3.71/3.94 713 -rel_str(A) | -subrelstr(B,A) | rel_str(B) # label(dt_m1_yellow_0) # label(axiom). [clausify(402)]. 3.71/3.94 714 -rel_str(A) | subrelstr(f302(A),A) # label(existence_m1_yellow_0) # label(axiom). [clausify(424)]. 3.71/3.94 Derived: -rel_str(A) | -rel_str(A) | -full_subrelstr(f302(A),A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -element(D,the_carrier(f302(A))) | -element(E,the_carrier(f302(A))) | E != C | -in(E,the_carrier(f302(A))) | -in(D,the_carrier(f302(A))) | -related(A,B,C) | D != B | related(f302(A),D,E). [resolve(714,b,708,b)]. 3.71/3.94 Derived: -rel_str(A) | -rel_str(A) | relation_restriction_as_relation_of(the_InternalRel(A),the_carrier(f302(A))) != the_InternalRel(f302(A)) | full_subrelstr(f302(A),A). [resolve(714,b,709,b)]. 3.71/3.94 Derived: -rel_str(A) | -rel_str(A) | relation_restriction_as_relation_of(the_InternalRel(A),the_carrier(f302(A))) = the_InternalRel(f302(A)) | -full_subrelstr(f302(A),A). [resolve(714,b,710,b)]. 3.71/3.94 Derived: -rel_str(A) | -rel_str(A) | -rel_str(f302(A)) | subset(the_InternalRel(f302(A)),the_InternalRel(A)). [resolve(714,b,711,d)]. 3.71/3.94 Derived: -rel_str(A) | -rel_str(A) | -rel_str(f302(A)) | subset(the_carrier(f302(A)),the_carrier(A)). [resolve(714,b,712,d)]. 3.71/3.94 Derived: -rel_str(A) | -rel_str(A) | rel_str(f302(A)). [resolve(714,b,713,b)]. 3.71/3.94 715 -rel_str(A) | -subrelstr(B,A) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -element(E,the_carrier(B)) | -element(F,the_carrier(B)) | E != C | -related(B,E,F) | F != D | related(A,C,D) # label(t60_yellow_0) # label(lemma). [clausify(545)]. 3.71/3.94 Derived: -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -element(D,the_carrier(E)) | -element(F,the_carrier(E)) | D != B | -related(E,D,F) | F != C | related(A,B,C) | -rel_str(A) | -rel_str(E) | -subset(the_InternalRel(E),the_InternalRel(A)) | -subset(the_carrier(E),the_carrier(A)). [resolve(715,b,707,e)]. 3.71/3.94 Derived: -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -element(D,the_carrier(f302(A))) | -element(E,the_carrier(f302(A))) | D != B | -related(f302(A),D,E) | E != C | related(A,B,C) | -rel_str(A). [resolve(715,b,714,b)]. 3.71/3.94 716 ordinal(A) | -epsilon_connected(A) | -epsilon_transitive(A) # label(d4_ordinal1) # label(axiom). [clausify(23)]. 3.71/3.94 717 epsilon_connected(c1) # label(rc1_ordinal2) # label(axiom). [clausify(12)]. 3.71/3.94 718 -ordinal(A) | epsilon_connected(A) # label(d4_ordinal1) # label(axiom). [clausify(23)]. 3.71/3.94 Derived: ordinal(c1) | -epsilon_transitive(c1). [resolve(716,b,717,a)]. 3.71/3.94 719 epsilon_connected(c2) # label(rc3_ordinal1) # label(axiom). [clausify(29)]. 3.71/3.94 720 -empty(A) | -ordinal(A) | epsilon_connected(A) # label(cc2_arytm_3) # label(axiom). [clausify(109)]. 3.71/3.94 721 -epsilon_connected(A) | -epsilon_transitive(A) | ordinal(A) # label(cc2_ordinal1) # label(axiom). [clausify(142)]. 3.71/3.94 Derived: -epsilon_transitive(c2) | ordinal(c2). [resolve(721,a,719,a)]. 3.71/3.94 722 -ordinal(A) | epsilon_connected(union(A)) # label(fc4_ordinal1) # label(axiom). [clausify(235)]. 3.71/3.94 723 -ordinal(A) | -natural(A) | epsilon_connected(succ(A)) # label(fc2_arytm_3) # label(axiom). [clausify(265)]. 3.71/3.94 724 -empty(A) | epsilon_connected(A) # label(cc3_ordinal1) # label(axiom). [clausify(304)]. 3.71/3.94 Derived: -empty(A) | ordinal(A) | -epsilon_transitive(A). [resolve(724,b,716,b)]. 5.20/5.45 725 epsilon_connected(c13) # label(rc2_ordinal1) # label(axiom). [clausify(335)]. 5.20/5.45 Derived: ordinal(c13) | -epsilon_transitive(c13). [resolve(725,a,716,b)]. 5.20/5.45 726 -ordinal(A) | -element(B,A) | epsilon_connected(B) # label(cc1_arytm_3) # label(axiom). [clausify(412)]. 5.20/5.45 727 epsilon_connected(c19) # label(rc1_ordinal1) # label(axiom). [clausify(451)]. 5.20/5.45 728 epsilon_connected(f314(A)) # label(rc2_finset_1) # label(axiom). [clausify(466)]. 5.20/5.45 729 epsilon_connected(empty_set) # label(fc2_ordinal1_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom). [assumption]. 5.20/5.45 Derived: ordinal(empty_set) | -epsilon_transitive(empty_set). [resolve(729,a,716,b)]. 5.20/5.45 730 epsilon_connected(omega) # label(fc1_ordinal2_AndRHS_AndRHS_AndRHS) # label(axiom). [assumption]. 5.20/5.45 Derived: ordinal(omega) | -epsilon_transitive(omega). [resolve(730,a,716,b)]. 5.20/5.45 731 -ordinal(A) | epsilon_connected(succ(A)) # label(fc3_ordinal1) # label(axiom). [clausify(561)]. 5.20/5.45 Derived: -ordinal(A) | ordinal(succ(A)) | -epsilon_transitive(succ(A)). [resolve(731,b,716,b)]. 5.20/5.45 732 -ordinal(A) | epsilon_connected(A) # label(cc1_ordinal1) # label(axiom). [clausify(621)]. 5.20/5.45 733 -element(A,omega) | epsilon_connected(A) # label(cc3_arytm_3) # label(axiom). [clausify(635)]. 5.20/5.45 734 epsilon_connected(c35) # label(rc1_arytm_3) # label(axiom). [clausify(681)]. 5.20/5.45 735 -epsilon_connected(A) | in(B,C) | B = C | in(C,B) | -in(B,A) | -in(C,A) # label(d3_ordinal1) # label(axiom). [clausify(695)]. 5.20/5.45 Derived: in(A,B) | A = B | in(B,A) | -in(A,c1) | -in(B,c1). [resolve(735,a,717,a)]. 5.20/5.45 Derived: in(A,B) | A = B | in(B,A) | -in(A,C) | -in(B,C) | -ordinal(C). [resolve(735,a,718,b)]. 5.20/5.45 Derived: in(A,B) | A = B | in(B,A) | -in(A,c2) | -in(B,c2). [resolve(735,a,719,a)]. 5.20/5.45 Derived: in(A,B) | A = B | in(B,A) | -in(A,union(C)) | -in(B,union(C)) | -ordinal(C). [resolve(735,a,722,b)]. 5.20/5.45 Derived: in(A,B) | A = B | in(B,A) | -in(A,succ(C)) | -in(B,succ(C)) | -ordinal(C) | -natural(C). [resolve(735,a,723,c)]. 5.20/5.45 Derived: in(A,B) | A = B | in(B,A) | -in(A,C) | -in(B,C) | -empty(C). [resolve(735,a,724,b)]. 5.20/5.45 Derived: in(A,B) | A = B | in(B,A) | -in(A,c13) | -in(B,c13). [resolve(735,a,725,a)]. 5.20/5.45 Derived: in(A,B) | A = B | in(B,A) | -in(A,C) | -in(B,C) | -ordinal(D) | -element(C,D). [resolve(735,a,726,c)]. 5.20/5.45 Derived: in(A,B) | A = B | in(B,A) | -in(A,c19) | -in(B,c19). [resolve(735,a,727,a)]. 5.20/5.45 Derived: in(A,B) | A = B | in(B,A) | -in(A,f314(C)) | -in(B,f314(C)). [resolve(735,a,728,a)]. 5.20/5.45 Derived: in(A,B) | A = B | in(B,A) | -in(A,empty_set) | -in(B,empty_set). [resolve(735,a,729,a)]. 5.20/5.45 Derived: in(A,B) | A = B | in(B,A) | -in(A,omega) | -in(B,omega). [resolve(735,a,730,a)]. 5.20/5.45 Derived: in(A,B) | A = B | in(B,A) | -in(A,succ(C)) | -in(B,succ(C)) | -ordinal(C). [resolve(735,a,731,b)]. 5.20/5.45 Derived: in(A,B) | A = B | in(B,A) | -in(A,C) | -in(B,C) | -element(C,omega). [resolve(735,a,733,b)]. 5.20/5.45 Derived: in(A,B) | A = B | in(B,A) | -in(A,c35) | -in(B,c35). [resolve(735,a,734,a)]. 5.20/5.45 736 epsilon_connected(A) | -in(f458(A),f457(A)) # label(d3_ordinal1) # label(axiom). [clausify(695)]. 5.20/5.45 Derived: -in(f458(A),f457(A)) | ordinal(A) | -epsilon_transitive(A). [resolve(736,a,716,b)]. 5.20/5.45 Derived: -in(f458(A),f457(A)) | in(B,C) | B = C | in(C,B) | -in(B,A) | -in(C,A). [resolve(736,a,735,a)]. 5.20/5.45 737 epsilon_connected(A) | f458(A) != f457(A) # label(d3_ordinal1) # label(axiom). [clausify(695)]. 5.20/5.45 Derived: f458(A) != f457(A) | ordinal(A) | -epsilon_transitive(A). [resolve(737,a,716,b)]. 5.20/5.45 Derived: f458(A) != f457(A) | in(B,C) | B = C | in(C,B) | -in(B,A) | -in(C,A). [resolve(737,a,735,a)]. 5.20/5.45 738 epsilon_connected(A) | -in(f457(A),f458(A)) # label(d3_ordinal1) # label(axiom). [clausify(695)]. 5.20/5.45 Derived: -in(f457(A),f458(A)) | ordinal(A) | -epsilon_transitive(A). [resolve(738,a,716,b)]. 5.20/5.45 Derived: -in(f457(A),f458(A)) | in(B,C) | B = C | in(C,B) | -in(B,A) | -in(C,A). [resolve(738,a,735,a)]. 5.20/5.45 739 epsilon_connected(A) | in(f458(A),A) # label(d3_ordinal1) # label(axiom). [clausify(695)]. 5.20/5.45 Derived: in(f458(A),A) | ordinal(A) | -epsilon_transitive(A). [resolve(739,a,716,b)]. 5.20/5.45 Derived: in(f458(A),A) | in(B,C) | B = C | in(C,B) | -in(B,A) | -in(C,A). [resolve(739,a,735,a)]. 5.38/5.62 740 epsilon_connected(A) | in(f457(A),A) # label(d3_ordinal1) # label(axiom). [clausify(695)]. 5.38/5.62 Derived: in(f457(A),A) | ordinal(A) | -epsilon_transitive(A). [resolve(740,a,716,b)]. 5.38/5.62 Derived: in(f457(A),A) | in(B,C) | B = C | in(C,B) | -in(B,A) | -in(C,A). [resolve(740,a,735,a)]. 5.38/5.62 741 -rel_str(A) | antisymmetric_relstr(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)) # label(d6_orders_2) # label(axiom). [clausify(89)]. 5.38/5.62 742 -rel_str(A) | -antisymmetric_relstr(A) | -element(B,the_carrier(A)) | element(f6(A,B,C),the_carrier(A)) | -relstr_set_smaller(A,C,B) | join_on_relstr(A,C) = B # label(t30_yellow_0) # label(lemma). [clausify(24)]. 5.38/5.62 743 -rel_str(A) | -antisymmetric_relstr(A) | -element(B,the_carrier(A)) | element(f6(A,B,C),the_carrier(A)) | -relstr_set_smaller(A,C,B) | ex_sup_of_relstr_set(A,C) # label(t30_yellow_0) # label(lemma). [clausify(24)]. 5.38/5.62 744 -rel_str(A) | -antisymmetric_relstr(A) | -element(B,the_carrier(A)) | relstr_set_smaller(A,C,f6(A,B,C)) | -relstr_set_smaller(A,C,B) | join_on_relstr(A,C) = B # label(t30_yellow_0) # label(lemma). [clausify(24)]. 5.38/5.62 745 -rel_str(A) | -antisymmetric_relstr(A) | -element(B,the_carrier(A)) | relstr_set_smaller(A,C,f6(A,B,C)) | -relstr_set_smaller(A,C,B) | ex_sup_of_relstr_set(A,C) # label(t30_yellow_0) # label(lemma). [clausify(24)]. 5.38/5.62 746 -rel_str(A) | -antisymmetric_relstr(A) | -element(B,the_carrier(A)) | -related(A,B,f6(A,B,C)) | -relstr_set_smaller(A,C,B) | join_on_relstr(A,C) = B # label(t30_yellow_0) # label(lemma). [clausify(24)]. 5.38/5.62 747 -rel_str(A) | -antisymmetric_relstr(A) | -element(B,the_carrier(A)) | -related(A,B,f6(A,B,C)) | -relstr_set_smaller(A,C,B) | ex_sup_of_relstr_set(A,C) # label(t30_yellow_0) # label(lemma). [clausify(24)]. 5.38/5.62 748 -rel_str(A) | -antisymmetric_relstr(A) | -element(B,the_carrier(A)) | -ex_sup_of_relstr_set(A,C) | join_on_relstr(A,C) != B | -element(D,the_carrier(A)) | -relstr_set_smaller(A,C,D) | related(A,B,D) # label(t30_yellow_0) # label(lemma). [clausify(24)]. 5.38/5.62 749 -rel_str(A) | -antisymmetric_relstr(A) | -element(B,the_carrier(A)) | -ex_sup_of_relstr_set(A,C) | join_on_relstr(A,C) != B | relstr_set_smaller(A,C,B) # label(t30_yellow_0) # label(lemma). [clausify(24)]. 5.38/5.62 750 -rel_str(A) | -antisymmetric_relstr(A) | is_antisymmetric_in(the_InternalRel(A),the_carrier(A)) # label(d6_orders_2) # label(axiom). [clausify(89)]. 5.38/5.62 Derived: -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -element(B,the_carrier(A)) | element(f6(A,B,C),the_carrier(A)) | -relstr_set_smaller(A,C,B) | join_on_relstr(A,C) = B. [resolve(741,b,742,b)]. 5.38/5.62 Derived: -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -element(B,the_carrier(A)) | element(f6(A,B,C),the_carrier(A)) | -relstr_set_smaller(A,C,B) | ex_sup_of_relstr_set(A,C). [resolve(741,b,743,b)]. 5.38/5.62 Derived: -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -element(B,the_carrier(A)) | relstr_set_smaller(A,C,f6(A,B,C)) | -relstr_set_smaller(A,C,B) | join_on_relstr(A,C) = B. [resolve(741,b,744,b)]. 5.38/5.62 Derived: -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -element(B,the_carrier(A)) | relstr_set_smaller(A,C,f6(A,B,C)) | -relstr_set_smaller(A,C,B) | ex_sup_of_relstr_set(A,C). [resolve(741,b,745,b)]. 5.38/5.62 Derived: -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -element(B,the_carrier(A)) | -related(A,B,f6(A,B,C)) | -relstr_set_smaller(A,C,B) | join_on_relstr(A,C) = B. [resolve(741,b,746,b)]. 5.38/5.62 Derived: -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -element(B,the_carrier(A)) | -related(A,B,f6(A,B,C)) | -relstr_set_smaller(A,C,B) | ex_sup_of_relstr_set(A,C). [resolve(741,b,747,b)]. 5.38/5.62 751 -rel_str(A) | -antisymmetric_relstr(A) | element(f63(A,B,C),the_carrier(A)) | -relstr_element_smaller(A,B,C) | -element(C,the_carrier(A)) | ex_inf_of_relstr_set(A,B) # label(t16_yellow_0) # label(lemma). [clausify(108)]. 5.38/5.62 Derived: -rel_str(A) | element(f63(A,B,C),the_carrier(A)) | -relstr_element_smaller(A,B,C) | -element(C,the_carrier(A)) | ex_inf_of_relstr_set(A,B) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(751,b,741,b)]. 5.63/5.86 752 -rel_str(A) | -antisymmetric_relstr(A) | relstr_element_smaller(A,B,f63(A,B,C)) | -relstr_element_smaller(A,B,C) | -element(C,the_carrier(A)) | ex_inf_of_relstr_set(A,B) # label(t16_yellow_0) # label(lemma). [clausify(108)]. 5.63/5.86 Derived: -rel_str(A) | relstr_element_smaller(A,B,f63(A,B,C)) | -relstr_element_smaller(A,B,C) | -element(C,the_carrier(A)) | ex_inf_of_relstr_set(A,B) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(752,b,741,b)]. 5.63/5.86 753 -rel_str(A) | -antisymmetric_relstr(A) | -related(A,f63(A,B,C),C) | -relstr_element_smaller(A,B,C) | -element(C,the_carrier(A)) | ex_inf_of_relstr_set(A,B) # label(t16_yellow_0) # label(lemma). [clausify(108)]. 5.63/5.86 Derived: -rel_str(A) | -related(A,f63(A,B,C),C) | -relstr_element_smaller(A,B,C) | -element(C,the_carrier(A)) | ex_inf_of_relstr_set(A,B) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(753,b,741,b)]. 5.63/5.86 754 -rel_str(A) | -antisymmetric_relstr(A) | -element(B,the_carrier(A)) | -relstr_element_smaller(A,C,B) | related(A,B,f64(A,C)) | -ex_inf_of_relstr_set(A,C) # label(t16_yellow_0) # label(lemma). [clausify(108)]. 5.63/5.86 Derived: -rel_str(A) | -element(B,the_carrier(A)) | -relstr_element_smaller(A,C,B) | related(A,B,f64(A,C)) | -ex_inf_of_relstr_set(A,C) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(754,b,741,b)]. 5.63/5.86 755 -rel_str(A) | -antisymmetric_relstr(A) | relstr_element_smaller(A,B,f64(A,B)) | -ex_inf_of_relstr_set(A,B) # label(t16_yellow_0) # label(lemma). [clausify(108)]. 5.63/5.86 Derived: -rel_str(A) | relstr_element_smaller(A,B,f64(A,B)) | -ex_inf_of_relstr_set(A,B) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(755,b,741,b)]. 5.63/5.86 756 -rel_str(A) | -antisymmetric_relstr(A) | element(f64(A,B),the_carrier(A)) | -ex_inf_of_relstr_set(A,B) # label(t16_yellow_0) # label(lemma). [clausify(108)]. 5.63/5.86 Derived: -rel_str(A) | element(f64(A,B),the_carrier(A)) | -ex_inf_of_relstr_set(A,B) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(756,b,741,b)]. 5.63/5.86 757 empty_carrier(A) | -rel_str(A) | -lower_bounded_relstr(A) | -antisymmetric_relstr(A) | ex_inf_of_relstr_set(A,the_carrier(A)) # label(t42_yellow_0) # label(lemma). [clausify(285)]. 5.63/5.86 Derived: empty_carrier(A) | -rel_str(A) | -lower_bounded_relstr(A) | ex_inf_of_relstr_set(A,the_carrier(A)) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(757,d,741,b)]. 5.63/5.86 758 empty_carrier(A) | -rel_str(A) | -lower_bounded_relstr(A) | -antisymmetric_relstr(A) | ex_sup_of_relstr_set(A,empty_set) # label(t42_yellow_0) # label(lemma). [clausify(285)]. 5.63/5.86 Derived: empty_carrier(A) | -rel_str(A) | -lower_bounded_relstr(A) | ex_sup_of_relstr_set(A,empty_set) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(758,d,741,b)]. 5.63/5.86 759 antisymmetric_relstr(c15) # label(rc2_orders_2) # label(axiom). [clausify(370)]. 5.63/5.86 Derived: -rel_str(c15) | -element(A,the_carrier(c15)) | element(f6(c15,A,B),the_carrier(c15)) | -relstr_set_smaller(c15,B,A) | join_on_relstr(c15,B) = A. [resolve(759,a,742,b)]. 5.63/5.86 Derived: -rel_str(c15) | -element(A,the_carrier(c15)) | element(f6(c15,A,B),the_carrier(c15)) | -relstr_set_smaller(c15,B,A) | ex_sup_of_relstr_set(c15,B). [resolve(759,a,743,b)]. 5.63/5.86 Derived: -rel_str(c15) | -element(A,the_carrier(c15)) | relstr_set_smaller(c15,B,f6(c15,A,B)) | -relstr_set_smaller(c15,B,A) | join_on_relstr(c15,B) = A. [resolve(759,a,744,b)]. 5.63/5.86 Derived: -rel_str(c15) | -element(A,the_carrier(c15)) | relstr_set_smaller(c15,B,f6(c15,A,B)) | -relstr_set_smaller(c15,B,A) | ex_sup_of_relstr_set(c15,B). [resolve(759,a,745,b)]. 5.63/5.86 Derived: -rel_str(c15) | -element(A,the_carrier(c15)) | -related(c15,A,f6(c15,A,B)) | -relstr_set_smaller(c15,B,A) | join_on_relstr(c15,B) = A. [resolve(759,a,746,b)]. 5.63/5.86 Derived: -rel_str(c15) | -element(A,the_carrier(c15)) | -related(c15,A,f6(c15,A,B)) | -relstr_set_smaller(c15,B,A) | ex_sup_of_relstr_set(c15,B). [resolve(759,a,747,b)]. 5.63/5.88 Derived: -rel_str(c15) | is_antisymmetric_in(the_InternalRel(c15),the_carrier(c15)). [resolve(759,a,750,b)]. 5.63/5.88 Derived: -rel_str(c15) | element(f63(c15,A,B),the_carrier(c15)) | -relstr_element_smaller(c15,A,B) | -element(B,the_carrier(c15)) | ex_inf_of_relstr_set(c15,A). [resolve(759,a,751,b)]. 5.63/5.88 Derived: -rel_str(c15) | relstr_element_smaller(c15,A,f63(c15,A,B)) | -relstr_element_smaller(c15,A,B) | -element(B,the_carrier(c15)) | ex_inf_of_relstr_set(c15,A). [resolve(759,a,752,b)]. 5.63/5.88 Derived: -rel_str(c15) | -related(c15,f63(c15,A,B),B) | -relstr_element_smaller(c15,A,B) | -element(B,the_carrier(c15)) | ex_inf_of_relstr_set(c15,A). [resolve(759,a,753,b)]. 5.63/5.88 Derived: -rel_str(c15) | -element(A,the_carrier(c15)) | -relstr_element_smaller(c15,B,A) | related(c15,A,f64(c15,B)) | -ex_inf_of_relstr_set(c15,B). [resolve(759,a,754,b)]. 5.63/5.88 Derived: -rel_str(c15) | relstr_element_smaller(c15,A,f64(c15,A)) | -ex_inf_of_relstr_set(c15,A). [resolve(759,a,755,b)]. 5.63/5.88 Derived: -rel_str(c15) | element(f64(c15,A),the_carrier(c15)) | -ex_inf_of_relstr_set(c15,A). [resolve(759,a,756,b)]. 5.63/5.88 Derived: empty_carrier(c15) | -rel_str(c15) | -lower_bounded_relstr(c15) | ex_inf_of_relstr_set(c15,the_carrier(c15)). [resolve(759,a,757,d)]. 5.63/5.88 Derived: empty_carrier(c15) | -rel_str(c15) | -lower_bounded_relstr(c15) | ex_sup_of_relstr_set(c15,empty_set). [resolve(759,a,758,d)]. 5.63/5.88 760 -lattice(A) | -latt_str(A) | empty_carrier(A) | antisymmetric_relstr(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(400)]. 5.63/5.88 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | -rel_str(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | element(f6(poset_of_lattice(A),B,C),the_carrier(poset_of_lattice(A))) | -relstr_set_smaller(poset_of_lattice(A),C,B) | join_on_relstr(poset_of_lattice(A),C) = B. [resolve(760,d,742,b)]. 5.63/5.88 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | -rel_str(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | element(f6(poset_of_lattice(A),B,C),the_carrier(poset_of_lattice(A))) | -relstr_set_smaller(poset_of_lattice(A),C,B) | ex_sup_of_relstr_set(poset_of_lattice(A),C). [resolve(760,d,743,b)]. 5.63/5.88 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | -rel_str(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | relstr_set_smaller(poset_of_lattice(A),C,f6(poset_of_lattice(A),B,C)) | -relstr_set_smaller(poset_of_lattice(A),C,B) | join_on_relstr(poset_of_lattice(A),C) = B. [resolve(760,d,744,b)]. 5.63/5.88 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | -rel_str(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | relstr_set_smaller(poset_of_lattice(A),C,f6(poset_of_lattice(A),B,C)) | -relstr_set_smaller(poset_of_lattice(A),C,B) | ex_sup_of_relstr_set(poset_of_lattice(A),C). [resolve(760,d,745,b)]. 5.63/5.88 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | -rel_str(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | -related(poset_of_lattice(A),B,f6(poset_of_lattice(A),B,C)) | -relstr_set_smaller(poset_of_lattice(A),C,B) | join_on_relstr(poset_of_lattice(A),C) = B. [resolve(760,d,746,b)]. 5.63/5.88 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | -rel_str(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | -related(poset_of_lattice(A),B,f6(poset_of_lattice(A),B,C)) | -relstr_set_smaller(poset_of_lattice(A),C,B) | ex_sup_of_relstr_set(poset_of_lattice(A),C). [resolve(760,d,747,b)]. 5.63/5.88 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | -rel_str(poset_of_lattice(A)) | is_antisymmetric_in(the_InternalRel(poset_of_lattice(A)),the_carrier(poset_of_lattice(A))). [resolve(760,d,750,b)]. 5.63/5.88 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | -rel_str(poset_of_lattice(A)) | element(f63(poset_of_lattice(A),B,C),the_carrier(poset_of_lattice(A))) | -relstr_element_smaller(poset_of_lattice(A),B,C) | -element(C,the_carrier(poset_of_lattice(A))) | ex_inf_of_relstr_set(poset_of_lattice(A),B). [resolve(760,d,751,b)]. 5.63/5.88 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | -rel_str(poset_of_lattice(A)) | relstr_element_smaller(poset_of_lattice(A),B,f63(poset_of_lattice(A),B,C)) | -relstr_element_smaller(poset_of_lattice(A),B,C) | -element(C,the_carrier(poset_of_lattice(A))) | ex_inf_of_relstr_set(poset_of_lattice(A),B). [resolve(760,d,752,b)]. 5.69/5.93 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | -rel_str(poset_of_lattice(A)) | -related(poset_of_lattice(A),f63(poset_of_lattice(A),B,C),C) | -relstr_element_smaller(poset_of_lattice(A),B,C) | -element(C,the_carrier(poset_of_lattice(A))) | ex_inf_of_relstr_set(poset_of_lattice(A),B). [resolve(760,d,753,b)]. 5.69/5.93 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | -rel_str(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | -relstr_element_smaller(poset_of_lattice(A),C,B) | related(poset_of_lattice(A),B,f64(poset_of_lattice(A),C)) | -ex_inf_of_relstr_set(poset_of_lattice(A),C). [resolve(760,d,754,b)]. 5.69/5.93 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | -rel_str(poset_of_lattice(A)) | relstr_element_smaller(poset_of_lattice(A),B,f64(poset_of_lattice(A),B)) | -ex_inf_of_relstr_set(poset_of_lattice(A),B). [resolve(760,d,755,b)]. 5.69/5.93 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | -rel_str(poset_of_lattice(A)) | element(f64(poset_of_lattice(A),B),the_carrier(poset_of_lattice(A))) | -ex_inf_of_relstr_set(poset_of_lattice(A),B). [resolve(760,d,756,b)]. 5.69/5.93 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -lower_bounded_relstr(poset_of_lattice(A)) | ex_inf_of_relstr_set(poset_of_lattice(A),the_carrier(poset_of_lattice(A))). [resolve(760,d,757,d)]. 5.69/5.93 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -lower_bounded_relstr(poset_of_lattice(A)) | ex_sup_of_relstr_set(poset_of_lattice(A),empty_set). [resolve(760,d,758,d)]. 5.69/5.93 761 -latt_str(A) | -lattice(A) | empty_carrier(A) | antisymmetric_relstr(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(406)]. 5.69/5.93 762 -antisymmetric_relstr(A) | -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -related(A,C,B) | -related(A,B,C) | C = B # label(t25_orders_2) # label(lemma). [clausify(440)]. 5.69/5.93 Derived: -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -related(A,C,B) | -related(A,B,C) | C = B | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(762,a,741,b)]. 5.69/5.93 Derived: -rel_str(c15) | -element(A,the_carrier(c15)) | -element(B,the_carrier(c15)) | -related(c15,B,A) | -related(c15,A,B) | B = A. [resolve(762,a,759,a)]. 5.69/5.93 Derived: -rel_str(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | -related(poset_of_lattice(A),C,B) | -related(poset_of_lattice(A),B,C) | C = B | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(762,a,760,d)]. 5.69/5.93 763 -antisymmetric_relstr(A) | -rel_str(A) | -transitive_relstr(A) | -reflexive_relstr(A) | relation(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(442)]. 5.69/5.93 Derived: -rel_str(A) | -transitive_relstr(A) | -reflexive_relstr(A) | relation(the_InternalRel(A)) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(763,a,741,b)]. 5.69/5.93 Derived: -rel_str(c15) | -transitive_relstr(c15) | -reflexive_relstr(c15) | relation(the_InternalRel(c15)). [resolve(763,a,759,a)]. 5.69/5.93 Derived: -rel_str(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -reflexive_relstr(poset_of_lattice(A)) | relation(the_InternalRel(poset_of_lattice(A))) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(763,a,760,d)]. 5.69/5.93 764 -antisymmetric_relstr(A) | -rel_str(A) | -transitive_relstr(A) | -reflexive_relstr(A) | reflexive(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(442)]. 5.69/5.93 Derived: -rel_str(A) | -transitive_relstr(A) | -reflexive_relstr(A) | reflexive(the_InternalRel(A)) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(764,a,741,b)]. 5.69/5.93 Derived: -rel_str(c15) | -transitive_relstr(c15) | -reflexive_relstr(c15) | reflexive(the_InternalRel(c15)). [resolve(764,a,759,a)]. 5.74/5.95 Derived: -rel_str(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -reflexive_relstr(poset_of_lattice(A)) | reflexive(the_InternalRel(poset_of_lattice(A))) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(764,a,760,d)]. 5.74/5.95 765 -antisymmetric_relstr(A) | -rel_str(A) | -transitive_relstr(A) | -reflexive_relstr(A) | antisymmetric(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(442)]. 5.74/5.95 Derived: -rel_str(A) | -transitive_relstr(A) | -reflexive_relstr(A) | antisymmetric(the_InternalRel(A)) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(765,a,741,b)]. 5.74/5.95 Derived: -rel_str(c15) | -transitive_relstr(c15) | -reflexive_relstr(c15) | antisymmetric(the_InternalRel(c15)). [resolve(765,a,759,a)]. 5.74/5.95 Derived: -rel_str(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -reflexive_relstr(poset_of_lattice(A)) | antisymmetric(the_InternalRel(poset_of_lattice(A))) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(765,a,760,d)]. 5.74/5.95 766 -antisymmetric_relstr(A) | -rel_str(A) | -transitive_relstr(A) | -reflexive_relstr(A) | transitive(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(442)]. 5.74/5.95 Derived: -rel_str(A) | -transitive_relstr(A) | -reflexive_relstr(A) | transitive(the_InternalRel(A)) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(766,a,741,b)]. 5.74/5.95 Derived: -rel_str(c15) | -transitive_relstr(c15) | -reflexive_relstr(c15) | transitive(the_InternalRel(c15)). [resolve(766,a,759,a)]. 5.74/5.95 Derived: -rel_str(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -reflexive_relstr(poset_of_lattice(A)) | transitive(the_InternalRel(poset_of_lattice(A))) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(766,a,760,d)]. 5.74/5.95 767 -antisymmetric_relstr(A) | -rel_str(A) | -transitive_relstr(A) | -reflexive_relstr(A) | v1_partfun1(the_InternalRel(A),the_carrier(A),the_carrier(A)) # label(fc2_orders_2) # label(axiom). [clausify(442)]. 5.74/5.95 Derived: -rel_str(A) | -transitive_relstr(A) | -reflexive_relstr(A) | v1_partfun1(the_InternalRel(A),the_carrier(A),the_carrier(A)) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(767,a,741,b)]. 5.74/5.95 Derived: -rel_str(c15) | -transitive_relstr(c15) | -reflexive_relstr(c15) | v1_partfun1(the_InternalRel(c15),the_carrier(c15),the_carrier(c15)). [resolve(767,a,759,a)]. 5.74/5.95 Derived: -rel_str(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -reflexive_relstr(poset_of_lattice(A)) | v1_partfun1(the_InternalRel(poset_of_lattice(A)),the_carrier(poset_of_lattice(A)),the_carrier(poset_of_lattice(A))) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(767,a,760,d)]. 5.74/5.95 768 -antisymmetric_relstr(A) | -rel_str(A) | -element(B,the_carrier(A)) | element(f322(A,C,B),the_carrier(A)) | -relstr_set_smaller(A,C,B) | ex_sup_of_relstr_set(A,C) # label(t15_yellow_0) # label(lemma). [clausify(478)]. 5.74/5.95 Derived: -rel_str(A) | -element(B,the_carrier(A)) | element(f322(A,C,B),the_carrier(A)) | -relstr_set_smaller(A,C,B) | ex_sup_of_relstr_set(A,C) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(768,a,741,b)]. 5.74/5.95 Derived: -rel_str(c15) | -element(A,the_carrier(c15)) | element(f322(c15,B,A),the_carrier(c15)) | -relstr_set_smaller(c15,B,A) | ex_sup_of_relstr_set(c15,B). [resolve(768,a,759,a)]. 5.74/5.95 Derived: -rel_str(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | element(f322(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))) | -relstr_set_smaller(poset_of_lattice(A),C,B) | ex_sup_of_relstr_set(poset_of_lattice(A),C) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(768,a,760,d)]. 5.74/5.95 769 -antisymmetric_relstr(A) | -rel_str(A) | -element(B,the_carrier(A)) | relstr_set_smaller(A,C,f322(A,C,B)) | -relstr_set_smaller(A,C,B) | ex_sup_of_relstr_set(A,C) # label(t15_yellow_0) # label(lemma). [clausify(478)]. 5.74/5.95 Derived: -rel_str(A) | -element(B,the_carrier(A)) | relstr_set_smaller(A,C,f322(A,C,B)) | -relstr_set_smaller(A,C,B) | ex_sup_of_relstr_set(A,C) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(769,a,741,b)]. 5.74/6.00 Derived: -rel_str(c15) | -element(A,the_carrier(c15)) | relstr_set_smaller(c15,B,f322(c15,B,A)) | -relstr_set_smaller(c15,B,A) | ex_sup_of_relstr_set(c15,B). [resolve(769,a,759,a)]. 5.74/6.00 Derived: -rel_str(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | relstr_set_smaller(poset_of_lattice(A),C,f322(poset_of_lattice(A),C,B)) | -relstr_set_smaller(poset_of_lattice(A),C,B) | ex_sup_of_relstr_set(poset_of_lattice(A),C) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(769,a,760,d)]. 5.74/6.00 770 -antisymmetric_relstr(A) | -rel_str(A) | -element(B,the_carrier(A)) | -related(A,B,f322(A,C,B)) | -relstr_set_smaller(A,C,B) | ex_sup_of_relstr_set(A,C) # label(t15_yellow_0) # label(lemma). [clausify(478)]. 5.74/6.00 Derived: -rel_str(A) | -element(B,the_carrier(A)) | -related(A,B,f322(A,C,B)) | -relstr_set_smaller(A,C,B) | ex_sup_of_relstr_set(A,C) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(770,a,741,b)]. 5.74/6.00 Derived: -rel_str(c15) | -element(A,the_carrier(c15)) | -related(c15,A,f322(c15,B,A)) | -relstr_set_smaller(c15,B,A) | ex_sup_of_relstr_set(c15,B). [resolve(770,a,759,a)]. 5.74/6.00 Derived: -rel_str(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | -related(poset_of_lattice(A),B,f322(poset_of_lattice(A),C,B)) | -relstr_set_smaller(poset_of_lattice(A),C,B) | ex_sup_of_relstr_set(poset_of_lattice(A),C) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(770,a,760,d)]. 5.74/6.00 771 -antisymmetric_relstr(A) | -rel_str(A) | element(f323(A,B),the_carrier(A)) | -ex_sup_of_relstr_set(A,B) # label(t15_yellow_0) # label(lemma). [clausify(478)]. 5.74/6.00 Derived: -rel_str(A) | element(f323(A,B),the_carrier(A)) | -ex_sup_of_relstr_set(A,B) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(771,a,741,b)]. 5.74/6.00 Derived: -rel_str(c15) | element(f323(c15,A),the_carrier(c15)) | -ex_sup_of_relstr_set(c15,A). [resolve(771,a,759,a)]. 5.74/6.00 Derived: -rel_str(poset_of_lattice(A)) | element(f323(poset_of_lattice(A),B),the_carrier(poset_of_lattice(A))) | -ex_sup_of_relstr_set(poset_of_lattice(A),B) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(771,a,760,d)]. 5.74/6.00 772 -antisymmetric_relstr(A) | -rel_str(A) | -element(B,the_carrier(A)) | -relstr_set_smaller(A,C,B) | related(A,f323(A,C),B) | -ex_sup_of_relstr_set(A,C) # label(t15_yellow_0) # label(lemma). [clausify(478)]. 5.74/6.00 Derived: -rel_str(A) | -element(B,the_carrier(A)) | -relstr_set_smaller(A,C,B) | related(A,f323(A,C),B) | -ex_sup_of_relstr_set(A,C) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(772,a,741,b)]. 5.74/6.00 Derived: -rel_str(c15) | -element(A,the_carrier(c15)) | -relstr_set_smaller(c15,B,A) | related(c15,f323(c15,B),A) | -ex_sup_of_relstr_set(c15,B). [resolve(772,a,759,a)]. 5.74/6.00 Derived: -rel_str(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | -relstr_set_smaller(poset_of_lattice(A),C,B) | related(poset_of_lattice(A),f323(poset_of_lattice(A),C),B) | -ex_sup_of_relstr_set(poset_of_lattice(A),C) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(772,a,760,d)]. 5.74/6.00 773 -antisymmetric_relstr(A) | -rel_str(A) | relstr_set_smaller(A,B,f323(A,B)) | -ex_sup_of_relstr_set(A,B) # label(t15_yellow_0) # label(lemma). [clausify(478)]. 5.74/6.00 Derived: -rel_str(A) | relstr_set_smaller(A,B,f323(A,B)) | -ex_sup_of_relstr_set(A,B) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(773,a,741,b)]. 5.74/6.00 Derived: -rel_str(c15) | relstr_set_smaller(c15,A,f323(c15,A)) | -ex_sup_of_relstr_set(c15,A). [resolve(773,a,759,a)]. 5.74/6.00 Derived: -rel_str(poset_of_lattice(A)) | relstr_set_smaller(poset_of_lattice(A),B,f323(poset_of_lattice(A),B)) | -ex_sup_of_relstr_set(poset_of_lattice(A),B) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(773,a,760,d)]. 5.74/6.00 774 -lower_bounded_relstr(A) | -rel_str(A) | -antisymmetric_relstr(A) | empty_carrier(A) | -element(B,the_carrier(A)) | related(A,bottom_of_relstr(A),B) # label(t44_yellow_0) # label(lemma). [clausify(538)]. 7.07/7.30 Derived: -lower_bounded_relstr(A) | -rel_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | related(A,bottom_of_relstr(A),B) | -rel_str(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)). [resolve(774,c,741,b)]. 7.07/7.30 Derived: -lower_bounded_relstr(c15) | -rel_str(c15) | empty_carrier(c15) | -element(A,the_carrier(c15)) | related(c15,bottom_of_relstr(c15),A). [resolve(774,c,759,a)]. 7.07/7.30 Derived: -lower_bounded_relstr(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | empty_carrier(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | related(poset_of_lattice(A),bottom_of_relstr(poset_of_lattice(A)),B) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(774,c,760,d)]. 7.07/7.30 775 -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | antisymmetric_relstr(rel_str_of(B,A)) # label(fc3_orders_2) # label(axiom). [clausify(663)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,the_carrier(rel_str_of(B,A))) | element(f6(rel_str_of(B,A),C,D),the_carrier(rel_str_of(B,A))) | -relstr_set_smaller(rel_str_of(B,A),D,C) | join_on_relstr(rel_str_of(B,A),D) = C. [resolve(775,f,742,b)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,the_carrier(rel_str_of(B,A))) | element(f6(rel_str_of(B,A),C,D),the_carrier(rel_str_of(B,A))) | -relstr_set_smaller(rel_str_of(B,A),D,C) | ex_sup_of_relstr_set(rel_str_of(B,A),D). [resolve(775,f,743,b)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,the_carrier(rel_str_of(B,A))) | relstr_set_smaller(rel_str_of(B,A),D,f6(rel_str_of(B,A),C,D)) | -relstr_set_smaller(rel_str_of(B,A),D,C) | join_on_relstr(rel_str_of(B,A),D) = C. [resolve(775,f,744,b)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,the_carrier(rel_str_of(B,A))) | relstr_set_smaller(rel_str_of(B,A),D,f6(rel_str_of(B,A),C,D)) | -relstr_set_smaller(rel_str_of(B,A),D,C) | ex_sup_of_relstr_set(rel_str_of(B,A),D). [resolve(775,f,745,b)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,the_carrier(rel_str_of(B,A))) | -related(rel_str_of(B,A),C,f6(rel_str_of(B,A),C,D)) | -relstr_set_smaller(rel_str_of(B,A),D,C) | join_on_relstr(rel_str_of(B,A),D) = C. [resolve(775,f,746,b)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,the_carrier(rel_str_of(B,A))) | -related(rel_str_of(B,A),C,f6(rel_str_of(B,A),C,D)) | -relstr_set_smaller(rel_str_of(B,A),D,C) | ex_sup_of_relstr_set(rel_str_of(B,A),D). [resolve(775,f,747,b)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,the_carrier(rel_str_of(B,A))) | -ex_sup_of_relstr_set(rel_str_of(B,A),D) | join_on_relstr(rel_str_of(B,A),D) != C | -element(E,the_carrier(rel_str_of(B,A))) | -relstr_set_smaller(rel_str_of(B,A),D,E) | related(rel_str_of(B,A),C,E). [resolve(775,f,748,b)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,the_carrier(rel_str_of(B,A))) | -ex_sup_of_relstr_set(rel_str_of(B,A),D) | join_on_relstr(rel_str_of(B,A),D) != C | relstr_set_smaller(rel_str_of(B,A),D,C). [resolve(775,f,749,b)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | is_antisymmetric_in(the_InternalRel(rel_str_of(B,A)),the_carrier(rel_str_of(B,A))). [resolve(775,f,750,b)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | element(f63(rel_str_of(B,A),C,D),the_carrier(rel_str_of(B,A))) | -relstr_element_smaller(rel_str_of(B,A),C,D) | -element(D,the_carrier(rel_str_of(B,A))) | ex_inf_of_relstr_set(rel_str_of(B,A),C). [resolve(775,f,751,b)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | relstr_element_smaller(rel_str_of(B,A),C,f63(rel_str_of(B,A),C,D)) | -relstr_element_smaller(rel_str_of(B,A),C,D) | -element(D,the_carrier(rel_str_of(B,A))) | ex_inf_of_relstr_set(rel_str_of(B,A),C). [resolve(775,f,752,b)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -related(rel_str_of(B,A),f63(rel_str_of(B,A),C,D),D) | -relstr_element_smaller(rel_str_of(B,A),C,D) | -element(D,the_carrier(rel_str_of(B,A))) | ex_inf_of_relstr_set(rel_str_of(B,A),C). [resolve(775,f,753,b)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,the_carrier(rel_str_of(B,A))) | -relstr_element_smaller(rel_str_of(B,A),D,C) | related(rel_str_of(B,A),C,f64(rel_str_of(B,A),D)) | -ex_inf_of_relstr_set(rel_str_of(B,A),D). [resolve(775,f,754,b)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | relstr_element_smaller(rel_str_of(B,A),C,f64(rel_str_of(B,A),C)) | -ex_inf_of_relstr_set(rel_str_of(B,A),C). [resolve(775,f,755,b)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | element(f64(rel_str_of(B,A),C),the_carrier(rel_str_of(B,A))) | -ex_inf_of_relstr_set(rel_str_of(B,A),C). [resolve(775,f,756,b)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -lower_bounded_relstr(rel_str_of(B,A)) | ex_inf_of_relstr_set(rel_str_of(B,A),the_carrier(rel_str_of(B,A))). [resolve(775,f,757,d)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -lower_bounded_relstr(rel_str_of(B,A)) | ex_sup_of_relstr_set(rel_str_of(B,A),empty_set). [resolve(775,f,758,d)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,the_carrier(rel_str_of(B,A))) | -element(D,the_carrier(rel_str_of(B,A))) | -related(rel_str_of(B,A),D,C) | -related(rel_str_of(B,A),C,D) | D = C. [resolve(775,f,762,a)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -transitive_relstr(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | relation(the_InternalRel(rel_str_of(B,A))). [resolve(775,f,763,a)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -transitive_relstr(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | reflexive(the_InternalRel(rel_str_of(B,A))). [resolve(775,f,764,a)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -transitive_relstr(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | antisymmetric(the_InternalRel(rel_str_of(B,A))). [resolve(775,f,765,a)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -transitive_relstr(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | transitive(the_InternalRel(rel_str_of(B,A))). [resolve(775,f,766,a)]. 7.07/7.30 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -transitive_relstr(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | v1_partfun1(the_InternalRel(rel_str_of(B,A)),the_carrier(rel_str_of(B,A)),the_carrier(rel_str_of(B,A))). [resolve(775,f,767,a)]. 10.83/11.05 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,the_carrier(rel_str_of(B,A))) | element(f322(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))) | -relstr_set_smaller(rel_str_of(B,A),D,C) | ex_sup_of_relstr_set(rel_str_of(B,A),D). [resolve(775,f,768,a)]. 10.83/11.05 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,the_carrier(rel_str_of(B,A))) | relstr_set_smaller(rel_str_of(B,A),D,f322(rel_str_of(B,A),D,C)) | -relstr_set_smaller(rel_str_of(B,A),D,C) | ex_sup_of_relstr_set(rel_str_of(B,A),D). [resolve(775,f,769,a)]. 10.83/11.05 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,the_carrier(rel_str_of(B,A))) | -related(rel_str_of(B,A),C,f322(rel_str_of(B,A),D,C)) | -relstr_set_smaller(rel_str_of(B,A),D,C) | ex_sup_of_relstr_set(rel_str_of(B,A),D). [resolve(775,f,770,a)]. 10.83/11.05 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | element(f323(rel_str_of(B,A),C),the_carrier(rel_str_of(B,A))) | -ex_sup_of_relstr_set(rel_str_of(B,A),C). [resolve(775,f,771,a)]. 10.83/11.05 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,the_carrier(rel_str_of(B,A))) | -relstr_set_smaller(rel_str_of(B,A),D,C) | related(rel_str_of(B,A),f323(rel_str_of(B,A),D),C) | -ex_sup_of_relstr_set(rel_str_of(B,A),D). [resolve(775,f,772,a)]. 10.83/11.05 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | relstr_set_smaller(rel_str_of(B,A),C,f323(rel_str_of(B,A),C)) | -ex_sup_of_relstr_set(rel_str_of(B,A),C). [resolve(775,f,773,a)]. 10.83/11.05 Derived: -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | -lower_bounded_relstr(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | empty_carrier(rel_str_of(B,A)) | -element(C,the_carrier(rel_str_of(B,A))) | related(rel_str_of(B,A),bottom_of_relstr(rel_str_of(B,A)),C). [resolve(775,f,774,c)]. 10.83/11.05 776 equipotent(A,B) | -are_equipotent(A,B) # label(redefinition_r2_wellord2) # label(axiom). [clausify(495)]. 10.83/11.05 777 -subset(A,f7(B)) | are_equipotent(A,f7(B)) | in(A,f7(B)) # label(t9_tarski) # label(axiom). [clausify(28)]. 10.83/11.05 778 -equipotent(A,B) | are_equipotent(A,B) # label(redefinition_r2_wellord2) # label(axiom). [clausify(495)]. 10.83/11.05 Derived: equipotent(A,f7(B)) | -subset(A,f7(B)) | in(A,f7(B)). [resolve(776,b,777,b)]. 10.83/11.05 779 -subset(A,f459(B)) | are_equipotent(A,f459(B)) | in(A,f459(B)) # label(t136_zfmisc_1) # label(lemma). [clausify(705)]. 10.83/11.05 Derived: -subset(A,f459(B)) | in(A,f459(B)) | equipotent(A,f459(B)). [resolve(779,b,776,b)]. 10.83/11.05 780 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(658)]. 10.83/11.05 781 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | -subset(A,C) | -closed_subset(D,B) | D != C | -element(D,powerset(the_carrier(B))) | -in(C,powerset(the_carrier(B))) | in(C,f11(B,A)) # label(s1_xboole_0__e1_40__pre_topc__1) # label(lemma). [clausify(35)]. 10.83/11.05 782 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | subset(A,C) | -in(C,f11(B,A)) # label(s1_xboole_0__e1_40__pre_topc__1) # label(lemma). [clausify(35)]. 10.83/11.05 783 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | closed_subset(f12(B,A,C),B) | -in(C,f11(B,A)) # label(s1_xboole_0__e1_40__pre_topc__1) # label(lemma). [clausify(35)]. 10.83/11.05 784 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f12(B,A,C) = C | -in(C,f11(B,A)) # label(s1_xboole_0__e1_40__pre_topc__1) # label(lemma). [clausify(35)]. 10.83/11.05 785 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | element(f12(B,A,C),powerset(the_carrier(B))) | -in(C,f11(B,A)) # label(s1_xboole_0__e1_40__pre_topc__1) # label(lemma). [clausify(35)]. 10.83/11.05 786 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | in(C,powerset(the_carrier(B))) | -in(C,f11(B,A)) # label(s1_xboole_0__e1_40__pre_topc__1) # label(lemma). [clausify(35)]. 10.83/11.05 787 -topological_space(A) | -closed_subset(B,A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | open_subset(subset_complement(the_carrier(A),B),A) # label(fc3_tops_1) # label(axiom). [clausify(100)]. 10.83/11.05 788 -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | -topological_space(A) | closed_subset(B,A) # label(t52_pre_topc) # label(lemma). [clausify(154)]. 10.83/11.05 789 -topological_space(A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | element(f124(A,B,C),powerset(the_carrier(A))) # label(s3_subset_1__e1_40__pre_topc) # label(lemma). [clausify(204)]. 10.83/11.05 790 -topological_space(A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | f124(A,B,C) = C # label(s3_subset_1__e1_40__pre_topc) # label(lemma). [clausify(204)]. 10.83/11.05 791 -topological_space(A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | closed_subset(f124(A,B,C),A) # label(s3_subset_1__e1_40__pre_topc) # label(lemma). [clausify(204)]. 10.83/11.05 792 -topological_space(A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | subset(B,C) # label(s3_subset_1__e1_40__pre_topc) # label(lemma). [clausify(204)]. 10.83/11.05 793 -topological_space(A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(C,f123(A,B)) | -element(D,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C) # label(s3_subset_1__e1_40__pre_topc) # label(lemma). [clausify(204)]. 10.83/11.05 794 -topological_space(A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f123(A,B),powerset(powerset(the_carrier(A)))) # label(s3_subset_1__e1_40__pre_topc) # label(lemma). [clausify(204)]. 10.83/11.05 795 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f131(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 796 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f131(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 797 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f131(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 798 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f131(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 799 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f131(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 800 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f131(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 801 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f131(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 802 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | element(f132(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 803 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | element(f132(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 804 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | element(f132(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 805 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | element(f132(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 806 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | element(f132(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 807 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | element(f132(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 808 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | element(f132(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 809 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f132(A,B) = f131(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 810 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f132(A,B) = f131(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 811 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f132(A,B) = f131(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 812 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f132(A,B) = f131(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 813 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f132(A,B) = f131(A,B) | subset(B,C) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 814 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f132(A,B) = f131(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 815 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f132(A,B) = f131(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 816 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | closed_subset(f132(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 817 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | closed_subset(f132(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 818 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | closed_subset(f132(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 819 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | closed_subset(f132(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 820 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | closed_subset(f132(A,B),A) | subset(B,C) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 821 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | closed_subset(f132(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 822 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | closed_subset(f132(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 823 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | subset(B,f131(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 824 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | subset(B,f131(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 825 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | subset(B,f131(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 826 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | subset(B,f131(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 827 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | subset(B,f131(A,B)) | subset(B,C) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 828 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | subset(B,f131(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 829 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | subset(B,f131(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 830 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | element(f133(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 831 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | element(f133(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 832 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | element(f133(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 833 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | element(f133(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 834 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | element(f133(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 835 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | element(f133(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 836 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | element(f133(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 837 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | subset(B,f130(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 838 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | subset(B,f130(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 839 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | subset(B,f130(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 840 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | subset(B,f130(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 841 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | subset(B,f130(A,B)) | subset(B,C) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 842 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | subset(B,f130(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 843 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | subset(B,f130(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 844 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | closed_subset(f133(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 845 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | closed_subset(f133(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 846 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | closed_subset(f133(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 847 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | closed_subset(f133(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 848 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | closed_subset(f133(A,B),A) | subset(B,C) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 849 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | closed_subset(f133(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 850 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | closed_subset(f133(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 851 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f133(A,B) = f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 852 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f133(A,B) = f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 853 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f133(A,B) = f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 854 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f133(A,B) = f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 855 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f133(A,B) = f130(A,B) | subset(B,C) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 856 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f133(A,B) = f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 857 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f133(A,B) = f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 858 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f130(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 859 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f130(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 860 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f130(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 861 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f130(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 862 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f130(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 863 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f130(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 864 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f130(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 865 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f131(A,B) != f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 866 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f131(A,B) != f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 867 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f131(A,B) != f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 868 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f131(A,B) != f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 869 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f131(A,B) != f130(A,B) | subset(B,C) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 870 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f131(A,B) != f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 871 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | f131(A,B) != f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(216)]. 10.83/11.05 872 -topological_space(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -open_subset(B,A) | closed_subset(subset_complement(the_carrier(A),B),A) # label(fc4_tops_1) # label(axiom). [clausify(237)]. 10.83/11.05 873 -top_str(A) | -topological_space(A) | element(f185(A),powerset(the_carrier(A))) # label(rc1_tops_1) # label(axiom). [clausify(279)]. 10.83/11.05 874 -top_str(A) | -topological_space(A) | open_subset(f185(A),A) # label(rc1_tops_1) # label(axiom). [clausify(279)]. 10.83/11.05 875 empty_carrier(A) | -topological_space(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)) # label(d1_connsp_2) # label(axiom). [clausify(289)]. 10.83/11.05 876 empty_carrier(A) | -topological_space(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)) # label(d1_connsp_2) # label(axiom). [clausify(289)]. 10.83/11.05 877 -element(A,powerset(powerset(the_carrier(B)))) | -top_str(B) | -topological_space(B) | -element(C,powerset(the_carrier(B))) | -in(set_difference(cast_as_carrier_subset(B),C),A) | in(C,f199(B,A)) # label(s3_subset_1__e2_37_1_1__pre_topc) # label(lemma). [clausify(294)]. 10.83/11.05 878 -element(A,powerset(powerset(the_carrier(B)))) | -top_str(B) | -topological_space(B) | -element(C,powerset(the_carrier(B))) | in(set_difference(cast_as_carrier_subset(B),C),A) | -in(C,f199(B,A)) # label(s3_subset_1__e2_37_1_1__pre_topc) # label(lemma). [clausify(294)]. 10.83/11.05 879 -element(A,powerset(powerset(the_carrier(B)))) | -top_str(B) | -topological_space(B) | element(f199(B,A),powerset(powerset(the_carrier(B)))) # label(s3_subset_1__e2_37_1_1__pre_topc) # label(lemma). [clausify(294)]. 10.83/11.05 880 -topological_space(A) | -top_str(A) | element(f235(A),powerset(the_carrier(A))) # label(rc2_tops_1) # label(axiom). [clausify(344)]. 10.83/11.05 881 -topological_space(A) | -top_str(A) | open_subset(f235(A),A) # label(rc2_tops_1) # label(axiom). [clausify(344)]. 10.83/11.05 882 -topological_space(A) | -top_str(A) | closed_subset(f235(A),A) # label(rc2_tops_1) # label(axiom). [clausify(344)]. 10.83/11.05 883 -topological_space(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A) # label(t51_tops_1) # label(lemma). [clausify(388)]. 10.83/11.05 884 -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -topological_space(A) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,powerset(the_carrier(A))) | in(C,f281(A,B)) # label(s1_xboole_0__e2_37_1_1__pre_topc__1) # label(lemma). [clausify(407)]. 10.83/11.05 885 -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -topological_space(A) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f281(A,B)) # label(s1_xboole_0__e2_37_1_1__pre_topc__1) # label(lemma). [clausify(407)]. 10.83/11.05 886 -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -topological_space(A) | in(C,powerset(the_carrier(A))) | -in(C,f281(A,B)) # label(s1_xboole_0__e2_37_1_1__pre_topc__1) # label(lemma). [clausify(407)]. 10.83/11.05 887 empty_carrier(A) | -topological_space(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))) # label(dt_m1_connsp_2) # label(axiom). [clausify(426)]. 10.83/11.05 888 -top_str(A) | -topological_space(A) | -element(B,powerset(the_carrier(A))) | element(f303(A,B),powerset(powerset(the_carrier(A)))) # label(t46_pre_topc) # label(lemma). [clausify(428)]. 10.83/11.05 889 -top_str(A) | -topological_space(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) = meet_of_subsets(the_carrier(A),f303(A,B)) # label(t46_pre_topc) # label(lemma). [clausify(428)]. 10.83/11.05 890 -top_str(A) | -topological_space(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -subset(B,C) | -closed_subset(C,A) | in(C,f303(A,B)) # label(t46_pre_topc) # label(lemma). [clausify(428)]. 10.83/11.05 891 -top_str(A) | -topological_space(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | subset(B,C) | -in(C,f303(A,B)) # label(t46_pre_topc) # label(lemma). [clausify(428)]. 10.83/11.05 892 -top_str(A) | -topological_space(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | closed_subset(C,A) | -in(C,f303(A,B)) # label(t46_pre_topc) # label(lemma). [clausify(428)]. 10.83/11.05 893 empty_carrier(A) | -topological_space(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B) # label(t13_compts_1) # label(lemma). [clausify(482)]. 10.83/11.05 894 empty_carrier(A) | -topological_space(A) | -top_str(A) | compact_top_space(A) | element(f324(A),powerset(powerset(the_carrier(A)))) # label(t13_compts_1) # label(lemma). [clausify(482)]. 10.83/11.05 895 empty_carrier(A) | -topological_space(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f324(A)) = empty_set # label(t13_compts_1) # label(lemma). [clausify(482)]. 10.83/11.05 896 empty_carrier(A) | -topological_space(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f324(A),A) # label(t13_compts_1) # label(lemma). [clausify(482)]. 10.83/11.05 897 empty_carrier(A) | -topological_space(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)) # label(t13_compts_1) # label(lemma). [clausify(482)]. 10.83/11.05 898 -topological_space(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A) # label(fc6_tops_1) # label(axiom). [clausify(486)]. 10.83/11.05 899 -top_str(A) | -topological_space(A) | closed_subset(f345(A),A) # label(rc6_pre_topc) # label(axiom). [clausify(510)]. 10.83/11.05 900 -top_str(A) | -topological_space(A) | element(f345(A),powerset(the_carrier(A))) # label(rc6_pre_topc) # label(axiom). [clausify(510)]. 10.83/11.05 901 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f346(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A) # label(t44_pre_topc) # label(lemma). [clausify(514)]. 10.83/11.05 902 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f346(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A) # label(t44_pre_topc) # label(lemma). [clausify(514)]. 10.83/11.05 903 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f346(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A) # label(t44_pre_topc) # label(lemma). [clausify(514)]. 10.83/11.05 904 empty_carrier(A) | -top_str(A) | -topological_space(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C) # label(t5_connsp_2) # label(lemma). [clausify(517)]. 10.83/11.05 905 -element(A,the_carrier(B)) | -top_str(B) | -topological_space(B) | empty_carrier(B) | point_neighbourhood(f351(B,A),B,A) # label(existence_m1_connsp_2) # label(axiom). [clausify(526)]. 10.83/11.05 906 -top_str(A) | -topological_space(A) | empty_carrier(A) | closed_subset(f352(A),A) # label(rc7_pre_topc) # label(axiom). [clausify(527)]. 10.83/11.05 907 -top_str(A) | -topological_space(A) | empty_carrier(A) | -empty(f352(A)) # label(rc7_pre_topc) # label(axiom). [clausify(527)]. 10.83/11.05 908 -top_str(A) | -topological_space(A) | empty_carrier(A) | element(f352(A),powerset(the_carrier(A))) # label(rc7_pre_topc) # label(axiom). [clausify(527)]. 10.83/11.05 909 -topological_space(A) | -top_str(A) | closed_subset(cast_as_carrier_subset(A),A) # label(fc5_pre_topc) # label(axiom). [clausify(566)]. 10.83/11.05 910 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.05 911 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.05 912 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.05 913 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.05 914 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.05 915 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.05 916 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.05 917 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.05 918 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.05 919 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.05 920 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.05 921 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.05 922 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.05 923 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.05 924 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.05 925 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.05 926 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.06 927 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.06 928 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.06 929 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(592)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -subset(B,C) | -closed_subset(D,A) | D != C | -element(D,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | in(C,f11(A,B)). [resolve(780,e,781,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | subset(B,C) | -in(C,f11(A,B)). [resolve(780,e,782,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | closed_subset(f12(A,B,C),A) | -in(C,f11(A,B)). [resolve(780,e,783,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | f12(A,B,C) = C | -in(C,f11(A,B)). [resolve(780,e,784,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f12(A,B,C),powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(780,e,785,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | in(C,powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(780,e,786,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -closed_subset(B,A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | open_subset(subset_complement(the_carrier(A),B),A). [resolve(780,e,787,a)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A). [resolve(780,e,788,d)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | element(f124(A,B,C),powerset(the_carrier(A))). [resolve(780,e,789,a)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | f124(A,B,C) = C. [resolve(780,e,790,a)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | closed_subset(f124(A,B,C),A). [resolve(780,e,791,a)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | subset(B,C). [resolve(780,e,792,a)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(C,f123(A,B)) | -element(D,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C). [resolve(780,e,793,a)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f123(A,B),powerset(powerset(the_carrier(A)))). [resolve(780,e,794,a)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(780,e,795,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,796,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,797,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(780,e,798,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(780,e,799,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,800,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,801,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(780,e,802,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,803,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,804,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(780,e,805,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(780,e,806,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,807,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,808,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(780,e,809,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,810,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,811,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(780,e,812,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(780,e,813,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,814,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,815,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(780,e,816,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,817,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,818,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(780,e,819,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(780,e,820,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,821,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,822,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(780,e,823,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,824,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,825,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(780,e,826,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(780,e,827,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,828,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,829,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(780,e,830,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,831,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,832,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(780,e,833,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(780,e,834,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,835,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,836,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(780,e,837,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,838,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,839,c)]. 10.83/11.06 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(780,e,840,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(780,e,841,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,842,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,843,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(780,e,844,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,845,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,846,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(780,e,847,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(780,e,848,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,849,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,850,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(780,e,851,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,852,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,853,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(780,e,854,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(780,e,855,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,856,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,857,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(780,e,858,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,859,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,860,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(780,e,861,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(780,e,862,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,863,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,864,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(780,e,865,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,866,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,867,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(780,e,868,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(780,e,869,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(780,e,870,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(780,e,871,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -open_subset(B,A) | closed_subset(subset_complement(the_carrier(A),B),A). [resolve(780,e,872,a)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f185(A),powerset(the_carrier(A))). [resolve(780,e,873,b)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f185(A),A). [resolve(780,e,874,b)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(780,e,875,b)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(780,e,876,b)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | in(C,f199(A,B)). [resolve(780,e,877,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f199(A,B)). [resolve(780,e,878,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f199(A,B),powerset(powerset(the_carrier(A)))). [resolve(780,e,879,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f235(A),powerset(the_carrier(A))). [resolve(780,e,880,a)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f235(A),A). [resolve(780,e,881,a)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f235(A),A). [resolve(780,e,882,a)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A). [resolve(780,e,883,a)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,powerset(the_carrier(A))) | in(C,f281(A,B)). [resolve(780,e,884,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f281(A,B)). [resolve(780,e,885,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,powerset(the_carrier(A))) | -in(C,f281(A,B)). [resolve(780,e,886,c)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(780,e,887,b)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f303(A,B),powerset(powerset(the_carrier(A)))). [resolve(780,e,888,b)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) = meet_of_subsets(the_carrier(A),f303(A,B)). [resolve(780,e,889,b)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -subset(B,C) | -closed_subset(C,A) | in(C,f303(A,B)). [resolve(780,e,890,b)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | subset(B,C) | -in(C,f303(A,B)). [resolve(780,e,891,b)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | closed_subset(C,A) | -in(C,f303(A,B)). [resolve(780,e,892,b)]. 10.83/11.07 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(780,e,893,b)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f324(A),powerset(powerset(the_carrier(A)))). [resolve(780,e,894,b)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f324(A)) = empty_set. [resolve(780,e,895,b)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f324(A),A). [resolve(780,e,896,b)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(780,e,897,b)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f345(A),A). [resolve(780,e,899,b)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f345(A),powerset(the_carrier(A))). [resolve(780,e,900,b)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f346(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(780,e,901,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f346(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(780,e,902,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f346(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(780,e,903,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(780,e,904,c)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(780,e,905,c)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | closed_subset(f352(A),A). [resolve(780,e,906,b)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -empty(f352(A)). [resolve(780,e,907,b)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | element(f352(A),powerset(the_carrier(A))). [resolve(780,e,908,b)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(cast_as_carrier_subset(A),A). [resolve(780,e,909,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(780,e,910,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(780,e,911,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(780,e,912,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(780,e,913,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(780,e,914,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(780,e,915,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(780,e,916,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(780,e,917,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(780,e,918,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(780,e,919,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(780,e,920,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(780,e,921,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(780,e,922,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(780,e,923,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(780,e,924,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(780,e,925,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(780,e,926,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(780,e,927,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(780,e,928,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(780,e,929,a)]. 10.83/11.08 930 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(658)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -subset(B,C) | -closed_subset(D,A) | D != C | -element(D,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | in(C,f11(A,B)). [resolve(930,e,781,c)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | subset(B,C) | -in(C,f11(A,B)). [resolve(930,e,782,c)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | closed_subset(f12(A,B,C),A) | -in(C,f11(A,B)). [resolve(930,e,783,c)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | f12(A,B,C) = C | -in(C,f11(A,B)). [resolve(930,e,784,c)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f12(A,B,C),powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(930,e,785,c)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | in(C,powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(930,e,786,c)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -closed_subset(B,A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | open_subset(subset_complement(the_carrier(A),B),A). [resolve(930,e,787,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A). [resolve(930,e,788,d)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | element(f124(A,B,C),powerset(the_carrier(A))). [resolve(930,e,789,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | f124(A,B,C) = C. [resolve(930,e,790,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | closed_subset(f124(A,B,C),A). [resolve(930,e,791,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | subset(B,C). [resolve(930,e,792,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(C,f123(A,B)) | -element(D,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C). [resolve(930,e,793,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f123(A,B),powerset(powerset(the_carrier(A)))). [resolve(930,e,794,a)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(930,e,795,c)]. 10.83/11.08 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,796,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,797,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(930,e,798,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(930,e,799,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,800,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,801,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(930,e,802,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,803,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,804,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(930,e,805,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(930,e,806,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,807,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,808,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(930,e,809,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,810,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,811,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(930,e,812,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(930,e,813,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,814,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,815,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(930,e,816,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,817,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,818,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(930,e,819,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(930,e,820,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,821,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,822,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(930,e,823,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,824,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,825,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(930,e,826,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(930,e,827,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,828,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,829,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(930,e,830,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,831,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,832,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(930,e,833,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(930,e,834,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,835,c)]. 10.83/11.09 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,836,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(930,e,837,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,838,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,839,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(930,e,840,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(930,e,841,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,842,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,843,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(930,e,844,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,845,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,846,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(930,e,847,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(930,e,848,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,849,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,850,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(930,e,851,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,852,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,853,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(930,e,854,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(930,e,855,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,856,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,857,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(930,e,858,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,859,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,860,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(930,e,861,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(930,e,862,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,863,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,864,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(930,e,865,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,866,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,867,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(930,e,868,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(930,e,869,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(930,e,870,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(930,e,871,c)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -open_subset(B,A) | closed_subset(subset_complement(the_carrier(A),B),A). [resolve(930,e,872,a)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f185(A),powerset(the_carrier(A))). [resolve(930,e,873,b)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f185(A),A). [resolve(930,e,874,b)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(930,e,875,b)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(930,e,876,b)]. 10.83/11.10 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | in(C,f199(A,B)). [resolve(930,e,877,c)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f199(A,B)). [resolve(930,e,878,c)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f199(A,B),powerset(powerset(the_carrier(A)))). [resolve(930,e,879,c)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f235(A),powerset(the_carrier(A))). [resolve(930,e,880,a)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f235(A),A). [resolve(930,e,881,a)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f235(A),A). [resolve(930,e,882,a)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A). [resolve(930,e,883,a)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,powerset(the_carrier(A))) | in(C,f281(A,B)). [resolve(930,e,884,c)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f281(A,B)). [resolve(930,e,885,c)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,powerset(the_carrier(A))) | -in(C,f281(A,B)). [resolve(930,e,886,c)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(930,e,887,b)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f303(A,B),powerset(powerset(the_carrier(A)))). [resolve(930,e,888,b)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) = meet_of_subsets(the_carrier(A),f303(A,B)). [resolve(930,e,889,b)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -subset(B,C) | -closed_subset(C,A) | in(C,f303(A,B)). [resolve(930,e,890,b)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | subset(B,C) | -in(C,f303(A,B)). [resolve(930,e,891,b)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | closed_subset(C,A) | -in(C,f303(A,B)). [resolve(930,e,892,b)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(930,e,893,b)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f324(A),powerset(powerset(the_carrier(A)))). [resolve(930,e,894,b)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f324(A)) = empty_set. [resolve(930,e,895,b)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f324(A),A). [resolve(930,e,896,b)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(930,e,897,b)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f345(A),A). [resolve(930,e,899,b)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f345(A),powerset(the_carrier(A))). [resolve(930,e,900,b)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f346(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(930,e,901,a)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f346(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(930,e,902,a)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f346(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(930,e,903,a)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(930,e,904,c)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(930,e,905,c)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | closed_subset(f352(A),A). [resolve(930,e,906,b)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -empty(f352(A)). [resolve(930,e,907,b)]. 10.83/11.11 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | element(f352(A),powerset(the_carrier(A))). [resolve(930,e,908,b)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(cast_as_carrier_subset(A),A). [resolve(930,e,909,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(930,e,910,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(930,e,911,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(930,e,912,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(930,e,913,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(930,e,914,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(930,e,915,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(930,e,916,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(930,e,917,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(930,e,918,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(930,e,919,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(930,e,920,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(930,e,921,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(930,e,922,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(930,e,923,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(930,e,924,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(930,e,925,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(930,e,926,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(930,e,927,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(930,e,928,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(930,e,929,a)]. 10.83/11.12 931 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(658)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -subset(B,C) | -closed_subset(D,A) | D != C | -element(D,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | in(C,f11(A,B)). [resolve(931,e,781,c)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | subset(B,C) | -in(C,f11(A,B)). [resolve(931,e,782,c)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | closed_subset(f12(A,B,C),A) | -in(C,f11(A,B)). [resolve(931,e,783,c)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | f12(A,B,C) = C | -in(C,f11(A,B)). [resolve(931,e,784,c)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f12(A,B,C),powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(931,e,785,c)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | in(C,powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(931,e,786,c)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -closed_subset(B,A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | open_subset(subset_complement(the_carrier(A),B),A). [resolve(931,e,787,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A). [resolve(931,e,788,d)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | element(f124(A,B,C),powerset(the_carrier(A))). [resolve(931,e,789,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | f124(A,B,C) = C. [resolve(931,e,790,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | closed_subset(f124(A,B,C),A). [resolve(931,e,791,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | subset(B,C). [resolve(931,e,792,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(C,f123(A,B)) | -element(D,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C). [resolve(931,e,793,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f123(A,B),powerset(powerset(the_carrier(A)))). [resolve(931,e,794,a)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(931,e,795,c)]. 10.83/11.12 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,796,c)]. 10.83/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,797,c)]. 10.83/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(931,e,798,c)]. 10.83/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(931,e,799,c)]. 10.83/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,800,c)]. 10.83/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,801,c)]. 10.83/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(931,e,802,c)]. 10.83/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,803,c)]. 10.83/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,804,c)]. 10.83/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(931,e,805,c)]. 10.83/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(931,e,806,c)]. 10.83/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,807,c)]. 10.83/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,808,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(931,e,809,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,810,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,811,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(931,e,812,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(931,e,813,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,814,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,815,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(931,e,816,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,817,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,818,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(931,e,819,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(931,e,820,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,821,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,822,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(931,e,823,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,824,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,825,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(931,e,826,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(931,e,827,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,828,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,829,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(931,e,830,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,831,c)]. 10.92/11.13 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,832,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(931,e,833,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(931,e,834,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,835,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,836,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(931,e,837,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,838,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,839,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(931,e,840,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(931,e,841,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,842,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,843,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(931,e,844,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,845,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,846,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(931,e,847,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(931,e,848,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,849,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,850,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(931,e,851,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,852,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,853,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(931,e,854,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(931,e,855,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,856,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,857,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(931,e,858,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,859,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,860,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(931,e,861,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(931,e,862,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,863,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,864,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(931,e,865,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,866,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,867,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(931,e,868,c)]. 10.92/11.14 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(931,e,869,c)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(931,e,870,c)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(931,e,871,c)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -open_subset(B,A) | closed_subset(subset_complement(the_carrier(A),B),A). [resolve(931,e,872,a)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f185(A),powerset(the_carrier(A))). [resolve(931,e,873,b)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f185(A),A). [resolve(931,e,874,b)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(931,e,875,b)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(931,e,876,b)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | in(C,f199(A,B)). [resolve(931,e,877,c)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f199(A,B)). [resolve(931,e,878,c)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f199(A,B),powerset(powerset(the_carrier(A)))). [resolve(931,e,879,c)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f235(A),powerset(the_carrier(A))). [resolve(931,e,880,a)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f235(A),A). [resolve(931,e,881,a)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f235(A),A). [resolve(931,e,882,a)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A). [resolve(931,e,883,a)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,powerset(the_carrier(A))) | in(C,f281(A,B)). [resolve(931,e,884,c)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f281(A,B)). [resolve(931,e,885,c)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,powerset(the_carrier(A))) | -in(C,f281(A,B)). [resolve(931,e,886,c)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(931,e,887,b)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f303(A,B),powerset(powerset(the_carrier(A)))). [resolve(931,e,888,b)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) = meet_of_subsets(the_carrier(A),f303(A,B)). [resolve(931,e,889,b)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -subset(B,C) | -closed_subset(C,A) | in(C,f303(A,B)). [resolve(931,e,890,b)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | subset(B,C) | -in(C,f303(A,B)). [resolve(931,e,891,b)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | closed_subset(C,A) | -in(C,f303(A,B)). [resolve(931,e,892,b)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(931,e,893,b)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f324(A),powerset(powerset(the_carrier(A)))). [resolve(931,e,894,b)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f324(A)) = empty_set. [resolve(931,e,895,b)]. 10.92/11.15 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f324(A),A). [resolve(931,e,896,b)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(931,e,897,b)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f345(A),A). [resolve(931,e,899,b)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f345(A),powerset(the_carrier(A))). [resolve(931,e,900,b)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f346(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(931,e,901,a)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f346(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(931,e,902,a)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f346(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(931,e,903,a)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(931,e,904,c)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(931,e,905,c)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | closed_subset(f352(A),A). [resolve(931,e,906,b)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -empty(f352(A)). [resolve(931,e,907,b)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | element(f352(A),powerset(the_carrier(A))). [resolve(931,e,908,b)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(cast_as_carrier_subset(A),A). [resolve(931,e,909,a)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(931,e,910,a)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(931,e,911,a)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(931,e,912,a)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(931,e,913,a)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(931,e,914,a)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(931,e,915,a)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(931,e,916,a)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(931,e,917,a)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(931,e,918,a)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(931,e,919,a)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(931,e,920,a)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(931,e,921,a)]. 10.92/11.16 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(931,e,922,a)]. 10.92/11.17 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(931,e,923,a)]. 10.92/11.17 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(931,e,924,a)]. 10.92/11.17 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(931,e,925,a)]. 10.92/11.17 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(931,e,926,a)]. 10.92/11.17 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(931,e,927,a)]. 10.92/11.17 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(931,e,928,a)]. 10.92/11.17 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(931,e,929,a)]. 10.92/11.17 932 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(658)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -subset(B,C) | -closed_subset(D,A) | D != C | -element(D,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | in(C,f11(A,B)). [resolve(932,e,781,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | subset(B,C) | -in(C,f11(A,B)). [resolve(932,e,782,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | closed_subset(f12(A,B,C),A) | -in(C,f11(A,B)). [resolve(932,e,783,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | f12(A,B,C) = C | -in(C,f11(A,B)). [resolve(932,e,784,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f12(A,B,C),powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(932,e,785,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | in(C,powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(932,e,786,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -closed_subset(B,A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | open_subset(subset_complement(the_carrier(A),B),A). [resolve(932,e,787,a)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A). [resolve(932,e,788,d)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | element(f124(A,B,C),powerset(the_carrier(A))). [resolve(932,e,789,a)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | f124(A,B,C) = C. [resolve(932,e,790,a)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | closed_subset(f124(A,B,C),A). [resolve(932,e,791,a)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | subset(B,C). [resolve(932,e,792,a)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(C,f123(A,B)) | -element(D,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C). [resolve(932,e,793,a)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f123(A,B),powerset(powerset(the_carrier(A)))). [resolve(932,e,794,a)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(932,e,795,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,796,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,797,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(932,e,798,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(932,e,799,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,800,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,801,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(932,e,802,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,803,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,804,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(932,e,805,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(932,e,806,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,807,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,808,c)]. 10.92/11.17 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(932,e,809,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,810,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,811,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(932,e,812,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(932,e,813,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,814,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,815,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(932,e,816,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,817,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,818,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(932,e,819,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(932,e,820,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,821,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,822,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(932,e,823,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,824,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,825,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(932,e,826,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(932,e,827,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,828,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,829,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(932,e,830,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,831,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,832,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(932,e,833,c)]. 10.92/11.18 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(932,e,834,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,835,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,836,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(932,e,837,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,838,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,839,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(932,e,840,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(932,e,841,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,842,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,843,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(932,e,844,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,845,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,846,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(932,e,847,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(932,e,848,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,849,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,850,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(932,e,851,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,852,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,853,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(932,e,854,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(932,e,855,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,856,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,857,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(932,e,858,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,859,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,860,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(932,e,861,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(932,e,862,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,863,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,864,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(932,e,865,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,866,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,867,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(932,e,868,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(932,e,869,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(932,e,870,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(932,e,871,c)]. 10.98/11.19 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -open_subset(B,A) | closed_subset(subset_complement(the_carrier(A),B),A). [resolve(932,e,872,a)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f185(A),powerset(the_carrier(A))). [resolve(932,e,873,b)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f185(A),A). [resolve(932,e,874,b)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(932,e,875,b)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(932,e,876,b)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | in(C,f199(A,B)). [resolve(932,e,877,c)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f199(A,B)). [resolve(932,e,878,c)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f199(A,B),powerset(powerset(the_carrier(A)))). [resolve(932,e,879,c)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f235(A),powerset(the_carrier(A))). [resolve(932,e,880,a)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f235(A),A). [resolve(932,e,881,a)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f235(A),A). [resolve(932,e,882,a)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A). [resolve(932,e,883,a)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,powerset(the_carrier(A))) | in(C,f281(A,B)). [resolve(932,e,884,c)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f281(A,B)). [resolve(932,e,885,c)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,powerset(the_carrier(A))) | -in(C,f281(A,B)). [resolve(932,e,886,c)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(932,e,887,b)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f303(A,B),powerset(powerset(the_carrier(A)))). [resolve(932,e,888,b)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) = meet_of_subsets(the_carrier(A),f303(A,B)). [resolve(932,e,889,b)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -subset(B,C) | -closed_subset(C,A) | in(C,f303(A,B)). [resolve(932,e,890,b)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | subset(B,C) | -in(C,f303(A,B)). [resolve(932,e,891,b)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | closed_subset(C,A) | -in(C,f303(A,B)). [resolve(932,e,892,b)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(932,e,893,b)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f324(A),powerset(powerset(the_carrier(A)))). [resolve(932,e,894,b)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f324(A)) = empty_set. [resolve(932,e,895,b)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f324(A),A). [resolve(932,e,896,b)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(932,e,897,b)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f345(A),A). [resolve(932,e,899,b)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f345(A),powerset(the_carrier(A))). [resolve(932,e,900,b)]. 10.98/11.20 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f346(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(932,e,901,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f346(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(932,e,902,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f346(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(932,e,903,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(932,e,904,c)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(932,e,905,c)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | closed_subset(f352(A),A). [resolve(932,e,906,b)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -empty(f352(A)). [resolve(932,e,907,b)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | element(f352(A),powerset(the_carrier(A))). [resolve(932,e,908,b)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(cast_as_carrier_subset(A),A). [resolve(932,e,909,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(932,e,910,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(932,e,911,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(932,e,912,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(932,e,913,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(932,e,914,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(932,e,915,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(932,e,916,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(932,e,917,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(932,e,918,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(932,e,919,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(932,e,920,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(932,e,921,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(932,e,922,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(932,e,923,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(932,e,924,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(932,e,925,a)]. 10.98/11.21 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(932,e,926,a)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(932,e,927,a)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(932,e,928,a)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(932,e,929,a)]. 10.98/11.22 933 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(658)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -subset(B,C) | -closed_subset(D,A) | D != C | -element(D,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | in(C,f11(A,B)). [resolve(933,e,781,c)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | subset(B,C) | -in(C,f11(A,B)). [resolve(933,e,782,c)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | closed_subset(f12(A,B,C),A) | -in(C,f11(A,B)). [resolve(933,e,783,c)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | f12(A,B,C) = C | -in(C,f11(A,B)). [resolve(933,e,784,c)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f12(A,B,C),powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(933,e,785,c)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | in(C,powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(933,e,786,c)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -closed_subset(B,A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | open_subset(subset_complement(the_carrier(A),B),A). [resolve(933,e,787,a)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A). [resolve(933,e,788,d)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | element(f124(A,B,C),powerset(the_carrier(A))). [resolve(933,e,789,a)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | f124(A,B,C) = C. [resolve(933,e,790,a)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | closed_subset(f124(A,B,C),A). [resolve(933,e,791,a)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | subset(B,C). [resolve(933,e,792,a)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(C,f123(A,B)) | -element(D,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C). [resolve(933,e,793,a)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f123(A,B),powerset(powerset(the_carrier(A)))). [resolve(933,e,794,a)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(933,e,795,c)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,796,c)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,797,c)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(933,e,798,c)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(933,e,799,c)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,800,c)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,801,c)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(933,e,802,c)]. 10.98/11.22 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,803,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,804,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(933,e,805,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(933,e,806,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,807,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,808,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(933,e,809,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,810,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,811,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(933,e,812,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(933,e,813,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,814,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,815,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(933,e,816,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,817,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,818,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(933,e,819,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(933,e,820,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,821,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,822,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(933,e,823,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,824,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,825,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(933,e,826,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(933,e,827,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,828,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,829,c)]. 10.98/11.23 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(933,e,830,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,831,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,832,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(933,e,833,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(933,e,834,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,835,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,836,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(933,e,837,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,838,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,839,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(933,e,840,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(933,e,841,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,842,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,843,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(933,e,844,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,845,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,846,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(933,e,847,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(933,e,848,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,849,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,850,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(933,e,851,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,852,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,853,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(933,e,854,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(933,e,855,c)]. 10.98/11.24 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,856,c)]. 10.98/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,857,c)]. 10.98/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(933,e,858,c)]. 10.98/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,859,c)]. 10.98/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,860,c)]. 10.98/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(933,e,861,c)]. 10.98/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(933,e,862,c)]. 10.98/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,863,c)]. 10.98/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,864,c)]. 10.98/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(933,e,865,c)]. 10.98/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,866,c)]. 10.98/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,867,c)]. 10.98/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(933,e,868,c)]. 10.98/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(933,e,869,c)]. 10.98/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(933,e,870,c)]. 11.05/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(933,e,871,c)]. 11.05/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -open_subset(B,A) | closed_subset(subset_complement(the_carrier(A),B),A). [resolve(933,e,872,a)]. 11.05/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f185(A),powerset(the_carrier(A))). [resolve(933,e,873,b)]. 11.05/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f185(A),A). [resolve(933,e,874,b)]. 11.05/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(933,e,875,b)]. 11.05/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(933,e,876,b)]. 11.05/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | in(C,f199(A,B)). [resolve(933,e,877,c)]. 11.05/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f199(A,B)). [resolve(933,e,878,c)]. 11.05/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f199(A,B),powerset(powerset(the_carrier(A)))). [resolve(933,e,879,c)]. 11.05/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f235(A),powerset(the_carrier(A))). [resolve(933,e,880,a)]. 11.05/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f235(A),A). [resolve(933,e,881,a)]. 11.05/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f235(A),A). [resolve(933,e,882,a)]. 11.05/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A). [resolve(933,e,883,a)]. 11.05/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,powerset(the_carrier(A))) | in(C,f281(A,B)). [resolve(933,e,884,c)]. 11.05/11.25 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f281(A,B)). [resolve(933,e,885,c)]. 11.05/11.26 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,powerset(the_carrier(A))) | -in(C,f281(A,B)). [resolve(933,e,886,c)]. 11.05/11.26 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(933,e,887,b)]. 11.05/11.26 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f303(A,B),powerset(powerset(the_carrier(A)))). [resolve(933,e,888,b)]. 11.05/11.26 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) = meet_of_subsets(the_carrier(A),f303(A,B)). [resolve(933,e,889,b)]. 11.05/11.26 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -subset(B,C) | -closed_subset(C,A) | in(C,f303(A,B)). [resolve(933,e,890,b)]. 11.05/11.26 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | subset(B,C) | -in(C,f303(A,B)). [resolve(933,e,891,b)]. 11.05/11.26 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | closed_subset(C,A) | -in(C,f303(A,B)). [resolve(933,e,892,b)]. 11.05/11.26 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(933,e,893,b)]. 11.05/11.26 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f324(A),powerset(powerset(the_carrier(A)))). [resolve(933,e,894,b)]. 11.05/11.26 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f324(A)) = empty_set. [resolve(933,e,895,b)]. 11.05/11.26 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f324(A),A). [resolve(933,e,896,b)]. 11.05/11.26 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(933,e,897,b)]. 11.05/11.26 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f345(A),A). [resolve(933,e,899,b)]. 11.05/11.26 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f345(A),powerset(the_carrier(A))). [resolve(933,e,900,b)]. 11.05/11.26 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f346(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(933,e,901,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f346(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(933,e,902,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f346(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(933,e,903,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(933,e,904,c)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(933,e,905,c)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | closed_subset(f352(A),A). [resolve(933,e,906,b)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -empty(f352(A)). [resolve(933,e,907,b)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | element(f352(A),powerset(the_carrier(A))). [resolve(933,e,908,b)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(cast_as_carrier_subset(A),A). [resolve(933,e,909,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(933,e,910,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(933,e,911,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(933,e,912,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(933,e,913,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(933,e,914,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(933,e,915,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(933,e,916,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(933,e,917,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(933,e,918,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(933,e,919,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(933,e,920,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(933,e,921,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(933,e,922,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(933,e,923,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(933,e,924,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(933,e,925,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(933,e,926,a)]. 11.05/11.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(933,e,927,a)]. 11.05/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(933,e,928,a)]. 11.05/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(933,e,929,a)]. 11.05/11.28 934 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(658)]. 11.05/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -subset(B,C) | -closed_subset(D,A) | D != C | -element(D,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | in(C,f11(A,B)). [resolve(934,e,781,c)]. 11.05/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | subset(B,C) | -in(C,f11(A,B)). [resolve(934,e,782,c)]. 11.05/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | closed_subset(f12(A,B,C),A) | -in(C,f11(A,B)). [resolve(934,e,783,c)]. 11.05/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | f12(A,B,C) = C | -in(C,f11(A,B)). [resolve(934,e,784,c)]. 11.05/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f12(A,B,C),powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(934,e,785,c)]. 11.05/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | in(C,powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(934,e,786,c)]. 11.05/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -closed_subset(B,A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | open_subset(subset_complement(the_carrier(A),B),A). [resolve(934,e,787,a)]. 11.05/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A). [resolve(934,e,788,d)]. 11.05/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | element(f124(A,B,C),powerset(the_carrier(A))). [resolve(934,e,789,a)]. 11.05/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | f124(A,B,C) = C. [resolve(934,e,790,a)]. 11.08/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | closed_subset(f124(A,B,C),A). [resolve(934,e,791,a)]. 11.08/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | subset(B,C). [resolve(934,e,792,a)]. 11.08/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(C,f123(A,B)) | -element(D,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C). [resolve(934,e,793,a)]. 11.08/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f123(A,B),powerset(powerset(the_carrier(A)))). [resolve(934,e,794,a)]. 11.08/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(934,e,795,c)]. 11.08/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,796,c)]. 11.08/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,797,c)]. 11.08/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(934,e,798,c)]. 11.08/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(934,e,799,c)]. 11.08/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,800,c)]. 11.08/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,801,c)]. 11.08/11.28 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(934,e,802,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,803,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,804,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(934,e,805,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(934,e,806,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,807,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,808,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(934,e,809,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,810,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,811,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(934,e,812,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(934,e,813,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,814,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,815,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(934,e,816,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,817,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,818,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(934,e,819,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(934,e,820,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,821,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,822,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(934,e,823,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,824,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,825,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(934,e,826,c)]. 11.08/11.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(934,e,827,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,828,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,829,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(934,e,830,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,831,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,832,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(934,e,833,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(934,e,834,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,835,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,836,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(934,e,837,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,838,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,839,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(934,e,840,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(934,e,841,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,842,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,843,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(934,e,844,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,845,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,846,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(934,e,847,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(934,e,848,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,849,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,850,c)]. 11.08/11.30 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(934,e,851,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,852,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,853,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(934,e,854,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(934,e,855,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,856,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,857,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(934,e,858,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,859,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,860,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(934,e,861,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(934,e,862,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,863,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,864,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(934,e,865,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,866,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,867,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(934,e,868,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(934,e,869,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(934,e,870,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(934,e,871,c)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -open_subset(B,A) | closed_subset(subset_complement(the_carrier(A),B),A). [resolve(934,e,872,a)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f185(A),powerset(the_carrier(A))). [resolve(934,e,873,b)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f185(A),A). [resolve(934,e,874,b)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(934,e,875,b)]. 11.08/11.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(934,e,876,b)]. 11.08/11.32 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | in(C,f199(A,B)). [resolve(934,e,877,c)]. 11.08/11.32 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f199(A,B)). [resolve(934,e,878,c)]. 11.08/11.32 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f199(A,B),powerset(powerset(the_carrier(A)))). [resolve(934,e,879,c)]. 11.08/11.32 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f235(A),powerset(the_carrier(A))). [resolve(934,e,880,a)]. 11.08/11.32 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f235(A),A). [resolve(934,e,881,a)]. 11.08/11.32 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f235(A),A). [resolve(934,e,882,a)]. 11.08/11.32 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A). [resolve(934,e,883,a)]. 11.08/11.32 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,powerset(the_carrier(A))) | in(C,f281(A,B)). [resolve(934,e,884,c)]. 11.08/11.32 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f281(A,B)). [resolve(934,e,885,c)]. 11.08/11.32 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,powerset(the_carrier(A))) | -in(C,f281(A,B)). [resolve(934,e,886,c)]. 11.08/11.32 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(934,e,887,b)]. 11.08/11.32 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f303(A,B),powerset(powerset(the_carrier(A)))). [resolve(934,e,888,b)]. 11.08/11.32 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) = meet_of_subsets(the_carrier(A),f303(A,B)). [resolve(934,e,889,b)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -subset(B,C) | -closed_subset(C,A) | in(C,f303(A,B)). [resolve(934,e,890,b)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | subset(B,C) | -in(C,f303(A,B)). [resolve(934,e,891,b)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | closed_subset(C,A) | -in(C,f303(A,B)). [resolve(934,e,892,b)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(934,e,893,b)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f324(A),powerset(powerset(the_carrier(A)))). [resolve(934,e,894,b)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f324(A)) = empty_set. [resolve(934,e,895,b)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f324(A),A). [resolve(934,e,896,b)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(934,e,897,b)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f345(A),A). [resolve(934,e,899,b)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f345(A),powerset(the_carrier(A))). [resolve(934,e,900,b)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f346(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(934,e,901,a)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f346(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(934,e,902,a)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f346(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(934,e,903,a)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(934,e,904,c)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(934,e,905,c)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | closed_subset(f352(A),A). [resolve(934,e,906,b)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -empty(f352(A)). [resolve(934,e,907,b)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | element(f352(A),powerset(the_carrier(A))). [resolve(934,e,908,b)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(cast_as_carrier_subset(A),A). [resolve(934,e,909,a)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(934,e,910,a)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(934,e,911,a)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(934,e,912,a)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(934,e,913,a)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(934,e,914,a)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(934,e,915,a)]. 11.13/11.33 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(934,e,916,a)]. 11.13/11.34 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(934,e,917,a)]. 11.13/11.34 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(934,e,918,a)]. 11.13/11.34 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(934,e,919,a)]. 11.13/11.34 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(934,e,920,a)]. 11.13/11.34 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(934,e,921,a)]. 11.13/11.34 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(934,e,922,a)]. 11.13/11.34 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(934,e,923,a)]. 11.13/11.34 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(934,e,924,a)]. 11.13/11.34 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(934,e,925,a)]. 11.13/11.34 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(934,e,926,a)]. 11.13/11.34 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(934,e,927,a)]. 11.13/11.34 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(934,e,928,a)]. 11.13/11.34 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(934,e,929,a)]. 11.13/11.34 935 -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(658)]. 11.13/11.34 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -subset(B,C) | -closed_subset(D,A) | D != C | -element(D,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | in(C,f11(A,B)). [resolve(935,e,781,c)]. 11.13/11.34 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | subset(B,C) | -in(C,f11(A,B)). [resolve(935,e,782,c)]. 11.13/11.34 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | closed_subset(f12(A,B,C),A) | -in(C,f11(A,B)). [resolve(935,e,783,c)]. 11.13/11.34 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | f12(A,B,C) = C | -in(C,f11(A,B)). [resolve(935,e,784,c)]. 11.13/11.34 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f12(A,B,C),powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(935,e,785,c)]. 11.13/11.34 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | in(C,powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(935,e,786,c)]. 11.13/11.34 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -closed_subset(B,A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | open_subset(subset_complement(the_carrier(A),B),A). [resolve(935,e,787,a)]. 11.13/11.34 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A). [resolve(935,e,788,d)]. 11.13/11.34 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | element(f124(A,B,C),powerset(the_carrier(A))). [resolve(935,e,789,a)]. 11.13/11.34 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | f124(A,B,C) = C. [resolve(935,e,790,a)]. 11.13/11.34 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | closed_subset(f124(A,B,C),A). [resolve(935,e,791,a)]. 11.13/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | subset(B,C). [resolve(935,e,792,a)]. 11.13/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(C,f123(A,B)) | -element(D,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C). [resolve(935,e,793,a)]. 11.13/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f123(A,B),powerset(powerset(the_carrier(A)))). [resolve(935,e,794,a)]. 11.13/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(935,e,795,c)]. 11.13/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,796,c)]. 11.13/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,797,c)]. 11.13/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(935,e,798,c)]. 11.13/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(935,e,799,c)]. 11.13/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,800,c)]. 11.13/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,801,c)]. 11.13/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(935,e,802,c)]. 11.13/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,803,c)]. 11.13/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,804,c)]. 11.16/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(935,e,805,c)]. 11.16/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(935,e,806,c)]. 11.16/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,807,c)]. 11.16/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,808,c)]. 11.16/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(935,e,809,c)]. 11.16/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,810,c)]. 11.16/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,811,c)]. 11.16/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(935,e,812,c)]. 11.16/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(935,e,813,c)]. 11.16/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,814,c)]. 11.16/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,815,c)]. 11.16/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(935,e,816,c)]. 11.16/11.35 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,817,c)]. 11.16/11.36 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,818,c)]. 11.16/11.36 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(935,e,819,c)]. 11.16/11.36 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(935,e,820,c)]. 11.16/11.36 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,821,c)]. 11.16/11.36 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,822,c)]. 11.16/11.36 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(935,e,823,c)]. 11.16/11.36 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,824,c)]. 11.16/11.36 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,825,c)]. 11.16/11.36 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(935,e,826,c)]. 11.16/11.36 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(935,e,827,c)]. 11.16/11.36 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,828,c)]. 11.16/11.36 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,829,c)]. 11.16/11.36 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(935,e,830,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,831,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,832,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(935,e,833,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(935,e,834,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,835,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,836,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(935,e,837,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,838,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,839,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(935,e,840,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(935,e,841,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,842,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,843,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(935,e,844,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,845,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,846,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(935,e,847,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(935,e,848,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,849,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,850,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(935,e,851,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,852,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,853,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(935,e,854,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(935,e,855,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,856,c)]. 11.16/11.37 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,857,c)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(935,e,858,c)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,859,c)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,860,c)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(935,e,861,c)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(935,e,862,c)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,863,c)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,864,c)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(935,e,865,c)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,866,c)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,867,c)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(935,e,868,c)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(935,e,869,c)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(935,e,870,c)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(935,e,871,c)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -open_subset(B,A) | closed_subset(subset_complement(the_carrier(A),B),A). [resolve(935,e,872,a)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f185(A),powerset(the_carrier(A))). [resolve(935,e,873,b)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f185(A),A). [resolve(935,e,874,b)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(935,e,875,b)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(935,e,876,b)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | in(C,f199(A,B)). [resolve(935,e,877,c)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f199(A,B)). [resolve(935,e,878,c)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f199(A,B),powerset(powerset(the_carrier(A)))). [resolve(935,e,879,c)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f235(A),powerset(the_carrier(A))). [resolve(935,e,880,a)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f235(A),A). [resolve(935,e,881,a)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f235(A),A). [resolve(935,e,882,a)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A). [resolve(935,e,883,a)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,powerset(the_carrier(A))) | in(C,f281(A,B)). [resolve(935,e,884,c)]. 11.16/11.38 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f281(A,B)). [resolve(935,e,885,c)]. 11.16/11.39 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,powerset(the_carrier(A))) | -in(C,f281(A,B)). [resolve(935,e,886,c)]. 11.16/11.39 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(935,e,887,b)]. 11.16/11.39 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f303(A,B),powerset(powerset(the_carrier(A)))). [resolve(935,e,888,b)]. 11.16/11.39 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) = meet_of_subsets(the_carrier(A),f303(A,B)). [resolve(935,e,889,b)]. 11.16/11.39 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -subset(B,C) | -closed_subset(C,A) | in(C,f303(A,B)). [resolve(935,e,890,b)]. 11.16/11.39 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | subset(B,C) | -in(C,f303(A,B)). [resolve(935,e,891,b)]. 11.16/11.39 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | closed_subset(C,A) | -in(C,f303(A,B)). [resolve(935,e,892,b)]. 11.16/11.39 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(935,e,893,b)]. 11.16/11.39 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f324(A),powerset(powerset(the_carrier(A)))). [resolve(935,e,894,b)]. 11.16/11.39 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f324(A)) = empty_set. [resolve(935,e,895,b)]. 11.16/11.39 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f324(A),A). [resolve(935,e,896,b)]. 11.16/11.39 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(935,e,897,b)]. 11.16/11.39 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f345(A),A). [resolve(935,e,899,b)]. 11.16/11.39 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f345(A),powerset(the_carrier(A))). [resolve(935,e,900,b)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f346(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(935,e,901,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f346(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(935,e,902,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f346(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(935,e,903,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(935,e,904,c)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(935,e,905,c)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | closed_subset(f352(A),A). [resolve(935,e,906,b)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -empty(f352(A)). [resolve(935,e,907,b)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | element(f352(A),powerset(the_carrier(A))). [resolve(935,e,908,b)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(cast_as_carrier_subset(A),A). [resolve(935,e,909,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(935,e,910,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(935,e,911,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(935,e,912,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(935,e,913,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(935,e,914,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(935,e,915,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(935,e,916,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(935,e,917,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(935,e,918,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(935,e,919,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(935,e,920,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(935,e,921,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(935,e,922,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(935,e,923,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(935,e,924,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(935,e,925,a)]. 11.16/11.40 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(935,e,926,a)]. 11.16/11.41 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(935,e,927,a)]. 11.16/11.41 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(935,e,928,a)]. 11.16/11.41 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(935,e,929,a)]. 11.16/11.41 936 -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(658)]. 11.16/11.41 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -subset(B,C) | -closed_subset(D,A) | D != C | -element(D,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | in(C,f11(A,B)). [resolve(936,e,781,c)]. 11.16/11.41 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | subset(B,C) | -in(C,f11(A,B)). [resolve(936,e,782,c)]. 11.16/11.41 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | closed_subset(f12(A,B,C),A) | -in(C,f11(A,B)). [resolve(936,e,783,c)]. 11.16/11.41 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | f12(A,B,C) = C | -in(C,f11(A,B)). [resolve(936,e,784,c)]. 11.16/11.41 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f12(A,B,C),powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(936,e,785,c)]. 11.16/11.41 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | in(C,powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(936,e,786,c)]. 11.16/11.41 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -closed_subset(B,A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | open_subset(subset_complement(the_carrier(A),B),A). [resolve(936,e,787,a)]. 11.16/11.41 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A). [resolve(936,e,788,d)]. 11.16/11.41 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | element(f124(A,B,C),powerset(the_carrier(A))). [resolve(936,e,789,a)]. 11.16/11.41 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | f124(A,B,C) = C. [resolve(936,e,790,a)]. 11.16/11.41 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | closed_subset(f124(A,B,C),A). [resolve(936,e,791,a)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | subset(B,C). [resolve(936,e,792,a)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(C,f123(A,B)) | -element(D,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C). [resolve(936,e,793,a)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f123(A,B),powerset(powerset(the_carrier(A)))). [resolve(936,e,794,a)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(936,e,795,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,796,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,797,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(936,e,798,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(936,e,799,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,800,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,801,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(936,e,802,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,803,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,804,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(936,e,805,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(936,e,806,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,807,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,808,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(936,e,809,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,810,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,811,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(936,e,812,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(936,e,813,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,814,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,815,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(936,e,816,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,817,c)]. 11.16/11.42 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,818,c)]. 11.24/11.43 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(936,e,819,c)]. 11.24/11.43 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(936,e,820,c)]. 11.24/11.43 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,821,c)]. 11.24/11.43 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,822,c)]. 11.24/11.43 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(936,e,823,c)]. 11.24/11.43 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,824,c)]. 11.24/11.43 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,825,c)]. 11.24/11.43 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(936,e,826,c)]. 11.24/11.43 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(936,e,827,c)]. 11.24/11.43 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,828,c)]. 11.24/11.43 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,829,c)]. 11.24/11.43 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(936,e,830,c)]. 11.24/11.43 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,831,c)]. 11.24/11.43 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,832,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(936,e,833,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(936,e,834,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,835,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,836,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(936,e,837,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,838,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,839,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(936,e,840,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(936,e,841,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,842,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,843,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(936,e,844,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,845,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,846,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(936,e,847,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(936,e,848,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,849,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,850,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(936,e,851,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,852,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,853,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(936,e,854,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(936,e,855,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,856,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,857,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(936,e,858,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,859,c)]. 11.24/11.44 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,860,c)]. 11.24/11.45 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(936,e,861,c)]. 11.24/11.45 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(936,e,862,c)]. 11.24/11.45 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,863,c)]. 11.24/11.45 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,864,c)]. 11.24/11.45 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(936,e,865,c)]. 11.24/11.45 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,866,c)]. 11.24/11.45 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,867,c)]. 11.24/11.45 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(936,e,868,c)]. 11.24/11.45 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(936,e,869,c)]. 11.24/11.45 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(936,e,870,c)]. 11.24/11.45 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(936,e,871,c)]. 11.24/11.45 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -open_subset(B,A) | closed_subset(subset_complement(the_carrier(A),B),A). [resolve(936,e,872,a)]. 11.24/11.45 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f185(A),powerset(the_carrier(A))). [resolve(936,e,873,b)]. 11.24/11.45 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f185(A),A). [resolve(936,e,874,b)]. 11.24/11.45 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(936,e,875,b)]. 11.24/11.46 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(936,e,876,b)]. 11.24/11.46 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | in(C,f199(A,B)). [resolve(936,e,877,c)]. 11.24/11.46 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f199(A,B)). [resolve(936,e,878,c)]. 11.24/11.46 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f199(A,B),powerset(powerset(the_carrier(A)))). [resolve(936,e,879,c)]. 11.24/11.46 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f235(A),powerset(the_carrier(A))). [resolve(936,e,880,a)]. 11.24/11.46 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f235(A),A). [resolve(936,e,881,a)]. 11.24/11.46 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f235(A),A). [resolve(936,e,882,a)]. 11.24/11.46 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A). [resolve(936,e,883,a)]. 11.24/11.46 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,powerset(the_carrier(A))) | in(C,f281(A,B)). [resolve(936,e,884,c)]. 11.24/11.46 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f281(A,B)). [resolve(936,e,885,c)]. 11.24/11.46 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,powerset(the_carrier(A))) | -in(C,f281(A,B)). [resolve(936,e,886,c)]. 11.24/11.46 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(936,e,887,b)]. 11.24/11.46 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f303(A,B),powerset(powerset(the_carrier(A)))). [resolve(936,e,888,b)]. 11.24/11.46 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) = meet_of_subsets(the_carrier(A),f303(A,B)). [resolve(936,e,889,b)]. 11.24/11.46 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -subset(B,C) | -closed_subset(C,A) | in(C,f303(A,B)). [resolve(936,e,890,b)]. 11.24/11.46 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | subset(B,C) | -in(C,f303(A,B)). [resolve(936,e,891,b)]. 11.24/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | closed_subset(C,A) | -in(C,f303(A,B)). [resolve(936,e,892,b)]. 11.24/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(936,e,893,b)]. 11.24/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f324(A),powerset(powerset(the_carrier(A)))). [resolve(936,e,894,b)]. 11.24/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f324(A)) = empty_set. [resolve(936,e,895,b)]. 11.24/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f324(A),A). [resolve(936,e,896,b)]. 11.24/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(936,e,897,b)]. 11.24/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f345(A),A). [resolve(936,e,899,b)]. 11.24/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f345(A),powerset(the_carrier(A))). [resolve(936,e,900,b)]. 11.24/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f346(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(936,e,901,a)]. 11.24/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f346(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(936,e,902,a)]. 11.24/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f346(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(936,e,903,a)]. 11.24/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(936,e,904,c)]. 11.24/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(936,e,905,c)]. 11.24/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | closed_subset(f352(A),A). [resolve(936,e,906,b)]. 11.24/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -empty(f352(A)). [resolve(936,e,907,b)]. 11.29/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | element(f352(A),powerset(the_carrier(A))). [resolve(936,e,908,b)]. 11.29/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(cast_as_carrier_subset(A),A). [resolve(936,e,909,a)]. 11.29/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(936,e,910,a)]. 11.29/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(936,e,911,a)]. 11.29/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(936,e,912,a)]. 11.29/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(936,e,913,a)]. 11.29/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(936,e,914,a)]. 11.29/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(936,e,915,a)]. 11.29/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(936,e,916,a)]. 11.29/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(936,e,917,a)]. 11.29/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(936,e,918,a)]. 11.29/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(936,e,919,a)]. 11.29/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(936,e,920,a)]. 11.29/11.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(936,e,921,a)]. 11.29/11.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(936,e,922,a)]. 11.29/11.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(936,e,923,a)]. 11.29/11.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(936,e,924,a)]. 11.29/11.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(936,e,925,a)]. 11.29/11.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(936,e,926,a)]. 11.29/11.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(936,e,927,a)]. 11.29/11.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(936,e,928,a)]. 11.29/11.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(936,e,929,a)]. 11.29/11.48 937 -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(658)]. 11.29/11.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -subset(B,C) | -closed_subset(D,A) | D != C | -element(D,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | in(C,f11(A,B)). [resolve(937,e,781,c)]. 11.29/11.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | subset(B,C) | -in(C,f11(A,B)). [resolve(937,e,782,c)]. 11.29/11.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | closed_subset(f12(A,B,C),A) | -in(C,f11(A,B)). [resolve(937,e,783,c)]. 11.29/11.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | f12(A,B,C) = C | -in(C,f11(A,B)). [resolve(937,e,784,c)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f12(A,B,C),powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(937,e,785,c)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | in(C,powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(937,e,786,c)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -closed_subset(B,A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | open_subset(subset_complement(the_carrier(A),B),A). [resolve(937,e,787,a)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A). [resolve(937,e,788,d)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | element(f124(A,B,C),powerset(the_carrier(A))). [resolve(937,e,789,a)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | f124(A,B,C) = C. [resolve(937,e,790,a)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | closed_subset(f124(A,B,C),A). [resolve(937,e,791,a)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | subset(B,C). [resolve(937,e,792,a)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(C,f123(A,B)) | -element(D,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C). [resolve(937,e,793,a)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f123(A,B),powerset(powerset(the_carrier(A)))). [resolve(937,e,794,a)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(937,e,795,c)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,796,c)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,797,c)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(937,e,798,c)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(937,e,799,c)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,800,c)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,801,c)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(937,e,802,c)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,803,c)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,804,c)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(937,e,805,c)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(937,e,806,c)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,807,c)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,808,c)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(937,e,809,c)]. 11.29/11.49 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,810,c)]. 11.29/11.50 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,811,c)]. 11.29/11.50 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(937,e,812,c)]. 11.29/11.50 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(937,e,813,c)]. 11.29/11.50 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,814,c)]. 11.29/11.50 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,815,c)]. 11.29/11.50 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(937,e,816,c)]. 11.29/11.50 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,817,c)]. 11.29/11.50 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,818,c)]. 11.29/11.50 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(937,e,819,c)]. 11.29/11.50 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(937,e,820,c)]. 11.29/11.50 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,821,c)]. 11.29/11.50 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,822,c)]. 11.29/11.50 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(937,e,823,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,824,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,825,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(937,e,826,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(937,e,827,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,828,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,829,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(937,e,830,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,831,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,832,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(937,e,833,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(937,e,834,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,835,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,836,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(937,e,837,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,838,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,839,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(937,e,840,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(937,e,841,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,842,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,843,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(937,e,844,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,845,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,846,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(937,e,847,c)]. 11.29/11.51 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(937,e,848,c)]. 11.29/11.52 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,849,c)]. 11.29/11.52 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,850,c)]. 11.29/11.52 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(937,e,851,c)]. 11.29/11.52 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,852,c)]. 11.29/11.52 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,853,c)]. 11.29/11.52 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(937,e,854,c)]. 11.29/11.52 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(937,e,855,c)]. 11.29/11.52 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,856,c)]. 11.29/11.52 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,857,c)]. 11.29/11.52 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(937,e,858,c)]. 11.29/11.52 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,859,c)]. 11.29/11.52 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,860,c)]. 11.29/11.52 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(937,e,861,c)]. 11.29/11.53 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(937,e,862,c)]. 11.29/11.53 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,863,c)]. 11.29/11.53 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,864,c)]. 11.29/11.53 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(937,e,865,c)]. 11.29/11.53 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,866,c)]. 11.29/11.53 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,867,c)]. 11.29/11.53 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(937,e,868,c)]. 11.29/11.53 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(937,e,869,c)]. 11.29/11.53 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(937,e,870,c)]. 11.29/11.53 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(937,e,871,c)]. 11.29/11.53 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -open_subset(B,A) | closed_subset(subset_complement(the_carrier(A),B),A). [resolve(937,e,872,a)]. 11.29/11.53 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f185(A),powerset(the_carrier(A))). [resolve(937,e,873,b)]. 11.29/11.53 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f185(A),A). [resolve(937,e,874,b)]. 11.29/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(937,e,875,b)]. 11.29/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(937,e,876,b)]. 11.29/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | in(C,f199(A,B)). [resolve(937,e,877,c)]. 11.29/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f199(A,B)). [resolve(937,e,878,c)]. 11.29/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f199(A,B),powerset(powerset(the_carrier(A)))). [resolve(937,e,879,c)]. 11.29/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f235(A),powerset(the_carrier(A))). [resolve(937,e,880,a)]. 11.29/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f235(A),A). [resolve(937,e,881,a)]. 11.29/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f235(A),A). [resolve(937,e,882,a)]. 11.29/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A). [resolve(937,e,883,a)]. 11.29/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,powerset(the_carrier(A))) | in(C,f281(A,B)). [resolve(937,e,884,c)]. 11.29/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f281(A,B)). [resolve(937,e,885,c)]. 11.29/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,powerset(the_carrier(A))) | -in(C,f281(A,B)). [resolve(937,e,886,c)]. 11.29/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(937,e,887,b)]. 11.29/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f303(A,B),powerset(powerset(the_carrier(A)))). [resolve(937,e,888,b)]. 11.37/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) = meet_of_subsets(the_carrier(A),f303(A,B)). [resolve(937,e,889,b)]. 11.37/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -subset(B,C) | -closed_subset(C,A) | in(C,f303(A,B)). [resolve(937,e,890,b)]. 11.37/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | subset(B,C) | -in(C,f303(A,B)). [resolve(937,e,891,b)]. 11.37/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | closed_subset(C,A) | -in(C,f303(A,B)). [resolve(937,e,892,b)]. 11.37/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(937,e,893,b)]. 11.37/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f324(A),powerset(powerset(the_carrier(A)))). [resolve(937,e,894,b)]. 11.37/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f324(A)) = empty_set. [resolve(937,e,895,b)]. 11.37/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f324(A),A). [resolve(937,e,896,b)]. 11.37/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(937,e,897,b)]. 11.37/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f345(A),A). [resolve(937,e,899,b)]. 11.37/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f345(A),powerset(the_carrier(A))). [resolve(937,e,900,b)]. 11.37/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f346(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(937,e,901,a)]. 11.37/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f346(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(937,e,902,a)]. 11.37/11.54 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f346(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(937,e,903,a)]. 11.37/11.55 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(937,e,904,c)]. 11.37/11.55 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(937,e,905,c)]. 11.37/11.55 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | closed_subset(f352(A),A). [resolve(937,e,906,b)]. 11.37/11.55 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -empty(f352(A)). [resolve(937,e,907,b)]. 11.37/11.55 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | element(f352(A),powerset(the_carrier(A))). [resolve(937,e,908,b)]. 11.37/11.55 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(cast_as_carrier_subset(A),A). [resolve(937,e,909,a)]. 11.37/11.55 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(937,e,910,a)]. 11.37/11.55 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(937,e,911,a)]. 11.37/11.55 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(937,e,912,a)]. 11.37/11.55 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(937,e,913,a)]. 11.37/11.55 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(937,e,914,a)]. 11.37/11.55 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(937,e,915,a)]. 11.37/11.55 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(937,e,916,a)]. 11.37/11.56 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(937,e,917,a)]. 11.37/11.56 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(937,e,918,a)]. 11.37/11.56 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(937,e,919,a)]. 11.37/11.56 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(937,e,920,a)]. 11.37/11.56 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(937,e,921,a)]. 11.37/11.56 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(937,e,922,a)]. 11.37/11.56 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(937,e,923,a)]. 11.37/11.56 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(937,e,924,a)]. 11.37/11.56 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(937,e,925,a)]. 11.37/11.56 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(937,e,926,a)]. 11.37/11.56 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(937,e,927,a)]. 11.37/11.56 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(937,e,928,a)]. 11.40/11.57 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(937,e,929,a)]. 11.40/11.57 938 -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(658)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -subset(B,C) | -closed_subset(D,A) | D != C | -element(D,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | in(C,f11(A,B)). [resolve(938,e,781,c)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | subset(B,C) | -in(C,f11(A,B)). [resolve(938,e,782,c)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | closed_subset(f12(A,B,C),A) | -in(C,f11(A,B)). [resolve(938,e,783,c)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | f12(A,B,C) = C | -in(C,f11(A,B)). [resolve(938,e,784,c)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f12(A,B,C),powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(938,e,785,c)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | in(C,powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(938,e,786,c)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -closed_subset(B,A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | open_subset(subset_complement(the_carrier(A),B),A). [resolve(938,e,787,a)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A). [resolve(938,e,788,d)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | element(f124(A,B,C),powerset(the_carrier(A))). [resolve(938,e,789,a)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | f124(A,B,C) = C. [resolve(938,e,790,a)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | closed_subset(f124(A,B,C),A). [resolve(938,e,791,a)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | subset(B,C). [resolve(938,e,792,a)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(C,f123(A,B)) | -element(D,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C). [resolve(938,e,793,a)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f123(A,B),powerset(powerset(the_carrier(A)))). [resolve(938,e,794,a)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(938,e,795,c)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,796,c)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,797,c)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(938,e,798,c)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(938,e,799,c)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,800,c)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,801,c)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(938,e,802,c)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,803,c)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,804,c)]. 11.40/11.57 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(938,e,805,c)]. 11.40/11.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(938,e,806,c)]. 11.40/11.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,807,c)]. 11.40/11.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,808,c)]. 11.40/11.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(938,e,809,c)]. 11.40/11.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,810,c)]. 11.40/11.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,811,c)]. 11.40/11.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(938,e,812,c)]. 11.40/11.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(938,e,813,c)]. 11.40/11.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,814,c)]. 11.40/11.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,815,c)]. 11.40/11.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(938,e,816,c)]. 11.40/11.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,817,c)]. 11.40/11.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,818,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(938,e,819,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(938,e,820,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,821,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,822,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(938,e,823,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,824,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,825,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(938,e,826,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(938,e,827,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,828,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,829,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(938,e,830,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,831,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,832,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(938,e,833,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(938,e,834,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,835,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,836,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(938,e,837,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,838,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,839,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(938,e,840,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(938,e,841,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,842,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,843,c)]. 11.40/11.59 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(938,e,844,c)]. 11.40/11.60 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,845,c)]. 11.40/11.60 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,846,c)]. 11.40/11.60 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(938,e,847,c)]. 11.40/11.60 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(938,e,848,c)]. 11.40/11.60 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,849,c)]. 11.40/11.60 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,850,c)]. 11.40/11.60 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(938,e,851,c)]. 11.40/11.60 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,852,c)]. 11.40/11.60 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,853,c)]. 11.40/11.60 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(938,e,854,c)]. 11.40/11.60 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(938,e,855,c)]. 11.40/11.60 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,856,c)]. 11.40/11.60 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,857,c)]. 11.40/11.61 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(938,e,858,c)]. 11.40/11.61 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,859,c)]. 11.40/11.61 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,860,c)]. 11.40/11.61 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(938,e,861,c)]. 11.40/11.61 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(938,e,862,c)]. 11.40/11.61 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,863,c)]. 11.40/11.61 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,864,c)]. 11.40/11.61 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(938,e,865,c)]. 11.40/11.61 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,866,c)]. 11.40/11.61 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,867,c)]. 11.40/11.61 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(938,e,868,c)]. 11.40/11.61 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(938,e,869,c)]. 11.40/11.61 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(938,e,870,c)]. 11.40/11.62 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(938,e,871,c)]. 11.40/11.62 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -open_subset(B,A) | closed_subset(subset_complement(the_carrier(A),B),A). [resolve(938,e,872,a)]. 11.40/11.62 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f185(A),powerset(the_carrier(A))). [resolve(938,e,873,b)]. 11.40/11.62 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f185(A),A). [resolve(938,e,874,b)]. 11.40/11.62 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(938,e,875,b)]. 11.40/11.62 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(938,e,876,b)]. 11.40/11.62 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | in(C,f199(A,B)). [resolve(938,e,877,c)]. 11.40/11.62 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f199(A,B)). [resolve(938,e,878,c)]. 11.40/11.62 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f199(A,B),powerset(powerset(the_carrier(A)))). [resolve(938,e,879,c)]. 11.40/11.62 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f235(A),powerset(the_carrier(A))). [resolve(938,e,880,a)]. 11.40/11.62 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f235(A),A). [resolve(938,e,881,a)]. 11.40/11.62 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f235(A),A). [resolve(938,e,882,a)]. 11.40/11.62 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A). [resolve(938,e,883,a)]. 11.40/11.62 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,powerset(the_carrier(A))) | in(C,f281(A,B)). [resolve(938,e,884,c)]. 11.40/11.62 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f281(A,B)). [resolve(938,e,885,c)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,powerset(the_carrier(A))) | -in(C,f281(A,B)). [resolve(938,e,886,c)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(938,e,887,b)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f303(A,B),powerset(powerset(the_carrier(A)))). [resolve(938,e,888,b)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) = meet_of_subsets(the_carrier(A),f303(A,B)). [resolve(938,e,889,b)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -subset(B,C) | -closed_subset(C,A) | in(C,f303(A,B)). [resolve(938,e,890,b)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | subset(B,C) | -in(C,f303(A,B)). [resolve(938,e,891,b)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | closed_subset(C,A) | -in(C,f303(A,B)). [resolve(938,e,892,b)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(938,e,893,b)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f324(A),powerset(powerset(the_carrier(A)))). [resolve(938,e,894,b)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f324(A)) = empty_set. [resolve(938,e,895,b)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f324(A),A). [resolve(938,e,896,b)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(938,e,897,b)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f345(A),A). [resolve(938,e,899,b)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f345(A),powerset(the_carrier(A))). [resolve(938,e,900,b)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f346(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(938,e,901,a)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f346(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(938,e,902,a)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f346(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(938,e,903,a)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(938,e,904,c)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(938,e,905,c)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | closed_subset(f352(A),A). [resolve(938,e,906,b)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -empty(f352(A)). [resolve(938,e,907,b)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | element(f352(A),powerset(the_carrier(A))). [resolve(938,e,908,b)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(cast_as_carrier_subset(A),A). [resolve(938,e,909,a)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(938,e,910,a)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(938,e,911,a)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(938,e,912,a)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(938,e,913,a)]. 11.45/11.63 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(938,e,914,a)]. 11.45/11.64 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(938,e,915,a)]. 11.45/11.64 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(938,e,916,a)]. 11.45/11.64 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(938,e,917,a)]. 11.45/11.64 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(938,e,918,a)]. 11.45/11.64 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(938,e,919,a)]. 11.45/11.64 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(938,e,920,a)]. 11.45/11.64 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(938,e,921,a)]. 11.45/11.64 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(938,e,922,a)]. 11.45/11.64 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(938,e,923,a)]. 11.45/11.64 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(938,e,924,a)]. 11.45/11.64 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(938,e,925,a)]. 11.45/11.64 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(938,e,926,a)]. 11.45/11.65 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(938,e,927,a)]. 11.45/11.65 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(938,e,928,a)]. 11.45/11.65 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(938,e,929,a)]. 11.45/11.65 939 -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(658)]. 11.45/11.65 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -subset(B,C) | -closed_subset(D,A) | D != C | -element(D,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | in(C,f11(A,B)). [resolve(939,e,781,c)]. 11.45/11.65 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | subset(B,C) | -in(C,f11(A,B)). [resolve(939,e,782,c)]. 11.45/11.65 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | closed_subset(f12(A,B,C),A) | -in(C,f11(A,B)). [resolve(939,e,783,c)]. 11.45/11.65 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | f12(A,B,C) = C | -in(C,f11(A,B)). [resolve(939,e,784,c)]. 11.45/11.65 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f12(A,B,C),powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(939,e,785,c)]. 11.45/11.65 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | in(C,powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(939,e,786,c)]. 11.45/11.65 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -closed_subset(B,A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | open_subset(subset_complement(the_carrier(A),B),A). [resolve(939,e,787,a)]. 11.45/11.65 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A). [resolve(939,e,788,d)]. 11.45/11.65 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | element(f124(A,B,C),powerset(the_carrier(A))). [resolve(939,e,789,a)]. 11.45/11.65 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | f124(A,B,C) = C. [resolve(939,e,790,a)]. 11.45/11.65 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | closed_subset(f124(A,B,C),A). [resolve(939,e,791,a)]. 11.48/11.66 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | subset(B,C). [resolve(939,e,792,a)]. 11.48/11.66 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(C,f123(A,B)) | -element(D,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C). [resolve(939,e,793,a)]. 11.48/11.66 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f123(A,B),powerset(powerset(the_carrier(A)))). [resolve(939,e,794,a)]. 11.48/11.66 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(939,e,795,c)]. 11.48/11.66 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,796,c)]. 11.48/11.66 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,797,c)]. 11.48/11.66 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(939,e,798,c)]. 11.48/11.66 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(939,e,799,c)]. 11.48/11.66 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,800,c)]. 11.48/11.66 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,801,c)]. 11.48/11.66 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(939,e,802,c)]. 11.48/11.66 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,803,c)]. 11.48/11.66 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,804,c)]. 11.48/11.66 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(939,e,805,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(939,e,806,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,807,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,808,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(939,e,809,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,810,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,811,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(939,e,812,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(939,e,813,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,814,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,815,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(939,e,816,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,817,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,818,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(939,e,819,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(939,e,820,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,821,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,822,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(939,e,823,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,824,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,825,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(939,e,826,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(939,e,827,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,828,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,829,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(939,e,830,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,831,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,832,c)]. 11.48/11.67 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(939,e,833,c)]. 11.48/11.68 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(939,e,834,c)]. 11.48/11.68 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,835,c)]. 11.48/11.68 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,836,c)]. 11.48/11.68 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(939,e,837,c)]. 11.48/11.68 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,838,c)]. 11.48/11.68 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,839,c)]. 11.48/11.68 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(939,e,840,c)]. 11.48/11.68 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(939,e,841,c)]. 11.48/11.68 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,842,c)]. 11.48/11.68 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,843,c)]. 11.48/11.68 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(939,e,844,c)]. 11.48/11.68 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,845,c)]. 11.48/11.68 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,846,c)]. 11.48/11.69 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(939,e,847,c)]. 11.48/11.69 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(939,e,848,c)]. 11.48/11.69 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,849,c)]. 11.48/11.69 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,850,c)]. 11.48/11.69 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(939,e,851,c)]. 11.48/11.69 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,852,c)]. 11.48/11.69 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,853,c)]. 11.48/11.69 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(939,e,854,c)]. 11.48/11.69 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(939,e,855,c)]. 11.48/11.69 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,856,c)]. 11.48/11.69 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,857,c)]. 11.48/11.69 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(939,e,858,c)]. 11.48/11.69 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,859,c)]. 11.48/11.69 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,860,c)]. 11.48/11.69 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(939,e,861,c)]. 11.48/11.70 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(939,e,862,c)]. 11.48/11.70 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,863,c)]. 11.48/11.70 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,864,c)]. 11.48/11.70 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(939,e,865,c)]. 11.48/11.70 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,866,c)]. 11.48/11.70 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,867,c)]. 11.48/11.70 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(939,e,868,c)]. 11.48/11.70 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(939,e,869,c)]. 11.48/11.70 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(939,e,870,c)]. 11.48/11.70 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(939,e,871,c)]. 11.48/11.70 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -open_subset(B,A) | closed_subset(subset_complement(the_carrier(A),B),A). [resolve(939,e,872,a)]. 11.48/11.70 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f185(A),powerset(the_carrier(A))). [resolve(939,e,873,b)]. 11.48/11.70 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f185(A),A). [resolve(939,e,874,b)]. 11.48/11.70 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(939,e,875,b)]. 11.48/11.70 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(939,e,876,b)]. 11.48/11.71 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | in(C,f199(A,B)). [resolve(939,e,877,c)]. 11.48/11.71 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f199(A,B)). [resolve(939,e,878,c)]. 11.48/11.71 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f199(A,B),powerset(powerset(the_carrier(A)))). [resolve(939,e,879,c)]. 11.48/11.71 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f235(A),powerset(the_carrier(A))). [resolve(939,e,880,a)]. 11.48/11.71 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f235(A),A). [resolve(939,e,881,a)]. 11.48/11.71 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f235(A),A). [resolve(939,e,882,a)]. 11.48/11.71 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A). [resolve(939,e,883,a)]. 11.48/11.71 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,powerset(the_carrier(A))) | in(C,f281(A,B)). [resolve(939,e,884,c)]. 11.48/11.71 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f281(A,B)). [resolve(939,e,885,c)]. 11.48/11.71 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,powerset(the_carrier(A))) | -in(C,f281(A,B)). [resolve(939,e,886,c)]. 11.48/11.71 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(939,e,887,b)]. 11.48/11.71 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f303(A,B),powerset(powerset(the_carrier(A)))). [resolve(939,e,888,b)]. 11.48/11.71 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) = meet_of_subsets(the_carrier(A),f303(A,B)). [resolve(939,e,889,b)]. 11.48/11.71 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -subset(B,C) | -closed_subset(C,A) | in(C,f303(A,B)). [resolve(939,e,890,b)]. 11.48/11.71 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | subset(B,C) | -in(C,f303(A,B)). [resolve(939,e,891,b)]. 11.48/11.72 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | closed_subset(C,A) | -in(C,f303(A,B)). [resolve(939,e,892,b)]. 11.48/11.72 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(939,e,893,b)]. 11.48/11.72 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f324(A),powerset(powerset(the_carrier(A)))). [resolve(939,e,894,b)]. 11.48/11.72 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f324(A)) = empty_set. [resolve(939,e,895,b)]. 11.48/11.72 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f324(A),A). [resolve(939,e,896,b)]. 11.48/11.72 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(939,e,897,b)]. 11.48/11.72 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f345(A),A). [resolve(939,e,899,b)]. 11.48/11.72 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f345(A),powerset(the_carrier(A))). [resolve(939,e,900,b)]. 11.48/11.72 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f346(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(939,e,901,a)]. 11.48/11.72 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f346(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(939,e,902,a)]. 11.48/11.72 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f346(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(939,e,903,a)]. 11.48/11.72 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(939,e,904,c)]. 11.48/11.72 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(939,e,905,c)]. 11.48/11.72 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | closed_subset(f352(A),A). [resolve(939,e,906,b)]. 11.48/11.72 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -empty(f352(A)). [resolve(939,e,907,b)]. 11.48/11.72 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | element(f352(A),powerset(the_carrier(A))). [resolve(939,e,908,b)]. 11.56/11.73 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(cast_as_carrier_subset(A),A). [resolve(939,e,909,a)]. 11.56/11.73 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(939,e,910,a)]. 11.56/11.73 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(939,e,911,a)]. 11.56/11.73 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(939,e,912,a)]. 11.56/11.73 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(939,e,913,a)]. 11.56/11.73 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(939,e,914,a)]. 11.56/11.73 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(939,e,915,a)]. 11.56/11.73 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(939,e,916,a)]. 11.56/11.73 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(939,e,917,a)]. 11.56/11.73 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(939,e,918,a)]. 11.56/11.73 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(939,e,919,a)]. 11.56/11.73 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(939,e,920,a)]. 11.56/11.73 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(939,e,921,a)]. 11.56/11.74 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(939,e,922,a)]. 11.56/11.74 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(939,e,923,a)]. 11.56/11.74 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(939,e,924,a)]. 11.56/11.74 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(939,e,925,a)]. 11.56/11.74 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(939,e,926,a)]. 11.56/11.74 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(939,e,927,a)]. 11.56/11.74 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(939,e,928,a)]. 11.56/11.74 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(939,e,929,a)]. 11.56/11.74 940 -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(658)]. 11.56/11.74 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -subset(B,C) | -closed_subset(D,A) | D != C | -element(D,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | in(C,f11(A,B)). [resolve(940,e,781,c)]. 11.56/11.74 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | subset(B,C) | -in(C,f11(A,B)). [resolve(940,e,782,c)]. 11.56/11.74 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | closed_subset(f12(A,B,C),A) | -in(C,f11(A,B)). [resolve(940,e,783,c)]. 11.56/11.74 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | f12(A,B,C) = C | -in(C,f11(A,B)). [resolve(940,e,784,c)]. 11.56/11.74 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f12(A,B,C),powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(940,e,785,c)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | in(C,powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(940,e,786,c)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -closed_subset(B,A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | open_subset(subset_complement(the_carrier(A),B),A). [resolve(940,e,787,a)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A). [resolve(940,e,788,d)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | element(f124(A,B,C),powerset(the_carrier(A))). [resolve(940,e,789,a)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | f124(A,B,C) = C. [resolve(940,e,790,a)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | closed_subset(f124(A,B,C),A). [resolve(940,e,791,a)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | subset(B,C). [resolve(940,e,792,a)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(C,f123(A,B)) | -element(D,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C). [resolve(940,e,793,a)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f123(A,B),powerset(powerset(the_carrier(A)))). [resolve(940,e,794,a)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(940,e,795,c)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,796,c)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,797,c)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(940,e,798,c)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(940,e,799,c)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,800,c)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,801,c)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(940,e,802,c)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,803,c)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,804,c)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(940,e,805,c)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(940,e,806,c)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,807,c)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,808,c)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(940,e,809,c)]. 11.56/11.75 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,810,c)]. 11.56/11.76 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,811,c)]. 11.56/11.76 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(940,e,812,c)]. 11.56/11.76 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(940,e,813,c)]. 11.56/11.76 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,814,c)]. 11.56/11.76 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,815,c)]. 11.56/11.76 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(940,e,816,c)]. 11.56/11.76 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,817,c)]. 11.56/11.76 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,818,c)]. 11.56/11.76 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(940,e,819,c)]. 11.56/11.76 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(940,e,820,c)]. 11.56/11.76 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,821,c)]. 11.56/11.76 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,822,c)]. 11.56/11.76 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(940,e,823,c)]. 11.61/11.77 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,824,c)]. 11.61/11.77 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,825,c)]. 11.61/11.77 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(940,e,826,c)]. 11.61/11.77 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(940,e,827,c)]. 11.61/11.77 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,828,c)]. 11.61/11.77 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,829,c)]. 11.61/11.77 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(940,e,830,c)]. 11.61/11.77 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,831,c)]. 11.61/11.77 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,832,c)]. 11.61/11.77 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(940,e,833,c)]. 11.61/11.77 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(940,e,834,c)]. 11.61/11.77 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,835,c)]. 11.61/11.78 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,836,c)]. 11.61/11.78 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(940,e,837,c)]. 11.61/11.78 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,838,c)]. 11.61/11.78 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,839,c)]. 11.61/11.78 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(940,e,840,c)]. 11.61/11.78 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(940,e,841,c)]. 11.61/11.78 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,842,c)]. 11.61/11.78 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,843,c)]. 11.61/11.78 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(940,e,844,c)]. 11.61/11.78 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,845,c)]. 11.61/11.78 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,846,c)]. 11.61/11.78 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(940,e,847,c)]. 11.61/11.78 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(940,e,848,c)]. 11.61/11.79 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,849,c)]. 11.61/11.79 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,850,c)]. 11.61/11.79 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(940,e,851,c)]. 11.61/11.79 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,852,c)]. 11.61/11.79 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,853,c)]. 11.61/11.79 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(940,e,854,c)]. 11.61/11.79 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(940,e,855,c)]. 11.61/11.79 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,856,c)]. 11.61/11.79 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,857,c)]. 11.61/11.79 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(940,e,858,c)]. 11.61/11.79 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,859,c)]. 11.61/11.79 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,860,c)]. 11.61/11.79 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(940,e,861,c)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(940,e,862,c)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,863,c)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,864,c)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(940,e,865,c)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,866,c)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,867,c)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(940,e,868,c)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(940,e,869,c)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(940,e,870,c)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(940,e,871,c)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -open_subset(B,A) | closed_subset(subset_complement(the_carrier(A),B),A). [resolve(940,e,872,a)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f185(A),powerset(the_carrier(A))). [resolve(940,e,873,b)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f185(A),A). [resolve(940,e,874,b)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(940,e,875,b)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(940,e,876,b)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | in(C,f199(A,B)). [resolve(940,e,877,c)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f199(A,B)). [resolve(940,e,878,c)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f199(A,B),powerset(powerset(the_carrier(A)))). [resolve(940,e,879,c)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f235(A),powerset(the_carrier(A))). [resolve(940,e,880,a)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f235(A),A). [resolve(940,e,881,a)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f235(A),A). [resolve(940,e,882,a)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A). [resolve(940,e,883,a)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,powerset(the_carrier(A))) | in(C,f281(A,B)). [resolve(940,e,884,c)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f281(A,B)). [resolve(940,e,885,c)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,powerset(the_carrier(A))) | -in(C,f281(A,B)). [resolve(940,e,886,c)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(940,e,887,b)]. 11.61/11.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f303(A,B),powerset(powerset(the_carrier(A)))). [resolve(940,e,888,b)]. 11.61/11.81 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) = meet_of_subsets(the_carrier(A),f303(A,B)). [resolve(940,e,889,b)]. 11.61/11.81 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -subset(B,C) | -closed_subset(C,A) | in(C,f303(A,B)). [resolve(940,e,890,b)]. 11.61/11.81 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | subset(B,C) | -in(C,f303(A,B)). [resolve(940,e,891,b)]. 11.61/11.81 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | closed_subset(C,A) | -in(C,f303(A,B)). [resolve(940,e,892,b)]. 11.61/11.81 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(940,e,893,b)]. 11.61/11.81 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f324(A),powerset(powerset(the_carrier(A)))). [resolve(940,e,894,b)]. 11.61/11.81 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f324(A)) = empty_set. [resolve(940,e,895,b)]. 11.61/11.81 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f324(A),A). [resolve(940,e,896,b)]. 11.61/11.81 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(940,e,897,b)]. 11.61/11.81 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f345(A),A). [resolve(940,e,899,b)]. 11.61/11.81 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f345(A),powerset(the_carrier(A))). [resolve(940,e,900,b)]. 11.61/11.81 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f346(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(940,e,901,a)]. 11.61/11.81 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f346(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(940,e,902,a)]. 11.61/11.81 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f346(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(940,e,903,a)]. 11.61/11.82 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(940,e,904,c)]. 11.61/11.82 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(940,e,905,c)]. 11.61/11.82 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | closed_subset(f352(A),A). [resolve(940,e,906,b)]. 11.61/11.82 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -empty(f352(A)). [resolve(940,e,907,b)]. 11.61/11.82 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | element(f352(A),powerset(the_carrier(A))). [resolve(940,e,908,b)]. 11.61/11.82 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(cast_as_carrier_subset(A),A). [resolve(940,e,909,a)]. 11.61/11.82 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(940,e,910,a)]. 11.61/11.82 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(940,e,911,a)]. 11.61/11.82 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(940,e,912,a)]. 11.61/11.82 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(940,e,913,a)]. 11.61/11.82 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(940,e,914,a)]. 11.61/11.82 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(940,e,915,a)]. 11.61/11.82 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(940,e,916,a)]. 11.61/11.82 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(940,e,917,a)]. 11.61/11.83 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(940,e,918,a)]. 11.61/11.83 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(940,e,919,a)]. 11.61/11.83 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(940,e,920,a)]. 11.61/11.83 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(940,e,921,a)]. 11.61/11.83 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(940,e,922,a)]. 11.61/11.83 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(940,e,923,a)]. 11.61/11.83 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(940,e,924,a)]. 11.61/11.83 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(940,e,925,a)]. 11.61/11.83 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(940,e,926,a)]. 11.61/11.83 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(940,e,927,a)]. 11.61/11.83 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(940,e,928,a)]. 11.61/11.84 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(940,e,929,a)]. 11.61/11.84 941 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(658)]. 11.61/11.84 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -subset(B,C) | -closed_subset(D,A) | D != C | -element(D,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | in(C,f11(A,B)). [resolve(941,e,781,c)]. 11.61/11.84 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | subset(B,C) | -in(C,f11(A,B)). [resolve(941,e,782,c)]. 11.61/11.84 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | closed_subset(f12(A,B,C),A) | -in(C,f11(A,B)). [resolve(941,e,783,c)]. 11.61/11.84 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | f12(A,B,C) = C | -in(C,f11(A,B)). [resolve(941,e,784,c)]. 11.61/11.84 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f12(A,B,C),powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(941,e,785,c)]. 11.61/11.84 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | in(C,powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(941,e,786,c)]. 11.61/11.84 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -closed_subset(B,A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | open_subset(subset_complement(the_carrier(A),B),A). [resolve(941,e,787,a)]. 11.61/11.84 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A). [resolve(941,e,788,d)]. 11.61/11.84 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | element(f124(A,B,C),powerset(the_carrier(A))). [resolve(941,e,789,a)]. 11.61/11.84 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | f124(A,B,C) = C. [resolve(941,e,790,a)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | closed_subset(f124(A,B,C),A). [resolve(941,e,791,a)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | subset(B,C). [resolve(941,e,792,a)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(C,f123(A,B)) | -element(D,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C). [resolve(941,e,793,a)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f123(A,B),powerset(powerset(the_carrier(A)))). [resolve(941,e,794,a)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(941,e,795,c)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,796,c)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,797,c)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(941,e,798,c)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(941,e,799,c)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,800,c)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,801,c)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(941,e,802,c)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,803,c)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,804,c)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(941,e,805,c)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(941,e,806,c)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,807,c)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,808,c)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(941,e,809,c)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,810,c)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,811,c)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(941,e,812,c)]. 11.61/11.85 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(941,e,813,c)]. 11.70/11.86 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,814,c)]. 11.70/11.86 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,815,c)]. 11.70/11.86 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(941,e,816,c)]. 11.70/11.86 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,817,c)]. 11.70/11.86 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,818,c)]. 11.70/11.86 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(941,e,819,c)]. 11.70/11.86 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(941,e,820,c)]. 11.70/11.86 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,821,c)]. 11.70/11.86 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,822,c)]. 11.70/11.86 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(941,e,823,c)]. 11.70/11.86 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,824,c)]. 11.70/11.87 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,825,c)]. 11.70/11.87 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(941,e,826,c)]. 11.70/11.87 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(941,e,827,c)]. 11.70/11.87 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,828,c)]. 11.70/11.87 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,829,c)]. 11.70/11.87 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(941,e,830,c)]. 11.70/11.87 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,831,c)]. 11.70/11.87 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,832,c)]. 11.70/11.87 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(941,e,833,c)]. 11.70/11.87 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(941,e,834,c)]. 11.70/11.87 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,835,c)]. 11.70/11.87 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,836,c)]. 11.70/11.88 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(941,e,837,c)]. 11.70/11.88 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,838,c)]. 11.70/11.88 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,839,c)]. 11.70/11.88 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(941,e,840,c)]. 11.70/11.88 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(941,e,841,c)]. 11.70/11.88 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,842,c)]. 11.70/11.88 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,843,c)]. 11.70/11.88 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(941,e,844,c)]. 11.70/11.88 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,845,c)]. 11.70/11.88 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,846,c)]. 11.70/11.88 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(941,e,847,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(941,e,848,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,849,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,850,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(941,e,851,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,852,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,853,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(941,e,854,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(941,e,855,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,856,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,857,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(941,e,858,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,859,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,860,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(941,e,861,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(941,e,862,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,863,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,864,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(941,e,865,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,866,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,867,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(941,e,868,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(941,e,869,c)]. 11.73/11.89 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(941,e,870,c)]. 11.73/11.90 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(941,e,871,c)]. 11.73/11.90 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -open_subset(B,A) | closed_subset(subset_complement(the_carrier(A),B),A). [resolve(941,e,872,a)]. 11.73/11.90 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f185(A),powerset(the_carrier(A))). [resolve(941,e,873,b)]. 11.73/11.90 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f185(A),A). [resolve(941,e,874,b)]. 11.73/11.90 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(941,e,875,b)]. 11.73/11.90 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(941,e,876,b)]. 11.73/11.90 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | in(C,f199(A,B)). [resolve(941,e,877,c)]. 11.73/11.90 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f199(A,B)). [resolve(941,e,878,c)]. 11.73/11.90 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f199(A,B),powerset(powerset(the_carrier(A)))). [resolve(941,e,879,c)]. 11.73/11.90 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f235(A),powerset(the_carrier(A))). [resolve(941,e,880,a)]. 11.73/11.90 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f235(A),A). [resolve(941,e,881,a)]. 11.73/11.90 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f235(A),A). [resolve(941,e,882,a)]. 11.73/11.90 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A). [resolve(941,e,883,a)]. 11.73/11.91 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,powerset(the_carrier(A))) | in(C,f281(A,B)). [resolve(941,e,884,c)]. 11.73/11.91 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f281(A,B)). [resolve(941,e,885,c)]. 11.73/11.91 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,powerset(the_carrier(A))) | -in(C,f281(A,B)). [resolve(941,e,886,c)]. 11.73/11.91 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(941,e,887,b)]. 11.73/11.91 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f303(A,B),powerset(powerset(the_carrier(A)))). [resolve(941,e,888,b)]. 11.73/11.91 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) = meet_of_subsets(the_carrier(A),f303(A,B)). [resolve(941,e,889,b)]. 11.73/11.91 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -subset(B,C) | -closed_subset(C,A) | in(C,f303(A,B)). [resolve(941,e,890,b)]. 11.73/11.91 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | subset(B,C) | -in(C,f303(A,B)). [resolve(941,e,891,b)]. 11.73/11.91 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | closed_subset(C,A) | -in(C,f303(A,B)). [resolve(941,e,892,b)]. 11.73/11.91 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(941,e,893,b)]. 11.73/11.91 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f324(A),powerset(powerset(the_carrier(A)))). [resolve(941,e,894,b)]. 11.73/11.91 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f324(A)) = empty_set. [resolve(941,e,895,b)]. 11.73/11.92 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f324(A),A). [resolve(941,e,896,b)]. 11.73/11.92 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(941,e,897,b)]. 11.73/11.92 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f345(A),A). [resolve(941,e,899,b)]. 11.73/11.92 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f345(A),powerset(the_carrier(A))). [resolve(941,e,900,b)]. 11.73/11.92 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f346(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(941,e,901,a)]. 11.73/11.92 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f346(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(941,e,902,a)]. 11.73/11.92 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f346(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(941,e,903,a)]. 11.73/11.92 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(941,e,904,c)]. 11.73/11.92 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(941,e,905,c)]. 11.73/11.92 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | closed_subset(f352(A),A). [resolve(941,e,906,b)]. 11.73/11.92 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -empty(f352(A)). [resolve(941,e,907,b)]. 11.73/11.92 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | element(f352(A),powerset(the_carrier(A))). [resolve(941,e,908,b)]. 11.73/11.92 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(cast_as_carrier_subset(A),A). [resolve(941,e,909,a)]. 11.73/11.93 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(941,e,910,a)]. 11.73/11.93 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(941,e,911,a)]. 11.73/11.93 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(941,e,912,a)]. 11.73/11.93 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(941,e,913,a)]. 11.73/11.93 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(941,e,914,a)]. 11.73/11.93 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(941,e,915,a)]. 11.73/11.93 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(941,e,916,a)]. 11.73/11.93 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(941,e,917,a)]. 11.73/11.93 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(941,e,918,a)]. 11.73/11.93 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(941,e,919,a)]. 11.73/11.93 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(941,e,920,a)]. 11.73/11.94 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(941,e,921,a)]. 11.73/11.94 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(941,e,922,a)]. 11.73/11.94 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(941,e,923,a)]. 11.73/11.94 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(941,e,924,a)]. 11.73/11.94 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(941,e,925,a)]. 11.73/11.94 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(941,e,926,a)]. 11.73/11.94 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(941,e,927,a)]. 11.73/11.94 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(941,e,928,a)]. 11.73/11.94 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(941,e,929,a)]. 11.73/11.94 942 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(658)]. 11.73/11.94 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -subset(B,C) | -closed_subset(D,A) | D != C | -element(D,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | in(C,f11(A,B)). [resolve(942,e,781,c)]. 11.79/11.94 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | subset(B,C) | -in(C,f11(A,B)). [resolve(942,e,782,c)]. 11.79/11.94 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | closed_subset(f12(A,B,C),A) | -in(C,f11(A,B)). [resolve(942,e,783,c)]. 11.79/11.94 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | f12(A,B,C) = C | -in(C,f11(A,B)). [resolve(942,e,784,c)]. 11.79/11.94 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f12(A,B,C),powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(942,e,785,c)]. 11.79/11.94 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | in(C,powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(942,e,786,c)]. 11.79/11.94 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -closed_subset(B,A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | open_subset(subset_complement(the_carrier(A),B),A). [resolve(942,e,787,a)]. 11.79/11.94 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A). [resolve(942,e,788,d)]. 11.79/11.95 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | element(f124(A,B,C),powerset(the_carrier(A))). [resolve(942,e,789,a)]. 11.79/11.95 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | f124(A,B,C) = C. [resolve(942,e,790,a)]. 11.79/11.95 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | closed_subset(f124(A,B,C),A). [resolve(942,e,791,a)]. 11.79/11.95 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | subset(B,C). [resolve(942,e,792,a)]. 11.79/11.95 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(C,f123(A,B)) | -element(D,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C). [resolve(942,e,793,a)]. 11.79/11.95 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f123(A,B),powerset(powerset(the_carrier(A)))). [resolve(942,e,794,a)]. 11.79/11.95 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(942,e,795,c)]. 11.79/11.95 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,796,c)]. 11.79/11.95 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,797,c)]. 11.79/11.95 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(942,e,798,c)]. 11.79/11.95 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(942,e,799,c)]. 11.79/11.95 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,800,c)]. 11.79/11.95 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,801,c)]. 11.79/11.95 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(942,e,802,c)]. 11.79/11.95 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,803,c)]. 11.79/11.95 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,804,c)]. 11.79/11.95 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(942,e,805,c)]. 11.79/11.95 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(942,e,806,c)]. 11.81/11.96 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,807,c)]. 11.81/11.96 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,808,c)]. 11.81/11.96 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(942,e,809,c)]. 11.81/11.96 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,810,c)]. 11.81/11.96 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,811,c)]. 11.81/11.96 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(942,e,812,c)]. 11.81/11.96 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(942,e,813,c)]. 11.81/11.96 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,814,c)]. 11.81/11.96 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,815,c)]. 11.81/11.96 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(942,e,816,c)]. 11.81/11.96 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,817,c)]. 11.81/11.96 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,818,c)]. 11.81/11.97 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(942,e,819,c)]. 11.81/11.97 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(942,e,820,c)]. 11.81/11.97 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,821,c)]. 11.81/11.97 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,822,c)]. 11.81/11.97 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(942,e,823,c)]. 11.81/11.97 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,824,c)]. 11.81/11.97 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,825,c)]. 11.81/11.97 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(942,e,826,c)]. 11.81/11.97 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(942,e,827,c)]. 11.81/11.97 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,828,c)]. 11.81/11.97 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,829,c)]. 11.81/11.97 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(942,e,830,c)]. 11.81/11.98 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,831,c)]. 11.81/11.98 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,832,c)]. 11.81/11.98 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(942,e,833,c)]. 11.81/11.98 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(942,e,834,c)]. 11.81/11.98 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,835,c)]. 11.81/11.98 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,836,c)]. 11.81/11.98 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(942,e,837,c)]. 11.81/11.98 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,838,c)]. 11.81/11.98 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,839,c)]. 11.81/11.98 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(942,e,840,c)]. 11.81/11.98 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(942,e,841,c)]. 11.81/11.98 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,842,c)]. 11.81/11.99 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,843,c)]. 11.81/11.99 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(942,e,844,c)]. 11.81/11.99 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,845,c)]. 11.81/11.99 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,846,c)]. 11.81/11.99 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(942,e,847,c)]. 11.81/11.99 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(942,e,848,c)]. 11.81/11.99 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,849,c)]. 11.81/11.99 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,850,c)]. 11.81/11.99 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(942,e,851,c)]. 11.81/11.99 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,852,c)]. 11.81/11.99 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,853,c)]. 11.81/11.99 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(942,e,854,c)]. 11.81/12.00 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(942,e,855,c)]. 11.81/12.00 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,856,c)]. 11.81/12.00 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,857,c)]. 11.81/12.00 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(942,e,858,c)]. 11.81/12.00 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,859,c)]. 11.81/12.00 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,860,c)]. 11.81/12.00 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(942,e,861,c)]. 11.81/12.00 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(942,e,862,c)]. 11.81/12.00 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,863,c)]. 11.81/12.00 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,864,c)]. 11.81/12.00 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(942,e,865,c)]. 11.81/12.00 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,866,c)]. 11.81/12.01 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,867,c)]. 11.81/12.01 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(942,e,868,c)]. 11.81/12.01 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(942,e,869,c)]. 11.81/12.01 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(942,e,870,c)]. 11.81/12.01 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(942,e,871,c)]. 11.81/12.01 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -open_subset(B,A) | closed_subset(subset_complement(the_carrier(A),B),A). [resolve(942,e,872,a)]. 11.81/12.01 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f185(A),powerset(the_carrier(A))). [resolve(942,e,873,b)]. 11.81/12.01 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f185(A),A). [resolve(942,e,874,b)]. 11.81/12.01 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(942,e,875,b)]. 11.81/12.01 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(942,e,876,b)]. 11.81/12.01 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | in(C,f199(A,B)). [resolve(942,e,877,c)]. 11.81/12.01 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f199(A,B)). [resolve(942,e,878,c)]. 11.81/12.01 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f199(A,B),powerset(powerset(the_carrier(A)))). [resolve(942,e,879,c)]. 11.87/12.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f235(A),powerset(the_carrier(A))). [resolve(942,e,880,a)]. 11.87/12.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f235(A),A). [resolve(942,e,881,a)]. 11.87/12.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f235(A),A). [resolve(942,e,882,a)]. 11.87/12.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A). [resolve(942,e,883,a)]. 11.87/12.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,powerset(the_carrier(A))) | in(C,f281(A,B)). [resolve(942,e,884,c)]. 11.87/12.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f281(A,B)). [resolve(942,e,885,c)]. 11.87/12.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,powerset(the_carrier(A))) | -in(C,f281(A,B)). [resolve(942,e,886,c)]. 11.87/12.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(942,e,887,b)]. 11.87/12.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f303(A,B),powerset(powerset(the_carrier(A)))). [resolve(942,e,888,b)]. 11.87/12.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) = meet_of_subsets(the_carrier(A),f303(A,B)). [resolve(942,e,889,b)]. 11.87/12.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -subset(B,C) | -closed_subset(C,A) | in(C,f303(A,B)). [resolve(942,e,890,b)]. 11.87/12.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | subset(B,C) | -in(C,f303(A,B)). [resolve(942,e,891,b)]. 11.87/12.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | closed_subset(C,A) | -in(C,f303(A,B)). [resolve(942,e,892,b)]. 11.87/12.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(942,e,893,b)]. 11.87/12.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f324(A),powerset(powerset(the_carrier(A)))). [resolve(942,e,894,b)]. 11.87/12.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f324(A)) = empty_set. [resolve(942,e,895,b)]. 11.87/12.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f324(A),A). [resolve(942,e,896,b)]. 11.87/12.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(942,e,897,b)]. 11.87/12.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f345(A),A). [resolve(942,e,899,b)]. 11.87/12.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f345(A),powerset(the_carrier(A))). [resolve(942,e,900,b)]. 11.87/12.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f346(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(942,e,901,a)]. 11.87/12.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f346(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(942,e,902,a)]. 11.87/12.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f346(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(942,e,903,a)]. 11.87/12.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(942,e,904,c)]. 11.87/12.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(942,e,905,c)]. 11.87/12.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | closed_subset(f352(A),A). [resolve(942,e,906,b)]. 11.87/12.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -empty(f352(A)). [resolve(942,e,907,b)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | element(f352(A),powerset(the_carrier(A))). [resolve(942,e,908,b)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(cast_as_carrier_subset(A),A). [resolve(942,e,909,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(942,e,910,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(942,e,911,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(942,e,912,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(942,e,913,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(942,e,914,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(942,e,915,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(942,e,916,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(942,e,917,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(942,e,918,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(942,e,919,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(942,e,920,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(942,e,921,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(942,e,922,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(942,e,923,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(942,e,924,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(942,e,925,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(942,e,926,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(942,e,927,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(942,e,928,a)]. 11.87/12.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(942,e,929,a)]. 11.87/12.04 943 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(658)]. 11.91/12.05 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -subset(B,C) | -closed_subset(D,A) | D != C | -element(D,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | in(C,f11(A,B)). [resolve(943,e,781,c)]. 11.91/12.05 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | subset(B,C) | -in(C,f11(A,B)). [resolve(943,e,782,c)]. 11.91/12.05 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | closed_subset(f12(A,B,C),A) | -in(C,f11(A,B)). [resolve(943,e,783,c)]. 11.91/12.05 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | f12(A,B,C) = C | -in(C,f11(A,B)). [resolve(943,e,784,c)]. 11.91/12.05 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f12(A,B,C),powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(943,e,785,c)]. 11.91/12.05 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | in(C,powerset(the_carrier(A))) | -in(C,f11(A,B)). [resolve(943,e,786,c)]. 11.91/12.05 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -closed_subset(B,A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | open_subset(subset_complement(the_carrier(A),B),A). [resolve(943,e,787,a)]. 11.91/12.05 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A). [resolve(943,e,788,d)]. 11.91/12.05 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | element(f124(A,B,C),powerset(the_carrier(A))). [resolve(943,e,789,a)]. 11.91/12.05 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | f124(A,B,C) = C. [resolve(943,e,790,a)]. 11.91/12.05 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | closed_subset(f124(A,B,C),A). [resolve(943,e,791,a)]. 11.91/12.05 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f123(A,B)) | subset(B,C). [resolve(943,e,792,a)]. 11.91/12.06 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(C,f123(A,B)) | -element(D,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C). [resolve(943,e,793,a)]. 11.91/12.06 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f123(A,B),powerset(powerset(the_carrier(A)))). [resolve(943,e,794,a)]. 11.91/12.06 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(943,e,795,c)]. 11.91/12.06 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,796,c)]. 11.91/12.06 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,797,c)]. 11.91/12.06 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(943,e,798,c)]. 11.91/12.06 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(943,e,799,c)]. 11.91/12.06 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,800,c)]. 11.91/12.06 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,801,c)]. 11.91/12.06 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(943,e,802,c)]. 11.91/12.06 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,803,c)]. 11.91/12.07 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,804,c)]. 11.91/12.07 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(943,e,805,c)]. 11.91/12.07 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(943,e,806,c)]. 11.91/12.07 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,807,c)]. 11.91/12.07 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f132(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,808,c)]. 11.91/12.07 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(943,e,809,c)]. 11.91/12.07 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,810,c)]. 11.91/12.07 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,811,c)]. 11.91/12.07 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(943,e,812,c)]. 11.91/12.07 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(943,e,813,c)]. 11.91/12.07 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,814,c)]. 11.91/12.08 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f132(A,B) = f131(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,815,c)]. 11.91/12.08 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(943,e,816,c)]. 11.91/12.08 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,817,c)]. 11.91/12.08 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,818,c)]. 11.91/12.08 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(943,e,819,c)]. 11.91/12.08 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(943,e,820,c)]. 11.91/12.08 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,821,c)]. 11.91/12.08 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f132(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,822,c)]. 11.91/12.08 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(943,e,823,c)]. 11.91/12.08 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,824,c)]. 11.91/12.08 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,825,c)]. 11.91/12.09 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(943,e,826,c)]. 11.91/12.09 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(943,e,827,c)]. 11.91/12.09 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,828,c)]. 11.91/12.09 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f131(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,829,c)]. 11.91/12.09 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(943,e,830,c)]. 11.91/12.09 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,831,c)]. 11.91/12.09 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,832,c)]. 11.91/12.09 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(943,e,833,c)]. 11.91/12.09 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | subset(B,C) | -in(C,f134(A,B)). [resolve(943,e,834,c)]. 11.91/12.09 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,835,c)]. 11.91/12.09 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f133(A,B),powerset(the_carrier(A))) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,836,c)]. 11.91/12.10 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(943,e,837,c)]. 11.91/12.10 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,838,c)]. 11.91/12.10 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,839,c)]. 11.91/12.10 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(943,e,840,c)]. 11.91/12.10 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | subset(B,C) | -in(C,f134(A,B)). [resolve(943,e,841,c)]. 11.91/12.10 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,842,c)]. 11.91/12.10 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,f130(A,B)) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,843,c)]. 11.91/12.10 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(943,e,844,c)]. 11.91/12.10 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,845,c)]. 11.91/12.10 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,846,c)]. 11.91/12.10 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(943,e,847,c)]. 11.91/12.11 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | subset(B,C) | -in(C,f134(A,B)). [resolve(943,e,848,c)]. 11.91/12.11 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,849,c)]. 11.91/12.11 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f133(A,B),A) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,850,c)]. 11.91/12.11 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(943,e,851,c)]. 11.91/12.11 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,852,c)]. 11.91/12.11 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,853,c)]. 11.91/12.11 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(943,e,854,c)]. 11.91/12.11 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(943,e,855,c)]. 11.91/12.11 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,856,c)]. 11.91/12.11 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f133(A,B) = f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,857,c)]. 11.91/12.11 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(943,e,858,c)]. 11.91/12.12 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,859,c)]. 11.91/12.12 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,860,c)]. 11.91/12.12 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(943,e,861,c)]. 11.91/12.12 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(943,e,862,c)]. 11.91/12.12 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,863,c)]. 11.91/12.12 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f130(A,B) = f129(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,864,c)]. 11.91/12.12 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | C != D | -element(E,powerset(the_carrier(A))) | -closed_subset(E,A) | -subset(B,D) | E != D | -in(C,powerset(the_carrier(A))) | in(D,f134(A,B)). [resolve(943,e,865,c)]. 11.91/12.12 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f135(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,866,c)]. 11.91/12.12 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | element(f136(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,867,c)]. 11.91/12.12 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | closed_subset(f136(A,B,C),A) | -in(C,f134(A,B)). [resolve(943,e,868,c)]. 11.91/12.12 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | subset(B,C) | -in(C,f134(A,B)). [resolve(943,e,869,c)]. 11.91/12.12 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | f136(A,B,C) = C | -in(C,f134(A,B)). [resolve(943,e,870,c)]. 11.91/12.13 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f131(A,B) != f130(A,B) | in(f135(A,B,C),powerset(the_carrier(A))) | -in(C,f134(A,B)). [resolve(943,e,871,c)]. 11.91/12.13 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -open_subset(B,A) | closed_subset(subset_complement(the_carrier(A),B),A). [resolve(943,e,872,a)]. 11.91/12.13 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f185(A),powerset(the_carrier(A))). [resolve(943,e,873,b)]. 11.91/12.13 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f185(A),A). [resolve(943,e,874,b)]. 11.91/12.13 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(943,e,875,b)]. 11.91/12.13 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(943,e,876,b)]. 11.91/12.13 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | in(C,f199(A,B)). [resolve(943,e,877,c)]. 11.91/12.13 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f199(A,B)). [resolve(943,e,878,c)]. 11.91/12.13 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f199(A,B),powerset(powerset(the_carrier(A)))). [resolve(943,e,879,c)]. 11.91/12.13 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f235(A),powerset(the_carrier(A))). [resolve(943,e,880,a)]. 11.91/12.13 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subset(f235(A),A). [resolve(943,e,881,a)]. 11.91/12.13 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f235(A),A). [resolve(943,e,882,a)]. 11.91/12.14 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A). [resolve(943,e,883,a)]. 11.91/12.14 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,powerset(the_carrier(A))) | in(C,f281(A,B)). [resolve(943,e,884,c)]. 11.91/12.14 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f281(A,B)). [resolve(943,e,885,c)]. 11.91/12.14 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,powerset(the_carrier(A))) | -in(C,f281(A,B)). [resolve(943,e,886,c)]. 11.91/12.14 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(943,e,887,b)]. 11.91/12.14 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f303(A,B),powerset(powerset(the_carrier(A)))). [resolve(943,e,888,b)]. 11.91/12.14 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) = meet_of_subsets(the_carrier(A),f303(A,B)). [resolve(943,e,889,b)]. 11.91/12.14 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -subset(B,C) | -closed_subset(C,A) | in(C,f303(A,B)). [resolve(943,e,890,b)]. 11.91/12.14 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | subset(B,C) | -in(C,f303(A,B)). [resolve(943,e,891,b)]. 11.91/12.14 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | closed_subset(C,A) | -in(C,f303(A,B)). [resolve(943,e,892,b)]. 11.91/12.14 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(943,e,893,b)]. 11.91/12.14 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f324(A),powerset(powerset(the_carrier(A)))). [resolve(943,e,894,b)]. 12.00/12.15 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f324(A)) = empty_set. [resolve(943,e,895,b)]. 12.00/12.15 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f324(A),A). [resolve(943,e,896,b)]. 12.00/12.15 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(943,e,897,b)]. 12.00/12.15 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(f345(A),A). [resolve(943,e,899,b)]. 12.00/12.15 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f345(A),powerset(the_carrier(A))). [resolve(943,e,900,b)]. 12.00/12.15 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f346(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(943,e,901,a)]. 12.00/12.15 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f346(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(943,e,902,a)]. 12.00/12.15 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f346(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A). [resolve(943,e,903,a)]. 12.00/12.15 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(943,e,904,c)]. 12.00/12.15 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(943,e,905,c)]. 12.00/12.15 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | closed_subset(f352(A),A). [resolve(943,e,906,b)]. 12.00/12.15 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -empty(f352(A)). [resolve(943,e,907,b)]. 12.00/12.16 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | element(f352(A),powerset(the_carrier(A))). [resolve(943,e,908,b)]. 12.00/12.16 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | closed_subset(cast_as_carrier_subset(A),A). [resolve(943,e,909,a)]. 12.00/12.16 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(943,e,910,a)]. 12.00/12.16 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(943,e,911,a)]. 12.00/12.16 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(943,e,912,a)]. 12.00/12.16 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f395(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(943,e,913,a)]. 12.00/12.16 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(943,e,914,a)]. 12.00/12.16 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(943,e,915,a)]. 12.00/12.16 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(943,e,916,a)]. 12.00/12.16 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) = f394(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(943,e,917,a)]. 12.00/12.16 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(943,e,918,a)]. 12.00/12.17 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(943,e,919,a)]. 12.00/12.17 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(943,e,920,a)]. 12.00/12.17 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f396(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(943,e,921,a)]. 12.00/12.17 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(943,e,922,a)]. 12.00/12.17 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(943,e,923,a)]. 12.00/12.17 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(943,e,924,a)]. 12.00/12.17 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f395(A,B)),B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(943,e,925,a)]. 12.00/12.17 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | -in(set_difference(cast_as_carrier_subset(A),C),B) | D != C | -in(D,powerset(the_carrier(A))) | in(C,f397(A,B)). [resolve(943,e,926,a)]. 12.00/12.17 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f397(A,B)). [resolve(943,e,927,a)]. 12.00/12.17 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | f398(A,B,C) = C | -in(C,f397(A,B)). [resolve(943,e,928,a)]. 12.00/12.18 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f396(A,B) != f395(A,B) | in(f398(A,B,C),powerset(the_carrier(A))) | -in(C,f397(A,B)). [resolve(943,e,929,a)]. 12.00/12.18 944 -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(B,the_topology(A)) | -in(C,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(658)]. 12.00/12.18 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(B,the_topology(A)) | -in(C,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(944,g,780,e)]. 12.00/12.18 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(B,the_topology(A)) | -in(C,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(944,g,930,e)]. 12.00/12.18 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(B,the_topology(A)) | -in(C,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(944,g,931,e)]. 12.00/12.18 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(B,the_topology(A)) | -in(C,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(944,g,932,e)]. 12.00/12.18 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(B,the_topology(A)) | -in(C,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(944,g,933,e)]. 12.00/12.18 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(B,the_topology(A)) | -in(C,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(944,g,934,e)]. 12.00/12.18 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(B,the_topology(A)) | -in(C,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(944,g,935,e)]. 12.00/12.18 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(B,the_topology(A)) | -in(C,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(944,g,936,e)]. 12.00/12.18 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(B,the_topology(A)) | -in(C,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(944,g,937,e)]. 12.04/12.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(B,the_topology(A)) | -in(C,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(944,g,938,e)]. 12.04/12.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(B,the_topology(A)) | -in(C,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(944,g,939,e)]. 12.04/12.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(B,the_topology(A)) | -in(C,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(944,g,940,e)]. 12.04/12.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(B,the_topology(A)) | -in(C,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(944,g,941,e)]. 12.04/12.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(B,the_topology(A)) | -in(C,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(944,g,942,e)]. 12.04/12.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(B,the_topology(A)) | -in(C,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(944,g,943,e)]. 12.04/12.19 945 -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -subset(B,the_topology(A)) | in(union_of_subsets(the_carrier(A),B),the_topology(A)) | -topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(658)]. 12.04/12.19 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -subset(B,the_topology(A)) | in(union_of_subsets(the_carrier(A),B),the_topology(A)) | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(945,e,780,e)]. 12.04/12.19 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -subset(B,the_topology(A)) | in(union_of_subsets(the_carrier(A),B),the_topology(A)) | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(945,e,930,e)]. 12.04/12.19 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -subset(B,the_topology(A)) | in(union_of_subsets(the_carrier(A),B),the_topology(A)) | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(945,e,931,e)]. 12.04/12.19 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -subset(B,the_topology(A)) | in(union_of_subsets(the_carrier(A),B),the_topology(A)) | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(945,e,932,e)]. 12.04/12.19 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -subset(B,the_topology(A)) | in(union_of_subsets(the_carrier(A),B),the_topology(A)) | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(945,e,933,e)]. 12.11/12.24 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -subset(B,the_topology(A)) | in(union_of_subsets(the_carrier(A),B),the_topology(A)) | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(945,e,934,e)]. 12.11/12.24 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -subset(B,the_topology(A)) | in(union_of_subsets(the_carrier(A),B),the_topology(A)) | -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(945,e,935,e)]. 12.11/12.24 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -subset(B,the_topology(A)) | in(union_of_subsets(the_carrier(A),B),the_topology(A)) | -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(945,e,936,e)]. 12.11/12.24 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -subset(B,the_topology(A)) | in(union_of_subsets(the_carrier(A),B),the_topology(A)) | -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(945,e,937,e)]. 12.11/12.24 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -subset(B,the_topology(A)) | in(union_of_subsets(the_carrier(A),B),the_topology(A)) | -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(945,e,938,e)]. 12.11/12.24 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -subset(B,the_topology(A)) | in(union_of_subsets(the_carrier(A),B),the_topology(A)) | -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(945,e,939,e)]. 12.11/12.24 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -subset(B,the_topology(A)) | in(union_of_subsets(the_carrier(A),B),the_topology(A)) | -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(945,e,940,e)]. 12.11/12.24 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -subset(B,the_topology(A)) | in(union_of_subsets(the_carrier(A),B),the_topology(A)) | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(945,e,941,e)]. 12.11/12.24 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -subset(B,the_topology(A)) | in(union_of_subsets(the_carrier(A),B),the_topology(A)) | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(945,e,942,e)]. 12.11/12.24 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -subset(B,the_topology(A)) | in(union_of_subsets(the_carrier(A),B),the_topology(A)) | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(945,e,943,e)]. 12.11/12.24 946 -top_str(A) | in(the_carrier(A),the_topology(A)) | -topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(658)]. 12.11/12.24 947 -topological_space(A) | -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | -open_subset(D,B) | interior(B,D) = D # label(t55_tops_1) # label(lemma). [clausify(697)]. 12.11/12.24 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | -open_subset(D,B) | interior(B,D) = D | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(947,a,780,e)]. 12.12/12.26 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | -open_subset(D,B) | interior(B,D) = D | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(947,a,930,e)]. 12.12/12.26 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | -open_subset(D,B) | interior(B,D) = D | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(947,a,931,e)]. 12.12/12.26 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | -open_subset(D,B) | interior(B,D) = D | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(947,a,932,e)]. 12.12/12.26 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | -open_subset(D,B) | interior(B,D) = D | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(947,a,933,e)]. 12.12/12.26 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | -open_subset(D,B) | interior(B,D) = D | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(947,a,934,e)]. 12.12/12.26 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | -open_subset(D,B) | interior(B,D) = D | -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(947,a,935,e)]. 12.12/12.26 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | -open_subset(D,B) | interior(B,D) = D | -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(947,a,936,e)]. 12.12/12.26 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | -open_subset(D,B) | interior(B,D) = D | -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(947,a,937,e)]. 12.12/12.26 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | -open_subset(D,B) | interior(B,D) = D | -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(947,a,938,e)]. 12.12/12.26 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | -open_subset(D,B) | interior(B,D) = D | -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(947,a,939,e)]. 12.12/12.26 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | -open_subset(D,B) | interior(B,D) = D | -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(947,a,940,e)]. 12.12/12.26 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | -open_subset(D,B) | interior(B,D) = D | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(947,a,941,e)]. 12.12/12.26 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | -open_subset(D,B) | interior(B,D) = D | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(947,a,942,e)]. 12.12/12.27 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | -open_subset(D,B) | interior(B,D) = D | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(947,a,943,e)]. 12.12/12.27 948 -topological_space(A) | -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | interior(A,C) != C | open_subset(C,A) # label(t55_tops_1) # label(lemma). [clausify(697)]. 12.12/12.27 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | interior(A,C) != C | open_subset(C,A) | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(948,a,780,e)]. 12.12/12.27 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | interior(A,C) != C | open_subset(C,A) | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(948,a,930,e)]. 12.12/12.27 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | interior(A,C) != C | open_subset(C,A) | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(948,a,931,e)]. 12.12/12.27 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | interior(A,C) != C | open_subset(C,A) | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(948,a,932,e)]. 12.12/12.27 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | interior(A,C) != C | open_subset(C,A) | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(948,a,933,e)]. 12.12/12.27 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | interior(A,C) != C | open_subset(C,A) | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(948,a,934,e)]. 12.12/12.27 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | interior(A,C) != C | open_subset(C,A) | -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(948,a,935,e)]. 12.12/12.27 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | interior(A,C) != C | open_subset(C,A) | -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(948,a,936,e)]. 12.12/12.27 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | interior(A,C) != C | open_subset(C,A) | -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(948,a,937,e)]. 12.12/12.27 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | interior(A,C) != C | open_subset(C,A) | -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(948,a,938,e)]. 12.12/12.27 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | interior(A,C) != C | open_subset(C,A) | -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(948,a,939,e)]. 12.12/12.29 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | interior(A,C) != C | open_subset(C,A) | -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(948,a,940,e)]. 12.12/12.29 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | interior(A,C) != C | open_subset(C,A) | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)). [resolve(948,a,941,e)]. 12.12/12.29 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | interior(A,C) != C | open_subset(C,A) | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(948,a,942,e)]. 12.12/12.29 Derived: -top_str(A) | -top_str(B) | -element(C,powerset(the_carrier(A))) | -element(D,powerset(the_carrier(B))) | interior(A,C) != C | open_subset(C,A) | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(948,a,943,e)]. 12.12/12.29 949 -topological_space(A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | closed_subset(topstr_closure(A,B),A) # label(fc2_tops_1) # label(axiom). [clausify(699)]. 12.12/12.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)). [resolve(949,a,780,e)]. 12.12/12.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(949,a,930,e)]. 12.12/12.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(949,a,931,e)]. 12.12/12.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)). [resolve(949,a,932,e)]. 12.12/12.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(949,a,933,e)]. 12.12/12.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(949,a,934,e)]. 12.12/12.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | in(f443(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)). [resolve(949,a,935,e)]. 12.12/12.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | in(f443(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(949,a,936,e)]. 12.12/12.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | in(f443(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(949,a,937,e)]. 20.65/20.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | in(f444(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)). [resolve(949,a,938,e)]. 20.65/20.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | in(f444(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(949,a,939,e)]. 20.65/20.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | in(f444(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(949,a,940,e)]. 20.65/20.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | -in(subset_intersection2(the_carrier(B),f443(B),f444(B)),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)). [resolve(949,a,941,e)]. 20.65/20.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | -in(subset_intersection2(the_carrier(B),f443(B),f444(B)),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(949,a,942,e)]. 20.65/20.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | -in(subset_intersection2(the_carrier(B),f443(B),f444(B)),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(949,a,943,e)]. 20.65/20.81 950 -relation(A) | -transitive(A) | -symmetric(A) | reflexive(A) # label(cc1_partfun1) # label(axiom). [clausify(416)]. 20.65/20.81 951 symmetric(f14(A)) # label(rc3_partfun1) # label(axiom). [clausify(38)]. 20.65/20.81 Derived: -relation(f14(A)) | -transitive(f14(A)) | reflexive(f14(A)). [resolve(950,c,951,a)]. 20.65/20.81 952 symmetric(identity_relation(A)) # label(fc2_partfun1) # label(axiom). [clausify(680)]. 20.65/20.81 Derived: -relation(identity_relation(A)) | -transitive(identity_relation(A)) | reflexive(identity_relation(A)). [resolve(952,a,950,c)]. 20.65/20.81 953 -latt_str(A) | join_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(348)]. 20.65/20.81 954 -element(A,the_carrier(B)) | -element(C,the_carrier(B)) | -join_semilatt_str(B) | -join_commutative(B) | empty_carrier(B) | join_commut(B,A,C) = join(B,A,C) # label(redefinition_k3_lattices) # label(axiom). [clausify(45)]. 20.65/20.81 955 -join_semilatt_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_join(A),B,C) = join(A,B,C) # label(d1_lattices) # label(axiom). [clausify(69)]. 20.65/20.81 956 -join_semilatt_str(A) | relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(dt_u2_lattices) # label(axiom). [clausify(166)]. 20.65/20.81 957 -join_semilatt_str(A) | quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(dt_u2_lattices) # label(axiom). [clausify(166)]. 20.65/20.81 958 -join_semilatt_str(A) | function(the_L_join(A)) # label(dt_u2_lattices) # label(axiom). [clausify(166)]. 20.65/20.81 959 -join_associative(A) | -join_semilatt_str(A) | empty_carrier(A) | relation(the_L_join(A)) # label(fc3_lattice2) # label(axiom). [clausify(187)]. 20.65/20.81 960 -join_associative(A) | -join_semilatt_str(A) | empty_carrier(A) | function(the_L_join(A)) # label(fc3_lattice2) # label(axiom). [clausify(187)]. 20.65/20.81 961 -join_associative(A) | -join_semilatt_str(A) | empty_carrier(A) | v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc3_lattice2) # label(axiom). [clausify(187)]. 20.65/20.81 962 -join_associative(A) | -join_semilatt_str(A) | empty_carrier(A) | v2_binop_1(the_L_join(A),the_carrier(A)) # label(fc3_lattice2) # label(axiom). [clausify(187)]. 20.65/20.81 963 -join_associative(A) | -join_semilatt_str(A) | empty_carrier(A) | quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc3_lattice2) # label(axiom). [clausify(187)]. 21.96/22.12 964 -join_semilatt_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below(A,B,C) | join(A,B,C) = C # label(d3_lattices) # label(axiom). [clausify(277)]. 21.96/22.12 965 -join_semilatt_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below(A,B,C) | join(A,B,C) != C # label(d3_lattices) # label(axiom). [clausify(277)]. 21.96/22.12 966 -join_semilatt_str(A) | one_sorted_str(A) # label(dt_l2_lattices) # label(axiom). [clausify(296)]. 21.96/22.12 Derived: -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -join_commutative(A) | empty_carrier(A) | join_commut(A,B,C) = join(A,B,C). [resolve(953,b,954,c)]. 21.96/22.12 Derived: -latt_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_join(A),B,C) = join(A,B,C). [resolve(953,b,955,a)]. 21.96/22.12 Derived: -latt_str(A) | relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)). [resolve(953,b,956,a)]. 21.96/22.12 Derived: -latt_str(A) | quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)). [resolve(953,b,957,a)]. 21.96/22.12 Derived: -latt_str(A) | function(the_L_join(A)). [resolve(953,b,958,a)]. 21.96/22.12 Derived: -latt_str(A) | -join_associative(A) | empty_carrier(A) | relation(the_L_join(A)). [resolve(953,b,959,b)]. 21.96/22.12 Derived: -latt_str(A) | -join_associative(A) | empty_carrier(A) | v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)). [resolve(953,b,961,b)]. 21.96/22.12 Derived: -latt_str(A) | -join_associative(A) | empty_carrier(A) | v2_binop_1(the_L_join(A),the_carrier(A)). [resolve(953,b,962,b)]. 21.96/22.12 Derived: -latt_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below(A,B,C) | join(A,B,C) = C. [resolve(953,b,964,a)]. 21.96/22.12 Derived: -latt_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below(A,B,C) | join(A,B,C) != C. [resolve(953,b,965,a)]. 21.96/22.12 Derived: -latt_str(A) | one_sorted_str(A). [resolve(953,b,966,a)]. 21.96/22.12 967 empty_carrier(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(join(A,B,C),the_carrier(A)) # label(dt_k1_lattices) # label(axiom). [clausify(385)]. 21.96/22.12 Derived: empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(join(A,B,C),the_carrier(A)) | -latt_str(A). [resolve(967,b,953,b)]. 21.96/22.12 968 -join_semilatt_str(A) | -join_commutative(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below(A,C,B) | -below(A,B,C) | C = B # label(t26_lattices) # label(lemma). [clausify(415)]. 21.96/22.12 Derived: -join_commutative(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below(A,C,B) | -below(A,B,C) | C = B | -latt_str(A). [resolve(968,a,953,b)]. 21.96/22.12 969 -join_commutative(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -join_semilatt_str(A) | empty_carrier(A) | join_commut(A,B,C) = join_commut(A,C,B) # label(commutativity_k3_lattices) # label(axiom). [clausify(492)]. 21.96/22.12 Derived: -join_commutative(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | empty_carrier(A) | join_commut(A,B,C) = join_commut(A,C,B) | -latt_str(A). [resolve(969,d,953,b)]. 21.96/22.12 970 empty_carrier(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -join_commutative(A) | element(join_commut(A,C,B),the_carrier(A)) # label(dt_k3_lattices) # label(axiom). [clausify(563)]. 21.96/22.12 Derived: empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -join_commutative(A) | element(join_commut(A,C,B),the_carrier(A)) | -latt_str(A). [resolve(970,b,953,b)]. 21.96/22.12 971 join_semilatt_str(c32) # label(existence_l2_lattices) # label(axiom). [clausify(642)]. 21.96/22.12 Derived: -element(A,the_carrier(c32)) | -element(B,the_carrier(c32)) | -join_commutative(c32) | empty_carrier(c32) | join_commut(c32,A,B) = join(c32,A,B). [resolve(971,a,954,c)]. 25.76/25.91 Derived: empty_carrier(c32) | -element(A,the_carrier(c32)) | -element(B,the_carrier(c32)) | apply_binary_as_element(the_carrier(c32),the_carrier(c32),the_carrier(c32),the_L_join(c32),A,B) = join(c32,A,B). [resolve(971,a,955,a)]. 25.76/25.91 Derived: relation_of2_as_subset(the_L_join(c32),cartesian_product2(the_carrier(c32),the_carrier(c32)),the_carrier(c32)). [resolve(971,a,956,a)]. 25.76/25.91 Derived: quasi_total(the_L_join(c32),cartesian_product2(the_carrier(c32),the_carrier(c32)),the_carrier(c32)). [resolve(971,a,957,a)]. 25.76/25.91 Derived: function(the_L_join(c32)). [resolve(971,a,958,a)]. 25.76/25.91 Derived: -join_associative(c32) | empty_carrier(c32) | relation(the_L_join(c32)). [resolve(971,a,959,b)]. 25.76/25.91 Derived: -join_associative(c32) | empty_carrier(c32) | v1_partfun1(the_L_join(c32),cartesian_product2(the_carrier(c32),the_carrier(c32)),the_carrier(c32)). [resolve(971,a,961,b)]. 25.76/25.91 Derived: -join_associative(c32) | empty_carrier(c32) | v2_binop_1(the_L_join(c32),the_carrier(c32)). [resolve(971,a,962,b)]. 25.76/25.91 Derived: empty_carrier(c32) | -element(A,the_carrier(c32)) | -element(B,the_carrier(c32)) | -below(c32,A,B) | join(c32,A,B) = B. [resolve(971,a,964,a)]. 25.76/25.91 Derived: empty_carrier(c32) | -element(A,the_carrier(c32)) | -element(B,the_carrier(c32)) | below(c32,A,B) | join(c32,A,B) != B. [resolve(971,a,965,a)]. 25.76/25.91 Derived: one_sorted_str(c32). [resolve(971,a,966,a)]. 25.76/25.91 Derived: empty_carrier(c32) | -element(A,the_carrier(c32)) | -element(B,the_carrier(c32)) | element(join(c32,A,B),the_carrier(c32)). [resolve(971,a,967,b)]. 25.76/25.91 Derived: -join_commutative(c32) | empty_carrier(c32) | -element(A,the_carrier(c32)) | -element(B,the_carrier(c32)) | -below(c32,B,A) | -below(c32,A,B) | B = A. [resolve(971,a,968,a)]. 25.76/25.91 Derived: -join_commutative(c32) | -element(A,the_carrier(c32)) | -element(B,the_carrier(c32)) | empty_carrier(c32) | join_commut(c32,A,B) = join_commut(c32,B,A). [resolve(971,a,969,d)]. 25.76/25.91 Derived: empty_carrier(c32) | -element(A,the_carrier(c32)) | -element(B,the_carrier(c32)) | -join_commutative(c32) | element(join_commut(c32,B,A),the_carrier(c32)). [resolve(971,a,970,b)]. 25.76/25.91 972 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | relation(the_L_join(A)) # label(fc2_lattice2) # label(axiom). [clausify(666)]. 25.76/25.91 Derived: empty_carrier(A) | -join_commutative(A) | relation(the_L_join(A)) | -latt_str(A). [resolve(972,c,953,b)]. 25.76/25.91 Derived: empty_carrier(c32) | -join_commutative(c32) | relation(the_L_join(c32)). [resolve(972,c,971,a)]. 25.76/25.91 973 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | function(the_L_join(A)) # label(fc2_lattice2) # label(axiom). [clausify(666)]. 25.76/25.91 974 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc2_lattice2) # label(axiom). [clausify(666)]. 25.76/25.91 975 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | v1_binop_1(the_L_join(A),the_carrier(A)) # label(fc2_lattice2) # label(axiom). [clausify(666)]. 25.76/25.91 Derived: empty_carrier(A) | -join_commutative(A) | v1_binop_1(the_L_join(A),the_carrier(A)) | -latt_str(A). [resolve(975,c,953,b)]. 25.76/25.91 Derived: empty_carrier(c32) | -join_commutative(c32) | v1_binop_1(the_L_join(c32),the_carrier(c32)). [resolve(975,c,971,a)]. 25.76/25.91 976 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc2_lattice2) # label(axiom). [clausify(666)]. 25.76/25.91 Derived: empty_carrier(A) | -join_commutative(A) | v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(976,c,953,b)]. 25.76/25.91 Derived: empty_carrier(c32) | -join_commutative(c32) | v1_partfun1(the_L_join(c32),cartesian_product2(the_carrier(c32),the_carrier(c32)),the_carrier(c32)). [resolve(976,c,971,a)]. 25.76/25.91 977 -rel_str(A) | -strict_rel_str(A) | rel_str_of(the_carrier(A),the_InternalRel(A)) = A # label(abstractness_v1_orders_2) # label(axiom). [clausify(544)]. 25.76/25.91 978 -relation_of2(A,B,B) | strict_rel_str(rel_str_of(B,A)) # label(dt_g1_orders_2) # label(axiom). [clausify(47)]. 30.40/30.54 979 strict_rel_str(c6) # label(rc1_orders_2) # label(axiom). [clausify(126)]. 30.40/30.54 980 empty(A) | -relation_of2(B,A,A) | strict_rel_str(rel_str_of(A,B)) # label(fc1_orders_2) # label(axiom). [clausify(305)]. 30.40/30.54 981 strict_rel_str(c15) # label(rc2_orders_2) # label(axiom). [clausify(370)]. 30.40/30.54 982 -lattice(A) | -latt_str(A) | empty_carrier(A) | strict_rel_str(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(400)]. 30.40/30.54 983 -latt_str(A) | -lattice(A) | empty_carrier(A) | strict_rel_str(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(406)]. 30.40/30.54 Derived: -rel_str(rel_str_of(A,B)) | rel_str_of(the_carrier(rel_str_of(A,B)),the_InternalRel(rel_str_of(A,B))) = rel_str_of(A,B) | -relation_of2(B,A,A). [resolve(977,b,978,b)]. 30.40/30.54 Derived: -rel_str(c6) | rel_str_of(the_carrier(c6),the_InternalRel(c6)) = c6. [resolve(977,b,979,a)]. 30.40/30.54 Derived: -rel_str(c15) | rel_str_of(the_carrier(c15),the_InternalRel(c15)) = c15. [resolve(977,b,981,a)]. 30.40/30.54 Derived: -rel_str(poset_of_lattice(A)) | rel_str_of(the_carrier(poset_of_lattice(A)),the_InternalRel(poset_of_lattice(A))) = poset_of_lattice(A) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(977,b,982,d)]. 30.40/30.54 984 -antisymmetric(A) | -relation_of2(A,B,B) | -v1_partfun1(A,B,B) | -transitive(A) | -reflexive(A) | strict_rel_str(rel_str_of(B,A)) # label(fc3_orders_2) # label(axiom). [clausify(663)]. 30.40/30.54 985 meet_semilatt_str(c4) # label(existence_l1_lattices) # label(axiom). [clausify(52)]. 30.40/30.54 986 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) != B | -element(C,the_carrier(A)) | meet(A,B,C) = B # label(d16_lattices) # label(axiom). [clausify(48)]. 30.40/30.54 987 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) != B | -element(C,the_carrier(A)) | meet(A,C,B) = B # label(d16_lattices) # label(axiom). [clausify(48)]. 30.40/30.54 988 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) = B | element(f16(A,B),the_carrier(A)) # label(d16_lattices) # label(axiom). [clausify(48)]. 30.40/30.54 989 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) = B | meet(A,B,f16(A,B)) != B | meet(A,f16(A,B),B) != B # label(d16_lattices) # label(axiom). [clausify(48)]. 30.40/30.54 Derived: empty_carrier(c4) | -lower_bounded_semilattstr(c4) | -element(A,the_carrier(c4)) | bottom_of_semilattstr(c4) != A | -element(B,the_carrier(c4)) | meet(c4,A,B) = A. [resolve(985,a,986,b)]. 30.40/30.54 Derived: empty_carrier(c4) | -lower_bounded_semilattstr(c4) | -element(A,the_carrier(c4)) | bottom_of_semilattstr(c4) != A | -element(B,the_carrier(c4)) | meet(c4,B,A) = A. [resolve(985,a,987,b)]. 30.40/30.54 Derived: empty_carrier(c4) | -lower_bounded_semilattstr(c4) | -element(A,the_carrier(c4)) | bottom_of_semilattstr(c4) = A | element(f16(c4,A),the_carrier(c4)). [resolve(985,a,988,b)]. 30.40/30.54 Derived: empty_carrier(c4) | -lower_bounded_semilattstr(c4) | -element(A,the_carrier(c4)) | bottom_of_semilattstr(c4) = A | meet(c4,A,f16(c4,A)) != A | meet(c4,f16(c4,A),A) != A. [resolve(985,a,989,b)]. 30.40/30.54 990 empty_carrier(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -meet_commutative(A) | meet_commut(A,B,C) = meet(A,B,C) # label(redefinition_k4_lattices) # label(axiom). [clausify(112)]. 30.40/30.54 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | -meet_commutative(c4) | meet_commut(c4,A,B) = meet(c4,A,B). [resolve(990,b,985,a)]. 30.40/30.54 991 -meet_semilatt_str(A) | -meet_commutative(A) | empty_carrier(A) | function(the_L_meet(A)) # label(fc4_lattice2) # label(axiom). [clausify(163)]. 30.40/30.54 Derived: -meet_commutative(c4) | empty_carrier(c4) | function(the_L_meet(c4)). [resolve(991,a,985,a)]. 30.40/30.54 992 -meet_semilatt_str(A) | -meet_commutative(A) | empty_carrier(A) | v1_binop_1(the_L_meet(A),the_carrier(A)) # label(fc4_lattice2) # label(axiom). [clausify(163)]. 30.40/30.54 Derived: -meet_commutative(c4) | empty_carrier(c4) | v1_binop_1(the_L_meet(c4),the_carrier(c4)). [resolve(992,a,985,a)]. 30.46/30.64 993 -meet_semilatt_str(A) | -meet_commutative(A) | empty_carrier(A) | v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc4_lattice2) # label(axiom). [clausify(163)]. 30.46/30.64 Derived: -meet_commutative(c4) | empty_carrier(c4) | v1_partfun1(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(993,a,985,a)]. 30.46/30.64 994 -meet_semilatt_str(A) | -meet_commutative(A) | empty_carrier(A) | quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc4_lattice2) # label(axiom). [clausify(163)]. 30.46/30.64 Derived: -meet_commutative(c4) | empty_carrier(c4) | quasi_total(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(994,a,985,a)]. 30.46/30.64 995 -meet_semilatt_str(A) | -meet_commutative(A) | empty_carrier(A) | relation(the_L_meet(A)) # label(fc4_lattice2) # label(axiom). [clausify(163)]. 30.46/30.64 Derived: -meet_commutative(c4) | empty_carrier(c4) | relation(the_L_meet(c4)). [resolve(995,a,985,a)]. 30.46/30.64 996 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | element(f142(A),the_carrier(A)) # label(d13_lattices) # label(axiom). [clausify(230)]. 30.46/30.64 Derived: empty_carrier(c4) | -lower_bounded_semilattstr(c4) | element(f142(c4),the_carrier(c4)). [resolve(996,b,985,a)]. 30.46/30.64 997 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | meet(A,f142(A),B) = f142(A) # label(d13_lattices) # label(axiom). [clausify(230)]. 30.46/30.64 Derived: empty_carrier(c4) | -lower_bounded_semilattstr(c4) | -element(A,the_carrier(c4)) | meet(c4,f142(c4),A) = f142(c4). [resolve(997,b,985,a)]. 30.46/30.64 998 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | meet(A,B,f142(A)) = f142(A) # label(d13_lattices) # label(axiom). [clausify(230)]. 30.46/30.64 Derived: empty_carrier(c4) | -lower_bounded_semilattstr(c4) | -element(A,the_carrier(c4)) | meet(c4,A,f142(c4)) = f142(c4). [resolve(998,b,985,a)]. 30.46/30.64 999 empty_carrier(A) | -meet_semilatt_str(A) | lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | element(f143(A,B),the_carrier(A)) # label(d13_lattices) # label(axiom). [clausify(230)]. 30.46/30.64 Derived: empty_carrier(c4) | lower_bounded_semilattstr(c4) | -element(A,the_carrier(c4)) | element(f143(c4,A),the_carrier(c4)). [resolve(999,b,985,a)]. 30.46/30.64 1000 empty_carrier(A) | -meet_semilatt_str(A) | lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | meet(A,B,f143(A,B)) != B | meet(A,f143(A,B),B) != B # label(d13_lattices) # label(axiom). [clausify(230)]. 30.46/30.64 Derived: empty_carrier(c4) | lower_bounded_semilattstr(c4) | -element(A,the_carrier(c4)) | meet(c4,A,f143(c4,A)) != A | meet(c4,f143(c4,A),A) != A. [resolve(1000,b,985,a)]. 30.46/30.64 1001 empty_carrier(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_meet(A),B,C) = meet(A,B,C) # label(d2_lattices) # label(axiom). [clausify(248)]. 30.46/30.64 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | apply_binary_as_element(the_carrier(c4),the_carrier(c4),the_carrier(c4),the_L_meet(c4),A,B) = meet(c4,A,B). [resolve(1001,b,985,a)]. 30.46/30.64 1002 empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -meet_semilatt_str(A) | element(meet(A,C,B),the_carrier(A)) # label(dt_k2_lattices) # label(axiom). [clausify(261)]. 30.46/30.64 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | element(meet(c4,B,A),the_carrier(c4)). [resolve(1002,d,985,a)]. 30.46/30.64 1003 -meet_semilatt_str(A) | quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(dt_u1_lattices) # label(axiom). [clausify(286)]. 30.46/30.64 Derived: quasi_total(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(1003,a,985,a)]. 30.46/30.64 1004 -meet_semilatt_str(A) | relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(dt_u1_lattices) # label(axiom). [clausify(286)]. 30.58/30.75 Derived: relation_of2_as_subset(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(1004,a,985,a)]. 30.58/30.75 1005 -meet_semilatt_str(A) | function(the_L_meet(A)) # label(dt_u1_lattices) # label(axiom). [clausify(286)]. 30.58/30.75 Derived: function(the_L_meet(c4)). [resolve(1005,a,985,a)]. 30.58/30.75 1006 -latt_str(A) | meet_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(348)]. 30.58/30.75 Derived: -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) != B | -element(C,the_carrier(A)) | meet(A,B,C) = B. [resolve(1006,b,986,b)]. 30.58/30.75 Derived: -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) != B | -element(C,the_carrier(A)) | meet(A,C,B) = B. [resolve(1006,b,987,b)]. 30.58/30.75 Derived: -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) = B | element(f16(A,B),the_carrier(A)). [resolve(1006,b,988,b)]. 30.58/30.75 Derived: -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) = B | meet(A,B,f16(A,B)) != B | meet(A,f16(A,B),B) != B. [resolve(1006,b,989,b)]. 30.58/30.75 Derived: -latt_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -meet_commutative(A) | meet_commut(A,B,C) = meet(A,B,C). [resolve(1006,b,990,b)]. 30.58/30.75 Derived: -latt_str(A) | -meet_commutative(A) | empty_carrier(A) | function(the_L_meet(A)). [resolve(1006,b,991,a)]. 30.58/30.75 Derived: -latt_str(A) | -meet_commutative(A) | empty_carrier(A) | v1_binop_1(the_L_meet(A),the_carrier(A)). [resolve(1006,b,992,a)]. 30.58/30.75 Derived: -latt_str(A) | -meet_commutative(A) | empty_carrier(A) | v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)). [resolve(1006,b,993,a)]. 30.58/30.75 Derived: -latt_str(A) | -meet_commutative(A) | empty_carrier(A) | quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)). [resolve(1006,b,994,a)]. 30.58/30.75 Derived: -latt_str(A) | -meet_commutative(A) | empty_carrier(A) | relation(the_L_meet(A)). [resolve(1006,b,995,a)]. 30.58/30.75 Derived: -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | element(f142(A),the_carrier(A)). [resolve(1006,b,996,b)]. 30.58/30.75 Derived: -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | meet(A,f142(A),B) = f142(A). [resolve(1006,b,997,b)]. 30.58/30.75 Derived: -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | meet(A,B,f142(A)) = f142(A). [resolve(1006,b,998,b)]. 30.58/30.75 Derived: -latt_str(A) | empty_carrier(A) | lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | element(f143(A,B),the_carrier(A)). [resolve(1006,b,999,b)]. 30.58/30.75 Derived: -latt_str(A) | empty_carrier(A) | lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | meet(A,B,f143(A,B)) != B | meet(A,f143(A,B),B) != B. [resolve(1006,b,1000,b)]. 30.58/30.75 Derived: -latt_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_meet(A),B,C) = meet(A,B,C). [resolve(1006,b,1001,b)]. 30.58/30.75 Derived: -latt_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(meet(A,C,B),the_carrier(A)). [resolve(1006,b,1002,d)]. 30.58/30.75 Derived: -latt_str(A) | quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)). [resolve(1006,b,1003,a)]. 30.58/30.75 Derived: -latt_str(A) | relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)). [resolve(1006,b,1004,a)]. 30.58/30.75 Derived: -latt_str(A) | function(the_L_meet(A)). [resolve(1006,b,1005,a)]. 30.58/30.75 1007 -meet_commutative(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | empty_carrier(A) | meet_commut(A,B,C) = meet_commut(A,C,B) # label(commutativity_k4_lattices) # label(axiom). [clausify(375)]. 30.58/30.75 Derived: -meet_commutative(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | empty_carrier(c4) | meet_commut(c4,A,B) = meet_commut(c4,B,A). [resolve(1007,b,985,a)]. 35.56/35.71 Derived: -meet_commutative(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | empty_carrier(A) | meet_commut(A,B,C) = meet_commut(A,C,B) | -latt_str(A). [resolve(1007,b,1006,b)]. 35.56/35.71 1008 -meet_associative(A) | -meet_semilatt_str(A) | empty_carrier(A) | function(the_L_meet(A)) # label(fc5_lattice2) # label(axiom). [clausify(584)]. 35.56/35.71 1009 -meet_associative(A) | -meet_semilatt_str(A) | empty_carrier(A) | v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc5_lattice2) # label(axiom). [clausify(584)]. 35.56/35.71 Derived: -meet_associative(c4) | empty_carrier(c4) | v1_partfun1(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(1009,b,985,a)]. 35.56/35.71 Derived: -meet_associative(A) | empty_carrier(A) | v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(1009,b,1006,b)]. 35.56/35.71 1010 -meet_associative(A) | -meet_semilatt_str(A) | empty_carrier(A) | v2_binop_1(the_L_meet(A),the_carrier(A)) # label(fc5_lattice2) # label(axiom). [clausify(584)]. 35.56/35.71 Derived: -meet_associative(c4) | empty_carrier(c4) | v2_binop_1(the_L_meet(c4),the_carrier(c4)). [resolve(1010,b,985,a)]. 35.56/35.71 Derived: -meet_associative(A) | empty_carrier(A) | v2_binop_1(the_L_meet(A),the_carrier(A)) | -latt_str(A). [resolve(1010,b,1006,b)]. 35.56/35.71 1011 -meet_associative(A) | -meet_semilatt_str(A) | empty_carrier(A) | quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc5_lattice2) # label(axiom). [clausify(584)]. 35.56/35.71 1012 -meet_associative(A) | -meet_semilatt_str(A) | empty_carrier(A) | relation(the_L_meet(A)) # label(fc5_lattice2) # label(axiom). [clausify(584)]. 35.56/35.71 Derived: -meet_associative(c4) | empty_carrier(c4) | relation(the_L_meet(c4)). [resolve(1012,b,985,a)]. 35.56/35.71 Derived: -meet_associative(A) | empty_carrier(A) | relation(the_L_meet(A)) | -latt_str(A). [resolve(1012,b,1006,b)]. 35.56/35.71 1013 -meet_commutative(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | empty_carrier(A) | element(meet_commut(A,C,B),the_carrier(A)) # label(dt_k4_lattices) # label(axiom). [clausify(597)]. 35.56/35.71 Derived: -meet_commutative(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | empty_carrier(c4) | element(meet_commut(c4,B,A),the_carrier(c4)). [resolve(1013,b,985,a)]. 35.56/35.71 Derived: -meet_commutative(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | empty_carrier(A) | element(meet_commut(A,C,B),the_carrier(A)) | -latt_str(A). [resolve(1013,b,1006,b)]. 35.56/35.71 1014 -meet_semilatt_str(A) | one_sorted_str(A) # label(dt_l1_lattices) # label(axiom). [clausify(652)]. 35.56/35.71 Derived: one_sorted_str(c4). [resolve(1014,a,985,a)]. 35.56/35.71 1015 empty_carrier(A) | -meet_semilatt_str(A) | element(bottom_of_semilattstr(A),the_carrier(A)) # label(dt_k5_lattices) # label(axiom). [clausify(675)]. 35.56/35.71 Derived: empty_carrier(c4) | element(bottom_of_semilattstr(c4),the_carrier(c4)). [resolve(1015,b,985,a)]. 35.56/35.71 Derived: empty_carrier(A) | element(bottom_of_semilattstr(A),the_carrier(A)) | -latt_str(A). [resolve(1015,b,1006,b)]. 35.56/35.71 1016 meet_absorbing(boole_lattice(A)) # label(fc2_lattice3) # label(axiom). [clausify(383)]. 35.56/35.71 1017 -meet_absorbing(A) | -latt_str(A) | -meet_commutative(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below(A,meet_commut(A,B,C),B) # label(t23_lattices) # label(lemma). [clausify(77)]. 35.56/35.71 1018 -element(A,the_carrier(B)) | -element(C,the_carrier(B)) | -latt_str(B) | -join_absorbing(B) | -meet_absorbing(B) | -meet_commutative(B) | empty_carrier(B) | -below(B,A,C) | below_refl(B,A,C) # label(redefinition_r3_lattices) # label(axiom). [clausify(88)]. 35.56/35.71 1019 -element(A,the_carrier(B)) | -element(C,the_carrier(B)) | -latt_str(B) | -join_absorbing(B) | -meet_absorbing(B) | -meet_commutative(B) | empty_carrier(B) | below(B,A,C) | -below_refl(B,A,C) # label(redefinition_r3_lattices) # label(axiom). [clausify(88)]. 35.56/35.71 1020 -latt_str(A) | empty_carrier(A) | -meet_associative(A) | -meet_absorbing(A) | -join_absorbing(A) | -meet_commutative(A) | -join_associative(A) | -join_commutative(A) | lattice(A) # label(cc2_lattices) # label(axiom). [clausify(96)]. 35.61/35.78 Derived: -latt_str(boole_lattice(A)) | -meet_commutative(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | below(boole_lattice(A),meet_commut(boole_lattice(A),B,C),B). [resolve(1016,a,1017,a)]. 35.61/35.78 Derived: -element(A,the_carrier(boole_lattice(B))) | -element(C,the_carrier(boole_lattice(B))) | -latt_str(boole_lattice(B)) | -join_absorbing(boole_lattice(B)) | -meet_commutative(boole_lattice(B)) | empty_carrier(boole_lattice(B)) | -below(boole_lattice(B),A,C) | below_refl(boole_lattice(B),A,C). [resolve(1016,a,1018,e)]. 35.61/35.78 Derived: -element(A,the_carrier(boole_lattice(B))) | -element(C,the_carrier(boole_lattice(B))) | -latt_str(boole_lattice(B)) | -join_absorbing(boole_lattice(B)) | -meet_commutative(boole_lattice(B)) | empty_carrier(boole_lattice(B)) | below(boole_lattice(B),A,C) | -below_refl(boole_lattice(B),A,C). [resolve(1016,a,1019,e)]. 35.61/35.78 1021 -meet_commutative(A) | -meet_absorbing(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -latt_str(A) | -join_absorbing(A) | empty_carrier(A) | below_refl(A,C,C) # label(reflexivity_r3_lattices) # label(axiom). [clausify(448)]. 35.61/35.78 Derived: -meet_commutative(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | -latt_str(boole_lattice(A)) | -join_absorbing(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | below_refl(boole_lattice(A),C,C). [resolve(1021,b,1016,a)]. 35.61/35.78 1022 empty_carrier(A) | -latt_str(A) | element(f335(A),the_carrier(A)) | meet_absorbing(A) # label(d8_lattices) # label(axiom). [clausify(494)]. 35.61/35.78 Derived: empty_carrier(A) | -latt_str(A) | element(f335(A),the_carrier(A)) | -latt_str(A) | -meet_commutative(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below(A,meet_commut(A,B,C),B). [resolve(1022,d,1017,a)]. 35.61/35.78 Derived: empty_carrier(A) | -latt_str(A) | element(f335(A),the_carrier(A)) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -latt_str(A) | -join_absorbing(A) | -meet_commutative(A) | empty_carrier(A) | -below(A,B,C) | below_refl(A,B,C). [resolve(1022,d,1018,e)]. 35.61/35.78 Derived: empty_carrier(A) | -latt_str(A) | element(f335(A),the_carrier(A)) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -latt_str(A) | -join_absorbing(A) | -meet_commutative(A) | empty_carrier(A) | below(A,B,C) | -below_refl(A,B,C). [resolve(1022,d,1019,e)]. 35.61/35.78 Derived: empty_carrier(A) | -latt_str(A) | element(f335(A),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -meet_associative(A) | -join_absorbing(A) | -meet_commutative(A) | -join_associative(A) | -join_commutative(A) | lattice(A). [resolve(1022,d,1020,d)]. 35.61/35.78 Derived: empty_carrier(A) | -latt_str(A) | element(f335(A),the_carrier(A)) | -meet_commutative(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -latt_str(A) | -join_absorbing(A) | empty_carrier(A) | below_refl(A,C,C). [resolve(1022,d,1021,b)]. 35.61/35.78 1023 empty_carrier(A) | -latt_str(A) | element(f336(A),the_carrier(A)) | meet_absorbing(A) # label(d8_lattices) # label(axiom). [clausify(494)]. 35.61/35.78 Derived: empty_carrier(A) | -latt_str(A) | element(f336(A),the_carrier(A)) | -latt_str(A) | -meet_commutative(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below(A,meet_commut(A,B,C),B). [resolve(1023,d,1017,a)]. 35.61/35.78 Derived: empty_carrier(A) | -latt_str(A) | element(f336(A),the_carrier(A)) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -latt_str(A) | -join_absorbing(A) | -meet_commutative(A) | empty_carrier(A) | -below(A,B,C) | below_refl(A,B,C). [resolve(1023,d,1018,e)]. 35.61/35.78 Derived: empty_carrier(A) | -latt_str(A) | element(f336(A),the_carrier(A)) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -latt_str(A) | -join_absorbing(A) | -meet_commutative(A) | empty_carrier(A) | below(A,B,C) | -below_refl(A,B,C). [resolve(1023,d,1019,e)]. 35.61/35.78 Derived: empty_carrier(A) | -latt_str(A) | element(f336(A),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -meet_associative(A) | -join_absorbing(A) | -meet_commutative(A) | -join_associative(A) | -join_commutative(A) | lattice(A). [resolve(1023,d,1020,d)]. 35.61/35.81 Derived: empty_carrier(A) | -latt_str(A) | element(f336(A),the_carrier(A)) | -meet_commutative(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -latt_str(A) | -join_absorbing(A) | empty_carrier(A) | below_refl(A,C,C). [resolve(1023,d,1021,b)]. 35.61/35.81 1024 empty_carrier(A) | -latt_str(A) | join(A,meet(A,f335(A),f336(A)),f336(A)) != f336(A) | meet_absorbing(A) # label(d8_lattices) # label(axiom). [clausify(494)]. 35.61/35.81 Derived: empty_carrier(A) | -latt_str(A) | join(A,meet(A,f335(A),f336(A)),f336(A)) != f336(A) | -latt_str(A) | -meet_commutative(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below(A,meet_commut(A,B,C),B). [resolve(1024,d,1017,a)]. 35.61/35.81 Derived: empty_carrier(A) | -latt_str(A) | join(A,meet(A,f335(A),f336(A)),f336(A)) != f336(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -latt_str(A) | -join_absorbing(A) | -meet_commutative(A) | empty_carrier(A) | -below(A,B,C) | below_refl(A,B,C). [resolve(1024,d,1018,e)]. 35.61/35.81 Derived: empty_carrier(A) | -latt_str(A) | join(A,meet(A,f335(A),f336(A)),f336(A)) != f336(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -latt_str(A) | -join_absorbing(A) | -meet_commutative(A) | empty_carrier(A) | below(A,B,C) | -below_refl(A,B,C). [resolve(1024,d,1019,e)]. 35.61/35.81 Derived: empty_carrier(A) | -latt_str(A) | join(A,meet(A,f335(A),f336(A)),f336(A)) != f336(A) | -latt_str(A) | empty_carrier(A) | -meet_associative(A) | -join_absorbing(A) | -meet_commutative(A) | -join_associative(A) | -join_commutative(A) | lattice(A). [resolve(1024,d,1020,d)]. 35.61/35.81 Derived: empty_carrier(A) | -latt_str(A) | join(A,meet(A,f335(A),f336(A)),f336(A)) != f336(A) | -meet_commutative(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -latt_str(A) | -join_absorbing(A) | empty_carrier(A) | below_refl(A,C,C). [resolve(1024,d,1021,b)]. 35.61/35.81 1025 empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | join(A,meet(A,B,C),C) = C | -meet_absorbing(A) # label(d8_lattices) # label(axiom). [clausify(494)]. 35.61/35.81 Derived: empty_carrier(boole_lattice(A)) | -latt_str(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | join(boole_lattice(A),meet(boole_lattice(A),B,C),C) = C. [resolve(1025,f,1016,a)]. 35.61/35.81 Derived: empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | join(A,meet(A,B,C),C) = C | empty_carrier(A) | -latt_str(A) | element(f335(A),the_carrier(A)). [resolve(1025,f,1022,d)]. 35.61/35.81 Derived: empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | join(A,meet(A,B,C),C) = C | empty_carrier(A) | -latt_str(A) | element(f336(A),the_carrier(A)). [resolve(1025,f,1023,d)]. 35.61/35.81 Derived: empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | join(A,meet(A,B,C),C) = C | empty_carrier(A) | -latt_str(A) | join(A,meet(A,f335(A),f336(A)),f336(A)) != f336(A). [resolve(1025,f,1024,d)]. 35.61/35.81 1026 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_absorbing(A) # label(cc1_lattices) # label(axiom). [clausify(536)]. 35.61/35.81 Derived: -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | -meet_commutative(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below(A,meet_commut(A,B,C),B). [resolve(1026,d,1017,a)]. 35.61/35.81 Derived: -latt_str(A) | empty_carrier(A) | -lattice(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -latt_str(A) | -join_absorbing(A) | -meet_commutative(A) | empty_carrier(A) | -below(A,B,C) | below_refl(A,B,C). [resolve(1026,d,1018,e)]. 35.61/35.81 Derived: -latt_str(A) | empty_carrier(A) | -lattice(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -latt_str(A) | -join_absorbing(A) | -meet_commutative(A) | empty_carrier(A) | below(A,B,C) | -below_refl(A,B,C). [resolve(1026,d,1019,e)]. 40.65/40.85 Derived: -latt_str(A) | empty_carrier(A) | -lattice(A) | -meet_commutative(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -latt_str(A) | -join_absorbing(A) | empty_carrier(A) | below_refl(A,C,C). [resolve(1026,d,1021,b)]. 40.65/40.85 Derived: -latt_str(A) | empty_carrier(A) | -lattice(A) | empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | join(A,meet(A,B,C),C) = C. [resolve(1026,d,1025,f)]. 40.65/40.85 1027 meet_absorbing(c26) # label(rc9_lattices) # label(axiom). [clausify(617)]. 40.65/40.85 Derived: -latt_str(c26) | -meet_commutative(c26) | empty_carrier(c26) | -element(A,the_carrier(c26)) | -element(B,the_carrier(c26)) | below(c26,meet_commut(c26,A,B),A). [resolve(1027,a,1017,a)]. 40.65/40.85 Derived: -element(A,the_carrier(c26)) | -element(B,the_carrier(c26)) | -latt_str(c26) | -join_absorbing(c26) | -meet_commutative(c26) | empty_carrier(c26) | -below(c26,A,B) | below_refl(c26,A,B). [resolve(1027,a,1018,e)]. 40.65/40.85 Derived: -element(A,the_carrier(c26)) | -element(B,the_carrier(c26)) | -latt_str(c26) | -join_absorbing(c26) | -meet_commutative(c26) | empty_carrier(c26) | below(c26,A,B) | -below_refl(c26,A,B). [resolve(1027,a,1019,e)]. 40.65/40.85 Derived: -latt_str(c26) | empty_carrier(c26) | -meet_associative(c26) | -join_absorbing(c26) | -meet_commutative(c26) | -join_associative(c26) | -join_commutative(c26) | lattice(c26). [resolve(1027,a,1020,d)]. 40.65/40.85 Derived: -meet_commutative(c26) | -element(A,the_carrier(c26)) | -element(B,the_carrier(c26)) | -latt_str(c26) | -join_absorbing(c26) | empty_carrier(c26) | below_refl(c26,B,B). [resolve(1027,a,1021,b)]. 40.65/40.85 Derived: empty_carrier(c26) | -latt_str(c26) | -element(A,the_carrier(c26)) | -element(B,the_carrier(c26)) | join(c26,meet(c26,A,B),B) = B. [resolve(1027,a,1025,f)]. 40.65/40.85 1028 -latt_str(A) | -strict_latt_str(A) | latt_str_of(the_carrier(A),the_L_join(A),the_L_meet(A)) = A # label(abstractness_v3_lattices) # label(axiom). [clausify(156)]. 40.65/40.85 1029 strict_latt_str(c5) # label(rc3_lattices) # label(axiom). [clausify(78)]. 40.65/40.85 1030 -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -relation_of2(C,cartesian_product2(B,B),B) | -quasi_total(C,cartesian_product2(B,B),B) | -quasi_total(A,cartesian_product2(B,B),B) | -function(A) | strict_latt_str(latt_str_of(B,A,C)) # label(dt_g3_lattices) # label(axiom). [clausify(105)]. 40.65/40.85 1031 strict_latt_str(boole_lattice(A)) # label(dt_k1_lattice3) # label(axiom). [clausify(140)]. 40.65/40.85 Derived: -latt_str(c5) | latt_str_of(the_carrier(c5),the_L_join(c5),the_L_meet(c5)) = c5. [resolve(1028,b,1029,a)]. 40.65/40.85 Derived: -latt_str(latt_str_of(A,B,C)) | latt_str_of(the_carrier(latt_str_of(A,B,C)),the_L_join(latt_str_of(A,B,C)),the_L_meet(latt_str_of(A,B,C))) = latt_str_of(A,B,C) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -relation_of2(C,cartesian_product2(A,A),A) | -quasi_total(C,cartesian_product2(A,A),A) | -quasi_total(B,cartesian_product2(A,A),A) | -function(B). [resolve(1028,b,1030,g)]. 40.65/40.85 Derived: -latt_str(boole_lattice(A)) | latt_str_of(the_carrier(boole_lattice(A)),the_L_join(boole_lattice(A)),the_L_meet(boole_lattice(A))) = boole_lattice(A). [resolve(1028,b,1031,a)]. 40.65/40.85 1032 -latt_str(A) | empty_carrier(A) | -latt_str(B) | empty_carrier(B) | strict_latt_str(k8_filter_1(B,A)) # label(dt_k8_filter_1) # label(axiom). [clausify(197)]. 40.65/40.85 Derived: -latt_str(A) | empty_carrier(A) | -latt_str(B) | empty_carrier(B) | -latt_str(k8_filter_1(B,A)) | latt_str_of(the_carrier(k8_filter_1(B,A)),the_L_join(k8_filter_1(B,A)),the_L_meet(k8_filter_1(B,A))) = k8_filter_1(B,A). [resolve(1032,e,1028,b)]. 40.65/40.85 1033 strict_latt_str(boole_lattice(A)) # label(fc1_lattice3) # label(axiom). [clausify(201)]. 40.65/40.85 1034 strict_latt_str(boole_lattice(A)) # label(fc2_lattice3) # label(axiom). [clausify(383)]. 40.65/40.85 1035 -function(A) | -relation_of2(A,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | -quasi_total(C,cartesian_product2(B,B),B) | -function(C) | -quasi_total(A,cartesian_product2(B,B),B) | empty(B) | strict_latt_str(latt_str_of(B,A,C)) # label(fc3_lattices) # label(axiom). [clausify(524)]. 40.65/40.85 1036 strict_latt_str(c26) # label(rc9_lattices) # label(axiom). [clausify(617)]. 41.76/41.92 Derived: -latt_str(c26) | latt_str_of(the_carrier(c26),the_L_join(c26),the_L_meet(c26)) = c26. [resolve(1036,a,1028,b)]. 41.76/41.92 1037 -strict_latt_str(A) | -latt_str(A) | element(f427(B,A),powerset(B)) | the_carrier(A) != powerset(B) | boole_lattice(B) = A # label(d1_lattice3) # label(axiom). [clausify(644)]. 41.76/41.92 Derived: -latt_str(c5) | element(f427(A,c5),powerset(A)) | the_carrier(c5) != powerset(A) | boole_lattice(A) = c5. [resolve(1037,a,1029,a)]. 41.76/41.92 Derived: -latt_str(latt_str_of(A,B,C)) | element(f427(D,latt_str_of(A,B,C)),powerset(D)) | the_carrier(latt_str_of(A,B,C)) != powerset(D) | boole_lattice(D) = latt_str_of(A,B,C) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -relation_of2(C,cartesian_product2(A,A),A) | -quasi_total(C,cartesian_product2(A,A),A) | -quasi_total(B,cartesian_product2(A,A),A) | -function(B). [resolve(1037,a,1030,g)]. 41.76/41.92 Derived: -latt_str(boole_lattice(A)) | element(f427(B,boole_lattice(A)),powerset(B)) | the_carrier(boole_lattice(A)) != powerset(B) | boole_lattice(B) = boole_lattice(A). [resolve(1037,a,1031,a)]. 41.76/41.92 Derived: -latt_str(k8_filter_1(A,B)) | element(f427(C,k8_filter_1(A,B)),powerset(C)) | the_carrier(k8_filter_1(A,B)) != powerset(C) | boole_lattice(C) = k8_filter_1(A,B) | -latt_str(B) | empty_carrier(B) | -latt_str(A) | empty_carrier(A). [resolve(1037,a,1032,e)]. 41.76/41.92 Derived: -latt_str(c26) | element(f427(A,c26),powerset(A)) | the_carrier(c26) != powerset(A) | boole_lattice(A) = c26. [resolve(1037,a,1036,a)]. 41.76/41.92 1038 -strict_latt_str(A) | -latt_str(A) | element(f428(B,A),powerset(B)) | the_carrier(A) != powerset(B) | boole_lattice(B) = A # label(d1_lattice3) # label(axiom). [clausify(644)]. 41.76/41.92 Derived: -latt_str(c5) | element(f428(A,c5),powerset(A)) | the_carrier(c5) != powerset(A) | boole_lattice(A) = c5. [resolve(1038,a,1029,a)]. 41.76/41.92 Derived: -latt_str(latt_str_of(A,B,C)) | element(f428(D,latt_str_of(A,B,C)),powerset(D)) | the_carrier(latt_str_of(A,B,C)) != powerset(D) | boole_lattice(D) = latt_str_of(A,B,C) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -relation_of2(C,cartesian_product2(A,A),A) | -quasi_total(C,cartesian_product2(A,A),A) | -quasi_total(B,cartesian_product2(A,A),A) | -function(B). [resolve(1038,a,1030,g)]. 41.76/41.92 Derived: -latt_str(boole_lattice(A)) | element(f428(B,boole_lattice(A)),powerset(B)) | the_carrier(boole_lattice(A)) != powerset(B) | boole_lattice(B) = boole_lattice(A). [resolve(1038,a,1031,a)]. 41.76/41.92 Derived: -latt_str(k8_filter_1(A,B)) | element(f428(C,k8_filter_1(A,B)),powerset(C)) | the_carrier(k8_filter_1(A,B)) != powerset(C) | boole_lattice(C) = k8_filter_1(A,B) | -latt_str(B) | empty_carrier(B) | -latt_str(A) | empty_carrier(A). [resolve(1038,a,1032,e)]. 41.76/41.92 Derived: -latt_str(c26) | element(f428(A,c26),powerset(A)) | the_carrier(c26) != powerset(A) | boole_lattice(A) = c26. [resolve(1038,a,1036,a)]. 41.76/41.92 1039 -strict_latt_str(A) | -latt_str(A) | apply_binary(the_L_join(A),f427(B,A),f428(B,A)) != subset_union2(B,f427(B,A),f428(B,A)) | apply_binary(the_L_meet(A),f427(B,A),f428(B,A)) != subset_intersection2(B,f427(B,A),f428(B,A)) | the_carrier(A) != powerset(B) | boole_lattice(B) = A # label(d1_lattice3) # label(axiom). [clausify(644)]. 41.76/41.92 Derived: -latt_str(c5) | apply_binary(the_L_join(c5),f427(A,c5),f428(A,c5)) != subset_union2(A,f427(A,c5),f428(A,c5)) | apply_binary(the_L_meet(c5),f427(A,c5),f428(A,c5)) != subset_intersection2(A,f427(A,c5),f428(A,c5)) | the_carrier(c5) != powerset(A) | boole_lattice(A) = c5. [resolve(1039,a,1029,a)]. 41.76/41.92 Derived: -latt_str(latt_str_of(A,B,C)) | apply_binary(the_L_join(latt_str_of(A,B,C)),f427(D,latt_str_of(A,B,C)),f428(D,latt_str_of(A,B,C))) != subset_union2(D,f427(D,latt_str_of(A,B,C)),f428(D,latt_str_of(A,B,C))) | apply_binary(the_L_meet(latt_str_of(A,B,C)),f427(D,latt_str_of(A,B,C)),f428(D,latt_str_of(A,B,C))) != subset_intersection2(D,f427(D,latt_str_of(A,B,C)),f428(D,latt_str_of(A,B,C))) | the_carrier(latt_str_of(A,B,C)) != powerset(D) | boole_lattice(D) = latt_str_of(A,B,C) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -relation_of2(C,cartesian_product2(A,A),A) | -quasi_total(C,cartesian_product2(A,A),A) | -quasi_total(B,cartesian_product2(A,A),A) | -function(B). [resolve(1039,a,1030,g)]. 41.76/41.93 Derived: -latt_str(boole_lattice(A)) | apply_binary(the_L_join(boole_lattice(A)),f427(B,boole_lattice(A)),f428(B,boole_lattice(A))) != subset_union2(B,f427(B,boole_lattice(A)),f428(B,boole_lattice(A))) | apply_binary(the_L_meet(boole_lattice(A)),f427(B,boole_lattice(A)),f428(B,boole_lattice(A))) != subset_intersection2(B,f427(B,boole_lattice(A)),f428(B,boole_lattice(A))) | the_carrier(boole_lattice(A)) != powerset(B) | boole_lattice(B) = boole_lattice(A). [resolve(1039,a,1031,a)]. 41.76/41.93 Derived: -latt_str(k8_filter_1(A,B)) | apply_binary(the_L_join(k8_filter_1(A,B)),f427(C,k8_filter_1(A,B)),f428(C,k8_filter_1(A,B))) != subset_union2(C,f427(C,k8_filter_1(A,B)),f428(C,k8_filter_1(A,B))) | apply_binary(the_L_meet(k8_filter_1(A,B)),f427(C,k8_filter_1(A,B)),f428(C,k8_filter_1(A,B))) != subset_intersection2(C,f427(C,k8_filter_1(A,B)),f428(C,k8_filter_1(A,B))) | the_carrier(k8_filter_1(A,B)) != powerset(C) | boole_lattice(C) = k8_filter_1(A,B) | -latt_str(B) | empty_carrier(B) | -latt_str(A) | empty_carrier(A). [resolve(1039,a,1032,e)]. 41.76/41.93 Derived: -latt_str(c26) | apply_binary(the_L_join(c26),f427(A,c26),f428(A,c26)) != subset_union2(A,f427(A,c26),f428(A,c26)) | apply_binary(the_L_meet(c26),f427(A,c26),f428(A,c26)) != subset_intersection2(A,f427(A,c26),f428(A,c26)) | the_carrier(c26) != powerset(A) | boole_lattice(A) = c26. [resolve(1039,a,1036,a)]. 41.76/41.93 1040 -strict_latt_str(A) | -latt_str(A) | -element(B,powerset(C)) | -element(D,powerset(C)) | apply_binary(the_L_join(A),B,D) = subset_union2(C,B,D) | boole_lattice(C) != A # label(d1_lattice3) # label(axiom). [clausify(644)]. 41.76/41.93 Derived: -latt_str(c5) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_join(c5),A,C) = subset_union2(B,A,C) | boole_lattice(B) != c5. [resolve(1040,a,1029,a)]. 41.76/41.93 Derived: -latt_str(latt_str_of(A,B,C)) | -element(D,powerset(E)) | -element(F,powerset(E)) | apply_binary(the_L_join(latt_str_of(A,B,C)),D,F) = subset_union2(E,D,F) | boole_lattice(E) != latt_str_of(A,B,C) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -relation_of2(C,cartesian_product2(A,A),A) | -quasi_total(C,cartesian_product2(A,A),A) | -quasi_total(B,cartesian_product2(A,A),A) | -function(B). [resolve(1040,a,1030,g)]. 41.76/41.93 Derived: -latt_str(boole_lattice(A)) | -element(B,powerset(C)) | -element(D,powerset(C)) | apply_binary(the_L_join(boole_lattice(A)),B,D) = subset_union2(C,B,D) | boole_lattice(C) != boole_lattice(A). [resolve(1040,a,1031,a)]. 41.76/41.93 Derived: -latt_str(k8_filter_1(A,B)) | -element(C,powerset(D)) | -element(E,powerset(D)) | apply_binary(the_L_join(k8_filter_1(A,B)),C,E) = subset_union2(D,C,E) | boole_lattice(D) != k8_filter_1(A,B) | -latt_str(B) | empty_carrier(B) | -latt_str(A) | empty_carrier(A). [resolve(1040,a,1032,e)]. 41.76/41.93 Derived: -latt_str(c26) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_join(c26),A,C) = subset_union2(B,A,C) | boole_lattice(B) != c26. [resolve(1040,a,1036,a)]. 41.76/41.93 1041 -strict_latt_str(A) | -latt_str(A) | -element(B,powerset(C)) | -element(D,powerset(C)) | apply_binary(the_L_meet(A),B,D) = subset_intersection2(C,B,D) | boole_lattice(C) != A # label(d1_lattice3) # label(axiom). [clausify(644)]. 41.76/41.93 Derived: -latt_str(c5) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_meet(c5),A,C) = subset_intersection2(B,A,C) | boole_lattice(B) != c5. [resolve(1041,a,1029,a)]. 41.76/41.93 Derived: -latt_str(latt_str_of(A,B,C)) | -element(D,powerset(E)) | -element(F,powerset(E)) | apply_binary(the_L_meet(latt_str_of(A,B,C)),D,F) = subset_intersection2(E,D,F) | boole_lattice(E) != latt_str_of(A,B,C) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -relation_of2(C,cartesian_product2(A,A),A) | -quasi_total(C,cartesian_product2(A,A),A) | -quasi_total(B,cartesian_product2(A,A),A) | -function(B). [resolve(1041,a,1030,g)]. 41.76/41.93 Derived: -latt_str(boole_lattice(A)) | -element(B,powerset(C)) | -element(D,powerset(C)) | apply_binary(the_L_meet(boole_lattice(A)),B,D) = subset_intersection2(C,B,D) | boole_lattice(C) != boole_lattice(A). [resolve(1041,a,1031,a)]. 45.32/45.53 Derived: -latt_str(k8_filter_1(A,B)) | -element(C,powerset(D)) | -element(E,powerset(D)) | apply_binary(the_L_meet(k8_filter_1(A,B)),C,E) = subset_intersection2(D,C,E) | boole_lattice(D) != k8_filter_1(A,B) | -latt_str(B) | empty_carrier(B) | -latt_str(A) | empty_carrier(A). [resolve(1041,a,1032,e)]. 45.32/45.53 Derived: -latt_str(c26) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_meet(c26),A,C) = subset_intersection2(B,A,C) | boole_lattice(B) != c26. [resolve(1041,a,1036,a)]. 45.32/45.53 1042 -strict_latt_str(A) | -latt_str(A) | the_carrier(A) = powerset(B) | boole_lattice(B) != A # label(d1_lattice3) # label(axiom). [clausify(644)]. 45.32/45.53 Derived: -latt_str(c5) | the_carrier(c5) = powerset(A) | boole_lattice(A) != c5. [resolve(1042,a,1029,a)]. 45.32/45.53 Derived: -latt_str(latt_str_of(A,B,C)) | the_carrier(latt_str_of(A,B,C)) = powerset(D) | boole_lattice(D) != latt_str_of(A,B,C) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -relation_of2(C,cartesian_product2(A,A),A) | -quasi_total(C,cartesian_product2(A,A),A) | -quasi_total(B,cartesian_product2(A,A),A) | -function(B). [resolve(1042,a,1030,g)]. 45.32/45.53 Derived: -latt_str(boole_lattice(A)) | the_carrier(boole_lattice(A)) = powerset(B) | boole_lattice(B) != boole_lattice(A). [resolve(1042,a,1031,a)]. 45.32/45.53 Derived: -latt_str(k8_filter_1(A,B)) | the_carrier(k8_filter_1(A,B)) = powerset(C) | boole_lattice(C) != k8_filter_1(A,B) | -latt_str(B) | empty_carrier(B) | -latt_str(A) | empty_carrier(A). [resolve(1042,a,1032,e)]. 45.32/45.53 Derived: -latt_str(c26) | the_carrier(c26) = powerset(A) | boole_lattice(A) != c26. [resolve(1042,a,1036,a)]. 45.32/45.53 1043 strict_latt_str(c34) # label(rc6_lattices) # label(axiom). [clausify(678)]. 45.32/45.53 Derived: -latt_str(c34) | latt_str_of(the_carrier(c34),the_L_join(c34),the_L_meet(c34)) = c34. [resolve(1043,a,1028,b)]. 45.32/45.53 Derived: -latt_str(c34) | element(f427(A,c34),powerset(A)) | the_carrier(c34) != powerset(A) | boole_lattice(A) = c34. [resolve(1043,a,1037,a)]. 45.32/45.53 Derived: -latt_str(c34) | element(f428(A,c34),powerset(A)) | the_carrier(c34) != powerset(A) | boole_lattice(A) = c34. [resolve(1043,a,1038,a)]. 45.32/45.53 Derived: -latt_str(c34) | apply_binary(the_L_join(c34),f427(A,c34),f428(A,c34)) != subset_union2(A,f427(A,c34),f428(A,c34)) | apply_binary(the_L_meet(c34),f427(A,c34),f428(A,c34)) != subset_intersection2(A,f427(A,c34),f428(A,c34)) | the_carrier(c34) != powerset(A) | boole_lattice(A) = c34. [resolve(1043,a,1039,a)]. 45.32/45.53 Derived: -latt_str(c34) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_join(c34),A,C) = subset_union2(B,A,C) | boole_lattice(B) != c34. [resolve(1043,a,1040,a)]. 45.32/45.53 Derived: -latt_str(c34) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_meet(c34),A,C) = subset_intersection2(B,A,C) | boole_lattice(B) != c34. [resolve(1043,a,1041,a)]. 45.32/45.53 Derived: -latt_str(c34) | the_carrier(c34) = powerset(A) | boole_lattice(A) != c34. [resolve(1043,a,1042,a)]. 45.32/45.53 1044 empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | directed_subset(B,A) | element(f46(A,B),powerset(B)) # label(t1_waybel_0) # label(lemma). [clausify(90)]. 45.32/45.53 1045 empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -directed_subset(B,A) | -element(C,powerset(B)) | -finite(C) | element(f45(A,B,C),the_carrier(A)) # label(t1_waybel_0) # label(lemma). [clausify(90)]. 45.32/45.53 1046 empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -directed_subset(B,A) | -element(C,powerset(B)) | -finite(C) | relstr_set_smaller(A,C,f45(A,B,C)) # label(t1_waybel_0) # label(lemma). [clausify(90)]. 45.32/45.53 1047 empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -directed_subset(B,A) | -element(C,powerset(B)) | -finite(C) | in(f45(A,B,C),B) # label(t1_waybel_0) # label(lemma). [clausify(90)]. 45.32/45.53 Derived: empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | element(f46(A,B),powerset(B)) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(C,powerset(B)) | -finite(C) | element(f45(A,B,C),the_carrier(A)). [resolve(1044,e,1045,f)]. 45.72/45.89 Derived: empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | element(f46(A,B),powerset(B)) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(C,powerset(B)) | -finite(C) | relstr_set_smaller(A,C,f45(A,B,C)). [resolve(1044,e,1046,f)]. 45.72/45.89 Derived: empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | element(f46(A,B),powerset(B)) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(C,powerset(B)) | -finite(C) | in(f45(A,B,C),B). [resolve(1044,e,1047,f)]. 45.72/45.89 1048 empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | directed_subset(B,A) | finite(f46(A,B)) # label(t1_waybel_0) # label(lemma). [clausify(90)]. 45.72/45.89 Derived: empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | finite(f46(A,B)) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(C,powerset(B)) | -finite(C) | element(f45(A,B,C),the_carrier(A)). [resolve(1048,e,1045,f)]. 45.72/45.89 Derived: empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | finite(f46(A,B)) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(C,powerset(B)) | -finite(C) | relstr_set_smaller(A,C,f45(A,B,C)). [resolve(1048,e,1046,f)]. 45.72/45.89 Derived: empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | finite(f46(A,B)) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(C,powerset(B)) | -finite(C) | in(f45(A,B,C),B). [resolve(1048,e,1047,f)]. 45.72/45.89 1049 empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | directed_subset(B,A) | -element(C,the_carrier(A)) | -relstr_set_smaller(A,f46(A,B),C) | -in(C,B) # label(t1_waybel_0) # label(lemma). [clausify(90)]. 45.72/45.89 Derived: empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -relstr_set_smaller(A,f46(A,B),C) | -in(C,B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(D,powerset(B)) | -finite(D) | element(f45(A,B,D),the_carrier(A)). [resolve(1049,e,1045,f)]. 45.72/45.89 Derived: empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -relstr_set_smaller(A,f46(A,B),C) | -in(C,B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(D,powerset(B)) | -finite(D) | relstr_set_smaller(A,D,f45(A,B,D)). [resolve(1049,e,1046,f)]. 45.72/45.89 Derived: empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -relstr_set_smaller(A,f46(A,B),C) | -in(C,B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(D,powerset(B)) | -finite(D) | in(f45(A,B,D),B). [resolve(1049,e,1047,f)]. 45.72/45.89 1050 -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f401(A,B),the_carrier(A)) | directed_subset(B,A) # label(d1_waybel_0) # label(axiom). [clausify(594)]. 45.72/45.89 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f401(A,B),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(C,powerset(B)) | -finite(C) | element(f45(A,B,C),the_carrier(A)). [resolve(1050,d,1045,f)]. 45.72/45.89 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f401(A,B),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(C,powerset(B)) | -finite(C) | relstr_set_smaller(A,C,f45(A,B,C)). [resolve(1050,d,1046,f)]. 45.72/45.89 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f401(A,B),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(C,powerset(B)) | -finite(C) | in(f45(A,B,C),B). [resolve(1050,d,1047,f)]. 45.72/45.89 1051 -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f402(A,B),the_carrier(A)) | directed_subset(B,A) # label(d1_waybel_0) # label(axiom). [clausify(594)]. 45.72/45.89 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f402(A,B),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(C,powerset(B)) | -finite(C) | element(f45(A,B,C),the_carrier(A)). [resolve(1051,d,1045,f)]. 45.72/45.89 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f402(A,B),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(C,powerset(B)) | -finite(C) | relstr_set_smaller(A,C,f45(A,B,C)). [resolve(1051,d,1046,f)]. 45.72/45.89 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f402(A,B),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(C,powerset(B)) | -finite(C) | in(f45(A,B,C),B). [resolve(1051,d,1047,f)]. 45.72/45.89 1052 -rel_str(A) | -element(B,powerset(the_carrier(A))) | in(f402(A,B),B) | directed_subset(B,A) # label(d1_waybel_0) # label(axiom). [clausify(594)]. 45.72/45.89 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | in(f402(A,B),B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(C,powerset(B)) | -finite(C) | element(f45(A,B,C),the_carrier(A)). [resolve(1052,d,1045,f)]. 45.72/45.89 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | in(f402(A,B),B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(C,powerset(B)) | -finite(C) | relstr_set_smaller(A,C,f45(A,B,C)). [resolve(1052,d,1046,f)]. 45.72/45.89 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | in(f402(A,B),B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(C,powerset(B)) | -finite(C) | in(f45(A,B,C),B). [resolve(1052,d,1047,f)]. 45.72/45.89 1053 -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -related(A,f402(A,B),C) | -related(A,f401(A,B),C) | -in(C,B) | directed_subset(B,A) # label(d1_waybel_0) # label(axiom). [clausify(594)]. 45.72/45.89 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -related(A,f402(A,B),C) | -related(A,f401(A,B),C) | -in(C,B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(D,powerset(B)) | -finite(D) | element(f45(A,B,D),the_carrier(A)). [resolve(1053,g,1045,f)]. 45.72/45.90 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -related(A,f402(A,B),C) | -related(A,f401(A,B),C) | -in(C,B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(D,powerset(B)) | -finite(D) | relstr_set_smaller(A,D,f45(A,B,D)). [resolve(1053,g,1046,f)]. 45.72/45.90 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -related(A,f402(A,B),C) | -related(A,f401(A,B),C) | -in(C,B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(D,powerset(B)) | -finite(D) | in(f45(A,B,D),B). [resolve(1053,g,1047,f)]. 45.72/45.90 1054 -rel_str(A) | -element(B,powerset(the_carrier(A))) | in(f401(A,B),B) | directed_subset(B,A) # label(d1_waybel_0) # label(axiom). [clausify(594)]. 45.72/45.90 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | in(f401(A,B),B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(C,powerset(B)) | -finite(C) | element(f45(A,B,C),the_carrier(A)). [resolve(1054,d,1045,f)]. 45.76/45.91 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | in(f401(A,B),B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(C,powerset(B)) | -finite(C) | relstr_set_smaller(A,C,f45(A,B,C)). [resolve(1054,d,1046,f)]. 45.76/45.91 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | in(f401(A,B),B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | empty(B) | -element(C,powerset(B)) | -finite(C) | in(f45(A,B,C),B). [resolve(1054,d,1047,f)]. 45.76/45.91 1055 -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | element(f403(A,B,C,D),the_carrier(A)) | -in(C,B) | -directed_subset(B,A) # label(d1_waybel_0) # label(axiom). [clausify(594)]. 45.76/45.91 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | element(f403(A,B,C,D),the_carrier(A)) | -in(C,B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | element(f46(A,B),powerset(B)). [resolve(1055,h,1044,e)]. 45.76/45.91 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | element(f403(A,B,C,D),the_carrier(A)) | -in(C,B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | finite(f46(A,B)). [resolve(1055,h,1048,e)]. 45.76/45.91 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | element(f403(A,B,C,D),the_carrier(A)) | -in(C,B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | -element(E,the_carrier(A)) | -relstr_set_smaller(A,f46(A,B),E) | -in(E,B). [resolve(1055,h,1049,e)]. 45.76/45.91 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | element(f403(A,B,C,D),the_carrier(A)) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f401(A,B),the_carrier(A)). [resolve(1055,h,1050,d)]. 45.76/45.91 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | element(f403(A,B,C,D),the_carrier(A)) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f402(A,B),the_carrier(A)). [resolve(1055,h,1051,d)]. 45.76/45.91 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | element(f403(A,B,C,D),the_carrier(A)) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | in(f402(A,B),B). [resolve(1055,h,1052,d)]. 45.76/45.91 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | element(f403(A,B,C,D),the_carrier(A)) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(E,the_carrier(A)) | -related(A,f402(A,B),E) | -related(A,f401(A,B),E) | -in(E,B). [resolve(1055,h,1053,g)]. 45.76/45.91 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | element(f403(A,B,C,D),the_carrier(A)) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | in(f401(A,B),B). [resolve(1055,h,1054,d)]. 45.76/45.91 1056 -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | related(A,D,f403(A,B,C,D)) | -in(C,B) | -directed_subset(B,A) # label(d1_waybel_0) # label(axiom). [clausify(594)]. 45.76/45.91 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | related(A,D,f403(A,B,C,D)) | -in(C,B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | element(f46(A,B),powerset(B)). [resolve(1056,h,1044,e)]. 45.76/45.91 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | related(A,D,f403(A,B,C,D)) | -in(C,B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | finite(f46(A,B)). [resolve(1056,h,1048,e)]. 45.76/45.92 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | related(A,D,f403(A,B,C,D)) | -in(C,B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | -element(E,the_carrier(A)) | -relstr_set_smaller(A,f46(A,B),E) | -in(E,B). [resolve(1056,h,1049,e)]. 45.76/45.92 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | related(A,D,f403(A,B,C,D)) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f401(A,B),the_carrier(A)). [resolve(1056,h,1050,d)]. 45.76/45.92 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | related(A,D,f403(A,B,C,D)) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f402(A,B),the_carrier(A)). [resolve(1056,h,1051,d)]. 45.76/45.92 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | related(A,D,f403(A,B,C,D)) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | in(f402(A,B),B). [resolve(1056,h,1052,d)]. 45.76/45.92 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | related(A,D,f403(A,B,C,D)) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(E,the_carrier(A)) | -related(A,f402(A,B),E) | -related(A,f401(A,B),E) | -in(E,B). [resolve(1056,h,1053,g)]. 45.76/45.92 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | related(A,D,f403(A,B,C,D)) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | in(f401(A,B),B). [resolve(1056,h,1054,d)]. 45.76/45.92 1057 -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | related(A,C,f403(A,B,C,D)) | -in(C,B) | -directed_subset(B,A) # label(d1_waybel_0) # label(axiom). [clausify(594)]. 45.76/45.92 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | related(A,C,f403(A,B,C,D)) | -in(C,B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | element(f46(A,B),powerset(B)). [resolve(1057,h,1044,e)]. 45.76/45.92 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | related(A,C,f403(A,B,C,D)) | -in(C,B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | finite(f46(A,B)). [resolve(1057,h,1048,e)]. 45.76/45.92 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | related(A,C,f403(A,B,C,D)) | -in(C,B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | -element(E,the_carrier(A)) | -relstr_set_smaller(A,f46(A,B),E) | -in(E,B). [resolve(1057,h,1049,e)]. 45.76/45.92 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | related(A,C,f403(A,B,C,D)) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f401(A,B),the_carrier(A)). [resolve(1057,h,1050,d)]. 45.76/45.92 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | related(A,C,f403(A,B,C,D)) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f402(A,B),the_carrier(A)). [resolve(1057,h,1051,d)]. 45.76/45.92 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | related(A,C,f403(A,B,C,D)) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | in(f402(A,B),B). [resolve(1057,h,1052,d)]. 55.52/55.70 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | related(A,C,f403(A,B,C,D)) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(E,the_carrier(A)) | -related(A,f402(A,B),E) | -related(A,f401(A,B),E) | -in(E,B). [resolve(1057,h,1053,g)]. 55.52/55.70 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | related(A,C,f403(A,B,C,D)) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | in(f401(A,B),B). [resolve(1057,h,1054,d)]. 55.52/55.70 1058 -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | in(f403(A,B,C,D),B) | -in(C,B) | -directed_subset(B,A) # label(d1_waybel_0) # label(axiom). [clausify(594)]. 55.52/55.70 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | in(f403(A,B,C,D),B) | -in(C,B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | element(f46(A,B),powerset(B)). [resolve(1058,h,1044,e)]. 55.52/55.70 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | in(f403(A,B,C,D),B) | -in(C,B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | finite(f46(A,B)). [resolve(1058,h,1048,e)]. 55.52/55.70 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | in(f403(A,B,C,D),B) | -in(C,B) | empty_carrier(A) | -rel_str(A) | -transitive_relstr(A) | -element(B,powerset(the_carrier(A))) | -element(E,the_carrier(A)) | -relstr_set_smaller(A,f46(A,B),E) | -in(E,B). [resolve(1058,h,1049,e)]. 55.52/55.70 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | in(f403(A,B,C,D),B) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f401(A,B),the_carrier(A)). [resolve(1058,h,1050,d)]. 55.52/55.70 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | in(f403(A,B,C,D),B) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f402(A,B),the_carrier(A)). [resolve(1058,h,1051,d)]. 55.52/55.70 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | in(f403(A,B,C,D),B) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | in(f402(A,B),B). [resolve(1058,h,1052,d)]. 55.52/55.70 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | in(f403(A,B,C,D),B) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(E,the_carrier(A)) | -related(A,f402(A,B),E) | -related(A,f401(A,B),E) | -in(E,B). [resolve(1058,h,1053,g)]. 55.52/55.70 Derived: -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -in(D,B) | in(f403(A,B,C,D),B) | -in(C,B) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | in(f401(A,B),B). [resolve(1058,h,1054,d)]. 55.52/55.70 1059 empty_set != A | -centered(A) # label(d2_compts_1) # label(axiom). [clausify(129)]. 55.52/55.70 1060 empty_set = A | empty_set != f81(A) | centered(A) # label(d2_compts_1) # label(axiom). [clausify(129)]. 55.52/55.70 1061 empty_set = A | set_meet(f81(A)) = empty_set | centered(A) # label(d2_compts_1) # label(axiom). [clausify(129)]. 55.52/55.70 1062 empty_set = A | finite(f81(A)) | centered(A) # label(d2_compts_1) # label(axiom). [clausify(129)]. 55.52/55.70 1063 empty_set = A | subset(f81(A),A) | centered(A) # label(d2_compts_1) # label(axiom). [clausify(129)]. 55.52/55.70 1064 empty_set = A | set_meet(A) != empty_set | -finite(A) | -subset(A,B) | -centered(B) # label(d2_compts_1) # label(axiom). [clausify(129)]. 55.52/55.70 Derived: empty_set = A | set_meet(A) != empty_set | -finite(A) | -subset(A,B) | empty_set = B | empty_set != f81(B). [resolve(1064,e,1060,c)]. 57.34/57.54 Derived: empty_set = A | set_meet(A) != empty_set | -finite(A) | -subset(A,B) | empty_set = B | set_meet(f81(B)) = empty_set. [resolve(1064,e,1061,c)]. 57.34/57.54 Derived: empty_set = A | set_meet(A) != empty_set | -finite(A) | -subset(A,B) | empty_set = B | finite(f81(B)). [resolve(1064,e,1062,c)]. 57.34/57.54 Derived: empty_set = A | set_meet(A) != empty_set | -finite(A) | -subset(A,B) | empty_set = B | subset(f81(B),B). [resolve(1064,e,1063,c)]. 57.34/57.54 1065 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(780,e,893,b)]. 57.34/57.54 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | empty_set != f81(B). [resolve(1065,k,1060,c)]. 57.34/57.54 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | set_meet(f81(B)) = empty_set. [resolve(1065,k,1061,c)]. 57.34/57.54 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | finite(f81(B)). [resolve(1065,k,1062,c)]. 57.34/57.54 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | subset(f81(B),B). [resolve(1065,k,1063,c)]. 57.34/57.54 1066 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(780,e,897,b)]. 57.34/57.54 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set != f324(A). [resolve(1066,h,1059,b)]. 57.34/57.54 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set = B | set_meet(B) != empty_set | -finite(B) | -subset(B,f324(A)). [resolve(1066,h,1064,e)]. 57.34/57.54 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1066,h,1065,k)]. 57.34/57.54 1067 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(930,e,893,b)]. 57.34/57.55 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | empty_set != f81(B). [resolve(1067,k,1060,c)]. 57.34/57.55 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | set_meet(f81(B)) = empty_set. [resolve(1067,k,1061,c)]. 57.34/57.55 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | finite(f81(B)). [resolve(1067,k,1062,c)]. 57.34/57.55 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | subset(f81(B),B). [resolve(1067,k,1063,c)]. 57.34/57.55 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1067,k,1066,h)]. 57.34/57.55 1068 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(930,e,897,b)]. 57.34/57.55 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set != f324(A). [resolve(1068,h,1059,b)]. 57.34/57.55 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set = B | set_meet(B) != empty_set | -finite(B) | -subset(B,f324(A)). [resolve(1068,h,1064,e)]. 57.34/57.55 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1068,h,1065,k)]. 57.34/57.55 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1068,h,1067,k)]. 57.49/57.72 1069 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(931,e,893,b)]. 57.49/57.72 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | empty_set != f81(B). [resolve(1069,k,1060,c)]. 57.49/57.72 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | set_meet(f81(B)) = empty_set. [resolve(1069,k,1061,c)]. 57.49/57.72 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | finite(f81(B)). [resolve(1069,k,1062,c)]. 57.49/57.72 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | subset(f81(B),B). [resolve(1069,k,1063,c)]. 57.49/57.72 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1069,k,1066,h)]. 57.49/57.72 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1069,k,1068,h)]. 57.49/57.72 1070 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(931,e,897,b)]. 57.49/57.72 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set != f324(A). [resolve(1070,h,1059,b)]. 57.49/57.72 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set = B | set_meet(B) != empty_set | -finite(B) | -subset(B,f324(A)). [resolve(1070,h,1064,e)]. 57.75/57.89 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1070,h,1065,k)]. 57.75/57.89 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1070,h,1067,k)]. 57.75/57.89 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1070,h,1069,k)]. 57.75/57.89 1071 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(932,e,893,b)]. 57.75/57.89 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | empty_set != f81(B). [resolve(1071,k,1060,c)]. 57.75/57.89 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | set_meet(f81(B)) = empty_set. [resolve(1071,k,1061,c)]. 57.75/57.89 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | finite(f81(B)). [resolve(1071,k,1062,c)]. 57.75/57.89 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | subset(f81(B),B). [resolve(1071,k,1063,c)]. 57.75/57.89 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1071,k,1066,h)]. 57.77/57.91 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1071,k,1068,h)]. 57.77/57.91 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1071,k,1070,h)]. 57.77/57.91 1072 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(932,e,897,b)]. 57.77/57.91 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set != f324(A). [resolve(1072,h,1059,b)]. 57.77/57.91 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set = B | set_meet(B) != empty_set | -finite(B) | -subset(B,f324(A)). [resolve(1072,h,1064,e)]. 57.77/57.91 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1072,h,1065,k)]. 57.77/57.91 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1072,h,1067,k)]. 57.77/57.91 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1072,h,1069,k)]. 57.77/57.91 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1072,h,1071,k)]. 57.88/58.08 1073 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(933,e,893,b)]. 57.88/58.08 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | empty_set != f81(B). [resolve(1073,k,1060,c)]. 57.88/58.08 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | set_meet(f81(B)) = empty_set. [resolve(1073,k,1061,c)]. 57.88/58.08 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | finite(f81(B)). [resolve(1073,k,1062,c)]. 57.88/58.08 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | subset(f81(B),B). [resolve(1073,k,1063,c)]. 57.88/58.08 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1073,k,1066,h)]. 57.88/58.08 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1073,k,1068,h)]. 57.88/58.08 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1073,k,1070,h)]. 57.88/58.08 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1073,k,1072,h)]. 57.96/58.09 1074 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(933,e,897,b)]. 57.96/58.09 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set != f324(A). [resolve(1074,h,1059,b)]. 57.96/58.09 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set = B | set_meet(B) != empty_set | -finite(B) | -subset(B,f324(A)). [resolve(1074,h,1064,e)]. 57.96/58.09 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1074,h,1065,k)]. 57.96/58.09 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1074,h,1067,k)]. 57.96/58.09 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1074,h,1069,k)]. 57.96/58.09 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1074,h,1071,k)]. 57.96/58.09 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1074,h,1073,k)]. 58.10/58.27 1075 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(934,e,893,b)]. 58.10/58.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | empty_set != f81(B). [resolve(1075,k,1060,c)]. 58.10/58.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | set_meet(f81(B)) = empty_set. [resolve(1075,k,1061,c)]. 58.10/58.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | finite(f81(B)). [resolve(1075,k,1062,c)]. 58.10/58.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | subset(f81(B),B). [resolve(1075,k,1063,c)]. 58.10/58.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1075,k,1066,h)]. 58.10/58.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1075,k,1068,h)]. 58.10/58.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1075,k,1070,h)]. 58.10/58.27 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1075,k,1072,h)]. 58.10/58.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1075,k,1074,h)]. 58.10/58.29 1076 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(934,e,897,b)]. 58.10/58.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set != f324(A). [resolve(1076,h,1059,b)]. 58.10/58.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set = B | set_meet(B) != empty_set | -finite(B) | -subset(B,f324(A)). [resolve(1076,h,1064,e)]. 58.10/58.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1076,h,1065,k)]. 58.10/58.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1076,h,1067,k)]. 58.10/58.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1076,h,1069,k)]. 58.10/58.29 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1076,h,1071,k)]. 58.28/58.47 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1076,h,1073,k)]. 58.28/58.47 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1076,h,1075,k)]. 58.28/58.47 1077 -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(935,e,893,b)]. 58.28/58.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | empty_set != f81(B). [resolve(1077,k,1060,c)]. 58.28/58.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | set_meet(f81(B)) = empty_set. [resolve(1077,k,1061,c)]. 58.28/58.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | finite(f81(B)). [resolve(1077,k,1062,c)]. 58.28/58.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | subset(f81(B),B). [resolve(1077,k,1063,c)]. 58.28/58.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1077,k,1066,h)]. 58.28/58.47 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1077,k,1068,h)]. 58.34/58.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1077,k,1070,h)]. 58.34/58.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1077,k,1072,h)]. 58.34/58.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1077,k,1074,h)]. 58.34/58.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1077,k,1076,h)]. 58.34/58.48 1078 -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(935,e,897,b)]. 58.34/58.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set != f324(A). [resolve(1078,h,1059,b)]. 58.34/58.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set = B | set_meet(B) != empty_set | -finite(B) | -subset(B,f324(A)). [resolve(1078,h,1064,e)]. 58.34/58.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1078,h,1065,k)]. 58.34/58.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1078,h,1067,k)]. 58.50/58.68 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1078,h,1069,k)]. 58.50/58.68 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1078,h,1071,k)]. 58.50/58.68 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1078,h,1073,k)]. 58.50/58.68 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1078,h,1075,k)]. 58.50/58.68 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1078,h,1077,k)]. 58.50/58.68 1079 -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(936,e,893,b)]. 58.50/58.68 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | empty_set != f81(B). [resolve(1079,k,1060,c)]. 58.50/58.68 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | set_meet(f81(B)) = empty_set. [resolve(1079,k,1061,c)]. 58.50/58.68 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | finite(f81(B)). [resolve(1079,k,1062,c)]. 58.50/58.68 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | subset(f81(B),B). [resolve(1079,k,1063,c)]. 58.50/58.68 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1079,k,1066,h)]. 58.50/58.68 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1079,k,1068,h)]. 58.50/58.68 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1079,k,1070,h)]. 58.50/58.68 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1079,k,1072,h)]. 58.50/58.68 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1079,k,1074,h)]. 58.50/58.68 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1079,k,1076,h)]. 58.50/58.70 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1079,k,1078,h)]. 58.50/58.70 1080 -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(936,e,897,b)]. 58.50/58.70 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set != f324(A). [resolve(1080,h,1059,b)]. 58.50/58.70 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set = B | set_meet(B) != empty_set | -finite(B) | -subset(B,f324(A)). [resolve(1080,h,1064,e)]. 58.50/58.70 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1080,h,1065,k)]. 58.50/58.70 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1080,h,1067,k)]. 58.50/58.70 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1080,h,1069,k)]. 58.50/58.70 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1080,h,1071,k)]. 58.50/58.70 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1080,h,1073,k)]. 58.50/58.70 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1080,h,1075,k)]. 58.74/58.89 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1080,h,1077,k)]. 58.74/58.89 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1080,h,1079,k)]. 58.74/58.89 1081 -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(937,e,893,b)]. 58.74/58.89 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | empty_set != f81(B). [resolve(1081,k,1060,c)]. 58.74/58.89 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | set_meet(f81(B)) = empty_set. [resolve(1081,k,1061,c)]. 58.74/58.89 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | finite(f81(B)). [resolve(1081,k,1062,c)]. 58.74/58.89 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | subset(f81(B),B). [resolve(1081,k,1063,c)]. 58.74/58.89 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1081,k,1066,h)]. 58.77/58.90 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1081,k,1068,h)]. 58.77/58.90 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1081,k,1070,h)]. 58.77/58.90 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1081,k,1072,h)]. 58.77/58.90 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1081,k,1074,h)]. 58.77/58.90 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1081,k,1076,h)]. 58.77/58.90 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1081,k,1078,h)]. 58.77/58.90 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1081,k,1080,h)]. 58.77/58.90 1082 -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(937,e,897,b)]. 58.77/58.91 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set != f324(A). [resolve(1082,h,1059,b)]. 58.77/58.91 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set = B | set_meet(B) != empty_set | -finite(B) | -subset(B,f324(A)). [resolve(1082,h,1064,e)]. 58.77/58.91 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1082,h,1065,k)]. 58.77/58.91 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1082,h,1067,k)]. 58.77/58.91 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1082,h,1069,k)]. 58.77/58.91 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1082,h,1071,k)]. 58.77/58.91 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1082,h,1073,k)]. 58.77/58.91 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1082,h,1075,k)]. 58.94/59.11 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1082,h,1077,k)]. 58.94/59.11 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1082,h,1079,k)]. 58.94/59.11 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1082,h,1081,k)]. 58.94/59.11 1083 -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(938,e,893,b)]. 58.94/59.11 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | empty_set != f81(B). [resolve(1083,k,1060,c)]. 58.94/59.11 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | set_meet(f81(B)) = empty_set. [resolve(1083,k,1061,c)]. 58.94/59.11 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | finite(f81(B)). [resolve(1083,k,1062,c)]. 58.94/59.11 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | subset(f81(B),B). [resolve(1083,k,1063,c)]. 58.94/59.11 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1083,k,1066,h)]. 58.94/59.11 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1083,k,1068,h)]. 58.94/59.11 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1083,k,1070,h)]. 58.94/59.11 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1083,k,1072,h)]. 58.94/59.11 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1083,k,1074,h)]. 58.94/59.11 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1083,k,1076,h)]. 58.94/59.11 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1083,k,1078,h)]. 58.94/59.11 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1083,k,1080,h)]. 58.94/59.12 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1083,k,1082,h)]. 58.94/59.12 1084 -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(938,e,897,b)]. 58.94/59.12 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set != f324(A). [resolve(1084,h,1059,b)]. 58.94/59.12 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set = B | set_meet(B) != empty_set | -finite(B) | -subset(B,f324(A)). [resolve(1084,h,1064,e)]. 58.94/59.12 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1084,h,1065,k)]. 58.94/59.12 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1084,h,1067,k)]. 58.94/59.12 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1084,h,1069,k)]. 58.94/59.12 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1084,h,1071,k)]. 58.94/59.12 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1084,h,1073,k)]. 59.19/59.33 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1084,h,1075,k)]. 59.19/59.33 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1084,h,1077,k)]. 59.19/59.33 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1084,h,1079,k)]. 59.19/59.33 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1084,h,1081,k)]. 59.19/59.33 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f444(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1084,h,1083,k)]. 59.19/59.33 1085 -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(939,e,893,b)]. 59.19/59.33 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | empty_set != f81(B). [resolve(1085,k,1060,c)]. 59.19/59.33 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | set_meet(f81(B)) = empty_set. [resolve(1085,k,1061,c)]. 59.19/59.34 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | finite(f81(B)). [resolve(1085,k,1062,c)]. 59.19/59.34 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | subset(f81(B),B). [resolve(1085,k,1063,c)]. 59.19/59.34 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1085,k,1066,h)]. 59.19/59.34 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1085,k,1068,h)]. 59.19/59.34 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1085,k,1070,h)]. 59.19/59.34 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1085,k,1072,h)]. 59.19/59.34 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1085,k,1074,h)]. 59.19/59.34 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1085,k,1076,h)]. 59.19/59.34 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1085,k,1078,h)]. 59.19/59.35 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1085,k,1080,h)]. 59.19/59.35 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1085,k,1082,h)]. 59.19/59.35 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f444(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1085,k,1084,h)]. 59.19/59.35 1086 -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(939,e,897,b)]. 59.19/59.35 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set != f324(A). [resolve(1086,h,1059,b)]. 59.19/59.35 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set = B | set_meet(B) != empty_set | -finite(B) | -subset(B,f324(A)). [resolve(1086,h,1064,e)]. 59.19/59.35 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1086,h,1065,k)]. 59.19/59.35 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1086,h,1067,k)]. 59.19/59.35 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1086,h,1069,k)]. 59.19/59.35 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1086,h,1071,k)]. 59.19/59.35 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1086,h,1073,k)]. 59.19/59.35 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1086,h,1075,k)]. 59.19/59.35 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1086,h,1077,k)]. 59.19/59.35 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1086,h,1079,k)]. 59.19/59.35 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1086,h,1081,k)]. 59.19/59.35 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f444(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1086,h,1083,k)]. 59.42/59.56 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f444(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1086,h,1085,k)]. 59.42/59.56 1087 -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(940,e,893,b)]. 59.42/59.56 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | empty_set != f81(B). [resolve(1087,k,1060,c)]. 59.42/59.56 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | set_meet(f81(B)) = empty_set. [resolve(1087,k,1061,c)]. 59.42/59.56 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | finite(f81(B)). [resolve(1087,k,1062,c)]. 59.42/59.56 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | subset(f81(B),B). [resolve(1087,k,1063,c)]. 59.42/59.56 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1087,k,1066,h)]. 59.42/59.56 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1087,k,1068,h)]. 59.42/59.56 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1087,k,1070,h)]. 59.42/59.56 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1087,k,1072,h)]. 59.42/59.56 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1087,k,1074,h)]. 59.42/59.56 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1087,k,1076,h)]. 59.42/59.56 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1087,k,1078,h)]. 59.42/59.56 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1087,k,1080,h)]. 59.42/59.56 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1087,k,1082,h)]. 59.42/59.56 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f444(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1087,k,1084,h)]. 59.42/59.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f444(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1087,k,1086,h)]. 59.42/59.58 1088 -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(940,e,897,b)]. 59.42/59.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set != f324(A). [resolve(1088,h,1059,b)]. 59.42/59.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set = B | set_meet(B) != empty_set | -finite(B) | -subset(B,f324(A)). [resolve(1088,h,1064,e)]. 59.42/59.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1088,h,1065,k)]. 59.42/59.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1088,h,1067,k)]. 59.42/59.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1088,h,1069,k)]. 59.42/59.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1088,h,1071,k)]. 59.42/59.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1088,h,1073,k)]. 59.42/59.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1088,h,1075,k)]. 59.42/59.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1088,h,1077,k)]. 59.42/59.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1088,h,1079,k)]. 59.42/59.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1088,h,1081,k)]. 59.42/59.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f444(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1088,h,1083,k)]. 59.42/59.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f444(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1088,h,1085,k)]. 59.42/59.58 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f444(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1088,h,1087,k)]. 59.63/59.79 1089 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(941,e,893,b)]. 59.63/59.79 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | empty_set != f81(B). [resolve(1089,k,1060,c)]. 59.63/59.79 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | set_meet(f81(B)) = empty_set. [resolve(1089,k,1061,c)]. 59.63/59.79 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | finite(f81(B)). [resolve(1089,k,1062,c)]. 59.63/59.79 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | subset(f81(B),B). [resolve(1089,k,1063,c)]. 59.63/59.79 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1089,k,1066,h)]. 59.63/59.79 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1089,k,1068,h)]. 59.63/59.79 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1089,k,1070,h)]. 59.63/59.79 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1089,k,1072,h)]. 59.63/59.79 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1089,k,1074,h)]. 59.63/59.79 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1089,k,1076,h)]. 59.63/59.79 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1089,k,1078,h)]. 59.63/59.79 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1089,k,1080,h)]. 59.63/59.79 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1089,k,1082,h)]. 59.63/59.79 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f444(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1089,k,1084,h)]. 59.67/59.80 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f444(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1089,k,1086,h)]. 59.67/59.80 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f444(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1089,k,1088,h)]. 59.67/59.80 1090 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(941,e,897,b)]. 59.67/59.80 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set != f324(A). [resolve(1090,h,1059,b)]. 59.67/59.80 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set = B | set_meet(B) != empty_set | -finite(B) | -subset(B,f324(A)). [resolve(1090,h,1064,e)]. 59.67/59.80 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1090,h,1065,k)]. 59.67/59.80 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1090,h,1067,k)]. 59.67/59.80 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1090,h,1069,k)]. 59.67/59.81 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1090,h,1071,k)]. 59.67/59.81 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1090,h,1073,k)]. 59.67/59.81 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1090,h,1075,k)]. 59.67/59.81 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1090,h,1077,k)]. 59.67/59.81 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1090,h,1079,k)]. 59.67/59.81 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1090,h,1081,k)]. 59.67/59.81 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f444(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1090,h,1083,k)]. 59.87/60.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f444(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1090,h,1085,k)]. 59.87/60.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f444(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1090,h,1087,k)]. 59.87/60.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | -in(subset_intersection2(the_carrier(B),f443(B),f444(B)),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1090,h,1089,k)]. 59.87/60.02 1091 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(942,e,893,b)]. 59.87/60.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | empty_set != f81(B). [resolve(1091,k,1060,c)]. 59.87/60.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | set_meet(f81(B)) = empty_set. [resolve(1091,k,1061,c)]. 59.87/60.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | finite(f81(B)). [resolve(1091,k,1062,c)]. 59.87/60.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | subset(f81(B),B). [resolve(1091,k,1063,c)]. 59.87/60.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1091,k,1066,h)]. 59.87/60.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1091,k,1068,h)]. 59.87/60.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1091,k,1070,h)]. 59.87/60.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1091,k,1072,h)]. 59.87/60.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1091,k,1074,h)]. 59.87/60.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1091,k,1076,h)]. 59.87/60.02 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1091,k,1078,h)]. 59.87/60.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1091,k,1080,h)]. 59.87/60.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1091,k,1082,h)]. 59.87/60.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f444(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1091,k,1084,h)]. 59.87/60.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f444(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1091,k,1086,h)]. 59.87/60.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f444(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1091,k,1088,h)]. 59.87/60.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | -in(subset_intersection2(the_carrier(B),f443(B),f444(B)),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1091,k,1090,h)]. 59.87/60.03 1092 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(942,e,897,b)]. 59.87/60.03 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set != f324(A). [resolve(1092,h,1059,b)]. 59.87/60.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set = B | set_meet(B) != empty_set | -finite(B) | -subset(B,f324(A)). [resolve(1092,h,1064,e)]. 59.87/60.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1092,h,1065,k)]. 59.87/60.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1092,h,1067,k)]. 59.87/60.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1092,h,1069,k)]. 59.87/60.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1092,h,1071,k)]. 59.87/60.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1092,h,1073,k)]. 59.87/60.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1092,h,1075,k)]. 59.87/60.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1092,h,1077,k)]. 59.87/60.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1092,h,1079,k)]. 59.87/60.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1092,h,1081,k)]. 59.87/60.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f444(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1092,h,1083,k)]. 59.87/60.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f444(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1092,h,1085,k)]. 59.87/60.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f444(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1092,h,1087,k)]. 59.87/60.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | -in(subset_intersection2(the_carrier(B),f443(B),f444(B)),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1092,h,1089,k)]. 59.87/60.04 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | -in(subset_intersection2(the_carrier(B),f443(B),f444(B)),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1092,h,1091,k)]. 60.11/60.26 1093 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | -centered(B). [resolve(943,e,893,b)]. 60.11/60.26 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | empty_set != f81(B). [resolve(1093,k,1060,c)]. 60.11/60.26 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | set_meet(f81(B)) = empty_set. [resolve(1093,k,1061,c)]. 60.11/60.26 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | finite(f81(B)). [resolve(1093,k,1062,c)]. 60.11/60.26 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),B) != empty_set | -closed_subsets(B,A) | empty_set = B | subset(f81(B),B). [resolve(1093,k,1063,c)]. 60.11/60.26 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1093,k,1066,h)]. 60.11/60.26 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1093,k,1068,h)]. 60.11/60.26 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1093,k,1070,h)]. 60.11/60.26 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1093,k,1072,h)]. 60.11/60.26 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1093,k,1074,h)]. 60.11/60.26 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1093,k,1076,h)]. 60.11/60.26 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1093,k,1078,h)]. 60.11/60.26 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1093,k,1080,h)]. 60.11/60.26 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f443(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1093,k,1082,h)]. 60.11/60.27 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f444(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1093,k,1084,h)]. 60.11/60.27 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f444(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1093,k,1086,h)]. 60.11/60.27 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | in(f444(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1093,k,1088,h)]. 60.11/60.27 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | -in(subset_intersection2(the_carrier(B),f443(B),f444(B)),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1093,k,1090,h)]. 60.11/60.27 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(f324(B),powerset(powerset(the_carrier(A)))) | meet_of_subsets(the_carrier(A),f324(B)) != empty_set | -closed_subsets(f324(B),A) | -top_str(B) | -in(subset_intersection2(the_carrier(B),f443(B),f444(B)),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | compact_top_space(B). [resolve(1093,k,1092,h)]. 60.11/60.27 1094 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f324(A)). [resolve(943,e,897,b)]. 60.11/60.27 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set != f324(A). [resolve(1094,h,1059,b)]. 60.11/60.27 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | empty_set = B | set_meet(B) != empty_set | -finite(B) | -subset(B,f324(A)). [resolve(1094,h,1064,e)]. 60.11/60.28 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1094,h,1065,k)]. 60.11/60.28 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1094,h,1067,k)]. 60.11/60.28 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f443(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1094,h,1069,k)]. 60.11/60.28 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1094,h,1071,k)]. 60.11/60.28 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1094,h,1073,k)]. 60.11/60.28 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | element(f444(B),powerset(the_carrier(B))) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1094,h,1075,k)]. 60.11/60.28 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1094,h,1077,k)]. 60.17/60.28 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1094,h,1079,k)]. 60.17/60.28 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f443(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1094,h,1081,k)]. 60.17/60.28 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f444(B),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1094,h,1083,k)]. 60.17/60.28 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f444(B),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1094,h,1085,k)]. 60.17/60.28 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | in(f444(B),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1094,h,1087,k)]. 60.17/60.28 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | -in(subset_intersection2(the_carrier(B),f443(B),f444(B)),the_topology(B)) | element(f445(B),powerset(powerset(the_carrier(B)))) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1094,h,1089,k)]. 83.66/83.83 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | -in(subset_intersection2(the_carrier(B),f443(B),f444(B)),the_topology(B)) | subset(f445(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1094,h,1091,k)]. 83.66/83.83 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | compact_top_space(A) | -top_str(B) | -in(subset_intersection2(the_carrier(B),f443(B),f444(B)),the_topology(B)) | -in(union_of_subsets(the_carrier(B),f445(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)) | empty_carrier(B) | -top_str(B) | -compact_top_space(B) | -element(f324(A),powerset(powerset(the_carrier(B)))) | meet_of_subsets(the_carrier(B),f324(A)) != empty_set | -closed_subsets(f324(A),B). [resolve(1094,h,1093,k)]. 83.66/83.83 1095 -diff_closed(A) | -cup_closed(A) | preboolean(A) # label(cc2_finsub_1) # label(axiom). [clausify(276)]. 83.66/83.83 1096 cup_closed(powerset(A)) # label(fc1_finsub_1) # label(axiom). [clausify(130)]. 83.66/83.83 1097 -preboolean(A) | cup_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(246)]. 83.66/83.83 Derived: -diff_closed(powerset(A)) | preboolean(powerset(A)). [resolve(1095,b,1096,a)]. 83.66/83.83 1098 -preboolean(A) | diff_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(246)]. 83.66/83.83 1099 preboolean(powerset(A)) # label(fc1_finsub_1) # label(axiom). [clausify(130)]. 83.66/83.83 Derived: diff_closed(powerset(A)). [resolve(1098,a,1099,a)]. 83.66/83.83 1100 -diff_closed(powerset(A)) | preboolean(powerset(A)). [resolve(1095,b,1096,a)]. 83.66/83.83 1101 -one_sorted_str(A) | net_str(f453(A),A) # label(existence_l1_waybel_0) # label(axiom). [clausify(689)]. 83.66/83.83 1102 -one_sorted_str(A) | -net_str(B,A) | function(the_mapping(A,B)) # label(dt_u1_waybel_0) # label(axiom). [clausify(184)]. 83.66/83.83 1103 -one_sorted_str(A) | -net_str(B,A) | quasi_total(the_mapping(A,B),the_carrier(B),the_carrier(A)) # label(dt_u1_waybel_0) # label(axiom). [clausify(184)]. 83.66/83.83 1104 -one_sorted_str(A) | -net_str(B,A) | relation_of2_as_subset(the_mapping(A,B),the_carrier(B),the_carrier(A)) # label(dt_u1_waybel_0) # label(axiom). [clausify(184)]. 83.66/83.83 1105 -one_sorted_str(A) | -net_str(B,A) | rel_str(B) # label(dt_l1_waybel_0) # label(axiom). [clausify(189)]. 83.66/83.83 1106 empty_carrier(A) | -element(B,the_carrier(C)) | -net_str(C,A) | empty_carrier(C) | -one_sorted_str(A) | element(apply_netmap(A,C,B),the_carrier(A)) # label(dt_k3_waybel_0) # label(axiom). [clausify(272)]. 83.66/83.83 1107 -one_sorted_str(A) | empty_carrier(A) | empty_carrier(B) | -net_str(B,A) | -is_eventually_in(A,B,C) | -element(D,the_carrier(B)) | -related(B,f206(A,B,C),D) | in(apply_netmap(A,B,D),C) # label(d11_waybel_0) # label(axiom). [clausify(309)]. 83.66/83.83 1108 -one_sorted_str(A) | empty_carrier(A) | empty_carrier(B) | -net_str(B,A) | -is_eventually_in(A,B,C) | element(f206(A,B,C),the_carrier(B)) # label(d11_waybel_0) # label(axiom). [clausify(309)]. 83.66/83.83 1109 -one_sorted_str(A) | empty_carrier(A) | empty_carrier(B) | -net_str(B,A) | is_eventually_in(A,B,C) | element(f207(A,B,C,D),the_carrier(B)) | -element(D,the_carrier(B)) # label(d11_waybel_0) # label(axiom). [clausify(309)]. 83.66/83.83 1110 -one_sorted_str(A) | empty_carrier(A) | empty_carrier(B) | -net_str(B,A) | is_eventually_in(A,B,C) | related(B,D,f207(A,B,C,D)) | -element(D,the_carrier(B)) # label(d11_waybel_0) # label(axiom). [clausify(309)]. 83.66/83.83 1111 -one_sorted_str(A) | empty_carrier(A) | empty_carrier(B) | -net_str(B,A) | is_eventually_in(A,B,C) | -in(apply_netmap(A,B,f207(A,B,C,D)),C) | -element(D,the_carrier(B)) # label(d11_waybel_0) # label(axiom). [clausify(309)]. 83.66/83.83 1112 empty_carrier(A) | -one_sorted_str(A) | empty_carrier(B) | -net_str(B,A) | -is_often_in(A,B,C) | -element(D,the_carrier(B)) | element(f236(A,B,C,D),the_carrier(B)) # label(d12_waybel_0) # label(axiom). [clausify(345)]. 83.66/83.84 1113 empty_carrier(A) | -one_sorted_str(A) | empty_carrier(B) | -net_str(B,A) | -is_often_in(A,B,C) | -element(D,the_carrier(B)) | related(B,D,f236(A,B,C,D)) # label(d12_waybel_0) # label(axiom). [clausify(345)]. 83.66/83.84 1114 empty_carrier(A) | -one_sorted_str(A) | empty_carrier(B) | -net_str(B,A) | -is_often_in(A,B,C) | -element(D,the_carrier(B)) | in(apply_netmap(A,B,f236(A,B,C,D)),C) # label(d12_waybel_0) # label(axiom). [clausify(345)]. 83.66/83.84 1115 empty_carrier(A) | -one_sorted_str(A) | empty_carrier(B) | -net_str(B,A) | is_often_in(A,B,C) | element(f237(A,B,C),the_carrier(B)) # label(d12_waybel_0) # label(axiom). [clausify(345)]. 83.66/83.84 1116 empty_carrier(A) | -one_sorted_str(A) | empty_carrier(B) | -net_str(B,A) | is_often_in(A,B,C) | -element(D,the_carrier(B)) | -related(B,f237(A,B,C),D) | -in(apply_netmap(A,B,D),C) # label(d12_waybel_0) # label(axiom). [clausify(345)]. 83.66/83.84 1117 -one_sorted_str(A) | empty_carrier(A) | -net_str(B,A) | empty_carrier(B) | -element(C,the_carrier(B)) | apply_netmap(A,B,C) = apply_on_structs(B,A,the_mapping(A,B),C) # label(d8_waybel_0) # label(axiom). [clausify(567)]. 83.66/83.84 Derived: -one_sorted_str(A) | -one_sorted_str(A) | function(the_mapping(A,f453(A))). [resolve(1101,b,1102,b)]. 83.66/83.84 Derived: -one_sorted_str(A) | -one_sorted_str(A) | quasi_total(the_mapping(A,f453(A)),the_carrier(f453(A)),the_carrier(A)). [resolve(1101,b,1103,b)]. 83.66/83.84 Derived: -one_sorted_str(A) | -one_sorted_str(A) | relation_of2_as_subset(the_mapping(A,f453(A)),the_carrier(f453(A)),the_carrier(A)). [resolve(1101,b,1104,b)]. 83.66/83.84 Derived: -one_sorted_str(A) | -one_sorted_str(A) | rel_str(f453(A)). [resolve(1101,b,1105,b)]. 83.66/83.84 Derived: -one_sorted_str(A) | empty_carrier(A) | -element(B,the_carrier(f453(A))) | empty_carrier(f453(A)) | -one_sorted_str(A) | element(apply_netmap(A,f453(A),B),the_carrier(A)). [resolve(1101,b,1106,c)]. 83.66/83.84 Derived: -one_sorted_str(A) | -one_sorted_str(A) | empty_carrier(A) | empty_carrier(f453(A)) | -is_eventually_in(A,f453(A),B) | -element(C,the_carrier(f453(A))) | -related(f453(A),f206(A,f453(A),B),C) | in(apply_netmap(A,f453(A),C),B). [resolve(1101,b,1107,d)]. 83.66/83.84 Derived: -one_sorted_str(A) | -one_sorted_str(A) | empty_carrier(A) | empty_carrier(f453(A)) | -is_eventually_in(A,f453(A),B) | element(f206(A,f453(A),B),the_carrier(f453(A))). [resolve(1101,b,1108,d)]. 83.66/83.84 Derived: -one_sorted_str(A) | -one_sorted_str(A) | empty_carrier(A) | empty_carrier(f453(A)) | is_eventually_in(A,f453(A),B) | element(f207(A,f453(A),B,C),the_carrier(f453(A))) | -element(C,the_carrier(f453(A))). [resolve(1101,b,1109,d)]. 83.66/83.84 Derived: -one_sorted_str(A) | -one_sorted_str(A) | empty_carrier(A) | empty_carrier(f453(A)) | is_eventually_in(A,f453(A),B) | related(f453(A),C,f207(A,f453(A),B,C)) | -element(C,the_carrier(f453(A))). [resolve(1101,b,1110,d)]. 83.66/83.84 Derived: -one_sorted_str(A) | -one_sorted_str(A) | empty_carrier(A) | empty_carrier(f453(A)) | is_eventually_in(A,f453(A),B) | -in(apply_netmap(A,f453(A),f207(A,f453(A),B,C)),B) | -element(C,the_carrier(f453(A))). [resolve(1101,b,1111,d)]. 83.66/83.84 Derived: -one_sorted_str(A) | empty_carrier(A) | -one_sorted_str(A) | empty_carrier(f453(A)) | -is_often_in(A,f453(A),B) | -element(C,the_carrier(f453(A))) | element(f236(A,f453(A),B,C),the_carrier(f453(A))). [resolve(1101,b,1112,d)]. 83.66/83.84 Derived: -one_sorted_str(A) | empty_carrier(A) | -one_sorted_str(A) | empty_carrier(f453(A)) | -is_often_in(A,f453(A),B) | -element(C,the_carrier(f453(A))) | related(f453(A),C,f236(A,f453(A),B,C)). [resolve(1101,b,1113,d)]. 83.66/83.84 Derived: -one_sorted_str(A) | empty_carrier(A) | -one_sorted_str(A) | empty_carrier(f453(A)) | -is_often_in(A,f453(A),B) | -element(C,the_carrier(f453(A))) | in(apply_netmap(A,f453(A),f236(A,f453(A),B,C)),B). [resolve(1101,b,1114,d)]. 83.66/83.84 Derived: -one_sorted_str(A) | empty_carrier(A) | -one_sorted_str(A) | empty_carrier(f453(A)) | is_often_in(A,f453(A),B) | element(f237(A,f453(A),B),the_carrier(f453(A))). [resolve(1101,b,1115,d)]. 83.66/83.84 Derived: -one_sorted_str(A) | empty_carrier(A) | -one_sorted_str(A) | empty_carrier(f453(A)) | is_often_in(A,f453(A),B) | -element(C,the_carrier(f453(A))) | -related(f453(A),f237(A,f453(A),B),C) | -in(apply_netmap(A,f453(A),C),B). [resolve(1101,b,1116,d)]. 90.49/90.70 Derived: -one_sorted_str(A) | -one_sorted_str(A) | empty_carrier(A) | empty_carrier(f453(A)) | -element(B,the_carrier(f453(A))) | apply_netmap(A,f453(A),B) = apply_on_structs(f453(A),A,the_mapping(A,f453(A)),B). [resolve(1101,b,1117,c)]. 90.49/90.70 1118 net_str(c38,c37) # label(t8_waybel_0) # label(negated_conjecture). [clausify(706)]. 90.49/90.70 Derived: -one_sorted_str(c37) | function(the_mapping(c37,c38)). [resolve(1118,a,1102,b)]. 90.49/90.70 Derived: -one_sorted_str(c37) | quasi_total(the_mapping(c37,c38),the_carrier(c38),the_carrier(c37)). [resolve(1118,a,1103,b)]. 90.49/90.70 Derived: -one_sorted_str(c37) | relation_of2_as_subset(the_mapping(c37,c38),the_carrier(c38),the_carrier(c37)). [resolve(1118,a,1104,b)]. 90.49/90.70 Derived: -one_sorted_str(c37) | rel_str(c38). [resolve(1118,a,1105,b)]. 90.49/90.70 Derived: empty_carrier(c37) | -element(A,the_carrier(c38)) | empty_carrier(c38) | -one_sorted_str(c37) | element(apply_netmap(c37,c38,A),the_carrier(c37)). [resolve(1118,a,1106,c)]. 90.49/90.70 Derived: -one_sorted_str(c37) | empty_carrier(c37) | empty_carrier(c38) | -is_eventually_in(c37,c38,A) | -element(B,the_carrier(c38)) | -related(c38,f206(c37,c38,A),B) | in(apply_netmap(c37,c38,B),A). [resolve(1118,a,1107,d)]. 90.49/90.70 Derived: -one_sorted_str(c37) | empty_carrier(c37) | empty_carrier(c38) | -is_eventually_in(c37,c38,A) | element(f206(c37,c38,A),the_carrier(c38)). [resolve(1118,a,1108,d)]. 90.49/90.70 Derived: -one_sorted_str(c37) | empty_carrier(c37) | empty_carrier(c38) | is_eventually_in(c37,c38,A) | element(f207(c37,c38,A,B),the_carrier(c38)) | -element(B,the_carrier(c38)). [resolve(1118,a,1109,d)]. 90.49/90.70 Derived: -one_sorted_str(c37) | empty_carrier(c37) | empty_carrier(c38) | is_eventually_in(c37,c38,A) | related(c38,B,f207(c37,c38,A,B)) | -element(B,the_carrier(c38)). [resolve(1118,a,1110,d)]. 90.49/90.70 Derived: -one_sorted_str(c37) | empty_carrier(c37) | empty_carrier(c38) | is_eventually_in(c37,c38,A) | -in(apply_netmap(c37,c38,f207(c37,c38,A,B)),A) | -element(B,the_carrier(c38)). [resolve(1118,a,1111,d)]. 90.49/90.70 Derived: empty_carrier(c37) | -one_sorted_str(c37) | empty_carrier(c38) | -is_often_in(c37,c38,A) | -element(B,the_carrier(c38)) | element(f236(c37,c38,A,B),the_carrier(c38)). [resolve(1118,a,1112,d)]. 90.49/90.70 Derived: empty_carrier(c37) | -one_sorted_str(c37) | empty_carrier(c38) | -is_often_in(c37,c38,A) | -element(B,the_carrier(c38)) | related(c38,B,f236(c37,c38,A,B)). [resolve(1118,a,1113,d)]. 90.49/90.70 Derived: empty_carrier(c37) | -one_sorted_str(c37) | empty_carrier(c38) | -is_often_in(c37,c38,A) | -element(B,the_carrier(c38)) | in(apply_netmap(c37,c38,f236(c37,c38,A,B)),A). [resolve(1118,a,1114,d)]. 90.49/90.70 Derived: empty_carrier(c37) | -one_sorted_str(c37) | empty_carrier(c38) | is_often_in(c37,c38,A) | element(f237(c37,c38,A),the_carrier(c38)). [resolve(1118,a,1115,d)]. 90.49/90.70 Derived: empty_carrier(c37) | -one_sorted_str(c37) | empty_carrier(c38) | is_often_in(c37,c38,A) | -element(B,the_carrier(c38)) | -related(c38,f237(c37,c38,A),B) | -in(apply_netmap(c37,c38,B),A). [resolve(1118,a,1116,d)]. 90.49/90.70 Derived: -one_sorted_str(c37) | empty_carrier(c37) | empty_carrier(c38) | -element(A,the_carrier(c38)) | apply_netmap(c37,c38,A) = apply_on_structs(c38,c37,the_mapping(c37,c38),A). [resolve(1118,a,1117,c)]. 90.49/90.70 1119 -relation_of2(A,B,C) | -quasi_total(A,B,C) | -onto(A,B,C) | -one_to_one(A) | -function(A) | bijective(A,B,C) # label(cc3_funct_2) # label(axiom). [clausify(580)]. 90.49/90.70 1120 -relation_of2(A,B,B) | -function(A) | -v1_partfun1(A,B,B) | -reflexive(A) | -quasi_total(A,B,B) | onto(A,B,B) # label(cc4_funct_2) # label(axiom). [clausify(258)]. 90.49/90.70 1121 onto(f304(A),A,A) # label(rc2_funct_2) # label(axiom). [clausify(431)]. 90.49/90.70 1122 -relation_of2(A,B,C) | -quasi_total(A,B,C) | -bijective(A,B,C) | -function(A) | onto(A,B,C) # label(cc2_funct_2) # label(axiom). [clausify(446)]. 90.49/90.70 Derived: -relation_of2(A,B,B) | -quasi_total(A,B,B) | -one_to_one(A) | -function(A) | bijective(A,B,B) | -relation_of2(A,B,B) | -function(A) | -v1_partfun1(A,B,B) | -reflexive(A) | -quasi_total(A,B,B). [resolve(1119,c,1120,f)]. 142.93/143.33 Derived: -relation_of2(f304(A),A,A) | -quasi_total(f304(A),A,A) | -one_to_one(f304(A)) | -function(f304(A)) | bijective(f304(A),A,A). [resolve(1119,c,1121,a)]. 142.93/143.33 1123 -relation_of2(A,B,C) | -quasi_total(A,B,C) | -bijective(A,B,C) | -function(A) | one_to_one(A) # label(cc2_funct_2) # label(axiom). [clausify(446)]. 142.93/143.33 1124 -relation_of2(A,B,B) | -function(A) | -v1_partfun1(A,B,B) | -reflexive(A) | -quasi_total(A,B,B) | bijective(A,B,B) # label(cc4_funct_2) # label(axiom). [clausify(258)]. 142.93/143.33 1125 bijective(f304(A),A,A) # label(rc2_funct_2) # label(axiom). [clausify(431)]. 142.93/143.33 Derived: -relation_of2(A,B,B) | -quasi_total(A,B,B) | -function(A) | one_to_one(A) | -relation_of2(A,B,B) | -function(A) | -v1_partfun1(A,B,B) | -reflexive(A) | -quasi_total(A,B,B). [resolve(1123,c,1124,f)]. 142.93/143.33 Derived: -relation_of2(f304(A),A,A) | -quasi_total(f304(A),A,A) | -function(f304(A)) | one_to_one(f304(A)). [resolve(1123,c,1125,a)]. 142.93/143.33 1126 -relation_of2(A,B,B) | -quasi_total(A,B,B) | -one_to_one(A) | -function(A) | bijective(A,B,B) | -relation_of2(A,B,B) | -function(A) | -v1_partfun1(A,B,B) | -reflexive(A) | -quasi_total(A,B,B). [resolve(1119,c,1120,f)]. 142.93/143.33 1127 -relation_of2(f304(A),A,A) | -quasi_total(f304(A),A,A) | -one_to_one(f304(A)) | -function(f304(A)) | bijective(f304(A),A,A). [resolve(1119,c,1121,a)]. 142.93/143.33 1128 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(780,e,876,b)]. 142.93/143.33 1129 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(780,e,875,b)]. 142.93/143.33 1130 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(780,e,887,b)]. 142.93/143.33 1131 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(780,e,904,c)]. 142.93/143.33 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(C,the_carrier(A)) | -element(B,powerset(the_carrier(A))) | in(C,interior(A,B)). [resolve(1131,k,1129,i)]. 142.93/143.33 1132 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(780,e,905,c)]. 142.93/143.33 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(f351(A,B),powerset(the_carrier(A))) | in(B,interior(A,f351(A,B))). [resolve(1132,h,1129,i)]. 143.67/144.04 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | element(f351(A,B),powerset(the_carrier(A))). [resolve(1132,h,1130,h)]. 143.67/144.04 1133 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(930,e,875,b)]. 143.67/144.04 1134 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(930,e,876,b)]. 143.67/144.04 1135 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(930,e,887,b)]. 143.67/144.04 1136 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(930,e,904,c)]. 143.67/144.04 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(C,the_carrier(A)) | -element(B,powerset(the_carrier(A))) | in(C,interior(A,B)). [resolve(1136,k,1133,i)]. 143.67/144.04 1137 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(930,e,905,c)]. 143.67/144.04 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(f351(A,B),powerset(the_carrier(A))) | in(B,interior(A,f351(A,B))). [resolve(1137,h,1133,i)]. 143.67/144.04 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | element(f351(A,B),powerset(the_carrier(A))). [resolve(1137,h,1135,h)]. 143.67/144.04 1138 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(931,e,875,b)]. 143.67/144.04 1139 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(931,e,876,b)]. 144.32/144.67 1140 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(931,e,887,b)]. 144.32/144.67 1141 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(931,e,904,c)]. 144.32/144.67 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(C,the_carrier(A)) | -element(B,powerset(the_carrier(A))) | in(C,interior(A,B)). [resolve(1141,k,1138,i)]. 144.32/144.67 1142 -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(931,e,905,c)]. 144.32/144.67 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(f351(A,B),powerset(the_carrier(A))) | in(B,interior(A,f351(A,B))). [resolve(1142,h,1138,i)]. 144.32/144.67 Derived: -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | element(f443(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | element(f351(A,B),powerset(the_carrier(A))). [resolve(1142,h,1140,h)]. 144.32/144.67 1143 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(932,e,875,b)]. 144.32/144.67 1144 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(932,e,876,b)]. 144.32/144.67 1145 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(932,e,887,b)]. 144.32/144.67 1146 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(932,e,904,c)]. 144.32/144.67 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(C,the_carrier(A)) | -element(B,powerset(the_carrier(A))) | in(C,interior(A,B)). [resolve(1146,k,1143,i)]. 144.92/145.31 1147 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(932,e,905,c)]. 144.92/145.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(f351(A,B),powerset(the_carrier(A))) | in(B,interior(A,f351(A,B))). [resolve(1147,h,1143,i)]. 144.92/145.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | element(f351(A,B),powerset(the_carrier(A))). [resolve(1147,h,1145,h)]. 144.92/145.31 1148 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(933,e,875,b)]. 144.92/145.31 1149 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(933,e,876,b)]. 144.92/145.31 1150 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(933,e,887,b)]. 144.92/145.31 1151 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(933,e,904,c)]. 144.92/145.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(C,the_carrier(A)) | -element(B,powerset(the_carrier(A))) | in(C,interior(A,B)). [resolve(1151,k,1148,i)]. 144.92/145.31 1152 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(933,e,905,c)]. 144.92/145.31 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(f351(A,B),powerset(the_carrier(A))) | in(B,interior(A,f351(A,B))). [resolve(1152,h,1148,i)]. 145.70/146.04 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | element(f351(A,B),powerset(the_carrier(A))). [resolve(1152,h,1150,h)]. 145.70/146.04 1153 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(934,e,875,b)]. 145.70/146.04 1154 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(934,e,876,b)]. 145.70/146.04 1155 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(934,e,887,b)]. 145.70/146.04 1156 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(934,e,904,c)]. 145.70/146.04 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(C,the_carrier(A)) | -element(B,powerset(the_carrier(A))) | in(C,interior(A,B)). [resolve(1156,k,1153,i)]. 145.70/146.04 1157 -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(934,e,905,c)]. 145.70/146.04 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(f351(A,B),powerset(the_carrier(A))) | in(B,interior(A,f351(A,B))). [resolve(1157,h,1153,i)]. 145.70/146.04 Derived: -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | element(f444(A),powerset(the_carrier(A))) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | element(f351(A,B),powerset(the_carrier(A))). [resolve(1157,h,1155,h)]. 146.82/147.22 1158 -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(935,e,875,b)]. 146.82/147.22 1159 -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(935,e,876,b)]. 146.82/147.22 1160 -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(935,e,887,b)]. 146.82/147.22 1161 -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(935,e,904,c)]. 146.82/147.22 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(C,the_carrier(A)) | -element(B,powerset(the_carrier(A))) | in(C,interior(A,B)). [resolve(1161,k,1158,i)]. 146.82/147.22 1162 -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(935,e,905,c)]. 146.82/147.22 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(f351(A,B),powerset(the_carrier(A))) | in(B,interior(A,f351(A,B))). [resolve(1162,h,1158,i)]. 146.82/147.22 Derived: -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | in(f443(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | element(f351(A,B),powerset(the_carrier(A))). [resolve(1162,h,1160,h)]. 146.82/147.22 1163 -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(936,e,875,b)]. 146.82/147.22 1164 -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(936,e,876,b)]. 146.82/147.22 1165 -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(936,e,887,b)]. 146.82/147.22 1166 -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(936,e,904,c)]. 147.86/148.22 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(C,the_carrier(A)) | -element(B,powerset(the_carrier(A))) | in(C,interior(A,B)). [resolve(1166,k,1163,i)]. 147.86/148.22 1167 -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(936,e,905,c)]. 147.86/148.22 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(f351(A,B),powerset(the_carrier(A))) | in(B,interior(A,f351(A,B))). [resolve(1167,h,1163,i)]. 147.86/148.22 Derived: -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | in(f443(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | element(f351(A,B),powerset(the_carrier(A))). [resolve(1167,h,1165,h)]. 147.86/148.22 1168 -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(937,e,875,b)]. 147.86/148.22 1169 -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(937,e,876,b)]. 147.86/148.22 1170 -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(937,e,887,b)]. 147.86/148.22 1171 -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(937,e,904,c)]. 147.86/148.22 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(C,the_carrier(A)) | -element(B,powerset(the_carrier(A))) | in(C,interior(A,B)). [resolve(1171,k,1168,i)]. 147.86/148.22 1172 -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(937,e,905,c)]. 147.86/148.22 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(f351(A,B),powerset(the_carrier(A))) | in(B,interior(A,f351(A,B))). [resolve(1172,h,1168,i)]. 149.14/149.48 Derived: -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | in(f443(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | element(f351(A,B),powerset(the_carrier(A))). [resolve(1172,h,1170,h)]. 149.14/149.48 1173 -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(938,e,875,b)]. 149.14/149.48 1174 -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(938,e,876,b)]. 149.14/149.48 1175 -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(938,e,887,b)]. 149.14/149.48 1176 -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(938,e,904,c)]. 149.14/149.48 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(C,the_carrier(A)) | -element(B,powerset(the_carrier(A))) | in(C,interior(A,B)). [resolve(1176,k,1173,i)]. 149.14/149.48 1177 -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(938,e,905,c)]. 149.14/149.48 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(f351(A,B),powerset(the_carrier(A))) | in(B,interior(A,f351(A,B))). [resolve(1177,h,1173,i)]. 149.14/149.48 Derived: -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | in(f444(A),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | element(f351(A,B),powerset(the_carrier(A))). [resolve(1177,h,1175,h)]. 149.14/149.48 1178 -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(939,e,875,b)]. 150.39/150.80 1179 -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(939,e,876,b)]. 150.39/150.80 1180 -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(939,e,887,b)]. 150.39/150.80 1181 -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(939,e,904,c)]. 150.39/150.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(C,the_carrier(A)) | -element(B,powerset(the_carrier(A))) | in(C,interior(A,B)). [resolve(1181,k,1178,i)]. 150.39/150.80 1182 -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(939,e,905,c)]. 150.39/150.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(f351(A,B),powerset(the_carrier(A))) | in(B,interior(A,f351(A,B))). [resolve(1182,h,1178,i)]. 150.39/150.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | in(f444(A),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | element(f351(A,B),powerset(the_carrier(A))). [resolve(1182,h,1180,h)]. 150.39/150.80 1183 -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(940,e,875,b)]. 150.39/150.80 1184 -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(940,e,876,b)]. 150.39/150.80 1185 -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(940,e,887,b)]. 150.39/150.80 1186 -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(940,e,904,c)]. 150.39/150.80 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(C,the_carrier(A)) | -element(B,powerset(the_carrier(A))) | in(C,interior(A,B)). [resolve(1186,k,1183,i)]. 151.51/151.88 1187 -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(940,e,905,c)]. 151.51/151.88 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(f351(A,B),powerset(the_carrier(A))) | in(B,interior(A,f351(A,B))). [resolve(1187,h,1183,i)]. 151.51/151.88 Derived: -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | in(f444(A),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | element(f351(A,B),powerset(the_carrier(A))). [resolve(1187,h,1185,h)]. 151.51/151.88 1188 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(941,e,875,b)]. 151.51/151.88 1189 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(941,e,876,b)]. 151.51/151.88 1190 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(941,e,887,b)]. 151.51/151.88 1191 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(941,e,904,c)]. 151.51/151.88 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(C,the_carrier(A)) | -element(B,powerset(the_carrier(A))) | in(C,interior(A,B)). [resolve(1191,k,1188,i)]. 151.51/151.88 1192 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(941,e,905,c)]. 152.88/153.24 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(f351(A,B),powerset(the_carrier(A))) | in(B,interior(A,f351(A,B))). [resolve(1192,h,1188,i)]. 152.88/153.24 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | element(f445(A),powerset(powerset(the_carrier(A)))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | element(f351(A,B),powerset(the_carrier(A))). [resolve(1192,h,1190,h)]. 152.88/153.24 1193 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(942,e,875,b)]. 152.88/153.24 1194 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(942,e,876,b)]. 152.88/153.24 1195 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(942,e,887,b)]. 152.88/153.24 1196 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(942,e,904,c)]. 152.88/153.24 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(C,the_carrier(A)) | -element(B,powerset(the_carrier(A))) | in(C,interior(A,B)). [resolve(1196,k,1193,i)]. 152.88/153.24 1197 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(942,e,905,c)]. 152.88/153.24 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(f351(A,B),powerset(the_carrier(A))) | in(B,interior(A,f351(A,B))). [resolve(1197,h,1193,i)]. 154.09/154.44 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | subset(f445(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | element(f351(A,B),powerset(the_carrier(A))). [resolve(1197,h,1195,h)]. 154.09/154.44 1198 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(943,e,875,b)]. 154.09/154.44 1199 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(943,e,876,b)]. 154.09/154.44 1200 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))). [resolve(943,e,887,b)]. 154.09/154.44 1201 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | point_neighbourhood(B,A,C). [resolve(943,e,904,c)]. 154.09/154.44 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -open_subset(B,A) | -in(C,B) | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(C,the_carrier(A)) | -element(B,powerset(the_carrier(A))) | in(C,interior(A,B)). [resolve(1201,k,1198,i)]. 154.09/154.44 1202 -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | point_neighbourhood(f351(A,B),A,B). [resolve(943,e,905,c)]. 154.09/154.44 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,the_carrier(A)) | -element(f351(A,B),powerset(the_carrier(A))) | in(B,interior(A,f351(A,B))). [resolve(1202,h,1198,i)]. 154.09/154.44 Derived: -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -element(B,the_carrier(A)) | -top_str(A) | empty_carrier(A) | -top_str(A) | -in(subset_intersection2(the_carrier(A),f443(A),f444(A)),the_topology(A)) | -in(union_of_subsets(the_carrier(A),f445(A)),the_topology(A)) | -in(the_carrier(A),the_topolAlarm clock 179.67/180.07 Prover9 interrupted 179.67/180.07 EOF